Incremental analysis method for force between limit equilibrium strips of three-dimensional slope stability

Abstract

The invention relates to a limit equilibrium analysis method for three-dimensional slope stability, and belongs to the field of slope engineering. According to the method, the advantages of an existing limit balance method are combined, the reasonability of assumption of the inter-strip force increment direction and the definition of physical significance are guaranteed, and meanwhile, the inter-strip force increment direction is adjusted in a self-adaptive mode by meeting the three-dimensional sliding body mechanical balance condition; a mechanical equilibrium condition required for solving is converted from a strip column mechanical equilibrium condition to a three-dimensional sliding body overall mechanical equilibrium condition, so that the dependence on strip column division is avoided, and the derivation process is simplified; the method is also used for solving the problems of low calculation precision, difficulty in solving convergence and deviation of an analysis result from reality caused by unreasonable inter-strip force hypothesis and single calculation algorithm of an existing three-dimensional slope stability analysis limit equilibrium method under complex conditions. According to the method, a simple, convenient, reliable, efficient-calculation and wide-application-range calculation approach and implementation process are provided for three-dimensional slope stability limit equilibrium analysis under complex conditions.

Description

Technical Field

[0001] The invention belongs to the field of traffic slope engineering, and in particular relates to a limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability. Background Art

[0002] my country has many mountainous areas and a wide distribution of geological disasters, among which slope landslides are the most frequent. Slope landslides seriously endanger the safety of people's lives and property, and seriously restrict national economic construction and social development. In order to prevent slope landslides and reduce the losses caused by slope landslides, it is necessary to carry out slope stability analysis. In the field of slope stability research, the most commonly used research method is to convert the actual slope into a plane strain model, and then use the two-dimensional limit equilibrium calculation method to carry out slope stability analysis. However, the two-dimensional limit equilibrium calculation method cannot consider factors such as three-dimensional spatial effects, resulting in the calculation results often being conservative, which in turn causes unnecessary waste in engineering slope management. Therefore, carrying out three-dimensional slope stability analysis is a reasonable and effective way to reduce costs and increase efficiency in slope engineering.

[0003] There are two main construction modes for the existing three-dimensional limit equilibrium calculation methods, namely, the inter-strip force assumption mode and the sliding surface stress assumption mode. As for the inter-strip force assumption mode, this method discretizes the sliding body into multiple vertical strips and makes appropriate assumptions on the position or direction of the inter-strip force. Then, the slope safety factor calculation formula is derived using the mechanical equilibrium conditions satisfied by the sliding body and the inter-strip force boundary conditions, thereby completing the three-dimensional slope stability analysis. In the existing methods, the inter-strip force assumption mode adopted is mostly extended from the assumption conditions of the inter-strip force in the two-dimensional limit equilibrium calculation method, such as the three-dimensional simplified Janbu method established by assuming that the position of the inter-strip force is 1 / 3 to 1 / 2 of the height of the strip, the three-dimensional unbalanced thrust method and the three-dimensional Morgenstern-Price method assuming that the direction of the inter-strip force satisfies a specific distribution law. Although the above methods inherit the advantages of the two-dimensional limit equilibrium calculation method such as simple calculation formulas and no need to solve a set of equations, the defects of the inter-strip force assumption mode are also retained or even amplified. For example, the partial inter-strip force assumption model ignores some inter-strip forces, making it impossible for the sliding body to meet all mechanical equilibrium conditions, resulting in low calculation accuracy. In addition, the partial inter-strip force assumption model is not in line with reality and is not rigorous enough in theory, which makes the calculation method have serious convergence problems and even causes the calculation results to deviate from reality. As for the sliding surface stress assumption model, this method assumes the distribution pattern of normal stress on the sliding surface, and then constructs the distribution pattern of shear stress on the sliding surface based on the shear strength failure criterion relationship. Further, the mechanical equilibrium conditions satisfied by the sliding body are used to solve the slope safety factor. This method does not need to assume the position or direction of action of the inter-strip force, avoids assuming the inter-strip force, and at the same time, can obtain a strict solution that meets all mechanical equilibrium conditions, with the characteristics of high calculation accuracy. However, the physical meaning of the sliding surface stress distribution model assumed by this method is unclear, and it is difficult to apply to slope stability analysis in complex situations. In addition, the slope safety factor calculation formula derived by this method is mostly a set of one-variable multi-time equations, which is difficult to solve, and the existence and uniqueness of the safety factor solution are difficult to guarantee. In summary, the existing three-dimensional limit equilibrium calculation method still has some shortcomings and is difficult to cope with actual slope engineering problems under complex conditions. It is urgent to establish a three-dimensional limit equilibrium calculation method that is practical, simple in theory, concise in calculation, and easy for engineers to master.

[0004] Chinese invention patent application CN201910680998.7 discloses a three-dimensional slope stability analysis method for a reservoir under water level fluctuation conditions, including the following steps: S1. Select a specific landslide body to be analyzed, determine its sliding surface, and discretize the landslide body into strips; S2. Give the basic assumptions for stability analysis; S3. Write the functional relationship of the basic assumptions in step S2 in incremental form, introduce the correction coefficient c, and assign initial values ​​to each parameter; S4. Solve the safety factor and the introduced correction coefficient and parameters according to the equilibrium equations of three forces, the equilibrium equations of three moments, and the boundary conditions; S5. Compare whether the safety factor solved in step S4 and the introduced correction coefficient and parameters meet the requirements. If not, use the iteration method to solve until they meet the requirements. This invention effectively improves the calculation efficiency of the safety factor and the reliability of the analysis. However, this method introduces a large number of unknown variables, making the calculation process more complicated, and the number of known equations is far less than the number of unknown variables. Therefore, the unknown variables cannot be solved one by one, and can only be reasonably selected based on the conditions of the inequality. When the calculation results are unreasonable, further adjustments are required manually, which impairs the ease of use and practicality of the method. At the same time, the inventive method fails to incorporate nonlinear strength criteria.

