Three-dimensional finite element simulation method for complex slope excavation unloading process

Abstract

The invention discloses a three-dimensional finite element simulation method for a complex slope excavation unloading process, which comprises the following steps of: 1) constructing a three-dimensional model of a complex slope, and establishing a finite element grid; 2) inputting boundary conditions of the model and material parameter information of each stratum; 3) calculating and simulating an initial stress field of the slope before excavation; (4) according to the initial stress field, the unloading load of the slope excavation part is calculated; (5) finite element calculation is conducted on stress deformation of the excavated slope; according to the method, the high-precision three-dimensional finite element model is established, various material parameters and actual boundary conditions are combined, the stress change and the unloading effect of the slope in the excavation process are simulated, the stress redistribution in the unloading process is accurately reproduced, the prediction precision of local instability and stress concentration areas is improved, and the prediction accuracy of the slope is improved. Therefore, a scientific basis is provided for safety assessment of slope excavation.

Description

Technical Field

[0001] The invention relates to the field of hydraulic and geotechnical engineering, and in particular to a three-dimensional finite element simulation method for a complex slope excavation and unloading process. Background Art

[0002] In modern civil engineering, transportation and mining engineering, slope excavation has become the core content of infrastructure construction, especially in engineering fields such as roads, railways, tunnels, mines and dams. The stability of the slope is directly related to the quality and safety of the project. As the excavation operation proceeds layer by layer, the stress field of the soil or rock mass changes significantly, the original stress state is broken and redistributed, and an unloading effect occurs. The stress redistribution caused by unloading often increases the tensile stress on the surface of the slope, and the shear stress in the local area may exceed the strength limit of the material, thereby causing instability. Based on this, in-depth research on the unloading effect of excavation is of great significance for scientifically evaluating and ensuring the long-term stability of the slope.

[0003] At present, the commonly used methods for numerical simulation of slope excavation mainly include the following two methods: ① Birth and death unit method: In finite element analysis, specific units are "activated" or "killed" to simulate the layer-by-layer deletion or addition of soil or rock during excavation. However, the birth and death unit method may cause discontinuous displacement fields in local areas when simulating slope excavation, especially in stress concentration areas, which may produce large calculation errors and affect the accuracy of local stress distribution. ② Zero stiffness method: The unloading state after excavation is simulated by setting the stiffness coefficients of certain units or nodes in the model to zero. Since the introduction of zero stiffness units will cause calculation discontinuity in local areas of the model, it may affect the reliability of the overall mechanical behavior. Under complex working conditions, especially when multiple failure modes coexist, the zero stiffness method may produce large errors and cannot accurately reflect the mechanical characteristics of the slope after excavation. Although these methods can be used to simulate slope excavation to a certain extent, there are still some limitations when dealing with complex slope excavation conditions, especially the accurate prediction of stress redistribution and local instability needs to be further improved. Summary of the invention

[0004] The purpose of the present invention is to overcome the above-mentioned shortcomings and provide a three-dimensional finite element simulation method for the complex slope excavation unloading process, aiming to solve the problems of insufficient analysis of slope excavation unloading effect and inaccurate prediction of stress redistribution in the prior art.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: a three-dimensional finite element simulation method for the complex slope excavation unloading process, which comprises the following steps: Step 1) construct a three-dimensional model of the complex slope and establish a finite element mesh; Step 2), input the boundary conditions of the model and the material parameter information of each formation; Step 3), calculate and simulate the initial stress field of the slope before excavation; Step 4), calculate the unloading load of the excavated part of the slope according to the initial stress field; Step 5) Perform finite element calculation on the slope stress and deformation after excavation.

[0006] Preferably, the step 1) further comprises: performing a plane scan on the slope, outputting mesh node data of the plane projection of the slope, obtaining three-dimensional mesh node coordinate data by inverse distance interpolation according to the slope interface elevation point data, and generating a three-dimensional finite element model.

[0007] Preferably, the step 2) further comprises, in the established finite element model, given known pore water pressure and boundary displacement constraint boundary conditions, inputting the bulk density, elastic modulus, Poisson's ratio, cohesion, internal friction angle, tensile strength mechanical parameters of each formation material.

