Model construction method for representing deep hard rock excavation true triaxial stress path

Abstract

The invention discloses a model construction method for representing a deep hard rock excavation true triaxial stress path, and the method comprises the steps: S1, constructing an excavation stress path coefficient, and quantifying different true triaxial excavation stress paths; s2, introducing an excavation stress path coefficient, correcting the anisotropic elastic stiffness matrix, and constructing an incremental expression of a stress-strain relationship; s3, establishing a three-dimensional yield function; s4-S7, constructing a brittleness index, an internal variable, a strength parameter evolution equation and a deformation parameter evolution equation representing the excavation stress path and the initial stress difference; s8, the formula is embedded into cellular automaton numerical calculation software for calculation; and S9, carrying out true triaxial rock tests of different excavation stress paths and stress differences, and verifying the accuracy of a stress-strain curve. According to the method, the stress-strain characteristics of the rock under the true triaxial excavation stress path are predicted, and a theoretical basis is provided for high-stress deep engineering hard rock excavation damage disaster prediction and stability analysis.

Description

Technical Field

[0001] The present invention relates to the field of rock mechanics and engineering research, and in particular to a method for constructing a model for characterizing true triaxial stress paths in deep hard rock excavation. Background Art

[0002] Deep hard rock failure is primarily caused by excavation-induced stress changes. During excavation, the surrounding rock undergoes a complex stress path, characterized by continuous variations in the magnitude of the three principal stresses. The instability of rock masses in underground engineering projects depends on the evolution of these stress paths. Establishing a mechanical model that can reasonably describe the stress paths of deep hard rock excavation provides the theoretical foundation for deep surrounding rock stability analysis.

[0003] Currently, scholars have conducted extensive research on rock mechanical models, but most are based on loading theory, describing the stress-strain relationship of rock under the applied stress path. These methods are unable to accurately describe the effects of the continuous changes in the three principal stresses on rock deformation and fracture during underground excavation, leading to inaccuracies in the prediction and assessment of many engineering disasters.

[0004] At the same time, a large number of studies have shown that after excavation of deep hard rock projects, the stress paths at different positions and depths of the surrounding rock are variable due to the influence of factors such as the magnitude and direction of ground stress and the shape of the excavation, resulting in differences in the location and degree of surrounding rock damage.

[0005] Therefore, how to effectively characterize the adjustment patterns under different stress paths during deep hard rock excavation, and how to accurately quantify the evolution of rock strength and deformation parameters caused by deep engineering excavation under the influence of multiple stress paths, is particularly urgent. Given this situation, it is particularly urgent to construct a three-dimensional mechanical model that can incorporate the stress path effects of deep hard rock excavation, but no relevant research reports have yet explored this in depth. Summary of the Invention

[0006] In order to solve the current problem of the lack of a three-dimensional mechanical model that can incorporate the stress path effects of deep hard rock excavation, the present invention proposes a model construction method for characterizing the true triaxial stress path of deep hard rock excavation, providing a theoretical basis for the prediction of damage disasters and stability analysis of high-stress deep engineering hard rock excavation, thereby solving the above-mentioned problems.

[0007] This application discloses a method for constructing a model to characterize the true triaxial stress path of deep hard rock excavation, comprising the following steps:

[0008] S1. Construct an excavation stress path coefficient to characterize the differences in true triaxial excavation stress paths and quantify different true triaxial excavation stress paths.

[0009] S2. Based on the generalized Hooke's law, the excavation stress path coefficient is introduced, the anisotropic elastic stiffness matrix is modified, and the incremental expression of the stress-strain relationship is constructed;

[0010] S3, using the 3DHRFC strength criterion to establish a three-dimensional yield function;

[0011] S4. Construct a brittleness index to characterize the excavation stress path and initial stress difference;

[0012] S5. Construct internal variables to characterize the excavation stress path and initial stress difference;

[0013] S6. Construct the strength parameter evolution equation to characterize the excavation stress path and initial stress difference;

[0014] S7. Construct deformation parameter evolution equations that characterize excavation stress path and initial stress difference;

[0015] S8, embedding the calculation formula obtained in S1-S7 into cellular automaton numerical calculation software for calculation;

[0016] S9. Conduct true triaxial rock tests with different excavation stress paths and stress differences to verify the accuracy of the stress-strain curve.

