U.S. patent application number 17/137388 was filed with the patent office on 2021-04-22 for experimental test method for subcritical propagation rate of rock fractures based on triaxial stress - strain curve.
This patent application is currently assigned to Chengdu University of Technology. The applicant listed for this patent is Chengdu University of Technology. Invention is credited to Kun Chang, Guanchang Pan, Jiping She, Xinyang Wang, Bin Yang, Yang Yang, Hao Zhang, Ying Zhong.
Application Number | 20210116341 17/137388 |
Document ID | / |
Family ID | 1000005339916 |
Filed Date | 2021-04-22 |
![](/patent/app/20210116341/US20210116341A1-20210422-D00000.png)
![](/patent/app/20210116341/US20210116341A1-20210422-D00001.png)
![](/patent/app/20210116341/US20210116341A1-20210422-D00002.png)
![](/patent/app/20210116341/US20210116341A1-20210422-D00003.png)
![](/patent/app/20210116341/US20210116341A1-20210422-M00001.png)
![](/patent/app/20210116341/US20210116341A1-20210422-M00002.png)
![](/patent/app/20210116341/US20210116341A1-20210422-M00003.png)
![](/patent/app/20210116341/US20210116341A1-20210422-M00004.png)
![](/patent/app/20210116341/US20210116341A1-20210422-M00005.png)
![](/patent/app/20210116341/US20210116341A1-20210422-M00006.png)
![](/patent/app/20210116341/US20210116341A1-20210422-M00007.png)
View All Diagrams
United States Patent
Application |
20210116341 |
Kind Code |
A1 |
Zhang; Hao ; et al. |
April 22, 2021 |
experimental test method for subcritical propagation rate of rock
fractures based on triaxial stress - strain curve
Abstract
The invention discloses an experimental test method for
subcritical propagation rate of rock fractures based on triaxial
stress-strain curve, including: Step 1: preparing test sample core
for experiment; Step 2: putting core into triaxial rock mechanics
test system, applying constant radial confining pressure to core,
and applying axial stress in the axial direction until the core is
macroscopically damaged; recording experimental parameters of axial
stress, strain and corresponding loading time of the core; Step 3:
drawing stress-strain curve of the test core according to detection
data points of axial stress and axial strain; Step 4: in the
stress-strain curve of the test core, starting time and ending time
of the subcritical propagation stage of fractures inside the core
correspond to the initiation stress .sigma.ci and damage stress
.sigma.cd, respectively, and calculating subcritical propagation
rate of the subcritical fracture propagation stage of the test
core.
Inventors: |
Zhang; Hao; (Chengdu,
CN) ; Yang; Bin; (Chengdu, CN) ; Zhong;
Ying; (Chengdu, CN) ; Yang; Yang; (Chengdu,
CN) ; She; Jiping; (Chengdu, CN) ; Pan;
Guanchang; (Chengdu, CN) ; Chang; Kun;
(Chengdu, CN) ; Wang; Xinyang; (Chengdu,
CN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Chengdu University of Technology |
Chengdu |
|
CN |
|
|
Assignee: |
Chengdu University of
Technology
CHENGDU
CN
|
Family ID: |
1000005339916 |
Appl. No.: |
17/137388 |
Filed: |
December 30, 2020 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01N 2203/0003 20130101;
G01N 2203/0256 20130101; G01N 2203/023 20130101; G01N 2203/0067
20130101; E21B 49/02 20130101; G01N 3/08 20130101; G01N 2203/0266
20130101; G01N 2203/0682 20130101; G01N 2203/0688 20130101; G01N
2203/0075 20130101; G01N 2203/0019 20130101; G01N 2203/0676
20130101; G01N 33/24 20130101; G01N 2203/0066 20130101 |
International
Class: |
G01N 3/08 20060101
G01N003/08; G01N 33/24 20060101 G01N033/24; E21B 49/02 20060101
E21B049/02 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 31, 2019 |
CN |
201911413223.X |
Claims
1. An experimental test method for subcritical propagation rate of
rock fractures based on triaxial stress-strain curve, comprising
the following steps: Step 1: preparing a test sample for
experiment: drilling and cutting a core used in the experiment, and
then drying the core to constant weight at a set temperature; Step
2: putting the dried core into a GCTS triaxial rock mechanics test
system, applying constant radial confining pressure to the core,
and then applying axial stress in an axial direction until the core
is macroscopically damaged; meanwhile, recording experimental
parameters of axial stress, strain and corresponding loading time
of the core throughout the loading test; Step 3: drawing a
stress-strain curve of the test core according to detection data
points of axial stress and axial strain during the experimental
loading process, and dividing the curve into the following five
stages: Stage I is defined as a compaction stage at which fractures
in the core are closed under stress, but for the dense core, this
stage is often not obvious and difficult to distinguish; Stage II
is defined as an elastic deformation stage at which pores between
particles in the core are compressed and deformed but the fractures
do not propagate, the core is deformed uniformly, and the
stress-strain curve is approximately straight; Stage III is defined
as a stable fracture propagation stage of which a starting point
corresponds to an initiation stress .sigma.ci of the test core;
when the applied stress is greater than the initiation stress, the
small fractures in the core will slowly propagate with the increase
of load, causing the whole rock to expand volumetrically; with
further propagation, external micro-fractures in the core begin to
arrange in a direction gradually; in this stage, the stress-strain
curve is also approximately straight; Stage IV is defined as an
unstable fracture propagation stage of which the stress at the
starting point is called fracture damage stress .sigma.cd; from the
starting point, the fracture propagation rate increases rapidly,
and the state of the core changes from volume compression to volume
expansion; the fractures will unstably propagate and begin to join
together, eventually making the sample completely damaged; and
Stage V is defined as a post-peak deformation stage of which the
starting point of this stage is a peak stress of the curve, that
is, the uniaxial/triaxial compressive strength .sigma.c of the
core; Step 4: in the stress-strain curve of the test core, a
starting time and a ending time of Stage III, correspond to the
initiation stress .sigma..sub.ci and the damage stress
.sigma..sub.cd, respectively; when the applied axial stress is
greater than the fracture initiation stress .sigma..sub.ci, the
fractures will continue to propagate slowly, but when the applied
stress disappears, the fractures will stop propagating and will not
damage the core macroscopically; when the applied axial stress is
greater than the fracture damage stress .sigma.cd, the fractures
will enter the Stage IV; calculating the initiation stress
.sigma.ci and the damage stress .sigma.cd of the fracture based on
the stress-strain curve of the test core, and working out the
starting time Tci and the ending time Tcd of the subcritical
fracture propagation corresponding to the initiation stress
.sigma.ci and the damage stress .sigma.cd of the fracture according
to the relationship between the axial stress and the time obtained
by monitoring the test process; further calculating fracture
lengths Cci and Ccd corresponding to the initiation stress
.sigma.ci and the damage stress .sigma.cd of the fracture according
to theory of fracture mechanics; then calculating subcritical
propagation rate of the Stage III of the test core according to
Formula (1): u = C c i - C c d T c i - T c d ; ( 1 ) ##EQU00016##
where, u--the subcritical propagation rate of the fracture in the
test core in the subcritical propagation stage, in m/s; Tci and
Tcd--the starting time and the ending time of the subcritical
