Sliding zone anti-sliding short column embedded finite element simulation method for landslide minimally invasive reinforcement

Abstract

The invention discloses an embedded finite element simulation method for an anti-sliding short column of a sliding zone for landslide minimally invasive reinforcement. The method comprises the following steps: 1) inputting information of landslide rock-soil body grids, boundary conditions, material parameters and control parameters; 2) generating an embedded grid of the anti-sliding short columns according to the spatial arrangement of the anti-sliding short columns and the landslide rock-soil body grid; 3) calculating an equivalent node load column vector and a load step increment; 4) calculating a landslide stress field and a displacement field of the load step; 5) calculating the interaction force between the landslide and the anti-sliding short column; 6) calculating an equivalent node load of the anti-sliding short column to the landslide rock-soil body grid; (7) calculating a load step landslide stress field and a displacement field after the anti-sliding short column is reinforced; 8) judging convergence; (9) judging the end of the load step; the internal stress and deformation of the landslide rock-soil body under the action of the anti-sliding short column can be effectively simulated, the calculation precision and efficiency are high, and an important basis is provided for reinforcement design of the landslide anti-sliding short column.

Description

Technical Field

[0001] The invention relates to the fields of water conservancy engineering and civil engineering, and in particular to an embedded finite element simulation method of a sliding belt anti-sliding short column for minimally invasive reinforcement of a landslide. Background Art

[0002] Minimally invasive landslide reinforcement is a new type of reinforcement method proposed under the requirements of landslide control and green and low-carbon development. It aims to achieve effective landslide control by minimizing interference and damage to the natural environment. The biggest feature of minimally invasive landslide reinforcement is its minimal invasiveness, which avoids large-scale, large-scale excavation and support, thereby greatly reducing the damage and interference to the natural environment, helping to maintain the original landform of the landslide and achieve harmonious coexistence with the surrounding environment. However, when calculating and analyzing the effect of this reinforcement, it is difficult to accurately simulate the reinforcement effect of the micro anti-sliding short column in the calculation and analysis because the size of the anti-sliding short column is much smaller than that of the landslide. For this reason, it is necessary to adopt appropriate analysis methods to deeply analyze the stress and displacement deformation of the landslide rock and soil after the anti-sliding short column reinforcement, so as to effectively guide the design and effect evaluation of the anti-sliding short column reinforcement.

[0003] The following methods are often used in the simulation and analysis of the anti-sliding short column reinforcement problem: ① Equivalent stiffness method. By introducing the "equivalent stiffness" parameter, the composite stiffness of the anti-sliding short column and the landslide soil is equivalent, thereby simplifying the model calculation and effectively simulating the reinforcement effect of the anti-sliding short column. This method has high calculation efficiency, but ignores the complex interactions such as slip, friction, and shear deformation between the anti-sliding short column and the soil. The simulation results of the spatial position distribution of the anti-sliding short column reinforcement may have large deviations and it is difficult to accurately reflect the local stability. ② Finite element substructure method. This method divides the entire structure into multiple substructures, sets dense grids on each substructure, and calculates the force and deformation of each substructure one by one, thereby realizing a fine simulation of the anti-sliding short column reinforcement problem. This method can more accurately capture the local interaction between the anti-sliding short column and the soil. Each substructure needs to be calculated separately. The dense grid division and the iterative calculation of the substructure greatly increase the calculation workload. The increase in degrees of freedom caused by the secondary subdivision also affects the efficiency of the stress field calculation. Therefore, there is an urgent need to develop a numerical simulation method that can accurately capture the local interaction between anti-sliding short columns and soil, and improve the computational efficiency of micro anti-sliding short column reinforcement problems. Summary of the invention

[0004] The purpose of the present invention is to overcome the above-mentioned shortcomings and provide an embedded finite element simulation method for sliding belt anti-sliding short columns for minimally invasive reinforcement of landslides, which can accurately calculate the stress and deformation of the anti-sliding short columns and the landslide soil, and can effectively simulate the internal stress and deformation of the landslide rock and soil under the action of the anti-sliding short columns, providing an important basis for the reinforcement design of the landslide anti-sliding short columns.