[0008] Preferably, the step 3) further comprises the following steps: Step 3.1): In the established finite element model, apply the deadweight load of each formation material; Step 3.2): Apply displacement boundary conditions to the rear and front edges of the slope to simulate the extrusion deformation of the slope caused by geological tectonic action; Step 3.3): Use the finite element program to calculate the corresponding internal stress field of the slope generated by the applied displacement boundary conditions; Step 3.4): Calculate the root mean square error by comparing the measured ground stress at the slope measuring point with the initial principal stress calculated at the corresponding point : ; In the formula, is the maximum stress value obtained by current calculation; is the maximum stress value at the measured point; is the minimum stress value obtained by current calculation; is the minimum stress value at the measured point; is the total number of computing nodes; like , then convergence, go to step 3.5); otherwise, increase the displacement values ​​of the rear edge and the front edge of the slope, return to step 3.3) and recalculate; Step 3.5): The calculated stress field is used as the initial stress field of the slope, including self-weight stress and structural stress.

[0009] Preferably, the step 4) further comprises the following steps: Step 4.1): Extract the Gaussian stress of the unit in the slope excavation part. In the three-dimensional finite element model, determine the stress of the Gaussian point of the unit in the unloading area. ; Step 4.2): Based on the initial stress of the Gaussian point, the volume integral of the Gaussian point is performed to obtain the magnitude of the resultant force on the Gaussian point inside the unit: ; In the formula, , Represents the index of different Gaussian points in different cells; is the force on the Gauss point in the unit; represents the gradient of the shape function; is the weight of the i-th Gaussian point; is the weight of the jth Gaussian point; is the gradient matrix of Gaussian points; is the Jacobian determinant, which is used to transform the integral of the local coordinate system into the integral of the global coordinate system and is related to the geometry of the unit; Step 4.3): According to the shape function of each Gauss point, the forces of all Gauss points in a single unit are applied to the equivalent nodes of the slope excavation part to obtain the equivalent load of each excavation unit at the node : ; In the formula, is the Gaussian point shape function, is the coordinate of the Gaussian point in the local coordinate system. For the eight-node element, when the 2×2×2 Gaussian integral is used, the coordinate positions of each point are (±0.57735, ±0.57735, ±0.57735); Step 4.4): For the entire 3D finite element model, sum all the excavation mesh elements to get the equivalent load of the node : ; In the formula, is the total number of excavation units in the model, which means summing all the unit pairs in the excavation area; Step 4.5): Get the equivalent node excavation unloading load, and finally reverse the sign of the equivalent node load in the slope excavation area, so that the unloading load is applied to the equivalent node to get the force : .

[0010] Preferably, the step 5) further comprises: solving the equilibrium differential equation again according to the boundary conditions and loads of the model grid units after excavation and the calculated unloading load of the excavation area, and calculating the stress distribution and corresponding displacement deformation after excavation.

[0011] Beneficial effects of the present invention: 1. The present invention can dynamically capture the evolution of the stress field and deformation field of the slope during the excavation process, and accurately reflect the stress redistribution of the slope under complex geological conditions and the influence of stratum deformation on the unloading process; this method has high calculation accuracy, provides a more comprehensive and effective scientific basis for complex slope excavation projects, and significantly improves the reliability of slope stability assessment.

[0012] 2. The calculation of the initial geostress field of the present invention comprehensively considers the dual effects of self-weight stress and tectonic stress, making the simulation closer to the actual working conditions; this method can more accurately reflect the influence of the initial stress state of the slope on the stress redistribution and deformation after unloading during the excavation process, thereby improving the accuracy and reliability of the slope stability assessment.

[0013] 3. The finite element simulation method provided by the present invention does not require complex unit activation and removal operations, which significantly simplifies the calculation process while ensuring calculation accuracy; this method effectively improves calculation efficiency and reduces processing complexity, and is suitable for engineering scenarios such as complex slope excavation, ensuring a balance between accuracy and efficiency.

