Deep rock high temperature-stress coupling strength calculation method considering mining disturbance
By constructing a rock yield surface expression that considers stress, temperature, damage, and strain rate, and combining the Ziegler orthogonal principle and the maximum dissipation principle, the formulas for calculating viscoplastic strain and damage are derived. This solves the problem of calculating rock strength under the coupled effects of high ground stress, high ground temperature, and mining disturbance, and realizes accurate assessment of rock strength and accurate simulation of damage evolution.
Patent Information
- Application Number
- CN202610079251.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-21
- Publication Date
- 2026-02-17
- Estimated Expiration
- 2046-01-21
AI Technical Summary
Existing technologies have failed to effectively characterize the profound impact of the coupling effects of high ground stress, high ground temperature and mining disturbance on rock strength and failure behavior, especially under extreme conditions, the damage evolution path, strength threshold and instability mode of rocks are significantly different.
A rock yield surface expression considering stress, temperature, damage, and strain rate was constructed. The viscoplastic strain and damage calculation formulas were derived using the Ziegler orthogonal principle and the maximum dissipation principle. A damage loading function was introduced, and the damage evolution expression was derived through the damage consistency criterion. The rock dynamic load-high temperature-stress damage constitutive model was embedded in the continuous medium finite element software for numerical implementation. The model parameters were calibrated by combining indoor tests.
It enables accurate calculation of rock strength under high temperature-stress coupling conditions, accurately assesses rock strength in complex environments, improves the accuracy and economy of calculation results, and is applicable to deep rock mass engineering design.
Smart Images

Figure CN121543375A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of geotechnical engineering strength assessment technology, and in particular to a method for calculating the high-temperature-stress coupling strength of deep rock considering mining disturbance. Background Technology
[0002] With the rapid development of deep mineral resource development and deep-earth space utilization projects, deep rock engineering faces increasingly complex occurrence environments. Deep rock masses are generally subjected to extreme multi-field coupling conditions of high ground stress, high ground temperature, high permeability pressure, and intense mining disturbance (referred to as "three highs and one disturbance"). Currently, most studies on the mechanical properties of deep rocks focus on single factors, such as the strength and deformation characteristics under only high ground stress, only high ground temperature, only high permeability pressure, or only specific types of dynamic loads, and have established corresponding theoretical models and calculation methods. These research results provide an important foundation for understanding the behavior of deep rocks under the action of single factors.
[0003] Besides high osmotic pressure, the combined effects of high ground stress, high ground temperature, and mining disturbance pose a significant challenge to almost every deep rock engineering project, severely threatening rock mechanical behavior and long-term engineering stability. Under such extreme conditions, rock materials will exhibit extremely complex nonlinear strength characteristics and damage mechanisms due to the combined influence of complex stress states caused by high ground stress, thermal damage and deterioration caused by high ground temperature, and dynamic loads induced by mining disturbances (such as blasting and mechanical vibration).
[0004] In real-world deep engineering environments, high ground stress, high ground temperature, and intense mining disturbances often coexist and couple, acting together on the rock mass. Existing research has largely failed to effectively characterize the profound impact of the synergistic coupling effect of these three key factors on rock strength and failure behavior. In particular, under coupled effects, the damage evolution path, strength threshold, and instability mode of the rock may differ significantly from those under single-factor effects. Therefore, there is an urgent need to propose a rock strength calculation method that can comprehensively consider the coupled effects of high ground stress, high ground temperature, and mining disturbances. Summary of the Invention
[0005] To address the problems existing in the prior art, this invention provides a method for calculating the high-temperature-stress coupling strength of deep rocks considering mining disturbances, comprising the following steps: Step 1: Construct the rock yield surface expression related to stress, temperature, damage, and strain rate.
[0006] Step 2: The formulas for calculating the viscoplastic strain and damage of rocks are derived using the Ziegler orthogonal principle and the maximum dissipation principle.
[0007] Step 3: Introduce a damage loading function to characterize the rock strength damage degradation effect, and derive the damage evolution expression through the damage consistency criterion.
[0008] Step 4: Embed the rock dynamic load-high temperature-stress damage constitutive model obtained in Steps 1-3 into the continuous medium finite element software for numerical implementation.
[0009] Step 5: Calibrate the parameters of the rock dynamic load-high temperature-stress damage constitutive model through indoor mechanical tests of rock under different dynamic loads, temperatures and stress coupling effects. The model calibration parameters include elastic parameters, yield surface parameters, viscoplastic parameters, damage parameters, temperature effect parameters and strain rate effect parameters.
