A method for numerical analysis of slope stability under complex conditions

Abstract

The present invention provides a method for numerical analysis of slope stability under complex conditions, and belongs to the field of transportation geological engineering. The present invention constructs the correlation between the instantaneous cohesion and instantaneous internal friction angle of rock and soil under the generalized nonlinear shear strength criterion and its corresponding principal stress, and realizes the iterative cycle solution of the instantaneous cohesion and instantaneous internal friction angle of rock and soil units in numerical simulation calculations, which solves the dilemma that the current strength reduction method still relies on strength parameter reduction to complete shear strength reduction under the generalized nonlinear shear strength criterion, thereby providing a reasonable and effective implementation path for embedding the strength reduction method under the generalized nonlinear shear strength criterion into the numerical analysis of slope stability. The present invention has the advantages of being simple and easy to operate, reliable in calculation, high in solution efficiency, wide in scope of application and strong in scalability, and finds a practical and feasible implementation path for the numerical analysis of slope stability under complex conditions.

Description

Technical Field

[0001] The invention belongs to the field of traffic geological engineering, and specifically relates to a method for carrying out numerical analysis of slope stability under complex conditions. Background Art

[0002] In order to prevent slope collapse and reduce the losses caused by slope collapse, it is necessary to carry out slope stability analysis.

[0003] At present, the main theoretical methods for slope stability analysis include the limit equilibrium method and the upper limit method of limit analysis. However, the theoretical method requires artificial assumptions that the slope is a rigid body and its failure mode is assumed in advance, which makes it difficult to reveal the actual failure mechanism of the slope under complex conditions. With the development of computer technology and the introduction of the strength reduction method, numerical analysis of slope stability has gradually been applied to practical engineering. Compared with theoretical methods, numerical simulation technology does not require artificial assumptions that the slope is a rigid body in advance and the introduction of slope failure mode assumptions. It divides the slope into multiple rock and soil units with the help of grids, and then uses the mechanical equilibrium equations, constitutive models and deformation coordination relationships of the rock and soil units to effectively carry out numerical calculations of the slope under known boundary conditions. Based on this, many information such as the slope stress field, strain field and plastic zone can be solved and derived, thereby facilitating the identification of the potential instability range of the slope and the evaluation of slope stability. Furthermore, the strength reduction method is embedded in the numerical analysis. By continuously reducing the shear strength of the rock and soil mass and using it to carry out numerical calculations of the corresponding slopes, the strength reduction factor corresponding to the critical shear failure state of the slope can be obtained, which is equivalent to the slope safety factor. Thus, the purpose of numerical analysis of slope stability is achieved.

[0004] Since the shear strength criterion truly reflects the shear mechanical behavior of rock and soil and its failure characteristics, the premise for reliable slope stability analysis is to adopt an appropriate shear strength criterion for rock and soil. The shear strength of rock and soil includes two parts: shear strength and friction strength. The shear strength is mainly related to the properties of the rock and soil itself, while the friction strength is related to the normal stress acting on it in addition to the properties of the rock and soil itself. Both parts can be described by corresponding strength parameters. The current strength reduction method is to reduce the shear strength of rock and soil, and achieve the purpose of shear strength reduction by reducing the strength parameter. If there is a linear relationship between the strength parameter and the shear strength, that is, the shear failure of the rock and soil is subject to the linear shear strength criterion, then the strength parameter reduction can be proportionally reflected in the shear strength reduction. Therefore, the current strength reduction method in numerical simulation analysis is mainly applicable to the linear shear strength criterion. However, the actual shear failure of rock and soil usually shows obvious nonlinear mechanical behavior, and the linear shear strength criterion cannot effectively reveal the true shear mechanical characteristics of rock and soil. At the same time, the currently commonly used nonlinear shear strength criterion is established based on the direct shear test of rock and soil. Its function expression is often related to the normal stress on the shear failure surface of the rock and soil, and the strength parameter in the function expression is obtained by curve fitting. This method makes the strength parameter in the nonlinear shear strength criterion not linearly related to its shear strength, that is, it is impossible to directly apply the current strength reduction method to achieve shear strength reduction. In addition, numerical simulation analysis is easy to obtain the principal stress of the rock and soil unit, but it is difficult to directly identify the normal stress on the shear failure surface, and thus the nonlinear shear strength of the rock and soil unit in the form of normal stress is not easy to calculate. In summary, in order to improve the reliability of numerical analysis of slope stability, it is necessary to introduce the nonlinear shear strength criterion of rock and soil, and solve the shortcomings of embedding the nonlinear shear strength criterion in the form of normal stress and combining it with the current strength reduction method.

