Nonlinear mechanical model for representing excavation damage-long-term deterioration effect of engineering rock mass

Abstract

The nonlinear mechanical model for representing the excavation damage-long-term deterioration effect of the engineering rock mass is provided and comprises the following steps that S1, a true triaxial static test is carried out, and a peak intensity rule is researched; s2, carrying out a true triaxial multi-stage aging static test, and analyzing an aging critical strength rule and anisotropic aging damage evolution characteristics; s3, establishing an anisotropic aging damage evolution equation; s4, constructing a homogeneous rock maximum failure constitutive equation under the true three-dimensional stress; s5, constructing a viscoelastic constitutive equation in which the true three-dimensional stress aging effect is introduced; s6, compiling the constitutive model established in S5 into a numeralization subprogram; s7, obtaining a maximum failure function parameter of the homogeneous rock in a peak state; s8, obtaining a three-dimensional aging yield function parameter of the homogeneous rock in an aging critical state; and S9, verifying the prediction effect and applicability of the model on the aging deformation evolution of the homogeneous rock. According to the method, theoretical characterization of the whole process of excavation damage and aging degradation of the engineering rock mass under the true three-dimensional stress is achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rock mechanics performance and engineering research, and particularly relates to a method for constructing a nonlinear mechanics model for characterizing excavation damage-long-term degradation effects of an engineering rock mass, which is suitable for simulation and analysis of rock mechanics behavior under complex stress environment. BACKGROUND

[0002] As a basic form of geological material, rock, such as sandstone, is widely used in various rock mass engineering. The internal mineral composition of rock is uniformly distributed, and the mechanical properties thereof are approximately the same on a macroscopic scale. In the fields of deep resource mining, underground space development, and high-level radioactive waste geological disposal, accurate description of the elastic-plastic deformation and failure mechanism of rock plays a key role in engineering stability evaluation and disaster prevention and control.

[0003] Existing rock mechanics models are mostly established based on conventional triaxial compression tests, and cannot fully reflect the complex evolution characteristics of the yield surface of the material under true three-dimensional stress state. There is a lack of rock mechanics models constructed based on static tests and multi-stage static aging tests under true triaxial conditions. When describing the pre-peak plastic flow and post-peak strength degradation of rock, traditional mechanics models are difficult to characterize the plastic deformation behavior in the three-dimensional stress space, and there is a significant deviation in predicting the mechanical response of rock under complex loading paths of true triaxial. It is difficult to accurately express the damage of rock under true triaxial static and aging conditions, especially the accelerated stage damage before failure.

[0004] Although current research has made progress in introducing damage variables, most models still use a single damage characterization method, and the internal relationship between three-dimensional stress state and damage evolution has not been established. With the development of the post-peak rock fracture process, the intermediate principal stress effect of rock bearing capacity is nonlinearly attenuated. However, existing strength criteria cannot characterize this law. Therefore, there is a need to establish a strength criterion that considers the attenuation of the intermediate principal stress effect.

[0005] Rock failure in underground engineering is divided into three stages: deceleration stage, constant speed stage, and acceleration stage. The damage evolution of rock is not the same under low stress state and high stress state. There are more nonlinear damage evolution results under high stress state under conventional triaxial, but there is a lack of theoretical nonlinear damage evolution law of rock under high stress state under true triaxial.

[0006] Underground excavation causes damage to underground rock, which continuously deteriorates under long-term time effect and eventually fails. Current rock mechanics models have made many achievements, but most of them are single static models or time degradation models under conventional triaxial. There are few unified models of static and time effect, and most of them are under conventional triaxial. There is a lack of unified expression model of static damage and time degradation of three-dimensional stress state in underground engineering.