[0010] Step 6: Conduct simulation tests using the calibrated rock dynamic load-high temperature-stress damage constitutive model to verify the rationality of the model calibration parameters.
[0011] Step 7: Input external loading conditions such as stress, temperature and dynamic disturbance into the rock dynamic load-high temperature-stress damage constitutive model according to the occurrence environment of deep rock engineering, and calculate the rock strength.
[0012] Optionally, step 1 specifically includes: Constructing expressions for rock yield surfaces related to stress, temperature, damage, and strain rate: .
[0013] In the formula, f vp Let σ be the rock yield surface function. ij For rock stress, For viscoplasticity, Let d be the viscoplastic strain rate, and d be the damage. Let I1 be the temperature, I1 = σ1 + σ2 + σ3 represent the first invariant of the stress tensor, and J2 = [(σ1 − σ2)]. 2 +(σ2−σ3) 2 +(σ3−σ1) 2 ] / 6 represents the second invariant of stress deviance, p a =1MPa is a parameter used for dimensionless transformation, k is the hydrostatic tensile strength of the rock, m is a parameter reflecting the change of the nonlinearity of the yield surface with the magnitude of the confining pressure, and α is a hardening parameter used to reflect the evolution trend of the rock yield surface with damage, strain rate, temperature and viscoplastic intrinsic variables.
[0014] α is represented as: .
[0015] In the formula, α i and α fκ represents the initial and peak positions of the yield surface on the meridional plane, respectively. vp Used to control the rate of yield surface evolution. and This is a function that reflects the effects of temperature and strain rate on rock strength.
[0016] The temperature effect function is expressed as: .
[0017] In the formula, κ T The evolution rate of the temperature effect function is used to control the rock strength at different temperatures, T. ref This is a reference temperature.
[0018] The strain rate effect function is expressed as: .
[0019] In the formula, The reference viscoplastic strain rate is χ, which is a parameter controlling the evolution rate of the strain rate effect function.
[0020] Rock stress is expressed as: .
[0021] In the formula, It is the linear thermal expansion coefficient. For Kronecker notation, when i=j, When =1, i≠j, =0, is the fourth-order elastic stiffness matrix of the non-destructive material.
[0022] Represented as: .
[0023] In the formula, and These are the elastic modulus and Poisson's ratio of the undamaged rock material, respectively.
[0024] Optionally, step 2 specifically includes: The formulas for calculating the viscoplastic strain and damage of rocks are derived using Ziegler's orthogonal principle and maximum dissipation theory: .
[0025] .
[0026] In the formula, λ vp and λ d These are the non-negative viscoplastic multiplier and the damage multiplier, respectively, f. d Let Y be the damage loading function, and Y be the damage driving force.
[0027] Y is represented as: .
[0028] In the formula, s is a parameter that controls the evolution of the damage driving force.
[0029] According to the viscoplastic overstress theory, the viscoplastic multiplier λ vp Represented as: .
[0030] In the formula, n is the viscous flow coefficient. vp This is the strain rate effect index.
[0031] The temperature effect and strain rate effect are coupled into the viscous flow coefficient using the weighting principle. middle, Represented as: .
[0032] In the formula, denoted as the viscoplastic flow coefficient under normal and quasi-static conditions, with a and b being weighting coefficients used to reflect the effects of temperature and dynamics on the viscous flow coefficient, respectively.
[0033] Optionally, step 3 specifically includes: Introducing the damage loading function, the damage loading function is expressed as: .
[0034] In the formula, ω is a parameter reflecting the influence of confining pressure on the rate of rock damage evolution.
[0035] The loading-unloading conditions for rock damage are expressed in Kuhn-Tucker form as follows: .
[0036] According to equations (12) and (13), the damage multiplier is expressed as: .
[0037] Substituting equations (12) and (14) into equation (8) and integrating, we obtain the expression for rock damage evolution as follows: .
[0038] Optionally, step 4 is achieved by building a numerical implementation framework in continuous medium finite element software, which includes a mechanics module, a viscoplasticity module, and a damage module.
[0039] The mechanics module solves equation (1) to calculate the constitutive stress-strain behavior of the rock material, in order to update the rock yield surface and damage state.
[0040] The viscoplastic module solves equation (7) to calculate the viscoplastic strain of the rock, which is used to update the rock stress state and serve as the damage driving force.
