Method And Apparatus For In Situ Measurement Of Soil Creep Strength

Handy July 4, 1

Patent Grant 3673861

U.S. patent number 3,673,861 [Application Number 04/837,216] was granted by the patent office on 1972-07-04 for method and apparatus for in situ measurement of soil creep strength. This patent grant is currently assigned to Iowa State University Research Foundation, Inc.. Invention is credited to Richard L. Handy.


United States Patent 3,673,861
Handy July 4, 1972

METHOD AND APPARATUS FOR IN SITU MEASUREMENT OF SOIL CREEP STRENGTH

Abstract

Soil creep rate is measured in situ by lowering a shear testing device into a bore hole and expanding it so that opposing pressure surfaces of the device engage facing surfaces of the bore hole with a constant normal pressure. A force less than that which would exceed the soil shearing strength under the applied normal pressure is then exerted on the device axially of the bore hole to induce a predetermined and constant shearing stress in the soil. A record is made of the deformation of the soil as a function of time for different shearing stresses to generate a family of characteristic deformation curves. The first derivative of each curve with respect to time is the shear rate, which tends to decrease to a substantially constant value with increasing time. This constant shear rate is referred to as the creep rate. A plot of the creep rate against shearing stress yields an empirical value for the creep threshold stress; and a plot of different creep threshold stresses for different values of normal stress defines a stable zone in the shearing stress-normal stress plot.


Inventors: Handy; Richard L. (Des Moines, IA)
Assignee: Iowa State University Research Foundation, Inc. (Ames, IA)
Family ID: 25273839
Appl. No.: 04/837,216
Filed: June 27, 1969

Current U.S. Class: 73/841; 73/84; 73/784; 73/787; 73/794; 92/98D
Current CPC Class: E02D 1/022 (20130101)
Current International Class: E02D 1/02 (20060101); E02D 1/00 (20060101); G01n 003/24 ()
Field of Search: ;73/88E,84,151,101,146 ;33/125 ;92/98D,99

References Cited [Referenced By]

U.S. Patent Documents
2725078 November 1955 Glancy
3222999 December 1965 Hager
2331577 October 1943 Sonntag
3327396 June 1967 Waddell
3377847 April 1968 Aske
3427871 February 1969 Handy et al.
3499320 March 1970 Fox et al.
Foreign Patent Documents
540,806 Dec 1931 DD
1,449,921 Jul 1966 FR

Other References

Sail Mechanics in Engineering Practice, K. Terzaghi & R. B. Peck, J. Wiley & Sons, N.Y., 1948, pp. 79-93 .
Sail Mechanics, Foundations, Earth Structures, by G. P. Tschebotarioff, McGraw-Hill Book Comp., N.Y., 1952, pp. 122-130 & 143-145.

Primary Examiner: Queisser; Richard C.
Assistant Examiner: Smollar; Marvin

Claims



I claim:

1. In a method of in situ measuring soil creep rate comprising the steps: forming a hole in the soil, forcing a contact surface against a side wall of said hole to exert a predetermined force thereon, inducing for a period of time in said contact surface engaging said side wall a predetermined substantially constant shear force less than the maximum or quick shear force for said soil; and measuring the deformation of said soil for said period of time after said shear force has been induced in said contact surface.

2. The method of claim 1 further comprising: then increasing said shearing force to a second value less than the maximum or quick shearing force, and again measuring the deformation of said soil for a period of time after said increased shearing force has been induced in said contact surface, whereby a family of curves may be generated relating deformation of the soil to time for discrete values of shearing stress.

3. The method of claim 2 further comprising plotting values of stabilized creep rates for said family of deformation curves as a function of said discrete values of shear force to define the creep threshold stress for a constant normal stress.

4. The method of claim 1 wherein said step of forcing said contact surface against said side wall comprises lowering an expandable device in said hole in a contracted state and expanding said device at a predetermined depth in said hole to engage said side wall with opposing contact surfaces.

5. The method of claim 3 wherein said step of inducing said shearing force comprises pulling said device longitudinally of said hole after said device has been expanded.