fracture propagation stage in the loading process of the test core,
in s; Cci and Ccd--the fracture lengths at the starting time and
the ending time of the subcritical fracture propagation stage of
the test core, in m; Step 5: in the stress-strain curve of the test
core, the fractures do not propagate and are usually in a
compressed state before the Stage III so the fracture volume strain
of the core generally increases with the increase of axial strain;
after entering the Stage III, the existing micro fractures in the
core slowly propagate as the axial stress increases, resulting in
the overall volume expansion of the core, and the volume of the
core fractures begins to change from compression to expansion,
therefore, the fracture volume strain starts to decrease with the
increase of axial strain; the axial stress corresponding to the
turning point where the fracture volume strain of the test core
changes from increasing to decreasing with the axial strain is the
fracture initiation stress .sigma..sub.ci of the core; wherein, for
the test core, the total volume strain .epsilon.v in the loading
process is composed of an elastic volume strain and a fracture
volume strain: .epsilon..sub.v=.epsilon..sub.ev+.epsilon..sub.fv
(2); where: .epsilon.v--the total volume strain of the test core in
loading process, dimensionless; .epsilon.ev--the elastic volume
strain of the test core in loading process, dimensionless;
.epsilon.fv--the fracture volume strain of the test core in loading
process, dimensionless; the total volume strain of the test core
satisfies the following relationship with its axial strain and
radial strain: .epsilon..sub.v=.epsilon..sub.1+2.epsilon..sub.3
(3); where: .epsilon.1 and .epsilon.3--an axial strain and a radial
strain of the test core in loading process, dimensionless, which is
directly monitored in the stress-strain curve test of the core;
according to Hooke's law, the theoretical elastic volume strain of
rock is calculated by the following formula: e v = 1 - 2 v E (
.sigma. 1 + 2 .sigma. 3 ) ; ( 4 ) ##EQU00017## where: .sigma.1--the
axial stress of the test core in loading process, in MPa;
.sigma.3--the radial stress under constant confining pressure
applied by the test equipment to the core, in MPa; E--the elastic
modulus of the test core, in GPa; .nu.--a Poisson's ratio of the
test core, dimensionless; combined with Formulas (2) to (4), the
fracture volume strain calculation formula of the test core is
obtained as follows: f v = 1 + 2 3 - 1 - 2 v E ( .sigma. 1 + 2
.sigma. 3 ) ; ( 5 ) ##EQU00018## according to the calculation
results, taking the axial strain as the abscissa and drawing the
fracture volume strain-axial strain curve of the core in the
testing process.
2. The experimental test method for subcritical propagation rate of
rock fractures based on triaxial stress-strain curve according to
claim 1, further comprising: Step 6: in the Stage III, although the
fracture volume of the test core begins to change from compression
to expansion, the core is still under compression, and the total
volume strain increases with the increase in axial strain; when the
fracture enters the Stage IV, the fracture propagation rate
increases sharply, the total volume of the core changes from
compression to expansion, and the total volume strain begins to
decrease with the increase of axial strain; the axial stress
corresponding to the turning point where the axial strain changes
from increasing to decreasing with the axial strain is the damage
stress .sigma..sub.cd of the core; and Step 7: according to the
above experimental test and calculation results, with the axial
strain of the core as the abscissa, drawing the axial stress-axial
strain curve, a fracture volume strain-axial strain curve, and a
total volume strain-axial strain curve; based on a turning point
where the fracture volume strain and the total volume strain first
increase and then decrease with the axial strain, the fracture
initiation stress .sigma..sub.ci and the damage stress
.sigma..sub.cd of the core at the starting time and the ending time
of the Stage III is directly determined on the stress-strain curve;
drawing the axial stress-loading time curve of the test process,
and determining the starting time T.sub.ci and the ending time
T.sub.cd of the subcritical fracture propagation stage on the basis
of the initiation stress and damage stress of the core.
3. The experimental test method for subcritical propagation rate of
rock fractures based on triaxial stress-strain curve according to
claim 2, further comprising: Step 8: for the test core under both
radial confining pressure and axial compression, the internal
fractures are closed under compression, and the effective shear
stress on the fracture surface is expressed as follows:
.tau..sub.eff=.tau..sub.n-.mu..sigma..sub.n=1/2(.sigma..sub.1-.sigma..sub-
.3)sin 2.beta.-.mu.(.sigma..sub.1 sin.sup.2.beta.+.sigma..sub.3
cos.sup.2.beta.) (6); where: .tau..sub.eff--an effective shear
stress of the test core on fracture surface, in MPa; .tau.n and
.sigma.m--a shear stress and a normal stress of the test core on
fracture surface, in MPa; .mu.--a friction coefficient of fracture
surface of the test core, dimensionless; .beta.--an inclination
angle of fracture surface of the test core, in .degree.; the stress
intensity factor of fracture tip inside the test core is: K.sub.II=
{square root over (.pi.C)}.tau..sub.eff= {square root over
(.pi.C)}[1/2(.sigma..sub.1-.sigma..sub.3)sin
2.beta.-.mu.(.sigma..sub.1 sin.sup.2.beta.+.sigma..sub.3
cos.sup.2.beta.)] (7); where: KII--a type II shear stress intensity
factor of the test core at fracture tip, in MPam0.5; C--the
fracture length of the test core in a certain stress state, in m;
when the stress intensity factor KII of the fracture tip inside the
core is greater than the fracture toughness KIIC of the core, the
core fracture enters the Stage IV; as there is more than one
fracture in the test core, the inclination angle of the fracture
that preferentially enters the unstable propagation stage usually
satisfies the following formula: tan 2 .beta. = 1 .mu. ; ( 8 )
##EQU00019## when the stress intensity factor KII of the fracture
tip inside the core is just equal to the fracture toughness KIIC,
and the core fracture is just at a critical point between the Stage
III and the Stage IV, the axial stress on the core at this moment
is just equal to its damage stress; the following formula is
obtained by combining Formulas (6) to (8): C c d = 1 .pi. [ 2 K I I
C ( .mu. 2 + 1 + .mu. ) .sigma. c d - ( .mu. 2 + 1 + .mu. ) 2
.sigma. 3 ] 2 ; ( 9 ) ##EQU00020## after obtaining the relevant
parameters of the damage stress of the test core, the fracture
length Ccd of the test core at the ending time of the subcritical
fracture propagation is obtained according to Formula (9); Step 9:
for the test core without subcritical fracture propagation but only
with micro fractures developed inside, at the starting time of the
subcritical fracture propagation stage, the fractures inside the
core are usually only a few microns to tens of microns long, which
is far less than the fracture length at the ending time of the
subcritical propagation stage, so the initial fracture length Cci
is approximately taken as zero; and Step 10: according to the above
experimental test and calculation results, obtaining the fracture
lengths Cci and Ccd and the corresponding time Tci and Tcd at the
starting time and the ending time of the subcritical fracture
propagation of the test core, and calculating the subcritical
fracture expansion rate of the core in the subcritical fracture
expansion stage according to Formula (1).
