Rock mass structural surface shear degradation constitutive model under true three-dimensional stress and numerical method

Abstract

The invention discloses a rock mass structural plane shear degradation constitutive model under true three-dimensional stress and a numeralization method, and the method comprises the following steps: carrying out a rock mass structural plane pre-peak and post-peak cyclic loading and unloading true triaxial shear test, and obtaining the strength, deformation and damage characteristics of the structural plane; based on a test result, establishing a three-dimensional structural surface shear strength criterion considering the lateral stress effect, and proposing a calculation method of shear modulus, cohesive force, friction angle and dilatancy angle in the shear fracture process of the structural surface; constructing a three-dimensional shear degradation constitutive model considering the lateral stress and shear parameter degradation effect and a continuous and discontinuous numeralization method of the three-dimensional shear degradation constitutive model; the three-dimensional shear degradation constitutive model is verified through numerical simulation of a true triaxial shear indoor test; and carrying out excavation response analysis on the complex stratum tunnel by adopting the three-dimensional shear degradation constitutive model. The invention provides a rock mass structural plane shear degradation constitutive model and a numerical method under true three-dimensional stress, and a theoretical basis is provided for rock mass structural plane underground engineering catastrophe prediction.

Description

Technical Field

[0001] The invention relates to the field of rock mass mechanical properties and engineering research, and in particular to a shear degradation constitutive model of rock mass structural surface under true three-dimensional stress and a numerical method. Background Art

[0002] As the depth of underground rock mass engineering continues to increase, the ground stress is usually in a complex true three-dimensional stress state. In deep buried engineering, the shear failure of the rock mass structure surface is not only subject to shear stress and normal stress, but also affected by large lateral stress. The shear failure of the rock mass structure surface induced engineering disasters has become a common type of disaster in deep rock mass engineering.

[0003] Shear strength criteria and mechanical models are used to describe the criterion and evolution of rock mass failure under shear load. Most of the shear strength criteria and mechanical models previously studied were established based on direct shear test results and Mohr–Coulomb strength criteria. They did not consider the influence of lateral stress on the mechanical properties of the structural surface, nor did they consider the degradation effect of the structural surface during shear failure under true three-dimensional stress state. It is difficult to reasonably reflect the shear failure conditions of the rock structural surface under true three-dimensional stress state. At present, the method for determining shear parameters and the degradation evolution law during the shear fracture of the rock structural surface under true three-dimensional stress are still unclear, and there is a lack of constitutive models and numerical methods that can effectively reflect the degradation process of the shear mechanical properties of the rock structural surface under true three-dimensional stress.

[0004] In view of the above shortcomings, the present invention proposes a constitutive model and numerical method for shear degradation of rock mass structural surface under true three-dimensional stress. According to the results of true triaxial shear test, a shear strength criterion applicable to true three-dimensional stress is proposed, and based on this criterion, the shear modulus G, cohesion c and shear strength of rock mass structural surface in the shear fracture process are established. jp , internal friction angle and dilatancy angle ψ jp The calculation method of mechanical parameters is also used. A three-dimensional shear degradation constitutive model considering the degradation effects of lateral stress and shear parameters is further constructed, and a corresponding numerical calculation program is developed based on three-dimensional block discrete element software to provide a theoretical basis for the prediction of underground engineering disasters on rock mass structural surfaces. Summary of the invention

[0005] The purpose of the present invention is to provide a constitutive model and numerical method for shear degradation of rock structure surface under true three-dimensional stress, analyze the shear mechanical behavior of rock structure surface under true three-dimensional stress, and provide a theoretical basis for the prediction of engineering disasters of deep rock structure surface.

