Control Blasting

Abstract

Disclosed herein is a new concept in blasting which is based on a unique theory that permits total utilization of the energy of a blasting charge. The method of this invention enables one, through a set procedure, to control the direction and distance of placement of huge volumes of earth and/or the degree of breakage of a volume of material adjacent the area effected by the blast. The method requires systematic test blasts to determine parameters for use in established formula so that the desired end of control blasting of huge volumes of earth can be attained. The scope of this invention is unlimited in its application to mining, hydropower development, construction projects, etc.

Description

BACKGROUND OF THE INVENTION

Classification

This invention relates to blasting and particularly a blasting method that enables one to control the trajectory, granulometry and stability of the material surrounding the charge and the use of these concepts in new and novel mining and hydropower development methods.

Blasting and Mining History

The art of mining has a history that extends back to the earliest recorded history of man. The introduction of explosives to the art of mining presented a major technological advance, but the use of explosives in mining has to this point been dominated by the absence of any scientific basis for their deployment. While it would appear that from the time when the Chinese originally began to experiment with explosives and with present day engineering capabilities, the reaction to explosives would be known and predictable, such is not the case; and the use of explosives in mining has been significantly inhibited since their deployment is based on a "hit-and-miss" approach and consequently the high cost of explosives has limited their use in mining, primarily to breakage applications.

Since the reaction to blasting and the basis therefor has not heretofore been known, the evaluation of blasting applications and the logical, systematic analysis of problems involving such applications in mining and other methods has not been possible.

The lack of an understanding of the reaction to blasting has made it impossible to effectively utilize the energy of the explosive. The new technology which I have evolved permits scientific analysis of the problems of blasting, and I have developed a trajectory control blasting method based on these principles.

Further, it has been generally considered that the breakage by blasting of the materials surrounding the charge was a function of the characteristics of the material, and that the lines of breakage are dictated by the lines of weakness in the surrounding material. I have found that not to be the case and this major technological breakthrough has permitted me to analyze the effect of blasting and develop unique product and stability control blasting methods based upon this scientific discovery.

Livingston Crater Disclosure and Experiments

My early experiments were conducted in crater blasting of many materials, including ice, snow, clay and a variety of ores. A crater blast must be distinguished from a bench blast, which is discussed later. A crater blast is a blast which is detonated beneath a surface that extends laterally in all directions beyond the point where the surrounding material would be effected by the blast. Conversely, a bench blast takes place beneath the surface that is stepped at a point sufficiently close to the charge that the vertical face of the step is affected by the explosion.

In analyzing crater blasts, I determined that there is a definite relation between the energy of the explosive, as represented by the weight and type of explosive, and the volume of material that is effected by the blast of such explosive, and that this relationship is significantly effected by the placement of the charge.

This scientific approach to the art of blasting and blast-mining is based on the scientific concepts which I have discovered and which form the basis for a new technology. This technology permits analysis of mining problems by a systematic engineering evaluation as opposed to the previous approach employed by industry of relying on experience and hit-and-miss blasting and has resulted in the method of this invention.

In order to understand the significance of the new technology disclosed herein and the associated control blasting and mining method, it is appropriate that the history of my experiments be summarized and the analysis that was required to reduce the data gained from these experiments to scientific principles.

From numerous blasting experiments, I determined that a strain-energy relation exists, which can be defined by the equation:

N=E.cuberoot. W (1)

wherein N, termed the "critical depth," is the depth in feet at which displacement of the surface above an explosive charge of spherical shape does not exceed a specified limit in response to a blast with the type and weight of explosive in a given homogeneous material beneath a horizontal surface of semi-infinite lateral extension. The limiting displacement is that at which cratering of the horizontal surface begins and the term "semi-infinite lateral extension" represents a surface sufficient that vertically arranged lines about its extremities are not effected by the blast;

wherein E, termed strain-energy factor, is a variable factor dependent upon the explosive and the material, but for the same explosive and material is a constant for charge weights in the same order of magnitude when cube root scaling is assumed; and

wherein W is the weight of the explosive charge in pounds.

This equation may be rewritten as:

d.sub.c =.DELTA. E.cuberoot. W (2)

wherein .DELTA. equals d.sub.c /N and d.sub.c is the depth in feet from the surface of a material to be blasted to the center of gravity of the explosive charge. Thus, .DELTA. is a dimensionless term which expresses the ratio of the depth of any charge as compared with the critical depth N.

When d.sub.c is such that the maximum volume of material is completely ruptured, d.sub.c = d.sub.o, which is the optimum depth. The optimum depth d.sub.o is that depth of charge which creates maximum pressure rise in the material, and is determined by the maximum coming of the material, and is that depth at which fracturing proceeds to completion, but no further.

The distinction between d.sub.o and N can be best illustrated by reference to FIGS. 1 and 2.

FIG. 1 illustrates a crater blast in material of semi-infinite extension with the explosive charge placed at critical depth N. As is illustrated by the concentric lines, the shock wave created by the explosion radiates outwardly, to form a spherical shock wave, passing through the material, and the largest or outside circle indicates the limit of participation of any materials in response to the explosion. In effect, this charge is placed at such a depth that the effect of the charge will just reach the surface of the material in which the explosive is set, and ground rise will not exceed that at which cratering begins, but ground rise may be sufficient to cause some cracks to form. N is the depth at which the charge will just begin to have a cratering effect, but is not so close to the surface that any significant crater will actually be formed.

Referring to FIG. 2, the effect of an explosion set at optimum depth is illustrated. The charge is placed at optimum depth d.sub.o from the surface of the material, and again the shock front which extends in spherical relation radially about the charge is illustrated by concentric circles in progressive stages of time. When the shock front reaches the surface of the material, the reflection of the shock at the free face as a factor of time is illustrated by the series of arcuate lines projecting down from the surface, and this reflection of the shock produces slabs of what is commonly called "fly rock." The extent of doming due to massive ground motion is illustrated by the hemispheric line raised above the surface. This doming characteristic of massive ground motion is produced at a later time by the pressure rise in the material as distinguished from the pressure at the shock front. Referring to FIG. 3, a representative pressure time chart is illustrated, which distinguishes the difference between the pressure due to the shock and later pressure due to molecular vibration. FIG. 4 shows the slabbing effect of arrival and reflection of the shock front as distinguished from maximum breakage per pound of explosive caused by maximum pressure rise within the material. When this ground rise, or doming, reaches maximum extent without escape of the gas bubble formed by the explosion, the energy of the explosion has been used to its ultimate; and in effect the greatest volume of material for a given charge has been broken. The difference between the effect of a blast resulting from a charge placed at critical depth and of a blast having a charge placed at optimum depth is this: The surrounding material effected by a charge placed at critical depth is not isolated by the cratering process, although a portion may be completely fractured. Rather, the material is weakened in some areas, although not completely broken, whereas the material effected by the blast of a charge placed at optimum depth has a significantly greater portion broken to recognizable loading and unloading fracture limits and forming a substantially homogeneous mass of a different texture.

The critical depth and optimum depth for any given explosive and a given material are determined by test crater blasts (i.e., the blasts are conducted in a material having a semi-infinite horizontal free face) and a number of test blasts may be required to determine these values for the given explosive and the material.

In performing these test blasts, several charges are placed at varying depths in bore holes and then each charge is detonated to determine the values for d.sub.o and N. The effect of an explosive and the manner in which the test blasts are conducted is illustrated in FIGS. 5 through 8.

FIG. 5 illustrates the effect of a blast which is detonated above the surface of the medium and shows the apparent crater formed by such a blast. FIG. 6 illustrates the result of a blast from a charge positioned at surface level and shows both the apparent crater and the true crater formed by such a blast. FIGS. 7 and 8 show further examples of the effect of different depths for the same charge weight on both the apparent crater and the true crater.

FIG. 9 illustrates what is meant by the terms "apparent crater" and "true crater," as well as other terms that are employed in connection with this description of the reaction of surrounding material in response to a blast. The apparent crater is the elevation of the broken rock within material below the original ground surface in response to the blast, while the true crater is the limit at which the broken rock is completely isolated from the surrounding material.

The limit of extreme rupture is a surface running through the ends of the fractures farthest from the center of the explosion. This extreme rupture limit contains material effected by the blast insufficiently to separate it from its surrounding material, but may contain a variety of types of cracks.

By understanding the effect of a blast of explosives on the surrounding material, it is readily apparent that it is preferable to utilize the energy of the explosive in most instances to create the maximum true crater so that the material effected by the blast is crushed to the maximum possible extent and thereby its rehandling facilitated. If the larger portion of the energy is directed to producing an extreme rupture limit of considerable thickness, then use of the energy is not maximized.

As previously stated, the value of d.sub.o for a given material and a given explosive is determined by test blast. I have determined that the optimum depth is that depth which produces maximum pressure rise within the material, and that maximum pressure rise occurs when maximum doming without venting is achieved. In understanding this concept, it is important to realize that an explosion creates, in addition to the shock effect, an explosion cavity including a gas bubble which swells and expands through the material. When the depth of the charge is such that the surface of the surrounding material rises to a hemispherical shape, but no further (i.e., doming), maximum pressure rise within the material is attained and the gas bubble just breaks through to the surface of the surrounding material. Thus, as can be seen in FIG. 2, the response to a blast set at optimum depth is a swelling of the surrounding material with the surface of the material expanding to hemispherical shape and the gas bubble created by the blast just breaking through the surface. Of course, maximum pressure rise is substantially reached when the depth of the charge is such that the gas bubble does not break through the surface of the material, but would require only de miminum additional pressure to cause such breakage. When the gas bubble is lost to the atmosphere, recoverable elastic potential energy stored during the rise to maximum pressure is released so as to produce unloading type fractures at the walls of the crater.

During an explosion, the disturbance consists of a "front" or shock front. An abrupt pressure rise occurs at this front, followed by a series of waves that cause a pressure rise within the material behind the shock front. It has been previously felt that when an explosion is detonated sufficiently close to ground surface such that the shock waves are not dissipated sufficiently during their travel through the medium as to be dampened out before reaching the surface, the movement of the surface is brought about by reflection of the shock at the free face. While this is true to some extent, I have found that the maximum energy utilization of an explosive creates what I term "massive ground motion," which effects a much greater volume of material than that due to the arrival and reflection of the shock and is produced by the pressure rise in the material behind the shock front and by reaching critical frequency of vibration of the particles themselves.

When the charge is detonated, the shock front radiates from the point of detonation and an explosion cavity containing a gas bubble is created within the medium. If the point of detonation is sufficiently close to the ground surface, ground rise is produced, which results in some fracture of the surface material. Upon an even closer relation of the charge to the surface, the gas bubble breaks through the surface, vents to the atmosphere and dissipates the energy of the explosive still remaining within the gas bubble, and creates a secondary explosion. The pressures defining the gas bubble radiate outwardly from the point of breakthrough so that the surface material that has risen with the explosion is fractured and projected in all areas to evidence the common occurrence of fly rock.

Two methods of determining d.sub.o are available.

One utilizes a technique in which V/W (volume of material broken per pound of explosive) within limits of complete rupture is plotted against the depth ratio, .DELTA., to determine the specific value of .DELTA..sub.o, where V/W is maximum. The other combines a technique including direct observation of ground rise to determine which charge depth produces maximum doming and pinpointing to determine critical depth. High speed motion pictures may be used in this method to assist in determining the velocity and duration of ground motion and when the gas bubble escapes from the hemispherical doming produced by a charge at optimum depth. A depth d.sub.o, the energy utilization number A is unity and the maximum proportion of the total energy of the explosion is expended in (1) fractures formed during the rise to peak pressure and (2) fractures formed during implosion or elastic rebound by release of potential energy stored during loading.

In either event, it is usually necessary to conduct a number of test blasts at various depths in order to determine the exact depth that is optimum. If a number of charges of constant weight are placed at a range of depths approximately at optimum depth, it is possible to observe the doming in response to the explosion and plot a curve based on depth of charge versus extent of doming and use this curve to determine the optimum depth.

Since cube root scaling is employed in evaluating the test blast, the optimum depth for any weight of explosive may be calculated from the parameters gathered during the test blast which are performed with a comparatively small explosive charge. Cube root scaling is a system of scaling in which is assumed the following preposition:

N.sub.1 /N.sub.2 = d.sub.1 /d.sub.2 = .cuberoot. W.sub.1 /.cuberoot. W.sub.2 ( 3)

wherein d.sub.1 is a given distance from an explosive charge of the weight W.sub.1, and d.sub.2 is the distance from a second charge at which the same damage effect is felt from the second geometrically similar charge of weight W.sub.2. Material and explosive type must be the same in both instances. However, this scaling, which has proved in practice to be based on a valid assumption, permits the art of blasting to be more properly analyzed as a science.

The equations discussed above and associated parameters are summarized in the breakage process equation which is definitive of the new technology that I have discovered and is written:

V/W = E.sup.3 ABC (4)

this breakage process equation can be used in understanding and establishing desired blasting effects for any given material with a given type explosive. The terms V, W, and E have been previously defined and the additional terms A, B, and C are defined as follows:

A is the ratio of volume of material broken in the true crater for a charge of given weight set at any depth as compared with the same charge set at optimum depth A = V/V.sub.o.

B is the "material behavior index" defined by the formula B = V.sub.o /N.sup.3 and is constant for a given explosive, a given material and a given weight of charge. It is a dimensionless number that may be thought of as a ratio of volumes at two different energy levels, one when the energy is utilized to a maximum and the other when the energy is used less efficiently.

C is the stress distribution number which is a dimensionless number that depends upon the energy distribution within the material and the duration of the action. It is included as a ratio of the volume excavated for any given condition to the volume excavated at the reference condition.

C stands for charge shape, one of the principal factors affecting stress distribution for the geometry of crater blasts, and through extensive test in crater blasting it has been found that the most efficient charge shape is spherical, so that the spherical charge shape has been used as a definitional reference. Thus, in crater blasting, C defines more specifically the effect of a charge of given weight and shape at a given depth as compared to the effect of a charge of spherical shape under similar conditions.

From these equations, it can be seen that the maximum utilization of energy of an explosive charge can be determined for any given type of explosive in a given material. Since cube root scaling is employed, a number of test blasts can be fired to determine the parameters of the equations, and these parameters can then be used for any other charge weights for determining the associated optimum depth.

For example, if the optimum depth for a 10-pound spherical charge in a given material is found by test blast to be 5 feet, and the associated critical depth is found to be 10 feet, then E can be calculated from the formula N = E.cuberoot.W.

e = n/.cuberoot.w

e = 10/.cuberoot.w

e = 10/2.15

e = 4.65

and .DELTA..sub.o = d.sub.o /N = 5/10 = 0.50

Assuming now that it is desired to employ a charge of 1,000 pounds of a spherical shape in the same type material, the optimum depth may be determined:

d.sub.o = .DELTA..sub.o E.cuberoot.W

d.sub.o = 0.5 .times. 4.65 .times. .cuberoot.1,000

d.sub.o = 0.5 .times. 4.65 .times. 10

d.sub.o = 23.2 feet

As a further example, assume the tests have given the same parameters and that it is desired to find the charge weight, that is optimum for a blast at 100 feet.

d.sub.o = .DELTA..sub.o E.cuberoot.W

100 = 0.5 .times. 4.65 .times. .cuberoot.w

.cuberoot.w = 100/2.325 = 43

w = 79,500 pounds

Understanding these relations of explosives and the reaction of surrounding materials to the blast of a given charge, it is now possible to evaluate and scientifically analyze blasting applications. Control of the results produced by a blast pre-designed and placed to achieve such controlled results is now possible.

The background material discussed to this point is directed primarily to crater blasting, but the true significance of the invention is the adaptation of the principles recognized in conjunction with crater blasting to the art of bench blasting, and the method that I have devised for controlling the trajectory and granulometry of the material surrounding the explosive charge in conjunction with bench blasting.

Accordingly, it is a primary object of this invention to provide a method for controlling the trajectory, granulometry and stability of the material surrounding an explosive charge in performing bench blasting.

It is another object of this invention to maximumize energy utilization of an explosive charge in bench blasting.

Still a further object of this invention is to provide a method for determining the optimum placement and weight of an explosive charge in bench blasting to control the trajectory, granulometry and stability of the material surrounding the charge.

A still further object of this invention is to provide a mining process that employs trajectory control, product control and stability control blasting to significantly reduce the cost per yard of ore mined.

These and other objects of the invention will become apparent to those of ordinary skill in the related art when consideration is given to the accompanying detailed description of the preferred embodiment of the method of the invention and steps in practising the invention along with the examples provided and when such consideration is taken in conjunction with the accompanying drawings.

DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the effect of an explosive charge placed at critical depth;

FIG. 2 illustrates the effect of an explosive placed at optimum depth;

FIG. 3 illustrates the time-pressure variation for a charge in the range d.sub.o following an explosion;

FIG. 4 illustrates the slabbing effect resulting from arrival and reflection of the shock front;

FIGS. 5-8 illustrate the various crater shapes resulting from charges placed at various depths;

FIG. 9 illustrates the material variation in response to an explosion and the terminology employed;

FIGS. 10 and 10a are representative of A vs. .DELTA. charts;

FIGS. 11, 12 and 13 illustrate the various fracture patterns resulting in rock in response to an explosion;

FIG. 14 is a chart showing representative curves of scaled slant distances vs. scaled charge depths for the various fracture patterns;

FIG. 15 is a scaled chart of curves based on scaled slant distances vs. scaled charge depths for the fracture patterns and having a superimposed predominate particle size chart;

FIG. 16 is a chart showing N-scaled crater depths plotted against .DELTA. ;

FIG. 17 is a blast pattern design for autogenous blasting;

FIG. 18 illustrates an autogenous blast design for a large cell mining unit;

FIGS. 19a-19c illustrate an exemplary N-scaled .DELTA..sub.b product control blast design;

FIGS. 20a-20c illustrate an exemplary N-scaled .DELTA..sub.v product control blast design;

FIG. 21 is an exemplary N-scaled autogenous product control blast design;

FIG. 22 is a typical preferred particle size or percent passing chart;

FIG. 23 is a plan schematic of the autogenous blast design of FIG. 21;

FIGS. 24-27 illustrate various stages of the mining method in progress; and

FIGS. 28-31 illustrate various aspects of the land reclamation and hydropower development phase of the invention.

DETAILED DESCRIPTION

Cratering Parameters and the Breakage Process Equation

Trajectory control and product control blasts are "bench type" blasts in which two or more free faces occur, as distinguished from crater blasting in which a single free face occurs. A typical bench blast usually contains several blast holes detonated in a predetermined sequence and delay interval, whereas a typical crater blast consists of a single blast hole.

Although I have previously published articles on the cratering theory and have written the Breakage Process Equation in its general form, I have not previously disclosed the fundamental relations between crater and bench blasting nor have I described the design technology of trajectory control and product control blasting.

To provide a background for the new technology of bench blasting, I will first relate some of the discoveries that made it possible for me to progress from cratering technology previously described to the technology of trajectory control, product control and stability control blasting for bench geometry. Of the various stages of development of my work, perhaps the most significant was the realization that "massive ground motion" and motion of the ground due to reflection of the shock wave were two different things. The relation between massive ground motion and motion of the ground due to the reflection of the shock wave became more apparent as my research was directed towards bench blasting.

Massive ground motion occurs later than the arrival of the shock wave at the free face and is closely associated with the pressure rise in the material. I have discovered that the pressure rise within the material due to blasting depends upon the charge depth and is maximum at d.sub.o.

The depth at which cratering begins does not necessarily coincide with the depth at which fracture or cracking begins. The critical depth is related to the charge weight by the previously stated equation:

N = E.cuberoot.W

The strain-energy factor E for the explosive, the material, and the scale of the experiment is constant and is computed using observed critical depth N and the known charge weight W. Similarly, using the equation .DELTA..sub.o = d.sub.o /N and the charge depth d.sub.o at which the presure rise is maximum, I can find the numerical value of .DELTA..sub.o at which the pressure rise in the material is maximum. Table 1 summarizes values of E and .DELTA..sub.o that I have determined for various explosives and materials.

I have discovered that the volume of material broken per pound of explosive (V)/W is maximum for a given explosive and a given material at .DELTA..sub.o in crater blasting. This relation makes it possible to determine the charge depth at which the pressure rise in the material is maximum without placing pressure guages in the material.

Now it so happens that venting of the gas bubble begins at precisely the instant and charge depth at which the volume of material broken per pound of explosive in crater blasting is maximum. Accordingly, it is possible at optimum depth to determine the time to massive ground motion using a wire wrapped around a charge which breaks the circuit at the instant of detonation and a wire along the surface by which the circuit is broken at the instant at which ground motion begins.

It is necessary to know the time to massive ground motion when blasting a number of sheet-like benches in rapid succession. In multiple row blasts, for example, the ground projected by detonation of the first row of holes must be displaced from the position in front of the next bench so as to expose the new free face. Accordingly, detonation of the second row must be delayed at least the length of time to massive ground motion. This is important because the motion of the ground from the second row of holes to be detonated must not be dampened by the pressure rise from the first row of holes, so that breakage limits due to any given hole or combination of holes is predictable, or so that the trajectory of a given row is not adversely influenced by the preceding row of holes.

To adjust for the geometry of the bench, I first get values of E and .DELTA..sub.o for the crater condition. Test blast in cratering conditions also gives me the numerical value of B, the materials behavior index, where

B = V.sub.o /N.sup.3

by measuring the volume of the true crater from an explosion at d.sub.o and performing the previously described test to determine N, where V.sub.o is the volume of the crater in cubic feet at .DELTA..sub.o, and N.sup.3 = E.sup.3 W

By definition, for the geometry of a prototype crater blast using a charge of spehrical shape, values of A and C of the Breakage Process Equation both are unity hence, the Breakage Process Equation V/W = E.sup.3 ABC reduces to V.sub.o /W = E.sup.3 B for a blast at charge depth d.sub.o and for a charge of spherical shape. Under these conditions, A = 1 and C also = 1.

The numerical value of the energy utilization number A of the equation V.sub. o /W = E.sup.3 ABC may be determined for cratering type blasts by measuring the actual crater volume V for a spherical charge of a given type and weight of explosive at any given charge depth d.sub.c, as compared to the volume measured at d.sub.o.

I have determined the variation in A, the energy utilization number, for many types of explosives when blasting in a variety of materials and have discovered that there are two basic A vs .DELTA. curve shapes: one for brittle materials and one for plastic acting materials.