4. The experimental test method for subcritical propagation rate of
rock fractures based on triaxial stress-strain curve according to
claim 1, wherein the rock used as the experimental test sample is
cylindrical, and the core is cut out with a diameter of 2.5 cm and
a length of 5.0 cm; it is required that there are no visible
fractures in the core and the drying temperature of the core is set
at 60.degree. C.
Description
BACKGROUND OF THE INVENTION
Technical Field
[0001] The present invention relates to the technical field of rock
mechanics research, in particular to the field of subcritical
propagation mechanics of rock fracture, more specifically relating
to an experimental test method for subcritical propagation rate of
rock fractures based on triaxial stress-strain curve.
Description of Prior Art
[0002] To deepen the understanding of the forming mechanism of
formation fractures, research on rock mechanics can effectively
improve fracturing efficiency and increase oil and gas production.
At present, the mainstream method is to use Griffith fracture
theory, which believes that the equilibrium fracture condition of
ideal brittle solid is determined by the surface energy of the
solid in vacuum. However, most materials such as rocks actually
fracture in environmental medium, and the environmental medium has
a very significant impact on fracture process. The most obvious
manifestation is that under the action of environmental medium,
fractures may propagate slowly under the continuous action of load
far lower than the applied critical stress. This kind of
propagation is also known as subcritical fracture propagation. In
oil and gas production, the subcritical fracture propagation is
relatively common, the most typical of which is subcritical
fracture propagation in formation rocks under the action of
external fluids after the original crustal stress balance is
destroyed in the drilling and completion process and the hydraulic
fracturing process. It is significant to study the fracture
propagation rate in subcritical propagation process for the
analysis and prevention of wellbore instability during drilling and
completion, and for optimization of shut-in measures after
hydraulic fracturing.
[0003] The existing methods to measure the subcritical propagation
rate of fractures in solid materials mainly include the
double-cantilever sample method and the double-torsion sample
method. As explained by Swanson et al. (Swanson P L. Subcritical
fracture growth and other time- and environment-dependent behavior
in crustal rocks [J]. Journal of Geophysical Research: Solid Earth,
1984, 89(B6):4137-52), the double-cantilever beam sample method is
mainly to treat the mechanical cut in the length direction of the
sample, then applies the same tensile load at both ends of the cut,
and establish stress intensity factor of fracture tip or relational
expression between mechanical energy release rate and fracture
extension length to analyze the subcritical propagation rate of
fractures. This method is widely used to test fracture propagation
rate of crystal materials and glass. The double-torsion sample
method, also known as load-relaxation method at constant
displacement, is mainly used to test the subcritical propagation
rate of fractures in ceramic materials and rocks. With this method,
it is required to machine the sample into a rectangular thin plate
(180 mm.times.60 mm.times.4 mm in size, with polished surface), and
mechanically make an artificial fracture along the center of one
side of the sample (a cut of 10 mm long and 1 mm wide) and a guide
groove (1 mm wide and as high as 1/3 of the width) throughout the
long axis. A four-point bending load is applied at the fracture
breakpoint to promote the fracture propagation, and then the
fracture propagation rate is calculated with relevant formulas. The
advantages of the above two methods lie in that the post-processing
of experimental data is relatively simple, a rate curve can be
obtained from a sample, and the data continuity is sound. However,
their limitations are also obvious: (1) The sample preparation
process of the two test methods is complicated and requires
artificial fracture prefabrication, but cannot completely reflect
the subcritical propagation process of natural fractures inside the
samples; (2) Due to the special configuration of samples, neither
of these two test methods can apply effective stress (confining
pressure) in the test, greatly restricting the study on subcritical
fracture propagation under high effective stress.
[0004] In the process of drilling, completion and hydraulic
fracturing of oil and gas production, the subcritical propagation
of fractures in deep formation usually takes place under the action
of high effective stress. Therefore, in view of the shortcomings of
the existing experimental test method for subcritical propagation
rate of rock fractures, the present invention proposes an
experimental test method for subcritical propagation rate of rock
fractures based on triaxial stress-strain curve, so as to realize
the experimental test for the subcritical propagation rate of rock
fractures under high effective stress.