6. A method of empirically determining the creep failure envelope for soil comprising inducing a shearing force on the soil under test while maintaining a constant normal force on said soil, recording the displacement of said soil under said shearing force over a period of time until said displacement per unit time becomes generally constant, thereby defining a creep rate for a known shearing stress, then incrementally changing said shearing stress and recording the displacement of said soil under said new shearing force over a period of time for a number of constant but incrementally changed shearing stresses to generate a relationship between creep rate and shear stress thereby to define a first value of creep threshold stress, then changing said normal stress on said soil to a second value and repeating the above-named steps to define a second value of creep threshold stress for said second normal stress, said values of creep threshold stress defining a creep failure envelope based on empirical data.

7. In a method of in situ determination of soil creep, the steps of: forming a hole in the soil under test, forcing a contact surface against soil surrounding said hole to induce a predetermined normal force in said soil; then urging said contact surface in a direction perpendicular to said normal force to induce a shearing force of substantially constant value less than the maximum or quick shear force in the soil; recording the displacement of said contact surface in the direction of shear force until the soil deformation becomes substantially linear with time, the slope of said linear relationship between deformation and time defining a creep rate for the applied normal force; increasing said shear force to a second, substantially constant, predetermined value less than the maximum or quick shear value; recording the displacement of said contact surface for said second shear force for a period of time until the deformation of said soil becomes substantially linear with time, thereby defining a second value of creep rate for a different normal force; and plotting said first and second values of creep rate against the two values of shear stress, the extrapolation of said plot to zero creep rate providing one data point on a creep envelope defining a stable zone in a shearing stress--normal stress plot.

8. The method of claim 7 further comprising the steps of increasing the normal force on the soil surrounding the hole to a second value and repeating the above-named steps to provide a second data point which, with said first data point, defines a stable zone in the normal stress/shear stress plot.

9. Apparatus for in situ testing of soil by forming a bore hole in said soil comprising: support means adapted for placement on said soil above said bore hole, frame means carried by said support means for vertical movement, means for exerting a force on said frame means to urge said frame relative to said force means, an expandable device connected to said frame means for being lowered into said bore hole and including first and second contact surfaces movable relative to each other for engaging opposing surfaces of said bore hole, said device including first and second flexible side straps, one of said contact surfaces mounted to each of said straps and further including a housing defining a double-acting piston rod and cylinder unit for selectively moving said contact surfaces apart, said housing further including first and second flexible bellows connected to said piston rod and cooperating with said housing to define first and second chambers for forcing said rod to expand or contract said contact surfaces, source means for selectively forcing pressurized fluid into one of said first and second chambers of said housing, and means for measuring the displacement of said contact surfaces when a shear force is applied thereto.
Description



BACKGROUND

The present invention relates to in situ testing of soils; more particularly, it pertains to a method of and apparatus for empirically determining soil creep in situ.

The economic importance and destructiveness of landslides, for example in construction of the Panama Canal, eventually led to the widespread involvement of soils engineers and resulted in development of analytic slope design methods now firmly established in engineering practice. These analyses are usually based on field data or laboratory observations of the processes involved. For example, the familiar Swedish circle method is based on extensive field studies which indicated that a cross section of failure surfaces in clays closely approximates a circular arc. Other failure surfaces commonly assumed in analytic treatment are planes or sections of a logarithmic spiral.

In addition to reasonable potential failure surfaces, slope design and analysis requires an evaluation of soil shear strength. Various strength tests have been successful for determining the soil shear strength based upon laboratory or in situ determination of the quick shear strength and applying a "safety factor." That is to say, based upon an actual determination of shear strength, engineers have applied a safety factor to account for slower shearing reactions which were not actually measured. Attempts to correlate laboratory-determined soil strength to actual observed slope stability have not been very successful. In some cases the test data may indicate considerable stability where none in fact exists. Laboratory test data may be used with confidence within certain geographic areas or single formations if based upon previous empirical correlations to performance.

Prevailing approaches to soil shear testing may be classified into sampling techniques and in situ testing. Conventional techniques used in the laboratory include triaxial tests and direct shear tests conducted on undisturbed samples of the soil.

One commonly used method of obtaining a sample is to insert a thin-wall cylindrical tube called a "Shelby tube" into the soil. Several types of laboratory tests may be performed in which the soil is subjected to a pressure and than a load is applied to cause shearing. In the direct shear test, a short cylinder of soil is loaded axially with a vertical load and sheared on a plane normal to the load in a shear box. That is, the top half of a shear box is made to slide laterally with respect to the bottom half; and the necessary force to accomplish this is measured.