[0005] In order to solve the above-mentioned technical problems, the technical solution adopted by the present invention is: an embedded finite element simulation method of a sliding belt anti-sliding short column for minimally invasive reinforcement of a landslide, which comprises the following steps:

[0006] 1) Input the landslide rock and soil mesh, boundary conditions, material parameters and control parameter information;

[0007] 2) Generate the embedded grid of the anti-sliding short columns according to the spatial arrangement of the anti-sliding short columns and the grid of the landslide rock and soil mass;

[0008] 3) Calculate the equivalent node load column vector and load step increment;

[0009] 4) Calculate the landslide stress field and displacement field of the load step;

[0010] 5) Calculate the interaction force between the landslide and the anti-sliding short column;

[0011] 6) Calculate the equivalent node load of the anti-sliding short column on the landslide rock and soil grid;

[0012] 7) Calculate the load-step landslide stress field and displacement field after the anti-sliding short column reinforcement;

[0013] 8) Convergence judgment;

[0014] 9) Determine the end of the load step.

[0015] Furthermore, the step 1) specifically includes: inputting unit and node information of the landslide rock and soil mesh, giving landslide load boundary conditions and displacement boundary conditions, and inputting material parameters of the landslide rock and soil and anti-sliding short columns, and load step control parameters.

[0016] Furthermore, the step 2) specifically includes: according to the spatial position of the anti-sliding short column, finding the intersection of the anti-sliding short column and the landslide rock and soil grid, establishing an embedded anti-sliding short column finite element calculation grid, inputting the unit and node information of the anti-sliding short column grid, and recording the landslide rock and soil grid unit number that intersects with the anti-sliding short column unit.

[0017] Furthermore, the step 4) specifically includes: calculating the Gaussian point stress increment and node displacement increment of the landslide rock and soil body grid of the load step, and integrating them to obtain the total stress and total displacement.

[0018] Furthermore, the step 5) calculates the interaction force between the landslide and the anti-sliding short column, specifically:

[0019] 5.1) Calculate the displacement increment of the anti-sliding short column unit node according to the displacement increment of the grid node of the landslide rock and soil mass in the load step;

[0020] δ 柱 j，k =N ij δ 坡i，k (1);

[0021]

[0022]

[0023] In the formula, δ 柱 j，k is the displacement increment of the anti-sliding short column unit node; is the displacement increment of the grid node of the landslide rock mass calculated in step 4); ij N represents the distance from the landslide rock mass grid node to the anti-sliding short column unit node; ij represents the weight function; j represents the node of the anti-sliding short column unit; i represents the grid node of the landslide rock and soil body; k represents the direction, k = x, y, z, x, y, z are the directions of the coordinate system;

[0024] 5.2) Calculate the strain increment of the anti-sliding short column unit;

[0025] {ε}=[B]{δ} (4);

[0026] 5.3) Calculate the force acting on the anti-sliding short column unit by the rock and soil;

[0027] [σ]=E{ε}=E[B]{δ} (5);

[0028] F 柱，i =∫∫∫[B] T E[B]{δ}dV=W i [B] T E[B]{δ}A|J| (6);

[0029]

[0030] Where, {δ} is the displacement increment of the anti-sliding short column; {ε} is the strain increment of the anti-sliding short column; [B] is the geometric matrix; E is the elastic modulus of the anti-sliding short column; [σ] is the stress of the anti-sliding short column unit; F 柱，i W is the force acting on the anti-sliding short column unit; i is the weight of the Gaussian point. When there are two Gaussian points, W i =1; |J| is the Jacobian determinant of the anti-sliding short column unit; A is the cross-sectional area of ​​the anti-sliding short column, A = πr 2 ; L is the length of the anti-sliding short column;

[0031] 5.4) Calculate the force on the landslide rock and soil. The force on the landslide is equal to the force on the anti-slide short column, but in the opposite direction:

[0032] F 坡 =-F 柱，i (8).

[0033] Furthermore, the step 6) calculates the equivalent node load of the anti-sliding short column on the landslide rock and soil grid, specifically:

[0034] F j =ψ ij F 柱，i (9);

[0035]

[0036] In the formula, F j is the equivalent load on the jth node of the landslide rock and soil grid, ψ ij is the weight of the equivalent load distributed from the i-th Gauss point of the anti-sliding short column to the j-th node of the landslide rock and soil mass, l ij is the i-th Gauss point of the anti-sliding short column (x GS，i ,y GS，i , z GS,i ) and the jth node (x j ,y j , z j ) and NG is the number of Gaussian points of the anti-sliding short column.