[0041] The damage module solves equation (14) to determine the rock damage evolution, which is used to update the rock stiffness and viscoplastic strain.
[0042] Optionally, step 6 specifically includes: The calibrated rock dynamic load-high temperature-stress damage constitutive model was used to simulate the triaxial compression test of rock under different confining pressures in a normal temperature environment. The rationality of elastic parameters, viscoplastic parameters and damage parameters was determined based on the agreement between the simulation results and the measured results.
[0043] The dynamic impact test of rock under different strain rate conditions was simulated using the calibrated rock dynamic load-high temperature-stress damage constitutive model. The rationality of the strain rate effect parameters was determined based on the agreement between the simulation results and the measured results.
[0044] The calibrated rock dynamic load-high temperature-stress damage constitutive model was used to simulate triaxial compression tests of rock under different temperature and confining pressure conditions. The rationality of the temperature effect parameters was determined based on the agreement between the simulation results and the measured results.
[0045] After adopting the above technical solution, the beneficial effects of the present invention are as follows: (1) This invention establishes a method for calculating the high temperature-stress coupling strength of rock considering the influence of dynamic disturbance, which makes up for the deficiency of the prior art that does not simultaneously consider the coupling effect of high temperature, stress and dynamic load on rock strength.
[0046] (2) The rock strength yield criterion proposed in this invention, which includes temperature, stress, damage and strain rate parameters, can more accurately evaluate rock strength under different complex environmental conditions.
[0047] (3) This invention quantifies the relative contribution of high temperature effect and strain rate effect to rock strength through the weighting principle. By adjusting the weighting parameters to adapt to different working conditions, it realizes accurate calculation of rock strength under different temperature-dynamic load coupling conditions.
[0048] (4) Compared with empirical formulas, the parameters of this invention have stronger physical meaning and higher accuracy of calculation results; compared with model tests or in-situ monitoring methods, it requires less time and less manpower and material resources, and has good economy and applicability. Attached Figure Description
[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0050] Figure 1 This is a framework diagram for the numerical implementation of the rock dynamic load-high temperature-stress damage constitutive model proposed in this invention.
[0051] Figure 2 The parameters of the dynamic load-high temperature-stress damage constitutive model for Beishan granite are calibrated as follows: (a) Evolution of the first invariant of stress tensor with viscoplastic intrinsic variable; (b) Evolution of the second invariant of stress deviator with viscoplastic intrinsic variable; (c) Calibration of rock yield surface corresponding to different viscoplastic intrinsic variables; and (d) Calibration of hardening parameters with the evolution of viscoplastic intrinsic variables.
[0052] Figure 3 This is a comparison of the simulation results and measured results of triaxial compression tests of Beishan granite under different confining pressures in a normal temperature environment, using the calibrated dynamic load-high temperature-stress damage constitutive model.
[0053] Figure 4 The figure shows a comparison between the simulation results and the measured results of dynamic impact tests on Beishan granite under different strain rate conditions using a calibrated constitutive model of dynamic load-high temperature-stress damage.
[0054] Figure 5 The figures show a comparison between the simulation results and the measured results of the dynamic load-high temperature-stress damage constitutive model of Beishan granite under different temperature and confining pressure conditions. (a) shows the simulation results and the measured results of the dynamic load-high temperature-stress damage constitutive model of Beishan granite under different temperature conditions. (b) shows the simulation results and the measured results of the dynamic load-high temperature-stress damage constitutive model of Beishan granite under different confining pressure conditions.
[0055] Figure 6 This is a comparison chart of the simulation results and measured results of the mechanical response of Beishan granite under dynamic load-high temperature-stress coupling conditions. Detailed Implementation
[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0057] In deep rock engineering, high ground stress, high ground temperature, and intense mining disturbance often coexist and couple, jointly influencing the mechanical behavior of rocks. However, current research methods mainly focus on the impact of single factors (such as high ground stress or high ground temperature alone) or simplified disturbance models (such as quasi-static loads) on rock strength. These models often fail to effectively characterize the complex coupling effects of high ground stress, high ground temperature, and mining disturbance. Currently, there is a lack of a comprehensive computational method to quantitatively predict and evaluate the high-temperature-stress coupling strength characteristics and damage evolution of deep rocks considering mining disturbance.