SUMMARY OF THE INVENTION
[0005] The technical solution of the present invention is as
follows:
[0006] An experimental test method for subcritical propagation rate
of rock fractures based on triaxial stress-strain curve, comprising
the following steps:
[0007] Step 1: Prepare the test sample for the experiment: drill
and cut the core used in the experiment and then dry the core at
set temperature to constant weight;
[0008] Step 2: Put the dried core into the GCTS triaxial rock
mechanics test system, apply constant radial confining pressure to
the core, and then apply axial stress in the axial direction until
the core is macroscopically damaged; meanwhile, record the
experimental parameters of axial stress, strain and corresponding
loading time of the core throughout the loading test;
[0009] Step 3: Draw the stress-strain relation curve of the test
core according to the detection data points of axial stress and
axial strain during the experimental loading process, and divide
the curve into the following five stages:
[0010] Stage I is defined as compaction stage at which the fracture
in the core is closed under stress, but for the dense core, this
stage is often not obvious and difficult to distinguish;
[0011] Stage II is defined as elastic deformation stage at which
the pores between particles in the core are compressed and deformed
but the fractures do not propagate, the core is deformed uniformly,
and the stress-strain curve is approximately straight;
[0012] Stage III is defined as stable fracture propagation stage of
which the starting point corresponds to the initiation stress
.sigma..sub.ci of the test core; when the applied stress is greater
than the initiation stress, the small fractures in the core will
slowly propagate with the increase of load, causing the whole rock
to expand volumetrically; with further propagation, the external
micro-fractures in the core begin to arrange in a direction
gradually; in this stage, the stress-strain curve is also
approximately straight;
[0013] Stage IV is defined as unstable fracture propagation stage
of which the stress at the starting point is called fracture damage
stress .sigma..sub.cd; from the starting point, the fracture
propagation rate increases rapidly, and the state of the core
changes from volume compression to volume expansion; the fractures
will unstably propagate and begin to join together, eventually
making the sample completely damaged;
[0014] Stage V is defined as post-peak deformation stage of which
the starting point of this stage is the peak stress of the curve,
that is, the uniaxial/triaxial compressive strength a of the
core;
[0015] Step 4: In the stress-strain curve of the test core, the
starting and ending time of Stage III, i.e., the subcritical
propagation stage of fractures inside the core, correspond to the
initiation stress .sigma..sub.ci and damage stress .sigma..sub.cd,
respectively; when the applied axial stress is greater than the
fracture initiation stress .sigma..sub.ci, the fractures will
continue to propagate slowly, but when the applied stress
disappears, the fractures will stop propagating and will not damage
the core macroscopically; when the applied axial stress is greater
than the fracture damage stress .sigma..sub.cd, the fractures will
enter the rapid unstable propagation stage, i.e., Stage IV;
[0016] Calculate the initiation stress .sigma..sub.ci and damage
stress .sigma..sub.cd of the fracture based on the stress-strain
curve of the test core, and work out the starting and ending time
T.sub.ci and T.sub.cd of the subcritical fracture propagation
corresponding to the initiation stress .sigma..sub.ci and damage
stress .sigma..sub.cd of the fracture according to the relationship
between the axial stress and the time obtained by monitoring the
test process; further calculate the fracture lengths C.sub.ci and
C.sub.cd corresponding to the initiation stress .sigma..sub.ci and
damage stress .sigma..sub.cd of the fracture according to the
theory of fracture mechanics; then calculate subcritical
propagation rate of Stage III, i.e., the subcritical fracture
propagation stage of the test core according to Formula (1):
u = C ci - C c d T ci - T c d . ( 1 ) ##EQU00001##
[0017] Where, u--subcritical propagation rate of the fracture in
the test core in the subcritical propagation stage, in m/s;
[0018] T.sub.ci and T.sub.cd--Starting and ending time of the
subcritical fracture propagation stage in the loading process of
the test core, in s;
[0019] C.sub.ci and C.sub.cd--Fracture length at the starting and
ending time of the subcritical fracture propagation stage of the
test core, in m.
[0020] Further, Step 5: in the stress-strain curve of the test
core, fractures do not propagate and are usually in a compressed
state before the subcritical fracture propagation stage (Stage
III), so the fracture volume strain of the core generally increases
with the increase of axial strain; after entering the subcritical
fracture propagation stage, i.e., Stage III, the existing micro
fractures in the core slowly propagate as the axial stress
increases, resulting in the overall volume expansion of the core,
and the volume of the core fractures begins to change from
compression to expansion, therefore, the fracture volume strain
starts to decrease with the increase of axial strain; the axial
stress corresponding to the turning point where the fracture volume
strain of the test core changes from increasing to decreasing with
the axial strain is the fracture initiation stress .sigma..sub.ci
of the core.
[0021] Further, for the test core, the total volume strain
.epsilon..sub.v in the loading process is composed of elastic
volume strain and fracture volume strain:
.epsilon..sub.v=.epsilon..sub.ev+.epsilon..sub.fv (2).
[0022] Where: .epsilon..sub.v--Total volume strain of the test core
in loading process, dimensionless;
[0023] .epsilon..sub.ev--Elastic volume strain of the test core in
loading process, dimensionless;
[0024] .epsilon..sub.fv--Fracture volume strain of the test core in
loading process, dimensionless.
[0025] At the same time, the total volume strain of the test core
also satisfies the following relationship with its axial strain and
radial strain:
.epsilon..sub.v=.epsilon..sub.1+2.epsilon..sub.3 (3).
[0026] Where: .epsilon..sub.1 and .epsilon..sub.3--Axial strain and
radial strain of the test core in loading process, dimensionless,
which can be directly monitored in the stress-strain curve test of
the core;
[0027] According to Hooke's law, the theoretical elastic volume
strain of rock can be calculated by the following formula:
e v = 1 - 2 v E ( .sigma. 1 + 2 .sigma. 3 ) . ( 4 )
##EQU00002##
[0028] Where: .sigma..sub.1--Axial stress of the test core in
loading process, in MPa;
[0029] .sigma..sub.3--Radial stress under constant confining
pressure applied by the test equipment to the core, in MPa;
[0030] E--Elastic modulus of the test core, in GPa; [0031]
.nu.--Poisson's ratio of the test core, dimensionless;
[0032] Combined with Formulas (2) to (4), the fracture volume
strain calculation formula of the test core can be obtained as
follows:
fv = 1 + 2 3 - 1 - 2 v E ( .sigma. 1 + 2 .sigma. 3 ) . ( 5 )
##EQU00003##
[0033] Further, Step 6: in the subcritical fracture propagation
stage, i.e., Stage III, although the fracture volume of the test
core begins to change from compression to expansion, the core is
still under compression, and the total volume strain increases with
the increase in axial strain; when the fracture enters the unstable
propagation stage, i.e., Stage IV, the fracture propagation rate
increases sharply, the total volume of the core changes from
compression to expansion, and the total volume strain begins to
decrease with the increase of axial strain; the axial stress
corresponding to the turning point where the axial strain changes
from increasing to decreasing with the axial strain is the damage
stress .sigma..sub.cd of the core;
[0034] Step 7: According to the above experimental test and
calculation results, with the axial strain of the core as the
abscissa, draw the curves, i.e., the axial stress-axial strain
curve, fracture volume strain-axial strain curve and total volume
strain-axial strain curve; based on the turning point where the
fracture volume strain and total volume strain first increase and
then decrease with the axial strain, the fracture initiation stress
.sigma..sub.ci and damage stress .sigma..sub.cd of the core at the
starting and ending time of the subcritical fracture propagation
stage (Stage III) can be directly determined on the stress-strain
curve; furthermore, draw the axial stress-loading time curve of the
test process, and determine the starting and ending time T.sub.ci
and T.sub.cd of the subcritical fracture propagation stage on the
basis of the initiation stress and damage stress of the core.
[0035] Further, Step 8: for the test core under both radial
confining pressure and axial compression, the internal fractures
are closed under compression, and the effective shear stress on the
fracture surface is expressed as follows:
.tau..sub.eff=.tau..sub.n-.mu..sigma..sub.n=1/2(.sigma..sub.1-.sigma..su-
b.3)sin 2.beta.-.mu.(.sigma..sub.1 sin.sup.2.beta.+.sigma..sub.3
cos.sup.2.beta.) (6).
