Irregular rock strength time-varying attenuation law testing method based on linear viscoelasticity theory

Abstract

The invention belongs to the technical field of geotechnical material tests, and relates to a method for testing the strength time-varying attenuation law of irregular rocks, in particular to a method for testing the strength time-varying attenuation law of the irregular rocks based on a linear viscoelasticity theory. According to the method, the creep compliance of the irregular rock is measured by using a uniaxial dead-load compression test, the time-varying evolution process of stress strain on a loading shaft of the irregular rock under the long-term action of a target constant load is solved based on a linear viscoelasticity theory, further, a failure time prediction model of the irregular rock under the long-term action of the target constant load is constructed, and the failure time prediction model is used for predicting the failure time of the irregular rock under the long-term action of the target constant load. Calculating the long-term strength level and the damage time under the long-term action of different target constant loads, and finally obtaining a mathematical expression for describing the irregular rock strength time-varying attenuation law by fitting the empirical relationship between the load level and the damage time.

Description

Technical Field

[0001] The invention belongs to the technical field of rock material testing, and relates to a testing method for the time-varying attenuation law of the strength of irregular rock blocks, and specifically to a testing method for the time-varying attenuation law of the strength of irregular rock blocks based on linear viscoelasticity theory. Background Art

[0002] Monitoring data show that after completion, high rockfill dams will experience deformation that continues to grow over time. This kind of deformation is called long-term deformation, which can easily lead to hollowing, cracking, crushing of the anti-seepage panel, or hydraulic fracturing inside the anti-seepage core wall. Such problems will greatly deteriorate the anti-seepage function of the dam body, resulting in a huge increase in maintenance costs, and even endanger the safety of the project in serious cases. After analyzing a large amount of dam settlement monitoring data, relevant researchers pointed out that the rheology of rockfill is one of the important reasons for long-term deformation. The so-called rheology of rockfill refers to the deformation of rockfill over time when the stress state remains unchanged. The higher the stress, the more significant the rheological phenomenon. With the increase in the design height of rockfill dams, the study of the rheology of rockfill has become a hot issue in the engineering community. At present, relevant researchers have reached the following consensus on the study of the rheology of rockfill: as a typical bulk material, the rheology of rockfill is the macroscopic manifestation of the rupture of particles over time and a series of microscopic changes caused by it. It is an important topic to deeply explore the relationship between the macroscopic rheology and microscopic mechanism of rockfill.

[0003] In the above context, researchers introduced the discrete element method to conduct a macro-micro joint analysis of the rheology of rockfill materials. This method uses a large number of particle units to simulate the object of study, and reflects the mechanical behavior of bulk materials by solving the motion state of each particle; each particle in the model is assigned microscopic parameters including but not limited to strength, size and mass. Parameters related to particle strength are the key to simulating particle crushing. In order to simulate the time effect of rheology, the particle strength will be set to decrease continuously over time. This special design is based on the qualitative understanding of the mesoscopic mechanism of rockfill rheology in the academic community, and can reproduce the phenomenon of particle crushing that gradually becomes significant during loading. At present, the mainstream methods for calibrating particle strength-related parameters are mostly aimed at making the macroscopic mechanical behavior of numerical samples closest to the actual performance of rockfill materials. However, the results obtained in this way may not have actual physical meaning, and the trial calculation process has a certain degree of blindness. Considering the modeling principle of the discrete element method, before calibrating the numerical particle strength-related parameters, particle physical and mechanical tests are carried out to obtain some regular results for reference and support, which is conducive to reducing the blindness of the calibration process and minimizing the loss of physical meaning of the calibration results. Therefore, it is necessary to test the time-varying attenuation law of rockfill particle strength.

[0004] Rockfill particles are a typical irregular rock mass, and there is currently no method specifically used to test its time-varying strength attenuation law. However, the description of the time-varying strength attenuation law of irregular rock masses, like conventional rock materials, should be based on the strength attenuation limit and attenuation process. The strength attenuation limit corresponds to the long-term strength level, that is, the ratio of the maximum load that will not cause damage under compression conditions no matter how long it lasts to the instantaneous failure load; the strength attenuation process corresponds to the empirical relationship between the load level and the failure time, and the load level is the ratio of the applied load to the instantaneous failure load. What can be used for reference now is the test method of the time-varying strength attenuation law of conventional rock materials, that is, the uniaxial compression creep test, which has two types: graded loading and single-stage loading. Graded loading is to apply constant pressures of different magnitudes to single cylindrical specimens in the same group step by step, and single-stage loading is to apply constant pressures of different magnitudes to multiple cylindrical specimens in the same group. They all require that the instantaneous strength of the same group of cylindrical specimens is basically consistent in order to determine the size of the target pressure, but each has its own advantages and disadvantages in application: graded loading can determine the strength attenuation limit, but it is difficult to give the strength attenuation process; single-stage loading can give the strength attenuation limit and attenuation process, but the time cost is high and there are many uncertain factors in the test, which makes the operation difficult. In fact, the instantaneous strength of irregular rock blocks is highly discrete, so single-stage loading is not suitable, and the results obtained by graded loading alone are not comprehensive. Therefore, it is urgent to design a test method for the time-varying attenuation law of irregular rock strength.

[0005] Rock materials exhibit linear viscoelasticity when subjected to rapidly increasing and then constant pressure, which is an important reason why their deformation is time-dependent, and this is no exception when the shape is irregular. If this mechanical property can be used to determine the time-varying evolution of stress and strain inside the object being studied, then it is not difficult to calculate the time required for the stress and strain to reach the limit state that causes the material to fail from the initial state. The time calculated here can obviously be used as the failure time corresponding to the target load level. Similarly, the long-term strength level can also be determined based on the time-varying evolution of stress and strain. In other words, by measuring the linear viscoelastic mechanical parameters of irregular rock blocks using specific tests and combining them with theoretical calculations, data used to describe the time-varying attenuation law of strength can be obtained. Accordingly, the present invention proposes a method for testing the time-varying attenuation law of strength of irregular rock blocks based on linear viscoelasticity theory. Summary of the invention

[0006] The purpose of the present invention is to provide a method for testing the time-varying attenuation law of irregular rock strength based on linear viscoelastic theory. The method uses a uniaxial constant load compression test to measure the creep compliance of irregular rock, and solves the time-varying evolution of stress and strain on the loading axis of irregular rock under the long-term action of target constant load based on linear viscoelastic theory. Further, a failure time prediction model of irregular rock under the long-term action of target constant load is constructed, and the long-term strength level and the failure time under the long-term action of target constant loads of different sizes are calculated. Finally, a mathematical expression describing the time-varying attenuation law of irregular rock strength is obtained by fitting the empirical relationship between load level and failure time.

[0007] The present invention adopts the following technical solutions to achieve the above purpose:

[0008] A method for testing the time-varying attenuation law of irregular rock strength based on linear viscoelasticity theory comprises the following steps:

[0009] Step 1: Measure the characteristic dimensions of the sample rock block and conduct a uniaxial constant load compression test to obtain the delayed deformation curve under graded equicyclic constant loads, and record the load value at the time of failure and the duration of the load action;

[0010] The characteristic dimensions of the sample rock block refer to its major axis, median axis and minor axis dimensions, which are L, W and H respectively and are defined as follows: first, the sample rock block is placed on a horizontal test bench in a self-stabilizing manner in various postures, and a stable placement posture is found that makes the distance between the highest point of the sample rock block and the horizontal test bench (i.e., the height) the shortest. The height at this time is defined as the minor axis dimension, and then in all horizontal sections, the maximum diameter is taken as the major axis dimension, and the maximum diameter in the direction perpendicular to the major axis is taken as the median axis dimension.

[0011] The uniaxial constant load compression test refers to a deformation test of a sample rock block under the action of time-varying pressure provided by two upper and lower parallel rigid plates. The characteristics of this test include but are not limited to: the two rigid plates themselves do not deform; the direction of pressure is parallel to the short axis direction of the sample rock block; the sample rock block placed on the lower rigid plate is in a self-stable state under its own weight.

[0012] The graded equicyclic constant load action refers to applying n≥1 different constant pressures step by step starting from time t=0. Each level increases rapidly on the basis of the previous level and then remains constant. Each level is designed to last for the same length of time and can make the sample rock block deform into a stable stage. The magnitude of each level of constant pressure should be appropriately given after examining the statistical laws of the strength of irregular rock blocks with the same lithology, but the first level of constant pressure should not destroy the sample rock block. The load action is specifically expressed as:

[0013]

[0014] Among them, Fms (t) is the graded equicyclic constant load action; t0 = 0 and t1-t0 = t2-t1 = ... = t n -t n-1 =Δt; ΔF0 is the first stage constant pressure, and the remaining ΔF k is the difference between the constant pressure of the k+1th stage and the kth stage; U(tt k ) is a step function, when tt k 1 if ≥0, otherwise 0.

[0015] The delayed deformation curve refers to the curve of the relationship between the deformation of the sample rock and time. The load value at the time of failure and the duration of the load refer to the pressure magnitude when the sample rock is destroyed and the duration of the pressure, which are defined as follows: If the sample rock is destroyed at the N=2,3,...,nth level constant pressure, the Nth level constant pressure magnitude is used as the load value at the time of failure, and the duration of the pressure is the duration of the Nth level constant pressure; otherwise, the pressure should be continued at the end of the test until the sample rock is destroyed, and the pressure magnitude at this time is used as the load value when the failure occurs, and the duration of the pressure is zero.

[0016] Step 2: Combined with the characteristics of uniaxial constant load compression test, the relationship between delayed deformation curve and equivalent deformation curve is established, see formula (9);

[0017] The equivalent deformation curve refers to the relationship curve between the equivalent value of the sample rock deformation and time. The establishment of the relationship between the delayed deformation curve and the equivalent deformation curve specifically refers to constructing a conversion relationship between the sample rock deformation and its equivalent value, and the method is as follows:

[0018] The distance δ(t) that two linear viscoelastic bodies p and q of arbitrary shapes approach each other under the action of time-varying pressure Γ(t) starting from a point contact state at time t=0 is given by equation (2). The derivation process can be found in Yang’s book “The contact problem for viscoelastic bodies” (Journal of Applied Mechanics, 1966, 33(2): 395-401. DOI: 10.1115 / 1.3625055).