[0058] Based on research, a method for calculating the high-temperature-stress coupling strength of deep rocks considering mining disturbance is proposed. This method can accurately calculate the rock strength evolution under different stress, temperature, and dynamic loading conditions. It can serve as a theoretical tool to guide the engineering strength design of rock masses in complex environments characterized by high temperature, high humidity, and high temperature, high temperature, and high stress, and high temperature ... (1) Rock strength criterion form: A rock strength criterion that simultaneously considers the coupling effects of temperature, stress, damage and strain rate is proposed, which truly reflects the nonlinear response characteristics of rock strength under complex external loads.
[0059] (2) Calculation method for viscoplastic strain and damage of rock: Based on Ziegler's orthogonal principle and the maximum dissipation principle, the calculation formula for viscoplastic strain and damage of rock is derived and established.
[0060] (3) Coupling method of temperature effect and strain rate effect: Based on the weighting principle, the relative contributions of temperature effect and strain rate effect to rock strength were quantified, and a method for calculating the viscoplastic strain of rock under temperature-dynamic load coupling conditions was constructed.
[0061] (4) Accurate calibration method for model parameters: Based on the principle that the same viscoplastic internal variable corresponds to the same yield surface, the evolution process of rock yield surface can be calibrated conveniently and quickly, thereby achieving accurate calibration of model parameters.
[0062] This invention provides a method for calculating the high-temperature-stress coupling strength of deep rock considering mining disturbance, comprising the following steps: Step 1: Construct the rock yield surface expression related to stress, temperature, damage, and strain rate.
[0063] Specifically, the expression for the rock yield surface related to stress, temperature, damage, and strain rate is as follows: .
[0064] In the formula, f vp Let σ be the rock yield surface function. ij For rock stress, For viscoplasticity, Let d be the viscoplastic strain rate, and d be the damage. Let I1 be the temperature, I1 = σ1 + σ2 + σ3 represent the first invariant of the stress tensor, and J2 = [(σ1 − σ2)]. 2 +(σ2−σ3) 2 +(σ3−σ1) 2 ] / 6 represents the second invariant of stress deviance, p a =1MPa is a parameter used for dimensionless transformation, k is the hydrostatic tensile strength of the rock, m is a parameter reflecting the change of the nonlinearity of the yield surface with the magnitude of the confining pressure, and α is a hardening parameter used to reflect the evolution trend of the rock yield surface with damage, strain rate, temperature and viscoplastic intrinsic variables.
[0065] α is represented as: .
[0066] In the formula, α i and α f κ represents the initial and peak positions of the yield surface on the meridional plane, respectively. vp Used to control the rate of yield surface evolution. and This is a function that reflects the effects of temperature and strain rate on rock strength.
[0067] The temperature effect function is expressed as: .
[0068] In the formula, κ T The evolution rate of the temperature effect function is used to control the rock strength at different temperatures, T. ref For reference temperature, it is set to 25°C.
[0069] The strain rate effect function is expressed as: .
[0070] In the formula, For reference, the viscoplastic strain rate is set to 1×10–5 / s, and χ is a parameter that controls the evolution rate of the strain rate effect function.
[0071] Rock stress is expressed as: .
[0072] In the formula, It is the linear thermal expansion coefficient. For Kronecker notation, when i=j, When =1, i≠j, =0, is the fourth-order elastic stiffness matrix of the non-destructive material.
[0073] Represented as: .
[0074] In the formula, and These are the elastic modulus and Poisson's ratio of the undamaged rock material, respectively.
[0075] Step 2: The formulas for calculating the viscoplastic strain and damage of rocks are derived using the Ziegler orthogonal principle and the maximum dissipation principle.
[0076] Specifically, using Ziegler's orthogonal principle and maximum dissipation theory, the formulas for calculating the viscoplastic strain and damage of rocks are derived as follows: .
[0077] .
[0078] In the formula, λ vp and λ d These are the non-negative viscoplastic multiplier and the damage multiplier, respectively, f. d Let Y be the damage loading function, and Y be the damage driving force.
[0079] Y is represented as: .
[0080] In the formula, s is a parameter that controls the evolution of the damage driving force.
[0081] Existing technologies have proposed solutions for viscoplastic multipliers λ. vp A series of calculation expressions, among which, the viscoplastic overstress theory, due to its simple structure and ease of numerical implementation, has been widely used to simulate the dynamic response characteristics of brittle materials such as rocks. According to the viscoplastic overstress theory, the viscoplastic multiplier λ vp Represented as: .
