Method for analyzing rock indoor creep test of underground cavern

Abstract

The application provides a method for analyzing an indoor creep test of a rock chamber of an underground cavern, and a creep behavior of a granite of an underground powerhouse is studied by using a creep test. d Expressions of instantaneous strain and creep strain are established. Then, confining pressure is introduced into the Nishihara model, and an expression capable of accurately describing time-dependent deformation of the granite under different confining pressures and deviatoric stresses is obtained. Changes of instantaneous and creep parameters under various applied stresses can be completely explained.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of geotechnical engineering, in particular to an analysis method for indoor creep test of underground cavern rock. BACKGROUND

[0002] Transient behavior of rock refers to the occurrence of sustained displacement under constant stress, including deformation, sliding and failure. It is an important mechanical property of rock material and an important basis for long-term stability of rock engineering projects. Many deformations occurring in rock engineering are not instantaneous, but develop over time. Therefore, the prediction of long-term stability of rock is increasingly valued. In many underground engineering projects, deformation and failure of rock occur for a long time, so the delayed deformation phenomenon must be considered. Excessive deformation caused by creep can lead to the destruction of rock infrastructure and increase the cost of repair. Soft rock is more prone to creep than hard rock, but hard rock can also exhibit significant creep behavior under high stress conditions.

[0003] In recent decades, continuous research has been conducted on the long-term deformation of various rocks based on experiments and models. Rock creep usually includes three stages from the beginning to failure: decaying creep, steady-state creep and accelerating creep. The decaying creep stage starts with a high creep strain rate, which then gradually decreases over time, as shown in Figure 1 The creep strain rate is a constant independent of time during the steady-state creep stage, and the strain increases uniformly. When the stress reaches the long-term strength, the rock enters the accelerating creep stage from the steady-state creep, and the strain rapidly increases and leads to rock failure. Many creep models can describe the true creep behavior of rock. These models are 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 not clear or not introduced into the expressions of these models; (2) confining pressure has a significant effect on rock deformation, but previous models have few expressions considering 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 changes in transient and creep parameters under various applied stresses. SUMMARY

[0005] The main purpose of the present application is to provide an analysis method for indoor creep test of underground cavern rock, which solves the problems in the background art.

[0006] To solve the above technical problems, the technical scheme adopted by the present application is: adopting creep test to study the creep behavior of underground cavern rock, according to the test results under multiple stress states, using the ratio R of confining pressure, deviatoric stress and peak strength d Expressions of instantaneous strain and creep strain are established, then the confining pressure stress is introduced into the Nishihara model, and an expression capable of accurately describing the deformation of granite with time under the action of different confining pressures and deviatoric stresses is obtained.

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

[0008] According to the stress state of the rock mass at different depths of the underground cavern to the cavern wall, the confining pressure and the axial pressure are selected, and the creep test is carried out under 1, 3, 5, 10 Map confining pressures, and the axial stress is 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 the test results of multiple single-step loading creep tests are obtained by using the test results of one-step multiple loading, and the creep test steps of each rock sample are as follows:

[0010] S1, the confining pressure is applied to the predetermined value at a speed of 0.1 MPa / s and is stabilized;

[0011] S2, while the confining pressure is applied, the axial pressure of 0.1 MPa / s is applied to the rock sample to the confining pressure value, the first level of axial stress is 55% of the peak strength, and the peak strength is determined by the triaxial compression test;

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

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

[0014] Preferably, according to the test pressure before the formal test, it is determined that the deviatoric stress needs to be kept constant for more than 15 hours or until the rock sample is damaged at each loading step, and the axial displacement is continuously recorded; the measurement information is automatically recorded and processed by the data collector every second, which avoids the error caused by manual measurement and recording; the real-time output displacement of the data collector is no longer increased, and then the next level of creep test can be carried out.

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

[0016]

[0017] The peak strength σ pis the maximum axial stress in a conventional triaxial compression test at a certain confining pressure; the deviatoric stress in the creep test is (55%-100%)σ p Therefore, R d is in the range of 0.55 to 1.

[0018] Preferably, the total strain ε is composed of the instantaneous strain ε m and the creep strain ε v , and increases step by step with time, the creep strain ε v is composed of the viscoelastic creep strain ε ve and the viscoplastic creep strain ε vp :

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

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

[0021] Preferably, the constitutive relationship between stress and instantaneous strain, which is the axial strain of rock under the action of confining pressure and axial stress and is independent of time, is in a positive linear relationship with R d , and can be expressed as:

[0022] ε m = k1 × R d + b1 (3)

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

[0024] Preferably, the constitutive relationship between stress and creep strain, which is the viscoelastic creep strain, is in a quadratic curve relationship with R d :

[0025]

[0026] wherein ε ve is the viscoelastic creep strain, and l1, m1 and n1 are parameters.