[0019]

[0020] where γ is the eccentricity of the elliptical contact domain between objects p and q, calculated by equation (3); K′(γ) is the first kind complete elliptic integral with γ as parameter; ν p and ν q are the Poisson's ratios of objects p and q respectively; Φ p (t) and Φ q(t) are the creep compliances of objects p and q respectively; β is a constant obtained by equation (4); “*” represents Stieltjes convolution, and the specific algorithm is shown in equation (7). Other mathematical properties of the convolution operation can be found in Gurtin et al., On the linear theory of viscoelasticity (Archive for Rational Mechanics and Analysis, 1962, 11(1): 291-356. DOI: 10.1007 / BF00253942).

[0021] (BA)(A+B) -1 =1-2γ -2 [E′(γ)] -1 (1-γ 2 )[K′(γ)-E′(γ)] (3)

[0022] β(1-γ 2 ) 1 / 2 [K′(γ)-E′(γ)]=γ 2 A (4)

[0023] Where E′(γ) is the complete elliptic integral of the second kind with γ as the parameter; A and B are geometric constants that satisfy the relationship given by equations (5) and (6).

[0024]

[0025] in, is the minimum radius of curvature of object p at the center of the elliptical contact zone between it and object q; is the maximum radius of curvature of object p at the center of the elliptical contact zone between it and object q; is the minimum radius of curvature of object q at the center of the elliptical contact zone between it and object p; is the maximum radius of curvature of object q at the center of the elliptical contact zone between it and object p; α is the radius of curvature and The angle between the normal sections.

[0026]

[0027] Among them, h1(t) is a function that is continuous on [0,+∞) and has h1(t)=0 when t<0; h2(t) is a function defined on [0,+∞), which is not required to be continuous but requires h2(t)=0 when t<0.

[0028] Combined with the characteristics of the uniaxial constant load compression test, the following assumptions are made: the contact between the sample rock block and the lower rigid plate is plane-to-plane, while the contact between the sample rock block and the upper rigid plate is point-to-plane; the deformation of the sample rock block comes entirely from the linear viscoelastic deformation of the sample rock block in the elliptical contact area between it and the upper rigid plate, that is, the distance between the sample rock block and the upper rigid plate from the point contact state at time t=0 under the action of the time-varying pressure Γ(t); the creep compliance of the rigid plate is zero; the creep compliance of the sample rock block is Φ(t), and the Poisson's ratio is ν. Based on the above assumptions, equation (8) can be derived from equation (2), and then equation (9) can be obtained by sorting equation (8). Equation (9) is the conversion relationship between the deformation of the sample rock block and its equivalent value, that is, the relationship between the delayed deformation curve and the equivalent deformation curve. Generally speaking, the equivalent deformation curve is derived based on the delayed deformation curve under a certain load, so it is the equivalent deformation curve corresponding to that load.

[0029] s(t)=βK′(γ)(1-γ 2 ) 1 / 2 {1.5β -1 π -1 (1-γ 2 ) -1 / 2 (1-ν 2 )Φ(t)*dΓ(t)} 2 / 3 (8)

[0030] Φ(t)*dΓ(t)=0.667π(1-ν 2 ) -1 β -1 / 2 [K′(γ)] -3 / 2 (1-γ 2 ) -1 / 4 [s(t)] 3 / 2 =Y(t) (9)

[0031] Where s(t) is the deformation of the sample rock block; Y(t) is the equivalent value of the deformation of the sample rock block.

[0032] Because the principal radius of curvature of the upper rigid plate at the center of the contact area between it and the sample rock block approaches infinity, equations (5) and (6) will become equations (10) and (11). A and B can be obtained from equations (10) and (11), and γ and β can be determined from equations (3) and (4).

[0033] 2(A+B)=1 / R I +1 / R II (10)

[0034] 4(BA) 2 =(1 / R I -1 / R II )2 (11)

[0035] Among them, R I is the minimum radius of curvature of the sample rock at the center of the elliptical contact area between it and the upper rigid plate; R II R is the maximum radius of curvature of the sample rock at the center of the elliptical contact area between it and the upper rigid plate. I and R II It can be obtained by, but not limited to, the following methods:

[0036] R I =(0.25W 2 +H 2 ) / (2H) (12)

[0037] R II =(0.25L 2 +H 2 ) / (2H) (13)

[0038] Step 3: Based on the delayed deformation curve of the sample rock block under the graded equal-periodic constant load obtained in the first step, firstly, with the help of the connection between the delayed deformation curve and the equivalent deformation curve established in the second step, the equivalent deformation curve corresponding to the graded equal-periodic constant load is deduced, and then the deduced curve is reconstructed with the help of the superposition principle to obtain the equivalent deformation curve cluster corresponding to the one-time action of constant loads of different sizes;

[0039] The constant loads of different magnitudes refer to a series of constant pressures with different values, and their values, from low to high, are equal to the magnitudes of n≥1 constant pressures that appear successively during the process of the graded equal-periodic constant load action in the first step. The one-time action refers to a rapid increase from zero to the target value at time t=0 and then remaining constant until time t=Δt. The one-time action of the constant loads of different magnitudes is specifically expressed as:

[0040]

[0041] Among them, F os,m (t) is the one-time action of the constant load of different magnitudes; U(Δt-t) is a step function, which is 1 when Δt-t≥0, otherwise it is 0.

[0042] The meaning of the superposition principle is: The equivalent deformation curve corresponding to the one-time action of a constant load can be regarded as The incremental load ΔF is superimposed on the equivalent deformation curve corresponding to the one-time action of the constant load i The additional effect caused within the time Δt is valid for 1≤i≤n-1. The proof is as follows: For graded equicyclic constant load, if time t=ti No incremental load ΔF is applied i , then the load at time 0≤t<t i+1 When t is t, it is expressed as formula (15), otherwise it is expressed as formula (16). Substituting formula (15) and (16) into formula (9) respectively, we can get the above two cases at time t i ≤t<t i+1 The deformation equivalent values ​​at the time of ΔF are shown in equations (17) and (18) respectively. By subtracting equation (17) from equation (18), the difference between the deformation equivalent values ​​of the two is ΔF. i Φ(tt i ), if tt i It is denoted as Δτ. Obviously, 0≤Δτ<Δt exists, so the incremental load ΔF i The additional effect caused within the duration of Δt is ΔF i Φ(Δτ); for a size of and The constant load of one-time action can be obtained from equation (9). The deformation equivalent values ​​at time t = Δτ are shown in equations (19) and (20). The difference between the deformation equivalent values ​​of the two can be obtained by subtracting equation (19) from equation (20): ΔF i Φ(Δτ), therefore, the superposition principle is proved.

[0043]

[0044] in, At time t = t i No incremental load ΔF is applied i In the case of graded equicyclic constant load acting at time 0≤t<t i+1 The expression when At time t = t i When the incremental load ΔF is applied i In the case of graded equicyclic constant load acting at time 0≤t<t i+1 The expression when At time t = t i No incremental load ΔF is applied i In the case of graded equicyclic constant load acting at time t i ≤t<t i+1 Equivalent value of sample rock deformation caused by At time t = t i When the incremental load ΔF is applied i In the case of graded equicyclic constant load acting at time t i ≤t<t i+1 The equivalent value of the sample rock deformation caused by os,i-1 (Δτ) refers to the size of The equivalent value of the sample rock deformation caused by a one-time constant load at time t = Δτ; Y os,i (Δτ) refers to the size of The equivalent value of the sample rock deformation caused by a one-time constant load at time t = Δτ.

[0045] The process of reconstructing the derived curve by means of the superposition principle to obtain a cluster of equivalent deformation curves corresponding to a one-time action of a constant load of different magnitudes is as follows:

[0046] First, the part of the equivalent deformation curve corresponding to the graded equal-periodic constant load with a time t0≤t<t1 is taken as the equivalent deformation curve corresponding to the one-time action of the constant load with a magnitude of ΔF0;

[0047] Secondly, the time t0≤t<t1 part of the equivalent deformation curve corresponding to the graded equal-periodic constant load is extended to time t=t2, and the difference between the time t1≤t<t2 part of the equivalent deformation curve corresponding to the graded equal-periodic constant load and the deformation equivalent value of the above extension line at the same time is calculated. These differences are used as the additional effect caused by the incremental load ΔF1 within the time length Δt and superimposed on the equivalent deformation curve corresponding to the one-time action of the constant load of magnitude ΔF0, and the size is obtained. The equivalent deformation curve corresponding to the one-time action of constant load;

[0048] Then, the time t1≤t<t2 on the equivalent deformation curve corresponding to the graded equal-periodic constant load is extended to time t=t3, and the difference between the time t2≤t<t3 on the equivalent deformation curve corresponding to the graded equal-periodic constant load and the deformation equivalent value of the extension line at the same time is calculated, and these differences are used as the additional effect caused by the incremental load ΔF2 within the time length Δt to add to the value of The equivalent deformation curve corresponding to the one-time action of the constant load is obtained. The equivalent deformation curve corresponding to the one-time action of constant load;

[0049] By analogy, if the sample rock is destroyed at the N = 2, 3, ..., nth level of constant pressure, then the final value will be The equivalent deformation curve corresponding to the one-time action of a constant load is Equivalent deformation curve corresponding to the one-time action of constant load.

[0050] Step 4: Using the equivalent deformation curve clusters corresponding to the one-time action of constant loads of different sizes obtained in the third step, the creep compliance values ​​at different times are obtained, and then the creep compliance expression is determined;

[0051] The method for obtaining the creep compliance values ​​at different moments is, for a certain moment, first finding a load sequence and a corresponding deformation equivalent value sequence from a cluster of equivalent deformation curves corresponding to the one-time action of constant loads of different magnitudes, and then fitting a linear model y0=λ·x0 with the load as the independent variable x0 and the deformation equivalent value as the dependent variable y0, and the size of λ calculated thereby is the creep compliance value at that moment.

[0052] The creep compliance expression refers to a mathematical expression used to quantitatively describe the changing trend of creep compliance values ​​at different times with the corresponding time series. This type of mathematical expression is derived based on common viscoelastic models. For example, the creep compliance expression derived from the standard linear solid model is as follows:

[0053]

[0054] Where Φ(t) is the creep compliance of the sample rock; E1, E2 and η1 are parameters in the standard linear solid model, and E1 / η1 can usually also be expressed as 1 / N1.