[0037] Further, the step 8) specifically includes: substituting the load step landslide displacement field calculated in step 4) and the load step landslide displacement field with anti-sliding short column reinforcement calculated in step 7) into formula (12) to judge the convergence; if γ≤ζ, it is judged to be converged and the next load step calculation is performed; otherwise, it is judged not to be converged and the next iterative solution is performed in step 4) until convergence;

[0038]

[0039] In the formula, NP represents the number of nodes; is the load step displacement calculated in step 4), is the load step displacement calculated in step 7); ζ represents a very small positive number judged by convergence, and ζ=0.0001 is taken.

[0040] Furthermore, the step 9) specifically includes: if F i <F max , then proceed to the next load step calculation, otherwise, if F i =F max , the calculation ends.

[0041] Compared with the existing methods, the beneficial effects of the present invention are as follows:

[0042] 1. It can accurately simulate the local interaction force between the anti-sliding short column and the soil, as well as the reinforcement effect of the anti-sliding short column position and direction on the landslide rock and soil, effectively reflect the actual reinforcement effect of the anti-sliding short column, and provide a reliable basis for the evaluation and design of the landslide anti-sliding short column reinforcement effect.

[0043] 2. The anti-sliding short column model is embedded in the three-dimensional finite element grid. There is no need to set a high-density grid around the anti-sliding short column, which reduces the complexity of grid division and improves modeling efficiency and calculation speed.

[0044] 3. The embedded finite element simulation method can adapt to complex geological conditions. While maintaining the consistency of the global structure, it can analyze the local stress distribution and the stress state of the anti-sliding short column, thereby improving the accuracy and operability of the calculation results.

[0045] 4. The present invention can accurately calculate the stress and deformation of anti-slip short columns and landslide soil, and can effectively simulate the internal stress and deformation of landslide rock and soil under the action of anti-slip short columns. It has high calculation accuracy and efficiency, and provides an important basis for the reinforcement design of landslide anti-slip short columns. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a program flow chart of the numerical calculation method of the present invention;

[0047] Figure 2 is a schematic diagram of an embedded finite element mesh of an embedded anti-sliding short column;

[0048] Figure 3 It is a schematic diagram of Gauss point distribution of equivalent load of embedded anti-sliding short column;

[0049] Figure 4 It is a schematic diagram of the model boundary condition constraints;

[0050] Figure 5 It is a comparison diagram of horizontal displacement distribution before and after minimally invasive reinforcement of the landslide. DETAILED DESCRIPTION

[0051] The present invention is further described in detail below with reference to the embodiments.

[0052] Example 1: Figure 1 As shown, a method for simulating the sliding belt anti-sliding short column embedded finite element of minimally invasive reinforcement of landslides comprises the following steps:

[0053] 1) Input the information of landslide rock and soil mesh, boundary conditions, material parameters and control parameters;

[0054] 2) Generate the embedded grid of the anti-sliding short columns according to the spatial arrangement of the anti-sliding short columns and the grid of the landslide rock and soil mass;

[0055] 3) Calculate the equivalent node load column vector and load step increment;

[0056] 4) Calculate the landslide stress field and displacement field of the load step;

[0057] 5) Calculate the interaction force between the landslide and the anti-sliding short column;

[0058] 6) Calculate the equivalent node load of the anti-sliding short column on the landslide rock and soil grid;

[0059] 7) Calculate the stress field and displacement field of the load-step landslide reinforced with anti-sliding short columns;

[0060] 8) Convergence judgment;

[0061] 9) Determine the end of the load step.

[0062] Furthermore, the step 1) specifically includes: inputting the unit and node information of the landslide rock and soil mesh, giving the landslide load boundary conditions and displacement boundary conditions, and inputting the material parameters of the landslide rock and soil and the anti-slide short column, load step length and other control parameters.