[0027] When the steady-state creep strain rate is not zero, there is a viscoplastic creep strain, which is in a linear relationship with the confining pressure, and can be expressed as:

[0028] ε vp= k2 x σ3 + b2 (5)

[0029] where k2 and b2 are parameters.

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

[0031]

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

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

[0034]

[0035] The viscoelastic creep strain ε ve can be obtained by Kelvin elastic modulus E K , when t→∞, ε ve = (σ1-σ3) / E K , based on equation (4), E K can be expressed as:

[0036]

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

[0038]

[0039] Introducing ε ve and t c into equation (9), the following expression can be obtained:

[0040]

[0041] where t c is the time before rock enters into accelerated creep;

[0042] Therefore η​K may be expressed as follows:

[0043]

[0044] Final visco-plastic creep strain ε vp may be expressed as:

[0045]

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

[0047]

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

[0049]

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

[0051]

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

[0053]

[0054] Thus, the elastic element in a three-dimensional stress state can be expressed as:

[0055]

[0056] where G0and K are the shear modulus and the bulk modulus;

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

[0058]

[0059] where G K and η K are the viscoelastic shear modulus and the shear viscous coefficient;

[0060] The three-dimensional constitutive of the visco-plastic element can be written as:

[0061]

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

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

[0064]

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

[0066]

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

[0068]

[0069] where (S ij ) s is the σ L corresponding deviatoric stress tensor;

[0070] In the triaxial compression test, σ2 is considered to be σ3 < σ1, and thus

[0071]

[0072] Formula (23) is brought into formula (22), and the initial yield function F0 is set to 1, and the axial creep strain equation of the improved Nishihara creep model under the three-dimensional stress state is:

[0073]

[0074] where the function expression of the parameters K, G0, G k , η K and η M in the model can be derived from formulas (7), (8), (11) and (13).

[0075] The present application provides an indoor creep test analysis method for underground cavern rock, and the creep behavior of the underground powerhouse granite is studied by using the creep test. According to the test results under multiple stress states, the ratio R dExpressions for transient and creep strains were established. By introducing confining pressure into the Nishihara model, an expression was derived that accurately describes the time-dependent deformation of granite under varying confining pressures and deviatoric stresses. This expression can fully account for the changes in transient and creep parameters under various applied stresses. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] The present invention will be further described below with reference to the accompanying drawings and examples:

[0077] Figure 1 Schematic diagram of rock creep behavior according to 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 =Rm d when viscoplastic creep strain under different confining pressures;

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

[0083] Figure 7 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 is 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 is used to calculate the creep behavior of underground powerhouse granite. d The expressions for instantaneous strain and creep strain were established. Then, confining pressure was introduced into the Nishihara model, and an expression was obtained that can accurately describe the time-dependent deformation of granite under different confining pressures and deviatoric stresses.

[0087] The creep tests were performed at different confining pressures, and each test was performed four times at different confining pressures. The confining pressure and axial stress were selected according to the stress state of the rock mass at different depths from the underground powerhouse to the tunnel wall, and the creep tests were performed at 1, 3, 5, and 10 MPa confining pressures. The axial stress was 0.55-1.00 times the peak strength. The test used one of the standard methods widely used in creep research: the multi-step loading method, i.e., the Chen loading method, which can reduce the time of the creep test and reduce the deviation caused by rock heterogeneity. The principle of the Chen 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 plotting the deformation-time curve of the rock sample, and the results of multiple single-level loading creep tests can be obtained from the test results of one multi-step loading. The creep test process of each rock sample is designed as follows:

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

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

[0090] (3) Keep the applied stress until the creep strain of the rock sample does not increase; then load the next level of axial stress, with a difference of 10%-20% of the peak strength between adjacent levels.

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

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

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

[0094]

[0095] The results and analysis of the creep compression test use the ratio R of deviatoric stress to peak strength d The creep test is analyzed, i.e.,

[0096]

[0097] Peak strength σ pis the maximum axial stress at a certain confining pressure in the conventional triaxial compression test. Since the deviatoric stress in the creep test is (55% - 100%)σ p , the value of R d ranges from 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. R d is an important variable in the study of the creep properties of granite under different confining pressures. Since R d simultaneously considers the confining pressure and the deviatoric stress, it is introduced into the traditional creep model to establish a unified equation describing the deviatoric stress, the confining pressure, and the strain.