[0017] Preferably, said S1 comprises the following steps:

[0018] S11. In the octahedral stress space, using β R Characterize the excavation stress adjustment coefficient, the calculation formula is as follows:

[0019]

[0020] Among them, β R is the excavation stress adjustment coefficient, σ1, σ2 and σ3 are the principal stresses in the effective stress space, is the stress state before stress adjustment in the σ1 direction, is the stress state before the stress adjustment in the σ2 direction, is the stress state before the stress adjustment in the σ3 direction, is the stress state after stress adjustment in the σ1 direction, is the stress state after the stress in the σ2 direction is adjusted, is the stress state after stress adjustment in the σ3 direction, q0 is the equivalent shear stress before stress adjustment, q1 is the equivalent shear stress after stress adjustment, p0 is the average stress state before stress adjustment, and p1 is the average stress state after adjustment;

[0021] S12. Introduce a dynamic correction term related to stress adjustment rate and strain energy into the excavation stress adjustment coefficient to characterize the influence of excavation rate on stress path and obtain the excavation stress path coefficient:

[0022]

[0023] in, is the excavation stress path coefficient, is the unloading rate, γ and θ are dynamic correction factors, and U is the strain energy;

[0024] S13. According to the true triaxial excavation stress path model, determine the stress state and rate before and after stress adjustment, substitute them into equations (1) to (6), and obtain the excavation stress path coefficient of the corresponding excavation stress path:

[0025] Preferably, the incremental expression of the stress-strain relationship in S2 is:

[0026]

[0027] in, is the incremental stress matrix, is the incremental strain matrix, is the incremental plastic strain tensor matrix, κ is the internal variable, E a is the anisotropic elastic stiffness matrix tensor based on deformation modulus, Poisson’s ratio and intrinsic variables, is the initial stiffness matrix.

[0028] Preferably, said S3 comprises the following steps:

[0029] S31. Based on the 3DHRFC strength criterion, the relationship between the three stresses is established as follows:

[0030]

[0031] Where c is the cohesion, is the internal friction angle, s and t are material parameters;

[0032] S32. The three-dimensional yield function based on the true triaxial stress relationship is:

[0033]

[0034] S33. Perform a true triaxial compression test on the rock sample to obtain the strength of the rock under true triaxial stress;

[0035] S34. Based on the strength of rock under true triaxial stress obtained in S33, substitute it into equations (9) and (10) to obtain material parameters s and t, and determine the yield function F.

[0036] Preferably, said S4 comprises the following steps:

[0037] S41. Conduct true triaxial tests with different excavation stress paths and stress difference to obtain rock stress-strain curves under different excavation stress paths;

[0038] S42. Based on the rock stress-strain curves under different excavation stress paths, the inverse of the plastic volume strain generated by rock fracture is used to represent the brittleness index, which is expressed as:

[0039]

[0040] Among them, B I is the brittleness index, is the plastic volume strain at peak strength;

[0041] S43. Based on the brittleness index, describe the relationship between the excavation stress path coefficient, stress difference and brittleness index:

[0042]

[0043] Among them, B IU is the brittleness index when the maximum principal stress and the intermediate principal stress are equal, and a, b, h, and d are material parameters.

[0044] Preferably, the S5 comprises the following steps:

[0045] The internal variables are expanded into a composite function of macroscopic plastic strain and microscopic crack strain, and the brittleness index and equivalent plastic volume strain are used to express the internal variables of hard rock degradation:

[0046] κ=κ p +κ d ; (16)

[0047]

[0048] Among them, κ p is the macroscopic plastic strain, κ d is the microscopic crack strain, is the critical plastic strain in the jth direction (j=1, 2, 3), is the critical stress for crack nucleation in the jth direction, which is equal to the crack propagation stress, and λ is the crack healing rate coefficient, which is characterized by the ratio of uniaxial compressive strength to tensile strength.

[0049] Preferably, the S6 comprises the following steps:

[0050] S61. Rock fracture development is divided into four stages, including elastic deformation stage, crack development stage, post-peak brittle fracture stage and residual stage;

[0051] S62. Analyze the evolution characteristics of rock strength parameters in four stages, including:

[0052] During the elastic deformation stage, no cracks are generated inside the specimen, and there is no need to consider the changes in strength parameters;

[0053] In the crack development stage, the rock begins to be damaged, the cohesion begins to weaken and decrease, and the internal friction angle begins to strengthen and increase due to the voids generated by the development of microcracks. At this time, the slope of cohesion weakening is w c , the slope of the internal friction angle enhancement is s c .

[0054]

[0055] in, is the plastic strain at the time of cohesion loss, is the plastic strain when the friction strength increases.

[0056] In the post-peak brittle fracture stage, macro cracks open or penetrate, causing a sudden loss of cohesion. Since this process is very short, the friction strength hardly changes. Therefore, it is believed that the internal friction angle remains unchanged in the brittle stage, and the cohesion weakening slope is w b , the slope of the internal friction angle enhancement is s b =0.

[0057]

[0058] in, is the equivalent plastic strain at peak strength during the uniaxial compression test, is the equivalent plastic strain at the residual starting point.