[0055] Step 5: Solve the problem of F based on linear viscoelasticity theory Gt The time-varying evolution of stress and strain on the loading axis of the sample rock block under the long-term action of the target constant load;

[0056] The target constant load is a constant pressure determined according to the actual problem. The long-term action refers to the pressure that increases rapidly from zero to the target value at time t=0 and then remains constant. The magnitude is F Gt The target constant load long-term action is specifically expressed as:

[0057] F G (t) = F Gt ·U(t) (22)

[0058] Among them, F G (t) is the target constant load long-term action; U(t) is a step function, which is 1 when t≥0, otherwise it is 0.

[0059] The sample rock block loading axis refers to the position in the sample rock block where the vertical line with the center of the elliptical contact area between the sample rock block and the upper rigid plate as the foot passes. The time-varying evolution process of stress and strain refers to the process in which the stress field and strain field continuously change with the extension of the time of the time-varying pressure. The process of solving based on the linear viscoelastic theory is as follows:

[0060] First, when two linear viscoelastic bodies p and q of arbitrary shapes approach each other from a point contact state at time t = 0 under the action of a time-varying pressure Γ(t), if a spatial rectangular coordinate system is established with the center of the elliptical contact domain between them as the origin, the plane where the elliptical contact domain is located as the xoy coordinate plane, the major axis of the elliptical contact domain as the x-axis, the minor axis of the elliptical contact domain as the y-axis, and the straight line passing through the origin and perpendicular to the xoy coordinate plane as the z-axis, and the positive direction of the z-axis pointing to either object p or q, then the contact pressure p(x, y, t) on the elliptical contact domain between them is given by equation (23). The derivation process can be found in Yang's book "The contact problem for viscoelastic bodies" (Journal of Applied Mechanics, 1966, 33(2): 395-401. DOI: 10.1115 / 1.3625055).

[0061]

[0062] Where a(t) is the semi-major axis size of the elliptical contact domain, see equation (24); b(t) is the semi-minor axis size of the elliptical contact domain, which is (1-γ 2 ) 1 / 2 times; g(t) is calculated by formula (25).

[0063]

[0064] Secondly, according to the assumptions made in the second step combined with the characteristics of the uniaxial constant load compression test, it can be obtained that when the sample rock block and the upper rigid plate are at a size of F Gt When they start to approach each other from the point contact state at time t=0 under the long-term action of the target constant load, if the center of the elliptical contact domain between them is taken as the origin, the plane where the elliptical contact domain is located is taken as the xoy coordinate plane, the major axis of the elliptical contact domain is taken as the x-axis, the minor axis of the elliptical contact domain is taken as the y-axis, and the straight line passing through the origin and perpendicular to the xoy coordinate plane is taken as the z-axis, and the positive direction of the z-axis points to the upper rigid plate, a spatial rectangular coordinate system is established, then the contact pressure on the elliptical contact domain between them is still as shown in formula (23), but at this time, the major semi-axis size a(t) of the elliptical contact domain needs to be calculated according to formula (26), and g(t) is calculated by formula (27).

[0065] a(t)=[1.5β -1 π -1 (1-γ 2 ) -1 / 2 (1-ν 2 )F Gt Φ(t)] 1 / 3 (26)

[0066] (1-ν 2 )Φ(t)*dg(t)=U(t) (27)

[0067] Then, since the size of the contact domain between the sample rock block and the upper rigid plate is very small compared to the size of the sample rock block and the relative curvature radius of the surface, the sample rock block can be regarded as a linear viscoelastic half-space body with the xoy coordinate plane as the flat surface, and the contact pressure on the contact domain is simplified to a load acting on a small elliptical area on the flat surface. The elliptical area is completely equivalent to the elliptical contact domain between the sample rock block and the upper rigid plate. At the same time, the normal of the flat surface is parallel to the z-axis and the tangent is parallel to the xoy coordinate plane. Therefore, by constructing a linear viscoelastic half-space boundary value problem, the stress field on the loading axis of the sample rock block can be calculated. The boundary conditions of the boundary value problem satisfy the expression of equations (28) to (30).

[0068] σ s (x,y,t)=0,(x,y)∈S (28)

[0069] σ n (x,y,t)=p(x,y,t),(x,y)∈S1(t) (29)

[0070] u n (x,y,t)=0,(x,y)∈S2(t) (30)

[0071] Among them, σ s (x,y,t) is the time-varying tangential stress at the point (x,y); σ n (x,y,t) is the time-varying normal stress at the point (x,y); u n (x,y,t) is the time-varying normal displacement at point (x,y); (x,y)∈S means that point (x,y) is located on the plane surface of the linear viscoelastic half-space; (x,y)∈S1(t) means that point (x,y) is located on a small elliptical region on the plane surface of the linear viscoelastic half-space, that is, within the loading region; (x,y)∈S2(t) means that point (x,y) is located on the complementary part of the plane surface of the linear viscoelastic half-space to the elliptical loading region, that is, the intersection of S1(t) and S2(t) is empty but the union is S.

[0072] Finally, the creep compliance expression obtained in the fourth step is introduced to specifically analyze the characteristics of the boundary conditions that change with the extension of the time of the time-varying pressure. According to this characteristic, a boundary value problem solving method is selected to solve the stress component σ on the loading axis of the sample rock block from the above linear viscoelastic half-space boundary value problem. j (t), and then use the linear viscoelastic constitutive relations given by equations (31) to (33) to calculate the strain component ε j(t), where j = x, y, z.

[0073] ε x (t) = {σ x (t)-ν[σ y (t)+σ z (t)]}*dΦ(t) (31)

[0074] ε y (t) = {σ y (t)-ν[σ z (t)+σ x (t)]}*dΦ(t) (32)

[0075] ε z (t) = {σ z (t)-ν[σ x (t)+σ y (t)]}*dΦ(t) (33)

[0076] Step 6: According to the time-varying evolution of stress and strain on the loading axis of the sample rock block obtained in the fifth step, first select a strength theory to describe its failure state, then build a failure time prediction model for the sample rock block under the long-term action of the target constant load, and combine the load value when the sample rock block is destroyed and the duration of the load recorded in the first step to obtain the allowable value of the rock block strength index, and then calculate the long-term strength level and the failure time under the long-term action of target constant loads of different sizes;

[0077] The failure time prediction model of the sample rock block under the long-term action of the target constant load, referred to as the failure time prediction model, includes three parameters: target constant load, failure time and allowable value of strength index. The specific meaning is that when the long-term action of the target constant load causes the maximum value of the strength index on the loading axis of the sample rock block to exceed its allowable value, it means that the sample rock block is destroyed. If the time when the target constant load begins to act is recorded as zero, then the time required for the maximum value of the strength index on the loading axis to reach the allowable value from the initial value is the failure time.

[0078] The strength index is a characteristic variable used to describe the stress or strain state of the material in the failure criterion expression corresponding to the selected strength theory. The calculation method of the allowable value of the sample rock strength index is to use the load value when the sample rock is destroyed and the duration of the load action recorded in the first step as the target constant load and the destruction time, respectively, and input them into the destruction time prediction model. At this time, the maximum value of the strength index calculated in reverse is the allowable value of the strength index.

[0079] The long-term strength level refers to the ratio of the maximum load that will not cause the sample rock to be damaged no matter how long the compression condition lasts to the instantaneous damage load. The maximum load and the instantaneous damage load are determined with the help of a damage time prediction model, as follows: a numerical value greater than or equal to Δt is assigned to the damage time, and it is input into the damage time prediction model together with the allowable value of the strength index. The target constant load calculated in reverse is the maximum load that will not cause the sample rock to be damaged no matter how long the compression condition lasts, and it is also the load corresponding to the long-term strength level; the damage time is set to zero, and it is input into the damage time prediction model together with the allowable value of the strength index. The target constant load calculated in reverse is the instantaneous damage load.

[0080] The target constant load index values ​​of different sizes exceed the load corresponding to the long-term strength level of the sample rock block but do not exceed its instantaneous failure load. The number of this series of target constant loads should not be less than 3.

[0081] Step 7: By fitting the empirical relationship between load level and failure time, a mathematical expression describing the time-varying attenuation law of the sample rock strength is given.

[0082] The load level refers to the ratio of target constant loads of different sizes to the instantaneous failure load. The failure time refers to the failure time under the long-term action of the target constant load. The mathematical expression can be in the following form but is not limited to:

[0083] S L =S ∞ +(1-S ∞ )exp(-μT f ) (34)

[0084] Among them, S L is the load level; T f is the failure time; μ is the material parameter; S ∞ is the long-term intensity level.