A more accurate laboratory test is the triaxial test in which a cylinder of soil is sealed in a membrane and confined laterally with fluid pressure. A vertical load is applied until the sample fails. In this test the orientation of the shear plane must be determined; and cohesion and internal friction are calculated using Mohr theory.

In either case of laboratory testing, normal procedure requires taking two or three samples and determining shear strength at different values of confining pressure in order to define the linear Coulomb relationship from which cohesion and internal friction may be determined.

Another problem in applying laboratory test results to field situations is the effect of the rate of shearing. Even when the shear rate is slow enough to assure a uniform distribution of pore pressures within a test sample, the rate is usually much higher than that which will occur in the field. The effect is most pronounced with clays where a higher shear rate tends to produce a higher strength.

Based on extremely slow triaxial tests, one researcher states that creep strength may be as low as 60 percent of the maximum shear strength (i.e., the quick shearing strength determined by most laboratory tests). Other researchers report that the creep strength of undisturbed clay varies from 40 to 80 percent of the laboratory compression strength. Still others report that from direct shear tests the creep strength of a clay is 60 percent of its ultimate strength, a figure which correlates with excessive settlement observations in the field. Still others advocate the use of residual (ultimate or remolded) strength rather than peak strength for landslide calculations in fractured clays, because in one sense, failure has already occurred and destroyed cohesion.

Normally, laboratory tests to evaluate susceptibility to slow shearing or creep may take from 2 to 3 weeks before results are achieved, and they are relatively expensive. Further, since the samples are tested in an artificial environment and the actual mechanism involved in soil creep is not known precisely, it is difficult to assess the validity of a laboratory test for determining creep rates.

Pore water pressures were recognized as an important factor in determining soil shear strength; and laboratory shear tests are commonly adapted to evaluate the pore pressure during shearing. Pore pressures are then subtracted from the applied normal stress to give shear strength parameters on an "effective stress basis." The major difficulty in applying the results of this method is anticipating the field pore pressure. The effective stress method of analysis is most applicable to slow field loading conditions where pore pressures are either monitored or are nearly zero.

For granular soils such as sand or gravel, a standard penetration test has been developed in which a probe or sampler is driven into the soil and the blow count (i.e., the number of blows of predetermined force) determines the angle of internal friction based upon previously obtained empirical data. Alternatively, the energy required to drive a predetermined distance is recorded and a similar correlation with empirical data is required.

For clay soils, the vane shear test has come into widespread use. In this case, a cross-bladed vane is inserted vertically into the soil, and a torque is applied to cause shearing about a cylindrical surface. The vane shear test gives a total shear strength, but it does not separate the two commonly recognized components of cohesion and internal friction.

A U. S. Pat. No. 3,427,871 of Handy and Fox for BORE-HOLE SOIL TESTING APPARATUS, discloses apparatus for in situ testing of soils to determine shear strength. The apparatus disclosed therein includes a device which is lowered into a preformed bore hole. The device includes two pressure surfaces which are movable relative to each other for engaging opposing sides of the bore hole.

With a constant radial pressure exerted on the pressure surfaces, a shearing force is applied by pulling the device axially of the bore hole. After a first maximum shear force is measured, the hydraulic pressure expanding the pressure surface is increased so that a second shearing force may be applied and measured. The data points relating shearing stress at failure to the normal pressure upon the shear plane defines the classical linear Coulomb relationship from which cohesion and internal friction may be determined by inspection. The teaching of that patent was principally directed toward the determination of the two parameters of cohesion and internal friction in determining the maximum shear strength of a given soil on an in situ basis.

SUMMARY

The present invention contemplates applying a constant pressure normal to the shearing plane and a constant, predetermined shear stress less than that which would cause the soil around the bore hole to fall in quick shear. The deformation of the soil as a function of time is measured for different shear stresses (all such shear stresses being less than the quick shear stress) thus generating a family of characteristic deformation curves. The first derivative of each curve for constant shear stress defines the rate of shear for that stress. This rate tends to decrease and approach a constant value with time; and it is referred to as the soil creep rate or creep rate in shear. A plot of the creep rate against shear stress for constant normal stress defines an empirical value for the creep threshold stress--that is, the lowest shearing stress which will produce deformation. The values for creep threshold stress in relation to normal pressure may also be obtained by following the same procedure but increasing the normal stress to a second constant value to generate a set of data points used to define a creep threshold envelope analogous to the Mohr-Coulomb shear failure envelope. Thus, a more accurate and reliable empirical value of minimum creep stress is derived from an in situ test which eliminates the delay and expense of prior sampling and laboratory testing methods as well as provides a more reliable basis on which to predict long-term stability of earthern slopes and embankments, soil bearing capacity against external loadings, and other engineering problems involving long-term soil shear strength.