[0005] Chinese invention patent application CN202111332366.5 discloses a method for predicting the three-dimensional stability of a vertically uniformly striped rock slope, which includes selecting a specific slope, discretizing the three-dimensional slope, and establishing a balance equation for the strip column force; establishing a strip column shear force expression according to the Moore-Coulomb criterion; combining the above equations, eliminating the shear force, and finally obtaining the expression of the horizontal seismic acceleration coefficient of the entire slope and discussing the direction of the inter-strip force. The relationship between the horizontal seismic acceleration coefficient and the safety factor can be obtained, thereby obtaining the three-dimensional slope stability coefficient under the state of no seismic load. The advantage of this invention is that it takes into account the size and direction of the inter-strip force, is easy to calculate, and improves the prediction accuracy. However, the inventive method does not meet all the boundary conditions of the inter-strip forces in the calculation method of the discrete inter-strip forces, the rigor of its calculation method is weak, and the constructed limit equilibrium equation does not directly solve the slope safety factor, which makes the calculation process still relatively complicated; at the same time, the invention limits the direction of the shear force of the discrete column sliding surface, and this direction is irrelevant to the main sliding direction of the slope, which is obviously deviated from the actual situation; in addition, the inventive method only combines the linear strength criterion, and it is difficult to solve the three-dimensional slope stability assessment problem under the nonlinear strength criterion.

[0006] Therefore, there is still a need in the art to provide a limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability. Summary of the invention

[0007] Among the existing three-dimensional limit equilibrium calculation methods, the calculation method established by the inter-strip force assumption model is difficult to effectively carry out three-dimensional slope stability analysis under complex conditions, which is mainly manifested in two aspects. First, the partial inter-strip force assumption model ignores some inter-strip forces, making the sliding body unable to meet all mechanical equilibrium conditions, resulting in low calculation accuracy. Second, the partial inter-strip force assumption model is not in line with reality and is not rigorous enough in theory, which makes the calculation method have serious convergence problems and even causes the calculation results to deviate from reality. At the same time, the calculation method established by the sliding surface stress assumption model has unclear physical meaning of the sliding surface stress distribution model, which is difficult to apply to slope stability analysis under complex conditions. Moreover, the derived slope safety factor calculation formula is mostly a set of one-variable multi-time equations, which is difficult to solve and the existence and uniqueness of the solution are difficult to guarantee.

[0008] To this end, the present invention designs a three-dimensional slope stability analysis limit equilibrium inter-strip force increment analysis method. The method takes the coordinate range of the three-dimensional sliding body in the longitudinal and transverse directions of the slope as the reference, and uses the equally spaced column plane and row plane to divide the three-dimensional sliding body into multiple strips with vertical boundaries. Then, by conducting mechanical analysis on the strips, the shear stress reciprocity theorem is applied to ignore the transverse shear force between the strips in the strips, and establish the functional relationship between the normal force between the strips and the vertical shear force increment. On this basis, combined with the shear strength criterion of the rock and soil body, the overall mechanical equilibrium equation of the three-dimensional sliding body is constructed, and the boundary conditions of the inter-strip normal force increment and the inter-strip vertical shear force increment are introduced, so as to achieve the strict solution of the three-dimensional slope stability analysis. In order to ensure the reliability and convergence of the solution process, the optimization objective function for calculating the easily divergent variables is constructed, and the optimization objective function calculation genetic algorithm and implementation process under the iterative cycle solution strategy are proposed to obtain the slope stability analysis calculation results. The present invention has the advantages of wide application range, simple theory, rigorous process, easy implementation, strong scalability, high solution efficiency, reliable calculation, strict answer, and easy for engineering personnel to master. It provides a reasonable and effective implementation approach for the limit equilibrium analysis of three-dimensional slope stability under complex conditions.

[0009] Therefore, the present invention provides a limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability, and the three-dimensional slope stability analysis method comprises the following steps:

[0010] Step 1: Given the geometric parameters of the three-dimensional slope surface and sliding surface and the physical and mechanical parameters of the rock and soil, then establish the xyz axis rectangular coordinate system and determine the range of the three-dimensional sliding body [x min , x max ] and [y min ,y max ];

[0011] Step 2: Given the row plane spacing dx and the column plane spacing dy, the three-dimensional sliding body is divided into n×m bars with vertical boundaries, and the total number of valid bars M is determined in combination with the range of the three-dimensional sliding body;

[0012] Step 3: Calculate the x, y and z axis coordinates of the center point on the sliding surface of column ij i,j ,y i,j and z i,j , where 1≤i≤n and 1≤j≤m; calculate the vertical height h of column ij i,j , the horizontal inclination angle α of the tangent direction of the sliding surface of the column ij in the x direction x_(i,j) , the horizontal inclination angle α of the tangent direction of the sliding surface of the column ij in the y direction y_(i,j) , inter-stripe force correction function f x_(i,j) and f y_(i,j) , and the normal force N on the sliding surface of column ij i,j Direction cosines n x_(i,j) 、n y_(i,j) and n z_(i,j) ;

[0013] Step 4: Given the three-dimensional slope seismic load and slope surface load, determine the known force acting on the column ij, that is, the gravity W acting on the centroid of the column ij i,j , horizontal earthquake force k H W i,j and vertical earthquake force k V W i,j , and the horizontal x-axis load PX acting on the slope of column ij i,j , horizontal y-axis load PY i,j and vertical load PZ i,j ;

[0014] Step 5: Combine the iterative loop solution strategy and use the optimization objective function to calculate the genetic algorithm to solve the slope safety factor F s , angle ρ, constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips, and proportional coefficients λ1 and λ2 of the vertical shear force increment correction between strips, and then the force N on the strip ij is given i,j , S i,j ,dE i,j 、dX i,j ,dL i,j and dV i,j , and then complete the stability analysis of the three-dimensional slope.

[0015] In a specific embodiment, in step 1, the physical and mechanical parameters of the rock and soil mass include the average weight of the soil mass and the cohesion c of the rock and soil mass on the sliding surface of the column ij. i,j and internal friction angle If the slope instability is subject to the linear shear strength criterion, then c i,j and is a constant. If the slope instability obeys the nonlinear shear strength criterion, then c i,j and is the normal force N on the sliding surface of column ij i,j Related functions need to be calculated using an iterative loop solution strategy.

[0016] In a specific implementation, in step 2, the 50≤n≤200, the 50≤m≤200.

[0017] In a specific implementation, the step 5 specifically includes the following steps:

[0018] Step 5A, setting the value range of proportional coefficients λ1 and λ2;

[0019] Step 5B: Based on the genetic algorithm, the value ranges of the proportional coefficients λ1 and λ2 are encoded, and a population with N individuals is randomly generated, that is, a population with N value combinations of the proportional coefficients λ1 and λ2 is randomly generated;

[0020] Step 5C: Calculate the slope safety factor F using an iterative solution strategy s , angle ρ and the constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips, and the force N on the strip ij is given accordingly i,j , S i,j ,dE i,j 、dX i,j ,dL i,j and dV i, j;

[0021] Step 5D, using formula (32) to calculate the objective function f value under different combinations of λ1 and λ2, and convert it into a fitness value;

[0022] f=min{[λ1-g(λ2)] 2 +[λ2-h(λ1)] 2} (32)

[0023] In the formula, g(λ2) is a function about λ2; h(λ1) is a function about λ1;

[0024] Step 5E: determine whether the number of iterations of the genetic algorithm reaches the genetic generation G. If so, stop searching; otherwise, perform selection, crossover and mutation operations to generate a new population, and repeat steps 5B to 5D.