[0098] The axial load applied is determined according to 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, and the creep strain rate gradually decreases to a constant over time for the decay creep. When the creep strain rate remains constant, it is considered to enter the steady-state creep stage. Therefore, when the creep strain rate reaches a constant, the next load level can be applied. When the rock test fails, the test is ended. The failure mode of granite is mainly shear band failure, and the rock failure surface is rough, with spalling.

[0099] Under different deviatoric stresses, the axial creep strain increases with time, 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 composed of the instantaneous strain ε m and the creep strain ε v , and increases step by step over time, and the creep strain ε v is composed of the viscoelastic creep strain ε ve and the viscoplastic creep strain ε vp :

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

[0101] The instantaneous strain ε m is the strain of the rock sample at the loading time, which can be obtained at t = 0. The viscoelastic creep strain ε ve is the reversible strain of the rock over time after loading, and the viscoplastic creep strain ε vpirreversible. The Nishihara model is used to describe the rock strain. The long-term strength in the model is the threshold to determine whether the viscoplastic strain exists. For the stress below the threshold, the creep strain is the fully reversible viscoelastic creep strain, and the creep strain rate is zero when t→∞. For the stress above the threshold, the plastic creep strain will occur 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 the viscoelastic creep strain exists in the creep strain. Otherwise, the creep strain will increase with time, which includes the viscoelastic creep strain and the viscoplastic creep strain. Figure 2 The final creep strain rate of the first four stages of creep tests under different confining pressures is zero, considering that only the viscoelastic creep strain exists, so the viscoelastic creep strain can be obtained by subtracting the instantaneous strain from the total strain. The creep strain rate of the fifth stage of each creep test is not zero, so both the viscoelastic and viscoplastic creep strains exist. The viscoplastic creep strain rate can be obtained in the steady-state creep stage Therefore, the viscoplastic creep strain ε vp with time can be calculated as ve The viscoelastic creep strain ε ve is equal to the total creep strain minus the viscoplastic strain. The instantaneous strain ε ve , the viscoelastic creep strain ε ve of the rock sample before entering the accelerated creep stage, and the viscoplastic creep strain ε ve at the end of the creep test under different confining pressures are listed in Table 2. m ve vp

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

[0103]

[0104]

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

[0106] ε m = k1× R d + b1 (3)

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

[0108] In this creep test, the instantaneous strain under different confining pressures can be calculated by equation (3). The instantaneous strain of R d = 0.55 can be calculated by εb m The relationship between confining pressure and ε b is linear:

[0109] Table 3: Calculated values of ε b m and ε p m

[0110] Confining pressure (MPa) εb m(10 -3 )]]> -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 Rmd, i.e. (σ p -σ3) / σ p In triaxial tests, Rmdcan be close to but not equal to 1, so the expression of Rmdcan be written as:

[0112]

[0113] The instantaneous strain of Rmd, εpm, can be calculated from equation (3) and listed in Table 3, and the relationship between εpmand confining pressure is shown as:

[0114]

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

[0116]

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

[0118] Constitutive relationship between stress and creep strain: under the action of deviatoric stress and confining pressure, 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 rock can be obtained. Figure 4 The relationship between the final viscoelastic creep strain and R d can be seen that, with the increase of R d , except for the rock sample with confining pressure of 1 MPa, the contribution of creep to the final viscoelastic creep strain of rock first decreases and then increases. The relationship between the final viscoelastic creep strain and R d can be described by a quadratic curve:

[0119]

[0120] where ε ve is the viscoelastic creep strain, and l1, m1and n1are parameters that can be obtained from Figure 4 .

[0121] ​It can be determined that when Rd = 0.63, the final viscoelastic creep strain is the smallest, indicating that the rock is 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 non-zero, viscoplastic creep strain exists. In this example, viscoplastic creep strain exists only at the 5th level of each creep test under different confining pressures. The deviatoric stress at the 5th level 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 This refers to the threshold at which rock creep deformation transitions from the steady-state creep stage to the unsteady-state creep stage. When the deviatoric stress is less than this threshold, the steady-state creep strain rate gradually decreases to zero over time, and the rock's creep strain ultimately stops increasing. When the deviatoric stress exceeds the threshold, the steady-state creep strain rate remains nonzero, and after a period of steady-state creep, the rock enters the accelerated creep stage. Therefore, long-term strength can be defined as the maximum deviatoric stress at which the rock's steady-state creep strain rate reaches zero. However, achieving zero creep strain rate is difficult during testing, so an acceptable threshold is necessary. When the creep rate falls below a sufficiently small value, the final creep rate is considered zero, and the creep deformation stabilizes. In this example, if the creep strain rate is less than 1.0×10-7(s-1), the creep rate can be considered zero. If the creep strain rate exceeds 1.0×10-7(s-1), the rock enters 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 steady-state creep strain rates under 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 measurement of RL d shows that when the deviatoric stress reaches 0.9501σ p When the rock enters the accelerated creep stage, and 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 in Figure 3, the aging properties of granite can be simulated using a conventional creep constitutive model. Figure 6 The Burgers model in