[0007] Therefore, it is urgent to construct a mechanical model capable of effectively describing the yield surface evolution in the true three-dimensional principal stress space, the non-associativity of the plastic flow direction, and the damage evolution development, and to realize the simulation of the whole process from the initial yield, hardening and softening to the final failure, so as to provide a theoretical basis for the prediction of the mechanical behavior of rock in a real engineering environment. SUMMARY

[0008] The purpose of the present application is to provide a construction method of a nonlinear mechanical model representing the excavation damage-long-term deterioration effect of an engineering rock mass, which can simulate and analyze the pre-peak and post-peak mechanical properties of rock under the action of true triaxial multistage static time effect.

[0009] In order to achieve the above technical purposes, the present application provides a construction method of a nonlinear mechanical model representing the excavation damage-long-term deterioration effect of an engineering rock mass, which comprises the following steps:

[0010] S1. Perform true triaxial static compression tests under different intermediate principal stresses σ 2 to obtain the peak strength of rock.

[0011] S2. According to the peak strength of rock obtained from the true triaxial static compression test, design and perform tests under the action of true triaxial multistage static time effect under different intermediate principal stresses σ 2, and use the isochronous curve cluster to determine the critical strength σ cs of rock under the action of true triaxial multistage static time effect, study the evolution law of the deformation evolution characteristics and the critical strength σ cs and the failure stress σ d of rock under the action of true triaxial multistage static time effect, and calculate the elastic modulus under different damage degrees in each direction to analyze the damage evolution characteristics of rock under the action of true triaxial multistage static time effect.

[0012] S3. Calculate the damage variable of rock under the action of true triaxial multistage static time effect according to the elastic modulus obtained from the test in step S2, analyze the damage characteristics, and establish a damage evolution equation representing the damage evolution characteristics.

[0013] S4. Construct the maximum failure constitutive equation of rock under true triaxial stress: based on the results of true triaxial static compression test, use a three-dimensional failure criterion considering the nonlinear attenuation of the effect of the intermediate principal stress in fracture to construct the maximum failure function F of rock and the maximum failure potential function G of rock.

[0014] S5. Construct a viscoelastic constitutive equation introducing the effect of true triaxial multistage static time effect: according to the maximum failure function F in step S4, establish the yield function F v and the three-dimensional rheological potential function G v of rock under the action of true triaxial multistage static time effect; based on the Perzyna over-stress theory, establish the time effect rheological multiplier dλ vSimultaneously, based on the evolution characteristics of rocks under true triaxial multi-stage static aging, time-dependent aging parameters related to time t are established. and the time-accelerated control equation V d (t).

[0015] The constitutive equations in steps S6, S4, and S5 are coupled with the time-dependent damage evolution equation in step S3 to construct a nonlinear mechanical model characterizing the damage-long-term deterioration effect of engineering rock mass excavation. This model is then compiled into a user-defined material subroutine for finite element software to establish a numerical simulation method for the mechanical model.

[0016] S7. Using the numerical simulation method established in step S6, simulate the true triaxial static compression test of rock in step S1, verify the maximum failure constitutive equation of rock established in step S4, and obtain the plastic part parameters of the model and the maximum failure function parameters of rock under the peak state.

[0017] S8. Using the numerical simulation method established in step S6, simulate the true triaxial multi-stage static aging test of rock in step S2, verify the viscoelastic constitutive equation established in step S5 that introduces the true triaxial multi-stage static aging effect, and obtain the stress parameter equations under different intermediate principal stresses σ2 and the yield function parameters of rock under critical state.

[0018] S9. Simulate the test under true triaxial multi-stage static aging with different intermediate principal stresses σ2 to verify the model's predictive effect and applicability for the deformation evolution of rocks under true triaxial multi-stage static aging.

[0019] In step S1, the true triaxial static compressive peak strength σ of the rock under different intermediate principal stresses σ2 was statistically analyzed. p ;

[0020] In step S2, the peak intensity σ from step S1 is used as a basis. p , 0.40σ p 0.75σ p 0.85σ p 0.90σ p σ p In the later stages of the experiment, the stress levels at each stage increased by 0.025σ. p Until the sample fails. After σ1 is applied to the specified stress level, static resting begins, with each resting period lasting 30 minutes, progressively increasing until the rock fails. Ten characteristic nodes with the same duration are selected under each resting condition, and their corresponding strain response data are statistically analyzed. Based on the stress-strain correspondence under the same resting time, a series of isochronous curves are plotted. By analyzing the curve separation characteristics within the isochronous curve cluster, the stress value corresponding to the critical point where the curve shows a significant inflection is determined as the critical strength σ of the rock. cs .

