Indoor creep test analysis method for underground cavern rock

Abstract

The invention provides an indoor creep test analysis method for underground cavern rocks. Creep behaviors of underground plant granite are researched by adopting a creep test. According to test results in multiple stress states, expressions of instantaneous strain and creep strain are established by using the ratio Rd of confining pressure, deviatoric stress and peak strength. Then, the confining pressure is introduced into a Nishihara model, and an expression which can accurately describe deformation of granite along with time under the action of different confining pressures and deviatoric stresses is obtained. Instantaneous and creep parameter changes under various applied stresses can be completely explained.

Description

Technical Field

[0001] The invention relates to the field of geotechnical engineering, and in particular to an indoor creep test analysis method for underground cavern rocks. Background Art

[0002] The transient behavior of rock refers to continuous displacement under constant stress, including deformation, sliding and failure. This is an important mechanical property of rock materials and an important basis for the long-term stability of rock engineering projects. Many deformations that occur in rock engineering are not formed instantly, but develop over time. Therefore, the prediction of long-term stability of rock is increasingly valued. In many underground engineering projects, the deformation and failure of rock will occur over a long period of time, so delayed deformation phenomena must be considered. Excessive deformation caused by creep can lead to the destruction of rock infrastructure and increase the cost of repair. Soft rock creep is more obvious than hard rock, but hard rock can also show obvious creep behavior under high stress conditions.

[0003] In recent decades, the long-term deformation of various rocks has been continuously studied based on experiments and models. Rock creep usually includes three stages from initiation to failure: decay creep, steady-state creep, and accelerated creep. The decay creep stage starts with a high creep strain rate and then gradually decreases with time, such as Figure 1 As shown. The creep strain rate is a constant independent of time in the steady-state creep stage, and the strain increases at a uniform rate. When the stress reaches the long-term strength, the rock enters the accelerated creep stage from the steady-state creep, and the strain increases rapidly and causes rock failure. Many creep models can describe the real creep behavior of rocks. These models can be roughly divided into three groups: empirical models, constitutive models based on rock mechanics, and element models. Empirical models usually use exponential, power, or logarithmic functions to represent the relationship between strain and time.

[0004] Although the previous creep models can accurately describe the relationship between creep strain and time, they still have the following shortcomings: (1) The parameters in the previous models have different values ​​under different deviatoric stresses, but the relationship between deviatoric stress and each parameter is unclear or not introduced into the expressions of these models; (2) Confining pressure has a significant effect on rock deformation, but the expressions of previous models rarely consider confining pressure. Therefore, previous models do not have a unified expression to describe various creep behaviors under different confining pressures and deviatoric stresses. These models cannot fully explain the transient and creep parameter changes under various applied stresses. Summary of the invention

[0005] The main purpose of the present invention is to provide an indoor creep test analysis method for underground cavern rocks to solve the problems in the above-mentioned background technology.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: creep test is used to study the creep behavior of underground cavern rock, and according to the test results under multiple stress states, the ratio of confining pressure, deviatoric stress and peak strength R is used to calculate the creep behavior of underground cavern rock. d The expressions of instantaneous strain and creep strain are established, and then the confining stress is introduced into the Nishihara model, and an expression is obtained which can accurately describe the time-dependent deformation of granite under different confining pressures and deviatoric stresses.

[0007] Preferably, the creep test is carried out at different confining pressures, and each test is carried out four times at different confining pressures;

[0008] Confining pressure and axial pressure were selected according to the stress state of the rock mass at different depths from the underground cavern to the cave wall, and creep tests were carried out under 1, 3, 5, and 10 Map confining pressures, with the axial stress being 0.55-1.00 times the peak strength;

[0009] In the creep test, the superposition relationship of the deformation process is established by drawing the deformation-time curve of the rock sample, and multiple single-stage loading creep test results are obtained using the test results of a multi-step loading. The creep test steps for each rock sample are as follows:

[0010] S1. Apply confining pressure to a predetermined value at a rate of 0.1 MPa / s and stabilize it;

[0011] S2. While applying confining pressure, an axial pressure of 0.1 MPa / s is applied to the rock sample to the confining pressure value. The first-level axial stress level is 55% of the peak strength, which is determined by the triaxial compression test;

[0012] S3, maintain the applied stress until the creep strain of the rock sample does not increase; then carry out the next level of axial compression loading, and the axial compression difference between two adjacent levels is 10%-20% of the peak strength;

[0013] S4. Repeat step S3 until the rock sample fails.