[0014] 4. The present invention solves the problems of insufficient analysis of the unloading effect of slope excavation and inaccurate prediction of stress redistribution in the prior art; this method establishes a high-precision three-dimensional finite element model, combines multiple material parameters and actual boundary conditions, simulates the stress changes and unloading effects of the slope during the excavation process, and improves the prediction accuracy of local instability and stress concentration areas by accurately reproducing the stress redistribution during the unloading process, thereby providing a scientific basis for the safety assessment of slope excavation. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of a three-dimensional finite element simulation method for the unloading process of complex slope excavation; Figure 2 It is a schematic diagram of the boundary constraint conditions of the slope model; Figure 3 It is the maximum principal stress distribution diagram before slope excavation; Figure 4 It is the minimum principal stress distribution diagram before slope excavation; Figure 5 It is the displacement deformation distribution diagram of slope excavation in X direction; Figure 6 This is the displacement deformation distribution diagram of the slope excavation in the Z direction. DETAILED DESCRIPTION

[0016] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0017] Example 1: Figure 1 As shown, a three-dimensional finite element simulation method for the complex slope excavation unloading process includes the following steps: (1) Construct a three-dimensional model of a complex slope and create a finite element mesh; (2) Input the model’s boundary conditions and material parameters of each formation; (3) Calculate the initial stress field of the slope; (4) Calculate the unloading load of the excavated part of the slope based on the initial stress field; (5) Perform finite element calculation on the slope stress and deformation after excavation.

[0018] Furthermore, the step (1) is specifically as follows: performing a plane scan on the slope, establishing grid node data of the plane projection of the slope, obtaining three-dimensional grid node coordinate data by inverse distance interpolation based on the slope interface elevation point data, generating a three-dimensional finite element model, and establishing grid units of the three-dimensional finite element model.

[0019] Furthermore, the step (2) is specifically as follows: in the three-dimensional finite element model, the boundary conditions of known pore water pressure and boundary displacement constraints are applied, and the mechanical parameters such as bulk density, elastic modulus, Poisson's ratio, cohesion, internal friction angle, tensile strength, etc. of the formation material are input to ensure that the mechanical properties of each formation in the model can accurately reflect the stress displacement deformation during the excavation process.

[0020] Furthermore, the step (3) is specifically as follows: the initial stress field of the slope, where the stress mainly comes from the self-weight stress caused by the weight of the formation material and the tectonic stress caused by the geological tectonic activity, is calculated as follows: 1) Apply the deadweight load of each formation material to the established finite element model; 2) Apply displacement boundary conditions to the rear and front edges of the slope to simulate the extrusion deformation of the slope caused by geological tectonic action; 3) Use the finite element program to calculate the corresponding internal stress field of the slope generated by the applied displacement boundary conditions; 4) By comparing the measured ground stress at each measuring point on the slope with the initial principal stress calculated at the corresponding point, the root mean square error control accuracy is calculated: ; If the calculation result , it converges and goes to the next step; otherwise, it does not converge, increase the displacement values ​​of the rear and front edges of the slope, and return to 3) to recalculate; 5) The calculated stress field is used as the initial stress field of the slope, including self-weight stress and structural stress.

[0021] Furthermore, the step (4) is specifically as follows: during the slope excavation process, since the deadweight of the soil and the external load no longer act on the excavation area, the stress field will change, forming an unloading load. The calculation steps are as follows: 1) Extract the Gaussian point stress of the unit in the excavated part of the slope. In the three-dimensional finite element model, determine the Gaussian point stress of the unit in the excavated unloading area. .

[0022] 2) Based on the initial stress of the Gaussian point, the volume integral of the Gaussian point is performed to obtain the resultant force on the Gaussian point inside the unit : ; 3) According to the force on each Gauss point, the force of all Gauss points in a single unit is combined with the shape function to be distributed to the equivalent nodes of the slope excavation part, and the equivalent load on the node of each excavation unit is obtained. : ; In the formula, is the shape function of the Gaussian point. For the eight-node element, when the 2×2×2 Gaussian integral is used, the coordinate positions of each Gaussian point in the local coordinate system are (±0.57735, ±0.57735, ±0.57735). Taking node 1 as an example, the shape function values ​​of each Gaussian point are calculated as follows: For node 1, the shape function value , Substituting the coordinates of each Gaussian point into the shape function values, they are:

[0023] Accordingly, for node 2, the shape function value of the Gaussian point is ; For node 3, the shape function value of the Gaussian point is ; For node 4, the shape function value of the Gaussian point is ; For node 5, the shape function value of the Gaussian point is ; For node 6, the shape function value of the Gaussian point is ; For node 7, the shape function value of the Gauss point is ; For node 8, the shape function value of the Gaussian point is , By substituting the coordinates of the Gaussian points respectively, the shape function values ​​of each Gaussian point for each node can be calculated.