[0082] In the formula, n is the viscous flow coefficient. vp This is the strain rate effect index.
[0083] To accurately quantify the effects of strain rate and temperature on rock strength, a weighted average is used to couple the temperature and strain rate effects into the viscous flow coefficient. middle, Represented as: .
[0084] In the formula, denoted as the viscoplastic flow coefficient under normal and quasi-static conditions, with a and b being weighting coefficients used to reflect the effects of temperature and dynamics on the viscous flow coefficient, respectively.
[0085] Step 3: Introduce a damage loading function to characterize the rock strength damage degradation effect, and derive the damage evolution expression through the damage consistency criterion.
[0086] Specifically, a damage loading function is introduced, which is expressed as: .
[0087] In the formula, ω is a parameter reflecting the influence of confining pressure (σ3) on the rock damage evolution rate.
[0088] The loading-unloading conditions for rock damage are expressed in Kuhn-Tucker form as follows: .
[0089] According to equations (12) and (13), the damage multiplier is expressed as: .
[0090] Substituting equations (12) and (14) into equation (8) and integrating, we obtain the expression for rock damage evolution as follows: .
[0091] Step 4: Embed the rock dynamic load-high temperature-stress damage constitutive model obtained in Steps 1-3 into the continuous medium finite element software for numerical implementation.
[0092] Specifically, a numerical implementation framework is built in continuous medium finite element software, such as... Figure 1 As shown, the numerical implementation framework includes a mechanics module, a viscoplasticity module, and a damage module.
[0093] The mechanics module solves equation (1) to calculate the constitutive stress-strain behavior of the rock material, in order to update the rock yield surface and damage state.
[0094] The viscoplastic module solves equation (7) to calculate the viscoplastic strain of the rock, which is used to update the rock stress state and serve as the damage driving force.
[0095] The damage module solves equation (14) to determine the rock damage evolution, which is used to update the rock stiffness and viscoplastic strain.
[0096] The numerical implementation framework employs a fully coupled solution strategy with unconditional stability, solving three modules simultaneously in a single iteration. Compared to traditional segregated solution methods for multiphysics problems, the fully coupled solution method typically offers better convergence and requires fewer iterations, although it generally incurs higher computational costs. The standard Galerkin method and the implicit backward differential formula (BDF) are used for spatial and temporal discretization, respectively. The Newton-Raphson iterative method is chosen to solve the nonlinear equations, with a relative tolerance of 0.001, an absolute tolerance of 0.1, and a maximum of 25 iterations.
[0097] Step 5: Calibrate the parameters of the rock dynamic load-high temperature-stress damage constitutive model through indoor mechanical tests of rocks under different dynamic loads, temperatures and stress coupling effects.
[0098] Specifically, based on the indoor mechanical test data of Beishan granite under different temperature, strain rate and confining pressure conditions, the elastic parameters ( and The viscoplastic parameter (α) can be determined by the linear segment of a triaxial compression test. i α f κ vp The damage parameters (α and χ) and (s and ω) can be obtained by calibrating the yield surface evolution process. Based on the principle that the same viscoplastic intrinsic variable lies on the same yield surface, the yield surface evolution under different viscoplastic intrinsic variables can be calibrated, thereby determining the viscoplastic parameter (α). i α f κ vp and χ) and damage parameters (s and ω), such as Figure 2 As shown in Table 1, the strain rate effect parameters and temperature effect parameters of the model can be determined by triaxial compression tests of rocks under different temperature conditions and strain rates.
[0099] Table 1. Constitutive model parameters for dynamic load-high temperature-stress damage of Beishan granite.
[0100] Step 6: Conduct simulation tests using the calibrated rock dynamic load-high temperature-stress damage constitutive model to verify the rationality of the model calibration parameters.
[0101] Step 6: Conduct simulation tests using the calibrated rock dynamic load-high temperature-stress damage constitutive model to verify the rationality of the model calibration parameters.
[0102] Specifically, the calibrated dynamic load-high temperature-stress damage constitutive model of Beishan granite was used to simulate triaxial compression tests of rock under different confining pressures in a normal temperature environment. The simulation results were compared with the measured results, such as... Figure 3 As shown, the simulation results are in good agreement with the measured results, indicating that the proposed dynamic load-high temperature-stress damage constitutive model can well reproduce the mechanical responses such as initial yielding, hardening and softening, as well as the characteristic stress states such as peak and residual strength of Beishan granite during triaxial compression. This proves that the elastic parameters, viscoplastic parameters and damage parameters listed in Table 1 are reasonable.