[0005] In other words, the current strength reduction method is difficult to combine with the generalized nonlinear shear strength criterion under the normal stress form to carry out numerical analysis of slope stability. This is mainly manifested in two aspects. First, the strength parameter in the nonlinear shear strength criterion is not linearly related to its shear strength, so that the current strength reduction method that uses strength parameter reduction to achieve proportional shear strength reduction cannot be directly applied. Second, numerical simulation analysis is easy to obtain the principal stress of the rock and soil unit, but it is difficult to directly identify the normal stress on the shear failure surface, and thus the nonlinear shear strength of the rock and soil unit under the normal stress form is not easy to calculate.

[0006] Therefore, the art needs a method for numerical analysis of slope stability under complex conditions, and specifically, a numerical implementation method combined with the current strength reduction method under the generalized nonlinear shear strength criterion in the form of normal stress. Summary of the invention

[0007] The present invention provides a method for numerical analysis of slope stability under complex conditions, which is a numerical analysis method incorporating strength reduction method under generalized nonlinear shear strength criterion and comprises the following steps:

[0008] S1: Use numerical simulation software to establish a slope numerical model;

[0009] S2: given reduction factor lower limit F s1 and upper limit F s2 ;Reduction factor lower limit F s1 A number between 0.01 and 0.2, the upper limit of the reduction factor F s2 A number between 1.0 and 50.0;

[0010] S3: Let the reduction factor be F s =(F s1 +F s2 ) / 2;

[0011] S4: Carry out numerical simulation calculation of slope under elastic conditions, obtain the slope stress field, and extract the minor principal stress σ3 of each rock and soil unit;

[0012] S5: Instantaneous cohesion c of soil elements under the generalized nonlinear shear strength criterion i and the instantaneous internal friction angle of the rock and soil unit The solution strategy is to update the strength parameters of each rock and soil unit in the slope numerical model, that is, to update c i and

[0013] S6: Introduce the strength reduction method, and let the strength parameter of each rock and soil unit in the slope numerical model after reduction be c i m =c i / F s and The c i m is the instantaneous cohesion of the rock-soil unit after reduction, is the instantaneous internal friction angle of the reduced rock and soil unit, and is used to carry out numerical simulation calculation of the slope under elastic-plastic conditions;

[0014] S7: Determine whether the slope is unstable based on the convergence of the numerical model calculation; if the calculation does not converge, it indicates that the slope is unstable, and let F s2 =F s Otherwise, let F s1 =F s ;

[0015] S8: Repeat steps S3 to S7 until |F s1 -Fs2 |≤0.001, and then complete the numerical analysis of slope stability and obtain the final reduction factor F s , which is the slope safety factor.

[0016] In a specific implementation, in step S2, the reduction factor lower limit F s1 is 0.1 and the upper limit of the reduction factor F s2 is 10.0.

[0017] In a specific implementation, in step S5, after the minor principal stress σ3 of the rock and soil unit is obtained through numerical simulation analysis, an iterative cycle calculation strategy is then used to solve the instantaneous cohesion c i and the instantaneous internal friction angle And specifically includes the following steps:

[0018] S5-1: Assuming the instantaneous cohesion c i and the instantaneous internal friction angle The initial values ​​are c i (0) and And in the first calculation, take c i (0) and are c when σ=0 i and

[0019] S5-2: Calculate the instantaneous internal friction angle using formula (9)

[0020]

[0021] Among them, τ f is the shear strength on the shear failure surface of the rock and soil mass; σ is the normal stress acting on the shear failure surface of the rock and soil mass;

[0022] S5-3: Calculate the instantaneous cohesion c using equation (10) i ;

[0023]

