Topological optimization method for arrangement mode of supports in foundation pit

Abstract

The invention provides a topological optimization method for a foundation pit inner support arrangement mode. The topological optimization method comprises the following steps that 1, a foundation pit inner support initial structure model to be optimized is established in ABAQ US finite element software; 2, defining a design area and design variables; 3, defining an objective function and constraint conditions; step 4, inputting a load value, and setting a constraint condition for iterative optimization; and step 5, ending the optimization when the optimization judgment condition is met, returning to the step 4 to continue the optimization when the optimization judgment condition is not met, and ending the optimization until the optimization judgment condition is met. According to the method, ABAQUS finite element software is utilized to introduce a progressive structure optimization algorithm to explore the optimal arrangement mode of the supports in the foundation pit, strain energy is minimized by optimizing distribution and shapes of materials in continuum topological optimization, the structure optimization algorithm can perform iterative search in a design domain, and the optimal arrangement mode of the supports in the foundation pit is optimized by adjusting the positions and shapes of the materials. And gradually searching an optimal solution. And finally, the optimal foundation pit inner support arrangement mode with the minimum strain energy is obtained.

Description

Technical Field

[0001] The invention relates to the technical field of underground engineering, and in particular to a topological optimization method for a support arrangement mode in a foundation pit. Background Art

[0002] Structural topology optimization is a mathematical method that aims to automatically design the material or structure layout to maximize its performance. This method is particularly important in engineering design because it can determine the optimal structural shape and material distribution during the design phase to meet specific performance criteria while taking into account material usage and cost-effectiveness. This method is often used in engineering, aerospace, automotive manufacturing, construction and other fields to improve the efficiency, strength, stability and weight reduction of structures. The goal of continuum topology optimization is to minimize strain energy by optimizing the distribution and shape of materials. The optimization algorithm iteratively searches within the design domain, gradually finding the optimal solution by adjusting the position and shape of the material. The resulting structure has the minimum strain energy while satisfying the given loading conditions and constraints.

[0003] Topology optimization algorithms are also widely used in the field of building structure design to improve structural design. With the help of topology optimization algorithms, structures such as truss structures, truss-type brackets, and nonlinear RC shear walls can all achieve the effect of reducing structural mass and improving performance. Topology optimization methods can also be innovatively introduced into foundation pit projects to explore the optimal layout of internal supports in support structures.

[0004] At present, the existing support structure optimization is mainly aimed at the pile structure, and no complete optimization process algorithm has been established. In addition, the optimization of the internal support structure is mostly carried out as a whole with other supporting structures, rather than optimizing the plane arrangement of the support structure alone. Summary of the invention

[0005] The present invention provides a topological optimization method for the arrangement of supports in a foundation pit. A progressive structural optimization algorithm is introduced based on ABAQUS finite element software to explore the optimal arrangement of supports in a foundation pit. Simulation verification is carried out in combination with common foundation pit support projects and specific engineering examples. Under the condition of satisfying given loading conditions and constraint conditions, a support arrangement structure in a foundation pit with minimum strain energy is obtained.

[0006] A topological optimization method for supporting arrangement in a foundation pit comprises the following steps:

[0007] Step 1: Establish the initial model to be optimized in ABAQUS;

[0008] Step 2: Define the design region and design variables;

[0009] Step 3: Define the objective function and constraints;

[0010] Step 4: Input the load value and set the constraint conditions for iterative optimization;

[0011] Step 5: If the iterative optimization result meets the optimization judgment condition, the optimization is terminated. If it does not meet the optimization judgment condition, the optimization is continued back to step 4 until the optimization judgment condition is met and the optimization is terminated.

[0012] Furthermore, in step 1, three types of built-in support structures of foundation pits are selected for modeling in ABAQUS. The three built-in structures of foundation pits include full support, annular support and full-plane support for special-shaped foundation pits. The supporting material of full support is Q235 steel support, the supporting material of annular support is Q235 steel, and the full-plane support of special-shaped foundation pits is C30 concrete.

[0013] Further, in step 2, according to the three foundation pit models selected in step 1, the design area directly selects the entire area of ​​the model, and divides the entire area of ​​the model into multiple grid units;

[0014] Define the design variables, define the mesh unit strain energy density as the design variable, and assign a unit strain energy density value to each unit according to whether the material of each mesh unit exists and the degree of existence;

[0015] The relationship between the physical properties of the material and the strain energy density of the mesh unit is defined by the interpolation method. The value range of the strain energy density of the mesh unit is [0 1]. When the unit density is 1, the mesh unit has the complete physical properties of the material. When the mesh unit density is 0, the physical properties of the mesh unit are close to the state without material.