[15] 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

[15] is presented. The elastic element in this model represents the instantaneous, time-independent elastic strain. The viscoplastic creep element represents the time-varying linear viscoplastic creep strain when the deviatoric stress is greater than the long-term strength and is absent when the deviatoric stress is less than the long-term strength. If the deviatoric stress is less than the long-term strength, the creep deformation is reversible; otherwise, plastic creep occurs in the steady-state creep phase. The viscoelastic creep element represents the viscoelastic creep strain, where 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 modulus and viscosity coefficient respectively.

[0132] The Nishihara model accurately describes the strain time in creep experiments. The instantaneous strain, viscoplastic strain, and viscoelastic strain in creep experiments are all related to the deviatoric stress and confining pressure. However, the Nishihara model does not consider confining pressure. In this example, an improved Nishihara model is developed by incorporating confining pressure and Rd into the Nishihara model. This model unifies 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 formula (6):M , based on equation (3), E M can be written as:

[0134]

[0135] Viscoelastic creep strain ε ve can be obtained by Kelvin elastic modulus E K , when t→∞, ε ve = (σ1-σ3) / E K , based on equation (4), E K can be expressed as:

[0136]

[0137] The 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 , which are related to the viscoelastic creep strain and the creep time t c of the viscoplastic creep strain. The expression of viscoelastic creep strain with time ε ve (t) is as follows:

[0138]

[0139] In the steady-state creep stage, the creep strain rate (s -1 ) of the first 4-stage creep test is 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. The creep time t c refers to the time for the rock to reach the final viscoelastic creep strain. In the 5th stage creep test, t c refers to the time before the rock enters the accelerated creep. The viscoelastic creep strain ε ve is listed in Table 2, and t c is listed in Table 4. Introducing ε ve and t c into equation (9), the following expression can be obtained:

[0140]

[0141] Table 4: Creep time t c values

[0142]

[0143] Since the exponential function cannot be zero, the value of η K cannot be directly calculated. Assuming 1-ε ve E K(10) is valid, so η K can be expressed as follows:

[0144]

[0145] η M Only exists in the 5th stage of creep test, based on Figure 8 and equation (5), the final visco-plastic creep strain ε vp can be expressed as:

[0146]

[0147] Introducing equation (5) and (1) into equation (12), η M 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 improved Nishihara creep model into the three-dimensional creep constitutive equation. Equation (6) is a one-dimensional creep model, and the total strain is composed of instantaneous strain, viscoelastic creep strain and visco-plastic creep strain. In three-dimensional state, the stress tensor σij of rock can be decomposed into deviatoric stress tensor Sij and spherical stress tensor σm, and the strain tensor εij can be decomposed into deviatoric strain tensor eij and spherical strain tensor εm, which can be written as:

[0150]

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

[0152]

[0153] The deviatoric stress tensor and the 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 the bulk modulus;

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

[0159]

[0160] where G K and η K are the viscoelastic shear modulus and shear viscous coefficient, respectively;

[0161] The three-dimensional constitutive equation of the viscoplastic element can be written as:

[0162]

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

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

[0165]

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

[0167]

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

[0169]

[0170] where (S ij ) s is the deviatoric stress tensor corresponding to σ L ;

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

[0172]

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

[0174]

[0175] where the functional expressions of the parameters K, G0, G k , η K and η M in the model can be derived from equations (7), (8), (11) and (13).

[0176] Improved Nishihara creep model validation: Both Nishihara model and improved Nishihara model can describe the strain-time curves in creep tests, and the improved Nishihara model is more accurate for the creep tests with higher confining pressure. The parameters of Nishihara model and improved Nishihara model are shown in Table 5. Except for the confining pressure of 1 MPa, the R2 of improved Nishihara model is greater than 0.9. Therefore, the improved Nishihara model expression can effectively describe the time-dependent behavior of rock and the decay and steady-state creep behavior.

[0177] Table 5: 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 influence of confining pressure and R d . In contrast, the improved Nishihara model calculates the parameters by a set of unified equations that internally consider the influence of confining pressure and R d . Although the improved Nishihara model has greater error on some curves than the traditional Nishihara model, the improved Nishihara model improves the integrity of the model by considering the influence of axial pressure and confining pressure, and better describes the mechanism that controls the development of creep strain.