[0063] Furthermore, the step 2) is specifically as follows: according to the spatial position of the anti-sliding short column, find the intersection of the anti-sliding short column and the landslide soil grid, establish an embedded anti-sliding short column finite element calculation grid, input the unit and node information of the anti-sliding short column grid, and record the landslide rock and soil grid unit number that intersects with the anti-sliding short column unit.

[0064] Furthermore, the step 4) is specifically as follows: calculating the Gaussian point stress increment and node displacement increment of the landslide rock and soil body grid of the load step, and integrating them to obtain the total stress and total displacement.

[0065] Furthermore, the step 5) is specifically as follows:

[0066] 1) According to the node displacement increment of the load step landslide, calculate the displacement increment of the anti-sliding short column unit node;

[0067] δ 柱 j，k =N ij δ 坡 i，k (1)

[0068]

[0069] In the formula, δ 柱 j，k is the displacement increment of the anti-sliding short column unit node; is the displacement increment of the grid node of the landslide rock mass calculated in step 4); ij N represents the distance from the landslide rock mass grid node to the anti-sliding short column unit node; ijrepresents the weight function; j represents the anti-sliding short column unit node; i represents the landslide rock and soil grid node; k represents the direction, k = x, y, z, x, y, z are the coordinates.

[0070] 2) Calculate the strain increment of the anti-sliding short column unit;

[0071] {ε}=[B]{δ} (4)

[0072] 3) Calculate the force acting on the anti-sliding short column unit by the rock and soil;

[0073] [σ]=E{ε}=E[B]{δ} (5)

[0074] F 柱，i =∫∫∫[B] T E[B]{δ}dV=W i [B] T E[B]{δ}A|J| (6)

[0075]

[0076] Where, {δ} is the displacement increment of the anti-sliding short column; {ε} is the strain increment of the anti-sliding short column; [B] is the geometric matrix; E is the elastic modulus of the anti-sliding short column; [σ] is the stress of the anti-sliding short column unit; F 柱，i W is the force acting on the anti-sliding short column unit; i is the weight of the Gaussian point. When there are two Gaussian points, W i =1; |J| is the Jacobian determinant of the anti-sliding short column unit; A is the cross-sectional area of ​​the anti-sliding short column, A = πr 2 ; L is the length of the anti-sliding short column.

[0077] 4) Calculate the force on the landslide rock and soil, which is equal in magnitude to the force on the anti-sliding short column but opposite in direction.

[0078] F 边坡 =-F 柱，i (8)

[0079] Furthermore, the step 6) is specifically as follows: firstly, the weight of the equivalent load ψ is calculated by equations (10) and (11): ij , and then solve the equivalent load F according to equation (9): j .

[0080] F j =ψ ij F 柱，i (9)

[0081]

[0082]

[0083] In the formula, F j is the equivalent load on the jth node of the landslide rock and soil grid, ψ ij is the weight of the equivalent load distributed from the i-th Gauss point of the anti-sliding short column to the j-th node of the landslide rock and soil mass, l ij is the i-th Gauss point of the anti-sliding short column (x GS，i ,y GS，i , z GS,i ) and the jth node (x j ,y j , z j ) and NG is the number of Gaussian points of the anti-sliding short column.

[0084] Furthermore, the step 8) is specifically as follows: the load-step landslide displacement field calculated in step 4) and the load-step landslide displacement field with anti-sliding short column reinforcement calculated in step 7) are substituted into formula (12) to judge the convergence. If γ≤ζ, it is judged to be converged and the next load step calculation is performed. Otherwise, it is judged not to be converged and the next iterative solution is performed in step 4) until convergence.

[0085]

[0086] In the formula, NP represents the number of nodes; is the load step displacement calculated in step 4), is the load step displacement calculated in step 7); ζ represents a very small positive number judged by convergence, and ζ=0.0001 is taken.

[0087] Furthermore, the step 9) is specifically as follows: if F i <F max , then proceed to the next load step calculation, otherwise, if F i =F max , the calculation ends.