[0021] The method for establishing the damage evolution equation representing the evolution characteristics of the damage in step S3 is:

[0022] Based on the damage evolution analysis of the rock under the true triaxial multi-stage static aging in step S2, a damage evolution formula varying with the stress level parameter is established:

[0023] (1)

[0024] wherein, is the damage variable in the direction of the maximum principal stress, A is the aging strength parameter with time hysteresis, λ is the percentage value of the peak strength of the rock at each stage of loading, λ0 is the percentage value of the peak strength of the rock corresponding to the initial stress level, controls the evolution rate of , when the stress level does not reach the damage starting threshold, the rock remains undamaged, and the damage variable is 0, once the stress exceeds the threshold, the rock enters the damage evolution stage, and the damage variable starts to accumulate.

[0025] The method for establishing the maximum damage constitutive equation of the rock under the true triaxial stress in step S4 is:

[0026] S4.1, based on the static test data analysis in step S1, a three-dimensional failure criterion considering the nonlinear attenuation of the effect of the intermediate principal stress in the fracture is adopted to construct the maximum damage function F of the rock and the maximum damage potential function G of the rock:

[0027] (2)

[0028] (3)

[0029] (4)

[0030] wherein, and are strength parameters, σ1, σ2 and σ3 are the maximum principal stress, the intermediate principal stress and the minimum principal stress respectively, p is the average stress, q is the generalized shear stress, is the internal friction angle, is the strength characteristic function, k d is the degradation parameter of the intermediate principal stress, σ p is the peak strength, σ * 2 is the corrected intermediate principal stress θ, which is the stress Lode angle, and the value range is The specific expression is as follows:

[0031] (5)

[0032] where J3 is the third invariant,

[0033] is the equivalent shear strain as an internal variable:

[0034] (6)

[0035] (7)

[0036] where, controls the initial yield threshold, controls the final yield threshold; characterizes the pre-peak nonlinear deformation behavior, controls the post-peak nonlinear evolution behavior, e p ij is the plastic deviatoric strain increment.

[0037] The maximum failure potential function G of rock takes the same form as the maximum failure function F of rock:

[0038] (8)

[0039] is the strength characteristic function:

[0040] (9)

[0041] is the characteristic length of the generalized loading direction.

[0042] S4.3, Plastic multiplier dλ is calculated from the plastic potential function p :

[0043] According to Hooke's law, the expression of the stress increment tensor is:

[0044] (10)

[0045] In addition, the plastic increment of rock in the plastic stage can be determined according to the plastic flow rule:

[0046] (11)

[0047] (12)

[0048] (13)

[0049] where dλ p is the plastic multiplier, which is non-negative. s is the compliance matrix, δ is the unit tensor, L is the characteristic length, and C is the flexibility matrix, and When the rock is in the plastic stress state, the stress will not pass through the yield surface, but fall on the yield surface (F = 0), that is, the plastic consistency condition dF = 0 is satisfied:

[0050] (14)

[0051] Bringing (12) and (13) into (14) can deduce the plastic multiplier dλ p :

[0052] (15)

[0053] The method for constructing the true triaxial multistage static aging effect viscoelastic constitutive equation in the step S5 is:

[0054] S5.1, the aging yield surface can be regarded as a plastic yield surface with hysteresis, and a yield function F v of the rock under the true triaxial multistage static aging effect is established: v

[0055] (16)

[0056] (17)

[0057] A plastic hardening function is taken as an internal variable of equivalent shear strain :

[0058] (18)

[0059] Wherein, , and The characteristic of the aging yield surface can take the same value as the plastic yield surface, is the strength characteristic function of the rock in the aging critical state, controls the post-peak nonlinear evolution behavior.