[0025] Step 5F: Output the proportional coefficients λ1 and λ2 corresponding to the minimum objective function f value, and give the slope safety factor Fs , angle ρ, constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips, and the force N on the strip ij i,j , S i,j ,dE i,j 、dX i,j ,dL i,j and dV i,j The calculation result of .

[0026] In a specific implementation, in step 5A, λ1 and λ2 have a value range of 0 to 1, in step 5B, N=40 to 60, and in step 5E, the value of the genetic generation G has a value of 50 to 200.

[0027] In a specific implementation, step 5C specifically includes the following steps:

[0028] Step 5C-1: Assume the slope safety factor F s The initial values ​​of the constant variables ΔF1 and ΔF2 for the vertical shear force increment correction between strips are F s (0) , (0) , ΔF1 (0) and ΔF2 (0) , and in the first calculation, take F s (0) =1,ρ (0) =0, ΔF1 (0) =0 and ΔF2 (0) =0;

[0029] Step 5C-2: Calculate the shear force S on the sliding surface of column ij using equations (10) to (12) respectively. i,j Direction cosines τ x_(i,j) , τ y_(i,j) and τ z_(i,j) Then, the parameters Φ are calculated using equations (22) to (24) respectively. i,j , R i,j and T i,j ;

[0030]

[0031] Step 5C-3: Calculate the slope safety factor F using formula (26) s ;

[0032]

[0033] Step 5C-4: Calculate the normal force increment dE between the bars on the front and rear sides of the bar ij using equation (21) and equation (1) respectively: i,j and the vertical shear force increment dX i,j ;

[0034]

[0035] dX i,j =ΔF1+λ1f x_(i,j) dE i,j (1)

[0036] Step 5C-5, use equation (19) and equation (20) to calculate the normal force N on the sliding surface of column ij: i,j and shear force S i,j ;

[0037]

[0038]

[0039] Step 5C-6, using equation (27) to calculate the angle ρ between the vertical plane where the main sliding direction of the three-dimensional sliding body is located and the xz plane;

[0040]

[0041] Step 5C-7, use equation (25) and equation (2) to calculate the inter-bar normal force increment dL on the left and right sides of the bar column ij respectively: i,j and the vertical shear force increment dV i,j ;

[0042]

[0043] dV i,j =ΔF2+λ2f y_(i,j) dL i,j (2)

[0044] Step 5C-8, using equations (28) and (29) to calculate the constant variables ΔF1 and ΔF2 for the correction of the inter-strip vertical shear force increment respectively;

[0045]

[0046] Step 5C-9, if |F s (0) -F s |≤ε1,|ρ (0) -ρ|≤ε2,|ΔF1 (0) -ΔF1|≤ε3 and |ΔF2 (0) -ΔF2|≤ε4, where ε1=0.001, ε2=0.001° and ε3=ε4=0.001kPa, then the iteration cycle ends; otherwise, let F s (0) =F s , (0) =ρ、ΔF1 (0)= ΔF1 and ΔF2 (0) =ΔF2, repeat steps 5C-2 to 5C-8;

[0047] Step 5C-10: Output slope safety factor F s , angle ρ and the constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips, and the force N on the strip ij is given accordingly i,j , S i,j ,dE i,j 、dX i,j ,dL i,j and dV i,j .

[0048] Compared with the patent application CN201910680998.7 in the background technology, the number of unknown variables introduced in the present invention is relatively small, and it fully matches the number of known equations; at the same time, the present invention can independently realize the efficient and reasonable calculation of the slope safety factor by combining the iterative loop solution strategy with the genetic algorithm, and can solve the slope stability analysis problem under the nonlinear strength criterion. Compared with the patent application CN202111332366.5 in the background technology, the present invention can well solve all the problems arising in the invention. In addition, for example, Chinese invention patent CN201310036626.3 discloses a three-dimensional slope stability prediction method, Chinese invention patent CN201310036780.0 discloses a three-dimensional slope stability prediction method under earthquake load, and Chinese invention patent CN201610405311.5 discloses a three-dimensional slope stability prediction method under rainfall conditions; compared with these existing patents, the present invention not only establishes a more reasonable and efficient method for calculating the inter-strip forces of discrete columns, but also can strictly meet all inter-strip force boundary conditions; at the same time, under the embedded iterative loop solution strategy, combined with the genetic algorithm, the slope safety factor is solved simply and quickly, and the reliability and validity of the calculation results are ensured; and in the process of three-dimensional slope stability analysis, the present invention associates the shear force direction of the discrete column sliding surface with the main sliding direction of the slope, and can integrate nonlinear strength criteria, which is more conducive to solving the slope stability problem under more complex conditions.

[0049] The advantages of the present invention are that it combines the advantages of the existing limit equilibrium method for three-dimensional slope stability analysis, constructs a reasonable inter-strip force increment function, realizes the simplification and lightweight of the calculation formula derivation process, and at the same time, proposes an optimization objective function for calculating easily divergent variables, and establishes an optimization objective function calculation genetic algorithm embedded with an iterative loop solution strategy, thereby overcoming the shortcomings of the existing limit equilibrium method for three-dimensional slope stability analysis under complex conditions, such as low calculation accuracy, difficulty in solution convergence, and deviation of analysis results from reality due to unreasonable inter-strip force assumptions and a single calculation algorithm. The present invention has the advantages of a wide range of applications, simple theory, rigorous process, easy implementation, strong expansibility, high solution efficiency, reliable calculation, strict solution, and easy mastery by engineering personnel, and provides a set of practical theoretical calculation methods and implementation processes for three-dimensional slope stability analysis under complex conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic diagram of the division of three-dimensional slope and three-dimensional sliding body columns of the present invention.

[0051] Figure 2 It is a schematic diagram of the force analysis of the column ij in the three-dimensional sliding body of the present invention.

[0052] Figure 3 It is a schematic diagram of the mechanical calculation of the column ij in the limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability analysis of the present invention.