[0014] Preferably, based on the pressure test before the formal test, it is determined that in each loading step, the deviatoric stress must be kept constant for more than 15 hours or until the rock sample is destroyed, and the axial displacement is continuously recorded; the measurement information is automatically recorded and processed by the data collector every second, avoiding errors caused by manual measurement records; the next level of creep test can only be carried out when the real-time output displacement of the data collector no longer increases.

[0015] Preferably, the ratio of deviator stress to peak strength R d , the creep test is analyzed and the calculation formula is as follows:

[0016]

[0017] Peak intensity σ pis the maximum axial pressure under a certain confining pressure in a conventional triaxial compression test; since the deviatoric stress in the creep test is (55%–100%)σ p , so R d The value range is from 0.55 to 1.

[0018] Preferably, the total strain ε is given by the instantaneous strain ε m and creep strain ε v Composition, and gradually increases with time, creep strain ε v From the viscoelastic creep strain ε ve and viscoplastic creep strain ε vp composition:

[0019] ε=ε m +ε v =ε m +ε ve +ε vp (2)

[0020] Where ε is the total strain, ε m is the instantaneous strain, ε v is the creep strain, ε ve is the viscoelastic creep strain, ε vp is the viscoplastic creep strain ε vp .

[0021] Preferably, the constitutive relation between stress and instantaneous strain, where instantaneous strain refers to the axial strain of rock that is independent of time under confining pressure and axial stress, and is related to R d There is a positive linear relationship, which can be expressed as:

[0022] ε m =k1×R d +b1 (3)

[0023] Among them, ε m is the instantaneous strain, k1 and b1 are parameters.

[0024] Preferably, the constitutive relation between stress and creep strain, the viscoelastic creep strain and R d The relationship can be described by a quadratic curve:

[0025]

[0026] Among them, ε ve is the viscoelastic creep strain, l1, m1 and n1 are parameters;

[0027] When the steady-state creep strain rate is not zero, there is viscoplastic creep strain. The linear relationship between viscoplastic creep strain and confining pressure can be expressed as:

[0028] ε vp=k2×σ3+b2 (5)

[0029] Among them, k2 and b2 are parameters.

[0030] Preferably, the expression of the Nishihara model is:

[0031]

[0032] where ε(t) is the total strain at time t; σ is the deviatoric stress; E M and η M are Maxwell elastic modulus and viscosity coefficient respectively; E K and η K They are Kelvin elastic modulus and viscosity coefficient respectively;

[0033] The instantaneous elastic modulus of rock is the elastic modulus E of the Maxwell element in equation (6): M , based on formula (3), E M can be written as:

[0034]

[0035] Viscoelastic creep strain ε ve The Kelvin modulus of elasticity E K We can get that when t→∞, ε ve =(σ1-σ3) / E K , based on formula (4), E K It can be expressed as:

[0036]

[0037] In the Nishihara model, there are two viscosity coefficients η K and η M Creep time t related to viscoelastic creep strain and viscoplastic creep strain c The viscoelastic creep strain over time ε ve The expression of (t) is as follows:

[0038]

[0039] ε ve and t c By introducing formula (9), we can get the following expression:

[0040]

[0041] Among them, t c It refers to the time before the rock enters accelerated creep;

[0042] Therefore ηK It can be expressed as follows:

[0043]

[0044] Final viscoplastic creep strain ε vp It can be expressed as:

[0045]

[0046] Introducing equation (5) into equation (12), η M It can be expressed as:

[0047]

[0048] Preferably, in a three-dimensional state, the stress tensor σ of the rock ij It can be decomposed into the deviatoric stress tensor S ij and the spherical stress tensor σ m , the strain tensor ε ij It can be decomposed into the deviatoric strain tensor e ij and the spherical strain tensor ε m , which can be written as:

[0049]

[0050] Among them, δ ij is the Kronecker function, and the spherical stress tensor and spherical strain tensor can be written as:

[0051]

[0052] The deviatoric stress tensor and deviatoric strain tensor can be written as:

[0053]

[0054] Therefore, the elastic element under three-dimensional stress state can be expressed as:

[0055]

[0056] Where G0 and K are the shear modulus and bulk modulus;

[0057] Assuming that the creep property is manifested by shear deformation and the volume change is elastic, the three-dimensional constitutive law of the viscoelastic element can be written as:

[0058]

[0059] Among them, G K and η K are the viscoelastic shear modulus and shear viscosity;

[0060] The three-dimensional constitutive model of viscoplastic elements can be written as:

[0061]

[0062] in, F is the yield function of rock, F0 is the initial value of the rock yield function, Q is the plastic potential function, φ(·) is the power function form, η M is the viscoplastic shear viscosity coefficient;