I have also discovered that the points of inflection (points at which a change in slope of the curves occur) corresponds with the charge depths at which a change in the partitioning of energy from the explosive to the material occur. Further, upon experimenting with various types of explosives in a given material and in various types of material with a given explosive, I have discovered that the explosive, the geometry, and the material are not separable, independent variables. Instead, they are dependent variables. This means that the fundamental variables in blasting are energy, mass, and time. It also indicates that there is a relationship between materials behavior in blasting and the theory or relativity.

The effect of the change from crater geometry to bench geometry is to decrease the mass to which the energy of the explosion is partitioned, and also to decrease the time to reach massive ground motion. Applied to bench blasting, this means that the distance from the charge to the bench free face must be increased as compared to the distance to the horizontal free face, because of the gravity forces on the material above the charge that are not on the material to the side of the charge, if the pressure rise within the material is to be maximum and the velocity of massive ground motion is to be the same as for crater geometry. The geometry of the bench blast differs from that of a crater blast in that two or more free faces are exposed -- one at the top of the bench and one at the face of the bench, possible one or more in the hole spacing direction depending upon the blasting sequence. The geometry of the bench, and hence the mass of materials to which the energy of the explosion is partitioned, differs from the cratering condition.

I have assigned a value of unity to A, the energy utilization number at optimum depth for crater blasting and at optimum burden for bench blasting. The term "burden" (d.sub.b) indicates the perpendicular distance from the bench free face to the charge, optimum burden occurs when the charge is at a burden distance from the free face to effect maximum energy utilization. The numerical value of B remains constant, and is determined for cratering conditions. However, values of B can be used in the Breakage Process Equation as applied to bench blasting so long as the crater and bench blasts are conducted with the same explosives, in the same material, and are of the same magnitude.

The only parameter that changes in the Breakage Process Equation for bench blasting at optimum burden and depth compared with crater blasting at optimum depth is the stress distribution number C. I have found that the numerical value of C for a blast of given charge shape and type of explosive varies with the bench geometry as compared to crater geometry as well as with the shape of the explosive charge.

If a single charge bench blast is detonated at a vertical depth d.sub.o using a spherical charge of given weight and type of explosive, the burden distance must be increased to a value greater than the value of the distance d.sub.o to compensate for the decrease in confinement and the fact that the material in the vertical direction is subject to a greater gravity pull than is the material in the horizontal direction. The burden at which the breakaway velocity is the same in the free face direction as for a cratering blast at .DELTA..sub.o is called "optimum burden," d.sub.bo. The numerical value of .DELTA..sub.bo (optimum burden ratio = d.sub.bo /N ) in the burden direction always is greater than .DELTA..sub.o and the difference .DELTA..sub.bo - .DELTA..sub.o is called "the delta increment." The numerical value of increment (.DELTA.inc) is determined by test blasts, as is also the velocity of ground motion at optimum burden. The .DELTA. increment should not be confused with the .DELTA. difference (.DELTA.diff) which is discussed later.

At optimum burden in bench blasting, the .DELTA. increment (.DELTA..sub.bo -.DELTA..sub.o) depends upon the explosive and the material, but usually is in the range of 0.02 to 0.10.

When blasting with a long column of explosive, either in crater blasting or in bench blasting, the energy distribution is effected. It may be impractical in conventional mining practice to use charges of spherical shape; if so, tests are conducted using the hole diameter and charge shape to be used in practice. The value of C thus obtained always is less than the true value for prototype conditions (i.e., spherical shaped charges).

When blasting with multiple charges detonated simultaneously, a reinforcement occurs which tends to increase C. Prior to the bench blasting, hole spacing cratering blasts are detonated simultaneously at optimum charge depth to determine the optimum spacing between adjacent charges d.sub.so which gives a depth ratio .DELTA..sub.so = d.sub.s /N at which V/W is maximum. The value of d.sub.so is determined by crater blasting tests with side-by-side charges detonated simultaneously. The charge spacing for a given weight of explosive which produces the maximum volume of broken material is d.sub.so and is converted to the spacing ratio by dividing by N (i.e., .DELTA..sub.so = d.sub.so /N ). The spacing ratio is thus a scaling factor which permits one to determine the optimum spacing for any given weight charges by the formula

d.sub.so = .DELTA..sub.so E.cuberoot.W

When changing to bench geometry blasting, the d.sub.so can be scaled using the parameters from the cratering test. The spacing d.sub.s may be adjusted from the value d.sub.so at the option of blast designer in order to control the breakaway velocity of the bench free face. Moving the adjacent charges closer together increases breakaway velocity and separating the charges decreases the velocity.

I have found that the optimum hole spacing depends upon the explosive and the material and is greater than the optimum depth. Usually, .DELTA..sub.so ranges from 1.05 to 1.2 .DELTA..sub.o for charges of spherical shape. Long, cylindrical charges are less effective and require closer spacing. The exact value of .DELTA..sub.so is determined for the explosive, the material, the drill hole geometry, and the bench geometry to be used in practice.

The optimum stress distribution number C.sub.o, for bench blasting, identifies the conditions at which maximum pressure rise occurs in the material and at which massive ground motion begins. The condition occurs at optimum burden, optimum charge depth and optimum hole spacing for bench blasting. It takes into account the shape of the explosive column and the reinforcement of adjacent charges. The prototype charge is spherical, and adjacent charges are detonated simultaneously. A change from spherical to cylindrical shape results in a decrease in volume broken per pound of explosives. Similarly, a departure from simultaneous detonation to delay detonation also results in a decrease in volume broken per pound of explosives at optimum pressure rise.

The numerical value of C.sub.o is evaluated using the Breakage Process Equation. At optimum burden, optimum depth and optimum hole spacing: A = 1.0, and B= (V.sub.o /W ) crater .sup.. (1/E.sup.3). At optimum bench geometry and optimum pressure rise within the material, C = C.sub.o and the Breakage Process Equation reduces from

(V/W) bench = E.sup.3 ABC.sub.o

to

(V/W) bench = (V.sub.o /W ) crater .sup.. C.sub.o

from which

C.sub.o = [(V/W) bench]/[(V.sub.o /W) crater]

where

(V/W) bench is the volume of material broken per pound of explosive in bench blasting at optimum pressure rise, and

(V.sub.o /W) crater is the volume of material broken per pound of explosive in cratering blasting at optimum pressure rise.

The optimum stress distribution number C.sub.o may be thought of as a conversion factor from crater blasting to bench blasting. More specifically, it may be thought of as relating the ratio of volumes broken in bench blasting and in cratering blasting for a charge of given weight, type and shape at that instant at which massive ground motion begins. At the reference condition where massive ground motion begins and the pressure rise in the material is maximum, stored elastic potential energy is released from the material, and the momentum of massive ground motion attributable to the explosion also is maximum. The momentum of massive ground motion equals the sum of the masses of all particles of the material broken times the sum of the breakaway velocities of all particles participating in ground motion.

Referring now to the Breakage Process Equation and recognizing that C.sub.o identifies a specific condition (whereas C does not) it follows that a bench blast might "liberate" either more or less rock than identified by the condition of energy partitioning at C.sub.o. The liberated rock may or may not be within limits of fracturing due to the blasting failure process.

It follows from the preceding discussion that the volume of material capable of being broken per pound of explosive is greater for bench blasting than for crater blasting, due to the decrease in confinement. It is important to recognize that volumes are compared at that condition of energy partitioning at which the pressure rise in the material is maximum. It is also important to recognize that the optimum volume in bench blasting occurs at optimum burden, optimum depth and optimum hole spacing where the velocity of ground motion equals that for crater blasting at optimum depth.

The determination of .DELTA..sub.so and C.sub.o involves both crater and bench blast tests. The volume of material broken per pound of explosive at optimum pressure rise in the material for the geometry of bench blasting is computed from the bench geometry at optimum charge depth, optimum burden and optimum hole spacing, and the value of C.sub.o the optimum stress distribution number is computed from the equation

C.sub.o = [(V/W) bench]/[(V.sub.o /W) crater]

or from the equation

C.sub.o = V/N.sup.3 B

It is important to know the optimum stress distribution number for bench blasting, because it provides a means of referring cratering performance to bench performance. The term "performance" should be thought of in relation to molecular behavior, energy partitioning and energy distribution rather than in relation to the volume of material excavated.

Consider for a moment the form of the Breakage Process Equation

(V/W) bench = E.sup.3 ABC

The left side of the equation may be thought of as a measure of the ratio of the mass of material broken to the energy of the explosion. Similarly, the right side of the equation also must represent a mass to energy relationship. The equation which defines B may be written in the form:

B = (V.sub.o /W) crater .sup.. (1/E.sup.3)

substituting the value of B into the Breakage Process Equation there results

(V/W) bench = (V.sub.o /W) crater .sup.. A .sup.. C

which states that for a given explosive, a given material and a charge of given shape, the volume of material broken per pound of explosive in bench blasting equals the volume broken per pound of explosive in crater blasting times the AC product. The energy utilization number is defined by the equation

A = (V/V.sub.o) crater

V = crater volume at charge depth d.sub.c

V.sub.o = crater volume at optimum depth d.sub.o

Numerical values of A depend upon energy partitioning and vary with the depth ratio. It is difficult, if not impossible, to describe energy partitioning in absolute units. The method I have devised is based upon relative units with the standard reference at .DELTA..sub.o. It is assumed that the volume of material broken by a given explosive charge of spherical shape is a measure of energy partitioning to rock breakage. FIGS. 8 and 9 illustrate the variation of A with .DELTA. as determined for various types of explosives and materials. It may be observed that the depth ratio at which V/W and pressure rise at that instant of massive ground motion are maximum depends both upon the explosive and the material. Observed and experimentally determined cratering parameters for various explosives and materials are summarized in Table 2.

Breakage Limits and Type of Failure

Three types of failure occur in blasting; they are (1) shock failure, (2) shear failure and (3) viscous damping failure. Shock failure is characteristic of brittle-acting substance, such as granite and anorthosite. Shear failure is characteristic of more ductile materials, such as altered rocks, soft iron ore and ice. Viscous damping failure is characteristic of composite substances, such as snow, which contain air in the voids. Both the solid portion (snow crystals) and the gas portion (air) influence the failure process.

Understanding the mechanics of the blasting failure process is important to the understanding of product control blasting. The mechanics of the blasting failure process differ for each of the three known types of failure. Hence, the slant distance from the center of the explosive charge to the end of a given type of fracture formed by the explosion also differs. FIG. 9 shows these slant distances which are important in determining the controlling factors of product control blasting. The slant distance from the center of gravity of the explosive charge to the rim of the true crater is C.sub.r, and to the limits of extreme rupture is C.sub.e.

Fractures may be classified into three main groups -- (1) R (radial) cracks which are vertical planes that radiate outwardly from the bore hole, (2) O (onion) cracks which form concentric shells resembling the form of the wave front, and (3) I (inward) cracks which appear on the surface as concentric circles surrounding the bore hole and dipping inwardly toward it and are generally conical. The R, I, and O cracks are mutually perpendicular and are oriented parallel to the three principal strain axes -- one oriented in the radial longitudinal direction, the other two in the spherical surface of the wave front.

Schematics of these different types of fractures are shown in FIGS. 11, 12, and 13. FIG. 11 illustrates the radial cracks which are shown radiating outwardly at 1 from the vertical bore hole as lines 2 extending from the center of gravity of the charge. Reproduction of the effect or appearance of the radial cracks is difficult, and it must be understood that FIG. 11 is schematic only and the cracks are shown by the lines of the drawing, the surrounding material defining the cracks not being illustrated for sake of clarity.

FIG. 12 illustrates the O cracks which are designated 3 and are in the form of stacked sphere surface segments perpendicular to the axis of the bore hole or to a vertical line passing through the center of gravity of the charge. This illustration is exploded relative to the other crack illustrations for the sake of clarity.

FIG. 13 illustrates the I cracks. These cracks outline a number of frustroconical sections in stacked relation with their axes perpendicular to each underlying layer of onion cracks.

Of course, it should be understood that these cracks are all formed in response to a single blast and are superimposed on the surrounding material. The types of cracks have been separated only to show them more clearly. Too, the onion cracks are illustrated relatively larger than the R and I cracks for clarity.

Crater formation is intimately associated with the cracking system defined by the principal strain axes, but may include shearing type fractures in which the failure surfaces are conical making an acute angle with the radial direction, or a shock type fracture in brittle-acting materials in which slabs are formed in successive layers parallel to the free face. Cratering of ductile material is accompanied by uplift and doming of the surface.

The R, I and O cracks, the shear fractures in ductile materials, and the slabs in brittle materials are formed during the rise to peak pressure and may be classed as loading type fractures. Unloading type fractures also may develop parallel to the walls of the excavation during the decline from peak pressure, and a secondary type of ground motion may occur within the crater due to migration of the high velocity gases from the explosive. The secondary type of motion is referred to here as the "vortex action" and control of vortex action may be used to supplement control of the primary massive ground motion in product control blasting where abundant fine size material is required.

The extent to which the fracture pattern develops and doming occurs in a given material depends upon the energy of the explosion, physical properties of the material and the depth of the charge. FIG. 14 identifies the relation between scaled slant distance to various breakage limits and scaled charge depth for sandstone conglomerate, using a high velocity explosive. The shape of the curves describes the variation of breakage limits with .DELTA. and is indicative of partitioning of energy to the material, or of venting of the gas bubble, which marks the beginning of loss of energy to the atmosphere. The Breakage Limit Curves are determined by energy partitioning and are functions of the A vs .DELTA. curve. In the example, doming develops to a lesser distance than radial cracks, but the reverse may be true in other materials. In other than brittle-acting materials, where shock type slabbing predominates, the R cracks extend outwardly to the greatest distance, the I cracks next, and the crater rim terminates to a lesser distance than the I cracks.

FIG. 10 is typical of the variation of A with .DELTA. in frozen iron ore when blasting with ANFO. Limits of fracturing and deformation are divided into ranges and subdivided into regions with limits defined by various key values .DELTA..sub.d, .DELTA..sub.ss, .DELTA..sub.f, .DELTA..sub.o, and .DELTA..sub.a. At charge depth .DELTA..sub.d = 1.4 doming begins. The region between .DELTA. = 1.4 and 1.0 is referred to as the uplift region. Cratering for the shearing type failure characteristic of frozen iron ore begins at .DELTA. =1. The region between .DELTA. = 1.0 and 0.87 is the shear region or "isolation" region of the doming range. The isolation region is one in which the granulometry of the broken material is coarse, but becomes less coarse as .DELTA..sub.f is approached. The crater radius is maximum at .DELTA..sub.f and for frozen ore when blasting with ANFO maximum crater radius occurs at .DELTA..sub.f = 0.87, which marks the completion of the primary or "loading-type" crater fracturing process.

The crater increases in volume from .DELTA..sub.f to .DELTA..sub.o which is referred to here as the primary region of the fragmentation range due (1) to the change in crater shape during development of loading type fractures and (2) to unloading type fractures which begin at .DELTA..sub.f and increase the volume of the crater to the abrupt change in slope near the top of the A vs .DELTA. curve (about .DELTA.=0.85 in this case). At .DELTA..sub.o =0.83 the gas from the explosion (gas bubble) vents to the atmosphere and energy remaining within the gas bubble is partitioned largely to the atmosphere. Venting marks the beginning of the secondary region of the fragmentation range, which for the blasts of ANFO in frozen iron ore ends at .DELTA..sub.a = 0.30 where the volume of the apparent crater is maximum. A blast within the secondary region of the fragmentation range becomes increasingly inefficient from the standpoint of the volume of broken material per pound of explosive. It also becomes increasingly hazardous due to uncontrolled throw of the flyrock and because of the airblast pressure in the vicinity of the explosion. Although inefficient from the standpoint of energy utilization, three additional types of fragmentation predominate with the secondary region of the fragmentation range (1) fracturing due to destruction of bond strength in a zone close to the charge; (2) fracturing due to the vortex ground movement of the rock as it implodes inwardly towards the explosion cavity and upwardly into the rising column of gas and flyrock; and (3) fracturing due to impact of rock falling upon the ground. The airblast range begins at .DELTA..sub.a and continues into negative values of .DELTA.. At .DELTA. = 0 the center of gravity of the charge is at the ground surface and d.sub.c = 0.

Cratering type test blasts are conducted to evaluate parameters E and B of the Livingston's equations, to measure breakage limits and the variation of A vs .DELTA., and to identify limits and sub-limits of the doming range, fragmentation range and airblast range. As the work proceeds, the velocity of flyrock travel, the velocity of massive ground motion and the time and duration of ground motion are measured.

Single crater blasts are supplemented by two hole and three hole crater blasts to determine the optimum hole spacing and to evaluate the "reinforcement" effect of simultaneous detonation upon crater volume and upon the velocity of massive ground motion at .DELTA..sub.o. Using the crater data, bench blasts are designed at optimum charge depth and optimum hole spacing to determine the optimum burden and to evaluate C.sub.o. The velocity, time, and duration of massive ground motion are measured with a high speed camera.

Preliminary blast pattern designs for trajectory control and product control blasting are made using Livingston's equations and cratering and bench tests employing design principles later discussed in detail. The preliminary designs finally are tested at full scale utilizing such field instrumentation as may be desirable, then are modified if necessary, to improve the economics of drilling.

Elements of Trajectory Control Blasting

The method of trajectory control blasting makes it possible to predetermine the breakaway velocity of the bench blast and to throw the material in a preferred direction. Control of trajectory may be accomplished so as to throw the major portion of the material horizontally, vertically, or in an inclined direction. If thrown horizontally, the trajectory is called a .DELTA..sub.b trajectory. If thrown vertically, the trajectory is called a .DELTA..sub.v trajectory. If thrown inclined upward at 45.degree., the trajectory is called a maximum range trajectory. A maximum range trajectory becomes a maximum economic range trajectory if the material breaks away at an upward inclination of 45.degree. with a velocity approaching that obtainable for a charge at optimum burden, optimum depth, and optimum hole spacing.

Control of trajectory depends upon controlling massive ground motion rather than upon the control of particles liberated by arrival and reflection of the shock wave. Massive ground motion of a bench blast occurs with maximum momentum at optimum burden, optimum depth, and optimum hole spacing, but the trajectory cannot be controlled under these conditions. To control trajectory requires use of a "buffer wall." A buffer wall is a mass of material located so as to inhibit ground motion in a given direction. The buffer wall delays the time and reduces the duration of ground motion in a direction other than that of the desired trajectory and reduces the velocity but does not necessarily eliminate the motion. The buffer wall may exist in space at the instant of blasting, or it may be created during the action of the blast. The thickness of the buffer wall is identified by the .DELTA. difference between the free face towards which massive ground motion is inhibited and that in the direction of the controlling burden toward which it is promoted. If .DELTA..sub.b is the .DELTA. value in the near horizontal burden direction, and .DELTA..sub.v is the .DELTA. value in the vertical direction, ground motion will be promoted vertically if .DELTA..sub.b exceeds .DELTA..sub.v. The .DELTA. difference controlling the direction of massive ground motion will be .DELTA..sub.v - .DELTA..sub.b. As the .DELTA. difference increases, the buffer wall remains intact for a greater period of time and less massive ground motion occurs in the unwanted direction.

Not only is it necessary to control the .DELTA. difference, but it is necessary also to control the .DELTA. value in the direction of desired ground motion. For example, for a horizontal trajectory .DELTA..sub.v must exceed .DELTA..sub.b and the value of .DELTA..sub.b determines the breakaway velocity. If .DELTA..sub.b is greater than .DELTA..sub.bo the breakaway velocity will be less than that at maximum economic range assuming the .DELTA. value in the spacing direction = .DELTA..sub.so. Conversely, if .DELTA..sub.b is less than .DELTA..sub.bo the breakaway velocity will be greater than that at .DELTA..sub.bo, but the momentum of massive ground motion will be less than maximum due to the loss of energy that escapes from the break-through of the gas bubble prior to the time when maximum pressure rise occurs. The decrease in momentum occurs because the mass in motion is reduced more than the velocity is increased.

I have observed from numerous blasting trials that a cratering charge at .DELTA..sub.o, or a bench blast at optimum burden .DELTA..sub.bo domes up the surface as a hemisphere equal to the doming radius at .DELTA..sub.o. Accordingly, for the condition of optimum burden, optimum charge depth, and optimum hole spacing, the breakaway velocity of massive ground motion equals

v = .sqroot.2gh

v = breakaway velocity, ft/second

g = the acceleration of gravity, and

h = the doming radius at .DELTA..sub.o

Using a breakage limit drawing such as constructed from the crater test, we may determine the doming radius and compute the breakaway velocity. The breakage limit chart is prepared by "scaling" the slant distances from the center of gravity of the charge to the extreme limits of doming for a number of charges and plotting these limits against the scaled depth of the charge. For example, using FIG. 14 for test blasts in sandstone conglomerate with a high velocity, high energy explosive, the cube root scaled doming radius at .DELTA..sub.o equals 3.6 and the doming radius for a 1,000 pound charge would be 3.6 .sup.. .cuberoot.1,000 = 36 feet. The velocity of ground motion would be v = .sqroot.2gh = .sqroot.64.4 .sup.. 36 = 48 feet per second. Thus, if the direction of the ground motion is known by design of the free face and use of the buffer wall, the placement of the material can be determined using the known velocity of the ground movement.

In addition to the relation between doming radius and breakaway velocity at .DELTA..sub.o, I have observed from numerous blasting trials that in the region of optimum burden, optimum depth, and optimum hole spacing the breakaway velocity changes along the face as the slant distance increases. The breakaway velocity also decreases as the charge depth increases. The relation describing these changes is in the form

v.sub.2 /v.sub.1 = r.sub.1.sup.2 /r.sub.2.sup.2

where

v.sub.1 is breakaway velocity at .DELTA..sub.o

v.sub.2 is breakaway velocity at desired burden

r.sub.1 is scaled charge depth at .DELTA..sub.o

r.sub.2 is scaled charge depth at new desired burden

If, as a continuation of the previous example, a breakaway velocity of 60 ft/second is required in the direction of the controlling burden, it would be necessary when blasting on a bench of given height in sandstone conglomerate to reduce the scaled burden from 2.05 at .DELTA..sub.o to 1.835 computed as follows:

60/48 = (2.05).sup.2 /r.sub.2.sup.2

giving

r.sub.2 = 1.835

If the reduction in burden were accomplished at constant .DELTA..sub.v, the thickness of the buffer wall would be increased, and more of the material would be thrown in the burden direction, but the momentum of massive ground motion would decrease. To achieve an increase in breakaway velocity and yet minimize the loss of momentum the designer might elect to hold the thickness of the buffer wall constant. By doing so, however, he would not recover all of the lost momentum of massive ground motion, because the numerical value of A in the breakage process equation for the new conditions would be less than 1.