[0024] Equations (9) and (10) are both the instantaneous cohesion c related to the minor principal stress σ3 i and the instantaneous internal friction angle Implicit calculation formula;

[0025] S5-4: If |c i -c i (0) |≤0.001 and Then the iteration loop ends, otherwise, let c i (0) =ci and Repeat steps S5-2 and S5-3;

[0026] S5-5: Output instantaneous cohesion c i and the instantaneous internal friction angle

[0027] In a specific implementation, in step S5-1, when σ=0, c i and To calculate, directly substitute σ=0 into equation (3) and equation (4);

[0028]

[0029] In a specific implementation, in step S5, if the minor principal stress σ3 of the rock and soil unit obtained by numerical simulation analysis is less than -σ t , where σ t is the tensile strength of rock and soil, then let σ3=-σ t , and use steps S5-1 to S5-5 to solve the instantaneous cohesion c of the rock and soil mass i and the instantaneous internal friction angle

[0030] In a specific embodiment, the shear failure characteristics of the rock mass obey the nonlinear MC strength criterion, and τ f The expression between and σ is formula (11):

[0031] τ f = c0(1 + σ / σ t ) 1 / m (11)

[0032] The c0 is the intensity parameter, the σ t is the tensile strength of the rock mass, and m is a nonlinear parameter.

[0033] In a specific embodiment, under the nonlinear MC strength criterion, c i and The relationship between σ3 and σ3 is respectively equation (12) and equation (13), that is, the specific expressions corresponding to the above equations (9) and (10) under the nonlinear MC intensity criterion are equations (12) and (13):

[0034]

[0035] In a specific embodiment, the numerical simulation software FLAC is used in step S1. 3D 6.0 Establish a three-dimensional slope numerical model.

[0036] In a specific implementation, in step S6 and step S7, the model calculation time step is set to 10,000 steps and the convergence condition is that the average unbalanced force ratio is less than 1e-5. If the average unbalanced force ratio of the slope numerical model is not less than 1e-5 within the specified calculation time step, the calculation is considered to be unconvergent; otherwise, the calculation is considered to be converged.

[0037] The advantage of the present invention is that the present invention utilizes tangent strength and combines the spatial geometric relationship between the Mohr stress circle and the envelope of the generalized nonlinear shear strength criterion when the rock mass is in a critical shear failure state, constructs the correlation between the instantaneous cohesion and instantaneous internal friction angle of the rock mass and its corresponding principal stress under the generalized nonlinear shear strength criterion, realizes the iterative cycle solution of the instantaneous cohesion and instantaneous internal friction angle of the rock mass unit in the numerical simulation calculation, solves the dilemma that the current strength reduction method still relies on the strength parameter reduction to complete the shear strength reduction in the generalized nonlinear shear strength criterion, and thus provides a reasonable and effective implementation path for embedding the strength reduction method under the generalized nonlinear shear strength criterion into the numerical analysis of slope stability. The present invention has the advantages of being simple and easy to operate, reliable in calculation, high in solution efficiency, wide in scope of application and strong in scalability, and finds a practical and feasible implementation path for the numerical analysis of slope stability under complex conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic diagram of the envelope of the generalized nonlinear shear strength criterion and the tangent strength under the normal stress form of the present invention.

[0039] Figure 2 It is a schematic diagram of the spatial geometric relationship between the Mohr stress circle and the envelope of the generalized nonlinear shear strength criterion in the critical shear failure state of the rock and soil mass of the present invention.

[0040] Figure 3 The present invention is a flowchart of iterative cycle calculation of instantaneous cohesion and instantaneous internal friction angle of rock and soil under the generalized nonlinear shear strength criterion.

[0041] Figure 4 Flowchart for the implementation of the method for numerical analysis of slope stability under complex conditions.