[0059] In the residual stage, the rock forms a complete macroscopic failure surface, the rock will shear and slip along the failure surface, and the values of cohesion and internal friction angle will remain constant;

[0060] S63. Based on the evolution characteristics of rock strength parameters in four stages, the strength parameter evolution equation of excavation stress path and initial stress difference is obtained as follows:

[0061] c=c0-∑w i Δk i (c0-c r ); (twenty two)

[0062]

[0063] Δκ i =κ i -κ i-1 -<κ i -κ>; (24)

[0064] Among them, w i is the weakening ratio of cohesion in a single sub-stage, si is the enhancement ratio of the internal friction angle in a single sub-stage, κ i is the final value of the internal variable in the i-th sub-stage, <x>is the positive operator, defined as max(0,x), c0 is the initial cohesion, c r is the residual cohesion, is the initial internal friction angle, is the residual internal friction angle.

[0065] Preferably, the S7 comprises the following steps:

[0066] S71. Rock deformation anisotropy is defined by the following two equations:

[0067] d j =R jr +(1-R jr )e -30κ ; (25)

[0068]

[0069] Among them, E j is σ j Deformation modulus in the direction, j = 1, 2, 3, E0 is the initial deformation modulus, R jr Characterizes the weakening rate of the deformation modulus of the specimen in the three principal stress directions in the residual stage, d j is the weakening rate of the deformation modulus of the specimen in the three principal stress directions, denoted by σ j The deformation modulus in the direction is related to the degree of weakening of the internal variables and the initial stress difference;

[0070] S72. According to the test results, obtain the weakening rate R of the deformation modulus of the three principal stress directions of the corresponding rock sample in the residual stage. jr , based on formula (25), the typical relationship between the weakening rate of rock deformation modulus and plastic internal variables is fitted;

[0071] S73. Based on S72, obtain d j and the initial deformation modulus E0, we get E j ;

[0072] S74. Obtain stable values of the weakening rate R1 of the deformation modulus in the direction of maximum principal stress and the weakening rate R3 of the deformation modulus in the direction of minimum principal stress of the corresponding rock based on the test results;

[0073] S75, establish the weakening rate R2 of the deformation modulus in the direction of the intermediate principal stress and the initial stress difference The relationship is:

[0074]

[0075] Among them, R S is the increasing slope of the weakening rate of the deformation modulus in the intermediate principal stress direction as the initial stress difference changes.

[0076] Preferably, the step S8 comprises the following steps:

[0077] S81. Calculate the current stress according to the strain increment formula in S2, then calculate the trial stress based on the elastic stiffness matrix. Use the three-dimensional failure criterion to determine if the failure condition is met. If so, calculate the true stress by resetting the stress. Use the current excavation stress path coefficient, brittleness index, and internal variables to update the deformation and strength parameters, and calculate the incremental unbalanced force caused by the failure.

[0078] S82. When the incremental unbalanced force calculation is completed, the update is completed and the calculation of the next convergence step is performed until the convergence requirements are met and the loop is exited.

[0079] Preferably, the S9 comprises the following steps:

[0080] S91. Conduct true triaxial tests on rock specimens with different excavation stress paths and stress differences, and obtain stress-strain curves;

[0081] S92. Obtain material parameters related to S1-S7 based on the test data obtained in S911;

[0082] S93, performing simulation calculations by combining the relevant parameters obtained in S92 with the cellular automaton numerical calculation software embedded in S8, which is a three-dimensional mechanical model considering the excavation stress path and the initial stress difference;

[0083] S94. Based on S94, true triaxial rock stress-strain curves of different excavation stress paths and stress differences are simulated and compared with the rock stress-strain curves generated by the test data.

[0084] Beneficial effects of the present invention:

[0085] (1) The present invention can accurately describe the effects of the continuous changes of the three principal stresses on the deformation and fracture of rocks during the excavation of underground engineering projects. It solves the problem that most rock constitutive models in the existing technology are based only on loading theory and cannot accurately describe the impact of stress path changes on rocks during excavation. It provides a more accurate theoretical basis for deep surrounding rock stability analysis.

[0086] (2) The present invention can quantify different true triaxial excavation stress paths, further improving the accuracy and applicability of the model. At the same time, it constructs brittleness indicators, internal variables, strength parameter evolution equations, and deformation parameter evolution equations that characterize the excavation stress path and initial stress difference, so that the model can more comprehensively consider the mechanical behavior of rock during the excavation process.