In a highly simplified form, the method of trajectory control blasting can be summarized as follows.

First, it is necessary to determine the values of N, E, d.sub.o, .DELTA..sub.o, d.sub.bo, .DELTA..sub.bo, d.sub.so, and .DELTA..sub.so (if more than one charge is to be blasted along the line of the free face). These determinations must be made for the particular explosive and material to be blasted.

These values are originally determined by test blast. Values for N, E, d.sub.o, and d.sub.so are found from crater blast. The values for d.sub.bo are determined from test bench blast. These test bench and crater blasts are made with small charges of the explosive in the material in which full scale blasting is to conducted.

Values for .DELTA..sub.o, .DELTA..sub.bo, and .DELTA..sub.so are calculated by dividing d.sub.o, d.sub.bo, and d.sub.so respectively by N.

The second step is to prepare the free face of the bench so that the angle of trajectory will be dictated by the .DELTA. difference and the angle with the horizontal made by the line connecting the charge center of gravity perpendicularly with the closest free face. Preparation of the free face is usually done by the design of a preceding blast. The velocity of breakaway of the bench free face is next calculated from the formula v = .sqroot.2gh with the h value taken from a chart showing the scaled doming radius plotted against the scaled charge depth, which chart is made from measurements of phenomena occurring during the crater test blast.

The .DELTA. difference depends also upon requirements of product control and is discussed more in detail in connection with product control blasting.

FIG. 15 shows the slant distances and the controlling factors for the .DELTA. difference. Some of these factors are:

1. .DELTA. difference fixes the back break limit and predetermines .alpha. for the next row of holes.

2. .DELTA. difference determines the breakaway velocity in the unwanted direction. As .DELTA. difference increases velocity in unwanted direction and duration of action decreases.

3. .DELTA. difference determines particle size in the buffer wall zone. As the .DELTA. difference increases, the particle size in the buffer wall zone increases and the volume of the particles of larger size also increases.

4. The .DELTA. difference must exceed .DELTA. increment; otherwise ground motion is at random.

The .DELTA. difference can be determined geometrically to gain the desired back break of the material. If the angle of trajectory .alpha. is to give maximum range, it will be maintained at 45.degree. so that the angle of the free face with the horizontal must be 45.degree.. Thus, if it is desired to continue with a maximum range trajectory, the back break will require a c.sub.r slant line of 45.degree. with the horizontal. In order to achieve this, the value of d.sub.v will be calculated from the geometric relation as d.sub.v = c.sub.r cos .alpha.. The value of d.sub.b will be dictated by the desired breakaway velocity and .DELTA. difference numerically established as .DELTA..sub.b - .DELTA..sub.v.

My earlier experiments had led me to believe that by placing the explosive charge at a depth of .DELTA..sub.o, and a distance from the mid-point of the free face, less than .DELTA..sub.bo, trajectory in the direction of the free face could be insured. However, I have now discovered that this analysis is incorrect or at least incorrect to the point that maximum utilization of the energy of the explosive charge is not available in such an arrangement. Rather, I have now found that more efficient control of the trajectory of the material is gained by placing the explosive charge a distance equal to .DELTA..sub.bo from the free face and a distance greater than .DELTA..sub.o from the horizontal face of the material. This, in effect, supplies a buffer area of material above the area in which maximum pressure rise within the material is attained, whereby maximum pressure rise within the material is gained to the point coinciding with the vertical free face with respect to the explosion and its spacing from the free face. In this regard, I attain maximum utilization of the energy of the explosive charge and get maximum pressure rise and ground rise which generally means optimum velocity of the mid-point of the free face when the explosive charge is placed a distance of d.sub.bo from the mid-point of the free face. While I do not get maximum utilization of the energy with respect to the horizontal surface or upper surface of the surrounding material due to the buffer zone, the buffer zone does operate to limit the movement of the material in response to the explosive charge and thus inhibits the ground rise in the direction of the upper surface of the material while permitting the maximum ground rise in the direction of the free face. Accordingly, by this placement of the explosive charge, the maximum trajectory of the surrounding material may be attained in the free face direction. The exact angle of trajectory, as previously described, is controlled by the angle of the free face and its relation angularly within the position of the charge.

In the trajectory control blasting, a number of charges along a free face may be desired in order to blast a considerable length of overburden along a free face from its in situ position into its final resting position. An additional factor must be considered in this situation, since there is considerable reinforcement of one charge by the detonation of an adjacent charge. The adjacent charge is not of sufficient strength so that the placement between charges can be equal to twice the value of .DELTA..sub.o. The distance between adjacent charges is given a value .DELTA..sub.s, and normally to attain maximum utilization of the energy in a trajectory control blast, the spacing between the adjacent charges .DELTA..sub.s is equal to somewhere in the range of 1.2 - 1.4.DELTA..sub.o.

In this spacing of charges, and the reinforcement effected by simultaneous blasting of the adjacent charges, an increase in utilization of the explosive energy is gained.

Elements of Product Control Blasting

1 -- Introduction

Product Control Blasting includes .DELTA..sub.b Product Control Blasting, .DELTA..sub.v Product Control Blasting and Autogenous Blasting, and is a blasting technology in which the size of the broken material and the range in granulometry in bench blasting is controlled.

The Breakage Process Control Mining Method utilizes .DELTA..sub.b and .DELTA..sub.v Product Control Blasting when excavating overburden to prepare material for various zones of the terraces, embankments, and pillar dams. The method also utilizes autogenous blasting of the orebody to prepare a suitable feed to the processing plants.

The technology involves the use of one or more or various combinations of:

a. Breakage limit control

b. Ground motion control

c. Bond strength control, and/or

d. Vortex action control

The granulometry of the broken material may be controlled so as to produce:

1. predominately coarse material

2. predominately fine material, or

3. a graded product of specified size and gradation.

Although the prior art recognizes a relationship between the quantity of explosives used and the size of the broken rock, Product Control Blasting provides a means of pre-determining particle size and of controlling the granulometry of the broken material and represents a substantial technological breakthrough. The new technology overcomes a series of erroneous concepts generally held under the present state-of-the-art.

For example, it is generally held that if predominately fine material is to be produced, small diameter blast holes must be used. Similarly, it also is held that the granulometry of the broken material is determined primarily by physical properties of the material or by geologic conditions such as the spacing between joints, rather than the design of the blast. As a result of my research, I have discovered that material as weak as snow can be blasted into large blocks, that a new fracture pattern can be superimposed upon the existing pattern governed by the geology, and that rock can be broken by blasting to a predetermined size and range in granulometry.

Under the present state-of-the-art of mining, it is assumed that the broken rock from a mine must pass successively through a coarse crushing circuit, an intermediate circuit, thence to fine grinding. However, with autogenous blasting as disclosed herein, a major portion of the ore can be reduced in a single step from run-of-mine size to finished product without the use of crushing machines. In autogenous blasting, as in an autogenous mill, the ore acts as the grinding media. In mining operations where conventional crushing and grinding circuits are employed, autogenous blasting can be used to reduce the overall cost of drilling, blasting, haulage, loading, crushing and grinding. This is possible because the low cost energy of explosives properly harnessed is capable of improving the output of loading, haulage and crushing equipment and of reducing labor costs and capital investment in mining equipment.

As further example of the need for Autogenous Blasting, first consider the growing tar sand industry. Due to the tremendous rate at which raw ore must be moved from mine to processing plant and the large volume of material that must be handled in a short time, it becomes economically impractical to screen, stockpile, or crush the material ahead of the processing plant. In my view, Autogenous Blasting, which has the capability of producing a product of pre-determined size and range in granulometry, either substantially reduces or completely eliminates the need for screening, stockpiling or crushing, and therefore provides a solution to a difficult problem.

In the application of Autogenous Blasting to oil shale mining, the raw material either may be fed to a TOSCO type retort, which requires a fine feed, or to a gravity type retort which accepts a graded product somewhat coarser in granulometry, but at the present stage of development, experiences difficulties of channeling and clinkering in the retort. The problems of feed preparation for oil shale mining--including the harder material, the more stringent feed requirements for the retorts than for tar sand separation drums, and the even greater feed rates to the processing plants--are perhaps even more acute than for tar sand mining. .DELTA..sub.b Product Control and .DELTA..sub.v Product Control Blasting supplement Autogenous Blasting and also are of economic importance because they are capable of more economically producing a graded product of coarse size such as rip-rap and break water stone than by conventional methods. Under conventional methods, the yield of stone meeting specifications usually is low, hence an excessive volume of material must be excavated to obtain a given quantity of usable material. Many instances can be cited under the present state of-the-art of the difficulty of economically producing a suitable graded product for the rock shell of a rolled rock-fill dam, or for filter and slope protection material for earth-filled dams. Product Control Blasting substantially minimizes this difficulty.

The economic advantages of Product Control Blasting and Autogenous Blasting and the probable effect of the technology of the invention upon the mining and construction industries should become readily apparent from the description in the following pages.

2 -- The Problem and the Breakthrough

Rock failure in blasting occurs in a definite, predictable sequence which is determined by the energy-mass relations. A first step towards control of the blasting failure process was my discovery that the energy/mass relations of blasting could be controlled so as in a series of blasts to duplicate each of the steps of a sequence for a single blast that might occur within the space of a few milliseconds.

The next step was to apply what I had learned about crater blasting to the new geometry of bench blasting, so as to control bench blasting results. Having learned how to control the trajectory of a bench blast, I concluded that it also should be possible to control the blasting failure process so as to predetermine the size of the broken material and the range in granulometry. As my work proceeded, I came to the conclusion that by combining several blast holes each of predetermined size and relation to each other that almost any type of gradation required in mining and construction could be designed for and produced. The steps which allow me to achieve this desired result and effect product control constitute this phase of the invention.

At this stage of the work, the search first was directed toward identifying design parameters and describing in numbers the variation in particle size when bench blasting with a single hole. Later, as the technology developed, the bench was directed toward determining how to convert data from a single hole bench blast to a multiple hole blast.

FIG. 15 summarizes results of a key stage of the work, which is this instance is illustrated for a given rock type, (Pottsville Sandstone) and for a given explosive (Hercomite 2). FIG. 15 shows the variation in breakage limits with charge depth for crater blasts graphically. Referring to FIG. 15, the scaled charge depth for a blast is plotted against scaled slant distance determined in the field for each of several breakage limits (radial) cracks, second ring I-cracks, first ring I-cracks and crater limits). Key .DELTA. values (.DELTA..sub.a, .DELTA..sub.o, .DELTA..sub.f, .DELTA..sub.ss, and .DELTA..sub.d, which can be converted to numerical values from the formula d.sub.c /.sqroot.W = E .sup.. .DELTA. ) are plotted for reference, because previously I had learned that changes in energy partitioning occur at these key .DELTA. values. I found from the breakage limit-particle size studies that the mechanics of the blasting failure process and energy partitioning could be broken down into various characteristic ranges and further sub-divided into regions representative of the granulometry. I found that:

1. The uplift region of the doming range was characterized by "pre-condition" of the rock into large blocks not completely isolated by the blast.

2. That the shear region of the doming range, in which shearing-type fractures are formed, is characterized by particles of coarse size -- or large "pie-shaped" blocks that are isolated from the material.

3. The primary region of the fragmentation range identifies completion of the primary fracture pattern and development of a secondary pattern due to the release of stored potential energy from the material -- it is characterized by a progressive decrease in particle size with decrease in .DELTA..

4. The secondary region of the fragmentation range is a region of premature breakway that follows venting; it is characterized by two extremes -- fine material near the blast hole and coarse material near the free face.

5. The air blast region of the fragmentation range is one in which airblast following venting is excessive, and much of the rock is scattered about the countryside.

When attempting to predict for a multiple hole bench blast the granulometry that results from blasting a series of holes each producing its individual gradation, it would be helpful to have a screen analysis for each type of blast hole. Unfortunately, it is impractical at the blast pattern design stage either to set up a screening plant or to recover all of the flyrock from a blast. Inasmuch as it is impractical to go directly to a blasting-screen analysis correlation, I concluded that it was more important to identify the interdependence of granulometry and .DELTA. than to attain screen analysis curves at various values of .DELTA..

My solution to the prediction of the granulometry that results from a multiple hole bench blast was to:

1. Extend the crater tests to identify the "predonderant particle size" at known .DELTA.-values, or within various characteristic regions of energy partitioning.

2. Relate preponderant particle size to the bond strength destruction zone, the intermediate zone, and the buffer -- limits of which are controllable by design.

3. Develop a fundamentally sound technique wherein preponderant particle and zone volume for a single crater blast could be converted to preponderant particle size and zone volume for a single hole bench blast.

4. Develop an analytical technique for the prediction of gradation curves for a multiple hole bench blast using single hole bench blast preponderant particle size and bond strength destruction data for each of three identifiable energy/mass zones of the borehole.

5. Provide a means of correlating the crater and bench granulometry design data with screen analysis curves obtainable during the production stage of blasting.

One of the problems is to estimate the volume and size of the "fine material" associated with a blast; it cannot be measured in the crater and cannot be sampled. I concluded, that the fine material is produced by bond strength damage, which is a function of .DELTA. and depends upon parameters of the breakage process equation. The volume of bond strength destruction is less difficult to calculate than it is to measure -- so I combined size and volume measurements of the preponderant particle size of material from the intermediate and buffer wall zones which I could measure, with volume calculations of bond strength damaged material.

Fine material is here defined as that smaller than some minimum size practical to sample by hand using a grid network at the surface of the muckpile (e.g. sand). The bond strength destruction zone is a zone of rock surrounding a blast hole and within which the material is crushed and reduced to fine material as above defined. The predominate particle size is defined here as the numerical average size of all particles measured using a grid network for sampling of the surface of the muckpile, and consists of particles larger than the minimum size as defined for fine materials

Now to review the steps leading to control of bond strength damage in blasting and to the method of calculating the volume of fine material.

The depth of the true crater, when blasting with a charge of spherical shape, extends beyond the center of gravity of the charge some radial distance which is referred to here as the "gas bubble radius." Strictly speaking, the term gas bubble radius equals the radius of the explosion cavity, but I found that limits of bond strength damage in "brittle-acting" materials and cavity limits in "plastic-acting" materials are inter-dependent. Referring now to FIG. 16, it may be observed that the gas bubble radius is greater for shallow than for deep charges. The gas bubble radius decreases to a minimum at .DELTA..sub.o with increase in depth of charge and remains nearly constant at depths greater than .DELTA..sub.o. The maximum pressure in the medium due to detonation of an explosive in a bore hole decreases with the radial distance from the bore hole. The decrease in pressure with distance for a given material and a given explosive is called the pressure decay law for that material.

Although the radius of the gas bubble and the limit of bond strength destruction depend upon the pressure decay law, they depend also upon the charge depth and the duration of the action. Rather than to compute the pressure at a given scaled distance or to correlate the pressure in the material with the radial distance from the bore hole, but which methods are available using pressure gauges, I found it simpler to use a prospector's pick and measure the radial distance from the center of the bore hole along the wall of the excavation at which the rock became strong enough so that it no longer could be readily excavated with a pick. In crater blast tests, the radial distance is measured at the elevation of the center of gravity of the explosive charge to the wall of the true crater. Using the radial distance as measured for a cylindrical charge such as used in practice, and assuming bond strength deterioration to occur within a cylindrical zone surrounding a long column of explosive, the volume of bond strength destruction is computed. The volume of material too fine to include within the grid network measurements for predominate particle size thus is estimated with reasonable accuracy.

The "preponderant particle size" is measured by constructing a grid work at the surface of the muckpile and sampling particles larger than say three inches by measfuring the length, width, and depth of each particle touching the grid line. The volume of the preponderant particle then is computed as a numerical average assuming particles to be rectangular, or of the same shape. In addition, the sampled rock also can be sized by hand and each fraction weighed so that preponderant particle size and screen analysis gradation can be correlated, say at the controlling burden intended to be used. Volumes of preponderant size material and the fine material are added mathematically to obtain the total volume of the broken material.

Referring now the lower portion of FIG. 15, which plots preponderant particle size vs d.sub.c /.cuberoot. W we may observe that the preponderant particle size gradually increases in the uplift region of the doming range with decrease in charge depth to a maximum size near .DELTA..sub.ss (See .DELTA. value where cratering begins). Further decrease in charge depth causes the particle size to decrease to a minimum at .DELTA..sub.o where the pressure rise in the material is maximum. If the controlling burden is decreased to less than .DELTA..sub.o, the blast falls either in the secondary region of the fragmentation range or in the air blast range and the preponderant particle size once again increases as indicated in the figure. I consider these changes to be consistent with my observation on energy partitioning, and attribute this increase in particle size at depths less than .DELTA..sub.o to "premature breakaway," because massive ground motion occures before the optimum magnitude and duration of pressure is reached in the rock. The observed particle size-energy partitioning relations are consistent with fundamentals of trajectory control blasting in that maximum pressure rise within the medium occurs at .DELTA..sub.o and the interval between zero time and the time of massive ground motion is maximum at .DELTA..sub.o. The term premature breakaway thus indicates to me that the energy of the explosion is substantially greater than that at the energy concentration at which V/W is maximum.

Referring now to FIG. 16, it may be observed that at least a part of the excess energy is utilized to enlarge the cavity as the confinement is decreased. The remainder is lost to venting and causes a decrease in the volume of material broken per pound of explosive and an observations in flyrock travel distance and airblast pressure. Energy lost to the atmosphere is not available to the material -- hence, the particle size at charge depths less than .DELTA..sub.o increases.

At first I interpreted the relations of FIG. 15, wherein the particle size increases with decrease in charge depth, at less than .DELTA..sub.o to indicate that it was theoretically impossible to reduce the proponderant particle size to less than that at .DELTA..sub.o. This is the condition that limits conventional bench blasting in open-pit mining and which results in primary crushers being required to handle the coarse material that is not size by blasting.

It was at this stage of my research that I conceived the idea of Autogenous Blasting. I had discovered that a vortex action immediately preceded venting, and I concluded that it was practical to control the direction of the vortex just as I had previously controlled the direction of the trajectory, and in doing so would modify energy partitioning. The vortex action is an effect of the escape of energy from adjacent the charge blast. In effect, the material surrounding the blast forms a venturi through which the broken rock is drawn by the reduced pressure of the escaping material.

As my research continued, I found that by directing the vortex into the medium rather than into the air, I could suppress both the airblast and the flyrock hazard and utilize the energy explosion to do useful work, provided that the depth of the charge was sufficient and the height to diameter ratio of the cylindrical charge did not exceed about eight to one. While promoting the vortex action, I found also that I could increase the volume of bond-strength-affected material relative to the total volume broken just as would be expected by preventing energy loss to the atmosphere.

These observations indicated to me that particle size could be reduced and blasting could safely be conducted in the air blast range -- something previously impossible to do. I consider these observations to be of extreme practical importance. Further research provided the proof I needed that air blast and flyrock could be controlled in the air blast range and material could be crushed finer by blasting than normally is done by conventional practice. I choose the term autogenous blasting to describe the new technology, because the attrition accompanying the vortex action scrubs bond-strength-damaged material to grain size. Without the controlled vortex action and attrition, moderately bond strength-damaged material otherwise would retain its cohesion. A principle of autogenous blasting design therefore is to produce a well-developed vortex by avoiding "confused" ground motion. Confused ground motion is ground motion in all directions or in a random direction rather than in a direction directly toward the free face. Avoidance of confused ground motion involves:

1. control of the depth of the breakaway point, and

2. control of the vortex pattern of several blast holes so as to avoid interference one with the other.

3 -- Basic Technology

The technology of Product Control Blasting consists of:

1. Relating particle size and breakage limits in cratering to the depth ratio .DELTA..

2. Adjusting breakage limits and particle size of crater blasting using the .DELTA.-increment adjustment method to compensate for the geometry of the bench in bench blasting.

3. Blasting in the .DELTA..sub.v direction to break horizontal slabs of rock and achieve coarse fragmentation, or blasting in the .DELTA..sub.b direction to break geological rock formations of basically vertical slab configuration. The product control blast may on the other hand be of the autogenous type wherein a vortex action is produced and a heretofore unachievably fine granulometry of material is produced. Autogenous blasting also enables one to control flyrock and minimize air blast.

4. Preparing the bench blast pattern in accordance with requirements of ground motion, breakage limit, bond strength, and vortex action control.

5. Combining particle sizes from each of several zones of a blast hole to find the volumes of each size fraction and combining them for several holes so as to represent the percentage passing a theoretical predominant particle size.

6. Determining the "percent passing" each of the predominate particle size and add or subtract various code blasts to conform the blasting pattern in accordance with gradation requirements.

4 -- Types of Product Control Blasting

The geometry of product control blasting may be classified into three main groups as follows:

1. .DELTA..sub.b product control bench blasting in which ground motion is directed towards the face of the bench.

2. .DELTA..sub.v product control bench blasting in which motion is directed towards the top of the bench.

3. Autogenous blasting in which a controlled vortex action is directed horizontally or in an inclined direction toward a third free face (at a subtantial distance behind the face of the bench) that is created in time as a result of the blasting delay sequence.

4. Autogenous modification of .DELTA..sub.b product control blasting in which the bottom of the bench is undercut by blasting in the air blast range so as to minimize breakage limits at the bottom of the bench, thus liberating relatively undisturbed rock at the top of the bench in particles of a size previously determined from the geological conditions.

5 -- Product Control Blasting and the ABC Product

Crater test blasts can be fired so as to permit one to measure the limit of bond strength destruction and the breakage limits and to define the variation in A with .DELTA.. During the work, predominate particle size can be measured and, if desired, a screen analysis made of a sample fraction of the broken material. As a result of this work, the variation in granulometry with .DELTA. can be determined and the effect of a variation in explosive type upon the numerical value of B, the materials behavior index, and upon granulometry at any desired value of .DELTA. can be measured.

The breakage process equation for a blast with a given explosive and a given material at a given scale of blasting can be written in the form:

V/W = E.sup.3 B .sup.. AC

By inspection of the breakage process equation as above written (since the left hand side must have the same dimensions as the right hand side) the AC product may be thought of as a mass to energy ratio just as is V/W.

In this form, the equation suggests to me that the AC product can be used as an index of particle size, because E and B are constant and the quantity E.sup.3 B is a constant. A and C are variables. A varies depending upon the controlling burden, and C varies depending upon the bench geometry and inter-relations among .DELTA..sub.b, .DELTA..sub.v, and .DELTA..sub.s. The variation in C for bench blasting can be related to a reference condition at C.sub.o where A is unity, using the equation:

C = (V/V.sub.ob) .sup.. C.sub.o

I tested the concept in the field and found that by manipulating the AC product when blasting with a given explosive in a given material, I could control the granulometry of the blast in any size fraction. Later, when expanding my research to autogenous blasting, I found that due to variation in the rate of energy release and bore hole pressure achievable with various types of explosives, it was sometimes advantageous to use two or more types of explosives in a single blast, or to combine two or more types of explosives in a single blast hole. Inasmuch as the materials behavior index B is sensitive both to explosive type and to the material (see Table 2), I adopted the ABC product as being representative of the general case and called the ABC product the "Product Control Index."