[0053] Figure 4 It is a schematic diagram of the mechanical equilibrium condition in the limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability analysis of the present invention.

[0054] Figure 5 The present invention is a flow chart of the genetic algorithm for optimizing the objective function calculation in the limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability analysis.

[0055] Figure 6 The present invention is a flowchart of iterative cycle solution in the limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability analysis.

[0056] Figure 7 The present invention is a flowchart for implementing the limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability analysis.

[0057] In the figure: 1. three-dimensional slope, 2. longitudinal slope, 3. transverse slope, 4. three-dimensional sliding body, 5. column, 6. slope surface, 7. slope sliding surface, 8. left side of column ij, 9. right side of column ij, 10. front side of column ij, 11. rear side of column ij, 12. slope surface of column ij, 13. sliding surface of column ij, 14. main sliding direction of three-dimensional sliding body, 15. vertical plane where the main sliding direction of three-dimensional sliding body is located, 16. xz plane, 17. projection of the sliding boundary line of three-dimensional sliding body on xy plane, 18. sliding boundary line of three-dimensional sliding body, 19. valid column, 20. invalid column. DETAILED DESCRIPTION

[0058] The implementation approach and implementation process of the present invention are as follows:

[0059] (1) Figure 1 As shown, in the three-dimensional slope, an xyz-axis rectangular coordinate system is established, where the x-axis direction is the longitudinal direction of the slope, the y-axis direction is the transverse direction of the slope, and the z-axis direction is the vertical direction. For the three-dimensional sliding body, its range in the x-axis direction is [x min , x max ] and the range in the y-axis direction is [y min ,y max ], then, a series of column planes parallel to the xz plane and row planes parallel to the yz plane are used to divide the three-dimensional sliding body into multiple bars with vertical boundaries, the spacing of the column planes is dy, which divides the three-dimensional sliding body into m columns in the horizontal direction, and the spacing of the row planes is dx, which divides the three-dimensional sliding body into n rows in the vertical direction.

[0060] (2) Figure 2 As shown, taking the i-th row and j-th column bar (named as bar ij, 1≤i≤n and 1≤j≤m) as an example, p i–1,j–1 、p i,j–1 、p i–1,j and p i,j is the point of column ij on the slope surface, s i–1,j–1 、s i,j–1 、s i–1,j and i,j is the point of column ij on the slope sliding surface, p i–1,j–1 s i–1,j–1 s i,j–1 p i,j–1 is the left side of column ij, p i–1,j s i–1,j s i,j p i,j is the right side of column ij, p i–1,j–1 s i–1,j–1 s i–1,j p i–1,j is the front side of column ij, p i,j–1s i,j–1 s i,j p i,j is the rear side of column ij, p i–1,j– 1p i,j–1 p i–1,j p i,j is the slope of column ij, s i–1,j–1 s i,j–1 s i–1,j s i,j is the sliding surface of column ij, and the known forces acting on column ij are gravity W i,j , horizontal earthquake force k H W i,j and vertical earthquake force k V W i,j , whose action points are all at the centroid of column ij, and the horizontal x-axis load PX acting on the slope of column ij i,j , horizontal y-axis load PY i,j and vertical load PZ i,j , whose action points are all at the center point of the slope surface of column ij. The unknown forces acting on the sliding surface of column ij are normal force N i,j and shear force S i,j , whose action points are all at the center point of the sliding surface of the column ij. The unknown forces acting on the left side of the column ij are the inter-bar normal force L i,j-1 , inter-strip vertical shear force V i,j-1 and the transverse shear force between strips Q i,j-1 The unknown forces acting on the right side of the bar ij are the inter-bar normal force L i,j , inter-strip vertical shear force V i,j and the transverse shear force between strips Q i,j The unknown forces acting on the front side of the bar ij are the inter-bar normal force E i-1,j , vertical shear force between strips X i-1,j and the transverse shear force between strips H i-1,j The unknown forces acting on the rear side of the bar ij are the inter-bar normal force E i,j , vertical shear force between strips X i,j and the transverse shear force between strips H i,j .

[0061] (3) Figure 3 As shown in the figure, considering that the scales of the bar ij in the longitudinal and transverse directions are all differential, based on the shear stress reciprocity theorem, it can be known that the transverse shear forces between the bars on each side of the bar ij not only appear in pairs but also offset each other. Therefore, the transverse shear forces between the bars on each side of the bar ij can be ignored. i-1,j , H i,j , Q i,j-1 and Q i,jAt the same time, this approach is conducive to ensuring the moment balance of the forces acting on the bar ij around the z-axis. Furthermore, the normal force increment between the bars on the front and rear sides of the bar ij is dE i,j =E i,j -E i-1,j , the vertical shear force increment between the strips on the front and rear sides is dX i,j =X i,j -X i-1,j , the normal force increment between the left and right sides is dL i,j =L i,j -L i,j-1 , and the vertical shear force increment between the strips on the left and right sides is dV i,j =V i,j -V i,j-1 , when the directions of the resultant forces of the front and rear side force increments and the left and right side force increments are parallel to the tangent direction of the sliding surface of column ij, the sliding force of the slope caused by the inter-strip force is the largest, which causes the sliding surface of the slope to be in the most unfavorable stress state. In fact, in order to meet all the static equilibrium conditions of column ij, the direction of the resultant forces of the inter-strip force increments is not necessarily parallel to the tangent direction of the sliding surface. Therefore, there will be a certain functional relationship between the inter-strip force increments. For this reason, it is assumed that the functional relationship of the inter-strip force increments is:

[0062] dX i,j =ΔF1+λ1f x_(i,j) dE i,j (1)

[0063] dV i,j =ΔF2+λ2f y_(i,j) dL i,j (2)

[0064] Where ΔF1 and ΔF2 are constant variables corresponding to the increment correction of the vertical shear force between the strips, the purpose of which is to ensure that the force between the strips strictly meets the boundary conditions; f x_(i,j) and f y_(i,j) is the inter-strip force correction function that needs to be satisfied when the inter-strip force increment direction is parallel to the strip column ij sliding surface, which is used to describe the influence of the geometric morphology characteristics of the strip column ij sliding surface on the inter-strip vertical shear force, and f x_(i,j) =tanα x_(i,j) and f y_(i,j) =tanα y_(i,j) , where α x_(i,j) is the horizontal inclination angle of the sliding surface of column ij in the x direction, α y_(i,j) is the horizontal inclination angle of the sliding surface of column ij in the y direction; λ1 and λ2 are the proportional coefficients for the correction of the vertical shear force increment between the corresponding bars.