[0063] The yield function F can be written as:

[0064]

[0065] Where J2 is the second invariant of the stress deviator. According to the associated flow criterion, when F is greater than or equal to 0, equation (19) can be written as:

[0066]

[0067] Assuming that rock is an isotropic material, and assuming that elastic strain is caused by the spherical stress tensor, and creep strain is caused by the deviatoric stress tensor, the creep model under three-dimensional stress state can be expressed as:

[0068]

[0069] Among them, (S ij ) s is L The corresponding deviator stress tensor;

[0070] In the triaxial compression test, it is considered that σ2=σ3<σ1, so

[0071]

[0072] Substituting equation (23) into equation (22) and setting the initial yield function F0 = 1, the axial creep strain equation of the improved Nishihara creep model in the three-dimensional stress state is:

[0073]

[0074] Among them, the parameters K, G0, G k , η K and η M The functional expression of can be derived from equations (7), (8), (11) and (13).

[0075] The present invention provides an indoor creep test analysis method for underground cavern rocks, and uses creep tests to study the creep behavior of underground powerhouse granite. Based on the test results under multiple stress states, the ratio of confining pressure, deviatoric stress and peak strength R is used to calculate the creep behavior of underground powerhouse granite. dThe expressions of transient strain and creep strain were established. Then the confining pressure was introduced into the Nishihara model, and an expression that can accurately describe the time-dependent deformation of granite under different confining pressures and deviatoric stresses was obtained. It can fully explain the changes of transient and creep parameters under various applied stresses. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0077] Figure 1 It is a schematic diagram of rock creep behavior of the present invention;

[0078] Figure 2 Schematic diagram of creep strain-time curve of the present invention;

[0079] Figure 3 is the curve of instantaneous strain and Rd under different confining pressures of the present invention;

[0080] Figure 4 is the relationship between the final viscoelastic creep strain and Rd of the present invention;

[0081] Figure 5 The present invention R d = Viscoplastic creep strain under different confining pressures when Rm d;

[0082] Figure 6 It is the Burgers model of the present invention;

[0083] Figure 7 It is the generalized Kelvin model of the present invention;

[0084] Figure 8 This is the Nishihara model of the present invention. DETAILED DESCRIPTION

[0085] Example 1

[0086] like Figures 1 to 5 As shown in the figure, the creep test analysis method of underground cavern rock indoors was used to study the creep behavior of underground powerhouse granite. According to the test results under multiple stress states, the ratio of confining pressure, deviatoric stress and peak strength R d The expressions of instantaneous strain and creep strain were established. Then the confining pressure was introduced into the Nishihara model, and an expression that can accurately describe the time-dependent deformation of granite under different confining pressures and deviatoric stresses was obtained.

[0087] The creep test was carried out under different confining pressures, and each test was carried out four times under different confining pressures. The confining pressure and axial pressure were selected according to the stress state of the rock mass at different depths from the underground powerhouse to the cave wall, and the creep tests under confining pressures of 1, 3, 5, and 10 MPa were determined. The axial stress was 0.55-1.00 times the peak strength. The test adopted one of the standard methods widely used in creep research: the multi-step loading method, namely the Chen loading method, which can reduce the time of the creep test and reduce the deviation caused by rock heterogeneity. The principle of Chen's loading method is to consider the memory effect of the rheological medium on the loading history. In the creep test, the superposition relationship of the deformation process can be established by drawing the deformation-time curve of the rock sample, and the test results of a multi-step loading can be used to obtain multiple single-stage loading creep test results. The creep test process design for each rock sample is as follows:

[0088] (1) Apply confining pressure to a predetermined value at a rate of 0.1 MPa / s and stabilize it.

[0089] (2) While applying the confining pressure, an axial pressure of 0.1 MPa / s is applied to the rock sample to the confining pressure value. The first-level axial stress level is 55% of the peak strength, which is determined by the triaxial compression test.

[0090] (3) Maintain the applied stress until the creep strain of the rock sample does not increase; then proceed to the next level of axial compression loading, with the axial compression difference between two adjacent levels being 10%–20% of the peak strength.

[0091] (4) Repeat step (3) until the rock sample fails.

[0092] According to the pressure test before the formal test, it is determined that in each loading step, the deviatoric stress must be kept constant for more than 15 hours or until the rock sample is destroyed, and the axial displacement is continuously recorded. The measurement information is automatically recorded and processed by the data collector every second, avoiding the error caused by manual measurement and recording. The next level of creep test can only be carried out when the real-time output displacement of the data collector no longer increases. The basic parameters of the granite specimens and the stress level schemes of the triaxial creep test are shown in Table 1.