[0085] The beneficial effects of the present invention are:

[0086] The testing method for the time-varying attenuation law of the strength of irregular rock blocks based on the linear viscoelastic theory has clear logic and is easy to implement, which makes up for the current lack of testing methods for the time-varying attenuation law of the strength of irregular rock blocks. The method only needs to use a uniaxial constant load compression test to test the deformation of the sample rock block under graded equicyclic constant loads, which not only avoids the influence of the discreteness of the instantaneous strength of the irregular rock blocks faced by the separate loading methods, but also obtains the load that causes the sample rock block to fail and the corresponding failure time while obtaining the time-dependent deformation of the sample rock block, thus achieving multiple goals at one stroke and effectively reducing the test cost. The method starts from the contact problem between the sample rock block and the rigid plate, based on the sample rock block under graded equicyclic constant loads. The delayed deformation curves under the action of a long-term constant load are processed by superposition to obtain a series of data related to the one-time action of a constant load that is difficult to obtain in practice, and then the creep compliance of the sample rock block is determined, which can be used as a reference for similar block research; this method is based on linear viscoelastic mechanics analysis to link the failure time of irregular rock blocks with the time-varying evolution of their internal stress and strain, which can not only obtain the long-term strength level of the sample block, but also calculate the failure time corresponding to a series of target constant loads of different sizes, overcoming the difficulty of obtaining these two types of data at the same time at this stage; other topics involving the time-varying attenuation law of the strength of irregular rock blocks, such as statistical analysis of these laws, can continue to be carried out based on this method or its improved form. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 This is a flow chart of a method for testing the time-varying attenuation law of irregular rock strength based on linear viscoelasticity theory proposed by the present invention;

[0088] Figure 2 It is a schematic diagram of a uniaxial constant load compression test of the present invention;

[0089] Figure 3 It is a schematic diagram of the process curve of graded equal-periodic constant load action with the target number of stages n≥1 of the present invention;

[0090] Figure 4 It is a schematic diagram of the process of reconstructing the equivalent deformation curve corresponding to the graded equal-periodic constant load action by means of the superposition principle in the present invention to obtain the equivalent deformation curve cluster corresponding to the one-time action of constant loads of different sizes;

[0091] Figure 5 It is a schematic diagram of a standard linear solid model of the present invention;

[0092] Figure 6 Schematic diagram of a spatial rectangular coordinate system used in the present invention for calculating the contact pressure on the elliptical contact area between the sample rock block and the upper rigid plate; (a) is the position of the coordinate system; (b) is the relationship between the elliptical contact area and the coordinate axis;

[0093] Figure 7 It is a schematic diagram of the positions of various regions on the plane surface of the linear viscoelastic half-space body and the spatial rectangular coordinate system of the present invention;

[0094] Figure 8 1 is a delayed deformation curve under graded isocyclic constant load in an embodiment of the present invention; (a) is sample rock block A; (b) is sample rock block B; (c) is sample rock block C;

[0095] Fig. 9 : The equivalent deformation curves corresponding to the graded equal-periodic constant load in the embodiment of the present invention; (a) is the sample rock block A; (b) is the sample rock block B; (c) is the sample rock block C;

[0096] Fig.10 The equivalent deformation curve clusters corresponding to the one-time action of constant loads of different magnitudes in the embodiments of the present invention; (a) is sample rock block A; (b) is sample rock block B; (c) is sample rock block C;

[0097] Fig.11 The creep compliance expression fitting effect in the embodiment of the present invention; (a) is sample rock block A; (b) is sample rock block B; (c) is sample rock block C;

[0098] Fig.12 The time-varying evolution process of the contact pressure distribution on the elliptical contact domain between the sample rock block A and the upper rigid plate after normalization in the embodiment of the present invention; (a) is the long axis position of the contact domain; (b) is the short axis position of the contact domain;

[0099] Fig.13 1 is the time-varying evolution process of the stress component on the loading axis of the sample rock block A in the embodiment of the present invention; (a) is the x-direction component; (b) is the y-direction component; (c) is the z-direction component;

[0100] Fig.14 1 is the time-varying evolution process of the strain component on the loading axis of the sample rock block A in the embodiment of the present invention; (a) is the x-direction component; (b) is the y-direction component; (c) is the z-direction component;

[0101] Fig.15 It is a schematic diagram of a failure time prediction model of a sample rock block A in an embodiment of the present invention;

[0102] Fig.16 The figure is a fitting result diagram of the empirical relationship between load level and failure time in the embodiment of the present invention; (a) is sample rock block A; (b) is sample rock block B; (c) is sample rock block C; DETAILED DESCRIPTION

[0103] The specific implementation of the present invention is described in detail below in conjunction with the technical scheme and the accompanying drawings.

[0104] like Figure 1 As shown, a method for testing the time-varying attenuation law of irregular rock strength based on linear viscoelasticity theory includes the following steps:

[0105] Step 1: Measure the characteristic dimensions of the sample rock block, including the major axis dimension L, the middle axis dimension W and the minor axis dimension H, and carry out a uniaxial constant load compression test, such as Figure 2 As shown in the figure, the delayed deformation curve under graded equicyclic constant load is obtained by this test, and the load value when failure occurs and the duration of the load are recorded. Figure 3 It is a schematic diagram of the graded equicyclic constant load action history curve with target number n≥1.

[0106] Step 2: Based on the characteristics of the uniaxial constant load compression test, the relationship between the delayed deformation curve and the equivalent deformation curve is established, that is, the conversion relationship between the sample rock deformation and its equivalent value, as shown in formula (9).

[0107] Φ(t)*dΓ(t)=0.667π(1-ν 2 ) -1 β -1 / 2 [K′(γ)] -3 / 2 (1-γ 2 ) -1 / 4 [s(t)] 3 / 2 =Y(t) (9)

[0108] Where s(t) is the deformation of the sample rock; ν is the Poisson’s ratio of the sample rock; γ is calculated by formula (3); K′(γ) is the first kind of complete elliptic integral with γ as parameter; β is the constant obtained by formula (4); Y(t) is the equivalent value of the deformation of the sample rock; Φ(t) is the creep compliance of the sample rock; Γ(t) is the time-varying pressure; “*” represents the Stieltjes convolution.

[0109] (BA)(A+B) -1 =1-2γ -2 [E′(γ)] -1 (1-γ 2 )[K′(γ)-E′(γ)] (3)

[0110] β(1-γ 2 ) 1 / 2 [K′(γ)-E′(γ)]=γ 2 A (4)

[0111] Where E′(γ) is the complete elliptic integral of the second kind with γ as the parameter. In the uniaxial constant load compression test, A and B satisfy the relationship given by equations (10) and (11).

[0112] 2(A+B)=1 / RI +1 / R II (10)

[0113] 4(BA) 2 =(1 / R I -1 / R II ) 2 (11)

[0114] Among them, R I is the minimum radius of curvature of the sample rock at the center of the elliptical contact area between it and the upper rigid plate; R II R is the maximum radius of curvature of the sample rock at the center of the elliptical contact area between it and the upper rigid plate. I and R II It can be obtained in the following ways:

[0115] R I =(0.25W 2 +H 2 ) / (2H) (12)

[0116] R II =(0.25L 2 +H 2 ) / (2H) (13)

[0117] Step 3: Based on the delayed deformation curve of the sample rock block under the graded equal-periodic constant load obtained in the first step, firstly, the equivalent deformation curve corresponding to the graded equal-periodic constant load is deduced by using the relationship between the delayed deformation curve and the equivalent deformation curve established in the second step, that is, formula (9), and then the deduced curve is reconstructed by using the superposition principle to obtain the equivalent deformation curve cluster corresponding to the one-time action of constant loads of different sizes, such as Figure 4 As shown, the details are as follows:

[0118] First, the part of the equivalent deformation curve corresponding to the graded equal-periodic constant load with a time of 0≤t<t1 is taken as the equivalent deformation curve corresponding to the one-time action of the constant load with a magnitude of ΔF0;

[0119] Secondly, the time 0≤t<t1 part of the equivalent deformation curve corresponding to the graded equal-periodic constant load is extended backward to time t=t2, and the difference between the time t1≤t<t2 part of the equivalent deformation curve corresponding to the graded equal-periodic constant load and the deformation equivalent value of the extension line at the same time is calculated. These differences are used as the additional effect caused by the incremental load ΔF1 within the time length Δt and superimposed on the equivalent deformation curve corresponding to the one-time action of the constant load of magnitude ΔF0, and the size is obtained. The equivalent deformation curve corresponding to the one-time action of constant load;

[0120] Then, the time t1≤t<t2 on the equivalent deformation curve corresponding to the graded equal-periodic constant load is extended to time t=t3, and the difference between the time t2≤t<t3 on the equivalent deformation curve corresponding to the graded equal-periodic constant load and the deformation equivalent value of the extension line at the same time is calculated, and these differences are used as the additional effect caused by the incremental load ΔF2 within the time length Δt to add to the value of The equivalent deformation curve corresponding to the one-time action of the constant load is obtained. The equivalent deformation curve corresponding to the one-time action of constant load;

[0121] By analogy, if the sample rock is destroyed at the N = 2, 3, ..., nth level of constant pressure, then the final value will be The equivalent deformation curve corresponding to the one-time action of a constant load is Equivalent deformation curve corresponding to the one-time action of constant load.

[0122] In the above reconstruction process, when the equivalent deformation curve corresponding to the graded equal-periodic constant load is extended, the part of the extended section where the deformation equivalent value enters the stable stage is taken, and the average of the deformation equivalent value of this part is calculated, and this average is used as the deformation equivalent value at each moment on the extension line.

[0123] Step 4: Using the equivalent deformation curve clusters corresponding to the one-time action of constant loads of different sizes obtained in the third step, obtain the creep compliance values ​​at different times, and then use the creep compliance values ​​at different times as the dependent variable, the corresponding time series as the independent variable, and formula (21) as the creep compliance expression, and use the nonlinear least squares method to fit the parameters in the expression. Formula (21) used here is based on Figure 5 The standard linear solid model shown is derived.

[0124]

[0125] Where Φ(t) is the creep compliance of the sample rock; E1, E2 and η1 are parameters in the standard linear solid model, and E1 / η1 can usually also be expressed as 1 / N1.

[0126] Step 5: Solve the problem of F based on linear viscoelasticity theory Gt The time-varying evolution of stress and strain on the loading axis of the sample rock block under the long-term action of the target constant load is as follows:

[0127] First, when the sample rock block and the upper rigid plate are at a size of F GtWhen they start to approach each other from the point contact state at time t=0 under the long-term action of the target constant load, if the center of the elliptical contact domain between them is taken as the origin, the plane where the elliptical contact domain is located is taken as the xoy coordinate plane, the major axis of the elliptical contact domain is taken as the x-axis, the minor axis of the elliptical contact domain is taken as the y-axis, and the straight line passing through the origin and perpendicular to the xoy coordinate plane is taken as the z-axis, let the positive direction of the z-axis point to the upper rigid plate, establish the following Figure 6 The spatial rectangular coordinate system shown in FIG. 1 is the contact pressure p(x, y, t) on the elliptical contact domain between them, as shown in formula (23).

[0128]

[0129] Where a(t) is the semi-major axis size of the elliptical contact domain, see equation (26); b(t) is the semi-minor axis size of the elliptical contact domain, which is (1-γ 2 ) 1 / 2 times; g(t) is calculated by formula (27).