[0088] Example 2: Combined with a typical landslide example, an embedded anti-sliding short column numerical simulation is carried out to further illustrate the embedded finite element simulation method of the sliding belt anti-sliding short column for minimally invasive reinforcement of landslide proposed by the present invention, specifically:

[0089] 1) Input the information of landslide rock and soil mesh, boundary conditions, material parameters and control parameters:

[0090] The calculation model of the embodiment is a landslide rock and soil body with a length of 98.80 meters, a width of 9.00 meters and a height of 55.00 meters. The calculation grid of the landslide rock and soil body and the calculation grid of the anti-sliding short column are relatively independent, the total number of the calculation grid units of the landslide rock and soil body is 27351, the total number of the nodes is 31110, the total number of the anti-sliding short column grid units is 21, and the total number of the nodes is 22.

[0091] Boundary conditions: such as Figure 4 Normal constraints are set at the bottom, front and back, and left and right surfaces of the landslide.

[0092] Material parameters: The elastic modulus of the landslide bedrock is 25000MPa, the Poisson's ratio is 0.167, and the bulk density is 24KN / m 3 , tensile strength is 2MPa, cohesion is 1MPa, internal friction angle is 50°; sliding belt elastic modulus is 2.5MPa, Poisson's ratio is 0.367, and bulk density is 19KN / m 3 , cohesion is 0.01MPa, internal friction angle is 20°; sliding body elastic modulus is 25MPa, Poisson's ratio is 0.23, and bulk density is 20KN / m 3 , cohesion is 0.1MPa, internal friction angle is 40°; the bulk density of the anti-slip short column is 25KN / m 3 , elastic modulus is 35000MPa, Poisson's ratio is 0.167, and cross-sectional area is 0.0123m 2 ;

[0093] 2) Numerical calculation results of landslide rock and soil after the slide belt is reinforced with anti-sliding short columns:

[0094] Figure 5 This is a comparison diagram of horizontal displacement distribution before and after minimally invasive reinforcement of the landslide. Figure 5 (a) is the horizontal displacement distribution diagram of the rock mass inside the landslide without anti-sliding short pillars. Figure 5 (b) is the distribution diagram of the internal horizontal displacement of the landslide rock mass with anti-sliding short columns. As can be seen from the figure, the maximum horizontal displacement is located at the top of the landslide, and the minimum is located at the bedrock of the landslide. The horizontal displacement gradually increases from the sliding zone to the slope surface. After the anti-sliding short column reinforcement, the horizontal displacement of the rock mass at the anti-sliding short column is significantly reduced. It can be seen that the anti-sliding short column plays a good supporting and reinforcing role, indicating that this method can better simulate the internal displacement changes of the landslide rock mass under the reinforcement of the anti-sliding short column.

[0095] The above embodiments are only preferred technical solutions of the present invention and should not be regarded as limiting the present invention. The protection scope of the present invention shall be the technical solutions recorded in the claims, including equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. An embedded finite element simulation method for anti-sliding short columns in a sliding belt for minimally invasive reinforcement of landslides, characterized in that: It includes the following steps: 1) Input the landslide rock and soil mesh, boundary conditions, material parameters and control parameter information; 2) Generate the embedded grid of the anti-sliding short columns according to the spatial arrangement of the anti-sliding short columns and the grid of the landslide rock and soil mass; 3) Calculate the equivalent node load column vector and load step increment; 4) Calculate the landslide stress field and displacement field of the load step; 5) Calculate the interaction force between the landslide and the anti-sliding short column; 6) Calculate the equivalent node load of the anti-sliding short column on the landslide rock and soil grid; 7) Calculate the load-step landslide stress field and displacement field after the anti-sliding short column reinforcement; 8) Convergence judgment; 9) Determine the end of the load step.

2. The method for simulating the sliding belt anti-sliding short column embedded finite element of the minimally invasive reinforcement of landslide according to claim 1 is characterized by: The step 1) specifically includes: inputting unit and node information of the landslide rock and soil mesh, giving landslide load boundary conditions and displacement boundary conditions, and inputting material parameters of the landslide rock and soil and anti-slide short columns and load step control parameters.

3. The method for simulating the sliding belt anti-sliding short column embedded finite element of the minimally invasive reinforcement of landslide according to claim 1 is characterized by: The step 2) specifically includes: finding the intersection of the anti-sliding short column and the landslide rock and soil grid according to the spatial position of the anti-sliding short column, establishing an embedded anti-sliding short column finite element calculation grid, inputting the unit and node information of the anti-sliding short column grid, and recording the landslide rock and soil grid unit number intersecting with the anti-sliding short column unit.