[0103] Dynamic impact tests of rock under different strain rate conditions were simulated using a calibrated constitutive model of Beishan granite subjected to dynamic load-high temperature-stress damage. The simulation results were compared with the measured results. Figure 4 As shown, the simulation results are in good agreement with the measured results, indicating that the proposed dynamic load-high temperature-stress damage constitutive model can capture the strengthening phenomenon of the mechanical strength of Beishan granite increasing with the increase of strain rate, proving that the strain rate effect parameters in Table 1 are reasonable.
[0104] The calibrated dynamic load-high temperature-stress damage constitutive model of Beishan granite was used to simulate triaxial compression tests of the rock under different temperature and confining pressure conditions. The simulation results were compared with the measured results. Figure 5 As shown, the simulation results are in good agreement with the measured results, indicating that the proposed dynamic load-high temperature-stress damage constitutive model can well characterize the characteristic mechanical responses of Beishan granite under thermo-mechanical coupling conditions, such as initial yielding, hardening and softening. At the same time, it can also accurately reflect the evolution trend of the mechanical strength of Beishan granite gradually decreasing with increasing temperature, proving that the temperature effect parameters in Table 1 are reasonable.
[0105] Step 7: Input external loading conditions such as stress, temperature and dynamic disturbance into the rock dynamic load-high temperature-stress damage constitutive model according to the occurrence environment of deep rock engineering, and calculate the rock strength.
[0106] Specifically, since the model parameters listed in Table 1 have been verified through simulations using three different tests—room temperature, thermo-coupling, and dynamic impact—the following simulations calculated the evolution trend of rock high-temperature-stress coupling strength considering mining dynamic disturbances. The simulation results were then compared with measured results. Figure 6As shown, the simulation results are in good agreement with the measured results, indicating that the developed dynamic load-high temperature-stress damage constitutive model for Beishan granite can capture the mechanical response of Beishan granite under the coupling of dynamic load, high temperature and stress fields in a unified and accurate manner.
[0107] The present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.
Claims
1. A deep rock high temperature-stress coupling strength calculation method considering mining disturbance, characterized in that, Includes the following steps: Step 1: Construct the rock yield surface expression related to stress, temperature, damage, and strain rate; Step 2: The formulas for calculating the viscoplastic strain and damage of rocks are derived using the Ziegler orthogonal principle and the maximum dissipation principle; Step 3: Introduce a damage loading function to characterize the rock strength damage degradation effect, and derive the damage evolution expression through the damage consistency criterion; Step 4: Embed the rock dynamic load-high temperature-stress damage constitutive model obtained in Steps 1-3 into the continuous medium finite element software for numerical implementation; Step 5: Calibrate the parameters of the rock dynamic load-high temperature-stress damage constitutive model through indoor mechanical tests of rock under different dynamic loads, temperatures and stress coupling effects. The model calibration parameters include elastic parameters, yield surface parameters, viscoplastic parameters, damage parameters, temperature effect parameters and strain rate effect parameters. Step 6: Conduct simulation tests using the calibrated rock dynamic load-high temperature-stress damage constitutive model to verify the rationality of the model calibration parameters; Step 7: Input stress, temperature and dynamic disturbance into the rock dynamic load-high temperature-stress damage constitutive model based on the occurrence environment of deep rock engineering, and calculate the rock strength.
2. The method according to claim 1, wherein, Step 1 specifically includes: Constructing expressions for rock yield surfaces related to stress, temperature, damage, and strain rate: (1); where f vp is the rock yield surface function, σ ij is the rock stress, is the viscoplastic internal variable, is the viscoplastic strain rate, d is the damage, is the temperature, I1=σ1+σ2+σ3 represents the first invariant of the stress tensor, J2=[(σ1−σ2) 2 +(σ2−σ3) 2 +(σ3−σ1) 2 ] / 6 represents the second invariant of the stress deviator, p a =1 MPa is a parameter for non-dimensionalization, k is the hydrostatic tensile strength of the rock, m is a parameter reflecting the variation of the degree of nonlinearity of the yield surface with the magnitude of the confining pressure, and α is a hardening parameter for reflecting the evolution trend of the rock yield surface with the damage, the strain rate, the temperature, and the viscoplastic internal variable. α is represented as: (2); where α i and α f denote the initial and peak positions of the yield surface in the meridian plane, respectively, κ vp is used to control the evolution rate of the yield surface, and are functions reflecting the influence of temperature effect and strain rate effect on rock strength; The temperature effect function is expressed as: (3); wherein κ T for controlling the rate of evolution of the temperature effect function, which determines the rock strength at different temperatures, T ref is the reference temperature; The strain rate effect function is expressed as: (4); wherein is the reference viscoplastic strain rate, and χ is a parameter that controls the evolution rate of the strain rate effect function. Rock stress is expressed as: (5); wherein is the linear thermal expansion coefficient, is the Kronecker symbol, i = j, = 1, i≠j, = 0, is the fourth order elastic stiffness matrix of the lossless material; is represented as: (6) ; wherein and E and v are the elastic modulus and Poisson's ratio of the intact rock material, respectively.