[0016] Furthermore, the objective function in step 3 is:

[0017] (1) Grid cell strain energy density:

[0018] u=∑(0.5×σ×ε×V)where,

[0019] Σ means the sum of each element, σ is the grid element stress, ε is the grid element displacement, and V is the grid element volume;

[0020] (2) Unit strain energy: E i =∫u dv

[0021] Among them, ∫ represents the integration of the volume of the entire unit, dV represents the microelement volume, ui represents the strain energy density of the grid unit, and Ei represents the strain energy of the grid unit;

[0022] (3) Overall strain energy of foundation pit:

[0023] Among them, E irepresents the strain energy of the grid unit, and E represents the overall strain energy of the foundation pit.

[0024] Furthermore, in step 3, the constraints include volume constraint, limit on the number of iterations, design variable stability and convergence test; the volume constraint is the proportion of the optimized volume in the total volume of the foundation pit, the limit on the number of iterations is less than or equal to 50 times, the design variable stability is to monitor that the density of the grid cells does not change much in several consecutive iterations to achieve the stability of the design variables, and the convergence test is to monitor the numerical change of the overall strain energy of the target foundation pit.

[0025] Further, in step 4, the load is a uniformly distributed load applied vertically toward the inside of the foundation pit around the foundation pit structure, and the load value is 180 kN / m.

[0026] Further, the iterative optimization step includes:

[0027] Step 4.1, input the load value into Abaqus finite element software;

[0028] Step 4.2: Set the constraint conditions, use the TOSCA topology optimization algorithm to minimize the solution, and perform iterative optimization.

[0029] Furthermore, the substitution constraint conditions are volume constraint and number of iterations.

[0030] Furthermore, in step 5, the optimization judgment condition is that after iterative optimization, the grid cells with a strain energy density value of 0.5 account for the majority, and the overall strain energy of the foundation pit has no significant change.

[0031] The beneficial effects of the present invention are:

[0032] (1) Flexible selection of design areas allows for targeted design of internal support structures with special requirements, making the entire optimization process more universal;

[0033] (2) The selection of design variables is to define the concept of unit density by integrating the influence of the two factors of unit stress and displacement, and to decide whether to keep or remove a unit based on the relative size of the density of each unit in the whole.

[0034] (3) The optimization results show that the topologically optimized internal support system can more effectively bear the load acting on the foundation pit while meeting all safety and service performance requirements (stress and deformation);

[0035] (4) The topology optimization method can significantly improve the efficiency of the support system design in the foundation pit, allowing a large number of potential design schemes to be automatically explored to find the optimal support layout;

[0036] (5) Topological optimization helps to reduce unnecessary material usage and minimize structural weight by optimizing material distribution while ensuring structural safety and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a unit grid density distribution diagram after optimization in Example 1 of a topology optimization method for supporting arrangement in a foundation pit of the present invention;

[0038] Figure 2 It is a stress distribution diagram after optimization in Example 1 of a topology optimization method for supporting arrangement in a foundation pit of the present invention;

[0039] Figure 3 It is a displacement distribution diagram after optimization in Example 1 of a topology optimization method for supporting arrangement in a foundation pit of the present invention;

[0040] Figure 4 It is a unit grid density distribution diagram after optimization in Example 2 of a topology optimization method for supporting arrangement in a foundation pit of the present invention;

[0041] Figure 5 It is a stress distribution diagram after optimization in Example 2 of a topology optimization method for supporting arrangement in a foundation pit of the present invention;

[0042] Figure 6 It is a displacement distribution diagram after optimization in Example 2 of a topology optimization method for supporting arrangement in a foundation pit of the present invention;

[0043] Figure 7 It is a unit grid density distribution diagram after optimization in Example 3 of a topology optimization method for supporting arrangement in a foundation pit of the present invention;

[0044] Figure 8 It is a stress distribution diagram after optimization in Example 3 of a topology optimization method for supporting arrangement in a foundation pit of the present invention;

[0045] Fig. 9 It is a displacement distribution diagram after optimization in Example 3 of a topology optimization method for supporting arrangement in a foundation pit of the present invention;

[0046] Fig.10 It is a flow chart of a topological optimization method for support arrangement in a foundation pit according to the present invention. DETAILED DESCRIPTION