[0087] (3) The present invention embeds the model into cellular automaton numerical calculation software, which can predict the stress-strain curve of rock under different excavation stress paths and stress differences through simulation calculation, providing an effective tool for the prediction of damage disasters and stability analysis of deep hard rock excavation. This not only reduces the risk of engineering disasters, but also improves the scientificity and accuracy of engineering design. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 A method for constructing a model for characterizing true triaxial stress paths in deep hard rock excavation according to an embodiment of the present invention;

[0089] Figure 2 Schematic diagram of different stress adjustments in the regular octahedron stress space according to an embodiment of the present invention;

[0090] Figure 3 This is a relationship diagram between different unloading rates and strain energy of granite under true triaxial unloading according to an embodiment of the present invention;

[0091] Figure 4 Schematic diagram of granite strength values under different true triaxial stress levels according to an embodiment of the present invention;

[0092] Figure 5 Schematic diagram of a true triaxial test of a typical excavation stress path and stress difference level according to an embodiment of the present invention;

[0093] Figure 6 Schematic diagram of the evolution of granite strength parameters at different fracture stages along with internal variables according to an embodiment of the present invention;

[0094] Figure 7 Schematic diagram of the typical relationship between the weakening rate of deformation modulus and plastic internal variables of different granites according to an embodiment of the present invention;

[0095] Figure 8 Schematic diagram of simulation and test results of granite at a hydropower station under different true triaxial loading and unloading stress paths according to an embodiment of the present invention;

[0096] Figure 9 Schematic diagram of simulation and test results of granite at a hydropower station under true triaxial loading and unloading stress paths with different stress differences according to an embodiment of the present invention. DETAILED DESCRIPTION

[0097] In order to make the objectives, technical solutions and advantages of this application more clear, the application is further described in detail below with reference to the accompanying drawings and examples.

[0098] The embodiment of the present invention discloses a method for constructing a model to characterize the true triaxial stress path of deep hard rock excavation. This embodiment provides a method for constructing and verifying the accuracy and rationality of the true triaxial stress path model to characterize deep hard rock excavation using granite as a rock sample. The process is as follows: Figure 1 As shown, the following steps are included:

[0099] S1. Construct an excavation stress path coefficient to characterize the differences in true triaxial excavation stress paths and quantify different true triaxial excavation stress paths.

[0100] S11. In the octahedral stress space, using β R Characterizes the excavation stress adjustment coefficient.

[0101] like Figure 2 As shown in the figure, a true triaxial test was conducted on granite with typical excavation stress paths and different stress difference levels, and the corresponding excavation stress adjustment coefficient β was calculated. R , the calculation formula is as follows:

[0102]

[0103] Among them, β R is the excavation stress adjustment coefficient, σ1, σ2 and σ3 are the principal stresses in the effective stress space, is the stress state before stress adjustment in the σ1 direction, is the stress state before the stress adjustment in the σ2 direction, is the stress state before the stress adjustment in the σ3 direction, is the stress state after stress adjustment in the σ1 direction, is the stress state after the stress in the σ2 direction is adjusted, is the stress state after stress adjustment in the σ3 direction, q0 is the equivalent shear stress before stress adjustment, q1 is the equivalent shear stress after stress adjustment, p0 is the average stress state before stress adjustment, and p1 is the average stress state after adjustment.

[0104] S12. Introduce a dynamic correction term related to stress adjustment rate and strain energy into the excavation stress adjustment coefficient to characterize the influence of excavation rate on stress path and obtain the excavation stress path coefficient:

[0105]

[0106] in, is the excavation stress path coefficient, is the unloading rate (MPa / s), γ and θ are dynamic correction factors calibrated by true triaxial tests at different excavation rates, and U is the strain energy.

[0107] The true triaxial unloading tests at different unloading rates were carried out on granite to obtain the unloading rate and strain energy of granite under true triaxial loading at different unloading rates. The logarithmic function was used for fitting, such as Figure 3 As shown in the figure, the dynamic correction factor of the unloading rate γ = 0.053, θ = 1.0677 is obtained by fitting, and the stress path coefficient of granite excavation is obtained as follows:

[0108]

[0109] S13. According to the true triaxial excavation stress path model, determine the stress state and rate before and after stress adjustment, substitute them into equations (1) to (6), and obtain the excavation stress path coefficient of the corresponding excavation stress path:

[0110] S2. Based on the generalized Hooke's law, the excavation stress path coefficient is introduced, the anisotropic elastic stiffness matrix is modified, and the incremental expression of the stress-strain relationship is constructed.

[0111]

[0112] in, is the incremental stress matrix, is the incremental strain matrix, is the incremental plastic strain tensor matrix, κ is the internal variable, E a is the anisotropic elastic stiffness matrix tensor based on deformation modulus, Poisson’s ratio and intrinsic variables, is the initial stiffness matrix.

[0113] S3. Perform true triaxial compression tests on granite at different stress levels to obtain the strength values of granite under true triaxial compression at different stress levels, and use the 3DHRFC strength criterion for fitting.

[0114] S31. Based on the 3DHRFC strength criterion, the relationship between the three stresses is established as follows:

[0115]

[0116] Where c is the cohesion, is the internal friction angle, s and t are material parameters, which are obtained by fitting the test data.

[0117] S32. The three-dimensional yield function based on the true triaxial stress relationship is:

[0118]

[0119] S33. Perform true triaxial compression tests on rock samples to obtain the strength of the rock under true triaxial stress.