[0006] In order to achieve the above technical objectives, the present invention provides a shear degradation constitutive model of rock mass structural surface under true three-dimensional stress and a numerical method, the steps of which include:

[0007] S1. Carry out true triaxial shear tests on the rock mass structural surface before and after the peak cyclic loading and unloading to obtain the strength, deformation and failure characteristics of the rock mass structural surface;

[0008] S2. Based on the true triaxial shear test results, a calculation method for the shear modulus G during the shear fracture process of the structural surface is established;

[0009] S3. Based on the Mohr–Coulomb strength criterion, a three-dimensional structural surface shear strength criterion considering the lateral stress effect is established;

[0010] S4. Establish the cohesion c of the rock mass structural surface during shear fracture jp and friction angle Calculation method of

[0011] S5. Establish the dilatancy angle ψ during the rupture of the rock mass structural surface jp Calculation method of

[0012] S6. Construct a three-dimensional shear degradation constitutive model considering the degradation effects of lateral stress and shear parameters;

[0013] S7. Discrete element continuous and discontinuous numerical methods for establishing shear degradation constitutive model of rock mass structural surface under true three-dimensional stress;

[0014] S8. Through numerical simulation of true triaxial shear laboratory test, the constitutive model of shear degradation of rock mass structural surface under true three-dimensional stress and its numerical method are verified;

[0015] S9. The shear degradation constitutive model of rock mass structural surface under true three-dimensional stress and its numerical method are used to analyze the excavation response of tunnels in complex strata.

[0016] In the step S1, a true triaxial shear indoor test is carried out on the rock mass structural surface with different normal stresses and lateral stresses before and after the peak cyclic loading and unloading to obtain the strength, deformation and failure characteristics of the rock mass structural surface;

[0017] In step S2, based on the true triaxial shear test results in step S1, a calculation method for the shear modulus G in the true triaxial cyclic loading and unloading shear test is determined, and the shear stress increment dτ in each cyclic loading and unloading is calculated by comparing the elastic shear strain increment dτ with the elastic shear strain increment dτ. The ratio is calculated:

[0018]

[0019] In step S3, the shear strength criterion of the three-dimensional structural surface considering the lateral stress effect is established as follows:

[0020] Based on the true triaxial shear test results, the Mohr–Coulomb strength criterion formula is modified to consider the influence of lateral stress on the shear strength law of rock mass, and a three-dimensional shear strength criterion suitable for true three-dimensional stress is proposed as follows:

[0021]

[0022] Where τ is the shear stress, σ n is the normal stress, σ p is the lateral stress, c jp is the cohesion of the structural surface, is the internal friction angle of the structural surface, P is σ p The effect of ρ is the lateral stress corresponding to the maximum shear stress, K is the lateral stress with the same shear strength as when the lateral stress is 0;

[0023] In step S4, the cohesion c of the rock mass structural surface during shear fracture is established. jp and friction angle The calculation method is as follows:

[0024] τ and σ in the three-dimensional shear strength criterion formula (2) n The slope of the curve is In true triaxial cyclic loading shear tests, the maximum and minimum damage shear stresses τ of all rock mass structural surfaces are determined. d With different normal stress σ n The slope of the curve between Calculate the initial structural surface friction angle size; according to and τ d The relationship between jp Calculation method:

[0025]

[0026] Using formula (3) to obtain c jp The friction angle of the structural surface is calculated by the peak value τ in each cycle of the shear test

[0027]

[0028] In step S5, the dilatancy angle ψ during the shear fracture of the structural surface is established. jp The calculation method is as follows:

[0029] Determination of the structural plane expansion angle ψ during the shear failure of rock mass based on the three-dimensional shear strength criterion and the non-associated plastic flow law jp Calculation method: The plastic potential function g is obtained from formula (2):

[0030]

[0031] Calculation of shear plastic strain increment based on plastic flow law and the normal plastic strain increment

[0032]

[0033] Where λ is the plasticity factor, and the expansion angle ψ is obtained from formula (6): jp The calculation formula is:

[0034]

[0035] In step S6, a three-dimensional shear degradation constitutive model considering the lateral stress and shear parameter degradation effects is constructed as follows:

[0036] According to Hooke's law, the shear stress increment Δτ and the normal stress increment Δσ n The expression is as follows:

[0037]

[0038] where k s , k n are shear stiffness and normal stiffness, Δu s and Δu n are the shear deformation and normal deformation increments, respectively;

[0039] According to the three-dimensional shear strength criterion formula (2), the three-dimensional slip yield function F of the mechanical model is defined as s as follows:

[0040]

[0041] The normal stress σ of the rock mass structural surface n and tensile strength σ t Define the three-dimensional tensile yield function F of the rock mass structural surface t as follows:

[0042] F t =σ t -σ n (10)

[0043] In step S7, a continuous and discontinuous numerical method for constructing a shear degradation constitutive model of a rock mass structural surface under true three-dimensional stress is specifically performed as follows:

[0044] Update the shear stress τ and normal stress σ on the structural surface using formula (8): n as follows:

[0045]

[0046] where τ (t+Δt) and is the shear stress and normal stress at time t+Δt, τ (t) and are the shear stress and normal stress at time t;

[0047] In three-dimensional stress space, assuming that the shear stress vector is τ = (τ x ,τ y ,τ z ) and the normal stress vector is σ n =(n x ,n y ,n z ), the lateral stress vector is σ p =(p x ,p y ,p z ). Due to σ p Perpendicular to τ and σ n , then the stress vector σ p It is expressed as:

[0048] σ p =(p x ,p y ,p z )=τ×σ n =(τ y n z -τ z n y ,τ z n x -τ x n z ,τ x n y -τ y n x ) (12)

[0049] Where × represents the vector cross product operation, and the principal stress vector σ of the element on the structural surface i (i=1,2,3) and vector σ p The angle θ i The cosine value is:

[0050]

[0051] where · represents the vector dot product operation, ||·|| is the vector modulus, and the principal stress vector σ of the element i (i=1,2,3) and vector σ p The projection size in the direction is:

[0052]

[0053] The lateral stress σ of the element on the structural surface p Size:

[0054] σ p =σ p1 +σ p2 +σ p3 (15)

[0055] Substituting the shear stress, normal stress formula (11) and lateral stress formula (15) into the shear yield function formula (9) yields:

[0056]

[0057] When the three-dimensional shear yield function F in formula (9) s = 0, the structural surface will undergo plastic yield or slip. During the yield or slip process of the rock mass, the shear displacement will cause the structural surface to produce normal expansion deformation and increase the normal stress. The normal stress is updated according to the shear dilatancy angle calculation formula (7) and the shear stress formula (11):

[0058]

[0059] Among them: = is the assignment symbol, ψ jp It represents the dilatancy angle of the structural surface;

[0060] When the tensile yield function F in formula (10) t = 0, the structural surface will undergo tensile yield; at this time, the normal stress remains unchanged, that is, σ n =σ t , shear stress is 0;

[0061] In step S8, by performing numerical simulation of true triaxial shear indoor test, the shear degradation constitutive model of rock mass structural surface under true three-dimensional stress and its numerical method are verified as follows:

[0062] Establish a numerical calculation model with the same size as the test specimen and divide the mesh units;

[0063] Boundary constraints are imposed on the numerical model, normal stress and lateral stress are applied to the model using stress control, and shear load is applied using displacement control;

[0064] According to the evolution of shear mechanics parameters obtained from the test results, they are assigned to the corresponding material parameters in the numerical model in a tabular form;

[0065] The fish function is used to monitor and record the changes of stress and strain in the numerical calculation process, and the simulation results are compared and analyzed with the test results;

[0066] In step S9, the shear degradation constitutive model of rock mass structural surface under true three-dimensional stress and its numerical method are applied in complex stratum tunnel engineering as follows:

[0067] Two three-dimensional tunnel numerical models, one with structured surface and one without structured surface, were established, and the tunnel grid cells were locally encrypted.

[0068] The same initial geostress was applied to the three-dimensional tunnel models with and without structural surfaces, and the three-dimensional shear degradation constitutive model was used to simulate the tunnel excavation. The deformation and failure characteristics of the surrounding rocks of the models with and without structural surfaces under the same initial geostress were compared and analyzed.