A further advantage of the in situ soil creep strength test described herein is a greatly reduced time requirement for testing. About 30 minutes are ordinarily required to establish a constant creep rate for a given shear and normal stress. Repetition at several shearing stresses to establish the creep threshold stress for a given normal stress requires about 2 hours. Repetition of the above complete sequence to establish a relationship between creep threshold stress and normal stress usually requires 4 to 6 hours. A similar investigation by way of conventional laboratory testing requires a minimum of several weeks.

Other features and advantages of the instant instant invention will be apparent to persons skilled in the art from the following detailed description of a preferred method and apparatus accompanied by the attached drawing.

THE DRAWING

FIG. 1 is an elevation view of a tripod for supporting the testing device;

FIGS. 2, 3 and 3A illustrate the testing device in detail;

FIGS. 4-5 illustrate the insertion and expansion of the testing device in a bore hole;

FIG. 6 is a plot of a family of characteristic deformation curves according to the present invention;

FIG. 7 is a plot of creep rate vs. shearing stress for determining the creep threshold stress; and

FIG. 8 is a plot of shearing stress against normal stress illustrating the classical Coulomb relationship.

DETAILED DESCRIPTION

Turning now to FIGS. 1-3A, the illustrated embodiment comprises a tripod seen in FIG. 1 and generally designated 10 for supporting the testing element, generally designated 11 and seen in FIG. 2. The device 11 is capable of assuming a contracted or an expanded condition, as will be explained in detail presently. The tripod supporting element includes legs 10a, two of which are illustrated in the drawing and supported on a base member 10b adapted to be placed on the surface of the soil to be tested. The base 10b defines a central aperture 10c through which the testing device 11 is lowered (in its contracted condition) into the pre-formed bore hole, as illustrated.

At the top of the tripod 10 there is a mounting plate 10d on which is mounted a pneumatic cylinder and piston rod unit 13 including a cylinder 13a which receives a piston, 13b to which is attached a cylinder 13a which receives a piston, 13b to which is attached a rod 13c. Gas under pressure is coupled into the cylinder 13a through a conduit 13d from a source (not shown) to force the piston head 13b and its associated rod 13c upwardly. The pressure of the gas (which may preferably be CO.sub.2) is regulated by any suitable means so that a constant upward force is generated independent of small displacements of the piston. To the underside of the mounting plate 10d there is attached a member 15 which serves as a reference measurement point.

The device 11 is supported on the tripod 10 by means of a yoke generally designated 12 and including two vertical side rods 12a and 12b connected together with upper and lower transverse end pieces 12c and 12d to form a rigid frame. The device 11 is attached to the lower end piece 12d of the yoke 12 by means of a pulling rod 16 and a flexible frame 17. The flexible frame 17 includes a cross bar 17a which threadably receives the lower end of the pulling rod 16 and first and second flexible straps 17b and 17c which may be made of strap steel.

The upper end piece 12c is provided with a threaded aperture through which an elongated externally threaded screw 20 is received. The screw member 20 is provided with a turning handle 20a and its lower end portion 20b engages the upper portion of the piston rod 13c. Thus, as pressurized gas is forced into the cylinder 13, the piston 13b and its associated rod 13c will be forced upward bearing against the end portion 20b of the screw 20 to exert an upward force on the yoke 12 and device 11.

Strain gauge means generally designated by reference numeral 21 is secured by means of a bracket 21a and thumb screw 21b to the side rod 12b of the yoke 12; and it includes a cantilever member 21c on which is mounted a strain gauge 21d. The distal end of the cantilever member 21c engages the reference surface 15 of the tripod 10. The strain gauge may be used to measure vertical displacement of the yoke 12 and device 11 relative to the tripod 10. Similarly, a direct-read dial gauge 22 may be secured by means of a bracket 22a and thumb screw 22b to the other side rod 12a of the yoke 12. The gauge 22 includes a movable arm 22c which engages the reference point 15 to measure displacement of the yoke 12 relative to the tripod 10.