[0130] a(t)=[1.5β -1 π -1 (1-γ 2 ) -1 / 2 (1-ν 2 )F Gt Φ(t)] 1 / 3 (26)

[0131] (1-ν 2 )Φ(t)*dg(t)=U(t) (27)

[0132] Then, the sample rock block is regarded as a linear viscoelastic half-space body with the xoy coordinate plane as the plane surface. The contact pressure on the contact domain between the sample rock block and the upper rigid plate is simplified to the load acting on a small elliptical area on the plane surface. The elliptical area is completely equivalent to the elliptical contact domain between the sample rock block and the upper rigid plate. At the same time, the normal of the plane surface is parallel to the z-axis and the tangent is parallel to the xoy coordinate plane, and a linear viscoelastic half-space boundary value problem is constructed with the boundary conditions satisfying the expression of equations (28) to (30).

[0133] σ s (x,y,t)=0,(x,y)∈S (28)

[0134] σ n (x,y,t)=p(x,y,t),(x,y)∈S1(t) (29)

[0135] u n (x,y,t)=0,(x,y)∈S2(t) (30)

[0136] Among them, σ s (x,y,t) is the time-varying tangential stress at the point (x,y); σ n (x,y,t) is the time-varying normal stress at the point (x,y); u n (x,y,t) is the time-varying normal displacement at point (x,y); (x,y)∈S means that point (x,y) is located on the plane surface of the linear viscoelastic half-space; (x,y)∈S1(t) means that point (x,y) is located on a small elliptical area on the plane surface of the linear viscoelastic half-space, that is, in the loading area; (x,y)∈S2(t) means that point (x,y) is located on the part of the plane surface of the linear viscoelastic half-space that is complementary to the elliptical loading area, that is, the intersection of S1(t) and S2(t) is empty but the union is S. The positions of the various areas on the plane surface of the linear viscoelastic half-space and the spatial rectangular coordinate system are as follows: Figure 7 shown.

[0137] Finally, the creep compliance expression obtained in the fourth step is introduced to specifically analyze the characteristics of the boundary conditions that change with the extension of the time of the time-varying pressure. According to this characteristic, a boundary value problem solving method is selected to solve the stress component σ on the loading axis of the sample rock block from the above linear viscoelastic half-space boundary value problem. j (t), and then use the linear viscoelastic constitutive relations given by equations (31) to (33) to calculate the strain component ε j (t), where j = x, y, z.

[0138] ε x (t) = {σ x (t)-ν[σ y (t)+σ z (t)]}*dΦ(t) (31)

[0139] ε y (t) = {σ y (t)-ν[σ z (t)+σ x (t)]}*dΦ(t) (32)

[0140] ε z (t) = {σ z (t)-ν[σ x (t)+σ y (t)]}*dΦ(t) (33)

[0141] Step 6: According to the time-varying evolution of stress and strain on the loading axis of the sample rock obtained in step 5, first select a strength theory to describe its failure state. Then, a failure time prediction model for the sample rock under the long-term action of the target constant load is constructed. The model describes the relationship between the three parameters of the target constant load, the failure time and the allowable value of the strength index: when the long-term action of the target constant load causes the maximum value of the strength index on the loading axis of the sample rock to exceed its allowable value, it means that the sample rock is destroyed. If the time when the target constant load starts to act is recorded as zero, then the time required for the maximum value of the strength index on the loading axis to reach the allowable value from the initial value is the failure time.

[0142] Next, perform the following operations: the load value recorded in the first step when the sample rock block is destroyed and the duration of the load are used as the target constant load and destruction time, respectively, and are input into the destruction time prediction model together, and the maximum value of the strength index calculated inversely is used as the allowable value of the strength index; the destruction time is set equal to Δt and is input into the destruction time prediction model together with the allowable value of the strength index, and the target constant load calculated inversely is used as the load corresponding to the long-term strength level; the destruction time is set equal to 0 and is input into the destruction time prediction model together with the allowable value of the strength index, and the target constant load calculated inversely is used as the instantaneous destruction load; the size of the long-term strength level is calculated.

[0143] Finally, at least 3 numbers are selected at equal intervals from the range that exceeds the long-term strength level but does not exceed 1, and they are multiplied by the instantaneous failure load of the sample rock block respectively. The results are used as the target constant load and are input into the failure time prediction model together with the allowable values ​​of the strength index in order from large to small to calculate the failure time of the sample rock block under the long-term action of this series of target constant loads.

[0144] Step 7: By fitting the empirical relationship between load level and failure time, a mathematical expression describing the time-varying attenuation law of the sample rock strength is given. The mathematical expression is as follows:

[0145] S L =S ∞ +(1-S ∞ )exp(-μT f ) (34)

[0146] Among them, S L is the load level; T f is the failure time; μ is the material parameter; S ∞ is the long-term intensity level.

[0147] Example

[0148] Three particles are randomly selected from a pile of rocks whose parent rock is limestone, and are marked as sample rock block A, sample rock block B and sample rock block C. The method proposed in the present invention is used to test their time-varying attenuation law of strength.

[0149] Step 1: First, measure the characteristic dimensions of the three sample rock blocks, and the measurement results are listed in Table 1. Then, uniaxial constant load compression tests were carried out on the three sample rock blocks respectively. In the test, a graded equicyclic constant load with a target level of 5 was applied. The design duration of each level of constant pressure was 7 days, and the deformation of the sample rock blocks was recorded every 1 hour. The magnitude of each level of constant pressure to which the three sample rock blocks were subjected in the test was given after referring to the statistical law of the particle strength of rockfill materials with the same rock type, and is listed in Table 2. The “×” in the table means that the sample rock block was destroyed before being subjected to the constant pressure of this level. Finally, the deformation of the sample rock block subjected to each level of constant pressure for 1 hour was taken out and regarded as the instantaneous deformation caused by the constant pressure of this level. The time was re-calculated with 1 hour as the starting point, and the results of the uniaxial constant load compression test were sorted out on the new time scale. The delayed deformation curves of the three sample rock blocks under the graded equicyclic constant load are shown as follows. Figure 8 As shown in Table 3, the load values ​​at which failure occurs and the duration of the load action are listed.

[0150] Table 1 Summary of characteristic size measurement results of sample rock blocks

[0151]

[0152]

[0153] Table 2 Summary of the magnitudes of the various constant pressures to which the sample rock blocks were subjected during the test

[0154] Sample rock name Level 1(N) Level 2 (N) Level 3 (N) Level 4 (N) Level 5 (N) Sample Rock Block A 2515.36 3142.56 3769.76 × × Sample rock block B 5714.08 6654.88 7595.68 8536.48 9477.28 Sample rock block C 3142.56 4396.96 × × ×

[0155] Table 3 Summary of load values ​​and load action duration when sample rock blocks fail

[0156] Sample rock name Load value when failure occurs (N) Load duration when failure occurs (hour) Sample Rock Block A 3769.76 17 Sample rock block B 11484.32 0 Sample rock block C 4396.96 0

[0157] Step 2: First, substitute the major axis size L, the median axis size W and the minor axis size H of the three sample rock blocks into equations (12) and (13) to calculate R I and R II The size of R I and R IISubstitute A and B into equations (10) and (11) to calculate the size of A and B, then substitute A and B into equation (3) to calculate the size of γ and further use equation (4) to calculate the size of β. Table 4 lists the results of a series of unknown parameters calculated in the above process. Finally, assume that the Poisson's ratio of the three sample rock blocks is 0.25, and substitute the Poisson's ratio and the results of γ, K′(γ) and β listed in Table 4 into equation (9) to obtain the specific expressions of the conversion relationship between the deformation of each of the three sample rock blocks and its equivalent value. Table 5 lists the specific expressions of these conversion relationships. At this point, the relationship between the delayed deformation curve and the equivalent deformation curve of each of the three sample rock blocks is established.

[0158] R I =(0.25W 2 +H 2 ) / (2H) (12)

[0159] R II =(0.25L 2 +H 2 ) / (2H) (13)

[0160] 2(A+B)=1 / R I +1 / R II (10)

[0161] 4(BA) 2 =(1 / R I -1 / R II ) 2 (11)

[0162] (BA)(A+B) -1 =1-2γ -2 [E′(γ)] -1 (1-γ 2 )[K′(γ)-E′(γ)] (3)

[0163] β(1-γ 2 ) 1 / 2 [K′(γ)-E′(γ)]=γ 2 A (4)

[0164] Φ(t)*dΓ(t)=0.667π(1-ν 2 ) -1 β -1 / 2 [K′(γ)] -3 / 2 (1-γ 2 ) -1 / 4 [s(t)] 3 / 2 =Y(t) (9)

[0165] Table 4 Summary of unknown parameters calculated from the characteristic dimensions of sample rock blocks

[0166]

[0167]

[0168] Table 5 Summary of specific expressions for the conversion relationship between sample rock deformation and its equivalent value

[0169] Sample rock name Specific expression of the conversion relationship between deformation and its equivalent value Sample Rock Block A <![CDATA[0.141×[s(t)] 3 / 2 =Y(t)]]> Sample rock block B <![CDATA[0.232×[s(t)] 3 / 2 =Y(t)]]> Sample rock block C <![CDATA[0.185×[s(t)] 3 / 2 =Y(t)]]>

[0170] Step 3: Based on the results from the first step Figure 8 The curves shown are the delayed deformation curves of the three sample rock blocks under graded equicyclic constant loads. First, with the help of the specific expressions of the conversion relationship listed in Table 5, the equivalent deformation curves corresponding to the graded equicyclic constant loads of the three sample rock blocks are deduced. The deduced curves are shown in Fig. 9 As shown in Figure 2, these derived curves are then reconstructed using the superposition principle to obtain the equivalent deformation curve clusters corresponding to the one-time action of constant loads of different sizes on each of the three sample rock blocks. The reconstruction process is as follows: Figure 4 The reconstruction result is shown in Fig.10 As shown in the figure, at the same time, in the above reconstruction process, when extending the equivalent deformation curve corresponding to the graded equal-periodic constant load, the average of the deformation equivalent values ​​of the last three days on the extended section is selected as the deformation equivalent value at each moment on the extended line.

[0171] Step 4: Use the data obtained in step 3 Fig.10 The curve clusters shown in FIG. 1 are the equivalent deformation curve clusters corresponding to the one-time action of constant loads of different sizes on the three sample rock blocks. The creep compliance values ​​of the three sample rock blocks at different times are obtained respectively. Then, the creep compliance values ​​at different times are used as dependent variables, the corresponding time series are used as independent variables, and formula (21) is used as the creep compliance expression. The nonlinear least squares method is used to fit the parameters in the creep compliance expressions of the three sample rock blocks. The parameter fitting results are listed in Table 6. The fitting effect is shown in Table 6. Fig.11 shown.