[0093] Table 1: Average basic parameters of rock samples in creep tests

[0094]

[0095] Creep compression test results and analysis, using the ratio of deviator stress to peak strength R d , the creep test is analyzed, namely:

[0096]

[0097] Peak intensity σ pIt is the maximum axial pressure under a certain confining pressure in a conventional triaxial compression test. Since the deviatoric stress in the creep test is (55%–100%)σ p , so R d The value range of is 0.55 to 1. In particular, when the confining pressure is 0, R d =1 means that the axial load of the rock sample is equal to the uniaxial compressive strength. d It is an important variable in studying the creep characteristics of granite under different confining pressures. d By considering the confining pressure and deviatoric stress at the same time and introducing them into the traditional creep model, a unified equation describing the deviatoric stress, confining pressure and strain can be established.

[0098] The applied axial load is determined based on the different proportions of the peak strength in the conventional triaxial compression test. The deviatoric stress corresponding to the axial load is listed in Table 1. The creep strain rate of the decay creep gradually decreases to a constant over time. When the creep strain rate remains constant, it is considered to have entered the steady-state creep stage. Therefore, when the creep strain rate reaches a constant, the next load level can be applied. The test ends when the rock test fails. The granite failure mode is mainly shear band failure, the rock failure surface is rough, and rock debris peeling occurs.

[0099] The axial creep strain increases with time under different deviatoric stresses, especially at high deviatoric stress levels. Failure is caused by the increase in axial strain, which leads to the accumulation of creep damage and the increase in strain rate. The total strain ε is given by the instantaneous strain ε m and creep strain ε v Composition, and gradually increases with time, creep strain ε v From the viscoelastic creep strain ε ve and viscoplastic creep strain ε vp composition:

[0100] ε=ε m +ε v =ε m +ε ve +ε vp (2)

[0101] Instantaneous strain ε m is the strain of the rock sample at the time of loading, which can be obtained at t = 0. Viscoelastic creep strain ε ve is the reversible strain of the rock after loading that changes with time, and the viscoplastic creep strain ε vpIrreversible. The Nishihara model is used to describe rock strain. The long-term strength in the model is the threshold for judging whether viscoplastic strain exists. For stresses below the threshold, the creep strain is a fully reversible viscoelastic creep strain, and the creep strain rate is zero when t→∞. For stresses above the threshold, plastic creep strain occurs in the steady-state creep stage with a non-zero constant strain rate. Therefore, if the creep strain rate in the steady-state creep stage is zero, the final creep strain is constant, and only viscoelastic creep strain exists in the creep strain. Otherwise, the creep strain increases with time, including viscoelastic creep strain and viscoplastic creep strain. Figure 2 The final creep strain rate of the first four creep tests under different confining pressures is zero. Considering that only viscoelastic creep strain exists, the viscoelastic creep strain can be obtained by subtracting the instantaneous strain from the total strain. The fifth creep strain rate of each creep test is not zero, so viscoelastic and viscoplastic creep strains exist at the same time. The viscoplastic creep strain rate can be obtained in the steady-state creep stage. Therefore, the time-varying viscoplastic creep strain ε can be calculated vp . Viscoelastic creep strain ε ve It is equal to the total creep strain minus the viscoplastic strain. Table 2 lists the instantaneous strain ε of the rock sample before it enters the accelerated creep. m , viscoelastic creep strain ε ve and the viscoplastic creep strain ε at the end of the creep test under different confining pressures vp .

[0102] Table 2: ε, ε m ,ε ve and ε vp value

[0103]

[0104]

[0105] The constitutive relationship between stress and instantaneous strain. Instantaneous strain refers to the axial strain of rock that is independent of time under the action of confining pressure and axial stress. d There is a positive linear relationship, which can be expressed as:

[0106] ε m =k1×R d +b1 (3)

[0107] Among them, ε m is the instantaneous strain, k1 and b1 are parameters that can be obtained from Figure 3 Obtained in.