Turning now to the device 11 and particularly to FIG. 3, the device includes first and second shoes 25 and 26 which provide pressure surfaces for engaging the soil at opposing sides of the bore hole for exerting a lateral pressure on that soil.

The soil-engaging exterior surfaces of the shoes 25 and 26 are serrated as seen at 27 and 28 to provide alternate ridges and grooves extending in a generally horizontal direction for firmly engaging the interior surface of the bore hole; and in horizontal cross section, the shoes 25 and 26 may be curved to conform to the interior shape of the cylindrical bore hole. The shoes 25 and 26 are attached respectively to the straps 17b and 17c; so they are freely movable relative to each other. A housing generally designated by reference numeral 30 in FIG. 2 includes a first side wall 31 and a second side wall 32 as seen in FIG. 3. The side walls 31 and 32 are rigidly secured together by means of four corner bolts 35 which extend through the side plate 32 and are threadably received in the second side plate 31.

The side plate 32 defines a central aperture 36 for receiving the piston 37 which is secured to the inside of the strap 17c at one end and fastened to a piston head 38 at the other end.

A first flexible bellows member 39 having the shape of a cup with a peripheral lip or flange is secured to the left side of the piston 38 as seen in FIG. 3 by means of a bolt 40 and washer 40a. The member 39 is commercially available under the tradename Bellofram. The flange 39a of the bellows member 39 is sealingly secured to the side plate 31 of the housing 30 to form a fluid cavity or chamber 41. A conduit 42 is formed through the side plate 31 and communicates with the cavity 41 for coupling a second source of gas under constant pressure into the chamber to expand the bellows 39. Preferably, the second source of gas is a regulated source of CO.sub.2. When pressurized fluid is forced into the chamber 41, the piston 38 will be moved to the right as viewed in FIG. 3 thus causing the shoe 28 to expand relative to the shoe 27 so that they will engage opposing sides of the bore hole.

A second cup-shaped bellows member 43 is secured to the right side of the piston 38 by means of a washer 44 and has a peripheral flange 43a secured to the side plate 32 to form a sealed chamber or cavity 45. A conduit 46 couples pressurized fluid through the side plate 32 to the cavity 45. When pressurized fluid is forced into the cavity 45, the piston 38 moves to the left thus retracting the shoe 28 under positive pressure; and this has been found to provide an advantage in moving the device 11 from a bore hole after tests. Use of the bellows members 39 and 43 has been found to significantly reduce the frictional forces in the device and thus enhance its accuracy and sensitivity; however, persons skilled in the art will be able to substitute other sealing structures (for example O-rings) having low friction and obtain similar results.

The devices seen in its contracted state in partially schematic form in FIG. 2; and in its expanded form, it is illustrated in FIG. 3. If desired, one or the other of the shoes 27 and 28 may be provided with a transducer for measuring pore pressure, as disclosed in the above-identified patent.

OPERATION

In operation, a bore hole of predetermined diameter is formed in the soil to be tested; and the tripod 10 is placed on the surface of the soil with the aperture 10c above the bore hole as illustrated in FIG. 1. With the device in its contracted stage (by forcing pressurized CO.sub.2 into the cavity 45 via line 46, if necessary), the device is lowered to a predetermined depth. The strain gauge 21 and dial gauge 22 are adjusted to the reference surface 16 form making subsequent readings. The screw 20 is lowered to a point at which the base 20b engages the rod 13c so that the entire weight of the yoke 12 and device is supported thereon. The device is then expanded by forcing pressurized CO.sub.2 from its regulated source into the cavity 41 via line 42; and the shoes 27 and 28 are forced apart and engage opposing inner surfaces of the bore hole to exert a predetermined force normal to these bore hole surfaces.

Having thus established a constant normal stress, a shearing force less than the quick shear force (for the existing normal stress) is induced in the soil surrounding the bore hole at the location of the device by forcing pressurized CO.sub.2 from the first regulated source to actuate the pneumatic cylinder and piston rod unit 13. This tends to lift the yoke 12 and exerts an upward force on the device 11. The vertical displacement of the device 11 as a function of time is then measured by either the strain gauge 21 or the dial gauge 22. The same measurement is recorded for an increased shear stress, still less than the quick shear value.

Equivalent results may be achieved by pushing the device 11 in a direction further into the bore hole since a similar shearing force is then induced in the soil.