[0024] 4) For the entire 3D finite element model, sum all the excavation mesh elements to obtain the node equivalent load : ; 5) Obtain the excavation unloading load on the equivalent node, and finally reverse the sign of the equivalent node load in the slope excavation area to obtain the force applied by the unloading load to the equivalent node in the excavation area. : ; Furthermore, the step (5) is specifically as follows: according to the boundary conditions and loads of the model grid units after excavation and the calculated unloading load of the excavation area, the equilibrium differential equation is solved again to calculate the stress distribution and corresponding displacement deformation after excavation.

[0025] Embodiment 2: A three-dimensional finite element simulation method for the excavation and unloading process of a complex slope proposed by the present invention is further described in combination with a typical complex slope, comprising the following steps: 1) Construct a three-dimensional model of a complex slope and establish a finite element mesh; The calculation model of the embodiment adopts a multi-layered complex slope with a bottom length of 98.8m, a width of 9.0m, and a height of 55.0m. The total number of grid units for slope calculation is 21771, and the total number of nodes is 24880.

[0026] 2) Input the model’s boundary conditions, material parameters of each layer, and other information; The bottom surface and four side surfaces of the slope have no displacement, and normal constraints are given respectively, such as Figure 2 As shown in the figure, the elastic modulus, Poisson’s ratio, bulk density, tensile strength, cohesion, and internal friction angle of the material are input for each stratum of the slope, which are as follows: ① The elastic modulus of the slope bedrock is 2.5×10 4 MPa, Poisson's ratio is 0.167, and bulk density is 24kN / m 3 , tensile strength is 2MPa, cohesion is 1MPa, internal friction angle is 50°; ② The elastic modulus of the slope sliding zone soil is 2.5MPa, Poisson's ratio is 0.367, and bulk density is 19kN / m 3 , tensile strength is 2MPa, cohesion is 0.01MPa, internal friction angle is 20°; ③ The elastic modulus of the slope soil is 25MPa, Poisson's ratio is 0.23, and the bulk density is 20kN / m 3, tensile strength is 2MPa, cohesion is 0.1MPa, and internal friction angle is 40°; ④ The elastic modulus of the soil in the slope surface to be excavated is 30MPa, Poisson's ratio is 0.13, and bulk density is 20kN / m 3 , tensile strength is 2MPa, cohesion is 1MPa, and internal friction angle is 40°.

[0027] 3) Calculate the initial stress field of the slope; Calculate the initial stress field before slope excavation, such as Figure 3 , 4 As shown in the figure, they are the maximum principal stress distribution diagram and the minimum principal stress distribution diagram before slope excavation. It can be seen that in the slope, due to the influence of factors such as soil self-weight and pore water pressure, the maximum principal stress and the minimum principal stress increase with the increase of depth, and the maximum principal stress changes more obviously.

[0028] 4) Finite element solution results of slope stress, displacement and deformation after simulated excavation; After simulating the slope excavation, the slope stress displacement deformation results were calculated, and the displacement deformation distribution diagram of the complex slope calculated in this example after excavation was drawn, as shown in Figure 2. Figure 5 , 6 As shown in the figure, the displacement and deformation of the slope in the X and Z directions after excavation, respectively. It can be seen that in the finite element simulation of this slope excavation, the soil displacement in the X direction shows a shrinkage, while in the Z direction it shows a pop-up phenomenon. After the slope is excavated, the soil loses part of its original support, resulting in a redistribution of the stress field at the edge of the excavation area. As the slope is gradually excavated, the horizontal stress of the soil in the X direction gradually decreases, and the soil in the unexcavated area shrinks inward to cope with the adjustment of the overall stress of the slope. In the Z direction, since the vertical compressive stress originally received is significantly reduced after excavation, the soil shows an upward displacement, which is manifested as the soil popping out in the Z direction. The simulation calculation results are consistent with the displacement and deformation of the actual slope after excavation and unloading.