[0172]

[0173] Among them, E1, E2 and η1 are parameters in the standard linear solid model, and E1 / η1 can usually also be expressed as 1 / N1.

[0174] Table 6 Summary of parameter fitting results in the creep compliance expression of sample rock blocks

[0175] Sample rock name <![CDATA[E2(Pa)]]> <![CDATA[E1(Pa)]]> <![CDATA[η1(Pa·hour)]]> <![CDATA[N1(hour)]]> Goodness of fit Sample Rock Block A <![CDATA[3.417×10 10 ]]> <![CDATA[2.039×10 11 ]]> <![CDATA[1.301×10 13 ]]> 63.81 0.937 Sample rock block B <![CDATA[1.318×10 10 ]]> <![CDATA[6.926×10 10 ]]> <![CDATA[1.967×10 12 ]]> 28.40 0.968 Sample rock block C <![CDATA[1.877×10 10 ]]> <![CDATA[9.099×10 10 ]]> <![CDATA[3.138×10 12 ]]> 34.49 0.780

[0176] Step 5: For any of the three sample rocks, when it is in contact with the upper rigid plate at a distance of FGt Under the long-term action of the target constant load, when they start to approach each other from the point contact state at time t=0, if the center of the elliptical contact domain between it and the upper rigid plate is taken as the origin, the plane where the elliptical contact domain is located is taken as the xoy coordinate plane, the major axis of the elliptical contact domain is taken as the x-axis, the minor axis of the elliptical contact domain is taken as the y-axis, and the straight line passing through the origin and perpendicular to the xoy coordinate plane is taken as the z-axis, let the positive direction of the z-axis point to the upper rigid plate, establish the following Figure 6 The spatial rectangular coordinate system shown in FIG. 1 is the contact pressure p(x, y, t) on the elliptical contact domain between it and the upper rigid plate, as shown in Equation (23).

[0177]

[0178] Where a(t) is the semi-major axis size of the elliptical contact domain, see equation (26); b(t) is the semi-minor axis size of the elliptical contact domain, which is (1-γ 2 ) 1 / 2 times; g(t) is calculated by formula (27).

[0179] a(t)=[1.5β -1 π -1 (1-γ 2 ) -1 / 2 (1-ν 2 )F Gt Φ(t)] 1 / 3 (26)

[0180] (1-ν 2 )Φ(t)*dg(t)=U(t) (27)

[0181] Furthermore, the sample rock block under study is regarded as a linear viscoelastic half-space body with the xoy coordinate plane as the plane surface. The contact pressure on the contact domain between the sample rock block and the upper rigid plate is simplified to the load acting on a small elliptical area on the plane surface. The elliptical area is completely equivalent to the elliptical contact domain between the sample rock block and the upper rigid plate. At the same time, the normal of the plane surface is parallel to the z-axis and the tangent is parallel to the xoy coordinate plane, and a linear viscoelastic half-space boundary value problem is constructed with the boundary conditions satisfying the expression of equations (28) to (30).

[0182] σ s (x,y,t)=0,(x,y)∈S (28)

[0183] σ n (x,y,t)=p(x,y,t),(x,y)∈S1(t) (29)

[0184] u n (x,y,t)=0,(x,y)∈S2(t) (30)

[0185] Among them, σ s (x,y,t) is the time-varying tangential stress at the point (x,y); σ n (x,y,t) is the time-varying normal stress at the point (x,y); u n (x,y,t) is the time-varying normal displacement at point (x,y); (x,y)∈S means that point (x,y) is located on the plane surface of the linear viscoelastic half-space; (x,y)∈S1(t) means that point (x,y) is located on a small elliptical area on the plane surface of the linear viscoelastic half-space, that is, in the loading area; (x,y)∈S2(t) means that point (x,y) is located on the part of the plane surface of the linear viscoelastic half-space that is complementary to the elliptical loading area, that is, the intersection of S1(t) and S2(t) is empty but the union is S. The positions of the various areas on the plane surface of the linear viscoelastic half-space and the spatial rectangular coordinate system are as follows: Figure 7 shown.

[0186] Furthermore, substituting the creep compliance expression obtained in the fourth step into equations (23), (26) and (27), we can obtain that the size of the elliptical contact domain between each of the three sample rock blocks and the upper rigid plate increases with time and finally approaches a fixed size infinitely; the contact pressure distribution on the contact domain is not much different from the Hertz distribution at any moment of time t ≥ 0, and all approximately obey the elastic theory. The time-varying evolution process of the contact pressure distribution on the elliptical contact domain between sample rock block A and the upper rigid plate after normalization is shown in the figure below: Fig.12 As shown, the results of the other two sample rocks are similar. It is not difficult to see that the correspondence principle generalized by Graham can be used to solve the above-mentioned linear viscoelastic half-space boundary value problem. This principle can be found in Graham's "The correspondence principle of linear viscoelasticity theory for mixed boundary value problems involving time-dependent boundary regions" (Quarterly of Applied Mathematics, 1968, 26 (2): 167-174. DOI: 10.1090 / qam / 99860). With the help of this principle, the stress component expression on the loading axis of the sample rock block is given as:

[0187]

[0188]

[0189] in, Ω′ y =-1+T+ξ[K″(φ,γ)-E″(φ,γ)]; K″(φ,γ) is the first kind of incomplete elliptic integral with φ and γ as parameters; E″(φ,γ) is the second kind of incomplete elliptic integral with φ and γ as parameters; z is the distance between the target point on the loading axis and the center of the elliptical contact domain; Depend on Calculate it.

[0190] Then, the strain components are calculated using the linear viscoelastic constitutive relations given by equations (31) to (33):

[0191] ε x (t) = {σ x (t)-ν[σ y (t)+σ z (t)]}*dΦ(t) (31)

[0192] ε y (t) = {σ y (t)-ν[σ z (t)+σ x (t)]}*dΦ(t) (32)

[0193] ε z (t) = {σ z (t)-ν[σ x (t)+σ y (t)]}*dΦ(t) (33)

[0194] When F Gt =3000N, the time-varying evolution of the stress component on the loading axis of sample rock block A is as follows: Fig.13 As shown in Fig.14 As shown in the figure, the results of the other two sample blocks are similar. In general, the stress distribution and strain distribution on the loading axis of the three sample blocks are highly uneven. The stress component shows a trend of gradually decreasing with time, while the strain component shows a trend of gradually increasing with time. The calculated stress and strain components here are positive for tension.

[0195] Step 6: Since the failure of irregular rock blocks is a typical brittle fracture, Fig.13 and 14The time-varying evolution of stress and strain components on the loading axis is shown in Figure 1. First, the maximum elongation strain theory is selected to describe the failure state of the three sample rock blocks. The strength index of this theory is the maximum elongation strain at a point in the material, that is, the first principal strain. Then, the failure time prediction model of each of the three sample rock blocks under the long-term action of the target constant load is constructed. The failure time prediction model of sample rock block A is as follows: Fig.15 As shown in the figure, the results of the other two sample rock blocks are similar. When the long-term action of the target constant load causes the maximum value of the first principal strain on the loading axis of the sample rock block to exceed the allowable value of the first principal strain, it means that the sample rock block is damaged. If the time when the target constant load starts to act is recorded as zero, then the time required for the maximum value of the first principal strain on the loading axis to reach the allowable value from the initial value is the damage time.

[0196] Next, the load values ​​and the duration of the load action of the sample rock blocks listed in Table 3 when they are destroyed are used as the target constant load and destruction time, respectively, and are input into the destruction time prediction model together to reversely calculate the first principal strain allowable value of each of the three sample rock blocks; the destruction time is set to be equal to 167 hours and input into the destruction time prediction model together with the first principal strain allowable value, and reversely calculate the load corresponding to the long-term strength level of each of the three sample rock blocks; the destruction time is set to be equal to 0 and input into the destruction time prediction model together with the first principal strain allowable value, and reversely calculate the instantaneous destruction load of each of the three sample rock blocks; the load corresponding to the long-term strength level is divided by the instantaneous destruction load to obtain the size of the long-term strength level of each of the three sample rock blocks. The physical quantity results calculated using the destruction time prediction model in the above process are listed in Table 7.

[0197] Table 7 Summary of physical quantity results calculated using the failure time prediction model

[0198]

[0199] Finally, 7 numbers are selected at equal intervals from the range that exceeds the long-term strength level but does not exceed 1, and are multiplied by the instantaneous failure loads of the three sample rock blocks respectively. The obtained results are used as the target constant loads and are input into the failure time prediction model together with the first principal strain allowable value in order from large to small. The failure time of the three sample rock blocks under the long-term action of the target constant loads of different sizes in this series is calculated. The calculation results are listed in Table 8.

[0200] Table 8 Summary of calculation results of failure time of sample rock blocks under long-term action of target constant loads of different sizes

[0201]

[0202] Step 7: With the load level and failure time listed in Table 8 as the dependent variable and independent variable respectively, and formula (34) as the mathematical expression to describe the time-varying attenuation law of the strength of irregular rock blocks, the nonlinear least squares method is used to fit the parameters in the expression of the time-varying attenuation law of the strength of the three sample rock blocks. The parameter fitting results are listed in Table 9. The fitting effect is shown in Fig.16 shown.

[0203] S L =S ∞ +(1-S ∞ )exp(-μT f ) (34)

[0204] Among them, S L is the load level; T f is the failure time; μ is the material parameter; S ∞ is the long-term intensity level.