3. The method for calculating the high-temperature-stress coupling strength of deep rock considering mining disturbance as described in claim 2, characterized in that, Step 2 specifically includes: The formulas for calculating the viscoplastic strain and damage of rocks are derived using Ziegler's orthogonal principle and maximum dissipation theory: (7); (8); where λ vp and λ d are non-negative viscoplastic and damage multipliers, respectively, f d is a damage loading function, and Y is a damage driving force. Y is represented as: (9); In the formula, s is a parameter that controls the evolution of the damage driving force; According to the viscoplastic overstress theory, the viscoplastic multiplier λ vp is expressed as: (10); In the formula, n is the viscous flow coefficient. vp The strain rate effect index; The temperature effect and strain rate effect are coupled into the viscous flow coefficient using the weighting principle. middle, Represented as: (11) ; In the formula, denoted as the viscoplastic flow coefficient under normal and quasi-static conditions, with a and b being weighting coefficients used to reflect the effects of temperature and dynamics on the viscous flow coefficient, respectively.
4. The method for calculating the high-temperature-stress coupling strength of deep rock considering mining disturbance as described in claim 3, characterized in that, Step 3 specifically includes: Introducing the damage loading function, the damage loading function is expressed as: (12); In the formula, ω is a parameter reflecting the influence of confining pressure on the rock damage evolution rate; The loading-unloading conditions for rock damage are expressed in Kuhn-Tucker form as follows: (13); According to equations (12) and (13), the damage multiplier is expressed as: (14); Substituting equations (12) and (14) into equation (8) and integrating, we obtain the expression for rock damage evolution as follows: (15)。 5. The method for calculating the high-temperature-stress coupling strength of deep rock considering mining disturbance as described in claim 4, characterized in that, Step 4 is achieved by building a numerical implementation framework in the continuous medium finite element software. The numerical implementation framework includes a mechanics module, a viscoplasticity module, and a damage module. The mechanics module solves equation (1) to calculate the constitutive stress-strain behavior of rock materials, in order to update the rock yield surface and damage state; The viscoplastic module solves equation (7) to calculate the viscoplastic strain of the rock, which is used to update the rock stress state and serve as the damage driving force. The damage module solves equation (14) to determine the rock damage evolution, which is used to update the rock stiffness and viscoplastic strain.
6. The method for calculating the high-temperature-stress coupling strength of deep rock considering mining disturbance as described in claim 1, characterized in that, Step 6 specifically includes: The calibrated rock dynamic load-high temperature-stress damage constitutive model was used to simulate the triaxial compression test of rock under different confining pressures in a normal temperature environment. The rationality of elastic parameters, viscoplastic parameters and damage parameters was determined based on the agreement between the simulation results and the measured results. The dynamic impact test of rock under different strain rate conditions was simulated using the calibrated rock dynamic load-high temperature-stress damage constitutive model. The rationality of the strain rate effect parameters was determined based on the agreement between the simulation results and the measured results. The calibrated rock dynamic load-high temperature-stress damage constitutive model was used to simulate triaxial compression tests of rock under different temperature and confining pressure conditions. The rationality of the temperature effect parameters was determined based on the agreement between the simulation results and the measured results.
Citation Information
Patent Citations
Rock secular deformation prediction method and application thereof
CN112329224A
Construction method suitable for rock dynamic constitutive model under earthquake load
CN113032955A
Rock constitutive model numerical analysis method considering high temperature-load coupling damage
CN116933538A
Rock mass high temperature-aging-elastoplastic coupling damage calculation method
CN118607315A
Slope aging deformation calculation method
CN120124352A