[0065] Slope instability is caused by the sliding of a three-dimensional sliding body along a main sliding direction. As a result, the shear force S on the sliding surface of the column ij i,jLet the vertical plane that is in or parallel to the main sliding direction of the three-dimensional sliding body be the vertical plane, and let the angle between the vertical plane where the main sliding direction of the three-dimensional sliding body is and the xz plane be ρ, and ρ is positive in the clockwise direction, otherwise it is negative.

[0066] When the slope instability is shear failure, the shear force S on the sliding surface of the column ij is i,j With normal force N i,j Satisfies the following relationship:

[0067]

[0068] In the formula, c i,j and are the cohesion and internal friction angle of the rock mass on the sliding surface of column ij respectively. If the slope instability obeys the linear shear strength criterion, then c i,j and is a constant. If the slope instability obeys the nonlinear shear strength criterion, then c i,j and is the normal force N on the sliding surface of column ij i,j Related functions need to be calculated using an iterative loop solution strategy; F s is the slope safety factor.

[0069] (4) Figure 4 As shown, the mechanical equilibrium equations of all forces acting on the bar ij along the x, y and z axes are:

[0070] n x_(i,j) N i,j +τ x_(i,j) S i,j -dE i,j -k H W i,j +PX i,j =0 (4)

[0071] n y_(i,j) N i,j +τ y_(i,j) S i,j -dL i,j +PY i,j =0 (5)

[0072] n z_(i,j) N i,j +τ z_(i,j) S i,j -dV i,j -dX i,j -(1-k V )W i,j -PZ i,j =0 (6)

[0073] Where nx_(i,j) 、n y_(i,j) and n z_(i,j) is the normal force N on the sliding surface of column ij i,j Direction cosines of x_(i,j) , τ y_(i,j) and τ z_(i,j) is the shear force S on the sliding surface of column ij i,j The direction cosines of the shear force S on the sliding surface of the column ij i,j The vertical plane in or parallel to the main sliding direction of the three-dimensional sliding body, and the angle between the vertical plane in which the main sliding direction of the three-dimensional sliding body is located and the xz plane is ρ, it can be known that τ y_(i,j) / τ x_(i,j) =tanρ.

[0074] In equations (4) to (6), the normal force N on the sliding surface of the column ij is i,j Direction cosines n x_(i,j) 、n y_(i,j) and n z_(i,j) The calculation formulas are:

[0075]

[0076] In equations (4) to (6), the shear force S on the sliding surface of the column ij is i,j Direction cosines τ x_(i,j) , τ y_(i,j) and τ z_(i,j) The calculation formulas are:

[0077]

[0078] Furthermore, the moment equilibrium equations of all forces acting on the three-dimensional sliding body around the x-axis and y-axis are:

[0079]

[0080] In the formula, x i,j ,y i,j and z i,j are the x-, y- and z-axis coordinates of the center point on the sliding surface of column ij; h i,j is the vertical height of column ij.

[0081] It should be noted that although the three-dimensional sliding body is divided into m columns in the horizontal direction and n rows in the vertical direction, not all bars consisting of m columns and n rows are within the range of the sliding body. For bar ij, the x- and y-axis coordinates of the center point on its sliding surface are x and i,j and i,j , and x i,j =x min +(i–0.5)×(x max –xmin ) / n and y i,j =y min +(j–0.5)×(y max –y min ) / m, if this point is within the projection range of the sliding boundary line of the three-dimensional sliding body on the xy plane, then the column ij is a valid column, otherwise it is an invalid column. For an invalid column, all the forces on it can be set to 0. The sliding boundary line of the three-dimensional sliding body is the boundary line where the slope sliding surface intersects with the slope surface.

[0082] As for the increment of normal force between strips and vertical shear force between strips, under the condition of satisfying boundary conditions, the calculation formulas are:

[0083]

[0084] (5) Combining equations (4) to (6) and combining equations (1) and (2), we can obtain the normal force N on the sliding surface of column ij: i,j and shear force S i,j The calculation formulas are:

[0085]

[0086] Furthermore, substituting equations (19) and (20) into equation (3), we can obtain the normal force increment dE between the bars on the front and rear sides of the bar ij: i,j The calculation formula is:

[0087]

[0088] In formula (21), the parameter Φ i,j , R i,j and T i,j The calculation formulas are:

[0089]

[0090]

[0091] Then, substituting equation (11) into equation (5), we can obtain the increment of normal force between the bars on the left and right sides of the bar ij: i,j The calculation formula is:

[0092]

[0093] After that, substituting equation (21) into equation (15), the slope safety factor F can be established. s The calculation formula is:

[0094]

[0095] At the same time, by substituting formula (25) into formula (16), the calculation formula of angle ρ can be established as follows:

[0096]

[0097] For the constant variable ΔF1 of the vertical shear force increment correction between strips, equation (1) can be substituted into equation (17) to establish its calculation formula:

[0098]

[0099] Where M is the total number of valid bars.

[0100] For the constant variable ΔF2 of the vertical shear force increment correction between strips, substitute equation (2) into equation (18) to establish its calculation formula:

[0101]

[0102] For the proportional coefficient λ1 of the vertical shear force increment correction between strips, substitute equations (5) and (6) into equation (13), and combine equations (1) and (2) to establish the calculation formula:

[0103]

[0104] For the proportional coefficient λ2 of the vertical shear force increment correction between strips, substitute equation (4) and equation (6) into equation (14), and combine equation (1) and equation (2) to establish its calculation formula:

[0105]

[0106] According to the above formula, N can be solved by using equations (19) to (21), (1), (25), (2) and (26) to (31): i,j , S i,j ,dE i,j 、dX i,j ,dL i,j , dV i,j 、F s , ρ, ΔF1, ΔF2, λ1 and λ2.

[0107] (6) Formula (26) to (31) give the slope safety factor F s, angle ρ, constant variables ΔF1 and ΔF2 of the inter-strip vertical shear force increment correction, and proportional coefficients λ1 and λ2 of the inter-strip vertical shear force increment correction. However, equations (26) to (31) are all implicit calculation equations and need to be calculated using an iterative loop solution strategy. At the same time, considering that there is a positive correlation between the calculation of the proportional coefficients λ1 and λ2, the convergence of the calculation cannot be guaranteed by relying solely on the iterative loop solution strategy. Therefore, equations (30) and (31) used to calculate the proportional coefficients λ1 and λ2 are converted into the following optimization objective function:

[0108] f=min{[λ1-g(λ2)] 2 +[λ2-h(λ1)] 2} (32)

[0109] Wherein, g(λ2) is the function on the right side of equation (30); h(λ1) is the function on the right side of equation (31).