My experiments have taught me that a high numerical value of the ABC product identifies a coarse range in granulometry and a coarse predominate particle size; whereas a low numerical value of the ABC product identifies a fine range in granulometry and a fine particle size. Although a given product control index number represents a range in particle sizes, which in crater and trial bench blasting can be correlated with a predominate particle size, the product control index number does not correlate directly with a particle of given size. Instead, the product control index number provides a means of increasing or decreasing particle size in bench blasting regardless of whether or not the predominate particle size has been measured.

The Vortex Action, Autogenous Blasting and Granulometry

1 -- Measurements

At a certain stage in blasting, the explosion cavity "implodes" inwardly and is destroyed. This marks the beginning of vortex motion within the muckpile. Rock is drawn laterally toward the focal point of the implosion; thence is directed as a jet stream toward the closest free face. The interior portion of the jet moves faster than the exterior portion and more of the gas is concentrated near the center than at the boundaries of the stream. Particles within the jet stream are predominantly those nearest the walls of the explosion cavity and are affected to the greatest degree by bond strength damage. Bond strength damage is the result of high frequency vibration of the walls of the explosion cavity due to impact and kinetic energy of the products of combustion. Thus, fundamental variables controlling bond strength damage are the energy of the explosion, physical properties of the material acted upon, and the duration of the action. Although the physical properties of the material are not within control of the blaster, the energy of the explosion, the shape of the charge, the depth and geometry of the vortex, nad the duration of the action are.

To produce a vortex action there must be implosion. Implosion occurs if the controlling burden is less than .DELTA..sub.o, or .DELTA..sub.bo and the controlling burden is in the direction of the free face, but the velocity of the vortex approaches a maximum at .DELTA..sub.a where the vortex is well developed, and the volume of the apparent crater is maximum. Thus, the upper limit of autogenous blasting occurs at .DELTA..sub.o, but the scouring action is best developed when the controlling burden is set at .DELTA..sub.a. The lower limit of autogenous blasting is determined largely by economics, but usually is somewhere near the mid-point of the air blast region.

To achieve autogenous blasting, the vortex must be directed both toward the free face and into a muckpile being formed by the blast. This is done by controlling massive ground motion using a buffer wall as previously described, and by predetermining the depth and inclination of the axis of the vortex. There is a limit, of course, to the magnitude of the .DELTA. difference in autogenous blasting and to the depth of the vortex action. As an ideal situation, .DELTA..sub.v should approach or exceed .DELTA..sub.o, otherwise vertical flyrock may not be sufficiently inhibited and the vortex action incompletely developed in the direction of the controlling burden. Typical vortex action control criteria are given in the design criteria for autogenous blasting, Table 3.

Due to the high velocity jet action, there is a tendency for the muckpile to become tightly packed. This packing, if not avoided by proper design of the blast pattern, makes the removal of muck more difficult. To overcome the packing action, the angle of inclination, .alpha., of the jet stream with the horizontal can be controlled to permit the muckpile to bulk rather than to pack. This is done by progressively increasing .alpha. to a maximum and then reducing it to a minimum. The technology of a .alpha. control later is illustrated in sample calculations.

The layout of an autogenous blast differs from that for other types of product control blasting and from that for conventional open-pit blasting. It more closely resembles the blasting pattern for an underground development heading than for a conventional surface mine. FIGS. 17 and 21 illustrate typical blasting patterns for autogenous blasting. The blast is opened up at the "cut" area near the center of the pattern, by a code 1 blast such as in FIG. 21; after creating the initial opening or cut, ground motion, rather than being directed toward the top of the bench, is directed toward the newly created free face at the cut area, which free face is backed by a muckpile mass being developed by preceeding holes of the blast. Autogenous blasting requires that a barrier mass be maintained at the perimeter of the pattern (see FIG. 18). Barrier masses are successively destroyed during the blasting sequence; but in order to do so back break must be minimized when blasting holes of the carrier zone. The code 5 design of FIG. 21 and Table 3, (see Appendix) illustrates applicable design criteria (.DELTA..sub.rc is less than .DELTA..sub.v), and the technology of backbreak control. Ground motion begins at the free face, whereas the vortex action begins at the explosion cavity. To obtain the most effective fracturing of the material, I control the vortex so that it occurs in a line connecting the center of gravity of the explosive charge and the breakaway point specified by the design criteria.

Autogenous blast pattern design illustrates the technology that makes it possible to produce a graded product in accordance with conventional screen analysis specifications. As a result of crater and bench trial blasts, the limits of bond strength destruction and the variation of predominate particle size with .DELTA. are known. Limits of the intermediate zone and of the buffer wall zone depend upon the .DELTA. difference and the controlling burden. Accordingly, the volume and predominate particle size from each of three zones of a blast can be determined and controlled. If one wishes to produce five times as much rock of predominate size X than of predominate size Y, five times as many holes with product control index numbers in the X range than in the Y range are included in the design.

2 -- The Conversion from Crater to Bench Geometry

The presence of a second free face affects energy partioning and in turn particle size. The effect of the second free face in bench blasting is to:

1. Reduce the duration of the action,

2. Modify the pressure distribution relative to that of a cratering blast,

3. Modify the fracture pattern, the direction of ground motion, and the degree of fragmentation, and

4. To increase V/W and C.

By definition, C is sensitive to the bench geometry, duration of the action, and the pressure distribution in the material. Of the several parameters of the breakage process equation, the stress distribution number C is the only one influenced by the second free face.

Fundamentally, the effect of the second free face is to decrease the mass of material to which energy might otherwise be partitioned during the interval between arrival of the shock front at the free face and the beginning of massive ground motion. The decrease in mass at constant energy is an energy/mass change and such changes are identified by the depth ratio, .DELTA.. The problem, as discussed previously, is to determine the change in depth ratio that is equivalent to the decrease in mass. In its application to product control blasting, not only is it necessary to describe the effect of the second free face, but also to evaluate it relative to the slant distance to breakage limits and to particle size.

The .DELTA. increment (.DELTA..sub.bo - .DELTA..sub.o) is measured at the reference condition at which the momentum of massive ground motion is maximum. The reference condition is identified as occurring at .DELTA..sub.v = .DELTA..sub.o at .DELTA..sub.s = .DELTA..sub.so, and .DELTA..sub.b =.DELTA..sub.bo. At the reference condition for bench blasting A = 1, and B = V.sub. o /N.sup.3 crater, by definition. The equivalent mass to be added in the burden direction to achieve the same breakaway velocity in the horizontal direction in bench blasting as previously was obtained in the vertical direction in crater blasting, thus is determined by test blasting.

When converting from crater geometry to bench geometry, we are concerned not only with bench geometry at the C.sub.o reference, but also with the general case where the controlling burden either may be greater than or may be less than .DELTA..sub.bo . A large portion of energy of the explosion is lost to the gas bubble at controlling burden .DELTA..sub.a. Similarly, much of the energy of the explosion is partitioned to inelastic behavior and seismic vibrations at .DELTA..sub.ss. Accordingly, when evaluating the effect of the second free face, energy partitioning also must be taken into account.

The method I use is called the .DELTA. increment adjustment. I compensate for the loss of confinement with a theoretical mass that varies from the maximum at .DELTA..sub.o to 0 at both .DELTA..sub.a and .DELTA..sub.ss. At maximum size, the theoretical energy may be visualized as a rectangular slab of thickness equal to the .DELTA. increment, of length equal to .DELTA..sub.so, and of height equal to .DELTA..sub.o. As the controlling burden decreases from .DELTA..sub.o to .DELTA..sub.a, the thickness of the theoretical mass decreases from the .DELTA. increment to 0. Similarly, as the controlling burden increases from .DELTA..sub.o to .DELTA..sub.ss, the thickness of the theoretical mass also decreases to 0. Thus, the method increases V/W and C and provides for the greatest adjustment in breakage limits and particle size for the condition where the pressure rise in the material is greatest. Energy partitioning automatically is taken into account, and may be thought of as due to an increase in the AC product.

FIG. 15 illustrates the adjustment as it applies both to breakage limits and to predominate particle size for .DELTA..sub.b -- and for .DELTA..sub.v -- product control blasting. Assume for example that the .DELTA. increment is determined by field test blast to be 0.07 and E has been determined to be 3.30. The value of 0.07 equals a scaled charge depth of 0.23 computed as follows:

d.sub.c /.cuberoot.W = .DELTA..sup.. E = 0.07 .sup.. 3.30 = 0.23

Since the chart of FIG. 15 is drawn to scale, the value 0.23 may be scaled up the line at .DELTA..sub.o to the point X and a straight line connecting the point X to the .DELTA..sub.a and .DELTA..sub.ss points at zero on the cratering scaled burden portion of the chart, the scaled value of .DELTA. increment for any .DELTA. value between .DELTA..sub.a and .DELTA..sub.ss can be taken from the chart.

In the example of FIG. 15, a bench blast due to the presence of the second free face, to be equivalent to a crater blast at the .DELTA..sub.o, must have a burden .DELTA..sub.bo = .DELTA..sub.o + 0.07. The .DELTA. increment adjustment of FIG. 15 is identified by the dimension line ".DELTA. increment adjustment at .DELTA..sub.o." Thus, the loss of confinement increases the scaled slant distance to the limit of radial cracking by shifting to the right along the radial crack curve from B to B'. Similarly, the effect upon the scaled slant distance to the crater lip is to shift to the right along the crater curve from C to C'. The adjustment for the second free face shifts the blast into the primary region of the fragmentation range and increases the predominate particle size from 0.75 cubic feet for the geometry of crater blasting to 1.05 cubic feet for the geometry of bench blasting.

Product Control Blast Pattern Design

1 --The Breakage Process Equation Applied to Product Control Blasting

A high value of the ABC product indicates a coarse product; whereas a low value indicates a fine product. The problems are: to control fragmentation by controlling bond strength damage, fragmentation in the intermediate zone, and fragmentation in the buffer wall zone; and to design a multiple hole bench blast so as to obtain an overall product of the desired size and granulometry from a series of blast holes. This requires that each of the parameters of the Breakage Process Equation be known for each type (code) of blast hole in the pattern.

Consider the equation V/W = E.sup.3 ABC and the available data. V/W depends upon the bench geometry which in turn depends upon the criteria set for bench design. Design criteria fix the direction of ground motion, and of the vortex action following implosion, the limits of bond strength destruction, the breakage limits, and the size of particle. We may view the resulting fragmentation as divided into three zones:

1. The bond strength damage zone near the blast hole;

2. The .DELTA. difference zone which acts as a buffer wall to control ground motion; and

3. The remaining portion between the bond strength zone and the .DELTA. difference or buffer wall zone.

In effect, the designer, by fixing the limits of each of these three zones, exercises control over fragmentation within each zone. The energy concentration is greatest in the bond strength destruction zone and least in the buffer wall zone. Because particle size is a function of energy concentration, the buffer wall zone is the chief contributor to the coarse fraction. Similarly, the contribution of the fine fraction from the bond strength destruction zone and of the intermediate fraction from the intermediate zone is proportional to the ratio of the volume of a given zone to the total volume excavated by the blast. The volume from each of the three zones may be computed from the field test data or from the scaled drawing. Once the design criteria are stated, the bench geometry is fixed, and V/W can be calculated.

The statement of the criteria depends on the desired predominant particle size and the values of the parameters found in the test blast. The test blast provides the parameters for preparing a chart similar to FIG. 15. Following the steps required to prepare the .DELTA..sub.b product control design of FIG. 19, one would first conduct test blast and prepare the chart of FIG. 15. The desired predominant particle size for the intermediate zone would be selected and the chart entered at the appropriate point; in this case, the desired size is 1.70 cu.ft. and entering the chart at 1.70 gives a scaled burden for crater geometry of 2.61. This value for d.sub.c /.cuberoot.w of 2.61 gives a .DELTA. value of 0.79 calculated as follows:

d.sub.c /.cuberoot.w = E .sup.. .DELTA.

.DELTA.=d.sub.c /.cuberoot.w / E) = 2.61/3.30 = 0.79

This .DELTA. value would be .DELTA..sub. v if blasting in crater geometry, but to adjust this value for the fact that it is to set the controlling burden in the free face direction, a .DELTA. increment must be used to adjust this controlling burden .DELTA. value. The scaled .DELTA. increment adjustment (from the previously prepared scaling chart of FIG. 15) at this .DELTA. value is 0.04 so that .DELTA..sub.bo would be 0.75.

To get the .DELTA..sub.v value, the predominant particle size for the buffer zone is selected (see Design criteria chart of Table 4), in this case 3.25 cu.ft. and the graphs of FIG. 15 entered to get a d.sub.c /.cuberoot.w value of 3.0. This value of d.sub.c /.cuberoot.w gives a .DELTA. value of 0.91 which in a crater blast would produce the desired predominant particle size. To adjust for the lack of confinement due to the bench geometry, a .DELTA. increment value must be subtracted from the .DELTA. value of 0.91. The scaled .DELTA. increment value is the distance y on FIG. 15 when compared to the distance which equals 0.07. Thus the value of .DELTA. increment is 0.03 and the adjusted value of .DELTA..sub.v is 0.88.

The statement of the criteria can now be adjusted for other factors and in the example shown, .DELTA..sub.b has been chosen as 0.73 rather than the optimum .DELTA. value of 0.75 in order to achieve more velocity in the burden direction. In setting the spacing of the charges, the .DELTA..sub.s value was determined by the geometry of the plan and section AA (FIG. 19 b) drawings to be 0.79. This value was determined by deciding that the distance to the midpoint toe of the bench should be less than .DELTA..sub.f by an arbitrary value of 0.05 so as to assure that the fracturing would reach the midpoint toe and the bench would be broken to grade line since .DELTA..sub.f is the value at which cratering is maximum. Once these .DELTA. values are known, a scaled bench geometry can be drawn from which other values may be determined.

In the general case, the bench geometry is described and drawn to scale using dimensionless .DELTA.-units (preferably as a function of N), but W, the weight of the explosive is unknown until the bench height is finally chosen.

The volume of excavation from the Breakage Process Equation is V = WE.sup.3 ABC = N.sup.3 ABC, and can be computed from the scaled drawing. For example, referring to the cross section for .DELTA..sub.b -Product Control Blasting, FIG. 19, V = 0.9038N.sup.3 and the quantity 0.9038 from the equation V = ABCN.sup.3 must be the ABC product.

The ABC product thus is fixed by the design criteria -- so the designer needs to know how to establish the design so as to achieve the desired type of fragmentation.

From the crater tests A, B, and E are known, from the bench tests C.sub.o and the .DELTA.-increment are known. C is the only parameter that depends upon the bench geometry rather than upon the crater geometry -- it can be greater than C.sub.o or less than C.sub.o.

The controlling burden of a bench blast is controlled by the scaled charge depth of FIG. 15. It may be described either in units of d.sub.c / .cuberoot.W or in units of .DELTA., and the units may be converted one to the other using the general equation in the form

d.sub.c /.cuberoot.w = .DELTA. E

The controlling burden determines the breakage limits and the granulometry. The controlling burden also determines the numerical value of the AC product. Hence, the numerical value of A is fixed by the bench design criteria and is equal to the value of A from the cratering tests. The value of C is unknown; but the value of C can be computed from the equation

C = V/N.sup.3 AB

and the value of the AC product can be computed from known values of V/W for bench blasting and V.sub.o /W for crater blasting. C can also be computed from the equation V = N.sup.3 ABC since V can be calculated from the scaled bench geometry and A and B are known from the cratering test.

The designer has as his option the selection of the explosive type. It sometimes is to his advantage to use more than one type of explosive in a given hole. The numerical value of B are fixed by the explosive and the material and is determined from the crater tests.

As illustrated in FIG. 16, the radial distance to the limit of bond strength destruction is maximum at .DELTA. = 0, decreases to a minimum at .DELTA..sub.o and remains nearly constant with further increase in controlling burden. The designer may increase bond strength damage by selecting an explosive or combination of explosives having a high value of B, and by blasting at controlling burdens less than .DELTA..sub.o. Bond strength damage thus may be controlled within certain limits, provided that the vortex action and venting also are controlled. Predominate particle size within each of the three zones may be evaluated after applying the .DELTA. -increment correction and is as follows:

1. Particle size within the bond strength destruction zone ranges from grain size to an arbitrary maximum size defined for grid sampling to determine the preponderant particle size.

2. Preponderant particle size within the intermediate zone is that determined by the controlling burden, and is determined using .DELTA..sub.b or .DELTA..sub.v whichever is least.

3. Predominate size within the buffer wall zone is determined by the burden to the outer limit of the ground motion control buffer wall.

Referring now to Table 4 the .DELTA..sub.b Product Control blasting design summary of FIG. 19, the volume of the buffer wall as previously calculated by a planimeter represents 23 percent of the total volume and the predominate particle size (after applying the energy partitioning adjusted .DELTA.-increment correction to .DELTA..sub.v using FIG. 15) is 3.25 cu. ft. from the buffer wall zone. Similarly, the bond strength destruction zone is cylindrical in shape and of radius 0.10N, the volume of bond strength destruction is

V.sub.b =.pi.r.sup.2 h= 3.14(0.10N).sup.2 . (0.82N) or V.sub.b =0.0258N.sup.3

The volume V.sub.m of the intermediate zone is

V = V.sub.b + V.sub.m + V.sub.w

V = 0.0258N.sup.3 +V.sub.m + 0.23V

v.sub.m = 0.77V - 0.0258N.sup.3 = (0.77 .times. 0.9038N.sup.3) - 0.0258N.sup.3 where

V = 0.9038N.sup.3 as determined from calculation or a planimeter measurement on a scaled chart of the blast design,

so that V.sub.m = 0.6959N.sup.3 - N.sup.3 = 0.670lN.sup.3

Now to find V/W and C for the .DELTA..sub.b Product Control cross section.

Using the Breakage Process Equation

V/W =E.sup.3 ABC

and given

A =0.95 B = 0.47

e = 3.30 abc = 0.9038 v/w = e.sup.3 abc

v/w = 35.94 .times. 0.9038 = 32.48 cu.ft./pound.

The V/W value is necessary in order to evaluate the total cost of the job.

The value of C may be computed directly from the Breakage Process Equation as follows:

C = V/N.sup.3 AB = 0.9038N.sup.3 /N.sup.3 (0.95) (0.47) = 0.9038/0.4465 = 2.02

2 -- the Explosive, the Material, and Bond Strength Control

The effect upon Product Control Blasting of a change in type of explosive usually is less than the effect due to a change in type of material. However, a change in explosive type when blasting in a given material effects each of the parameters of the Breakage Process Equation to some degree. In general, an increase in energy of the explosive at constant weight increases V/W, but this is not always true. If more than one type of explosive is to be used either in a single blast hole or in various holes of the given blast, it is essential during the crater and bench test blasts to determine the effect of explosive type and to obtain curves similar to those of FIG. 15 for each type or combination of types of explosive intended to be used.

It may be desirable either to suppress bond strength damage in .DELTA..sub.v - .DELTA..sub.b -- Product Control Blasting if predominately coarse product is desired, or to promote it in Autogenous Blasting if a predominately fine product is desired. A high yield of coarse product usually is best achieved in the shear region using low energy, low velocity explosives; whereas for .DELTA..sub.v - .DELTA..sub.b -- Product Control Blasting as contrasted to Autogenous blasting a high yield of fine product usually is best achieved in the primary region using high energy, high velocity explosives. A change in explosive type usually requires a change in hole diameter, and may also require a change in bench height to achieve optimum economic benefit and optimum yield of size-graded product.

The dashed line to the left side of the predominate particle size curve of FIG. 15 indicates for Autogenous Blasting a continuing decrease in particle size in the Secondary and Air Blast Regions of the Fragmentation Range. The decrease in particle size at controlling burdens less than .DELTA..sub.o is characteristic of Autogenous Blasting and fundamental thereto and is made possible by:

1. The geometry of the blast pattern (See FIG. 17);

2. by suppressing premature breakaway and breaking to a newly created, third free face bounded by buffer means (see FIG. 18); and

3. By promoting the vortex action and avoiding confused ground motion following implosion.

3 -- Blast Pattern Design and Granulometry Correlation

FIGS. 19, 20 and 21 illustrate typical blast pattern designs for .DELTA..sub.b -- Product Control, .DELTA..sub.v -- Product Control and Autogenous Blasting, respectively. The figures also serve to illustrate the calculations and the application of the .DELTA. increment adjustment for .DELTA..sub.b and .DELTA..sub.v bench blasting to determine breakage limits and particle sizes. The .DELTA. increment adjustment is unnecessary for autogenous blasting. The figures are not intended to indicate that a single design for .DELTA..sub.b -.DELTA..sub.v -- Product Control Blasting or for Autogenous Blasting is necessary to the invention. Instead, it is intended merely to illustrate the application of basic principles some of which apply also too Trajectory Control Blasting.

Elements of .DELTA..sub.b - .DELTA..sub.v -- Product Control Blasting are:

1. Ground motion control;

2. Breakage limits control; and

3. Bond strength control.

Autogenous Blasting includes these three elements plus a fourth -- vortex action control.

Ground motion control is governed by the same basic principles as previously discussed in detail for Trajectory Control Blasting. Tables 3, 4 and 5, in connection with FIGS. 19, 20 and 21, illustrate criteria of design for ground motion control for a single hole for .DELTA..sub.b and .DELTA..sub.v Product Control Blasting and for a series of holes for Autogenous Blasting. The figures and associated tables should not be construed to indicate that .DELTA..sub.b and .DELTA..sub.v product control blasting are limited to a single hole. On the contrary, multiple hole blasting patterns for these two types of blasting can be as complex as that described in greater detail for Autogenous Blasting. The basic principles are similar, only the chosen criteria changes.

In the .DELTA..sub.b Product Control example of FIG. 19, ground motion is towards the face of the bench because .DELTA..sub.b is less than .DELTA..sub.v. Ground motion is not at random because the .DELTA. difference of 0.15 is greater than the .DELTA. increment of 0.07.