[0069] The initial geostress in different directions was applied to the three-dimensional structural surface tunnel model, and the three-dimensional shear degradation constitutive model was used to simulate the tunnel excavation. The influence of geostress change on the continuous and discontinuous deformation and failure of the surrounding rock containing the structural surface was compared and analyzed.

[0070] The beneficial effects of the present invention are:

[0071] 1. The three-dimensional shear strength criterion proposed in the present invention taking into account the lateral stress effect can better reflect the strength characteristics of the rock structure surface under true three-dimensional stress.

[0072] 2. The present invention proposes shear modulus G, cohesion c jp , internal friction angle and dilatancy angle ψ jp The calculation method can be used to solve the mechanical parameters of the shear fracture evolution process of rock mass structural surface under true three-dimensional stress.

[0073] 3. The present invention constructs a three-dimensional shear degradation constitutive model of rock structure surface taking into account the degradation effects of lateral stress and shear parameters and a discrete element numerical method, which can be used to simulate and analyze the continuous and discontinuous deformation and failure characteristics of deep rock structure surfaces.

[0074] 4. The model established by the present invention can be applied to the prediction and analysis of engineering disasters of deep rock mass structural surfaces after secondary development based on three-dimensional discrete element software. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 It is a flow chart of constructing the shear degradation mechanical model of rock mass structural surface under true three-dimensional stress of the present invention;

[0076] Figure 2 For different normal stresses σ n and the lateral stress σ p Total stress-strain curve of true triaxial cyclic loading and unloading shear test of lower limestone;

[0077] Figure 3The calculation diagram of the shear modulus G during the shear fracture process under true triaxial cyclic loading and unloading and its evolution during the shear fracture process. Figure 3 a is a schematic diagram for calculating the shear modulus G, Figure 3 b is the evolution of G during shear fracture;

[0078] Figure 4 For different σ n and σ p The cohesion c of the structural surface during shear fracture under true triaxial cyclic loading and unloading jp , friction angle and the expansion angle ψ jp The evolution of Figure 4 a is c jp The evolution of Figure 4 b is The evolution of Figure 4 c is ψ jp evolution;

[0079] Figure 5 is the specimen numerical model and its boundary conditions;

[0080] Figure 6 For different σ n and σ p The full stress-strain curve of the numerical simulation under true triaxial shear of the lower limestone is compared with the true triaxial shear test results;

[0081] Figure 7 is the deformation displacement cloud map of the surrounding rock after tunnel excavation, where Figure 7 a is the simulation result of the unstructured surface model, Figure 7 b is the simulation result of the structural surface model. Figure 7 c is the simulation result of the structural surface model's ground stress rotated 30°. Figure 7 d is the simulation result of the structural surface model's ground stress rotated by 75°;

[0082] Figure 8 It is the plastic zone of surrounding rock after tunnel excavation, Figure 8 a is the simulation result of the unstructured surface model, Figure 8 b is the simulation result of the structural surface model. Figure 8 c is the simulation result of the structural surface model's ground stress rotated 30°. Figure 8 d is the simulation result of the structural surface model's ground stress rotated 75°. DETAILED DESCRIPTION

[0083] The specific implementation of the present invention is described below in conjunction with the accompanying drawings, but the present invention is not limited to the scope of the specific implementation. It should be noted that all creations based on or dependent on the present invention are within the protection scope of the present invention.

[0084] This embodiment provides the accuracy and rationality of constructing and verifying the shear degradation mechanical model of rock mass structural surface under true three-dimensional stress using bedding limestone as a rock sample and engineering application.