[0120] S34. Based on the strength of rock under true triaxial stress obtained in S33, substitute it into equations (9) and (10) to obtain material parameters s and t, and determine the yield function F.

[0121] like Figure 4 As shown, the material parameters s = 0.95, t = 0.9 are obtained by fitting in this embodiment, and the yield function equation F is obtained:

[0122]

[0123] S4. Construct a brittleness index to characterize the excavation stress path and initial stress difference.

[0124] S41, such as Figure 5 As shown in Figure 2, typical true triaxial tests with different excavation stress paths and stress difference were carried out to obtain the rock stress-strain curves under different excavation stress paths.

[0125] S42. Based on the rock stress-strain curves under different excavation stress paths, the inverse of the plastic volume strain generated by rock fracture is used to represent the brittleness index, which is expressed as:

[0126]

[0127] Among them, B I is the brittleness index, is the plastic volume strain at peak strength.

[0128] The granite brittleness results under different true triaxial excavation stress paths and initial stress differences are shown in Table 1:

[0129] Table 1 Results of granite brittleness under different true triaxial excavation stress paths and initial stress differences

[0130]

[0131]

[0132] S43. Based on the brittleness index, describe the relationship between the excavation stress path coefficient, stress difference and brittleness index:

[0133]

[0134] Among them, B IU is the brittleness index when the maximum principal stress and the intermediate principal stress are equal, and a, b, h, and d are material parameters. The material parameters of granite fitted in this embodiment are: B IU =10.03, a=4.4729, b=0.0693, h=0.001, d=0.017.

[0135] S5. Construct internal variables to characterize the excavation stress path and initial stress difference.

[0136] The internal variables are expanded into a composite function of macroscopic plastic strain and microscopic crack strain, and the brittleness index and equivalent plastic volume strain are used to express the internal variables of hard rock degradation:

[0137] κ=κ p +κ d ; (16)

[0138]

[0139] Among them, κ p is the macroscopic plastic strain, κ d is the microscopic crack strain, is the critical plastic strain in the jth direction (j=1, 2, 3), is the critical stress for crack nucleation in the jth direction, which is equal to the crack propagation stress. In this example, 80% of the peak strength is used. λ is the crack healing rate coefficient, characterized by the ratio of uniaxial compressive strength to tensile strength. The granite selected in this example has a uniaxial compressive strength of 170 MPa and a tensile strength of 10 MPa, so λ = 17.

[0140] S6. Construct the strength parameter evolution equation that characterizes the excavation stress path and initial stress difference.

[0141] S61, such as Figure 6 As shown, the evolution model of cohesion and internal friction angle is established. The rock fracture development is divided into four stages, including elastic deformation stage, crack development stage, post-peak brittle fracture stage and residual stage;

[0142] S62. Analyze the evolution characteristics of rock strength parameters in four stages, including:

[0143] During the elastic deformation stage, no cracks are generated inside the specimen, and there is no need to consider the changes in strength parameters;

[0144] In the crack development stage, the rock begins to be damaged, the cohesion begins to weaken and decrease, and the internal friction angle begins to strengthen and increase due to the voids generated by the development of microcracks. At this time, the slope of cohesion weakening is w c , the slope of the internal friction angle enhancement is s c .

[0145]

[0146] In this embodiment, based on the experimental data of granite, the crack development stage s is obtained. c The expression of the excavation stress path coefficient is:

[0147]

[0148] in, is the plastic strain at the time of cohesion loss, is the plastic strain when the friction strength increases.

[0149] In the post-peak brittle fracture stage, macro cracks open or penetrate, causing a sudden loss of cohesion. Since this process is very short, the friction strength hardly changes. Therefore, it is believed that the internal friction angle remains unchanged in the brittle stage, and the cohesion weakening slope is w b , the slope of the internal friction angle enhancement is s b =0.

[0150]

[0151] in, is the equivalent plastic strain at peak strength during the uniaxial compression test, is the equivalent plastic strain at the residual starting point.

[0152] In the residual stage, the rock forms a complete macroscopic failure surface, the rock will shear and slip along the failure surface, and the values of cohesion and internal friction angle will remain constant.

[0153] S63. Based on the evolution characteristics of rock strength parameters in four stages, the strength parameter evolution equation of excavation stress path and initial stress difference is obtained as follows:

[0154] c=c0-∑w i Δκ i (c0-c r ); (twenty two)

[0155]

[0156] Δκ i =κ i -κ i-1 - <k i -k> (24)

[0157] Among them, w i is the weakening ratio of cohesion in a single sub-stage, s i is the enhancement ratio of the internal friction angle in a single sub-stage, k i is the final value of the internal variable in the i-th sub-stage, <x>is the positive operator, defined as max(0,x), c0 is the initial cohesion, c r is the residual cohesion, is the initial internal friction angle, is the residual internal friction angle.