[0036] Where: .tau..sub.eff--Effective shear stress of the test
core on fracture surface, in MPa;
[0037] .tau..sub.n and .sigma..sub.n--Shear stress and normal
stress of the test core on fracture surface, in MPa;
[0038] .mu.--Friction coefficient of fracture surface of the test
core, dimensionless;
[0039] .beta.--Inclination angle of fracture surface of the test
core, in .degree.;
[0040] The stress intensity factor of fracture tip inside the test
core is:
K.sub.II= {square root over (.pi.C)}.tau..sub.eff= {square root
over (.pi.C)}[1/2(.sigma..sub.1-.sigma..sub.3)sin
2.beta.-.mu.(.sigma..sub.1 sin.sup.2.beta.+.sigma..sub.3
cos.sup.2.beta.)] (7).
[0041] Where: K.sub.II--Type II shear stress intensity factor of
the test core at fracture tip, in MPam.sup.0.5;
[0042] C--Fracture length of the test core in a certain stress
state, in m;
[0043] When the stress intensity factor K.sub.II of the fracture
tip inside the core is greater than the fracture toughness
K.sub.IIC of the core, the core fracture enters the unstable
propagation stage (Stage IV); at the same time, as there is more
than one fracture in the test core, the inclination angle of the
fracture that preferentially enters the unstable propagation stage
usually satisfies the following formula:
tan 2 .beta. = 1 .mu. . ( 8 ) ##EQU00004##
[0044] When the stress intensity factor K.sub.II of the fracture
tip inside the core is just equal to the fracture toughness
K.sub.IIC, that is, the core fracture is just at the critical point
between the subcritical fracture propagation stage (Stage III) and
the unstable propagation stage (Stage IV), the axial stress on the
core at this moment is just equal to its damage stress; the
following formula can be obtained by combining Formula (6) to
(8):
C c d = 1 .pi. [ 2 K IIC ( .mu. 2 + 1 + .mu. ) .sigma. c d - ( .mu.
2 + 1 + .mu. ) 2 .sigma. 3 ] 2 . ( 9 ) ##EQU00005##
[0045] After obtaining the relevant parameters of the damage stress
of the test core, the fracture length C.sub.cd of the test core at
the ending time of the subcritical fracture propagation can be
obtained according to Formula (9);
[0046] Step 9: For the test core without subcritical fracture
propagation but only with micro fractures developed inside, at the
starting time of the subcritical fracture propagation stage, the
fractures inside the core are usually only a few microns to tens of
microns long, which is far less than the fracture length at the
ending time of the subcritical propagation stage, so normally, the
initial fracture length C.sub.c, can be approximately taken as
zero;
[0047] Step 10: According to the above experimental test and
calculation results, obtain the fracture length C.sub.ci and
C.sub.cd and the corresponding time T.sub.ci and T.sub.cd at the
starting and ending time of the subcritical fracture propagation of
the test core, and calculate the subcritical fracture expansion
rate of the core in the subcritical fracture expansion stage
according to Formula (1).
[0048] Further, the rock used as the experimental test sample is
cylindrical, and the core is cut out with a diameter of 2.5 cm and
a length of 5.0 cm; it is required that there are no visible
fractures in the core and the drying temperature of the core is set
at 60.degree. C.
[0049] The present invention has the following beneficial
effects:
[0050] (1) The method disclosed in the present invention adopts a
small core plunger sample for testing. It only needs to drill and
cut the core, without prefabricated artificial fractures and
surface polishing. Compared with the double-torsion sample method
commonly used in the prior art, the core preparation process is
greatly simplified, and the success rate of sample preparation and
test is enhanced significantly;
[0051] (2) Compared with the double-torsion sample method, the
method disclosed in the present invention does not require
artificial fracture prefabrication but can reflect the subcritical
propagation process of the original natural fractures in the
core;
[0052] (3) The present invention innovatively deduces the
calculation formula of the subcritical fracture propagation rate of
the core in the subcritical propagation stage, which greatly
simplifies the experimental data acquisition and can obtain more
accurate results;
[0053] (4) The double-torsion sample method can only test the
subcritical propagation rate of the rock under point load, but
cannot test the subcritical propagation rate of the fracture under
high applied effective stress; it is difficult to reflect the
influence of the effective formation stress on the subcritical
propagation of the fracture; the method disclosed in the present
invention can simulate the high effective stress of deep reservoir
to test the subcritical fracture propagation rate of the core.
BRIEF DESCRIPTION OF THE DRAWINGS
[0054] FIG. 1A and FIG. 1B show the axial stress/fracture volume
strain/total volume strain-axial strain curves of the test cores
L-1 and L-2 in the embodiment.
[0055] FIG. 2A and FIG. 2B show the axial stress-loading time curve
of the test core.
[0056] FIG. 3A and FIG. 3B show the fracture image observed by
scanning electron microscope when the test core does not
subcritically propagate before the experiment.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0057] The present invention is further described with reference to
the drawings and embodiments.
[0058] An experimental test method for subcritical propagation rate
of rock fractures based on triaxial stress-strain curve, comprising
the following steps:
[0059] Step 1: Prepare the test sample for the experiment according
to the rock sample preparation method stated in SYT5358-2010: drill
and cut a core with a diameter of about 2.5 cm and a length of
about 5.0 cm, without visible fractures, and dry the core the core
at 60.degree. C. to constant weight.
[0060] Step 2: Put the dried core into the GCTS triaxial rock
mechanics test system, apply constant confining pressure (radial
stress) to the core, and then apply axial stress in the axial
direction until the core is macroscopically damaged; meanwhile,
record the experimental parameters of axial stress, strain and
corresponding loading time of the core throughout the loading
test.
[0061] Step 3: Draw the stress-strain relation curve of the test
core according to the detection data points of axial stress and
axial strain during the experimental loading process, and generally
divide the curve into the following five stages: Stage I is defined
as compaction stage at which the fracture in the core is closed
under stress, but for the dense core, this stage is often not
obvious and difficult to distinguish; Stage II is defined as
elastic deformation stage at which the pores between particles in
the core are compressed and deformed but the fractures do not
propagate, the core is deformed uniformly, and the stress-strain
curve is approximately straight; Stage III is defined as stable
fracture propagation stage of which the starting point corresponds
to the initiation stress .sigma..sub.ci of the test core; when the
applied stress is greater than the initiation stress, the small
fractures in the core will slowly propagate with the increase of
load, causing the whole rock to expand volumetrically; with further
propagation, the external micro-fractures in the core begin to
arrange in a direction gradually; in this stage, the stress-strain
curve is also approximately straight; Stage IV is defined as
unstable fracture propagation stage of which the stress at the
starting point is called fracture damage stress .sigma..sub.cd;
from the starting point, the fracture propagation rate increases
rapidly, and the state of the core changes from volume compression
to volume expansion; the fractures will unstably propagate and
begin to join together, eventually making the sample completely
damaged; Stage V is defined as post-peak deformation stage of which
the starting point of this stage is the peak stress of the curve,
that is, the uniaxial/triaxial compressive strength a of the
core.