[0205] Table 9 Summary of parameter fitting results in the expression of time-varying attenuation law of sample rock strength

[0206] Sample rock name <![CDATA[S ∞ ]]> μ Goodness of fit Sample Rock Block A 0.861 0.021 0.997 Sample rock block B 0.840 0.045 0.999 Sample rock block C 0.829 0.037 0.999

Claims

1. A method for testing the time-varying attenuation law of irregular rock strength based on linear viscoelasticity theory, characterized in that: The steps include: Step 1: Measure the characteristic dimensions of the sample rock block and conduct a uniaxial constant load compression test to obtain the delayed deformation curve under graded equicyclic constant loads, and record the load value at the time of failure and the duration of the load action; The characteristic dimensions of the sample rock block refer to its major axis, median axis and minor axis dimensions, which are L, W and H respectively, and are defined as follows: firstly, the sample rock block is placed on the horizontal test bench in a self-stable manner in various postures, and a stable placement posture is found that makes the distance between the highest point of the sample rock block and the horizontal test bench the shortest. The height at this time is defined as the minor axis dimension, and then in all horizontal sections, the maximum diameter is taken as the major axis dimension, and the maximum diameter in the direction perpendicular to the major axis is taken as the median axis dimension; The uniaxial constant load compression test refers to a deformation test of a sample rock block under a time-varying pressure provided by two parallel rigid plates above and below; The graded equal-periodic constant load action refers to applying n≥1 different constant pressures step by step starting from time t=0, each level is rapidly increased on the basis of the previous level and then kept constant, each level is designed to last for the same length of time and can make the sample rock block deform into a stable stage, the size of each level of constant pressure is given after examining the statistical law of the strength of irregular rock blocks with the same lithology, but the first level of constant pressure does not destroy the sample rock block; the load action is specifically expressed as: Wherein, Fms(t) is the graded equicyclic constant load action; t0=0 and t1-t0=t2-t1=…=t n -t n-1 =Δt; ΔF0 is the first stage constant pressure, and the remaining ΔF k is the difference between the constant pressure of the k+1th stage and the kth stage; U(t-tk) is a step function. When tt k 1 if ≥0, otherwise 0; The delayed deformation curve refers to the curve of the relationship between the deformation of the sample rock and time; the load value at the time of failure and the duration of the load action refer to the pressure magnitude of the sample rock when it is destroyed and the duration of the pressure, which are defined as follows: if the sample rock is destroyed at the N=2, 3, ..., nth level of constant pressure, the Nth level of constant pressure is used as the load value at the time of failure, and the duration of the pressure is the duration of the Nth level of constant pressure; otherwise, the pressure should be continued at the end of the test until the sample rock is destroyed, and the pressure magnitude at this time is used as the load value at the time of failure, and the duration of the pressure is zero; Step 2: Combine the characteristics of uniaxial constant load compression test to establish the relationship between delayed deformation curve and equivalent deformation curve, see formula (9); The equivalent deformation curve refers to the relationship curve between the equivalent value of the sample rock deformation and time; the establishment of the connection between the delayed deformation curve and the equivalent deformation curve specifically refers to constructing a conversion relationship between the sample rock deformation and its equivalent value, and the method is as follows: The distance δ(t) that two linear viscoelastic bodies p and q of arbitrary shapes approach each other under the action of time-varying pressure Γ(t) starting from the point contact state at time t = 0 is shown in equation (2); where γ is the eccentricity of the elliptical contact domain between objects p and q, calculated by equation (3); K′(γ) is the first kind complete elliptic integral with γ as parameter; ν p and ν q are the Poisson's ratios of objects p and q respectively; Φ p (t) and Φ q (t) are the creep compliances of objects p and q respectively; β is the constant obtained by equation (4); "*" represents Stieltjes convolution, and the specific algorithm is shown in equation (7); (BA)(A+B) -1 =1-2c -2 [E′(c)] -1 (1-c 2 )[K′(γ)-E′(γ)] (3) β(1-γ 2 ) 12 [K′(γ)-E′(γ)]=γ 2 A (4) Where E′(γ) is the complete elliptic integral of the second kind with γ as the parameter; A and B are geometric constants that satisfy the relationship given by equations (5) and (6); in, is the minimum radius of curvature of object p at the center of the elliptical contact zone between it and object q; is the maximum radius of curvature of object p at the center of the elliptical contact zone between it and object q; is the minimum radius of curvature of object q at the center of the elliptical contact zone between it and object p; is the maximum radius of curvature of object q at the center of the elliptical contact zone between it and object p; α is the radius of curvature and The angle between the normal sections; Among them, h1(t) is a function that is continuous on [0, +∞) and holds h1(t) = 0 when t < 0; h2(t) is a function defined on [0, +∞), which is not required to be continuous but requires h2(t) = 0 when t < 0; Combined with the characteristics of uniaxial constant load compression test, the following assumptions are made: the contact between the sample rock block and the lower rigid plate is plane-to-plane, while the contact between the sample rock block and the upper rigid plate is point-to-plane; the deformation of the sample rock block comes entirely from the linear viscoelastic deformation of the sample rock block in the elliptical contact domain between it and the upper rigid plate, that is, the distance between the sample rock block and the upper rigid plate from the point contact state at time t=0 under the action of time-varying pressure Γ(t); the creep compliance of the rigid plate is zero; the creep compliance of the sample rock block is Φ(t), and the Poisson's ratio is ν; based on the above assumptions, equation (8) is derived from equation (2), and then equation (9) is obtained by sorting equation (8); equation (9) is the conversion relationship between the deformation of the sample rock block and its equivalent value, that is, the relationship between the delayed deformation curve and the equivalent deformation curve; s(t)=βK′(γ)(1-γ 2 ) 12 {1.5b -1 p -1 (1-c 2 ) -12 (1-n 2 )Φ(t)*dΓ(t)} 23 (8) Φ(t)*dΓ(t)=0.667π(1-ν 2 ) -1 b -12 [K′(γ)] -32 (1-c 2 ) -14 [s(t)] 32 =Y(t) (9) Where, s(t) is the deformation of the sample rock block; Y(t) is the equivalent value of the deformation of the sample rock block; Since the principal radius of curvature of the upper rigid plate at the center of the contact area between it and the sample rock block approaches infinity, equations (5) and (6) will become equations (10) and (11); A and B can be obtained from equations (10) and (11), and γ and β can be determined from equations (3) and (4); 2(A+B)=1 / R I +1 / R II (10) 4(B-A) 2 =(1 / R I -1 / R II ) 2 (11) Among them, R I is the minimum radius of curvature of the sample rock at the center of the elliptical contact area between it and the upper rigid plate; R II is the maximum radius of curvature of the sample rock at the center of the elliptical contact area between it and the upper rigid plate; R I and R II It is obtained in the following way: <h2 style=";text-align:left;direction:ltr">R<h2 style=";text-align:left;direction:ltr"> I <h2 style=";text-align:left;direction:ltr"> =(0.25W<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +H<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> ) / (2H) (12) <h2 style=";text-align:left;direction:ltr">R<h2 style=";text-align:left;direction:ltr"> II <h2 style=";text-align:left;direction:ltr"> (0.25L)<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +H<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> ) / (2H) (13) Step 3: Based on the delayed deformation curve of the sample rock block under the graded equal-periodic constant load obtained in the first step, firstly, with the help of the connection between the delayed deformation curve and the equivalent deformation curve established in the second step, the equivalent deformation curve corresponding to the graded equal-periodic constant load is deduced, and then the deduced curve is reconstructed with the help of the superposition principle to obtain the equivalent deformation curve cluster corresponding to the one-time action of constant loads of different sizes; The constant loads of different magnitudes refer to a series of constant pressures with different values, whose values, from low to high, are equal to the magnitudes of n≥1 constant pressures that appear successively in the process of the graded equal-periodic constant load action in the first step; the one-time action refers to a rapid increase from zero to the target value at time t=0 and then remaining constant until time t=Δt; the one-time action of the constant loads of different magnitudes is specifically expressed as: Among them, F os,m (t) is the one-time action of the constant load of different magnitudes; U(Δt-t) is a step function, which is 1 when Δt-t≥0, otherwise it is 0; The meaning of the superposition principle is: The equivalent deformation curve corresponding to the one-time action of a constant load is considered to be The incremental load ΔF is superimposed on the equivalent deformation curve corresponding to the one-time action of the constant load i The additional effect caused within the time Δt is valid for 1≤i≤n-1. The proof is as follows: For graded equicyclic constant load, if time t=t i No incremental load ΔF is applied i , then the load at time 0≤t<t i+1 When t is t, it is expressed as formula (15), otherwise it is expressed as formula (16). Substituting formula (15) and (16) into formula (9) respectively, we can get the above two cases at time t i ≤t<t i+1 The deformation equivalent values ​​at tt are shown in equations (17) and (18) respectively. By subtracting equation (17) from equation (18), the difference between the deformation equivalent values ​​of the two is ΔFiΦ(t-ti). If tt i It is denoted as Δτ. Obviously, 0≤Δτ<Δt exists, so the incremental load ΔF i The additional effect caused within the duration of Δt is ΔFiΦ(Δτ); for and The constant load of one-time action can be obtained from equation (9). The deformation equivalent values ​​at time t = Δτ are shown in equations (19) and (20). The difference between the deformation equivalent values ​​of the two can be obtained by subtracting equation (19) from equation (20): ΔF i Φ(Δτ), therefore, the superposition principle is proved; in, At time t = t i No incremental load ΔF is applied i In the case of graded equicyclic constant load acting at time 0≤t<t i+1 The expression when At time t = t i When the incremental load ΔF is applied i In the case of graded equicyclic constant load acting at time 0≤t<t i+1 The expression when At time t = t i No incremental load ΔF is applied i In the case of graded equicyclic constant load acting at time t i ≤t<t i+1 Equivalent value of sample rock deformation caused by At time t = t i When the incremental load ΔF is applied i In the case of graded equicyclic constant load acting at time t i ≤t<t i+1 The equivalent value of the sample rock deformation caused by the time; Yos,i-1(Δτ) refers to the size of The equivalent value of the sample rock deformation caused by a one-time constant load at time t = Δτ; Y os,i (Δτ) refers to the size of The equivalent value of the sample rock deformation caused by a one-time constant load at time t = Δτ; The process of reconstructing the derived curve by means of the superposition principle to obtain a cluster of equivalent deformation curves corresponding to a one-time action of a constant load of different magnitudes is as follows: First, the part of the equivalent deformation curve corresponding to the graded equal-periodic constant load with a time t0≤t<t1 is taken as the equivalent deformation curve corresponding to the one-time action of the constant load with a magnitude of ΔF0; Secondly, the time t0≤t<t1 part of the equivalent deformation curve corresponding to the graded equal-periodic constant load is extended to time t=t2, and the difference between the time t1≤t<t2 part of the equivalent deformation curve corresponding to the graded equal-periodic constant