[0047] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0048] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on this patent; in order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0049] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "inner", "outer", etc. appear, the orientation or position relationship indicated is based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as a limitation on this patent. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0050] In the description of this patent, unless otherwise clearly specified and limited, if the term "connection" or the like appears to indicate the connection relationship between components, the term should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two components or the interaction relationship between two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0051] Example 1

[0052] like Fig.10 As shown, a topology optimization method for supporting arrangement in a foundation pit in this embodiment 1 includes the following steps:

[0053] Step 1: In the ABAQUS finite element software, a square foundation pit structure with a side length of 36m and a fully supported Q235 steel support is established as the model to be optimized;

[0054] Step 2: When establishing the initial structural model of the support in this embodiment, the initial optimized shape has been taken into consideration. Therefore, the design area in this embodiment directly takes the entire area of ​​the model. The supporting structure in the foundation pit is generally provided with surrounding purlins on all sides. Therefore, the units in the initial load application area around the model are set as non-optimized areas. Other units in the pit can be optimized normally, and multiple grid units are divided in the entire area of ​​the model.

[0055] Define the mesh unit strain energy density as the design variable, and assign a unit strain energy density value to each unit according to whether the material of each mesh unit exists and the degree of existence;

[0056] The relationship between the physical properties of the material and the strain energy density of the unit mesh is defined by the interpolation method. The value range of the unit strain energy density is [0 1]. When the unit density is 1, the unit has the complete physical properties of the material. When the unit density is 0, the physical properties of the unit are close to the state without material.

[0057] The physical properties of the material refer to the stresses and displacements that occur in the model supports due to the loads applied to them;

[0058] Strain energy is the energy possessed by an object when it is deformed due to force, and is a factor affected by the dual elements of stress and displacement, so the strain energy density of the grid unit is selected as the design variable;

[0059] Step 3: Define the objective function.

[0060] (1) Grid cell strain energy density:

[0061] u=∑(0.5×σ×ε×V)where,

[0062] Σ means the sum of each element, σ is the grid element stress, ε is the grid element displacement, and V is the grid element volume;

[0063] (2) Grid unit strain energy: E i =∫u dv

[0064] Among them, ∫ represents the integration of the volume of the entire unit, dV represents the volume of the microelement, and u represents the unit strain energy density, which represents the strain energy in each unit grid volume;

[0065] (3) Overall strain energy of foundation pit:

[0066] Among them, E i represents the strain energy of the grid unit, and E represents the overall strain energy of the foundation pit.

[0067] In step 3, the constraints include volume constraint, limiting the number of iterations, design variable stability and convergence test; the volume constraint is the proportion of the optimized volume in the total volume of the foundation pit, limiting the number of iterations means that during the optimization process, the number of iterations is set to be less than or equal to 50 times, the design variable stability is to monitor that the strain energy density of the grid unit does not change much in several consecutive iterations, that is, to achieve the stability of the design variables, and the convergence test is to monitor the numerical change of the overall strain energy of the foundation pit.

[0068] Step 4: The load is a uniformly distributed load applied vertically toward the inside of the foundation pit around the foundation pit structure, and the load value is 180 kN / m.

[0069] Iterative optimization includes,

[0070] Step 4.1, input the load value of 180kN / m into the Abaqus finite element software, and obtain the stress value and displacement value of the grid unit through the structural model of a fully supported square foundation pit with a side length of 36m and Q235 steel support material established in the Abaqus software;

[0071] Step 4.2, in the initial optimization, the constraint condition is set to be less than or equal to 19% of the original volume, and it is iterated 30 times. The TOSCA topology optimization algorithm is used to minimize the solution, and the strain energy density value of the grid cells in the entire area is obtained. The grid cell with the smallest strain energy density value is deleted, thereby changing the grid cell volume, and the second iterative optimization is started. The optimization iteration is repeated 30 times to obtain the iterative optimization result.

[0072] Step 5: Iterative optimization structural analysis. The results of iterative optimization in step 4 are as follows: Figure 1 , 2 , and 3. From Figure 1 It can be seen that when the volume is reduced to 19% of the original volume, the units with density greater than 0.5 account for the majority of the model. Figure 2 and 3 It can also be seen that the stress and displacement levels around the model are in a relatively low range, and only a few areas have stress concentration. At this time, the overall strain energy has no significant change, which meets the optimization termination judgment conditions and ends the optimization.