[0060] S5.2, the true triaxial multistage static aging irreversible strain equation is established:

[0061] (19)

[0062] Based on the Perzyna over-stress theory, the aging rheological multiplier expression is established:

[0063] (20)​

[0064] S5.3, based on the evolution characteristics of the deceleration stage and the constant speed stage of the rock true triaxial multi-stage static aging test, the aging parameter equation is established:

[0065] (21)

[0066] wherein, A v controls the aging constant speed evolution behavior, B v controls the aging deceleration evolution behavior, is the initial aging parameter.

[0067] S5.4, analysis of the deformation evolution characteristics of homogeneous sandstone under the action of true triaxial multi-stage static aging can know that when the stress exceeds the critical strength σ cs , the rheological strain develops rapidly, and the rock crack penetrates rapidly; In order to characterize this instability and failure characteristics, the degradation parameter is introduced ; When the rheological stress level does not exceed σ cs , the value is zero, when the stress level exceeds σ cs , increases rapidly, and the strain develops rapidly:

[0068] (22)

[0069] wherein, controls the evolution rate of , which evolves between 0 and 1.

[0070] The method of integrating the constitutive equation in steps S3 and S4 and the damage evolution equation in step S2 into a rock aging damage viscoelastic plastic mechanics model in step S6, and compiling it into a numerical subprogram is:

[0071] S6.1, the total strain is divided into elastic strain, plastic strain and irreversible strain, and the elastic prediction is carried out first:

[0072] (23)

[0073] (24)

[0074] S6.2, apply the elastic prediction stress, calculate the yield function under the stress state at this time. If the stress state does not exceed the yield surface , the variable is directly output; if the stress state exceeds the yield surface , calculate the irreversible strain increment , correct the stress:​​​

[0075] (25)

[0076] S6.3、According to the modified stress state, the yield function is calculated If , the stress is plastic. The correction ; if , the output variable.

[0077] In the step S9, the true triaxial multistage static aging test under different intermediate principal stresses σ2 is simulated, and the method for verifying the prediction effect and applicability of the model on the deformation evolution of the rock under the true triaxial multistage static aging is as follows: based on the model parameters under different intermediate principal stresses σ2 obtained in the step S6, the true triaxial multistage static aging tests under σ 2 = 2, 5, 10, 15 MPa are simulated, the deformation curves of the model tests are compared, and the prediction effect of the model on the rock mechanics behavior is verified.

[0078] The beneficial effects of the present application are:

[0079] 1、The damage evolution equation established by the present application which changes with the stress level can represent the mechanical response prediction of the rock under the complex loading path of the true triaxial and the damage evolution of the true triaxial static force and aging, and can accurately describe the damage evolution in the acceleration stage.

[0080] 2、The model of the present application can represent the expression of the intermediate principal stress effect attenuation effect of the rock cracking strength under the true triaxial.

[0081] 3、The present application establishes a unified expression model of the whole process of the static damage and the time decay, the equal speed stage and the acceleration stage, and can completely represent the deformation process of the rock under the true triaxial multistage static aging. BRIEF DESCRIPTION OF DRAWINGS

[0082] Figure 1 It is a flowchart for each step;

[0083] Figure 2 It is a true triaxial multistage static aging test scheme diagram;

[0084] Figure 3 It is a definition diagram of the aging critical strength;

[0085] Figure 4 It is an elastic modulus calculation schematic diagram under different damages in each direction;

[0086] Figure 5 It is a damage fitting diagram under different intermediate principal stresses;

[0087] Figure 6 It is a rock maximum damage function parameter fitting diagram;

[0088] Figure 7 a fitting diagram for rock three-dimensional time-dependent yield function parameters;

[0089] Figure 8 an algorithm flowchart;

[0090] Figure 9 a comparison diagram of time-dependent test results and simulation results under different intermediate principal stress conditions; DETAILED DESCRIPTION

[0091] The specific embodiments of the present application will be described below in conjunction with the accompanying drawings, but the present application is not limited to the scope of the specific embodiments. It should be noted that any creation based on or dependent on the present application is within the protection scope of the present application.