[0108] In this creep test, the instantaneous strain under different confining pressures can be calculated using formula (3). d = 0.55 can be expressed by εb m As shown in Table 3. Confining pressure and ε b Linear relationship:

[0109] Table 3: ε b m and ε p m The calculated value of

[0110] Confining pressure(MPa) <![CDATA[εb m(10 -3 )]]> <![CDATA[εp m(10 -3 )]]> 1 4.24 6.65 3 4.58 7.28 5 4.93 7.92 10 5.79 9.51

[0111] Each confining pressure has a maximum deviatoric stress-peak strength ratio Rm d, that is, (σ p -σ3) / σ p In the triaxial test, Rmd can be close to but not equal to 1, so the expression of Rmd can be written as:

[0112]

[0113] The instantaneous strain of Rm d can be calculated from εp m by formula (3) and is listed in Table 3. Its relationship with the confining pressure is expressed as:

[0114]

[0115] Instantaneous strain and R d The relationship between is linear, so formula (3) can be written as:

[0116]

[0117] The above formula can effectively describe R d The relationship between the instantaneous strain.

[0118] Constitutive relation between stress and creep strain, viscoelastic creep strain: Under the action of deviatoric stress and confining pressure, the viscoelastic creep strain increases with time, but the viscoelastic creep strain rate gradually decreases. When the viscoelastic creep strain rate decreases to 0, the viscoelastic creep strain will increase to a constant value. Therefore, the final viscoelastic creep strain of the rock can be obtained. Figure 4 is the final viscoelastic creep strain and R d It can be seen that as R d With the increase of R, except for the rock sample with a confining pressure of 1 MPa, the contribution of creep to the final viscoelastic creep strain of rock first decreases and then increases. d The relationship can be described by a quadratic curve:

[0119]

[0120] Among them, ε ve is the viscoelastic creep strain, l1, m1 and n1 are parameters that can be obtained from Figure 4 Obtained in.

[0121] It can be determined that when Rd = 0.63, the final viscoelastic creep strain is the smallest, indicating that the rock d When =0.63, the recoverable aging deformation is the smallest, and its ability to resist the recoverable deformation of external load is the strongest.

[0122] Viscoplastic creep strain: When the steady-state creep strain rate is not zero, viscoplastic creep strain exists. In this example, viscoplastic creep strain exists only at level 5 in each creep test under different confining pressures. The deviatoric stress at level 5 in the creep test is σ p ×Rm d. Figure 5 is the linear relationship between viscoplastic creep strain and confining pressure, which can be expressed as:

[0123] ε vp =k2×σ3+b2 (5)

[0124] Among them, k2 and b2 are parameters that can be obtained from Figure 5 middle.

[0125] Long-term strength of rock σ L It refers to the threshold value when the rock creep deformation changes from the steady-state creep stage to the unsteady-state creep stage. When the deviatoric stress is less than this threshold value, the steady-state creep strain rate gradually decreases to zero over time, and the rock creep strain will not increase in the end. When the deviatoric stress is greater than the threshold value, the steady-state creep strain rate will remain a non-zero constant, and the rock will enter the accelerated creep stage after a period of steady-state creep. Therefore, the long-term strength can be defined as the maximum deviatoric stress that makes the rock steady-state creep strain rate zero. However, it is difficult to obtain zero creep strain rate during the test, so an acceptable threshold value needs to be proposed. When the creep rate is less than a sufficiently small value, the final creep rate is considered to be zero and the creep deformation is stable. In this case, if the creep strain rate is less than 1.0×10-7(s-1), the creep rate can be considered to be zero. If the creep strain rate is greater than 1.0×10-7(s-1), the rock will enter the unsteady-state creep stage.

[0126] The long-term strength increases with the increase of confining pressure. The ratio of long-term strength to peak strength RL d = σ L / σ p , which is 0.92-0.96 at different confining pressures. Since the RL d values ​​obtained at different confining pressures are similar, a unified RL d can be given at σ3 = 1, 3, 5 and 10 MPa. d With the increase of R, the trends of the steady-state creep strain rates under the four confining pressures are similar. d The relationship with the steady-state creep strain rate can be expressed by an exponential function, and RL d = 0.9501 can be obtained. The determination of RL d shows that when the deviator stress reaches 0.9501σ p When R dWhen it is less than 95.01%, the steady-state creep strain rate will decrease to zero over time. Therefore, the long-term strength of granite σ L =0.9501σp.

[0127] Example 2

[0128] like Figures 6 to 8 As shown, the aging characteristics of granite can be simulated using a conventional creep constitutive model. Figure 6 The Burgers model in the paper consists of the Maxwell model and the Kelvin model, which can accurately describe the decay creep and steady-state creep stages of rocks when the applied stress exceeds the long-term strength. Figure 7 is the generalized Kelvin model, which can describe the decay creep and steady-state creep when the deviatoric stress is less than the long-term strength. Combining the Burgers model with the generalized Kelvin model, we can get Figure 8 The Nishihara model in . The elastic element in this model represents the instantaneous, time-independent elastic strain. The viscoplastic creep element represents the linear viscoplastic creep strain that varies with time when the deviator stress is greater than the long-term strength and does not exist when the deviator stress is less than the long-term strength. If the deviator stress is less than the long-term strength, the creep deformation is reversible; otherwise, plastic creep will occur in the steady-state creep stage. The viscoelastic creep element represents the viscoelastic creep strain, in which the creep strain rate gradually decreases to zero with time.