[0085] refer to Figure 1 , Figure 1 A flow chart of building a mechanical model of shear degradation of rock mass structural surface under true three-dimensional stress is shown, and the method includes steps S1 to S9;

[0086] In step S1, a stratified limestone sample with a size of 100 mm × 100 mm × 100 mm is subjected to different normal stresses σ n and the lateral stress σ p True triaxial cyclic loading and unloading shear test under Figure 2 The full stress-strain curves of the true triaxial cyclic loading and unloading shear test of bedding limestone are shown in Table 1. n and σ p Strength results of true triaxial shear tests under pre-peak and post-peak cyclic loading and unloading; Table 1 True triaxial shear test results before and after peak cyclic loading and unloading

[0087] In step S2, based on the stress-strain results of the true triaxial shear test obtained in step S1, the shear modulus G is calculated by the shear stress increment dτ and the elastic shear strain increment in each cyclic loading and unloading process. The ratio is determined by:

[0088]

[0089] Figure 3 a is a schematic diagram for calculating the shear modulus G in a true triaxial cyclic loading and unloading shear test. Figure 3 b is the different normal stress σ n and the lateral stress σ p Evolution of shear modulus G during shear rupture under true triaxial cyclic loading and unloading;

[0090] In step S3, the shear strength criterion of the three-dimensional structural surface considering the lateral stress effect is established as follows:

[0091]

[0092] Where τ is the shear stress, σ n is the normal stress, σ p is the lateral stress, c jp is the cohesion of the structural surface, is the internal friction angle of the structural surface, P is σ p The effect of ρis the lateral stress corresponding to the maximum shear stress, and K is the lateral stress with the same shear strength as when the lateral stress is 0.

[0093] The nonlinear fitting method is used to fit the test data to obtain the relevant parameters: σ ρ =6.97MPa, P=4.226MPa, K=4.89MPa;

[0094] In step S4, the cohesion c during the shear fracture of the structural surface is established. jp and friction angle The calculation method is as follows:

[0095]

[0096] In different σ n Under this condition, the maximum and minimum damage shear stress τ are calculated. d The slope of the two parallel lines of the value is about 1.05, and the initial friction angle is 46°;

[0097] According to the above formula, c jp The friction angle of the structural surface is calculated by the peak value τ in each cycle of the shear test

[0098]

[0099] In different σ n and σ p Under true triaxial cyclic loading and unloading, the cohesion c of the structural surface during shear fracture jp and friction angle The evolution of Figure 4 As shown in a and b;

[0100] In step S5, the dilatancy angle ψ during the shear fracture of the structural surface is established. jp The calculation method is as follows:

[0101] The plastic potential function g determined by the three-dimensional structural surface shear strength criterion formula is:

[0102]

[0103] Calculation of shear plastic strain increment based on plastic flow law and the normal plastic strain increment

[0104]

[0105] Where λ is the plasticity factor, and the expansion angle ψ jp The calculation formula is:

[0106]

[0107] Where λ is the plasticity factor, and the expansion angle ψ jp The calculation formula is:

[0108] Different σ n and σ p Structural surface expansion angle ψ during shear fracture under true triaxial cyclic loading and unloading jp The results are as follows Figure 4 As shown in c;

[0109] In step S6, a three-dimensional shear degradation constitutive model considering the lateral stress and shear parameter degradation effects is constructed as follows:

[0110] According to Hooke's law, the shear stress increment Δτ and the normal stress increment Δσ n expression:

[0111]

[0112] where k s , k n are shear stiffness and normal stiffness, Δu s and Δu n are the shear deformation and normal deformation increments, respectively;

[0113] The three-dimensional slip yield function F of the mechanical model is defined according to the three-dimensional shear strength criterion formula. s :

[0114]

[0115] The normal stress σ of the rock mass structural surface n and tensile strength σ t Define the three-dimensional tensile yield function F of the rock mass structural surface t :

[0116] F t =σ t -σ n

[0117] In step S7, the continuous and discontinuous numerical methods for establishing the shear degradation constitutive model of the rock mass structural surface under true three-dimensional stress are as follows:

[0118] Shear stress τ and normal stress σ on the structural surface n The stress update formula is as follows:

[0119]