[0062] Step 4: In the stress-strain curve of the test core, the
starting and ending time of Stage III, i.e., the subcritical
propagation stage of fractures inside the core, correspond to the
initiation stress .sigma..sub.ci and damage stress .sigma..sub.cd,
respectively; when the applied axial stress is greater than the
fracture initiation stress the fractures will continue to propagate
slowly, but when the applied stress disappears, the fractures will
stop propagating and will not damage the core macroscopically; when
the applied axial stress is greater than the fracture damage stress
.sigma..sub.cd, the fractures will enter the rapid unstable
propagation stage (Stage IV).
[0063] Calculate the initiation stress .sigma..sub.ci and damage
stress .sigma..sub.cd of the fracture based on the stress-strain
curve of the test core, and work out the starting and ending time
T.sub.ci and T.sub.cd of the subcritical fracture propagation
corresponding to the initiation stress .sigma..sub.ci and damage
stress .sigma..sub.cd of the fracture according to the relationship
between the axial stress and the time obtained by monitoring the
test process; further calculate the fracture lengths C.sub.ci and
C.sub.cd corresponding to the initiation stress .sigma..sub.ci and
damage stress .sigma..sub.cd of the fracture according to the
theory of fracture mechanics; then calculate subcritical
propagation rate of the subcritical fracture propagation stage
(Stage III) of the test core according to Formula (1):
u = C c i - C c d T c i - T c d . ( 1 ) ##EQU00006##
[0064] Where, u--subcritical propagation rate of the fracture in
the test core in the subcritical propagation stage, in m/s;
[0065] T.sub.ci and T.sub.cd--Starting and ending time of the
subcritical fracture propagation stage in the loading process of
the test core, in s;
[0066] C.sub.ci and C.sub.cd--Fracture length at the starting and
ending time of the subcritical fracture propagation stage of the
test core, in m.
[0067] Step 5: in the stress-strain curve of the test core,
fractures do not propagate and are usually in a compressed state
before the subcritical fracture propagation stage (Stage III), so
the fracture volume strain of the core generally increases with the
increase of axial strain; after entering the subcritical fracture
propagation stage (Stage III), the existing micro fractures in the
core slowly propagate as the axial stress increases, resulting in
the overall volume expansion of the core, and the volume of the
core fractures begins to change from compression to expansion,
therefore, the fracture volume strain starts to decrease with the
increase of axial strain; the axial stress corresponding to the
turning point where the fracture volume strain of the test core
changes from increasing to decreasing with the axial strain is the
fracture initiation stress .sigma..sub.ci of the core;
[0068] For the test core, the total volume strain .epsilon..sub.v
in the loading process is composed of elastic volume strain and
fracture volume strain:
.epsilon..sub.v=.epsilon..sub.ev+.epsilon..sub.fv (2).
[0069] Where: .epsilon..sub.v--Total volume strain of the test core
in loading process, dimensionless;
[0070] .epsilon..sub.ev--Elastic volume strain of the test core in
loading process, dimensionless;
[0071] .epsilon..sub.fv--Fracture volume strain of the test core in
loading process, dimensionless;
[0072] At the same time, the total volume strain of the test core
also satisfies the following relationship with its axial strain and
radial strain:
.epsilon..sub.v=.epsilon..sub.1+2.epsilon..sub.3 (3).
[0073] Where: .epsilon..sub.1 and .epsilon..sub.3--Axial strain and
radial strain of the test core in loading process, dimensionless,
which can be directly monitored in the stress-strain curve test of
the core;
[0074] According to Hooke's law, the theoretical elastic volume
strain of rock can be calculated by the following formula:
e v = 1 - 2 v E ( .sigma. 1 + 2 .sigma. 3 ) . ( 4 )
##EQU00007##
[0075] Where: .sigma..sub.1--Axial stress of the test core in
loading process, in MPa;
[0076] .sigma..sub.3--Radial stress under constant confining
pressure applied by the test equipment to the core, in MPa;
[0077] E--Elastic modulus of the test core, in GPa;
[0078] .nu.--Poisson's ratio of the test core, dimensionless;
[0079] Combined with Formulas (2) to (4), the fracture volume
strain calculation formula of the test core can be obtained as
follows:
f v = 1 + 2 3 - 1 - 2 v E ( .sigma. 1 + 2 .sigma. 3 ) . ( 5 )
##EQU00008##
[0080] Step 6: in the subcritical fracture propagation stage (Stage
III), although the fracture volume of the test core begins to
change from compression to expansion, the core is still under
compression, and the total volume strain increases with the
increase in axial strain; when the fracture enters the unstable
propagation stage (Stage IV), the fracture propagation rate
increases sharply, the total volume of the core changes from
compression to expansion, and the total volume strain begins to
decrease with the increase of axial strain; similarly, the axial
stress corresponding to the turning point where the axial strain
changes from increasing to decreasing with the axial strain is the
damage stress .sigma..sub.cd of the core.
[0081] Step 7: according to the above experimental test and
calculation results, with the axial strain of the core as the
abscissa, draw the curves, i.e., the axial stress-axial strain
curve, fracture volume strain-axial strain curve and total volume
strain-axial strain curve; based on the turning point where the
fracture volume strain and total volume strain first increase and
then decrease with the axial strain, the fracture initiation stress
.sigma..sub.ci and damage stress .sigma..sub.cd of the core at the
starting and ending time of the subcritical fracture propagation
stage (Stage III) can be directly determined on the stress-strain
curve; furthermore, draw the axial stress-loading time curve of the
test process, and determine the starting and ending time T.sub.ci
and T.sub.cd of the subcritical fracture propagation stage (Stage
III) on the basis of the initiation stress and damage stress of the
core;
[0082] Step 8: for the test core under both radial (confining
pressure) and axial compression, the internal fractures are closed
under compression, and the effective shear stress on the fracture
surface is expressed as follows:
.tau..sub.eff=.tau..sub.n-.mu..sigma..sub.n=1/2(.sigma..sub.1-.sigma..su-
b.3)sin 2.beta.-.mu.(.sigma..sub.1 sin.sup.2.beta.+.sigma..sub.3
cos.sup.2.beta.) (6).
[0083] Where: .tau..sub.eff--Effective shear stress of the test
core on fracture surface, in MPa;
[0084] .tau..sub.n and .sigma..sub.n--Shear stress and normal
stress of the test core on fracture surface, in MPa;
[0085] .mu.--Friction coefficient of fracture surface of the test
core, dimensionless;
[0086] .beta.--Inclination angle of fracture surface of the test
core, in .degree..
[0087] The stress intensity factor of fracture tip inside the test
core is:
K.sub.II= {square root over (.pi.C)}.tau..sub.eff= {square root
over (.pi.C)}[1/2(.sigma..sub.1-.sigma..sub.3)sin
2.beta.-.mu.(.sigma..sub.1 sin.sup.2.beta.+.sigma..sub.3
cos.sup.2.beta.)] (7).