[0129] The expression of Nishihara model is:

[0130]

[0131] where ε(t) is the total strain at time t; σ is the deviatoric stress; E M and η M are Maxwell elastic modulus and viscosity coefficient respectively; E K and η K are the Kelvin elastic modulus and viscosity coefficient respectively.

[0132] The Nishihara model can accurately describe the strain time in creep tests. The instantaneous strain, viscoplastic strain, and viscoelastic strain in creep tests are all related to the deviatoric stress and confining pressure. However, the confining pressure is not considered in the Nishihara model. In this case, an improved Nishihara model is established by introducing the confining pressure and Rd into the Nishihara model. This model uniformly expresses the creep parameters and can describe the creep behavior of granite in the decay and steady-state creep stages under different deviatoric stresses and confining pressures.

[0133] The creep model parameters are determined, and the instantaneous elastic modulus of the rock is the elastic modulus E of the Maxwell element in equation (6):M , based on formula (3), E M can be written as:

[0134]

[0135] Viscoelastic creep strain ε ve The Kelvin modulus of elasticity E K We can get that when t→∞, ε ve =(σ1-σ3) / E K , based on formula (4), E K It can be expressed as:

[0136]

[0137] Creep strain is a time-dependent strain, and the viscosity coefficient is related to the creep time to reach a certain creep strain. In the Nishihara model, there are two viscosity coefficients η K and η M Creep time t related to viscoelastic creep strain and viscoplastic creep strain c The viscoelastic creep strain over time ε ve The expression of (t) is as follows:

[0138]

[0139] In the steady-state creep stage, the creep strain rate (s -1 ) are all less than 1.0×10-7, so the creep strain rate is considered to be 0 and the rock reaches the final viscoelastic creep strain. Creep time t c It refers to the time it takes for the rock to reach the final viscoelastic creep strain. In the fifth level creep test, t c It refers to the time before the rock enters accelerated creep. Viscoelastic creep strain ε ve As shown in Table 2, t c Listed in Table 4. ve and t c By introducing formula (9), we can get the following expression:

[0140]

[0141] Table 4: Creep time t c value

[0142]

[0143] Since the exponential function cannot be zero, η cannot be calculated directly. K Assume 1-ε ve E K / (σ1-σ3)≤0.0001, formula (10) is feasible, so η K It can be expressed as follows:

[0144]

[0145] η M Only exists in the 5th level creep test, based on Figure 8 And (5), the final viscoplastic creep strain ε vp It can be expressed as:

[0146]

[0147] Introducing equations (5) and (1) into equation (12), η M It can be expressed as:

[0148]

[0149] Rock mass is in a complex three-dimensional stress state in actual engineering, so it is necessary to derive the three-dimensional creep constitutive equation from the improved Nishihara creep model. Equation (6) is a creep model under one-dimensional conditions, and its total strain is composed of instantaneous strain, viscoelastic creep strain, and viscoplastic creep strain. In the three-dimensional state, the rock stress tensor σij can be decomposed into the deviatoric stress tensor Sij and the spherical stress tensor σm, and the strain tensor εij can be decomposed into the deviatoric strain tensor eij and the spherical strain tensor εm, which can be written as:

[0150]

[0151] Among them, δ ij is the Kronecker function, and the spherical stress tensor and spherical strain tensor can be written as:

[0152]

[0153] The deviatoric stress tensor and deviatoric strain tensor can be written as:

[0154]

[0155] Therefore, the elastic element under three-dimensional stress state can be expressed as:

[0156]

[0157] Where G0 and K are the shear modulus and bulk modulus;

[0158] Assuming that the creep property is manifested by shear deformation and the volume change is elastic, the three-dimensional constitutive law of the viscoelastic element can be written as:

[0159]

[0160] Among them, G K and η K are the viscoelastic shear modulus and shear viscosity;

[0161] The three-dimensional constitutive model of viscoplastic elements can be written as:

[0162]

[0163] in, F is the yield function of rock, F0 is the initial value of the rock yield function, Q is the plastic potential function, φ(·) is the power function form, η M is the viscoplastic shear viscosity coefficient;