[0110] In formula (32), the value range of λ1 and λ2 is usually 0 to 1. When λ1 and λ2 are within this range, if formula (32) can be made close to 0, the corresponding λ1 and λ2 results are the approximate solutions of formula (30) and formula (31).

[0111] like Figure 5 As shown, the specific implementation steps of the genetic algorithm for optimizing the objective function calculation are as follows:

[0112] ① Given the value range of the proportional coefficients λ1 and λ2, here, let the value range of λ1 and λ2 be 0 to 1;

[0113] ② Based on the genetic algorithm, the value range of the proportional coefficients λ1 and λ2 is encoded, and a population with N individuals (i.e., N value combinations of the proportional coefficients λ1 and λ2) is randomly generated. It is recommended to take N = 50;

[0114] ③ Using the iterative cycle solution strategy, calculate the slope safety factor F s , angle ρ and the constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips, and the force N on the strip ij is given accordingly i,j , S i,j ,dE i,j 、dX i,j ,dL i,j and dV i,j ;

[0115] ④ Use formula (32) to calculate the objective function f value under different combinations of λ1 and λ2, and convert it into fitness value;

[0116] ⑤ Determine whether the number of iterations of the genetic algorithm has reached the genetic algebra G (G = 100 is recommended). If so, stop searching. Otherwise, perform selection, crossover and mutation operations to generate a new population and repeat steps ② to ④.

[0117] ⑥ Output the proportional coefficients λ1 and λ2 corresponding to the minimum objective function f value, and give the slope safety factor F s , angle ρ, constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips, and the force N on the strip ij i,j , S i,j ,dE i,j 、dX i,j ,dL i,j and dV i,j The calculation result of .

[0118] (7) Figure 6 As shown, the slope safety factor F s The iterative loop solution strategy and specific implementation steps of the constant variables ΔF1 and ΔF2 for the correction of the vertical shear force increment between strips are as follows:

[0119] ① Assuming the slope safety factor F s The initial values ​​of the constant variables ΔF1 and ΔF2 for the vertical shear force increment correction between strips are F s (0) , (0) , ΔF1 (0) and ΔF2 (0) , and in the first calculation, take F s (0) =1,ρ (0) =0, ΔF1 (0) =0 and ΔF2 (0) =0;

[0120] ② Use equations (10) to (12) to calculate the direction cosine τ x_(i,j) , τ y_(i,j) and τ z_(i,j) Then, the parameters Φ are calculated using equations (22) to (24) respectively. i,j , R i,j and T i,j ;

[0121] ③ Calculate the slope safety factor F using formula (26) s ;

[0122] ④ Use equation (21) and equation (1) to calculate the normal force increment dE between the strips on the front and rear sides of the strip ij respectively: i,j and the vertical shear force increment dX i,j ;

[0123] ⑤ Use equations (19) and (20) to calculate the normal force N on the sliding surface of column ij: i,j and shear force S i,j ;

[0124] ⑥ Calculate the angle ρ between the vertical plane where the main sliding direction of the three-dimensional sliding body is located and the xz plane using formula (27);

[0125] ⑦ Use equation (25) and equation (2) to calculate the normal force increment dL between the strips on the left and right sides of the strip ij: i,j and the vertical shear force increment dV i,j ;

[0126] ⑧Use equations (28) and (29) to calculate the constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips respectively;

[0127] ⑨If |F s (0) -F s |≤ε1,|ρ (0) -ρ|≤ε2,|ΔF1 (0) -ΔF1|≤ε3 and |ΔF2 (0) -ΔF2|≤ε4(ε1=0.001, ε2=0.001° and ε3=ε4=0.001kPa), then the iteration cycle ends, otherwise, let F s (0) =F s , (0) =ρ、ΔF1 (0) = ΔF1 and ΔF2 (0) =ΔF2, repeat steps ② to ⑧;

[0128] ⑩Output slope safety factor F s , angle ρ and the constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips, and the force N on the strip ij is given accordingly i,j , S i,j ,dE i,j 、dX i,j ,dL i,j and dV i,j .

[0129] (8) Figure 7 As shown in the figure, the implementation process of the limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability analysis is as follows:

[0130] ① Given the geometric parameters of the three-dimensional slope surface and sliding surface and the physical and mechanical parameters of the rock and soil, the xyz axis rectangular coordinate system is established and the range of the three-dimensional sliding body [x min , x max ] and [y min ,y max];

[0131] ② Given the row plane spacing dx and the column plane spacing dy, the three-dimensional sliding body is divided into n×m bars with vertical boundaries, and the total number of valid bars M is determined in combination with the range of the three-dimensional sliding body;

[0132] ③ Calculate the x, y and z axis coordinates x of the center point on the sliding surface of the column ij (1≤i≤n and 1≤j≤m) i,j ,y i,j and z i,j , vertical height h i,j , the horizontal inclination angle α of the tangent direction of the sliding surface of the column ij in the x direction x_(i,j) , the horizontal inclination angle α of the tangent direction of the sliding surface of the column ij in the y direction y_(i,j) , inter-stripe force correction function f x_(i,j) and f y_(i,j) , and the normal force N on the sliding surface of column ij i,j Direction cosines n x_(i,j) 、n y_(i,j) and n z_(i,j) ;

[0133] ④ Given the three-dimensional slope seismic load and slope surface load, the known force acting on the column ij is determined accordingly, that is, the gravity W acting on the centroid of the column ij i,j , horizontal earthquake force k H W i,j and vertical earthquake force k V W i,j , and the horizontal x-axis load PX acting on the slope of column ij i,j , horizontal y-axis load PY i,j and vertical load PZ i,j ;

[0134] ⑤ Combined with the iterative loop solution strategy, the specific implementation steps of the genetic algorithm are calculated using the optimization objective function to solve the slope safety factor F s , angle ρ, constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips, and proportional coefficients λ1 and λ2 of the vertical shear force increment correction between strips, and then the force N on the strip ij is given i,j , S i,j ,dE i,j 、dX i,j ,dL i,j and dV i,j , and then, complete the three-dimensional slope stability analysis.