[0181] The above-described embodiments are merely preferred technical solutions of the present application, and should not be regarded as a limitation on the present application. The protection scope of the present application should be based on the technical solutions recited in the claims, and include equivalent replacement solutions of the technical features recited in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present application.

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, based on 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 were established, and then the confining pressure was introduced into the Nishihara model, resulting in an expression that can accurately describe the time-dependent deformation of granite under different confining pressures and deviatoric stresses. 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 confining pressures of 1, 3, 5, and 10 MPa, with axial stress of 0.55-1.00 times the peak strength; In creep tests, the superposition relationship of the deformation process is established by plotting the deformation-time curve of the rock sample. The test results of a multi-step loading are used to obtain multiple single-stage loading creep test results. 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 allow it to stabilize; S2. While applying confining pressure, apply 0.1 MPa / s axial pressure to the rock sample until the confining pressure value is reached. 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 proceed to the next level of axial compression loading, with the axial compression difference between adjacent levels being 10%-20% of the peak strength; S4, repeat step S3 until the rock sample fails; The ratio of deviatoric stress to peak strength R is used d , the creep test is analyzed and the calculation formula is as follows: （1）； Peak intensity It is the maximum axial pressure under a certain confining pressure in a conventional triaxial compression test; Total strain By instantaneous strain and creep strain Composition, and gradually increases with time, creep strain Viscoelastic creep strain and viscoplastic creep strain composition: （2）； 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: （3）； Among them, k1 and b1 are parameters; Viscoelastic creep strain and R d The relationship is described by a quadratic curve: （4）； Among them, l1, m1 and n1 are parameters; When the steady-state creep strain rate is not zero, viscoplastic creep strain exists. The linear relationship between viscoplastic creep strain and confining pressure is expressed as: （5）； Among them, k2 and b2 are parameters; The expression of the Nishihara model is: （6）； in, 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 Kelvin elastic modulus and viscosity coefficient respectively; The long-term strength of the rock. The instantaneous elastic modulus of rock is the Maxwell elastic modulus E in formula (6): M , based on formula (3), E M Written as: （7）； Viscoelastic creep strain ε ve Kelvin modulus E K We can get that when t→∞, ε ve = (σ1 - σ3) / E K , based on formula (4), E K Expressed as: （8）； In the Nishihara model, η K and η M Creep time t related to viscoelastic creep strain and viscoplastic creep strain c The viscoelastic creep strain with time ε ve The expression of (t) is as follows: （9）； ε ve and t c Introducing formula (9), we get the following expression: （10）； Assumptions =0.0001, so η K It is expressed as follows: （11）； Final viscoplastic creep strain ε vp Expressed as: （12）； Introducing Equation (5) into Equation (12), η M Expressed as: （13）。 2. The method for analyzing creep test of underground cavern rock according to claim 1, characterized in that: Based on 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 fails, and the axial displacement is continuously recorded; the measurement information is automatically recorded and processed by the data logger every second; the next level of creep testing can only be carried out when the real-time output displacement of the data logger no longer increases.

3. The method for analyzing creep test of underground cavern rock according to claim 1, characterized in that: In three-dimensional state, the stress tensor of rock Decomposed into the deviatoric stress tensor and the spherical stress tensor , the strain tensor Decomposed into the deviatoric strain tensor and spherical strain tensor , written as: （14）； in, is the Kronecker function, and the spherical stress tensor and spherical strain tensor are written as: （15）； The deviatoric stress and strain tensors are written as: （16）； Therefore, the elastic element under three-dimensional stress state is expressed as: （17）； Where, G0 and K are the shear modulus and bulk modulus; Assuming that the creep behavior is characterized by shear deformation and the volume change is elastic, the three-dimensional constitutive formula of the viscoelastic element can be written as: （18）； Among them, G K and η K are the shear modulus and shear viscosity of viscoelasticity; The three-dimensional constitutive formula of viscoplastic elements is written as: （19）； in, , F is the yield function of rock, F0 is the initial value of the rock yield function, Q is the plastic potential function, (·) is a power function, η M is the shear viscosity coefficient of viscoplasticity; The yield function F is written as: （20）； 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: （21）； 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: （22）； in, is σ L The corresponding deviatoric stress tensor; In triaxial compression test, σ2 = σ3 < σ1, so: （23）； 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: （24）； Among them, the parameters K, G0, G k ,η K and η M The functional expression of is derived from Equations (7), (8), (11) and (13).

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