[0120] where τ (t+Δt) and is the shear stress and normal stress at time t+Δt, τ(t) and are the shear stress and normal stress at time t;

[0121] In three-dimensional stress space, assuming that the shear stress vector is τ = (τ x ,τ y ,τ z ) and the normal stress vector is σ n =(n x ,n y ,n z ), the lateral stress vector is σ p =(p x ,p y ,p z ). Due to σ p Perpendicular to τ and σ n , then the stress vector σ p It is expressed as:

[0122] σ p =(p x ,p y ,p z )=τ×σ n =(τ y n z -τ z n y ,τ z n x -τ x n z ,τ x n y -τ y n x ) (18)

[0123] Where × represents the vector cross product operation, the principal stress vector σ i (i=1,2,3) and vector σ p The projection size in the direction is:

[0124]

[0125] where · represents the dot product of the vector, |||| is the modulus of the vector, and the lateral stress σ of the unit on the structural surface p Size:

[0126] σ p =σ p1 +σ p2 +σ p3

[0127] Substituting the shear stress, normal stress and lateral stress formulas into the shear yield function formula yields:

[0128]

[0129] When the three-dimensional shear yield function F s = 0, the structural surface will undergo plastic yield or slip. During the yield or slip process of the rock mass, the shear displacement will cause the structural surface to produce normal expansion deformation and increase the normal stress. The normal stress is updated according to the shear angle calculation formula and the shear stress formula:

[0130]

[0131] Among them: = is the assignment symbol, ψ jp It represents the dilatancy angle of the structural surface;

[0132] When the tensile yield function F t = 0, the structural surface will undergo tensile yield. At this time, the normal stress remains unchanged, that is, σ n =σ t , shear stress is 0;

[0133] In step S8, by performing numerical simulation of true triaxial shear indoor test, the shear degradation constitutive model of rock mass structural surface under true three-dimensional stress and its numerical method are verified as follows:

[0134] A numerical calculation model with a size of 100mm×100mm×100mm was established. The 15mm area in the middle shear surface of the model was finely cut into 2.5mm×2.5mm×2.5mm block elements to more accurately simulate the shear mechanical behavior. The other areas were divided into 5mm×5mm×5mm block elements to maintain the calculation efficiency and properly describe the overall mechanical behavior.

[0135] In the numerical calculation, the Z-direction velocity of the bottom boundary of the numerical model is set to 0, and the normal stress and lateral stress are applied to the model by stress control. After solving the equilibrium, a constant displacement velocity is applied to the model to apply the shear load. The numerical model and its boundary conditions are as follows: Figure 5 As shown;

[0136] According to the evolution of shear mechanics parameters obtained from the test results, the corresponding material parameters in the numerical model are assigned in a tabular form, and the changes of stress and strain in the numerical calculation process are monitored and recorded using the fish function;

[0137] Figure 6 For different normal stresses σ n and the lateral stress σ p The total stress-strain curve of the bedding limestone simulated by true triaxial shear is compared with the true triaxial shear test results;

[0138] In step S9, the shear degradation constitutive model of rock mass structural surface under true three-dimensional stress and its numerical method are used to analyze the excavation response of a tunnel in a complex stratum as follows:

[0139] Two three-dimensional tunnel numerical models, one with and without structural surface, were established. The size of the tunnel model was 40m×40m×12m, and the tunnel radius was 3.6m. Two joints with an inclination angle of 60° were set on the arch of the structural surface tunnel model, and the tunnel grid units were locally encrypted.