[0092] Embodiment:

[0093] The present embodiment provides a nonlinear mechanical model for characterizing the excavation damage-long-term degradation effect of engineering rock mass, which is constructed and verified by using homogeneous red sandstone as a rock sample

[0094] As Figure 1 shown, a flowchart of each step is given, including steps S1 to S9.

[0095] In step S1, different intermediate principal stress σ2 true triaxial static compression tests are carried out to obtain the peak strength of the homogeneous red sandstone.

[0096] In step S2, according to the strength of the red sandstone obtained by the true triaxial static compression test, a true triaxial multistage time-dependent rheological test under different intermediate principal stress σ2 is designed and carried out, as Figure 2 shown. And the critical strength σ cs of the homogeneous red sandstone under the true triaxial multistage static time-dependent is determined by using the isochronous curve cluster, the deformation evolution characteristics of the red sandstone and the evolution law of the critical strength σ cs and the failure stress σ d of the red sandstone are studied; at the same time, the elastic modulus under different damage degrees in each direction is calculated, and the time-dependent damage evolution characteristics of the homogeneous red sandstone under the true triaxial multistage static time-dependent are analyzed, as Figure 4 shown. Table 1 lists the peak strength σ p , the failure stress σ d , the elastic modulus E0 and the critical strength σ cs of the red sandstone under different intermediate principal stress conditions.

[0097] In step S3, a damage evolution equation characterizing the damage evolution characteristics is established:

[0098]

[0099] wherein, is the damage variable of the maximum principal stress direction, A is the time-aging strength parameter with time hysteresis, λ is the percentage value of the peak strength of red sandstone at each loading level, λ0 is the percentage value of the peak strength of red sandstone corresponding to the initial stress level, controls the evolution rate of When the stress level does not reach the damage starting threshold, the red sandstone remains undamaged, and the damage variable is 0. Once the stress exceeds the threshold, the red sandstone enters the damage evolution stage, and the damage variable starts to accumulate.

[0100] Based on the true triaxial multistage static aging test results under different intermediate principal stress conditions, the fitted damage evolution characteristic formula parameters are as shown in Figure 5 .

[0101] In step S4, the maximum damage function F parameters are fitted according to the red sandstone peak strength σ p data obtained by the true triaxial static compression test. Under different intermediate principal stress conditions, the maximum damage function F of the red sandstone is The fitting results are as shown in Figure 6 .

[0102] Under different intermediate principal stress conditions, the maximum damage function F of the red sandstone and the maximum damage potential function G of the red sandstone are:

[0103]

[0104]

[0105]

[0106] In step S5, the red sandstone critical strength σ cs data obtained by the true triaxial multistage static aging test are used to establish the aging rheological multiplier dλ v ; at the same time, according to the rheological strain evolution characteristics of the homogeneous red sandstone, the aging parameters and the aging acceleration control equation V d (t) are established.

[0107] In step S6, the constitutive equations in steps S3 and S4 and the damage evolution equation in step S2 are integrated into a nonlinear mechanical model representing the excavation damage-long-term deterioration effect of the red sandstone, and the algorithm flow of the numerical subprogram is as shown in Figure 8 .

[0108] The total strain is divided into elastic strain, plastic strain and irreversible strain, and elastic prediction is performed first:

[0109]

[0110]

[0111] If the stress state exceeds the static aging yield surface, calculate the irreversible strain increment , the stress is corrected:

[0112] (29)

[0113] S6.3, according to the corrected stress state, calculate the yield function If , the stress is plastic. Corrected ; if , the output variable.