[0088] Where: K.sub.II--Type II shear stress intensity factor of
the test core at fracture tip, in MPam.sup.0.5;
[0089] C--Fracture length of the test core in a certain stress
state, in m.
[0090] When the stress intensity factor K.sub.II of the fracture
tip inside the core is greater than the fracture toughness
K.sub.IIC of the core, the core fracture enters the unstable
propagation stage (Stage IV); at the same time, as there is more
than one fracture in the test core, the inclination angle of the
fracture that preferentially enters the unstable propagation stage
usually satisfies the following formula:
tan 2 .beta. = 1 .mu. . ( 8 ) ##EQU00009##
[0091] When the stress intensity factor K.sub.II of the fracture
tip inside the core is just equal to the fracture toughness
K.sub.IIC, that is, the core fracture is just at the critical point
between the subcritical fracture propagation stage (Stage III) and
the unstable propagation stage (Stage IV), the axial stress on the
core at this moment is just equal to its damage stress; the
following formula can be obtained by combining Formula (6) to
(8):
C c d = 1 .pi. [ 2 K I I C ( .mu. 2 + 1 + .mu. ) .sigma. c d - (
.mu. 2 + 1 + .mu. ) 2 .sigma. 3 ] 2 . ( 9 ) ##EQU00010##
[0092] After obtaining the relevant parameters of the damage stress
of the test core, the fracture length C.sub.cd of the test core at
the ending time of the subcritical fracture propagation can be
obtained according to Formula (9).
[0093] Step 9: For the test core without subcritical fracture
propagation but only with micro fractures developed inside, at the
starting time of the subcritical fracture propagation stage, the
fractures inside the core are usually only a few microns to tens of
microns long, which is far less than the fracture length at the
ending time of the subcritical propagation stage, so normally, the
initial fracture length C.sub.ci can be approximately taken as
zero.
[0094] Step 10: According to the above experimental test and
calculation results, obtain the fracture length (C.sub.ci and
C.sub.cd) and the corresponding time (T.sub.ci and T.sub.cd) at the
starting and ending time of the subcritical fracture propagation of
the test core, and calculate the subcritical fracture expansion
rate of the core in the subcritical fracture expansion stage
according to Formula (1).
EMBODIMENT
[0095] Cores was selected and taken from deep shale formation in a
block in Sichuan Basin to conduct experiments based on the detailed
implementation of the above steps. The specific process is
described as follows.
[0096] Step 1: Select and take cores from deep shale formation in a
block in Sichuan Basin, drill and prepare test cores L-1 and L-2
(Table 1) according to the rock sample preparation method stated in
SYT5358-2010; the cores had no visible fractures and were dried at
60.degree. C. to constant weight.
[0097] Step 2: Put the dried core into the GCTS triaxial rock
mechanics test system, apply constant confining pressure (radial
stress) of 30 MPa to the core, and apply axial stress in the axial
direction after the confining pressure is stable; in order to
satisfy the quasi-static loading requirement in test, the axial
loading rate is only 0.005 mm/s; record the experimental parameters
such as axial stress, strain and corresponding loading time of the
core throughout the loading test until the core is macroscopically
damaged and the loading is stopped.
[0098] Step 3: According to the data on axial stress and axial
strain of the core measured in the experiment, draw the axial
stress-axial strain curve (FIG. 1A and FIG. 1B) of the core with
the axial strain as the abscissa, and generally divide the curve
into the five stages: Stage I, compaction stage; Stage II, elastic
deformation stage; Stage III, stable fracture propagation stage;
Stage IV, unstable fracture propagation stage; and Stage V,
post-peak deformation stage, of which Stage III (stable fracture
propagation stage) is the subcritical fracture propagation stage of
rock; test the subcritical propagation rate of rock fractures; the
key is to clarify the parameters such as the starting and ending
time of the subcritical fracture propagation stage (Stage III) of
the core.
[0099] Step 4: In the stress-strain curve of the test core, the
starting and ending time of the subcritical fracture propagation
stage (Stage III) of the core correspond to the initiation stress
.sigma..sub.ci and damage stress .sigma..sub.cd; after determining
the initiation stress .sigma..sub.ci and damage stress
.sigma..sub.cd of cores L-1 and L-2, obtain the values of starting
and ending time T.sub.ci and T.sub.cd of the subcritical fracture
propagation stage according to the relation curves of axial stress
and loading time of cores L-1 and L-2; further calculate the
fracture lengths C.sub.ci and C.sub.cd corresponding to the
initiation stress .sigma..sub.ci and damage stress .sigma..sub.cd
of the fracture according to the theory of fracture mechanics; then
calculate subcritical propagation rate of Stage III, i.e., the
subcritical fracture propagation stage of the test core according
to Formula (1):
u = C c i - C c d T c i - T c d . ( 1 ) ##EQU00011##
[0100] Step 5: for the test cores L-1 and L-2, the total volume
strain .epsilon..sub.v in the loading process is composed of
elastic volume strain and fracture volume strain:
.epsilon..sub.v=.epsilon..sub.ev+.epsilon..sub.fv (2).
[0101] At the same time, the total volume strain of the test core
also satisfies the following relationship with its axial strain and
radial strain:
.epsilon..sub.v=.epsilon..sub.1+2.epsilon..sub.3 (3).
[0102] According to Hooke's law, the theoretical elastic volume
strain of rock can be calculated by the following formula:
e v = 1 - 2 v E ( .sigma. 1 + 2 .sigma. 3 ) . ( 4 )
##EQU00012##
[0103] In Formulas (2) to (4), the axial stress (.sigma..sub.1),
axial strain (.epsilon..sub.1) and radial strain (.epsilon..sub.3)
of the test cores L-1 and L-2 can be monitored and recorded
directly in the experimental process; the radial stress
(.sigma..sub.3) is a fixed value of 30 MPa applied by the
instrument; the elastic modulus (E) and Poisson's ratio (.nu.) of
the cores L-1 and L-2 are determined in advance through other
experiments, and their values are shown in Table 1; according to
Formula (5), the fracture volume strain of the cores L-1 and L-2 at
different loading time can be calculated;
f v = 1 + 2 3 - 1 - 2 v E ( .sigma. 1 + 2 .sigma. 3 ) . ( 5 )
##EQU00013##
[0104] According to the calculation results, take the axial strain
as the abscissa and draw the fracture volume strain-axial strain
relation curve of the core in the testing process; as shown in FIG.