Turning now to FIGS. 4-5, an alternative device, based on the disclosure of the above-identified U. S. patent, is schematically illustrated; and it includes a winch schematically illustrated at 50 and provided with a flexible cable 51 at the bottom of which there is located an expandable pressure-inducing device 52. The device 52 includes a wrist pin 53 which slidably receives first and second side elements 54 and 55 which are respectively provided with shoes 56 and 57 for engaging opposing sides of a bore hole 59.

Coil springs 60 are fitted about the wrist pin 53 for urging the side halves 54 and 55 respectively into a contracted state; and the left side 54 of the device 52 is provided with upper and lower cylinder and piston rod units generally designated by reference numerals 62 and 63. The rod portion of each of the cylinder and piston rod units 62 and 63 is attached to the right hand side 55 of the device 52; and pressurized fluid introduced into the cavities of these cylinder and piston rod units force the sides of the device apart. Operation of this embodiment is otherwise similar to that which has already been described. The shear force may be measured by a dynamometer (not shown).

THEORY

As mentioned above, with a constant normal stress (hereinafter designated by the symbol .sigma.) exerted against the walls of the bore hole, a predetermined constant shearing stress (.tau.) is induced in the soil surrounding the bore hole by means of the cylinder and piston rod unit 13; and the deformation of the soil is measured by means of the strain gauge 21 or the dial gauge 22 as a function of time. The shearing stress is then increased to another constant value (while keeping the normal stress constant); and again, the deformation of the soil is measured as a function of time. In this manner, a family of characteristic deformation curves is generated. The results from one example have been plotted in the graph of FIG. 6 for shearing stresses of 3.0 psi, 4.8 psi, 5.5 psi, and 6.2 psi. For this single graph, the normal stress was held constant.

Referring to the family of characteristic deformation curves in FIG. 6, it will be observed that after an initial consolidation of the soil (represented in the graph by the portion closest to the origin), each of the deformation curves defines a "knee" and thereafter is essentially linear. The first derivative of each curve defines a deformation per unit time, and this is herein referred to as creep rate. For purposes of defining a creep threshold stress, the creep rates used are those calculated by the linear portion of the characteristic deformation curves; in other words, the creep rates used have a constant value which is a function of a predetermined applied shearing stress and a predetermined applied normal stress. It will be observed that as the shearing stress increases, the creep rate also increases for the same normal stress.

Turning now to FIG. 7, the creep rate (ordinate) is plotted against the shear stress values determined as in FIG. 6 by the hollow circles. It is seen that a generally linear relationship is defined as illustrated by the straight line 65 in FIG. 7. As the creep rate increases, the curve 65 curves upwardly as illustrated by the portion 66 and asymptotically approaches the vertical line 67 which defines the quick shearing stress (i.e., the maximum shearing strength of the soil) for the applied normal stress. By extending the line 65 until it intersects the abscissa (as at A') there is defined a shear stress corresponding to a zero creep rate. This is identified in FIG. 7 as the creep threshold stress; and it is denoted .tau..sub.o '. In practice, the .tau..sub.o ' will mark a safety level below which there will be no appreciable creep for any value of shear stress.

In order to define a stable zone in the plot of normal stress (.sigma.) against shearing stress (.tau.), a second deformation record as shown in FIG. 6 and described above is made for a different (preferably higher) normal stress. This may simply be accomplished with the same apparatus by increasing the pressure in the chamber 41 of the device 11 to generate a higher normal stress; and then inducing a small shearing stress and measuring the resultant deformation as a function of time. The shearing stress is increased in incremental steps while holding the normal stress constant; and for each increase, deformation is measured to generate a second family of deformation curves of the kind illustrated in FIG. 6.

From this second record of deformation curves, the creep rates (i.e., derivatives) of constant value are determined and plotted as the hollow triangles in FIG. 7 as a function of the incremental values of shearing stress .tau.. This defines the straight line 68 which is extended to intersect the abscissa (as at A") to define a shear stress .tau..sub.o " corresponding to a zero creep rate for the then applied normal stress.

The creep envelope is the interrelationship between the normal sress and the shear stress for which no shearing of the soil will take place. That is to say, the creep envelope defines a zone in which all values of shearing stress are permissible without having to fear that shearing of the soil will take place--even over an extended period of time.