In the Autogenous Blasting example of FIG. 21, ground motion starts vertically with the crater blast so as first to develop a third free face at a substantial distance from the face of the bench. The code 2 blast directs the broken rock in an inclined upwardly direction towards the cut area without excessive backbreak. The code 2 parameter controlling backbreak is .DELTA..sub.cr and is equal to or less than .DELTA..sub.v. The breakaway point of the code 2 trajectory is below the midpoint of the code 1 excavation limit. The code 3 blast directs the vortex nearly horizontally underneath the code 2 muckpile. The code 4 blast directs the vortex inclined upwardly at 18.degree. so as not to pack the code 3 muck too tightly and to permit the muckpile to bulk vertically. The code 5 blast directs the vortex upwardly at 32.degree..

FIG. 15, which is the basis for the calculations of FIG. 19, applies to a given explosive and a given material; hence, similar breakage limit diagrams must be prepared from trial blasts for other materials and other explosives. Breakage limit control not only determines C, V/W, and granulometry for a given blast, but also determines the geometry of the resulting excavation.

To illustrate that the ABC product is an index of particle size and that the granulometry of a blast is determined both by the intermediate zone and by the buffer wall zone, compare criteria and particle sizes for .DELTA..sub.b Product Control of FIG. 19 and Table 4 with those of .DELTA..sub.v Product Control of FIG. 20 and Table 5. Both the .DELTA..sub.b and the .DELTA..sub.v example designs produce relatively large size material such as might be required for the shell of a rolled rock-fill dam, or a graded product having a high yield of coarse material, or for rip-rap or slope protection. In general, the top of the bench is a larger free face than the face of the bench and .DELTA..sub.v Product Control is better adapted to coarse blasting than .DELTA..sub.b Product Control.

Breakage limits for the .DELTA..sub.v Product Control example are determined by the criteria .DELTA..sub.v =.DELTA..sub.f = 0.88, to give maximum crater scaled slant distance, and by the criteria .DELTA..sub.b = .DELTA..sub.ss = 1.0. These criteria fix the .DELTA. difference at 0.12, determine C to be 6.48, .DELTA..sub.rc to be 1.12, V/W to be 40.4, the predominate particle size from the buffer wall at the face of the bench to be 3.8 cu. ft., and from the top of the bench to be 3.15 cu. ft.

Principles of breakage limit control illustrated in the figure for Autogenous Blasting fix the angle of inclination, .alpha., that the trajectory of the following hole makes with the horizontal. The inclination of the trajectory and the inclination of the axis of the vortex are determined by the same fundamentals even though the vortex action begins later and commences at the explosions cavity rather than the free face. Charge shape influences both the trajectory and the vortex. Short columns of explosives are preferable to long columns because the confinement at implosion is more uniform and hence there is less tendency at a given charge depth towards imperfect development of the vortex.

Breakage limit control (i.e., extent of backbreak) for Autogenous Blasting obviously is of extreme importance. Without it there would be neither symetrical development of the vortex, controlled fragmentation, or control of flyrock or air blast. With it:

1. the predominate particle size is successively reduced from 1.0 cu.ft. for the Code 1 holes to 0.03 cu.ft. for the Code 5 holes;

2. the bench is broken to grade;

3. the muckpile is properly bulked so that loading is made easier; and

4. the barrier wall at the Code 5 excavation limit is straightened up so as both to minimize the required barrier wall thickness and later to permit the wall to be systematically destroyed by blasting after it has served its purpose.

Referring to the example of autogenous blasting illustrated in FIG. 21, the method for determining an autogenous blast pattern to meet a stated objective will now be described. The design of FIG. 21 is prepared for the type of material and explosive for which the chart of FIG. 15 was prepared.

The design of FIG. 21 was prepared to meet the granulometry curve shown in FIG. 22. As can be seen from the granulometry curve, a large percentage of the material is desired to be of a relatively small mesh size. Accordingly, resort must be had to autogenous blasting, since, as can be observed from FIG. 15, the fine gradation cannot be achieved with .DELTA..sub.b or .DELTA..sub.v product control blasting.

The first step is to perform a crater blast to provide a newly created bench free face behind barrier walls, into which the vortex of the code 2 charges can be directed.

The code 1 crater blast is chosen for placement at a .DELTA..sub.v somewhat less than .DELTA..sub.o, in order to achieve greater bond strength destruction. Since .DELTA..sub.o is 0.68 from the previous determination, an arbitrary value of 0.61 is chosen for placement of the charge in the .DELTA..sub.v direction. From this .DELTA..sub.v value, FIG. 15 can be used to find the limit of backbreak. The .DELTA. value will have to be converted to d.sub.c /.cuberoot.w value, where the chart is entered. When the crater limit line is reached, the corresponding value of the scaled slant distance is found, which can be converted from its d.sub.c /.cuberoot.w value to the .DELTA..sub.cr value. These values are sufficient to show the geometry of the crater formed by the code 1 blast and the predominate particle size can be found from FIG. 15 in a manner similar to that illustrated in connection with the .DELTA..sub.b product control blast example. In autogenous blasting, however, the .DELTA. increment adjustment does not have to be made, since in effect the blasts are of the crater type.

The code 2 blast design must be directed into the muckpile being formed by the code 1 blast. In order to achieve a smaller predominate particle size, the trajectory of the code 2 blast must be directed perpendicular to the free face formed by the code 1 and the vortex of the code 2 blast directed into the expanding code 1 muckpile. In order to avoid a .DELTA. difference which would produce a larger range of granulometry, the .DELTA..sub.b value should be chosen so as to produce a substantially vertical limit of backbreak. By directing the trajectory of the code 2 blast perpendicular to the midpoint of the free face minus 0.12 the axis of the vortex is oriented to minimize surface venting, and from this selection of the design criteria (see Table 5), the .DELTA..sub.b value was found to be 0.41, the value being dictated by the selection of a .DELTA..sub.v value equal to the bench height. These design criteria from the chart of FIG. 15 result in 100 percent of the material broken being in the intermediate and bond strength destruction zones and having a predominate particle volume of 0.10 cubic feet. The spacing between the code 2 charges is dictated by the geometry of the blasting pattern (see FIG. 22) and by the amount of material which is desired in the 0.10 cubic feet predominate particle size range.

The code 3 design is primarily concerned with trajecting the broken material in a horizontal direction in order to avoid packing of the previously broken muckpile. The geometry of the code 2 blast which can be graphically drawn out in the example gives the new free face into which the material is blasted. In the code 3 design, the .DELTA..sub.b value is shown equal to .DELTA..sub.a in order to produce high bond strength destruction. From the geometry of the layout, the value of .DELTA..sub.v can now be calculated to be 0.71. With this blast design, it will be seen that a .DELTA.-difference will exist which will produce a buffer wall zone, the predominant particle size of which can be determined to be 0.80 cu. ft. from the graph of FIG. 15. The volume of the material within the buffer zone can be calculated from the geometry of the blast. The volume of material broken in the intermediate zone can similarly be calculated so that the predominant size of the percentage of material which is found to be in the range of predominate particle volume is 0.25 cubic feet. The selection of these design criteria establish the geometry of the code 3 blast and give the volume of material falling within the particular predominant particle size ranges. The spacing of the holes is determined by the number of holes selected which, in turn, is dictated by the geometry of the blasting pattern and the amount of the material desired in the predominant volume range previously calculated. Similarly, calculations are made for the code 4 and code 5 blast designs and the number of charges placed in each design will be determined by the percentage passing graph shown in FIG. 22. If the design as laid out in the autogenous blasting example did not produce the desired range of granulometry, the number of blasts of any particular code could be adjusted to adjust the range of predominant particle size produced. For example, were it found from the calculations previously described that an insufficient amount of material would be produced to pass 45 percent of the material at 0.25 in the screen analysis, additional blast charges of the code 3 type could be set, or on the other hand, if more than 45 percent of the material were passing at 0.25, the number of code 3 blasts would be reduced. The volume of the total blast design for this example is shown in Table 6.

The significance of the autogenous blasting method is that the design layout for a complete mining or other application could be made prior to any field blasting other than the test blasting to attain the chart of FIG. 15. The small amount of time required to make these calculations is more than offset by the tremendous investment in machinery and crushing costs that would be required to produce the same range of granulometry if the blasting were conducted on a hit-and-miss basis.

Bond strength control is not a simple function of explosive selection or of hole size. Maximum bond strength damage depends upon developing a maximum impulse within the material at and beyond walls of the borehole. The pressure rise does not continue beyond the time of massive ground motion, but the duration of the action is increased by increasing the depth at which the vortex occurs.

Bond strength damage may be seen by direct observation, with the aid of a microscope and polished or thin sections, or by post blasting strength tests. From blast tests in sandstone with TNT the limit of complete bond strength destruction was found to extend outwardly a radial distance from 0.32N at .DELTA. = 0 to 0.15N at .DELTA..sub.o. In granite the limit extended from 0.27N at .DELTA. = 0 to 0.12N at .DELTA..sub.o. At controlling burdens greater than .DELTA..sub.o the limit appears to remain constant and approximately equal to that at .DELTA..sub.o.

Table 6 identifies limits of bond strength destruction for the example Product Control Blasting pattern of FIGS. 19, 20 and 21, and illustrates a typical calculation to determine the volume of fine material produced by a blast, which otherwise could not be compensated for. The table also illustrates that the FIG. 19 .DELTA..sub.b Product Control design produces a higher proportion of fines than does the .DELTA..sub.v design of FIG. 20, and that an Autogenous Blasting pattern is capable of reducing a substantial portion of the total volume of material to grain size. Referring to Table 6, note that nearly 50 percent of the code 5 material and roughly 15 percent of the total is smaller than the cut-off size for surface grid sample preponderant particle size measurements.

The total volume broken by a blast hole equals the sum of the volumes of rock from the bond strength destruction zone, the intermediate zone, and the barrier zone. Table 6 records the volumes of the bond strength destruction zone for each type (code) of blast hole of the example Autogenous Blasting design of FIG. 21. Using Table 6, the design summary Table 3, and the plan layout of the Autogenous Blast of FIG. 21, we may summarize the particle size distribution from each blast hole and combine all the blast holes for the Autogenous Blasting pattern to obtain a gradation curve for the entire pattern.

The left side of Table 7 summarizes the particle size distribution for each type hole included in the Autogenous Blasting example Cross Section 21 of FIG. 23. The volume of bond strength destruction zone for holes, codes 1 through 5 of Table 7, is obtained from Table 6. The total volume of excavation per hole, controlling dimensions, and particle sizes from the intermediate and buffer wall zones of each hole as given in the cross section and summary tables of FIG. 21 provide all data necessary for the volume calculations of the left side of Table 7. "Particle Size Distribution Per Hole."

Using the particle size distribution per hole and a plan of the blast holes for the Autogenous pattern, we may compute the total volume of grain size material in the pattern and construct a predominate particle size distribution curve for the blast. As may be observed, the right side of the table summarizes preponderant particle size volumes in order of increasing particle sizes. The percent passing column is the ratio of cumulative volumes smaller than a given size to the total volume expressed as a percentage. The pattern particle size distribution data are presented graphically in FIG. 22 in a form usually used for gradation curves, except that "size" is referred to volume rather than to linear dimensions.

By inspection of the composite predominate particle size gradation curve (see FIG. 22) for the exemplary Autogenous Blast we may conclude:

1. A blast hole may be designed so as to predetermine the predominate particle size in each of the zones of a blast hole, and so as within certain limits to control the volume of each zone and the overall granulometry of the hole.

2. A series of blast holes, each of known granulometry distribution, may be combined so as to obtain a composite granulometry distribution for the pattern of holes. Within limits imposed by the technology of ground motion, breakage limit, and vortex action control, a product control blasting pattern may be adjusted so as to produce a range of granulometry in accordance with gradation specifications.

3. If a test blast for which a composite gradation curve is available is fired, and the resulting muckpile sampled as for a conventional screen analysis, the proportion of any size fraction either can be increased or decreased as desired by expanding the partial plan of FIG. 21 to an overall plan such as illustrated for a given unit in FIG. 18.

4. composite patterns may be designed for .DELTA..sub.b Product Control Blasting and for .DELTA..sub.v Product Control Blasting utilizing the technology described here and illustrated more in detail for Autogenous Blasting. Similarly, control blocks at the boundaries of an Autogeneous Blast can be destroyed using .DELTA..sub.b Product Blasting to produce a product of predetermined size and range in granulometry.

In 1968 the cost of coarse crushing for large mining operations in the United States ranged from 7 to 12 cents per ton. The cost of fine crushing ranged from 13 to 21 cents per ton, and the cost of loading and haulage ranged from 13 to 21 cents per ton. The technology of Product Control Blasting makes possible a substantial reduction in the overall cost of drilling blasting, mucking, haulage, and crushing and I consider it to be of extreme importance to the mining and construction industries.

Elements of Stability Control Blasting

Stability Control Blasting is a phase of the technology which I have discovered which enables one to control the backbreak of material in response to a blast and, thus, ensure the stability of the material beyond the backbreak limit. This phase of the invention is adaptable to the mining process as well as standard mining procedures in that it permits one to make a substantially predesigned cut by use of proper placement of an explosive charge.

Stability Control Blasting is a method and control blasting of surface and underground excavation having as its objective the control of static and dynamic elastic rebound. Static elastic rebound is due to release of elastic potential energy stored in the rock and releaseable as a result of a change in rock load or a reduction in lateral restraint. Dynamic elastic rebound is due to release of elastic potential energy stored in rock due to dynamic loading for an explosion, a portion of which is recoverable.

The stability control phase of the invention is very closely related in some aspects to the Product Control Blasting in that it requires test blasts and production of breakage limit curves substantially as illustrated and described in connection with FIG. 15. The test blasts required to produce these curves will not be described again but considering that these preliminary phases of this aspect of the invention have been completed, the factors and controlling steps of Stability Control Blasting will be substantially as follows.

Once the chart of the type illustrated in FIG. 15 is prepared from the test crater blasts, the basic criterion for Stability Control Blasting is available in deployment of this criterion to the specific blast design may proceed. The objects of the Stability Control Blasting is to break away the surrounding material to a predefined limit without effecting the stability of the material beyond that limit. In doing this, what is termed a stability control zone is selected which is in effect an area adjacent the material that is desired to leave uneffected in which some fracturing of the material could be accomplished by the normal blasting procedure but this normal blasting is controlled to not produce any fracturing beyond the stability control zone. In accomplishing this, the control criterion is to assure that the limit of extreme rupture from the particular charge, weight, and placement deployed will not extend beyond the stability control zone. These factors must be realized when normal production blasting is performed since otherwise, a production blast would produce fracturing into the area of material that it is desired to maintain as a stable rock formation and the objectives of Stability Control Blasting could not be accomplished.

As the limit between the predetermined stability control zone and the area that is not to be effected is approached, the weight of the charge must be successively reduced and in order to get appropriate breakage and energy utilization, the depth of placement of these reduced charge weights consequently will have to be reduced. These relations are controlled by Product Control Blasting and the Livingston equations and previously discussed. The significant factor of Stability Control Blasting is that for the given charge, weight, and depth of placement, the controlling burden including that for the perimeter holes at the excavation limit must be such that the limit of extreme rupture does not extend beyond the stability control zone.

The controlling burden will normally be in the range determined by .DELTA. = .DELTA..sub.o - 0.10 to .DELTA..sub.o - 0.20. Employing this method for charge placement, one can thus assure that energy partitioning does not extend beyond the stability control zone to the point that the molecular organization of the material is effected.

Elements of the Mining Method

The mining method is basically the deployment of trajectory and product control blasting methods in a set procedure. FIG. 24 shows a mining layout in progress. The ore body is indicated at 10 with the overburden shown at 12. The overburden bench free face 13 has been prepared by a trajectory control blast which projected the overburden that had covered the active mining cells 14 to fill the previously mined out cells 15. Buildup muck that is not completely projected to the desired location is hauled to complete the terracing 16. The terracing 16 is maintained at a slope or grade of generally 6 percent to the horizontal whereby the terracing may be used as a ramp for equipment carrying the overburden to terrace dikes and doms as later described.

As has been previously indicated, the mining layout of this invention is economical at present basically for mining applications covering extended areas having the same basic material characteristics. The layout shown in FIG. 24 could be particularly adaptable, however, to such deposits as the oil shale deposits in Utah, Wyoming and Colorado or the Athabaska tar sands deposits of Canada. The layout illustrated would in these situations represent an area some 3 to 5 miles wide and 10 to 15 miles long, the cells being approximately 1 mile long, and the overburden being some 400 feet in depth.

From an original free face preparation, the overburden will be blasted by trajectory control blasting substantially to the final resting place of a majority of the overburden and at the same time expose the ore body. The exposed ore body is then mined by product control blasting. A number of cells will be planned along the length of the face and mining will begin in the first of these cells. The cells will be separated by pillars in order to assure drainage control, access, reclamation of the surface and water resources development.

The mining of each cell is conducted using product control blasting. Since it is necessary to have the ore crushed to a reasonably small granulometry prior to its introduction to the milling devices, any portions of the material not sufficiently broken by the product control blasts will be crushed by crushing machines in the cells or at the ore preparation plant adjacent the mills.

Referring now to FIG. 25, an elevation of a mining layout in progress, pursuant to the mining method of the present invention, is illustrated. The elevation indicates a face preparation zone 31, separated from a mining section by a barrier pillar 32 and a number of barrier pillars 32 are spaced along the length of area through which the mining process proceeds. The barrier pillars are stable areas of the same ore body that is being mined and separate the cellular mining units that are laid out pursuant to the method of this invention. In the mining layout shown in FIG. 25, a relatively thin overburden covers the body of ore to be mined. This overburden may be stripped by conventional mining techniques including heavy equipment soil removing vehicles or other conventional mining processes. Once the overburden is stripped from the face preparation zone, the surface of the mining layout has substantially the stepped arrangement shown at 33 by limiting the blast backbreak, the face zone shown being the left face of the first barrier pillar 32 in the layout illustrated.

In the initial stages of the mining process, test blasts to determine the characteristics of the material and their response to the particular explosive to be used are conducted in the face preparation zone and the proceeding of tests moves to the point that the face of the mining area is prepared in the manner illustrated at 33. These test blasts are conducted as previously described in order to determine the values in the Livingston equations of N, E, and d.sub.o. Once the overburden covering an ore body is stripped and the face zone is prepared, the actual mining process can begin. In the first mining cell, product control blasting is conducted to break and crush the ore to the desired granulometry and stability control blasting is used to establish the barrier pillars in the desired stepped construction. The blasting in the face zones of each cell is performed to provide ramps along one face of the barrier pillar, and, referring to FIG. 25, the ramp 34 is shown which provides access to the lower portion of the cell as the mining progresses downwardly into the ore body. These ramps are of considerable width and the one illustrated at 34 would be in the nature of some 50 to 80 feet to provide passing room on the ramp for heavy earth moving vehicles moving up and down the ramp into the cell and returning from the cell with the ore to transport same to the milling plant.

Once the first cell 35 is depleted, and usually before completion of the first cell, the mining begins in the second cell indicated at 36. The mining of the second cell, similar to the first proceeds in steps and the first step indicated at 37 is stripped out of the cell area and transported to the various processing plants.

As the waste from the processed ore accumulates, an area for disposal must be provided. The waste accumulated from the ore mined out of the first cell 35 may be disposed of in the open area of the first cell 35 that has been completed to this point and thus the terrain re-established for the area in question.

In the oil shale industry, a unique problem not previously faced by the mining industry must be overcome -- namely, the swelling of the waste material of an extremely fine nature that must be disposed of. In the present mining process, the muck that is not projected to its new position may be used to form terrace ponds designed for receiving the shale waste materials.

Prior to disposing of the waste in the mined-out cell 35, a water quality filter bed 38 may be placed on the floor of the mining cell. This filter bed may be of any standard nature such as limestone, sand or minute gravel particles, charcoal, etc., and is designed to control the hydrogen ion concentration of the water and to filter out the waste and poisonous by-products from the various ore processing plants so that the water passing through the filter bed and into streams, rivers, etc., will not contaminate the rivers and destroy fish and wild life using these water supplies. The mined-out cell also provides a disposal area for overburden that is stripped from the adjacent and progressing areas of minings.

In conducting the product control blasting in the mining process illustrated in FIG. 27, large diameter bores, termed entries and cross-entries, are drilled through the material. The entries will be drilled parallel to and in the access entry pillars and the cross-entries will be drilled through the mining cells perpendicular to the access entry pillars to provide access of placement for the charges in the product control blasting. Alternatively, product control blasting within a given cell or portion thereof may be done using vertical bore holes as in conventional open pit mining as shown in FIG. 25.

Irrespective of the depth of the entries and cross-entries, once the parameters of Livingston's equations are known for the particular material and type of explosive to be used, the weight of explosive can be adapted and chosen to gain maximum utilization of the energy and avoid waste of the explosive charge. In this manner, it is permissible to drive the entries and cross-entries at arbitrary depths and the depth of the entries and cross-entries may be governed by other factors than the weight of the blast to be employed. These additional factors include the preparation of the faces of the barrier pillars to provide ramps for access to the lower part of the mining cell as well as other natural characteristics of the terrain being mined. Once the depth of the entries and cross-entries is selected, the value of d.sub.c is known, and it is merely necessary to equate d.sub.c to d.sub.o and employ the Livingston equations to determine the appropriate weight of charge to be placed at the given depth of the cross-entries in order to gain maximum utilization of the energy of the charge and thus economize the entire mining process.

As the product control blasting approaches the areas of the barrier pillars, stability control zones are formed. In effect, stability control zones are areas in which the charge weight and shape are changed to eliminate backbreak so as to avoid any detrimental effect to the barrier pillars. Accordingly, the blast designer will reduce his charge weight and then choose the value of d.sub.o which effects maximum utilization of the energy and control backbreak of the surrounding material in response to the blast. The backbreak of the material must be controlled so that it will not reach into the barrier pillars.

The system of entries and cross-entries which extend through the barrier pillar also provide drainage tunnels for controlling the flow of accumulated water in the mined-out cells and may be employed with valving devices to control the flow and supply of water to the surrounding areas to be explained more fully in connection with hydro development.

Referring now to FIG. 26, the adaptation of the mining process of the present invention is illustrated in connection with an ore body having an overburden of a depth equal at least that of the ore body and which is greater than what would be called the economical break-even bench height for trajectory control blasting. This bench height is where conventional mining equipment would be economically ineffective as compared to trajectory control blasting to remove the overburden and expose the underlying ore body. In this particular arrangement, the face preparation is conducted as previously described by performing test blasts and, at the same time, evaluating the parameters of Livingston's equations for the particular material of the overburden and the explosive employed. Some crater blast may be originally performed and as the evaluation of the parameters proceeds, test bench blasts may be conducted in order to finalize and pin-point the values of the associated parameters.