[0042] In the figure: 1. Envelope of generalized nonlinear shear strength criterion; 2. Normal stress acting on the shear failure surface of rock and soil; 3. Shear strength on the shear failure surface of rock and soil; 4. Tangent of the envelope of generalized nonlinear shear strength criterion; 5. Instantaneous cohesion of rock and soil unit; 6. Instantaneous internal friction angle of rock and soil unit; 7. Mohr stress circle; 8. Major principal stress of rock and soil unit; 9. Minor principal stress of rock and soil unit. DETAILED DESCRIPTION

[0043] In order to solve the above technical problems, the present invention designs a method for numerical analysis of slope stability under complex conditions. First, it is assumed that the shear failure of the rock mass obeys the generalized nonlinear shear strength criterion under the normal stress form. Then, when the normal stress σ is given on the shear failure surface, the tangent method is applied to equate the nonlinear shear strength to the tangent strength, and the nonlinear shear strength is converted into the instantaneous cohesion c in the tangent strength. i and the instantaneous internal friction angle The nonlinear shear strength reduction can be expressed as two strength parameters, thus the nonlinear shear strength reduction can be converted into a feasible strength parameter reduction in numerical simulation analysis. Secondly, based on the tangent definition and the functional relationship of the generalized nonlinear shear strength criterion in the normal stress form, the instantaneous cohesion c is derived. i and the instantaneous internal friction angle Based on the mathematical formula of the normal stress σ on the shear failure surface, the instantaneous cohesion c is established by combining the spatial geometric relationship between the Mohr stress circle and the envelope of the generalized nonlinear shear strength criterion at the critical shear failure state of the rock mass. i and the instantaneous internal friction angle Finally, based on the minor principal stress σ3 of the rock and soil unit obtained by numerical simulation analysis, an iterative cycle calculation strategy is introduced to solve the instantaneous cohesion c of the rock and soil unit. i and the instantaneous internal friction angle Realize strength reduction under generalized nonlinear shear strength criterion.

[0044] The present invention solves the problem that it is difficult to combine the generalized nonlinear shear strength criterion with the current strength reduction method in the form of normal stress to carry out numerical calculations, thereby breaking the dilemma of numerical analysis of slope stability under the generalized nonlinear shear strength criterion.

[0045] The implementation approach and implementation steps of the present invention are as follows:

[0046] (1) Assume that the shear failure of rock and soil mass obeys the generalized nonlinear shear strength criterion under normal stress form, and the functional expression of the generalized nonlinear shear strength criterion under normal stress form is:

[0047] τ f =f(σ)(1)In the formula, τ f is the shear strength of rock and soil; σ is the normal stress acting on the shear failure surface of rock and soil.

[0048] (2) In numerical simulation analysis, the strength reduction method is used to actively reduce the shear strength of rock and soil, so as to obtain the critical shear failure state of rock and soil structures, and the strength reduction coefficient at this time is used as an evaluation index to reflect the stability of rock and soil structures. For example, in the numerical analysis of slope stability, the strength reduction method is introduced to make the slope in the critical shear failure state. The corresponding strength reduction coefficient at this time is called the slope safety factor, which is used to evaluate the stability of the slope. However, the current strength reduction method reduces the shear strength of rock and soil by reducing the strength parameter, and the reduced strength parameter is directly related to the shear strength of the rock and soil and has a linear relationship with it. For rock and soil, its shear strength consists of two parts, namely shear strength and friction strength. Among them, the shear strength is mainly related to the properties of the rock and soil itself, and its representative parameter is cohesion. In addition to being related to the properties of the rock and soil itself, the friction strength is also related to the magnitude of the normal stress acting on it, and its representative parameter is the internal friction angle. Therefore, the strength reduction is the reduction of the cohesion and internal friction angle of the rock and soil.

[0049] (3) For the generalized nonlinear shear strength criterion, the strength parameters involved in its function expression are obtained by curve fitting. Usually, these strength parameters have a nonlinear relationship with the shear strength of the rock and soil mass, which means that the reduction of these strength parameters cannot be proportionally reflected in the reduction of the shear strength of the rock and soil mass. As a result, it is difficult to directly apply the current strength reduction method to the generalized nonlinear shear strength criterion in numerical simulation analysis.