[0164] The yield function F can be written as:

[0165]

[0166] Where J2 is the second invariant of the stress deviator. According to the associated flow criterion, when F is greater than or equal to 0, equation (19) can be written as:

[0167]

[0168] Assuming that rock is an isotropic material, and assuming that elastic strain is caused by the spherical stress tensor, and creep strain is caused by the deviatoric stress tensor, the creep model under three-dimensional stress state can be expressed as:

[0169]

[0170] Among them, (S ij ) s is L The corresponding deviator stress tensor;

[0171] In the triaxial compression test, it is considered that σ2=σ3<σ1, so

[0172]

[0173] Substituting equation (23) into equation (22) and setting the initial yield function F0 = 1, the axial creep strain equation of the improved Nishihara creep model in the three-dimensional stress state is:

[0174]

[0175] Among them, the parameters K, G0, G k , η K and η M The functional expression of can be derived from equations (7), (8), (11) and (13).

[0176] Verification of the improved Nishihara creep model: Both the Nishihara model and the improved Nishihara model can describe the strain-time curve in the creep test, and the accuracy is better for the creep test with higher confining pressure. The parameters of the Nishihara model and the improved Nishihara model are shown in Table 5. Except for the confining pressure of 1MPa, the R2 of the improved Nishihara model is greater than 0.9. Therefore, the improved expression of the Nishihara model can effectively describe the aging behavior of the rock mass as well as the attenuation and steady-state creep behavior.

[0177] Table 4: Parameters calculated by Nishihara model fitting and improved Nishihara model

[0178]

[0179]

[0180] The traditional Nishihara model needs to determine the parameters by fitting each test curve without considering the confining pressure and R d In contrast, the modified Nishihara model considers the confining pressure and R d Although the improved Nishihara model has larger errors than the traditional Nishihara model on some curves, the improved Nishihara model considers the effects of axial pressure and confining pressure at the same time, which improves the integrity of the model and better describes the mechanism controlling the development of creep strain.

[0181] The above embodiments are only preferred technical solutions of the present invention and should not be regarded as limiting the present invention. The protection scope of the present invention shall be the technical solutions recorded in the claims, including equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. Indoor creep test analysis method for underground cavern rock, the method is: creep test is used to study the creep behavior of underground cavern rock, according to the test results under multiple stress states, using the ratio of confining pressure, deviatoric stress and peak strength R d The expressions of instantaneous strain and creep strain are established, and then the confining stress is introduced into the Nishihara model, and an expression is obtained which can accurately describe the time-dependent deformation of granite under different confining pressures and deviatoric stresses.

2. The method for analyzing creep test of underground cavern rock according to claim 1 is characterized by: The creep tests were conducted at different confining pressures, and each test was performed four times at different confining pressures; Confining pressure and axial pressure were selected according to the stress state of the rock mass at different depths from the underground cavern to the cave wall, and creep tests were carried out under 1, 3, 5, and 10 Map confining pressures, with the axial stress being 0.55-1.00 times the peak strength; In the creep test, the superposition relationship of the deformation process is established by drawing the deformation-time curve of the rock sample, and multiple single-stage loading creep test results are obtained using the test results of a multi-step loading. The creep test steps for each rock sample are as follows: S1. Apply confining pressure to a predetermined value at a rate of 0.1 MPa / s and stabilize it; S2. While applying confining pressure, an axial pressure of 0.1 MPa / s is applied to the rock sample to the confining pressure value. The first-level axial stress level is 55% of the peak strength, which is determined by the triaxial compression test; S3, maintain the applied stress until the creep strain of the rock sample does not increase; then carry out the next level of axial compression loading, and the axial compression difference between two adjacent levels is 10%-20% of the peak strength; S4. Repeat step S3 until the rock sample fails.

3. The method for analyzing creep test of underground cavern rock according to claim 1 is characterized by: According to the pressure test before the formal test, it is determined that in each loading step, the deviatoric stress must remain constant for more than 15 hours or until the rock sample is destroyed, and the axial displacement is continuously recorded; the measurement information is automatically recorded and processed by the data collector every second, avoiding the errors caused by manual measurement records; the next level of creep test can only be carried out when the real-time output displacement of the data collector no longer increases.

4. The method for analyzing creep test of underground cavern rock according to claim 1 is characterized by: The ratio of deviator stress to peak strength R d , the creep test is analyzed and the calculation formula is as follows: Peak intensity σ p is the maximum axial pressure under a certain confining pressure in a conventional triaxial compression test; since the deviatoric stress in the creep test is (55%–100%)σ p , so R d The value range is from 0.55 to 1.