[0140] Tables 2 and 3 list the model parameters and the corresponding initial geostress components in different directions. The same initial geostress is applied to the three-dimensional tunnel model with and without structural surface, and the three-dimensional shear degradation constitutive model is used to simulate tunnel excavation. Figure 7 a and b are the deformation and displacement cloud diagrams of the surrounding rock blocks after excavation of the tunnel model without structural surface and the tunnel model with structural surface. Figure 8 a and b are the plastic zone results of the surrounding rock of the model without structural surface and the model with structural surface;

[0141] The initial geostresses in different directions of 0°, 30° and 75° clockwise along the tunnel axis (y-axis) were applied to the three-dimensional structural surface tunnel model, and the tunnel excavation simulation was performed using the three-dimensional shear degradation constitutive model. Figure 7 bd are the deformation displacement cloud diagrams of the surrounding rock after the structural surface tunnel model is excavated by rotating 0°, 30° and 75° clockwise along the tunnel axis in the initial geostress direction, respectively. Figure 8 bd respectively show the surrounding rock plastic zone of the structural surface tunnel model under different initial ground stress directions.

[0142] Finally, it should be noted that the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are included in the protection scope of the present invention. Table 2 Model parameters Table 3 Initial geostress and stress boundary conditions under changes in tunnel axis layout

Claims

1. The constitutive model and numerical method of shear degradation of rock mass structural surface under true three-dimensional stress include the following steps: S1. Carry out true triaxial shear tests on the rock mass structural surface before and after the peak cyclic loading and unloading to obtain the strength, deformation and failure characteristics of the rock mass structural surface; S2. Based on the true triaxial shear test results, the shear stress increment dτ and the elastic shear strain increment in each cyclic loading and unloading are calculated. The calculation method of the shear modulus G during the shear fracture of the structural surface is established as follows: S3. Based on the true triaxial shear test results, the shear strength criterion for three-dimensional structural surfaces considering the lateral stress effect is established as follows: Where τ is the shear stress, σ n is the normal stress, σ p is the lateral stress, c jp is the cohesion of the structural surface, is the internal friction angle of the structural surface, P is σ p The effect of ρ is the lateral stress corresponding to the maximum shear stress, K is the lateral stress with the same shear strength as when the lateral stress is 0; S4. Establish the cohesion c of the rock mass structural surface during shear fracture jp , friction angle and dilatancy angle ψ jp The calculation method is: S4.

1. τ and σ in the three-dimensional shear strength criterion formula n The slope of the curve is In the true triaxial cyclic loading shear test, the maximum and minimum damage shear stresses τ of all rock mass structural surfaces are determined. d With different normal stress σ n The slope of the curve between Calculate the initial friction angle The size of and τ d The relationship between jp Calculation method: S4.2, through the obtained c jp The friction angle of the structural surface is calculated by the peak value τ in each cycle of the shear test S4.

3. Determination of the structural plane expansion angle ψ during the shear failure of the rock mass based on the three-dimensional shear strength criterion and the non-associated plastic flow law jp Calculation method: The plastic potential function g is obtained from the three-dimensional shear strength criterion formula: S4.

4. Calculation of shear plastic strain increment according to the plastic flow law and the normal plastic strain increment where λ is the plasticity factor; S4.5, expansion angle ψ jp The calculation formula is: S5. Construct a three-dimensional shear degradation constitutive model considering the degradation effects of lateral stress and shear parameters; S5.

1. According to Hooke's law, the shear stress increment Δτ and the normal stress increment Δσ n The expression is as follows: Δτ=k s Thu s Board n =k n Thu n where k s , k n are shear stiffness and normal stiffness, Δu s and Δu n are the shear deformation and normal deformation increments, respectively; S5.

2. Define the three-dimensional slip yield function F of the mechanical model according to the three-dimensional shear strength criterion formula s and the three-dimensional tensile yield function F t for: F t =s t -s n Among them, σ n is the normal stress of the rock mass structural surface, σ t is the tensile strength of the rock mass structural surface; S6. The discrete element continuous and discontinuous numerical methods for establishing a three-dimensional shear degradation constitutive model considering the lateral stress and shear parameter degradation effects are as follows: S6.

1. Shear stress τ and normal stress σ on the structural surface n The stress update formula is: t (t+Δt) =t (t) +Δτ=τ (t) +k s Thu s Among them, τ (t+Δt) and is the shear stress and normal stress at time t+Δt, τ (t) and are the shear stress and normal stress at time t; S6.