[0050] (4) Figure 1 As shown in the figure, in the normal stress and shear stress space, the envelope of the generalized nonlinear shear strength criterion is a curve. If the normal stress on the shear failure surface of the given rock and soil is σ, then the corresponding shear strength of the rock and soil under the generalized nonlinear shear strength criterion is τ f , accordingly, it can be represented by point P on the envelope of the generalized nonlinear shear strength criterion. If a tangent line is drawn through point P to the envelope of the generalized nonlinear shear strength criterion, then the tangent strength at point P is equivalent to the nonlinear shear strength. At the same time, the intercept of the tangent line of the envelope of the generalized nonlinear shear strength criterion at point P and the shear stress axis is c i And the inclination angle in the horizontal direction is They represent the shear strength of the rock mass and the friction strength related to the normal stress. i and is related to the normal stress and changes with the change of normal stress, so c i and They are called instantaneous cohesion and instantaneous internal friction angle respectively. Therefore, the reduction of the shear strength of rock and soil under the generalized nonlinear shear strength criterion can be converted into the reduction of the instantaneous cohesion and instantaneous internal friction angle of rock and soil.

[0051] (5) Figure 1 As shown in the figure, based on the equivalence of the tangent strength at point P with the nonlinear shear strength, the criterion expression of the generalized nonlinear shear strength in the normal stress form can be converted to:

[0052]

[0053] At the same time, according to the definition of tangent and the equivalence of tangent strength and nonlinear shear strength at point P, the calculation formulas for instantaneous internal friction angle and instantaneous cohesion of rock and soil are:

[0054]

[0055] (6) In the generalized nonlinear shear strength criterion under normal stress form, the instantaneous cohesion c of the rock mass is i and the instantaneous internal friction angle Related to the normal stress σ on the shear failure surface, however, the stress results obtained by numerical simulation analysis are the principal stresses of the rock and soil unit, namely the major principal stress σ1 and the minor principal stress σ3. Therefore, in numerical simulation analysis, in order to achieve the shear strength reduction of the rock and soil under the generalized nonlinear shear strength criterion, it is necessary to construct the instantaneous cohesion c of the rock and soil i and the instantaneous internal friction angle The correlation relationship between it and the corresponding principal stress.

[0056] (7) Figure 2 As shown in the figure, based on the principal stress of the rock and soil unit, the Mohr stress circle reflecting the stress state of the rock and soil unit is drawn. When the rock and soil unit is in the critical shear failure state, the Mohr stress circle will be tangent to the envelope of the generalized nonlinear shear strength criterion. Based on this spatial geometric relationship, the normal stress σ and its shear strength τ on the shear failure surface of the rock and soil are established. f The mathematical expression related to the corresponding principal stress is as follows:

[0057]

[0058] Substituting equations (5) and (6) into equation (2), we can obtain the correlation between the major principal stress σ1 and the minor principal stress σ3 when the rock and soil unit is in the critical shear failure state. The specific calculation formula is:

[0059]

[0060] Then, substituting formula (7) into formula (5), we can obtain the relationship between the normal stress σ on the shear failure surface of the rock mass and its corresponding minor principal stress σ3. The specific calculation formula is:

[0061]

[0062] Furthermore, by substituting equation (8) into equation (3) and equation (4), we can obtain the instantaneous cohesion c of the rock mass: i and the instantaneous internal friction angle The relationship between the corresponding minor principal stress σ3 and the specific calculation formula are:

[0063]

[0064] (8) Figure 3 As shown in Figure 1, equations (9) and (10) are the instantaneous cohesion c of the rock mass related to the minor principal stress σ3. i and the instantaneous internal friction angle Implicit calculation formula: after obtaining the minor principal stress σ3 of the rock and soil unit through numerical simulation analysis, it is necessary to use an iterative cycle calculation strategy to solve the instantaneous cohesion c of the rock and soil i and the instantaneous internal friction angle The specific implementation steps are as follows: ① Assuming the instantaneous cohesion c i and the instantaneous internal friction angle The initial values ​​are c i (0) and And in the first calculation, take c i (0) and are c when σ=0 i and ② Calculate the instantaneous internal friction angle using formula (9) ③ Calculate the instantaneous cohesion c using formula (10) i ; ④If |c i -c i (0) |≤0.001 and Then the iteration loop ends, otherwise, let c i (0) =c i and Repeat steps ② and ③; ⑤ Output instantaneous cohesion c i and the instantaneous internal friction angle