In this particular layout, once the parameters of Livingston's equations are known, the overburden is blasted to a remote area in order to expose the ore body. Since the depth of the overburden and the distance .DELTA..sub.bo from the prepared free face of the overburden can be measured, by using the Livingston's equations and the parameters previously evaluated the weight and exact placement of the charge can be determined in order to traject the overburden to the desired area in response to the explosion of the charge.

In order to determine the exact placement of the overburden in response to the trajectory control blast, the velocity of the free face mid-point for the particular material must be calculated per unit weight of charge. This is done in the test blasting procedure and is calculated by the formula V = .sqroot.2gh.

When the velocity of the mid-point free face, indicated at 40, is known, and the angle of trajectory is determined, the exact primary placement of the overburden can be calculated. The angle of trajectory is determined by the angle of the free face and the placement of the charge to control the buffer zone. When the charge is placed at a distance .DELTA..sub.bo from the mid-point of the free face and at some distance greater than .DELTA..sub.o from the surface of the overburden, the angle of trajectory of the free face mid-point will be the angle complementary to the angle of the free face itself.

Once the overburden has been blasted by trajectory control blasting into the mined-out cellular units additional terracing may be constructed over the filled cellular units from the waste products of the milling plant in order to conserve the terrain and establish same at a layout similar to that previous to the mining process.

FIG. 27 illustrates the use of product control blasting in order to crush the ore within a particular cell area to a predetermined granulometry. The product control blasting is conducted in layers for an ore body of considerable thickness in order to control the backbreak adjacent the barrier pillars and to avoid disturbing or weakening the barrier pillars. The layers of ore subjected to the product control blasting may be of substantially any desired depth depending on the explosive and type of material so long as the proper weight of charge is selected by Livingston's equations.

A number of entries and cross-entries are drilled horizontally through the ore body by heavy drilling equipment and the explosive charges are placed along the first level or bench 41. The weight of the charge to be placed in these areas is determined by calculations using the Livingston's equations. Since the distance beneath the ore body surface is known and since test blasts have been conducted in the ore material to determine the parameters of the Livingston's equations, the formula d.sub.o = .DELTA..sub.o E .cuberoot.W can be used to calculate the charge weight for maximum energy utilization as previously discussed. Alternatively, the charge weight may be selected on the basis of factors involving .DELTA..sub.b, .DELTA..sub.v, or autogenous blasting. When the depth of the charge placement is known, the weight of the charge may be calculated for maximum energy utilization and total energy partitioning to the material in order to fracture it to a desired granulometry. Autogenous blasting may also be conducted if a small screen size of material is needed. The blasting conducted in the product control zone may be performed basically on consideration of factors such as desired granulometry of the crushed ore material as opposed to the additional factors which are considered in the trajectory control blasting areas.

In the zones adjacent the barrier pillars, the limit of backbreak in response to a blast must be considered and the depth, weight and shape of the particular charge must be calculated with respect to the amount of backbreak that will occur in response to such a charge and preferably stability control blasting should be used in order to avoid weakening the barrier pillars or damaging the entries and cross-entries.

Once a first bench has been completed or is approaching completion in the blasting and removal of the ore in the product control zone, it is possible to begin the blasting at the opposite end of the cell for the second bench or strip to be crushed by the product control blasting. This progressive movement of mining both downwardly and in one direction may continue until the limit of the ore within the cell is reached.

Alternatively, the mining benches within a particular cell may be subdivided into product control unit blast areas which in effect permits a step-by-step control of the product blasting as the crushing of the ore and its removal progress.

The mining method of this invention is unique in the flow pattern that it provides for the waste materials and valuable minerals recovered during deployment of the process. The ore processing plant is located, according to the present mining method, on a processing plant pillar which is provided at the upper surface of the ore body and within the confines of the mining field.

By this arrangement, the handling of the material is greatly facilitated. The overburden is projected by trajectory control blasting over and down into the openings in the ore body formed by the previously mined cells. The ore body is then exposed and mined by product control and stability control blasting with the ramps formed in the face of the cell for moving the material to the processing plant either by heavy land moving vehicle or conveyors. The oil can be recovered from the shale and the spent shale is then passed further upwardly by pumping slurry to the terrace and pillar ponds. This flow control is unique in that it permits the orderly development and reclamation of the land as the mining process proceeds. None of the prior art mining methods have recognized or employed this unique flow procedure of the process and have been faced with a great amount of expense due to the necessity of hauling the ore to processing plants that are a considerable distance from the mining field. Moreover, the vast areas of oil shale deposts in Utah, Wyoming, and Colorado have heretofore been considered unavailable for commercial exploitation due to the fact of the swelling of the shale and the unavailability of disposal areas in which to deposit this tremendous amount of material.

The present method provides areas for depositing this spent shale by-product and makes economically available a tremendous amount of oil reserve previously considered by the industry as impossible to recover.

Hydropower Devleopment and Land Reclamation

Objectives of the reclamation plan for agricultural reuse of the land are:

1. To provide a soil cover suitable for agricultural development;

2. To develop a stable land surface free from effects of subsidence and suited to surface irrigation;

3. To recover for reuse processing plant water discharged with the trailings;

4. To provide for drainage and control of surface runoff; and

5. To provide a dependable water supply for irrigation.

These objectives are embodied in the reclamation plan of FIGS. 30 and 31.

Land reclamation above plant terrace elevation is accomplished in three stages -- the first "terrace pond stage," the second "pillar pond stage," and the third "retreating pond stage." During the first stage, the reclamation area above plant terrace elevation is divided symmetrically about the central plant pillar as in FIG. 30, and in each half, a terrace pond is developed with its long axis parallel to the pillar. During the second stage, pillar dams and pillar ponds are constructed in "valleys" between adjacent mining units. The third stage begins upon completion of cell mining and provides for reclamation of the T-shaped plan area formed by the plant pillar and the final row of active mining cells.

Terrace ponds, as indicated in FIG. 30, are formed during the first stage of reclamation using dykes built of embankment muck. The dykes are built in a U-shaped pattern starting from the face barrier pillar end. As cell mining advances, the dykes that form the sides of the U are lengthened and increased in height until finally they reach "high terrace" elevation. The high terrace is the final flat-lying reclamation surface that is to become agricultural land. It lies at an elevation above the original ground surface that depends upon the original topography and upon the overall swell factor of the material as excavated and placed. The overburden swell factor is reduced somewhat due to deposition of tailings in the voids of the underlying material and surrounding dykes. "Low ramp dykes" are constructed across the open end of the U-shaped enclosure at intervals as cell mining advances and as the level of tailings pumped into the terrace pond as a water-slime-sand slurry rises.

An objective of the reclamation is to recover for reuse processing plant water discharged into the reclamation ponds. The bottom and sides of the ponds, if constructed of dump-fill embankment muck, are permeable. The face barrier pillar end of the pond, although constructed of embankment muck, is zoned, compacted as placed, and is impermeable. The fast settling sand portion of a slurry pipeline discharge settles first, and the upper surface of the deposited tailings slopes away from the pipeline. Water percolating through the fill carries some sand and slime with it, but the fill acts as a filter as the water continues downwardly into the mining cells where it is trapped within the voids of the trajectory muck and build-up-muck to form an underground water reservoir.

Control of the stratigraphy and elevation of sand-slime deposition within the terrace ponds is done by lengthening the slurry pipeline and moving the discharge end as required. The objective is to prepare a soil cover at final high terrace elevation, and to form a gently sloping land surface to control drainage runoff. Of course, the illustration of FIG. 30 cannot clearly show this sloping lay of the land due to the need for a definite representation of the various stages of the reclamation process. However, it is to be understood that FIG. 30 is basically schematic for the purposes of clarity.

During the second pillar pond stage of land reclamation cell mining is in progress within the mining unit, an ore processing plant occupies the V-shaped valley between terrace ponds, and underground pillar mining may be in progress in an adjacent mining area. The reclamation layout of FIG. 30 provides for: access to processing plant, stockpiling of ore at plant terrace elevation, distribution of tailings either to the ponds or to underground cut-and-fill slopes, haulage roads between pillar recovery access slots and the processing plant, and continuing access to all active working places.

As cell mining advances, a condition eventually is reached where more space is required for tailings storage than is available in terrace ponds alone. At that time, the pillar dam nearest the area where pillar recovery by underground cut-and-fill is being conducted and the first ramp dyke at the end of the proposed pillar pond must be completed. Filling of the pillar pond and raising it to high terrace elevation is done in the same manner as for the terrace ponds.

Proportions of tailings and overburden to be disposed of depend upon the thickness of overburden and ore body and vary from place to place as work progresses. Attention now is directed towards the flexibility provided by the reclamation layout so as to permit the required ore waste materials balance to be maintained. The depth of a terrace pond may be increased to provide additional storage space for tailings, or decreased to provide additional storage space for overburden. Similarly, the bottom of a pillar pond may be filled with overburden to any desired depth if additional overburden storage space is required, or the bottom of the pond may be built directly upon the top of the access pillar if maximum tailings space is required. In addition, the cross section of the dyke that separates a terrace pond and a pillar pond either may be increased or may be decreased or the pillar pond stage of reclamation either may be merged or may be separated timewise to accomodate local field conditions.

Eventually cell mining advances to its design limit and is completed in a thickness cell mining unit. At that time, an alternative step of the method may be chosen, either to fill the last row of mining cells by trajectory control blasting of overburden or with tailings confined between boundary limit dykes. The choice depends to some extent upon the progress of underground cut-and-fill mining in the adjacent cell mining unit.

In the retreating pond stage of reclamation, tailings deposition begins at the design mining limit and retreats towards the processing plant. Concurrently, a pillar dam is constructed on the highwall side near the processing plant. Doing so permits land reclamation to be completed and the plant to operate until pillar mining is completed. Both cell mining and pillar recovery minimg are completed at the close of the retreating pond stage and the cell mining unit is left in a condition suitable for the continuation of hydropower and water resources development.

The mining method previously described is also adaptable to hydropower development. The valves placed in the openings forming the entries and cross-entries that remain as stub openings communicating adjacent cells may be used to control the flow of water and conserve the water passing into the ground during the heavy rain periods of the year and then to disperse the water over a wide area of terrain during the draught seasons. The water control permitted by this mining method is an integral feature of the concepts of reclaiming the land under set mining procedure.

Referring to FIGS. 28 and 29 and 30, an exemplary water utilization diagram is illustrated. During the periods of high water flow, water will be collected in the lower pools which could be a dammed river or other convenient water storage facility and can be selectively pumped to an upper project power plant or to lower pool plants or passed over a lower spillway. Water passing over the lower spillway is designed for augmenting the water supply during low flow periods.

Water pumped to the upper project power plant may be stored in the open cell water storage area, which in most situations would be a mine cell that has not been filled by the overburden of trajectory control blasting or with the spent shale or other by-products of the milling process. The open cells are maintained specifically for this feature of hydropower development and provide in effect a lake in the area of the mining process. The water of the open cell storage area may be passed through the valve structures connecting the various cells to the voids of the adjacent cells that have been filled with the trajectory muck from the trajectory control blasting.

The mined-out cells form substantially impervious water storage areas and permit very little seepage of the water between underground pools, except as controlled by the valving structure. Thus, by metering the water through the valves interconnecting the various cells to supply stored water beneath the surface of the terrain, the mined land is reclaimed for agricultural usage. The cells adjacent the open cell storage area, while filled with trajectory muck, may have void storage areas of up to 40 percent of the volume of the cell. This is due to the loosely packed nature of the material within the cell.

Drainage collection cells are provided adjacent the voids storage cells and operate as a reserve collection area into which the water may be directed during periods of heavy rainfall, melting of snow, etc.

Water within the open cell storage area may also be passed through a pump station to the ore processing plant and since the ore processing plant is located at a process plant pillar on the surface of the ore body, the use of the water in the open cell storage area is greatly facilitated. From the ore processing plant the water is used in a number of ways, one of which is to combine the water with the spent shale and form a slurry which is pumped into terrace ponds and pillar ponds which have been previously formed in the terrain by dykes constructed on the build up muck.

The water portion of the slurry passing to the ponds flows through the material of the terrain and into the voids storage cells where it may pass to the seepage control cells during periods of heavy rainfall. The water passing from the seepage control cells passes through filter beds which have been previously placed on the floor of the mined out cells to filter out impurities which would accumulate in the water from the ore processing plant. As the water level of the lower pools recedes, the valves of the drainage collection cells and seepage control cells may be opened to permit the water to drain and pass through water quality and drainage tunnels and water conditioning facilities and then to the lower pool.

The terms "void storage cells", "drainage storage cells", "seepage storage cells", etc., are characteristic of the function of the cells in these physical relations to the open water storage cell as illustrated in FIG. 28, these cells all being previously mined cells that have been filled with trajectory muck.

Thus, the mining method which employs the mining cells, as opposed to the standard procedure of complete ore stripping, greatly facilitates the land reclamation and water control by the hydropower development phase of the invention.

Water resources development depends in the method of the invention upon elevating water from a "lower pool" to open cell reservoirs, collecting and utilizing underground water that exists within the ore body and overburden, and upon collecting and utilizing surface runoff. Normally, the upper pool for a conventional pumped storage hydropower project is fed by large streams. The method of the invention introduces a new set of conditions. It is the lower pool rather than the upper pool that is fed by the stream; and the upper pool is developed high above the valley floor in workings excavated during Breakage Process Control Mining.

The hydropower and water resources development plan embodied in the method of the invention depends upon the layout and geometry of Breakage Process Control Mining. Although the plan includes a conventional lower project for pumped storage power generation, the upper project layout departs from conventional practice, and is part of the invention.

A conventional upper project (in addition to electric power distribution facilities and a power plant containing reversible turbines) receives water from upstream, and consists of a dam, an upper pool, diversion tunnels, cofferdams and spillway. Employing the method of the invention, water is received from the lower pool and a face barrier pillar replaces the dam. A combination of upper pool units, each unit consisting of an open cell reservoir, a void storage cell developed during cell mining advance stage, and completed pillar recovery units, replaces the upper pool of a pumped storage hydropower plant. Diversion tunnels are replaced by a system of filter beds, drain holes, and tunnels for seepage and water quality control. Cofferdams are eliminated; the spillway of conventional dam construction is replaced by an overflow structure and segments of trajectory control cross entree tunnels between adjacent upper pool units.

The hydropower and water resources development plan embodied in the invention includes the following elements:

1. Diversion of normal stream flow to storage during periods of high stream flow and return of the stored water to the stream during periods of low stream flow.

2. Pumping of lower pool water to ore processing plant elevation with upper project turbines using "off-peak" power, and generating electricity from upper pool unit water storage during peak demand.

3. Recovering, conditioning, and reusing ore process-plant water.

4. Collecting underground water and surface runoff so as to supplement the normal stream flow and preserve the existing drainage pattern and water sheds.

5. Developing land for agricultural reuse by depositing in a system of terrace ponds and pillar ponds a slime fraction of conditioned tailings.

6. Utilizing the cell structure of Breakage Process Control Mining to develop an irrigation water supply for the reclaimed agricultural land.

Before describing the manner in which hydro-power and water resources development evolves from the mining and reclamation layout, it is appropriate to consider the significance of the water resources development plan as it relates to a possible future shale oil industry in Colorado, Utah, and Wyoming.

Heavy demands have been made by downstream Colorado River water users upon water, which is in short supply in the arid Western United States. Due to downstream water commitments, diversion of water during periods of excess supply and its return to the stream during periods of inadequate supply are essential to the development of a shale oil industry. Before a shale oil industry can be developed the following problems must be solved:

1. Disposal of spent shale

2. Control of subsidence

3. Reclamation of the land surface

4. Efficient conservation of the oil shale and associated nahcolite and dawsonite.

5. Preservation of existing drainage patterns.

6. Systematic exploitation of a vast area of land that occupies parts of three states.

The above problems cannot be solved using conventional methods; but, on the contrary, are solved using the method of the invention. In addition, water stored underground in the rocks of three natural basins is utilized; waste canyon land is converted to usable agricultural land; the region is benefited by a comprehensive water resources development plan financed by industry and contributed to society; a growing demand within the region for water and electric power, otherwise difficult if not impossible to meet is satisfied; and a comprehensive plan is provided for systematic development of 16,000 or more square miles of land.

A portion of the idealized layout is shown in detail in FIG. 30 and is based upon the assumption that mining commences at the outcrop and advances in a series of parallel slices. To apply the idealized mining and reclamation layout to hydropower and water resources development, the powerplant must be located as adjacent the outcrop as shown in FIGS. 28, 30, and 31 to receive water backed up by the lower pool, and the open cell water storage reservoir must be located so as to receive water from within voids of the mined-out cells.

In the course of mining, cell mining units are converted to pillar recovery units. Interior pillars of a pillar recovery unit are extracted during the underground cut and fill pillar recovery stage of mining, leaving the exterior pillars intact as permanent boundary pillars. The term upper pool unit refers to a complex of cell mining units and mined-out pillar recovery units interconnected by cell water passages. The complex is composed of a series of smaller segments each at one time having been a cell mining unit. A single, open-cell water reservoir if properly located at the down-dip corner serves the entire upper pool unit.

Referring again to FIGS. 28, 30, and 31, the face barrier pillar and plant processing pillars are permanent pilars between adjacent upper pool units. Overflow structure and lined spillway tunnels near the open-cell storage reservoir take the place of the channel type spillway of the conventional hydro-power construction. They prevent upper pool units from overflowing the face barrier pillar, and route excess water to void storage in cells of an adjacent pool unit in an earlier stage of development. During the earlier stage, cells increase in number as mining advances, and water is needed to fill them. Excess capacity for water storage always is available in seepage control cells.

To be economical, hydro-power units must be of high capacity and dispersed in accordance with electric power load requirements. Individual pool units may be served by a separate off-peak pumping plant at lower pool elevation or by a spillway system fed from a nearby up-dip hydro-power pumped storage plant. Several upper pool units can be served by a single hydro-power plant designed to increase in pumping and generating capacity as additional upper pool units are completed.

FIG. 28 is idealized and identifies elements of the layout during an early stage of work. The processing plant pillar is the permanent pillar that separates adjacent upper pool units. The open cell water storage reservoir is serviced by the intake channel, powerhouse, pressure tunnels and penstocks, intake structure, and processing plant pump station. The adjacent mining unit of the figure is the first of a series of additional upper pool units which may or may not be equipped for hydropower generation depending upon projected needs, water resources functions of all upper pool units are similar.

As mining advances, each mining cell functions first as a seepage control cell, next as a drainage collection cell, and finally as a void storage cell; thus, the volume of underground voids storage increases with time as cell mining progresses. Prior to pillar recovery, water is withdrawn from void storage cells of a given mining unit and is discharged into the lower pool. Following pillar recovery, the area between pillar recovery boundary pillars, except the row of seepage control cells alongside the face barrier pillar, may if desired be reconverted to void storage.

Seepage control cells, except those opposite the open cell water reservoir, take the place in conventional dam construction of grout barrier and drainage tunnels. A seepage control cell is a muck-filled cell containing little water. It may receive seepage water from adjacent water-filled cells or from the orebody, but normally is kept dry by pumping or grouting. Seepage control cells serve to keep water out of active mining cells. In addition to their location near the active mining cells they are placed to form a seepage barrier between void storage cells and the face barrier pillar. Seepage water that collects within a seepage control cell passes through a water-quality filter bed and is removed through a complex of drainage holes drilled from seepage control tunnels into the cell bottom.

Water pumped from the lower pool during the pumped storage hydro-power pumping cycle is discharged into the open-cell storage reservoir. Cell water-passage tunnels, driven through pillars between cells during cell development, route the water into and out of void storage cells so as to balance the hydro-static head on adjacent sides of the pillars during pumping and generating. Water of the upper pool void storage complex equivalent in conventional practice to the power pool is returned to the lower pool during the power generating cycle.

During filling of voids of the void storage cell complex, the hydraulic gradient slopes away from the water level of the open cell water reservoir depending upon the elevation of water in the drainage collection cell. The water level rises in a drainage collection cell as surface run-off and underground water from overburden and orebody is received. When filled, a drainage collection cell becomes a void storage cell and supplements the water supply diverted from streams or diverted to storage from surface run-off and the spillway system of an adjacent upper pool unit.

Recovery, reconditioning, and reuse of water are integral parts of the water resources and hydro-power development plan. Water in tailings from the processing plant is recovered by downward percolation from terrace ponds and pillar ponds into void storage cells. Reconditioning usually is necessary due to requirements of plant growth for reclaimed agricultural land, oxidation of sulfides in overburden and ore, or due to reagents added or produced during processing, and may be accomplished:

1. At the processing plant prior to slurry pipeline pumping,

2. In filter beds at the bottom of mining cells,

3. At a water conditioning plant receiving the flow issuing from drainage tunnels, and

4. In the open-cell water reservoir as a result of surface areation or sand and slime settlement from water that is returned periodically from void storage during the hydro-power generating cycle.

FIG. 29 is a water utilization diagram which identifies the several routes for water entering and leaving the system. The diagram if used in connection with FIGS. 28, 30, and 31 extends the materials handling system of the method of the invention to include water as a natural resource.

Attention is directed to the list of objectives of the hydro-power and water resources development plan--specifically to Item 4, -- as it relates to the development of a shale oil industry in Colorado, Wyoming and Utah. The Colorado River drainage system has cut through the oil shale measures leaving, in most places, the oil shale beds high above river elevation. Sites for conventional dams or lower projects are chosen along tributary streams so as to pre-determine pool limits and to back water up to where diversion to open-cell water reservoirs is practical. In effect, the design and layout for hydro-power and water resources development is determined by, rather than independent of mining requirements.

The method of the invention introduces a new mining technology and provides a comprehensive development plan and layout in which mining, land reclamation, hydro-power and water resources development are integrated to the benefit of society. As mining progresses, a vast underground water storage system free from surface evaporation in an arid climate is developed, and the land, rather than being ravaged and destroyed, is improved to the benefit of mankind.