[0158] S7. Construct the deformation parameter evolution equation that characterizes the excavation stress path and initial stress difference.

[0159] S71. Rock deformation anisotropy is defined by the following two equations:

[0160] d j =R jr +(1-R jr )e -30κ ; (25)

[0161]

[0162] Among them, E j is σ j Deformation modulus in the direction, j = 1, 2, 3, E0 is the initial deformation modulus, R jr Characterizes the weakening rate of the deformation modulus of the specimen in the three principal stress directions in the residual stage, d j is the weakening rate of the deformation modulus of the specimen in the three principal stress directions, denoted by σ j The deformation modulus in the direction is related to the degree of weakening of the internal variables and the initial stress difference.

[0163] S72. According to the test results, obtain the weakening rate R of the deformation modulus of the three principal stress directions of the corresponding rock sample in the residual stage. jr The typical relationship between the weakening rate of rock deformation modulus and plastic internal variables is fitted based on formula (25).

[0164] S73. Based on S72, obtain d j and the initial deformation modulus E0, we get E j ;

[0165] S74. Obtain stable values of the weakening rate R1 of the deformation modulus in the direction of maximum principal stress and the weakening rate R3 of the deformation modulus in the direction of minimum principal stress of the corresponding rock based on the test results;

[0166] S75, establish the weakening rate R2 of the deformation modulus in the direction of the intermediate principal stress and the initial stress difference The relationship is:

[0167]

[0168] Among them, R S is the weakening rate of the deformation modulus in the intermediate principal stress direction with the initial stress difference The increasing slope of the change.

[0169] like Figure 7 As shown in the figure, the typical relationship between the weakening rate of deformation modulus and plastic internal variables of different granites is obtained. The stable values of the weakening rate R1 of the deformation modulus in the direction of maximum principal stress and the weakening rate R3 of the deformation modulus in the direction of minimum principal stress of granite are 0.53 and 0.03 respectively. S = 0.003. Therefore, the weakening rate R2 of the deformation modulus in the direction of the intermediate principal stress is related to the initial stress difference The relationship is:

[0170]

[0171] S8. Embed the calculation formula obtained in S1-S7 into CASRock cellular automation numerical calculation software for calculation.

[0172] S81. Calculate the current stress based on the strain increment formula in S2. Then, calculate the trial stress based on the elastic stiffness matrix. Use the three-dimensional failure criterion to determine if the failure condition is met. Then, use the stress callback to calculate the true stress. Use the current excavation stress path coefficient, brittleness index, and internal variables to update the deformation and strength parameters, and calculate the incremental unbalanced force caused by the failure. The internal variables are calculated based on equations (1) to (18) based on the current equivalent plastic body strain, initial stress difference, and excavation stress path coefficient. The strength parameters are updated based on equations (19) to (24) and the current internal variables to calculate the evolution of cohesion and internal friction angle. The deformation parameters are updated based on equations (25) to (27) to obtain the evolution of the deformation parameters.

[0173] S82: When the incremental unbalanced force calculation is completed, the next convergence step calculation is performed until the convergence requirement is met and the loop is exited. In this embodiment, the convergence condition is that the absolute value of the yield function is less than 1‰, and the calculation termination condition is that the yield function is close to 0.

[0174] S9. Conduct true triaxial rock tests with different excavation stress paths and stress differences to verify the accuracy of the stress-strain curve.

[0175] S91. Conduct true triaxial tests on rock specimens with different excavation stress paths and stress differences, and obtain stress-strain curves.

[0176] S92. Obtain material parameters related to S1-S7 based on the test data obtained in S911.

[0177] S93. The relevant parameters obtained in S92 are combined with the cellular automaton numerical calculation software embedded in S8, which is a three-dimensional mechanical model considering the excavation stress path and the initial stress difference, to perform simulation calculations.

[0178] S94. Based on S94, true triaxial rock stress-strain curves of different excavation stress paths and stress differences are simulated and compared with the rock stress-strain curves generated by the test data.

[0179] Figure 8 This is a schematic diagram of simulation and test results of granite at a hydropower station under different true triaxial loading and unloading stress paths in this embodiment. Figure 9 The schematic diagram of the simulation and test results of granite in a hydropower station under different stress difference true triaxial loading and unloading stress paths in the embodiment. Figure 8 and Figure 9 Comparing the true triaxial rock test curves of different excavation stress paths and stress differences with the predicted curves of the model of the present invention, it can be seen that the method proposed in the embodiment of the present application can characterize the deformation and strength characteristics of granite with different excavation stress paths and stress differences.