[0065] As for σ=0, c i and , we can directly substitute σ=0 into equation (3) and equation (4). In addition, if the minor principal stress σ3 of the rock and soil unit obtained by numerical simulation analysis is less than -σ t , where σ t is the tensile strength of rock and soil, then let σ3=-σ t , and adopt Figure 3 Implement the steps to solve the instantaneous cohesion c of the rock mass i and the instantaneous internal friction angle

[0066] (9) Figure 4 As shown in the figure, in the numerical simulation calculation, the solution strategy of instantaneous cohesion and instantaneous internal friction angle of rock and soil under the generalized nonlinear shear strength criterion is embedded to realize the integration of strength reduction method under the generalized nonlinear shear strength criterion and use it to carry out numerical analysis of slope stability. The specific implementation steps are as follows: ① Use numerical simulation software to establish a numerical model of the slope; ② Give the lower limit of the reduction coefficient F s1 and upper limit F s2 It should be noted that if the upper and lower limits of the given reduction coefficient are too large, the calculation time will increase, thereby reducing the calculation efficiency. If the upper and lower limits of the given reduction coefficient are too small, the upper and lower limits will not cover the actual slope safety factor, and the slope stability analysis results cannot be effectively obtained. Here, F is taken s1 = 0.1 and F s2 =10.0; ③Let the reduction factor be F s =(F s1 +F s2 ) / 2; ④ Carry out numerical simulation calculation of slope under elastic conditions, obtain the slope stress field, and extract the minor principal stress σ3 of each rock and soil unit from it; ⑤ Implement the instantaneous cohesion c of rock and soil under the generalized nonlinear shear strength criterion i and the instantaneous internal friction angle Solution strategy, update the strength parameters of each rock and soil unit in the slope numerical model; ⑥ Introduce the strength reduction method, let the strength parameter of each rock and soil unit in the slope numerical model after reduction be c i m =c i / F s and And carry out numerical simulation calculation of slope under elastic-plastic conditions; ⑦ According to the convergence of numerical model calculation, judge whether the slope is unstable. If the calculation does not converge, it means that the slope is unstable, and let F s2 =F s Otherwise, let F s1 =F s ;⑧Repeat steps ③~⑦ until |F s1 -F s2 |≤0.001, and then complete the slope stability analysis and obtain the final reduction factor F s , which is the slope safety factor.

[0067] Example

[0068] A kind of Figure 1 to Figure 4The numerical implementation method of the strength reduction method under the generalized nonlinear shear strength criterion is shown in the figure. In a highway construction project, a slope is planned to be excavated. The slope height after excavation is expected to be 20m and the average slope angle is 33.69°. In order to identify whether the slope will collapse after excavation and guide the subsequent possible slope reinforcement work, the numerical implementation method of the strength reduction method under the generalized nonlinear shear strength criterion is used to carry out slope stability analysis.

[0069] The specific operations are as follows:

[0070] (1) According to the requirements of the Code for Geotechnical Engineering Investigation (GB50021-2001), the slope of the project was investigated and tested on site to determine the physical and mechanical parameters of the rock and soil mass, and to determine the shear strength criterion and corresponding shear strength parameters of the rock and soil mass to reflect the shear mechanical characteristics of the rock and soil mass. The on-site investigation and testing showed that the rock and soil layer of the slope was relatively simple, and the average weight of the rock and soil mass was 18.82 kN / m 3 , the average water content is 12%, the average elastic modulus is 17.2MPa and the average Poisson's ratio is 0.42. At the same time, the shear failure characteristics of the rock mass obey the nonlinear MC strength criterion. The specific expression corresponding to formula (1) is formula (11):

[0071] τ f = c0(1 + σ / σ t ) 1 / m (11)

[0072] The c0 is the intensity parameter, the σ t is the tensile strength of the rock mass, and m is a nonlinear parameter; where c0 = 61.65 kPa, σ t =155.44kPa and m=1.22.