APPENDIX ##SPC1##

table 2 --------------------------------------------------------------------------- breakage process equation parameters -- ores and rocks

explo- sive Material Vo/W o E B __________________________________________________________________________ 60% Giant Thin Bedded Gel Magnetite 57.6 .45 4.60 .594 Hi Cap Sandy Siltstone 47.4 .645 4.20 .63 ANFO Hard Blue Iron Ore 46.7 .65 3.7 .915 60% Giant Gel Granite 44.7 .55 4.15 .622 Hi Cap Arkose Sandstone 41.7 .59 4.25 .66 60% Giant Gel Magnetite-Taconite 40.4 .48 4.35 .49 ANFO Soft Blue Iron Ore 39.8 .90 3.2 1.20 50% Forcite Greywacke 37.8 .48 4.0 .59 60% Sandstone Seismo Conglomerate 35.5 .39 5.30 .24 Slurry Iron Formation 34.3 .58 4.26 .44 60% Giant Magnetite 23.7 .45 4.35 .29 TNT, C2 Navajo Sandstone 22.8 .41 3.3 .63 C3 Unaweep Granite 15.4 .40 3.9 .22 __________________________________________________________________________

TABLE 3

AUTOGENOUS BLASTING DESIGN SUMMARY

CODE 1

Predom Design Particle Criteria Parameters Vol, cu ft .DELTA. BH=.75N E=3.30 Top 1.0 .DELTA..sub.v = .61 1/2 Col=.24 A=.97 = .79 Sub=.10 B=.47 .DELTA..sub.y = .DELTA..sub.o - .07 V=.375N.sup.3 .DELTA..sub.v trajectory ABC=.375 V/W=13.48 V.sub.o /W=16.9 AC=.798 C=.823 E.sup.3 =35.94

AC= (V/W)/(V.sub.o /W)

CODE 2

Predom Design Particle Criteria Parameters Vol, cu ft .DELTA. cg+mid-.12 E=3.30 Face 0.10 .DELTA..sub.b = .415 .DELTA..sub.v =BH A=0.20 V.sub.w =0% .DELTA..sub.v =.75 1/2 Col=.14 B=0.47 V-W.sub.w = 100% .DELTA..sub.s =.+-. .60 Sub=.14 V=.1275N.sup.3 =.66 Find .DELTA.b ABC=.1275 =.64 .DELTA..sub.s =.pi. d/6=.60 V/W=4.58 BH=.75 .DELTA..sub.mt =<.DELTA..sub.rc V.sub.o /W= 16.9 ee. Find .alpha. AC=0.271 .DELTA..sub.cr .ltoreq. .DELTA..sub.v C=1.26 Inclined trajectory

CODE 3

Predom Design Particle Criteria Parameters Vol, cu ft .DELTA. .DELTA..sub.b =.DELTA..sub.a = .49 E=3.30 Face 0.25 .DELTA..sub.b = .49 cg below mid A=.25 Top 0.80 .DELTA..sub.s =.+-. .67 1/2 Col=14,.25 B=.47 V.sub.w =40% .DELTA..sub.v =.71 Find .DELTA..sub.v V=.229N.sup.3 V-W.sub.w =60% f =.22 Find .DELTA..sub.diff ABC=.229 e. .DELTA..sub.mt <.DELTA..sub.rc V/W=8.2 = .76 Steeper trajectory V.sub.o /W=16.9 =.61 BH=0.75N AC=.4852 .DELTA..sub.inc =.07 C=1.95 Sub=.10

C=V/N.sup.3 AB

CODE 4

Predom Design Particle Criteria Parameters Vol, cu ft .DELTA..sub.b = .DELTA..sub.o - 0.10 E = 3.30 Face 0.48 b= .58 cg + mid- 0.11 A = .44 Top 0.75 v =.70 Col =.14, .25 B = .47 V.sub.w =26% s =.68 Find .DELTA..sub.v V=.428N.sup.3 V-V.sub.w =74% Sub= .09 .DELTA..sub.s =.DELTA..sub.o ABC =.428 .alpha.=18 Find Sub V/W= 15.4 f =.12 Find .DELTA..sub.diff V.sub.o /W= 16.9 BH= 0.75N AC= .9112 Find .alpha.4 .alpha.3 C= 2.07 E.sup.3 =35.94

C.sub.o =V/N.sup.3 B

CODE 5

Predom Design Particle Criteria Parameters Vol, cu ft .DELTA..sub.rc .DELTA..sub.r E= 3.30 Face .03 v= .61 cg+ mid- .02 A= 0.20 b= .32 .alpha. = 18.degree. B= 0.47 mt= .61 1/2Col= 0.24 V= .07866N s=.38 Sub= 0.10 ABC= .07866 rc= .53 .DELTA..sub.b < .DELTA..sub.a V/W= 2.827 t= .58 Find .DELTA..sub.v, .DELTA..sub.b V.sub.o /W= 16.9 ee. .DELTA..sub.mt= .DELTA..sub.v AC= 0.1673 .DELTA..sub.diff f= .29 Find .DELTA..sub.s C= 0.84

TABLE 4

PRODUCT CONTROL BLASTING DESIGN SUMMARY

.DELTA..sub.b --PRODUCT CONTROL

Predom Design Particle Criteria Parameters Vol, cu ft .DELTA. .DELTA.-Inc .07 E= 3.30 Face 1.70 .DELTA..sub.b = .73 .DELTA.-Diff .15 A= .95 Top 3.25 .DELTA..sub.v = .88 .DELTA..sub.V> .DELTA..sub.T B= .47 V.sub.w =23% =.95 .DELTA..sub.B .DELTA..sub.T V= .9038N.sup.3 V- V.sub.w = 77% .DELTA..sub.s = .79 .DELTA..sub.B =.DELTA..sub.bo - .02 ABC= .9038 = 1.11 .DELTA..sub.V =.DELTA..sub.B +.DELTA..sub.Diff V/W= 32.5 Shape BH= 1.12 .DELTA..sub.mt = .DELTA..sub.f -.05 V.sub.o /W=16.9 1.4.times.1.0.times.0.7 1/2Col= .30.UPSILON.5 2 Find .DELTA..sub.s AC= 1.92 Sub= .06 .DELTA..sub.o = .68 C= 2.02 =.75 .DELTA..sub.bo =.75 C.sub.o = 2.67 = 1.15

TABLE 5

.DELTA..sub.v --PRODUCT CONTROL

Predom Design Particle Criteria Parameters Vol, Cu Ft .DELTA. .DELTA.-Inc. =.07 E= 3.30 Top 3.15 .DELTA..sub.v = .88 .DELTA..sub.v =.DELTA..sub.f =.88 A= 0.37 Face 3.8 .DELTA..sub.b = 1.00 .DELTA..sub.b =.DELTA..sub.ss =1.0 B= 0.47 V.sub.w 21% .DELTA..sub.s = .82 .DELTA..sub.diff = 0.12 V=1.1242N.sup.3 V-V .sub.w =79% =1.085 .DELTA..sub.s =1.2 .sub.o ABC=1.1242 =1.12 Find .DELTA..sub.mt V/W=40.44 Shape BH=1.02 Find Cr/.cuberoot. W V.sub.o /W=16.9 1.5.times.1.0.times..65 1/2Col=.20 .DELTA..sub.o =.68 AC=2.39 Sub=.06 .DELTA..sub.bo =.75 C=6.48 E.sup.3 =35.94

V/W = E.sup.3 ABC ##SPC2## ##SPC3##

Claims

What is claimed is:

1. In bench geometry blasting, where for the particular material to be blasted and explosive to be employed, the values of d, d.sub.o, N, .DELTA.o and E are known for a given weight of explosive charge W,

d being any depth of burden of the charge;

d.sub.o being the depth of placement of a charge of the given weight which produces upon explosion of the charge maximum pressure rise within the material;

N being the depth of placement of a charge of the given weight which first begins to produce upon explosion of the charge fractures on the surface of the material in which the charge is placed (as illustrated in accompanying FIG. 1);

.DELTA..sub.o being the value of d.sub.o /N for the given charge weight; and

E being the value calculated from the formula N = E .cuberoot.W using the value of N for the given weight;

and where for the same particular material to be blasted and explosive to be employed, the values of d.sub.bo, N, and .DELTA..sub.bo are known,

d.sub.bo being the perpendicular distance from the vertical free face to the center of gravity of explosive charge which produces upon explosion of said charge maximum pressure rise within the material;

N being as previously defined for the same charge weight used in determining d.sub.bo ; and

.DELTA..sub.bo being the value of d .sub.bo /N for the given charge weight;

the improvement comprising controlling the trajectory of material formed as bench geometry surrounding a blast charge in response to explosion of the charge by;

a. placing a charge of weight W at a vertical depth .DELTA..sub.v wherein .DELTA..sub.v = d.sub.v /N wherein d.sub.v is the vertical depth;

b. positioning said charge of weight W along a rearward extension of a line perpendicular to the bench free face at a burden .DELTA..sub.b wherein .DELTA..sub.b = d.sub.b /N wherein d.sub.b is the burden distance and .DELTA..sub.b = .DELTA..sub.v + .DELTA..sub.diff wherein .DELTA..sub.diff is a predetermined positive value, the trajectory being substantially in a vertical direction when .DELTA..sub.v is less than .DELTA..sub.b and substantially in the horizontal face direction when .DELTA..sub.b is less than .DELTA..sub.v ; and

c. detonating the charge.

2. The method as defined in Claim 1, wherein the charge is placed at a vertical depth beneath the surface equal to d.sub.b + d.sub.diff d.sub.diff being calculated from a .DELTA..sub.diff equalling d.sub.diff/ N and .DELTA..sub.diff is within the range of 0.02 - 0.20.

3. The method as defined in claim 1 wherein the known values and .DELTA..sub.diff are determined by conducting test crater and bench blasts.

4. In bench geometry blasting the method of controlling the trajectory of material surrounding a blast charge in response to explosion of the charge comprising:

a. Conducting test crater blasts to determine values for d.sub.o, N, and E for the surrounding material and type of explosive, where d.sub.o is the depth of placement of a charge of known weight which produces upon explosion of the charge maximum pressure rise in the material; where N is the depth of placement of a charge of a known weight which first begins to produce upon explosion of the charge a crater on the surface of the material in which the charge is placed and where E is calculated from the formula N = E .cuberoot. W using the determined value of N and its known charge weight;

b. Conducting test bench blasts to determine the value of .DELTA..sub.bo for the surrounding material and type of explosive, where .DELTA..sub.bo is d.sub.bo /N and d.sub.bo is the perpendicular distance from the free face of a bench geometry to the center of gravity of an explosive charge placed at a depth d.sub.o which produces maximum pressure rise within the material;

c. Placing a charge of weight determined by the formula d.sub.o = .DELTA..sub.o E .cuberoot. W at a depth of d.sub.o + d.sub.diff beneath the upper surface of the material bench, d.sub.diff being a predetermined positive value;

d. Placing the charge along a rearward extension of the line of preferred trajectory a distance equal d.sub.bo, whereby trajectory is controlled to be substantially in the horizontal direction; and

e. Detonating the charge.

5. The method as defined in claim 4, wherein d.sub.diff is based on a .DELTA..sub.diff in the range of 0.02- 0.20 and .DELTA..sub.diff = d.sub.diff /N.

6. A method according to claim 4 wherein d.sub.bo is determined by placing a series of test blasts of known weight at depths d.sub.o and at various distances d.sub.b from the the bench free face, detonating said charges and measuring the response of the material surrounding the blast to determine which burden distance produces the maximum doming without venting in the direction of the bench free face.

7. A method according to claim 4 wherein d.sub.bo is determined by placing a series of test blasts of known weight at depths d.sub.o and at various distances d.sub.b from the bench free face, detonating said charges and measuring the response of the material surrounding the blast to determine which burden distance produces the maximum volume of material broken per pound of explosive.

8. In bench blasting, the method of controlling the trajectory of the material surrounding the blast charge in response to explosion of the charge including preparing the bench face to have a disposition of substantially 45.degree. with the horizontal, placing the charge along a line projecting perpendicular from substantially mid-point of the free face but within a range on either side of the free face equal to 70 percent of the free face length a distance from the free face substantially equal to the d.sub.bo for the material and explosive, d.sub.bo being the perpendicular distance from the vertical free face to the center of gravity of explosive charge which produces upon explosion of said charge maximum pressure rise within the material, spacing the charge a distance from the upper horizontal surface of the bench a distance equal to d, wherein d is any depth of the charge when d is determined from .DELTA..sub.o + .DELTA..sub.diff + .DELTA..sub.inc and .DELTA. is related to d by the formula .DELTA. = d/N, .DELTA..sub.o being the value of d.sub.o /N for the given charge weight, .DELTA..sub.diff being a predetermined positive value, .DELTA..sub.inc being .DELTA..sub.bo minus .DELTA..sub.o, .DELTA..sub.bo being the value of d.sub.bo /N for the given charge weight, d.sub.o being the depth of placement of a charge of the given weight which produces upon explosion of the charge maximum pressure rise within the material, N being the critical depth (as described in conjunction with FIG. 2), .DELTA..sub.diff being in the range of 0.05 to 0.25.

9. The method according to claim 8, wherein the distance from the free face is in the range of d.sub.bo to d.sub.b where d.sub.bo is a function of .DELTA..sub.bo and d.sub.b is a function of .DELTA..sub.bo - 0.15 and .DELTA..sub.bo is related by d.sub.bo by the formula .DELTA..sub.bo = d.sub.bo /N.

10. The method of autogenous blasting to produce a fine grain particle comprising:

a. forming a crater by detonating a first explosive charge, the explosive set beneath the surface of earthen material to produce a muck pile backed against the free face formed by the blast;

b. detonating at least one second explosive charge adjacent the first named charge, the distance of the second charge from the free face created by the first explosion being in the range where implosion occurs and the vortex is well developed and is directed toward the muck pile and corresponds to d values defined by .DELTA..sub.bo to .DELTA..sub.a where .DELTA. = d/N and .DELTA..sub.bo and .DELTA..sub.a are determined from test crater blasts, .DELTA..sub.bo being the value of d.sub.bo /N for the given charge weight, d.sub.bo being the perpendicular distance from the vertical free face to the center of gravity of explosive charge which produces upon explosion of said charge maximum pressure rise within the material, N being the depth of placement of a charge of the given weight which first begins to produce upon explosion of the charge a crater on the surface of the material in which the charge is place, .DELTA..sub.a being the burden distance at which the velocity of the vortex is maximum.

11. The method as defined in claim 10 wherein the depth of the charge is controlled so as to predetermine breakage limits of the second blast whereby the angle of inclination .alpha. of a subsequent blast is controlled within the range of .alpha. o.degree. to 45.degree. .

12. The method of controlling the granulometry of material surrounding a charge of explosive in response to explosion of the charge comprising:

a. conducting test crater blasts at various depths to determine the breakage limits of the material in response to the blasts;

b. preparing a chart by plotting the slant distance to each of the types of fractures in the blasting failure process and to the doming limit from test crater blasts;

c. establishing a grid over the crater formed by each test blast and measuring the particle size of the broken material touched by the grid;

d. preparing a chart by plotting the variation of the predominate particle size with various charge depths at scaled depth ratios .DELTA.;

e. determining in the range .DELTA..sub.d to .DELTA..sub.o from the chart of (d) the value in the controlling burden direction at which the desired predominate particle size can be achieved, .DELTA..sub.d is the .DELTA. value at which doming begins and .DELTA..sub.o is the value of d.sub.o /N for the given charge weight, d.sub.o being the depth of placement of a charge of the given weight which produces upon explosion of the charge maximum pressure rise within the material, and N being the depth of placement of a charge of the given weight which first begins to produce upon explosion of the charge fractures on the surface of the material in which the charge is placed; or in the range .DELTA..sub.o to .DELTA. equals 0 the value at which the desired particle size can be achieved where predominant particle size from autogenous blasting ranges from near zero to that measured at .DELTA. .sub.o of the crater tests;

f. decreasing the crater chart value (e) by subtracting for bench geometry a .DELTA. .sub.increment adjustment ranging linearly from a maximum at .DELTA..sub.bo -.DELTA..sub.o for a controlling burden of magnitude .DELTA..sub.o to zero for a controlling burden .DELTA..sub.a or less or for a controlling burden .DELTA..sub.ss or greater, .DELTA. .sub.increment being .DELTA. .sub.bo minus .DELTA. .sub.o, .DELTA..sub.bo being the value of d.sub.bo /N for the given charge weight, d.sub.bo being the perpendicular distance from the vertical free face to the center of gravity of explosive charge which produces upon explosion of said charge maximum pressure rise within the material, .DELTA..sub.a is the .DELTA. value at which the volume of the apparent crater is maximum, and .DELTA..sub.ss being the .DELTA. value at which cratering begins;

g. placing the charge at a distance from the controlling burden toward the face of the bench corresponding to the adjusted .DELTA. value;

h. placing the charge at a distance from the non-controlling free face at the crater test determined value; and

i. detonating the charge.

13. The method of stability control bench blasting, including:

a. conducting test crater blasts and preparing a chart by plotting the slant distance to limits of each of the types of fractures in the blasting failure process and to the doming limit, by plotting the slant distances to the crater lip against charge depth and the zone of bond strength destruction against charge depth, R cracks defining the limits of extreme rupture and by plotting the variation in predominant particle size against charge depth from the parameters determined from said blasts;

b. selecting a predetermined limit part which the material in which the blasts are conducted is not to be affected;

c. progressively setting and detonating explosive charges in the direction approaching said limit, each successive charge being decreased in .DELTA..sub.b value and increased in .DELTA..sub.v value so as to progressively increase the .DELTA..sub.v -.DELTA..sub.b difference approaching said limit, the .DELTA..sub.b value being determined from the cratering results using the relation b/N, where b is the bench burden in feet and N is the distance in feet at which cratering begins for the bench charge, the .DELTA..sub.v value being determined from the relation d.sub.c /N, where d.sub.c is the distance beneath the top of bench in feet to the bench charge; and

d. the placement of the charge being such that the limits of extreme rupture as defined in said chart do not for any given blast extend beyond the predetermined limit.

14. The method as defined in claim 13, wherein the burden of any charge approaching said limit is of a distance d.sub.b controlled by .DELTA., and .DELTA. is in the range .DELTA..sub.0 - 0.10 and .DELTA..sub.0 -0.20, and where .DELTA. =d.sub.b /N.

15. The method as defined in claim 13, further including the step of placing rock bolts in the material prior to blasting to reinforce the material beyond said limit.

16. The method as defined in claim 13, further including digging breakage limit trenches in the surface of the surrounding material along the line of the predetermined limit.

17. The method as defined in claim 1 wherein the charge is placed at a controlling burden from the vertical free face equal to d.sub.v +d .sub.diff being calculated from a .DELTA..sub.diff equalling d.sub.diff /N and .DELTA..sub.diff is within the range of 0.20 - 0.20.

18. The method as defined in claim 3 wherein said test crater and bench blasts include:

a. conducting cratering tests so as to measure the limits of R cracks, I cracks, O cracks, shock slabs, rebound slabs, crater and doming;

b. measuring time, velocity, and duration of massive ground motion for each of the charges of said cratering tests and determining the variation with scaled charge depth for the series of charges for a given type, shape, weight and depth of charge;

c. excavating the craters formed in said cratering tests so as to measure the limits of the bond strength destruction zone, intermediate zone, and the barrier zone and to determine the granulometry, size and shape of particles in each zone and for each blast, and summarizing the variation for the series of blasts with scaled charge depth;

d. conducting test bench blasts so as to:

i. observe the effect of the second free face upon breakage limits, particle size, and volume of material broken per pound of explosive;

ii. determine the variation in time, velocity and duration of massive ground motion in the .DELTA..sub.v direction towards the top of the bench and in the .DELTA..sub.b direction towards the face of the bench at various values of .DELTA..sub.v - .DELTA..sub.b, and

iii. determine the scaled slant distance to the doming limit at various values of .DELTA..sub.b, the controlling burden;

e. determine the .DELTA..sub.increment adjustment from said test bench blasts and applying the adjustment to correct fracture, crater, doming limits, particle size, granulometry and shape to the geometry of bench blasting;

f. utilizing a chart plotting and slant distances to the doming limit for a given blast to predetermine excavation limits in bench blasting to determine .DELTA..sub.v given .DELTA..sub.b, or to determine .DELTA..sub.b given .DELTA..sub.b so as to predetermine the position and inclination of the free face prior to a bench blast or successive bench blasts;

g. predetermining the time, velocity, duration and trajectory of a blast in the .DELTA..sub.b direction towards the face of the bench and the .DELTA..sub.v direction towards the top of the bench so as to achieve the desired throw in either or both directions, such determination of the throw being based upon the results of the crater tests; and

h. predetermining excavation limits as in (a) and simultaneously controlling trajectory and granulometry towards the top and towards the face of the bench so as to predetermine both trajectory and granulometery from results of the crater and bench tests.

19. A method of trajectory control blasting comprising:

a. conducting crater and bench blast tests to predetermine limits of fracturing, cratering and doming in bench blasting and so as to determine the variation in time, velocity and duration of massive ground motion with variation in controlled burden and variation in .DELTA. difference, .DELTA..sub.v -.DELTA..sub.b, wherein .DELTA..sub.v = d.sub.v /N wherein d.sub.v is the vertical depth and N is the depth of placement of a charge of the given weight which first begins to produce upon explosion of the charge fractures on the surface of the material in which the charge is placed, and .DELTA..sub.b = d.sub.b /N wherein d.sub.b is the burden distance;

b. creating a free face at a predetermined angle perpendicular to the angle of desired trajectory of a subsequent blast by placing and detonating a charge of known weight at a burden, .DELTA..sub. b, and depth of center of gravity of the explosive charge, .DELTA..sub.v, at which the inclination of a line from the center of gravity of the charge to the doming limit of the bench test produces the desired inclination;

c. determining .DELTA..sub.v, .DELTA..sub.b, and .DELTA..sub.v -.DELTA..sub.b from cratering and bench tests and placing the charge so that:

i. the desired proportions of massive ground motion both in the .DELTA..sub.v direction towards the top of the bench and in the .DELTA..sub.b direction towards the face of the bench are predetermined to produce the desired trajectory, granulometry, or both, and

ii. so that the time, velocity and duration of massive ground motion will be such as to produce the desired throw;

d. placing the charge on the rearward extension of the line of desired trajectory at a distance .DELTA..sub.b so as to obtain the desired breakway velocity in a direction normal to the free face and as indicated by the bench tests, and so as to predetermine the time, velocity and duration of massive ground motion in the .DELTA..sub.v direction toward the top of the bench; and

e. detonating the charge.