5. The method for analyzing creep test of underground cavern rock according to claim 1 is characterized by: The total strain ε is given by the instantaneous strain ε m and creep strain ε v Composition, and gradually increases with time, creep strain ε v From the viscoelastic creep strain ε ve and viscoplastic creep strain ε vp composition: e=e m +e v =e m +e ve +e vp (2) Where ε is the total strain, ε m is the instantaneous strain, ε v is the creep strain, ε ve is the viscoelastic creep strain, ε vp is the viscoplastic creep strain ε vp .

6. The method for analyzing creep test of underground cavern rock in indoor according to claim 5 is characterized in that: The constitutive relationship between the instantaneous strain and the rock mass is the time-independent axial strain under the action of confining pressure and axial stress. d There is a positive linear relationship, which can be expressed as: e m =k1×R d +b1 (3) Among them, ε m is the instantaneous strain, k1 and b1 are parameters.

7. The method for analyzing creep test of underground cavern rock in indoor according to claim 5 is characterized in that: The constitutive relationship between creep strain and viscoelastic creep strain and R d The relationship can be described by a quadratic curve: Among them, ε ve is the viscoelastic creep strain, l1, m1 and n1 are parameters; When the steady-state creep strain rate is not zero, there is viscoplastic creep strain. The linear relationship between viscoplastic creep strain and confining pressure can be expressed as: ε vp =k2×σ3+b2 (5) Among them, k2 and b2 are parameters.

8. The method for analyzing creep test of underground cavern rock according to claim 1 is characterized by: The expression of Nishihara model is: where ε(t) is the total strain at time t; σ is the deviatoric stress; E M and η M are Maxwell elastic modulus and viscosity coefficient respectively; E K and η K They are Kelvin elastic modulus and viscosity coefficient respectively; The instantaneous elastic modulus of rock is the elastic modulus E of the Maxwell element in equation (6): M , based on formula (3), E M can be written as: Viscoelastic creep strain ε ve The Kelvin modulus of elasticity E K We can get that when t→∞, ε ve =(σ1-σ3) / E K , based on formula (4), E K It can be expressed as: In the Nishihara model, there are two viscosity coefficients η K and η M Creep time t related to viscoelastic creep strain and viscoplastic creep strain c The viscoelastic creep strain over time ε ve The expression of (t) is as follows: ε ve and t c By introducing formula (9), we can get the following expression: Among them, t c It refers to the time before the rock enters accelerated creep; Therefore η K It can be expressed as follows: Final viscoplastic creep strain ε vp It can be expressed as: Introducing equation (5) into equation (12), η M It can be expressed as:

9. The method for analyzing creep test of underground cavern rock in indoor environment according to claim 8 is characterized by: In three-dimensional state, the stress tensor of rock σ ij It can be decomposed into the deviatoric stress tensor S ij and the spherical stress tensor σ m , the strain tensor ε ij It can be decomposed into the deviatoric strain tensor e ij and the spherical strain tensor ε m , which can be written as: Among them, δ ij is the Kronecker function, and the spherical stress tensor and spherical strain tensor can be written as: The deviatoric stress tensor and deviatoric strain tensor can be written as: Therefore, the elastic element under three-dimensional stress state can be expressed as: Where G0 and K are the shear modulus and bulk modulus; Assuming that the creep property is manifested by shear deformation and the volume change is elastic, the three-dimensional constitutive law of the viscoelastic element can be written as: Among them, G K and η K are the viscoelastic shear modulus and shear viscosity; The three-dimensional constitutive model of viscoplastic elements can be written as: in, F is the yield function of rock, F0 is the initial value of the rock yield function, Q is the plastic potential function, φ(·) is the power function form, η M is the viscoplastic shear viscosity coefficient; The yield function F can be written as: Where J2 is the second invariant of the stress deviator. According to the associated flow criterion, when F is greater than or equal to 0, equation (19) can be written as: Assuming that rock is an isotropic material, and assuming that elastic strain is caused by the spherical stress tensor, and creep strain is caused by the deviatoric stress tensor, the creep model under three-dimensional stress state can be expressed as: Among them, (S ij ) s is L The corresponding deviator stress tensor; In the triaxial compression test, it is considered that σ2=σ3<σ1, so Substituting equation (23) into equation (22) and setting the initial yield function F0 = 1, the axial creep strain equation of the improved Nishihara creep model in the three-dimensional stress state is: Among them, the parameters K, G0, G k , η K and η M The functional expression of can be derived from equations (7), (8), (11) and (13).

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