[0180] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.< / x> < / x>

Claims

1. A method for constructing a model to characterize the true triaxial stress path of deep hard rock excavation, characterized in that: The following steps are involved: S1. Construct an excavation stress path coefficient to characterize the differences in true triaxial excavation stress paths and quantify different true triaxial excavation stress paths. S2. Based on the generalized Hooke's law, the excavation stress path coefficient is introduced, the anisotropic elastic stiffness matrix is modified, and the incremental expression of the stress-strain relationship is constructed; S3, using the 3DHRFC strength criterion to establish a three-dimensional yield function; S4. Construct a brittleness index to characterize the excavation stress path and initial stress difference; S5. Construct internal variables to characterize the excavation stress path and initial stress difference; S6. Construct the strength parameter evolution equation to characterize the excavation stress path and initial stress difference; S7. Construct deformation parameter evolution equations that characterize excavation stress path and initial stress difference; S8, embedding the calculation formula obtained in S1-S7 into cellular automaton numerical calculation software for calculation; S9. Conduct true triaxial rock tests with different excavation stress paths and stress differences to verify the accuracy of the stress-strain curve.

2. The method for constructing a model for characterizing true triaxial stress paths in deep hard rock excavation according to claim 1, characterized in that: Said S1 comprises the following steps: S11. In the octahedral stress space, using β R Characterize the excavation stress adjustment coefficient, the calculation formula is as follows: Among them, β R is the excavation stress adjustment coefficient, σ1, σ2 and σ3 are the principal stresses in the effective stress space, is the stress state before stress adjustment in the σ1 direction, is the stress state before the stress adjustment in the σ2 direction, is the stress state before the stress adjustment in the σ3 direction, is the stress state after stress adjustment in the σ1 direction, is the stress state after the stress in the σ2 direction is adjusted, is the stress state after stress adjustment in the σ3 direction, q0 is the equivalent shear stress before stress adjustment, q1 is the equivalent shear stress after stress adjustment, p0 is the average stress state before stress adjustment, and p1 is the average stress state after adjustment; S12. Introduce a dynamic correction term related to stress adjustment rate and strain energy into the excavation stress adjustment coefficient to characterize the influence of excavation rate on stress path and obtain the excavation stress path coefficient: in, is the excavation stress path coefficient, is the unloading rate, γ and θ are dynamic correction factors, and I is the strain energy; S13. According to the true triaxial excavation stress path model, determine the stress state and rate before and after stress adjustment, substitute them into equations (1) to (6), and obtain the excavation stress path coefficient of the corresponding excavation stress path:

3. The method for constructing a model for characterizing true triaxial stress paths in deep hard rock excavation according to claim 2, characterized in that: The incremental expression of the stress-strain relationship in S2 is: in, is the incremental stress matrix, is the incremental strain matrix, is the incremental plastic strain tensor matrix, κ is the internal variable, E a is the anisotropic elastic stiffness matrix tensor based on deformation modulus, Poisson’s ratio and intrinsic variables, is the initial stiffness matrix.

4. The method for constructing a model for characterizing true triaxial stress paths in deep hard rock excavation according to claim 3, characterized in that: The S3 includes the following steps: S31. Based on the 3DHRFC strength criterion, the relationship between the three stresses is established as follows: Where c is the cohesion, is the internal friction angle, s and t are material parameters; S32. The three-dimensional yield function based on the true triaxial stress relationship is: S33. Perform a true triaxial compression test on the rock sample to obtain the strength of the rock under true triaxial stress; S34. Based on the strength of rock under true triaxial stress obtained in S33, substitute it into equations (9) and (10) to obtain material parameters s and t, and determine the yield function F.

5. The method for constructing a model for characterizing true triaxial stress paths in deep hard rock excavation according to claim 4, characterized in that: The S4 comprises the following steps: S41. Conduct true triaxial tests with different excavation stress paths and stress difference to obtain rock stress-strain curves under different excavation stress paths; S42. Based on the rock stress-strain curves under different excavation stress paths, the inverse of the plastic volume strain generated by rock fracture is used to represent the brittleness index, which is expressed as: Among them, B I is the brittleness index, is the plastic volume strain at peak strength; S43. Based on the brittleness index, describe the relationship between the excavation stress path coefficient, stress difference and brittleness index: Among them, B IU is the brittleness index when the maximum principal stress and the intermediate principal stress are equal, and a, b, h, and d are material parameters.

6. The method for constructing a model for characterizing true triaxial stress paths in deep hard rock excavation according to claim 5, characterized in that: The S5 comprises the following steps: The internal variables are expanded into a composite function of macroscopic plastic strain and microscopic crack strain, and the brittleness index and equivalent plastic volume strain are used to express the internal variables of hard rock degradation: k=k p +k d ;(16) Among them, κ p is the macroscopic plastic strain, κ d is the microscopic crack strain, is the critical plastic strain in the jth direction (j=1, 2, 3), is the critical stress for crack nucleation in the jth direction, which is equal to the crack propagation stress, and λ is the crack healing rate coefficient, which is characterized by the ratio of uniaxial compressive strength to tensile strength.