4. The method for simulating the sliding belt anti-sliding short column embedded finite element of the minimally invasive reinforcement of landslide according to claim 1 is characterized by: The step 4) specifically includes: calculating the Gaussian point stress increment and node displacement increment of the landslide rock and soil body grid in the load step, and integrating them to obtain the total stress and total displacement.

5. The method for simulating the sliding belt anti-sliding short column embedded finite element of the minimally invasive reinforcement of landslide according to claim 1 is characterized by: The step 5) calculates the interaction force between the landslide and the anti-sliding short column, specifically: 5.1) Calculate the displacement increment of the anti-sliding short column unit node according to the displacement increment of the grid node of the landslide rock and soil mass in the load step; d 柱 j，k =N ij d 坡 i，k (1); In the formula, δ 柱 j，k is the displacement increment of the anti-sliding short column unit node; is the displacement increment of the grid node of the landslide rock mass calculated in step 4); ij N represents the distance from the landslide rock mass grid node to the anti-sliding short column unit node; ij represents the weight function; j represents the node of the anti-sliding short column unit; i represents the grid node of the landslide rock and soil body; k represents the direction, k = x, y, z, x, y, z are the directions of the coordinate system; 5.2) Calculate the strain increment of the anti-sliding short column unit; {ε}=[B]{δ} (4); 5.3) Calculate the force acting on the anti-sliding short column unit by the rock and soil; [σ]=E{ε}=E[B]{δ} (5); F 柱，i =∫∫∫[B] T E[B]{δ}dV=W i [B] T E[B]{δ}A|J| (6); Where, {δ} is the displacement increment of the anti-sliding short column; {ε} is the strain increment of the anti-sliding short column; [B] is the geometric matrix; E is the elastic modulus of the anti-sliding short column; [σ] is the stress of the anti-sliding short column unit; F 柱，i W is the force acting on the anti-sliding short column unit; i is the weight of the Gaussian point. When there are two Gaussian points, W i =1; |J| is the Jacobian determinant of the anti-sliding short column unit; A is the cross-sectional area of ​​the anti-sliding short column, A = πr 2 ; L is the length of the anti-sliding short column; 5.4) Calculate the force on the landslide rock and soil. The force on the landslide is equal to the force on the anti-slide short column, but in the opposite direction: F 坡 =-F 柱，i (8)。 6. The method for simulating the sliding belt anti-sliding short column embedded finite element of the minimally invasive reinforcement of landslide according to claim 1 is characterized by: The step 6) calculates the equivalent node load of the anti-sliding short column on the landslide rock and soil grid, specifically: F j =ψ ij F 柱，i (9); In the formula, F j is the equivalent load on the jth node of the landslide rock and soil grid, ψ ij is the weight of the equivalent load distributed from the i-th Gauss point of the anti-sliding short column to the j-th node of the landslide rock and soil mass, l ij is the i-th Gauss point of the anti-sliding short column (x GS，i ,y GS，i , z GS,i ) and the jth node (x j ,y j , z j ) and NG is the number of Gaussian points of the anti-sliding short column.

7. The method for simulating the sliding belt anti-sliding short column embedded finite element of the minimally invasive reinforcement of landslide according to claim 1 is characterized by: The step 8) specifically includes: substituting the load step landslide displacement field calculated in step 4) and the load step landslide displacement field with anti-sliding short column reinforcement calculated in step 7) into formula (12) to judge the convergence. If γ≤ζ, it is judged to be converged and the next load step calculation is performed. Otherwise, it is judged not to be converged and the next step of iterative solution is performed in step 4) until convergence. In the formula, NP represents the number of nodes; is the load step displacement calculated in step 4), is the load step displacement calculated in step 7); ζ represents a very small positive number judged by convergence, and ζ=0.0001 is taken.

8. The method for simulating the sliding belt anti-sliding short column embedded finite element of the minimally invasive reinforcement of landslide according to claim 1 is characterized by: The step 9) specifically includes: if F i <F max , then proceed to the next load step calculation, otherwise, if F i =F max , the calculation ends.

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