20. A method of maximizing the quantity of fine material from a blast including:

a. conducting crater blast tests so as to determine limits of R cracks, I cracks, O cracks, slabs, rebound slabs, and limits both of the apparent crater and the true crater, and to determine the variation in predominant particle size with scaled charge depth and the time, velocity and duration of massive ground motion, including excavating the craters to observe the limits of bond strength destruction, the intermediate zone, and the barrier zone, and determining by observation of cratering results the depth at which the explosion cavity collapses and a ground motion vortex action begins;

b. preparing a chart by plotting the slant distances to limits of each of the types of fractures in the blasting failure process and to the doming limit, by plotting the slant distances to the crater lip against charge depth and the zone of bond strength destruction against charge depth, R cracks defining the limits of extreme rupture and by plotting the variation in predominant particle size against charge depth from the parameters determined from said blasts;

c. preparing an opening cut or free face by blasting so as to predetermine the inclination of the sides within the range of 45.degree. from the horizontal to vertical and so as to produce a muckpile to inhibit ground motion of subsequent blasts;

d. placing a charge of given type of explosive of given weight, W, behind the face so that the distance .DELTA..sub.v beneath the top of the bench is in the range of .DELTA..sub.o -0.02 to .DELTA..sub.o -0.10 and the distance .DELTA..sub.b perpendicular to the face is in the range .DELTA.= .DELTA..sub.mb to (.DELTA. .sub.a + .DELTA..sub.o)/2 where .DELTA..sub.a is the charge depth at which the volume of the apparent crater is maximum, .DELTA..sub.o is the charge depth at which the volume of the true crater is maximum, .DELTA..sub.mb is the charge depth at which the slant distance from the charge to the limit of bond strength destruction is maximum; the weight of the charge W, the depth of charge d.sub.c, and the burden b being determined by the equations

i. N = E .cuberoot. W wherein N is the depth of placement of a charge of the given weight which first begins to produce upon explosion of the charge fractures on the surface of the material in which the charge is placed, and E is the value calculated using the value of N for the given weight,

ii. .DELTA..sub.b = b/N,and .DELTA..sub.v = d.sub.c /N,

iii. d.sub.c = .DELTA.E .cuberoot. W, and

iv. V/W = E.sup.3 ABC, wherein A = V/V.sub.o, V being the crater volume, V.sub.o being the crater volume at optimum charge depth d, B = V.sub.o /N.sup.3, and C = (V/V.sub.ob).sup.. C.sub.o wherein C.sub.o = (V/W bench)/(V.sub.o /W crater);

e. placing said charge such that a vortex action is produced as a result of implosion and ground motion following collapse of the explosion cavity, and the venting gas bubble is directed into the muckpile so as to develop a scouring action between particles and so as to minimize excessive flyrock which otherwise would occur, said vortex action occurring within the range .DELTA. = 0 to .DELTA. = .DELTA..sub.o, the venting gas bubble being controlled in the direction of .DELTA..sub.b, if .DELTA..sub.v is sufficiently larger than .DELTA..sub.b, and the scouring action between particles is developed for the particular controlling value of .DELTA..sub.b if the duration of the action equals that measured for a cratering blast of the same explosive at the same .DELTA. value and charge shape; and

f. detonating the charge.

21. The method as defined in claim 20 including

a. directing the vortex action into the muckpile by assuring that ground motion towards the opening cut or inclined free face will predominate over that in the vertical direction by predetermining .DELTA..sub.v to exceed .DELTA..sub.b and defining the .DELTA..sub.b -.DELTA..sub.v difference to be within the limitations: .DELTA..sub.b is greater than .DELTA..sub.mb and less than (.DELTA..sub.a + .DELTA..sub.o)/2 and .DELTA..sub.v is greater than .DELTA..sub.o -0.02 and less than or equal to .DELTA..sub.0 -0.10;

b. predetermining the particle size attributable to ground motion in the .DELTA..sub.b direction to be smaller than that attributable to ground motion in the .DELTA..sub.v direction due to:

i. the scouring action within the vortex attributable to the greater velocity near the center than the edges of the vortex, and

ii. containment of the vortex due to the .DELTA..sub.v -.DELTA..sub.b difference; and

c. predetermining the particle size in the .DELTA..sub.b and .DELTA..sub.v directions using a chart plotting predominant particle size, zones and charge depth from test crater blasts.

22. The method as defined in claim 20 including:

a. determining the spacing between rows of holes of a multiple hole blast by: controlling the position and inclination of the free face; predetermining the excavation limit from the preceding row of holes using results of the cratering tests and plotting a chart of the variation in slant distance to crater, cracks and doming limits against charge depth; and placing the charge behind the free face next to be created so that .DELTA..sub.b is greater than .DELTA..sub.mb and .DELTA..sub.b is less than (.DELTA..sub.a + .DELTA..sub.o)/2 and .DELTA..sub.v is greater than .DELTA..sub.o -0.02 and less than or equal to .DELTA..sub.o -0.10;

b. minimizing random ground motion by controlling the delay interval between successive rows of holes so that the velocity of massive ground motion in the vertical direction will not exceed that as determined from cratering blast tests at a charge depth for the range of .DELTA..sub.v previously specified;

c. minimizing random ground motion by detonating charges of successive rows in such a sequence that a barrier mass determined by the .DELTA..sub.diff of thickness not less than 1.4N exists or that the barrier mass is destroyed by detonating charges in it at the same instant as the row blast holes approaching the barrier mass reaches a distance of 1.4N or less;

d. promoting the vortex action between successive rows of holes so that the delay interval between successive rows will not be less than the duration of ground motion as determined by a crater blast test for a charge of the same shape, type and weight of explosive at the same controlling burden;

e. minimizing excessive packing of the muckpile by varying the angle of inclination .alpha. of the vortex within the range 0 to 45.degree. from the horizontal by predetermining the inclination of successive free faces by predetermining with the controlling burden the slant distance from the charge to the doming limit at the top of the bench; and

f. increasing the proportion of fine material available to the vortex action by controlling the spacing .DELTA..sub.s between holes of a given row within the range .DELTA..sub.s = .DELTA..sub.b to .DELTA..sub.s = 1.4.DELTA. .sub.b where .DELTA..sub.b previously has been defined as being in the range .DELTA..sub.mb to (.DELTA..sub.a + .DELTA..sub.o)/2, which are approximate limits of the bond strength destruction zone as determined from the test crater blasts.

23. The method as defined in claim 12 wherein said test crater and bench blasts are conducted to:

a. determine parameters A and B using test crater blasts wherein A = V/V.sub.o wherein V = the crater volume and V.sub.0 = the crater volume at optimum charge depth d, and B = V.sub.o /N.sup. 3 ;

b. determine various values of parameter C using test bench blasts for various heights of bench, burden and .DELTA..sub.v - .DELTA..sub.b difference, wherein .DELTA..sub.v = d.sub.v /N wherein d.sub.v is the vertical depth and .DELTA..sub.b = d.sub.b /N wherein d.sub.b is the burden distance, and C = (V/V.sub.ob) .sup.. C.sub.o wherein C.sub.o = (V/W bench)/(V.sub.o /W crater) wherein V.sub.ob is the optimum crater volume in the burden direction and the .DELTA. and V.sub.o are the volume of the crater in the depth direction and burden direction, respectively; and

c. determine the geometry of the bench for a given explosive, weight and shape of charge from measurements of breakage limits and particle size in bench blasting and identified by the product control index number, ABC of the equation V/W = E.sup.3 ABC, where E is calculated from the formula N = E .cuberoot.W.

24. A method of multiple row product control blasting consisting of:

a. conducting crater and bench blast tests to predetermine limits of fracturing, cratering and doming in bench blasting and so as to determine the variation in time, velocity and duration of massive ground motion with variation in controlling burden and variation in .DELTA..sub.difference, .DELTA..sub.v -.DELTA..sub.b, wherein .DELTA..sub.v = d.sub.v /N wherein d.sub.v is the vertical depth and N is the depth of placement of a charge of the given weight which first begins to produce upon explosion of the charge fractures on the surface of the material in which the charge is placed, and .DELTA..sub.b = d.sub.b /N wherein d.sub.b is the burden distance;

b. creating successive free faces at a predetermined angle by placing a charge at a depth .DELTA..sub.v and a burden .DELTA..sub.b and at a .DELTA..sub.diff, .DELTA..sub.diff being a predetermined positive value, the trajectory being substantially in the vertical direction when the burden equals .DELTA..sub.v + .DELTA..sub.diff and substantially in the horizontal direction when the depth equals .DELTA..sub.b + .DELTA..sub.diff, thereby allowing predetermining of the controlling burden for the succeeding rows of holes;

c. predetermining from results of the crater and bench tests from the proper delay interval between blasts using time, velocity and duration of ground motion measurements so that motion of a given row does not begin before motion of the previous row is complete;

d. placing a charge or series of charges with respect to the top of the bench and the face of the bench so as to predetermine for each charge the proportions of massive ground motion in each of the depth and burden directions according to the granulometry desired; and

e. successively detonating charges of the series at the predetermined delay interval between charges.

25. A method of stability control blasting including:

a. conducting crater and bench blast tests to predetermine limits of fracturing, cratering and doming in bench blasting and so as to determine the variation in time, velocity and duration of massive ground motion with variation in controlling burden and variation in .DELTA..sub.difference, .DELTA..sub.v -.DELTA..sub.b, wherein .DELTA..sub.v = d.sub.v /N wherein d.sub.v is the vertical depth and N is the depth of placement of a charge of the given weight which first begins to produce upon explosion of the charge fractures on the surface of the material in which the charge is placed, and .DELTA..sub.b = d.sub.b /N wherein d.sub.b is the burden distance;

b. defining a predetermined limiting part which the material in which the blasts are conducted is not to be affected, and defining a stability control zone between the limiting part in the main body to be excavated such that breakage limits and doming due to blasting within said stability control zone will not extend beyond limits of the stability control zone;

c. progressively setting and detonating explosive charges within the stability control zone approaching the limiting part so that the .DELTA..sub.v -.DELTA..sub.b difference progressively increases so as to progressively suppress massive ground motion towards the top of the bench and so as to progressively increase the velocity of ground motion towards the face of the bench, .DELTA..sub.v = d.sub.v /N wherein d.sub.v is the vertical depth and N is the depth of placement of a charge of the given weight which first begins to produce upon explosion of the charge a crater on the surface of the material in which the charge is placed, and .DELTA..sub.b = d.sub.b /N wherein d.sub.b is the burden distance; and

d. placing the charge such that .DELTA..sub.v exceeds the slant distance to R cracks or to the doming limit, and rebound cracks do not for any given blast extend beyond the predetermined limits.

26. A method of stability control blasting including:

a. conducting bench blast tests to predetermine limits of fracturing, cratering and doming in bench blasting and so as to determine the variation in time, velocity and duration of massive ground motion with variation in controlling burden and variation in .DELTA..sub.difference, .DELTA..sub.v -.DELTA..sub.b, wherein .DELTA..sub.v = d.sub.v /N wherein d.sub.v is the vertical depth and N is the depth of placement of a charge of the given weight which first begins to produce upon explosion of the charge fractures on the surface of the material in which the charge is placed, and .DELTA..sub.b = d.sub.b /N wherein d.sub.b is the burden distance; and to determine the .DELTA..sub.v -.DELTA..sub.b difference at which massive ground motion towards the top of the bench is insufficient to cause blasting damage at the collar of the borehole in row blasting;

b. measuring the time, velocity and duration of massive ground motion in the .DELTA..sub.b direction at the .DELTA..sub.v -.DELTA..sub.b difference, as defined in step (a);

c. progressively setting and detonating charges in the direction of mining advance based upon time, velocity and duration measurements of the bench blast tests so that ground motion toward the top of the bench is not predetermined by the duration of horizontal ground motion of the previous charge; and

d. placing the charge such that .DELTA..sub.b equals the burden determined experimentally for the .DELTA..sub.v -.DELTA..sub.b difference, determined in step (a), and the delay interval between successive charges is such that horizontal ground motion from successive charges does not affect vertical ground motion, and the weight of explosive detonated per delay does not exceed that for which said .DELTA..sub.v -.DELTA..sub.b was determined.

27. The method as defined in claim 25 wherein the .DELTA..sub.v -.DELTA..sub.b difference is determined within the range .DELTA..sub.v is greater than 1.0 and less than 1.4, and .DELTA..sub.b is within the range .DELTA..sub.o -0.10 and .DELTA..sub.o -0.20.

28. In bench geometry blasting, the method of controlling the trajectory of material surrounding a blast charge in response to explosion of the charge comprising:

a. Conducting test crater blasts to determine values for d.sub.o, N, and E for the surrounding material and type of explosive, where d.sub.o is the depth of placement of a charge of known weight which produces upon explosion of the charge maximum pressure rise in the material; where N is the depth of placement of a charge of a known weight which first begins to produce upon explosion of the charge a crater on the surface of the material in which the charge is placed; and where E is calculated from the formula N = E .cuberoot.W using the determined value of N and its known charge weight, said test crater blasts being carried out by setting charges of known weight, shape and type of explosive at various depths, detonating charges, measuring the limits of R cracks, I cracks, O cracks, shock slabs, rebound slabs, cratering and doming on the surface; and excavating the crater so as to determine the shape of the true crater, limits of bond strength destruction zone, the intermediate zone, barrier zone and transition limits;

b. Conducting test bench blasts to determine the value of .DELTA..sub.bo for the surrounding material and type of explosive, where .DELTA..sub.bo is d.sub.bo /N and d.sub.bo is the perpendicular distance from the free face of a bench geometry to the center of gravity of an explosive charge placed at a depth d.sub.o which produces maximum pressure rise within the material;

c. Placing a charge of weight determined by the formula d.sub.o = .DELTA..sub.o E .cuberoot.W at a depth d.sub.o + d.sub.diff beneath the upper surface of the material bench, d.sub.diff being a predetermined positive value;

d. Placing the charge along a rearward extension of the line of preferred trajectory a distance equal d.sub.bo, whereby trajectory is controlled to be substantially in the horizontal direction; and

e. Detonating the charge.

29. In bench geometry blasting, the method of controlling the trajectory of material surrounding a blast charge in response to explosion of the charge comprising:

a. Conducting test crater blasts to determine values for d.sub.o, N, and E for the surrounding material and type of explosive, where d.sub.o is the depth of placement of a charge of known weight which produces upon explosion of the charge maximum pressure rise in the material; where N is the depth of placement of a charge of a known weight which first begins to produce upon explosion of the charge a crater on the surface of the material in which the charge is placed and where E is calculated from the formula N = E .cuberoot.W using the determined value of N and its known charge weight, said test crater blasts being performed by detonating a series of charges of given type and known shape and weight at various depths measuring the ground rise to determine the time, velocity and duration of ground motion to differentiate between effects attributable to the arrival of the shock wave, the pressure rise in the material, and the venting of the gas bubble;

b. Conducting test bench blasts to determine the value of .DELTA..sub.bo for the surrounding material and type of explosive, where .DELTA..sub.bo is (d.sub.bo /N) and d.sub.bo is the perpendicular distance from the free face of a bench geometry to the center of gravity of an explosive charge placed at a depth d.sub.o which produces maximum pressure rise within the material;

c. Placing a charge of weight determined by the formula d.sub.o = .DELTA. .sub.o E .cuberoot.W at a depth d.sub.o + d.sub.diff beneath the upper surface of the material bench, d.sub.diff being a predetermined positive value;

d. Placing the charge along a rearward extension of the line of preferred trajectory a distance equal d.sub.bo, whereby trajectory is controlled to be substantially in the horizontal direction; and

e. Detonating the charge.

30. In bench geometry blasting, the method of controlling the trajectory of material surrounding a blast charge in response to explosion of the charge comprising:

a. Conducting test crater blasts to determine values for d.sub.o, N, and E for the surrounding material and type of explosive, where d.sub.o is the depth of placement of a charge of known weight which produces upon explosion of the charge maximum pressure rise in the material; where N is the depth of placement of a charge of a known weight which first begins to produce upon explosion of the charge a crater on the surface of the material in which the charge is placed; and where E is calculated from the formula N = E .cuberoot.W using the determined value of N and its known charge weight;

b. Conducting test bench blasts to determine the value of .DELTA..sub.bo for the surrounding material and type of explosive, where .DELTA..sub.bo is (d.sub.bo /N) and d.sub.bo is the perpendicular distance from the free face of a bench geometry to the center of gravity of an explosive charge placed at a depth d.sub.o which produces maximum pressure rise within the material, said test crater and bench blasts being conducted to:

i. determine parameters A and B using test crater blasts wherein A = (V/V.sub. o) wherein V = the crater volume and V.sub.o = the crater volume at optimum charge depth d, and B = (V.sub.o /N.sup.3);

ii. determine various values of parameter C using test bench blasts for various heights of bench, burden and .DELTA..sub.v -.DELTA..sub.b difference, wherein .DELTA..sub.v = (d.sub.v /N) wherein d.sub.v is the vertical depth and .DELTA..sub.b = (d.sub.b /N) wherein d.sub.b is the burden distance, and C = (V/V.sub. ob) .sup.. C.sub.o wherein C.sub.o = (V/W bench)/(V.sub.o /W crater);

iii. determine the geometry of the bench for a given explosive, weight and shape of charge from measurements of breakage limits and particle size in bench blasting and identified by the product control index number, ABC of the equation (V/W) = E.sup.3 ABC, where E is calculated from the formula N = E .cuberoot. W;

c. Placing a charge of weight determined by the formula d.sub.o = .DELTA..sub.o E .cuberoot. W at a depth d.sub.o + d.sub.diff beneath the upper surface of the material bench, d.sub.diff being a predetermined positive value;

d. Placing the charge along a rearward extension of the line of preferred trajectory a distance equal d.sub.bo, whereby trajectory is controlled to be substantially in the horizontal direction; and

e. Detonating the charge.

31. In bench geometry blasting, the method of controlling the trajectory of material surrounding a blast charge in response to explosion of the charge comprising:

a. Conducting test crater blasts to determine values for d.sub.o, N, and E for the surrounding material and type of explosive, where d.sub.o is the depth of placement of a charge of known weight which produces upon explosion of the charge maximum pressure rise in the material; where N is the depth of placement of a charge of a known weight which first begins to produce upon explosion of the charge a crater on the surface of the material in which the charge is placed; and where E is calculated from the formula N = E .cuberoot. W using the determined value of N and its known charge weight;

b. Conducting test bench blasts to determine the value of .DELTA..sub.bo for the surrounding material and type of explosive, where .DELTA..sub.bo is (d.sub.bo /N) and d.sub.bo is the perpendicular distance from the free face of a bench geometry to the center of gravity of an explosive charge placed at a depth d.sub.o which produces maximum pressure rise within the material;

c. Conducting crater blasts so as to determine the breakaway velocity at .DELTA..sub.o as to identify granulometry representative of each of the bond strength destruction zone, the intermediate zone and the barrier zone surrounding the charge;

d. Conducting bench blasts to determine .DELTA..sub.bo and .DELTA..sub.increment adjustment .DELTA..sub.bo -.DELTA..sub.o, by placing a charge of substantially spherical shape at depth, .DELTA..sub.o, as determined by the crater blasting and varying the burden in the range .DELTA..sub.b greater than .DELTA..sub.o to determine the .DELTA..sub.increment, .DELTA..sub.bo -.DELTA..sub.o where (V/W) is maximum and the breakaway velocity towards the face of the bench equals that toward the top of the bench;

e. Correcting cratering granulometry, limits of the bond strength destructive zone, the intermediate zone, the barrier zone and limits of the crater to the geometry of bench blasting;

f. Placing a charge of weight determined by the formula d.sub.o = .DELTA..sub.o E .cuberoot. W at a depth d.sub.o + d.sub.diff beneath the upper surface of the material bench, d.sub.diff being a predetermined positive value;

g. Placing the charge along a rearward extension of the line of preferred trajectory a distance equal d.sub.bo, whereby trajectory is controlled to be substantially in the horizontal direction; and

h. Detonating the charge.

32. A method of stability control blasting including:

a. Conducting crater and bench blast tests to predetermine limits of fracturing, cratering and doming in bench blasting and so as to determine the variation in time, velocity and duration of massive ground motion with variation in controlling burden and variation in .DELTA..sub.difference, .DELTA..sub.v -.DELTA..sub.b, wherein .DELTA..sub.v = (d.sub.v /N) wherein d.sub.v is the vertical depth and N is the depth of placement of a charge of the given weight which first begins to produce upon explosion of the charge fractures on the surface of the material in which the charge is placed, and .DELTA..sub.b = (d.sub.b /N) wherein d.sub.b is the burden distance;

b. Defining a predetermined limiting part which the material in which the blasts are conducted is not to be affected, and defining a stability control zone between the limiting part in the main body to be excavated such that breakage limits and doming due to blasting within said stability control zone will not extend beyond limits of the stability control zone;

c. Progressively setting and detonating explosive charges within the stability control zone approaching the limiting part so that the .DELTA..sub.v -.DELTA..sub.b difference progressively increases so as to progressively suppress massive ground motion towards the top of the bench and so as to progressively increase the velocity of ground motion towards the face of the bench, .DELTA..sub.v = (d.sub.v /N) wherein d.sub.v is the vertical depth and N is the depth of placement of a charge of the given weight which first begins to produce upon explosion of the charge a crater on the surface of the material in which the charge is placed, and .DELTA..sub.b = (d.sub.b /N) wherein d.sub.b is the burden distance;

d. Placing the charge such that .DELTA..sub.v exceeds the slant distance to R cracks or to the doming limit, and rebound cracks do not for any given blast extend beyond the predetermined limits;

e. Excavating a breakage limit trench, one wall of which coincides with said limiting part;

f. Placing rock bolts into the permanent wall along the line of the limiting part; and

g. backfilling the breakage limit trench prior to production blasting so that the fill material both acts as a shock dampening substance and prevents fractures from developing beyond the predetermined limit.

33. In bench geometry blasting, the method of controlling the trajectory of material surrounding a blast charge in response to explosion of the charge comprising:

a. Conducting test crater blasts to determine values for d.sub.o, N, and E for the surrounding material and type of explosive, where d.sub.o is the depth of placement of a charge of known weight which produces upon explosion of the charge maximum pressure rise in the material; where N is the depth of placement of a charge of a known weight which first begins to produce upon explosion of the charge a crater on the surface of the material in which the charge is placed; and where E is calculated from the formula N = E .cuberoot. W using the determined value of N and its known charge weight;

b. Conducting test bench blasts to determine the value of .DELTA..sub.bo for the surrounding material and type of explosive, where .DELTA..sub.bo is (d.sub.bo /N) and d.sub.bo is the perpendicular distance from the free face of a bench geometry to the center of gravity of an explosive charge placed at a depth d.sub.o which produces maximum pressure rise within the material;

c. Placing a charge of weight determined by the formula d.sub.o = .DELTA..sub.o E .cuberoot. W at a depth d.sub.o beneath the upper surface of the material bench;

d. Placing the charge along a rearward extension of the line where trajectory is to be substantially inhibited a distance equal to d.sub.bo + d.sub.diff, d.sub.diff being a predetermined positive value, whereby trajectory is controlled to be substantially in the vertical direction; and

e. Detonating the charge.