[0135] The characteristic of the inter-strip force increment function relationship of the present invention is that it combines the advantages of the existing limit equilibrium method, ensures the rationality of the assumption of the inter-strip force increment direction and the clarity of the physical meaning, and at the same time adaptively adjusts the inter-strip force increment direction by satisfying the mechanical equilibrium conditions of the three-dimensional sliding body. At the same time, the mechanical equilibrium conditions required for solving are converted from the strip-column mechanical equilibrium conditions to the overall mechanical equilibrium conditions of the three-dimensional sliding body, avoiding the dependence on the strip-column division, simplifying the derivation process, and facilitating the calculation to be fast, effective and reliable. In addition, it also makes up for the deficiency that the existing inter-strip force assumption model is difficult to consider the boundary conditions of the inter-strip shear force ends.

[0136] Example

[0137] A kind of Figure 1 to Figure 7 The three-dimensional slope stability analysis limit equilibrium inter-strip force increment analysis method is shown in the figure. The slope height of the embankment slope along a highway is about 12.2m, and the slope angle is about 26.57°. In order to explore the stability of this three-dimensional slope and the rationality of the slope design, the three-dimensional slope stability analysis limit equilibrium inter-strip force increment analysis method is used to analyze it.

[0138] The specific operations are as follows:

[0139] (1) In accordance with the requirements of the Code for Geotechnical Engineering Investigation (GB50021-2001), field investigation and testing of the slope soil was carried out to determine the physical and mechanical parameters of the rock and soil. It was determined that the rock and soil obeyed the Mohr-Coulomb shear strength criterion when the slope slides. The specific test results are: the average soil weight is 19.2 kN / m 3 The cohesion of the rock and soil on the sliding surface is 29.3 kPa and the internal friction angle is 20° (which indicates that the cohesion of the rock and soil on the sliding surface of the subsequent column ij is c i,j =29.3kPa and internal friction angle );

[0140] (2) The xyz rectangular coordinate system is established with the slope foot point as the origin, where the x-axis direction is the longitudinal direction of the slope, the y-axis direction is the transverse direction of the slope, and the z-axis direction represents the vertical direction. According to the geological survey and slope displacement monitoring results, the potential sliding surface of the slope is approximately an ellipsoid, that is, the three-dimensional sliding body is approximately an ellipsoid, and the symmetry plane of the ellipsoid is parallel to the xz plane. The equation of the potential sliding surface of the slope is:

[0141]

[0142] (3) Based on the potential sliding surface equation of the slope and the slope surface morphology, determine the lateral range of the three-dimensional sliding body [x min , x max ] and the vertical range [y min ,y max] are [-10.000m, 28.487m] and [-58.159m, 58.159m] respectively, thus, the row plane spacing dx is set to 0.385m and the column plane spacing dy is set to 1.163m, and then the three-dimensional sliding body is divided into n×m bars with vertical boundaries, where n=100, m=100 and the total number of valid bars M=7626;

[0143] (4) Obtain the z-axis coordinate (i.e., z) of the center point on the sliding surface of column ij (1≤i≤n and 1≤j≤m) i,j , where the x- and y-axis coordinates of the center point on the sliding surface of column ij are x i,j =x min +(i–0.5)×(x max –x min ) / n and y i,j =y min +(j–0.5)×(y max –y min ) / m), vertical height h i,j , the horizontal inclination angle α of the sliding surface of column ij in the x direction x_(i,j) and the horizontal inclination angle α in the y direction y_(i,j) , inter-strip force correction function f x_(i,j) and f y_(i,j) and the normal force N on the sliding surface of column ij i,j Direction cosines n x_(i,j) 、n y_(i,j) and n z_(i,j) ;

[0144] (5) Calculate the gravity W acting on the centroid of column ij i,j At the same time, geological data show that this slope is not in a seismic activity zone and the seismic effect can be ignored. At the same time, there is no slope load on the slope. Therefore, the horizontal seismic force k H W i,j and vertical earthquake force k V W i,j are all 0, and the horizontal x-axis load PX acting on the slope of column ij i,j , horizontal y-axis load PY i,j and vertical load PZ i,j are also 0;

[0145] (6) Combined with the iterative solution strategy, the specific implementation steps of the genetic algorithm are calculated using the optimization objective function to solve the slope safety factor F s , angle ρ, constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips, and proportional coefficients λ1 and λ2 of the vertical shear force increment correction between strips, and then the force N on the strip ij is given i,j , Si,j ,dE i,j 、dX i,j ,dL i,j and dV i,j , where the slope safety factor F s =2.235, angle ρ = 0.000°, constant variables ΔF1 = 5.578 kPa and ΔF2 = 0.191 kPa for the correction of the vertical shear force increment between strips, and proportional coefficients λ1 = 0.693 and λ2 = 0.199 for the correction of the vertical shear force increment between strips;

[0146] (7) According to the stability evaluation standard of the Technical Code for Slope Engineering (GB 50330-2013), combined with the slope safety factor calculated by the limit equilibrium inter-strip force increment analysis method of three-dimensional slope stability analysis, it is determined that this slope is stable and meets the first-level safety grade assessment standard, which shows that the design of this roadbed slope is reasonable.

[0147] In general, the present invention relates to a limit equilibrium analysis method for three-dimensional slope stability, and belongs to the field of slope engineering. The present invention combines the advantages of existing limit equilibrium methods, ensuring the rationality of the assumption of the direction of the inter-strip force increment and the clarity of the physical meaning, while adaptively adjusting the direction of the inter-strip force increment by satisfying the mechanical equilibrium conditions of the three-dimensional sliding body, and converting the mechanical equilibrium conditions required for the solution from the column mechanical equilibrium conditions to the overall mechanical equilibrium conditions of the three-dimensional sliding body, avoiding the dependence on the column division, simplifying the derivation process, and in addition, it can also be used to solve the existing three-dimensional slope stability analysis limit equilibrium method under complex conditions. The problem of low calculation accuracy, difficult solution convergence, and deviation of analysis results from reality due to unreasonable assumptions of inter-strip forces and a single calculation algorithm. The present invention provides a simple, reliable, efficient, and widely applicable calculation approach and implementation process for the limit equilibrium analysis of three-dimensional slope stability under complex conditions.