[0114] In step S7, by establishing the model numerical simulation method in step S6, the red sandstone true triaxial static compression test in step S1 is simulated, the red sandstone maximum damage constitutive equation established in step S3 is verified, and the plastic part parameters of the model and the red sandstone maximum damage function parameters under the peak state are obtained. The yield function F under the action of true triaxial multistage static aging is fitted v Parameters. Under different intermediate principal stress conditions: 、 、 、 And ; the fitting results are shown in Figure 7 .

[0115] Under different intermediate principal stress conditions, the yield function F under the action of true triaxial multistage static aging v And the three-dimensional rheological potential function G of red sandstone v Are:

[0116]

[0117]

[0118]

[0119] In S8, by establishing the model numerical simulation method in step S6, the true triaxial multistage aging rheological test in step S2 is simulated, the true triaxial multistage static aging effect viscoelastic constitutive equation established in step S5 is verified, and the parameter equation of red sandstone under the action of true triaxial multistage static aging under different intermediate principal stress σ2 and the yield function parameter of red sandstone under the action of true triaxial multistage static aging under the critical state are obtained.

[0120] In S9, a true triaxial multistage static aging experiment under different intermediate principal stresses σ2 is simulated, the prediction effect and applicability of the model on the deformation evolution of red sandstone under the true triaxial multistage static aging are verified, and the characterization ability and prediction effect of the model on the deformation evolution of red sandstone under the true triaxial multistage static aging are obtained as shown in the following table. Figure 9 ​

Claims

1. A nonlinear mechanical model characterizing the damage-long-term deterioration effect of engineering rock mass excavation, characterized in that, Its construction method includes the following steps: S1. Conduct true triaxial static compression tests with different intermediate principal stresses σ2 to obtain the peak strength of the rock; S2. Based on the peak rock strength obtained from the true triaxial static compression test, conduct tests under true triaxial multi-stage static aging at different intermediate principal stresses σ2, and determine the critical strength σ of the rock under true triaxial multi-stage static aging using isochronous curve clusters. cs This study investigates the deformation evolution characteristics and critical strength σ of rocks under true triaxial multi-stage static aging. cs and the destructive stress σ d The evolution law of rock damage was analyzed; the elastic modulus under different damage levels in each direction was calculated, and the damage evolution characteristics of rock under true triaxial multi-stage static aging were analyzed. S3. Calculate the damage variables of the rock under true triaxial multi-stage static aging based on the elastic modulus obtained from the experiment in step S2, analyze the damage characteristics, and establish a damage evolution equation that characterizes the damage evolution characteristics. S4. Constructing the constitutive equation for maximum failure of rock under true triaxial stress: Based on the results of true triaxial static compression test, a three-dimensional failure criterion considering the nonlinear decay of principal stress effect during fracture is adopted to construct the maximum failure function F and the maximum failure potential function G of rock. S5. Construct the viscoelastic constitutive equation incorporating the true triaxial multi-stage static aging effect: Based on the maximum failure function F in step S4, establish the yield function F of the rock under true triaxial multi-stage static aging. v and the three-dimensional rheological potential function G of the rock v Based on Perzyna overstress theory, a time-dependent rheological multiplier dλ is established. v Simultaneously, based on the evolution characteristics of rocks under true triaxial multi-stage static aging, time-dependent aging parameters related to time t are established. and the time-accelerated control equation V d (t); S6. Couple the constitutive equations in steps S4 and S5 with the time-dependent damage evolution equation in step S3 to construct a nonlinear mechanical model characterizing the damage-long-term deterioration effect of engineering rock mass excavation; compile the model into a user-defined material subroutine of the finite element software to establish a numerical simulation method for the mechanical model. S7. Using the numerical simulation method established in step S6, simulate the true triaxial static compression test of rock in step S1, verify the maximum failure constitutive equation established in step S4, and obtain the plastic part parameters of the model and the maximum failure function parameters of rock under the peak state. S8. Using the numerical simulation method established in step S6, simulate the true triaxial multi-stage static aging test of rock in step S2, verify the viscoelastic constitutive equation established in step S5 that introduces the true triaxial multi-stage static aging effect, and obtain the stress parameter equations under different intermediate principal stresses σ2 and the yield function parameters of rock under critical state. S9. Simulate the test under true triaxial multi-stage static aging with different intermediate principal stresses σ2 to verify the model's predictive effect and applicability for the deformation evolution of rocks under true triaxial multi-stage static aging.