[0073] (2) Select a representative cross section of the slope and use the numerical simulation software FLAC 3D 6.0, a three-dimensional slope numerical model was established, in which the slope height was 20m and the slope angle was 33.69°. At the same time, in order to reduce the influence of size factors on the numerical results of slope stability, the slope analysis range was expanded outward by 1 to 2 times the slope height, and this was used as the boundary of the numerical model. In addition, in order to ensure the accuracy of slope stability calculation, the side length of the divided rock and soil unit was not higher than 0.5m, and it was appropriately encrypted at the foot of the slope.

[0074] (3) Given the lower limit of the reduction factor F s1 and upper limit F s2 , here, take F s1 = 0.1 and F s2 =10.0.

[0075] (4) Let the reduction factor be F s =(F s1 +F s2 ) / 2.

[0076] (5) Using numerical simulation software FLAC 3D In 6.0, the “zone property elastic” command defines the rock and soil unit as an elastic material, and directly assigns the rock and soil weight, elastic modulus and Poisson’s ratio obtained from field tests to each rock and soil unit in the slope numerical model.

[0077] (6) Using numerical simulation software FLAC 3D In 6.0, the “model solve elastic” command is used to carry out numerical simulation calculations of slopes under elastic conditions, obtain the slope stress field, and extract the minor principal stress σ3 of each rock and soil unit.

[0078] (7) Implementation of the generalized nonlinear shear strength criterion for the instantaneous cohesion c of rock and soil i and the instantaneous internal friction angle Solution strategy to obtain the instantaneous cohesion c of each rock and soil unit in the slope numerical model under the nonlinear MC strength criterion i and the instantaneous internal friction angle Among them, the instantaneous cohesion c of rock and soil under the nonlinear MC strength criterion is i and instantaneous internal friction The relationship between them and the corresponding minor principal stress σ3 is respectively, that is, the specific expressions corresponding to the above equations (9) and (10) are equations (12) and (13):

[0079]

[0080] (8) Using numerical simulation software FLAC 3D In 6.0, the "zone property mohr-coulomb" command defines the geotechnical unit as an elastic-plastic material and assigns the shear strength parameters of the geotechnical unit to c i m =c i / F s and

[0081] (9) Using numerical simulation software FLAC 3DIn 6.0, the "model solve" command is used to carry out numerical simulation calculation of the slope under elastic-plastic conditions, and the model calculation step is set to 10,000 steps and the convergence condition is that the average unbalanced force ratio is less than 1e-5. If the average unbalanced force ratio of the slope numerical model is not less than 1e-5 within the specified calculation step, the calculation is considered to be unconvergent, otherwise, the calculation is considered to be converged.

[0082] (10) If the calculation in step (9) does not converge, it indicates that the slope is unstable, and F s2 =F s Otherwise, let F s1 =F s .

[0083] (11) Repeat steps (4) to (10) until |F s1 -F s2 |≤0.001, and then complete the slope stability analysis and obtain the final reduction factor F s , which is the slope safety factor.

[0084] (12) According to the stability evaluation standard of the Technical Code for Slope Engineering (GB 50330-2013), combined with the slope safety factor obtained by numerical calculation, it is believed that the slope will not collapse after excavation, and its safety level is rated as Level 2. In addition, based on the maximum shear strain rate cloud map obtained by numerical simulation, the potential failure range of the slope during damage is preliminarily identified, thus providing favorable assistance for possible subsequent slope reinforcement work.