1A and FIG. 1B, when the axial stress corresponding to the turning
point where the fracture volume strain of test cores L-1 and L-2
changes from increasing to decreasing with the axial strain is the
fracture damage stress .sigma..sub.ci of the core; the method for
obtaining values at the turning point is to first perform
polynomial fitting on the fracture volume strain-axial strain
relation curve, and then calculate the derivative and the extreme
value to obtain the corresponding values at the turning point, that
is, the turning point value is obtained by calculating the
derivative and the extreme value of the curve; in this embodiment,
the .sigma..sub.ci values of the cores L-1 and L-2 are 97 MPa and
85 MPa respectively.
TABLE-US-00001 TABLE 1 Basic Rock Mechanics Parameters of Test Core
L-1 Parameters L-1 L-2 Length (cm) 5.04 5.02 Diameter (cm) 2.51
2.51 Mass (g) 68.1275 67.9461 Fracture toughness K.sub.IIC, MPa
m.sup.0.5 1.62 1.58 Elastic modulus E, GPa 27.4 31.6 Poisson's
ratio .nu., dimensionless 0.23 0.22 Friction coefficient of
fracture surface .mu., 0.54 0.51 dimensionless Confining pressure
(radial stress) .sigma..sub.3, MPa 30 30
[0105] Step 6: According to Formula (3) and monitoring data during
experiment, calculate the total volume strain .epsilon..sub.v of
the test core in the loading process, take the axial strain as the
abscissa and draw the total volume strain-axial strain relation
curve of the cores L-1 and L-2 in the test process; as shown in
FIG. 1A and FIG. 1B, when the axial stress corresponding to the
turning point where the total volume strain of the cores L-1 and
L-2 changes from increasing to decreasing with the axial strain is
the damage stress .sigma..sub.cd of the core; the method for
obtaining values at the turning point is to first perform
polynomial fitting on the fracture volume strain-axial strain
relation curve, and then calculate the derivative and the extreme
value to obtain the corresponding values at the turning point; in
this embodiment, the values of .sigma..sub.cd of the cores L-1 and
L-2 are 206 MPa and 175 MPa.
[0106] Step 7: According to the experimental monitoring data, draw
the axial stress-loading time curve of the cores L-1 and L-2 in the
test process (FIG. 2A and FIG. 2B); with given core fracture stress
.sigma..sub.ci and damage stress .sigma..sub.cd, calibrate the
starting and ending time T.sub.ci and T.sub.cd of the cores L-1 and
L-2 in the subcritical fracture propagation stage based on the
axial stress-loading time curve as shown in FIG. 2A and FIG. 2B; in
this embodiment, T.sub.ci and T.sub.cd of the cores L-1 and L-2 are
taken as 96.13 s and 381.52 s, and 246.87 s and 468.75 s,
respectively.
[0107] Step 8: for the test core under both radial (confining
pressure) and axial compression, the internal fractures are closed
under compression, and the effective shear stress on the fracture
surface is expressed as follows:
.tau..sub.eff=.tau..sub.n-.mu..sigma..sub.n=1/2(.sigma..sub.1-.sigma..su-
b.3)sin 2.beta.-.mu.(.sigma..sub.1 sin.sup.2.beta.+.sigma..sub.3
cos.sup.2.beta.) (6).
[0108] The stress intensity factor of fracture tip inside the test
core is:
K.sub.II= {square root over (.pi.C)}.tau..sub.eff= {square root
over (.pi.C)}[1/2(.sigma..sub.1-.sigma..sub.3)sin
2.beta.-.mu.(.sigma..sub.1 sin.sup.2.beta.+.sigma..sub.3
cos.sup.2.beta.)] (7).
[0109] When the stress intensity factor K.sub.II of the fracture
tip inside the core is greater than the fracture toughness
K.sub.IIC of the core, the core fracture enters the unstable
propagation stage (Stage IV); at the same time, as there is more
than one fracture in the test core, the inclination angle of the
fracture that preferentially enters the unstable propagation stage
usually satisfies the following formula:
tan 2 .beta. = 1 .mu. . ( 8 ) ##EQU00014##
[0110] When the stress intensity factor K.sub.II of the fracture
tip inside the core is just equal to the fracture toughness
K.sub.IIC, that is, the core fracture is just at the critical point
between the subcritical fracture propagation stage (Stage III) and
the unstable propagation stage (Stage IV), the axial stress on the
core at this moment is just equal to its damage stress; the
following formula can be obtained by combining Formula (6) to
(8):
C c d = 1 .pi. [ 2 K I I C ( .mu. 2 + 1 + .mu. ) .sigma. c d - (
.mu. 2 + 1 + .mu. ) 2 .sigma. 3 ] 2 . ( 9 ) ##EQU00015##
[0111] If relevant parameters such as fracture toughness of the
test cores L-1 and L-2 are known (Table 1), work out the fracture
length C.sub.cd of the test core at the ending time of the
subcritical fracture propagation stage according to Formula (9);
the calculated values of C.sub.al of the cores L-1 and L-2 in this
embodiment are 6.34.times.10.sup.-4 m and 5.28.times.10.sup.-4 m,
respectively.
[0112] Step 9: For cores L-1 and L-2, as observed by scanning
electron microscope, before the subcritical propagation of
fractures in the core (as shown in FIG. 3A and FIG. 3B), there are
only micro fractures with length ranging from several to tens of
microns, which is far less than the fracture length C.sub.cd at the
ending time of the subcritical fracture propagation stage of the
core (less than 2% of the C.sub.cd value); therefore, at the
starting time of the subcritical fracture propagation stage, the
initial fracture length Gi of the cores L-1 and L-2 can be
approximately zero, so it is taken as 0.
[0113] Step 10: According to Formula (1), calculate the subcritical
fracture propagation rates of test cores L-1 and L-2 in the
subcritical fracture propagation stage to be 4.21.times.10.sup.-6 m
and 6.05.times.10.sup.-6 m, respectively; test the subcritical
propagation rate of rock fractures under high effective stress
(confining pressure) for the first time based on the stress-strain
curve; the measured values are generally lower than the subcritical
propagation rate of Devonian shale fractures measured by Swanson et
al. (Swanson P L. Subcritical fracture growth and other time- and
environment-dependent behavior in crustal rocks [J]. Journal of
Geophysical Research: Solid Earth, 1984, 89(B6):4137-52) through
the double-torsion sample method; the main reason is that the
method simulates the high effective stress conditions of the rock
in the formation, and more objectively reflects the effect of
effective stress on inhibiting the subcritical propagation process
of shale fractures.
[0114] The above are not intended to limit the present invention in
any form. Although the present invention has been disclosed as
above with embodiments, it is not intended to limit the present
invention. Those skilled in the art, within the scope of the
technical solution of the present invention, can use the disclosed
technical content to make a few changes or modify the equivalent
embodiment with equivalent changes. Within the scope of the
technical solution of the present invention, any simple
modification, equivalent change and modification made to the above
embodiments according to the technical essence of the present
invention are still regarded as a part of the technical solution of
the present invention.
* * * * *