2. The nonlinear mechanical model for characterizing the damage-long-term deterioration effect of engineering rock mass excavation according to claim 1, characterized in that, In step S3, the method for establishing the time-dependent damage evolution equation characterizing the time-dependent damage evolution features is as follows: In step S1, the true triaxial static compressive peak strength σ of the rock under different intermediate principal stresses σ2 was statistically analyzed. p ; In step S2, the peak intensity σ from step S1 is used as a basis. p , 0.400σ p 0.750σ p 0.850σ p 0.900σ p σ p In the later stages of the experiment, the stress levels at each stage increased by 0.025σ. p Until the sample fails; after σ1 is applied to the specified stress level, static resting begins, with each resting period lasting 30 minutes, progressively increasing until the rock fails; under each static resting condition, ten characteristic nodes with the same time are selected, and their corresponding strain response data are statistically analyzed; based on the stress-strain correspondence under the same resting time, a series of isochronous curve clusters are plotted. By analyzing the curve separation characteristics in the isochronous curve clusters, the stress value corresponding to the critical point where the curve shows a significant inflection is determined as the critical strength σ of the rock. cs； The method for establishing the damage evolution equation characterizing the damage evolution features in step S3 is as follows: Based on the damage evolution analysis of the rock under true triaxial multi-stage static aging in step S2, a damage evolution formula that varies with stress level parameters is established: in, Let A be the damage variable in the direction of maximum principal stress, λ be the time-dependent strength parameter with time lag, λ be the percentage of peak strength of the rock at each loading level, and λ0 be the percentage of peak strength of the rock corresponding to the initial stress level. Controlling The rate of evolution is such that when the stress level does not reach the damage initiation threshold, the rock remains in an undamaged state and the damage variable is 0. When the stress exceeds the threshold, the rock enters the damage evolution stage and the damage variable begins to accumulate.

3. The nonlinear mechanical model for characterizing the damage-long-term deterioration effect of engineering rock mass excavation according to claim 1, characterized in that, In step S4, the method for constructing a three-dimensional failure criterion, maximum failure function F, and maximum failure potential function G of rock considering the nonlinear decay of principal stress effects during fracture is as follows: S4.1 Based on the static test data analysis in step S1, a three-dimensional failure criterion considering the nonlinear decay of principal stress effects during fracture is adopted to construct the maximum failure function F and the maximum failure potential function G of the rock: in, and Here, σ1, σ2, and σ3 are the strength parameters, representing the maximum principal stress, intermediate principal stress, and minimum principal stress, respectively; p is the mean stress; and q is the generalized shear stress. It is the internal friction angle. Let k be the intensity characteristic function. d It is the degradation parameter of the intermediate principal stress, σ p For peak intensity, σ * 2. The corrected intermediate principal stress, where θ is the Lod angle of stress, and its value range is... The specific expression is as follows: Among them, J3 is the third invariant. Therefore, equivalent shear strain Plastic hardening function as an internal variable: in, Control the initial yield threshold, Control the final yield threshold; Characterizes the nonlinear deformation features before the peak. Controlling the post-peak nonlinear evolution behavior, e p ij This is the plastic deviatoric strain increment; The maximum failure potential function G of the rock takes the same form as the maximum failure function F of the rock: For intensity characteristic functions: The characteristic length of the generalized loading direction; S4.3 Calculating the plastic multiplier dλ from the plastic potential function p : According to Hooke's law, the expression for the stress increment tensor is: Plastic increment during the plastic stage of rock Determined according to the plastic flow law: Where, dλ p It is a plasticity multiplier, which is non-negative, where s is the flexibility matrix and δ is the unit tensor. For material parameters, For characteristic length, flexibility matrix When rock is in a state of plastic stress, the stress will not pass through the yield surface, but will fall on the yield surface (F = 0), that is, the plastic consistency condition dF = 0 is satisfied: The plastic multiplier dλ is derived from the above four formulas. p :