[0073] Example 2

[0074] like Fig.10 As shown, a topology optimization method for supporting arrangement in a foundation pit in this embodiment 2 includes the following steps:

[0075] Step 1: In the ABAQUS finite element software, a circular section with a side length of 36m and a center diameter of 30m is used as a reserved area. No foundation pit is arranged in this part. The square initial foundation pit structure of Q235 steel is used as the supporting material to establish the model to be optimized;

[0076] Step 2: When establishing the initial structural model of the support in this embodiment, the initial optimized shape has been taken into consideration. Therefore, the design area in this embodiment directly takes the entire area of ​​the model. The supporting structure in the foundation pit is generally provided with surrounding purlins on all sides. Therefore, the units in the initial load application area around the model are set as non-optimized areas. Other units in the pit can be optimized normally, and multiple grid units are divided in the entire area of ​​the model.

[0077] Define the mesh unit strain energy density as the design variable, and assign a unit strain energy density value to each unit according to whether the material of each mesh unit exists and the degree of existence;

[0078] The relationship between the physical properties of the material and the strain energy density of the mesh unit is defined by the interpolation method. The value range of the unit strain energy density is [0 1]. When the unit density is 1, the unit has the complete physical properties of the material. When the unit density is 0, the physical properties of the unit are close to the state without material.

[0079] The physical properties of the material refer to the stresses and displacements that occur in the model supports due to the loads applied to them;

[0080] Strain energy is the energy possessed by an object when it is deformed due to force. It is a factor affected by the dual elements of stress and displacement. Therefore, the strain energy density of the grid unit is selected as the design variable.

[0081] Step 3: Define the objective function.

[0082] (1) Grid cell strain energy density:

[0083] u=∑(0.5×σ×ε×V)where,

[0084] Σ means the sum of each element, σ is the grid element stress, ε is the grid element displacement, and V is the grid element volume;

[0085] (2) Grid unit strain energy: E i =∫u dv where ∫ represents the integration of the volume of the entire unit, dV represents the volume of the microelement, and u represents the strain energy density in the volume of the grid unit;

[0086] (3) Overall strain energy of foundation pit:

[0087] Where Ei represents the strain energy of the grid unit and E represents the overall strain energy of the foundation pit.

[0088] In step 3, the constraints include volume constraint, limiting the number of iterations, design variable stability and convergence test; the volume constraint is the proportion of the optimized volume in the total volume of the foundation pit, limiting the number of iterations means that during the optimization process, the number of iterations is set to be less than or equal to 50 times, the design variable stability is to monitor that the strain energy density of the grid unit does not change much in several consecutive iterations, that is, to achieve the stability of the design variable, and the convergence test is to monitor the numerical change of the overall strain energy of the target.

[0089] Step 4: The load is a uniformly distributed load applied vertically toward the inside of the foundation pit around the foundation pit structure, and the load value is 180 kN / m.

[0090] Iterative optimization includes,

[0091] Step 4.1, input the load value of 180kN / m into the Abaqus finite element software, and establish the model to be optimized by using the circular section with a side length of 36m and a center diameter of 30m established in the Abaqus software as the reserved area. No foundation pit is arranged in this part, and the square initial foundation pit structure of Q235 steel is selected as the supporting material to obtain the stress value and displacement value of the grid unit;

[0092] Step 4.2, optimize and substitute the constraint condition to set the volume to be less than or equal to 43% of the original volume, iterate 40 times, and use the TOSCA topology optimization algorithm to minimize the solution, obtain the strain energy density value of the grid cells that divide multiple grid cells in the entire area, delete the grid cell with the smallest strain energy density value, thereby changing the grid cell volume, and start the second iterative optimization. Repeat the optimization iteration 40 times to obtain the iterative optimization result.

[0093] Step 5: Iterative optimization structural analysis. The results of iterative optimization in step 4 are as follows: Figure 4 , 5 , and 6. Figure 4 When the volume is reduced to 43% of the original volume, it can be seen that the optimized unit structure still maintains basic symmetry. The units with density greater than 0.5 still account for the majority of the model. Figure 5 and 6 The medium stress is basically maintained at a low level, and the maximum displacement of the supporting structure is also limited to less than 2 mm. At this time, the overall strain energy has no significant change, which meets the conditions for ending the optimization, and the optimization is ended.

[0094] Example 3

[0095] like Fig.10 As shown, a topology optimization method for supporting arrangement in a foundation pit in this embodiment 2 includes the following steps:

[0096] Step 1: In ABAQUS finite element software, C30 concrete is selected as the full support material, and the full plane support structure of the special-shaped foundation pit is used to establish the model to be optimized;

[0097] Step 2: When establishing the initial structural model of the support in this embodiment, the initial optimized shape has been taken into consideration. Therefore, the design area in this embodiment directly takes the entire area of ​​the model. The supporting structure in the foundation pit is generally provided with surrounding purlins on all sides. Therefore, the units in the initial load application area around the model are set as non-optimized areas. Other units in the pit can be optimized normally, and multiple grid units are divided in the entire area of ​​the model.