[0029] 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. A three-dimensional finite element simulation method for the unloading process of complex slope excavation, characterized by: It includes the following steps: Step 1) construct a three-dimensional model of the complex slope and establish a finite element mesh; Step 2), input the boundary conditions of the model and the material parameter information of each formation; Step 3), calculate and simulate the initial stress field of the slope before excavation; Step 4), calculate the unloading load of the excavated part of the slope according to the initial stress field; Step 5) Perform finite element calculation on the slope stress and deformation after excavation.

2. The three-dimensional finite element simulation method for the complex slope excavation and unloading process according to claim 1 is characterized by: The step 1) further includes: performing a plane scan on the slope, outputting grid node data of the plane projection of the slope, obtaining three-dimensional grid node coordinate data through inverse distance interpolation according to the elevation point data of the slope interface, and generating a three-dimensional finite element model.

3. The three-dimensional finite element simulation method for the complex slope excavation and unloading process according to claim 1 is characterized by: The step 2) further includes, in the established finite element model, given the known pore water pressure and boundary displacement constraint boundary conditions, inputting the bulk density, elastic modulus, Poisson's ratio, cohesion, internal friction angle, and tensile strength mechanical parameters of each formation material.

4. The three-dimensional finite element simulation method for the complex slope excavation and unloading process according to claim 1 is characterized by: The step 3) specifically also includes the following steps: Step 3.1): In the established finite element model, apply the deadweight load of each formation material; Step 3.2): Apply displacement boundary conditions to the rear and front edges of the slope to simulate the extrusion deformation of the slope caused by geological tectonic action; Step 3.3): Use the finite element program to calculate the corresponding internal stress field of the slope generated by the applied displacement boundary conditions; Step 3.4): Calculate the root mean square error by comparing the measured ground stress at the slope measuring point with the initial principal stress calculated at the corresponding point : ； In the formula, is the maximum stress value obtained by current calculation; is the maximum stress value at the measured point; is the minimum stress value obtained by current calculation; is the minimum stress value at the measured point; is the total number of computing nodes; like , then convergence, go to step 3.5); otherwise, increase the displacement values ​​of the rear edge and the front edge of the slope, return to step 3.3) and recalculate; Step 3.5): The calculated stress field is used as the initial stress field of the slope, including self-weight stress and structural stress.

5. The three-dimensional finite element simulation method for the complex slope excavation and unloading process according to claim 1 is characterized by: The step 4) specifically also includes the following steps: Step 4.1): Extract the Gaussian stress of the unit in the slope excavation part. In the three-dimensional finite element model, determine the stress of the Gaussian point of the unit in the unloading area. ; Step 4.2): Based on the initial stress of the Gaussian point, perform volume integration on the Gaussian point to obtain the magnitude of the resultant force on the Gaussian point inside the unit: ； In the formula, , Represents the index of different Gaussian points in different cells; is the force on the Gauss point in the unit; represents the gradient of the shape function; is the weight of the i-th Gaussian point; is the weight of the j-th Gaussian point; is the gradient matrix of Gaussian points; is the Jacobian determinant, which is used to transform the integral of the local coordinate system into the integral of the global coordinate system and is related to the geometric shape of the unit; Step 4.3): According to the shape function of each Gaussian point, the forces of all Gaussian points in a single unit are applied to the equivalent nodes of the slope excavation part to obtain the equivalent load of each excavation unit at the node : ； In the formula, is the Gaussian point shape function, is the coordinate of the Gaussian point in the local coordinate system. For the eight-node element, when the 2×2×2 Gaussian integral is used, the coordinate positions of each point are (±0.57735, ±0.57735, ±0.57735); Step 4.4): For the entire 3D finite element model, sum all the excavation mesh elements to get the node equivalent load : ； In the formula, is the total number of excavation units in the model, which means summing all the unit pairs in the excavation area; Step 4.5): Get the equivalent node excavation unloading load, and finally reverse the sign of the equivalent node load in the slope excavation area, so that the unloading load is applied to the equivalent node to get the force : 。 6. The three-dimensional finite element simulation method for the complex slope excavation and unloading process according to claim 1 is characterized by: The step 5) further includes: solving the equilibrium differential equation again according to the boundary conditions and loads of the model grid units after excavation and the calculated unloading load of the excavation area, and calculating the stress distribution and corresponding displacement deformation after excavation.

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