[0148] 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 limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability, characterized in that: The three-dimensional slope stability analysis method includes the following steps: Step 1: Given the geometric parameters of the three-dimensional slope surface and sliding surface and the physical and mechanical parameters of the rock and soil, then establish the xyz axis rectangular coordinate system and determine the range of the three-dimensional sliding body [x min , x max ] and [y min ,y max ]; Step 2: Given the row plane spacing dx and the column plane spacing dy, the three-dimensional sliding body is divided into n×m bars with vertical boundaries, and the total number of valid bars M is determined in combination with the range of the three-dimensional sliding body; Step 3: Calculate the x, y and z axis coordinates of the center point on the sliding surface of column ij i,j ,y i,j and z i,j , where 1≤i≤n and 1≤j≤m; calculate the vertical height h of column ij i,j , the horizontal inclination angle α of the tangent direction of the sliding surface of the column ij in the x direction x_(i,j) , the horizontal inclination angle α of the tangent direction of the sliding surface of the column ij in the y direction y_(i,j) , inter-stripe force correction function f x_(i,j) and f y_(i,j) , and the normal force N on the sliding surface of column ij i,j Direction cosines n x_(i,j) 、n y_(i,j) and n z_(i,j) ; Step 4: Given the three-dimensional slope seismic load and slope surface load, determine the known force acting on the column ij, that is, the gravity W acting on the centroid of the column ij i,j , horizontal earthquake force k H W i,j and vertical earthquake force k V W i,j , and the horizontal x-axis load PX acting on the slope of column ij i,j , horizontal y-axis load PY i,j and vertical load PZ i,j ; Step 5: Combine the iterative loop solution strategy and use the optimization objective function to calculate the genetic algorithm to solve the slope safety factor F s , angle ρ, constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips, and proportional coefficients λ1 and λ2 of the vertical shear force increment correction between strips, and then the force N on the strip ij is given i,j , S i,j ,dE i,j 、dX i,j ,dL i,j and dV i,j , and then complete the stability analysis of the three-dimensional slope.

2. The limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability according to claim 1 is characterized in that: In step 1, the physical and mechanical parameters of the rock and soil mass include the average weight of the soil mass and the cohesion c of the rock and soil mass on the sliding surface of the column ij. i,j and internal friction angle If the slope instability is subject to the linear shear strength criterion, then c i,j and is a constant. If the slope instability obeys the nonlinear shear strength criterion, then c i,j and is the normal force N on the sliding surface of column ij i,j Related functions need to be calculated using an iterative loop solution strategy.

3. The limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability according to claim 1 is characterized in that: In step 2, the 50≤n≤200, and the 50≤m≤200.

4. The limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability according to any one of claims 1 to 3, characterized in that: The step 5 specifically includes the following steps: Step 5A, setting the value range of proportional coefficients λ1 and λ2; Step 5B: Based on the genetic algorithm, the value ranges of the proportional coefficients λ1 and λ2 are encoded, and a population with N individuals is randomly generated, that is, a population with N value combinations of the proportional coefficients λ1 and λ2 is randomly generated; Step 5C: Calculate the slope safety factor F using an iterative solution strategy s , angle ρ and the constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips, and the force N on the strip ij is given accordingly i,j , S i,j ,dE i,j 、dX i,j ,dL i,j and dV i ,j; Step 5D, using formula (32) to calculate the objective function f value under different combinations of λ1 and λ2, and convert it into a fitness value; f=min{[λ1-g(λ2)] 2 +[λ2-h(λ1)] 2 } (32) In the formula, g(λ2) is a function about λ2; h(λ1) is a function about λ1; Step 5E: determine whether the number of iterations of the genetic algorithm reaches the genetic generation G. If so, stop searching; otherwise, perform selection, crossover and mutation operations to generate a new population, and repeat steps 5B to 5D. Step 5F: Output the proportional coefficients λ1 and λ2 corresponding to the minimum objective function f value, and give the slope safety factor F s , angle ρ, constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips, and the force N on the strip ij i,j , S i,j ,dE i,j 、dX i,j ,dL i,j and dV i,j The calculation result of .

5. The limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability according to claim 4 is characterized in that: In step 5A, the value range of λ1 and λ2 is 0-1, in step 5B, N=40-60, and in step 5E, the value of the genetic generation G is 50-200.

6. The limit equilibrium inter-strip force increment analysis method for three-dimensional slope stability according to claim 5 is characterized in that: Step 5C specifically includes the following steps: Step 5C-1: Assume the slope safety factor F s The initial values ​​of the constant variables ΔF1 and ΔF2 for the vertical shear force increment correction between strips are F s (0) , (0) , ΔF1 (0) and ΔF2 (0) , and in the first calculation, take F s (0) =1,ρ (0) =0, ΔF1 (0) =0 and ΔF2 (0) =0; Step 5C-2: Calculate the shear force S on the sliding surface of column ij using equations (10) to (12) respectively. i,j The direction cosines τ x_(i ,j),τ y_(i,j) and τ z_(i,j) Then, the parameters Φ are calculated using equations (22) to (24) respectively. i,j , R i,j and T i,j ; Step 5C-3: Calculate the slope safety factor F using formula (26) s ; Step 5C-4: Calculate the normal force increment dE between the bars on the front and rear sides of the bar ij using equation (21) and equation (1) respectively: i,j and the vertical shear force increment dX i,j ; dX i,j =ΔF1+λ1f x_(i,j) dE i,j (1) Step 5C-5, use equation (19) and equation (20) to calculate the normal force N on the sliding surface of column ij: i,j and shear force S i,j ; Step 5C-6, using equation (27) to calculate the angle ρ between the vertical plane where the main sliding direction of the three-dimensional sliding body is located and the xz plane; Step 5C-7, use equation (25) and equation (2) to calculate the inter-bar normal force increment dL on the left and right sides of the bar column ij respectively: i,j and the vertical shear force increment dV i,j ; dV i,j =ΔF2+λ2f y_(i,j) dL i,j (2) Step 5C-8, using equations (28) and (29) to calculate the constant variables ΔF1 and ΔF2 for the correction of the inter-strip vertical shear force increment respectively; Step 5C-9, if |F s (0) -F s |≤ε1,|ρ (0) -ρ|≤ε2,|ΔF1 (0) -ΔF1|≤ε3 and |ΔF2 (0) -ΔF2|≤ε4, where ε1=0.001, ε2=0.001° and ε3=ε4=0.001kPa, then the iteration cycle ends; otherwise, let F s (0) =F s , (0) =ρ、ΔF1 (0) = ΔF1 and ΔF2 (0) =ΔF2, repeat steps 5C-2 to 5C-8; Step 5C-10: Output slope safety factor F s , angle ρ and the constant variables ΔF1 and ΔF2 of the vertical shear force increment correction between strips, and the force N on the strip ij is given accordingly i,j , S i,j ,dE i,j 、dX i,j ,dL i,j and dV i,j .

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