4. The nonlinear mechanical model for characterizing the damage-long-term deterioration effect of engineering rock mass excavation according to claim 1, characterized in that, In step S5, the yield function F under true triaxial multi-stage static aging is... v and the three-dimensional time-dependent potential function G of the rock v Time-dependent multipliers dλ v The timeliness parameter k related to the timeliness t v (t) and the governing equation for accelerated rock aging V d The construction method of (t) is as follows: The method for constructing the viscoelastic constitutive equation for the true triaxial multi-stage static aging effect in step S5 is as follows: S5.

1. The aging yield surface is regarded as a hysteretic plastic yield surface, and the yield function F of the rock under true triaxial multi-stage static aging is established. v and the three-dimensional rheological potential function G of the rock v : Therefore, equivalent shear strain Plastic hardening function as an internal variable: in, , and The characteristic value of the controlled aging yield surface is taken to be the same as that of the plastic yield surface. This represents the strength characteristic function of rock under time-critical conditions. Controlling post-peak nonlinear evolution behavior; S5.2 Establish the true triaxial multi-stage static aging irreversible strain equation: Based on Perzyna's overstress theory, the expression for the time-dependent rheological multipliers is established: S5.

3. Based on the evolution characteristics of the deceleration and isochronous phases of the rock under true triaxial multi-stage static aging, the aging parameter equations are established: Among them, A v Controlling the time-bound evolution behavior, B v Controlling the time-deceleration evolution behavior, This refers to the initial aging parameters; S5.4 Analysis of the deformation evolution characteristics of rocks under true triaxial multi-stage static aging shows that when the stress exceeds the critical strength σ cs Subsequently, the rheological strain accelerates, and rock cracks penetrate more rapidly; to characterize this unstable failure feature, the degradation parameter can be... Introduction When the rheological stress level does not exceed σ cs hour, The value is zero when the stress level exceeds σ. cs hour, Rapid growth and accelerated development: in, control The rate of evolution, It evolves between 0 and 1.

5. The nonlinear mechanical model for characterizing the damage-long-term deterioration effect of engineering rock mass excavation according to claim 1, characterized in that, In step S6, the numerical simulation method for establishing the mechanical model is as follows: The method for integrating the constitutive equations in steps S3 and S4 and the damage evolution equations in step S2 into a viscoelastic-plastic mechanical model of rock aging damage in step S6 and compiling it into a numerical subroutine is as follows: S6.

1. Divide the total strain into elastic strain, plastic strain, and irreversible strain, and first perform elastic prediction: S6.2 Apply elastic predicted stress and calculate the yield function under this stress state. If the stress state does not exceed the yield surface If so, the variable will be output directly; If the stress state exceeds the yield surface Then calculate the irreversible strain increment. To correct the stress: S6.3 Calculate the yield function based on the corrected stress state. ,if Then, the stress is plastically adjusted to correct the stress. ;if Then the variable will be output.

6. The nonlinear mechanical model for characterizing the damage-long-term deterioration effect of engineering rock mass excavation according to claim 1, characterized in that, In step S9, the method for simulating true triaxial multi-stage static aging tests under different intermediate principal stresses σ2 to verify the model's predictive effect and applicability for deformation evolution of rocks under true triaxial multi-stage static aging is as follows: Based on the model parameters obtained in step S6 under different intermediate principal stresses σ2, simulate σ... 2 = True triaxial multi-stage static aging tests at 2, 5, 10, and 15 MPa were conducted, and the deformation curves of the model tests were compared to verify the predictive effect of the model on the mechanical behavior of rocks.

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