load and the deformation equivalent value of the above extension line at the same time is calculated. These differences are used as the additional effect caused by the incremental load ΔF1 within the time length Δt and superimposed on the equivalent deformation curve corresponding to the one-time action of the constant load of magnitude ΔF0, and the size is obtained. The equivalent deformation curve corresponding to the one-time action of constant load; Then, the time t1≤t<t2 on the equivalent deformation curve corresponding to the graded equal-periodic constant load is extended to time t=t3, and the difference between the time t2≤t<t3 on the equivalent deformation curve corresponding to the graded equal-periodic constant load and the deformation equivalent value of the extension line at the same time is calculated, and these differences are used as the additional effect caused by the incremental load ΔF2 within the time length Δt to add to the value of The equivalent deformation curve corresponding to the one-time action of the constant load is obtained. The equivalent deformation curve corresponding to the one-time action of constant load; By analogy, if the sample rock is destroyed at the N = 2, 3, ..., nth level of constant pressure, then the final value will be The equivalent deformation curve corresponding to the one-time action of a constant load is The equivalent deformation curve corresponding to the one-time action of constant load; Step 4: Using the equivalent deformation curve clusters corresponding to the one-time action of constant loads of different sizes obtained in the third step, the creep compliance values ​​at different times are obtained, and then the creep compliance expression is determined; The method for obtaining the creep compliance values ​​at different moments is, for a certain moment, firstly, to find a load sequence and a corresponding deformation equivalent value sequence from the equivalent deformation curve cluster corresponding to the one-time action of constant loads of different magnitudes, and then, with the load as the independent variable x0 and the deformation equivalent value as the dependent variable y0, to fit the linear model y0=λ·x0, and the value of λ calculated thereby is the creep compliance value at the moment; The creep compliance expression refers to a mathematical expression used to quantitatively describe the changing trend of creep compliance values ​​at different times with the corresponding time series. The creep compliance expression derived from the standard linear solid model is as follows: Where Φ(t) is the creep compliance of the sample rock; E1, E2 and η1 are parameters in the standard linear solid model; Step 5: Solve the problem of F based on linear viscoelasticity theory Gt The time-varying evolution of stress and strain on the loading axis of the sample rock block under the long-term action of the target constant load; The target constant load is a constant pressure determined according to the actual problem; the long-term action refers to the pressure that increases rapidly from zero to the target value at time t=0 and then remains constant; the magnitude is F Gt The target constant load long-term action is specifically expressed as: F G (t)=F Gt ·U(t) (22) Among them, F G (t) is the target constant load long-term action; U(t) is a step function, which is 1 when t≥0, otherwise it is 0; The sample rock block loading axis refers to the position in the sample rock block where the vertical line with the center of the elliptical contact area between the sample rock block and the upper rigid plate as the foot passes; the time-varying evolution process of stress and strain refers to the process in which the stress field and strain field continuously change with the extension of the time of the time-varying pressure; the process of solving based on the linear viscoelastic theory is as follows: First, when two linear viscoelastic bodies p and q of arbitrary shapes approach each other from a point contact state at time t = 0 under the action of time-varying pressure Γ(t), if the center of the elliptical contact domain between them is taken as the origin, the plane where the elliptical contact domain is located is taken as the xoy coordinate plane, the major axis of the elliptical contact domain is taken as the x-axis, the minor axis of the elliptical contact domain is taken as the y-axis, and the straight line passing through the origin and perpendicular to the xoy coordinate plane is taken as the z-axis, and the positive direction of the z-axis points to either of the objects p and q, a spatial rectangular coordinate system is established, then the contact pressure p(x, y, t) on the elliptical contact domain between them is shown in formula (23); Where a(t) is the semi-major axis size of the elliptical contact domain, see equation (24); b(t) is the semi-minor axis size of the elliptical contact domain, which is (1-γ 2 ) 12 times; g(t) is calculated by formula (25); Secondly, according to the assumptions made in the second step combined with the characteristics of the uniaxial constant load compression test, it can be obtained that when the sample rock block and the upper rigid plate are at a size of F Gt When they start to approach each other from the point contact state at time t=0 under the long-term action of the target constant load, if the center of the elliptical contact domain between them is taken as the origin, the plane where the elliptical contact domain is located is taken as the xoy coordinate plane, the major axis of the elliptical contact domain is taken as the x-axis, the minor axis of the elliptical contact domain is taken as the y-axis, and the straight line passing through the origin and perpendicular to the xoy coordinate plane is taken as the z-axis, and the positive direction of the z-axis points to the upper rigid plate, a spatial rectangular coordinate system is established, then the contact pressure on the elliptical contact domain between them is still as shown in formula (23), but at this time, the major semi-axis size a(t) of the elliptical contact domain is calculated according to formula (26), and g(t) is calculated by formula (27); a(t)=[1.5β -1 p -1 (1-c 2 ) -12 (1-n 2 )F Gt [Φ(t)] 13 (26) (1-ν 2 )Φ(t)*dg(t)=U(t) (27) Then, since the size of the contact domain between the sample rock block and the upper rigid plate is very small compared to the size of the sample rock block and the relative curvature radius of the surface, the sample rock block is regarded as a linear viscoelastic half-space body with the xoy coordinate plane as the flat surface, and the contact pressure on the contact domain is simplified to a load acting on a small elliptical area on the flat surface. The elliptical area is completely equivalent to the elliptical contact domain between the sample rock block and the upper rigid plate. At the same time, the normal of the flat surface is parallel to the z-axis and the tangent is parallel to the xoy coordinate plane. Therefore, the stress field on the loading axis of the sample rock block is calculated by constructing a linear viscoelastic half-space boundary value problem. The boundary conditions of the boundary value problem satisfy the expression of equations (28) to (30). σ s (x,y,t)=0,(x,y)∈S (28) σ n (x,y,t)=p(x,y,t),(x,y)∈S1(t) (29) u n (x,y,t)=0,(x,y)∈S2(t) (30) Among them, σ s (x,y,t) is the time-varying tangential stress at the point (x,y); σ n (x,y,t) is the time-varying normal stress at the point (x,y); u n (x,y,t) is the time-varying normal displacement at point (x,y); (x,y)∈S means that point (x,y) is located on the plane surface of the linear viscoelastic half-space; (x,y)∈S1(t) means that point (x,y) is located on a small elliptical region on the plane surface of the linear viscoelastic half-space, that is, in the loading region; (x,y)∈S2(t) means that point (x,y) is located on the complementary part of the plane surface of the linear viscoelastic half-space to the elliptical loading region, that is, the intersection of S1(t) and S2(t) is empty but the union is S; Finally, the creep compliance expression obtained in the fourth step is introduced to specifically analyze the characteristics of the boundary conditions that change with the extension of the time of the time-varying pressure. According to this characteristic, a boundary value problem solving method is selected to solve the stress component σ on the loading axis of the sample rock block from the above linear viscoelastic half-space boundary value problem. j (t), and then use the linear viscoelastic constitutive relations given by equations (31) to (33) to calculate the strain component ε j (t), where j = x, y, z; e x (t)={σ x (t)-ν[σ y (t)+σ z (t)]}*dΦ(t) (31) e y (t)={σ y (t)-ν[σ z (t)+σ x (t)]}*dΦ(t) (32) e z (t)={σ z (t)-ν[σ x (t)+σ y (t)]}*dΦ(t) (33) Step 6: According to the time-varying evolution of stress and strain on the loading axis of the sample rock block obtained in the fifth step, first select a strength theory to describe its failure state, then build a failure time prediction model for the sample rock block under the long-term action of the target constant load, and combine the load value when the sample rock block is destroyed and the duration of the load recorded in the first step to obtain the allowable value of the rock block strength index, and then calculate the long-term strength level and the failure time under the long-term action of target constant loads of different sizes; The failure time prediction model of the sample rock block under the long-term action of the target constant load, referred to as the failure time prediction model, includes three parameters: the target constant load, the failure time and the allowable value of the strength index. Specifically, when the maximum value of the strength index on the loading axis of the sample rock block exceeds its allowable value due to the long-term action of the target constant load, it means that the sample rock block is destroyed. If the time when the target constant load starts to act is recorded as zero, then the time required for the maximum value of the strength index on the loading axis to reach the allowable value from the initial value is the failure time. The strength index is a characteristic variable used to describe the stress or strain state of the material in the failure criterion expression corresponding to the selected strength theory; the calculation method of the allowable value of the strength index of the sample rock block is to use the load value when the sample rock block is destroyed and the duration of the load action recorded in the first step as the target constant load and the destruction time, respectively, and input them into the destruction time prediction model. At this time, the maximum value of the strength index calculated in reverse is the allowable value of the strength index; The long-term strength level refers to the ratio of the maximum load that will not cause the sample rock block to be damaged no matter how long it lasts under compression conditions to the instantaneous damage load. The maximum load and the instantaneous damage load are determined with the help of a damage time prediction model, specifically as follows: a value greater than or equal to Δt is assigned to the damage time, and it is input into the damage time prediction model together with the allowable value of the strength index. At this time, the target constant load calculated inversely is the maximum load that will not cause the sample rock block to be damaged no matter how long it lasts under compression conditions, and is also the load corresponding to the long-term strength level; the damage time is set to zero, and it is input into the damage time prediction model together with the allowable value of the strength index. At this time, the target constant load calculated inversely is the instantaneous damage load; A series of target constant loads whose target constant load index values ​​of different sizes exceed the load corresponding to the long-term strength level of the sample rock block but do not exceed its instantaneous failure load, and the number of the series of target constant loads is not less than 3; Step 7: By fitting the empirical relationship between load level and failure time, a mathematical expression describing the time-varying attenuation law of the sample rock strength is given; The load level refers to the ratio of target constant loads of different sizes to the instantaneous failure load; the failure time refers to the failure time under the long-term action of the target constant load; the mathematical expression is as follows: S L =S ∞ +(1-S ∞ )exp(-μT f ) (34) Among them, S L is the load level; T f is the failure time; μ is the material parameter; S ∞ is the long-term intensity level.

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