7. The method for constructing a model for characterizing true triaxial stress paths in deep hard rock excavation according to claim 6, characterized in that: The S6 comprises the following steps: S61. Rock fracture development is divided into four stages, including elastic deformation stage, crack development stage, post-peak brittle fracture stage and residual stage; S62. Analyze the evolution characteristics of rock strength parameters in four stages, including: During the elastic deformation stage, no cracks are generated inside the specimen, and there is no need to consider the changes in strength parameters; In the crack development stage, the rock begins to be damaged, the cohesion begins to weaken and decrease, and the internal friction angle begins to strengthen and increase due to the voids generated by the development of microcracks. At this time, the slope of cohesion weakening is w c , the slope of the internal friction angle enhancement is s c ; In the post-peak brittle fracture stage, macro cracks open or penetrate, causing a sudden loss of cohesion. Since this process is very short, the friction strength hardly changes. Therefore, it is believed that the internal friction angle remains unchanged in the brittle stage, and the cohesion weakening slope is w b , the slope of the internal friction angle enhancement is s b =0; In the residual stage, the rock forms a complete macroscopic failure surface, the rock will shear and slip along the failure surface, and the values of cohesion and internal friction angle will remain constant; S63. Based on the evolution characteristics of rock strength parameters in four stages, the strength parameter evolution equation of excavation stress path and initial stress difference is obtained as follows: c=c0-Σw i Dk i (c0-c r ); (22) Dk i =k i -k i-1 -<k i -κ>; (24) Among them, w i is the weakening ratio of cohesion in a single sub-stage, s i is the enhancement ratio of the internal friction angle in a single sub-stage, κ i is the final value of the internal variable in the i-th sub-stage, <x>is the positive operator, defined as max(0,x), c0 is the initial cohesion, c r is the residual cohesion, is the initial internal friction angle, is the residual internal friction angle.< / x> 8. The method for constructing a model for characterizing true triaxial stress paths in deep hard rock excavation according to claim 7, characterized in that: The S7 comprises the following steps: S71. Rock deformation anisotropy is defined by the following two equations: d j =R jr +(1-R jr )e -30κ ; (25) Among them, E j is σ j Deformation modulus in the direction, j = 1, 2, 3, E0 is the initial deformation modulus, R jr Characterizes the weakening rate of the deformation modulus of the specimen in the three principal stress directions in the residual stage, d j is the weakening rate of the deformation modulus of the specimen in the three principal stress directions, denoted by σ j The deformation modulus in the direction is related to the degree of weakening of the internal variables and the initial stress difference; S72. Obtain the weakening rate R of the deformation modulus of the three principal stress directions of the corresponding rock sample in the residual stage jr , based on formula (25), the typical relationship between the weakening rate of rock deformation modulus and plastic internal variables is fitted; S73. Based on S72, obtain d j and the initial deformation modulus E0, we get E j ; S74, obtaining stable values of the weakening rate R1 of the deformation modulus in the direction of the maximum principal stress of the corresponding rock and the weakening rate R3 of the deformation modulus in the direction of the minimum principal stress; S75, establish the weakening rate R2 of the deformation modulus in the direction of the intermediate principal stress and the initial stress difference The relationship is: Among them, R S is the increasing slope of the weakening rate of the deformation modulus in the intermediate principal stress direction as the initial stress difference changes.

9. The method for constructing a model for characterizing true triaxial stress paths in deep hard rock excavation according to claim 8, characterized in that: The S8 comprises the following steps: S81. Calculate the current stress according to the strain increment formula in S2, then calculate the trial stress based on the elastic stiffness matrix. Use the three-dimensional failure criterion to determine if the failure condition is met. If so, calculate the true stress by resetting the stress. Use the current excavation stress path coefficient, brittleness index, and internal variables to update the deformation and strength parameters, and calculate the incremental unbalanced force caused by the failure. S82. When the incremental unbalanced force calculation is completed, the update is completed and the calculation of the next convergence step is performed until the convergence requirements are met and the loop is exited.

10. The method for constructing a model for characterizing true triaxial stress paths in deep hard rock excavation according to claim 9, characterized in that: The S9 comprises the following steps: S91. Conduct true triaxial tests on rock specimens with different excavation stress paths and stress differences, and obtain stress-strain curves; S92. Obtain material parameters related to S1-S7 based on the test data obtained in S911; S93, performing simulation calculations by combining the relevant parameters obtained in S92 with the cellular automaton numerical calculation software embedded in S8, which is a three-dimensional mechanical model considering the excavation stress path and the initial stress difference; S94. Based on S94, true triaxial rock stress-strain curves of different excavation stress paths and stress differences are simulated and compared with the rock stress-strain curves generated by the test data.

Images