[0085] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for numerical analysis of slope stability under complex conditions, characterized in that: The method is a numerical analysis method that incorporates the strength reduction method under the generalized nonlinear shear strength criterion, and includes the following steps: S1: Use numerical simulation software to establish a slope numerical model; S2: given reduction factor lower limit F s1 and upper limit F s2 ;Reduction factor lower limit F s1 A number between 0.01 and 0.2, the upper limit of the reduction factor F s2 A number between 1.0 and 50.0; S3: Let the reduction factor be F s =(F s1 +F s2 ) / 2; S4: Carry out numerical simulation calculation of slope under elastic conditions, obtain the slope stress field, and extract the minor principal stress σ3 of each rock and soil unit; S5: Instantaneous cohesion c of soil elements under the generalized nonlinear shear strength criterion i and the instantaneous internal friction angle of the rock and soil unit The solution strategy is to update the strength parameters of each rock and soil unit in the slope numerical model, that is, to update c i and In step S5, after the minor principal stress σ3 of the rock and soil unit is obtained through numerical simulation analysis, an iterative cycle calculation strategy is then used to solve the instantaneous cohesion c i and the instantaneous internal friction angle And specifically includes the following steps: S5-1: Assuming the instantaneous cohesion c i and the instantaneous internal friction angle The initial values ​​are c i (0) and And in the first calculation, take c i (0) and are c when σ=0 i and S5-2: Calculate the instantaneous internal friction angle using formula (9) Among them, τ f is the shear strength on the shear failure surface of the rock and soil mass; σ is the normal stress acting on the shear failure surface of the rock and soil mass; S5-3: Calculate the instantaneous cohesion c using equation (10) i ; Equations (9) and (10) are both the instantaneous cohesion c related to the minor principal stress σ3 i and the instantaneous internal friction angle Implicit calculation formula; S5-4: If |c i -c i (0) |≤0.001 and Then the iteration loop ends, otherwise, let c i (0) =c i and Repeat steps S5-2 and S5-3; S5-5: Output instantaneous cohesion c i and the instantaneous internal friction angle S6: Introduce the strength reduction method and set the strength parameter of each rock and soil unit in the slope numerical model after reduction to c i m =c i / F s and The c i m is the instantaneous cohesion of the rock-soil unit after reduction, is the instantaneous internal friction angle of the reduced rock and soil unit, and is used to carry out numerical simulation calculation of the slope under elastic-plastic conditions; S7: Determine whether the slope is unstable based on the convergence of the numerical model calculation; if the calculation does not converge, it indicates that the slope is unstable, and let F s2 =F s Otherwise, let F s1 =F s ; S8: Repeat steps S3 to S7 until |F s1 -F s2 |≤0.001, and then complete the numerical analysis of slope stability and obtain the final reduction factor F s , which is the slope safety factor.

2. The method for numerical analysis of slope stability under complex conditions according to claim 1, characterized in that: In step S2, the reduction factor lower limit F s1 is 0.1 and the upper limit of the reduction factor F s2 is 10.

0.

3. The method for numerical analysis of slope stability under complex conditions according to claim 1, characterized in that: In step S5-1, when σ=0, c i and To calculate, directly substitute σ=0 into equation (3) and equation (4); 4. The method for numerical analysis of slope stability under complex conditions according to claim 1, characterized in that: In step S5, if the minor principal stress σ3 of the rock and soil unit obtained by numerical simulation analysis is less than -σ t , where σ t is the tensile strength of rock and soil, then let σ3=-σ t , and use steps S5-1 to S5-5 to solve the instantaneous cohesion c of the rock and soil mass i and the instantaneous internal friction angle 5. The method for numerical analysis of slope stability under complex conditions according to claim 4 is characterized in that: The shear failure characteristics of rock and soil are subject to the nonlinear MC strength criterion, and τ f The expression between and σ is formula (11): t f = c0(1 + σ / σ t ) 1 / m (11) The c0 is the intensity parameter, the σ t is the tensile strength of the rock mass, and m is a nonlinear parameter.

6. The method for numerical analysis of slope stability under complex conditions according to claim 5, characterized in that: Nonlinear MC strength criterion i and The relationship between σ3 and σ3 is respectively equation (12) and equation (13), that is, the specific expressions corresponding to the above equations (9) and (10) under the nonlinear MC intensity criterion are equations (12) and (13):

7. The method for numerical analysis of slope stability under complex conditions according to claim 1, characterized in that: In step S1, the numerical simulation software FLAC is used 3D 6.0 Establish a three-dimensional slope numerical model.

8. The method for numerical analysis of slope stability under complex conditions according to any one of claims 1 to 7, characterized in that: In step S6 and step S7, the model calculation time step is set to 10,000 steps and the convergence condition is that the average unbalanced force ratio is less than 1e-5. If the average unbalanced force ratio of the slope numerical model is not less than 1e-5 within the specified calculation time step, the calculation is considered to be unconvergent; otherwise, the calculation is considered to be converged.

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