2. In three-dimensional stress space, assume that the shear stress vector is τ = (τ x ,τ y ,τ z ) and the normal stress vector is σ n =(n x ,n y ,n z ), the lateral stress vector is σ p =(p x ,p y ,p z ), due to σ p Perpendicular to τ and σ n , then the stress vector σ p It is expressed as: s p =(p x ,p y ,p z )=τ×σ n =(t y n z -t z n y ,t z n x -t x n z ,t x n y -t y n x ) Where × represents the vector cross product operation, and the principal stress vector σ of the element on the structural surface i (i=1,2,3) and vector σ p The angle θ i The cosine value is: Where · represents the vector dot product operation, |||| is the modulus of the vector; S6.

3. Element principal stress vector σ i (i=1,2,3) and vector σ p The projection size in the direction is: S6.

4. Lateral stress σ of the element on the structural surface p Size: s p =s p1 +s p2 +s p3 S6.

5. Substituting the shear stress, normal stress, and lateral stress formulas into the shear yield function formula yields: S6.

6. When the three-dimensional shear yield function F s = 0, the structural surface will undergo plastic yield or slip. During the yield or slip process of the rock mass, the shear displacement will cause the structural surface to produce normal expansion deformation and increase the normal stress. The normal stress is updated according to the shear angle calculation formula and the shear stress formula: Among them: = is the assignment symbol, ψ jp It represents the dilatancy angle of the structural surface; S6.7, when the tension yield function F t = 0, the structural surface will undergo tensile yield; at this time, the normal stress remains unchanged, that is, σ n =σ t , shear stress is 0; S7. Through numerical simulation of true triaxial shear laboratory test, the constitutive model of shear degradation of rock mass structural surface under true three-dimensional stress and its numerical method are verified; S8. The shear degradation constitutive model of rock mass structural surface under true three-dimensional stress and its numerical method are used to analyze the excavation response of tunnels in complex strata.

2. The shear degradation constitutive model and numerical method of rock mass structural surface under true three-dimensional stress according to claim 1 is characterized in that: In step S1, a true triaxial cyclic loading and unloading test is carried out on the rock sample under different normal stresses and lateral stresses to obtain the strength, deformation and failure results of the rock mass structural surface.

3. The shear degradation constitutive model and numerical method of rock mass structural surface under true three-dimensional stress according to claim 1 is characterized in that: In step S7, by performing numerical simulation of true triaxial shear indoor test, the shear degradation constitutive model of rock mass structural surface under true three-dimensional stress and its numerical method are verified as follows: Boundary constraints are imposed on the numerical model, normal stress and lateral stress are applied to the model using stress control, and shear load is applied using displacement control; According to the evolution results of shear mechanical parameters obtained from the true triaxial shear test, they are assigned to the corresponding material parameters in the numerical model in tabular form. The fish function is used to monitor and record the changes in stress and strain during the numerical calculation process, and the simulation results are compared and analyzed with the experimental results.

4. The shear degradation constitutive model and numerical method of rock mass structural surface under true three-dimensional stress according to claim 1, characterized in that: In step S8, the three-dimensional shear degradation constitutive model and its numerical method are used to analyze the response of tunnel excavation in complex strata as follows: Two three-dimensional tunnel numerical models with and without structural surfaces were established, and the tunnel grid units were locally encrypted. The same initial geostress was applied to the three-dimensional tunnel models with and without structural surfaces, and the three-dimensional shear degradation constitutive model was used to simulate tunnel excavation. The deformation and failure characteristics of the surrounding rocks of the models with and without structural surfaces under the same initial geostress were compared and analyzed. The initial geostress in different directions was applied to the three-dimensional structural surface tunnel model, and the three-dimensional shear degradation constitutive model was used to simulate the tunnel excavation. The influence of geostress change on the continuous and discontinuous deformation and failure of the surrounding rock containing the structural surface was compared and analyzed.

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