Referring to FIG. 8, a creep envelope is shown based on the previous example. As will be recalled, two values of the creep threshold stress (A.sub.o ' and A.sub.o " ) were there developed--each value of creep threshold stress being for a different value of applied normal stress. These two values of creep threshold stress are then plotted in the shearing stress-normal stress plane, or .sigma. and .tau. plot (FIG. 8). In FIG. 8, the two values A.sub.o ' and A.sub.o " define a line 68 which is labeled the CREEP ENVELOPE (or creep failure envelope). Beneath the CREEP ENVELOPE is the stable zone for the soil.

It will be appreciated that the CREEP ENVELOPE in the present example was determined from only two sets of deformation data; and in the interest of reliability and accuracy, one may wish to generate a number of creep threshold stresses (by changing the normal shearing force on the soil surrounding the bore hole). However, in either case, the inventive method permits an empirical determination of the CREEP ENVELOPE on an in situ basis for the design of stable slopes.

In distinguishing this empirical approach to the determination of a minimum creep stress from the prevailing prior approach, the inventive method may be compared to the conventional method by referring to FIG. 8. In FIG. 8, the solid line 69 represents the linear Coulomb relation (i.e., .tau. = C + .sigma. tan .phi. where .tau. is shearing strength, C is cohesion, .sigma. is the normal stress, and tan .phi. is the angle of internal friction) for quick shear.

In this prior method, a maximum allowable shearing stress is calculated based on a calculated value of normal stress; and the result is divided by a "factor of safety" to give an allowable value. Since the normal stress usually varies along the potential shear surface depending on the geometry of a problem, equations and charts have been drawn by expert members of the profession, which equations utilize the parameters C and .phi. to describe the shearing resistance of the soil, and .gamma. to describe its bulk density.

For example, the well-known Terzaghi equation for the maximum bearing capacity of a long footing is:

where q.sub.o represents the bearing capacity, .gamma. and C are soil parameters as previously described, b is the width of the footing, D.sub.f is the depth of the footing below the adjacent ground surface, and N , N.sub.c and N.sub.q are dimensionless parameters which depend on the soil friction angle .phi.. In the graph of FIG. 7, .phi. is approximately 25.degree., which gives according to the Terzaghi calculation N =10, N.sub.c =25, and N.sub.q =14. Using these values and C = 1,000 pounds per square foot we may for example calculate the bearing capacity of a 4-foot wide footing located at 5 feet depth in soil with .gamma. =120 pounds per cubic foot:

By the prior method this would be divided by an appropriate "factor of safety" which is usually of the order of 2 to 5, depending on the cost of the building, presumed reliability of the soil data, and willingness of the owner to pay for apparent over-design or accept a risk of failure. A common compromise is a factor of safety of 3.0, which would give an allowable bearing capacity of

a = 35,800 .div. 3 = 11,933 pounds per foot.

The same mathematical solutions may be used with the parameters for creep strength C.sub.o and .phi..sub.o substituted for the normal shear strength parameters C and .phi., and applying a relatively low factor of safety because of the greater assurance of the soil data. From the data of FIG. 7, C.sub.o = 0 and .phi..sub.o = 25.degree., which gives for the bearing capacity by the Terzaghi equations:

which is somewhat higher than the prior method solutions with a presumed "factor of safety" of 3.0. Thus the true safety factor with conventional design would be much less than 3.0, and in fact in this case would have been 12,800 .div. 11,933 = 1.07, indicating that the prior method design was on the verge of failure, and if the used "factor of safety" had been 2.5, as is often the case, the footing and building would have failed. The use of the term "factor of safety" to describe the divisive factor used to overcome deficiencies and inadequacies in the soil strength data has been widely criticized within the soil engineering profession. By use of more accurate soil data as made possible by the instant method, the "factor of safety," may be safely reduced, a value of 1.2 to 2.0 being tentatively suggested. Whereas in some cases as in the example illustrated this will result in a more conservative and safer design, in other cases it will allow recognition of an overly conservative design and institution of design economies.

It will be appreciated that the present invention provides a more accurate method of empirically determining the creep failure envelope while maintaining all the advantages of in situ testing.

Having thus described a preferred embodiment of the inventive method, it will be obvious that other apparatus may be employed while continuing to practice the inventive principle; further, that certain variations in the method are possible without departing from the inventive principle. It is, therefore, intended that all such modifications and equivalents be covered as they are embraced within the spirit and scope of the invention.

* * * * *


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