[0098] Define the mesh unit strain energy density as the design variable, and assign a unit strain energy density value to each unit according to whether the material of each mesh unit exists and the degree of existence;

[0099] The relationship between the physical properties of the material and the strain energy density of the unit mesh is defined by the interpolation method. The value range of the unit strain energy density is [0 1]. When the unit density is 1, the unit has the complete physical properties of the material. When the unit density is 0, the physical properties of the unit are close to the state without material.

[0100] The physical properties of the material refer to the stresses and displacements that occur in the model supports due to the loads applied to them;

[0101] Strain energy is the energy possessed by an object when it is deformed due to force, and is a factor affected by the dual elements of stress and displacement, so the strain energy density of the grid unit is selected as the design variable;

[0102] Step 3: Define the objective function.

[0103] u=∑(0.5×σ×ε×V)where,

[0104] Σ means the sum of each element, σ is the grid element stress, ε is the grid element displacement, and V is the grid element volume;

[0105] (2) Grid unit strain energy: E i =∫u dv where,

[0106] ∫ represents the integration of the volume of the entire unit, dV represents the volume of the microelement, and u represents the unit strain energy density, which represents the strain energy in each unit grid volume;

[0107] (3) Overall strain energy of foundation pit:

[0108] Among them, E i represents the strain energy of the grid unit, and E represents the overall strain energy of the foundation pit.

[0109] In step 3, the constraints include volume constraint, limiting the number of iterations, design variable stability and convergence test; the volume constraint is the proportion of the optimized volume in the total volume of the foundation pit, limiting the number of iterations means that during the optimization process, the number of iterations is set to be less than or equal to 50 times, the design variable stability is to monitor that the strain energy density of the grid unit does not change much in several consecutive iterations, that is, to achieve the stability of the design variables, and the convergence test is to monitor the numerical change of the overall strain energy of the foundation pit.

[0110] Step 4: The load is a uniformly distributed load applied vertically toward the inside of the foundation pit around the foundation pit structure, and the load value is 180 kN / m.

[0111] Iterative optimization includes,

[0112] Step 4.1, input the load value of 180kN / m into the Abaqus finite element software, select C30 concrete as the full support material in the Abaqus software, and establish the model to be optimized for the full plane support structure of the special-shaped foundation pit, and obtain the stress value and displacement value of the grid unit;

[0113] Step 4.2, optimize the constraint condition that the volume is reduced to 24% of the original volume, iterate 50 times, use the TOSCA topology optimization algorithm to minimize the solution, obtain the strain energy density value of the grid cells that divide multiple grid cells in the entire area, delete the grid cell with the smallest strain energy density value, thereby changing the grid cell volume, start the second iterative optimization, repeat the optimization iteration 40 times, and obtain the iterative optimization result.

[0114] Step 5: Iterative optimization structural analysis. The results of iterative optimization in step 4 are as follows: Figure 7 , 8 , and 9 are shown. Depend on Figure 7 It can be seen that when the volume is reduced to 24% of the original volume, the structure after program optimization is very clear, and the units with density greater than 0.5 in the model occupy the vast majority. Figure 8 and 9 It can be seen from the figure that the overall stress of the structure is still at a low level, and the displacement of the stress concentration area in the pit corner is larger than that in other areas, which is in line with the objective law. At this time, the overall strain energy has no significant change, which meets the optimization judgment condition and ends the optimization.

[0115] It should be noted that the above specific implementations are only preferred embodiments of the present invention and the technical principles used. Those skilled in the art should understand that various modifications, equivalent substitutions, changes, etc. can be made to the present invention. However, as long as these changes do not deviate from the spirit of the present invention, they should be within the scope of protection of the present invention. In addition, some terms used in the specification and claims of this application are not restrictive, but are only for the convenience of description.

Claims

1. A topological optimization method for support arrangement in a foundation pit, characterized in that: The following steps are involved: Step 1: Establish the initial structural model of the support in the foundation pit to be optimized in ABAQUS finite element software; Step 2: Define the design region and design variables; Step 3: Define the objective function and constraints; Step 4: Input the load value and set the constraint conditions for iterative optimization; Step 5: If the iterative optimization result meets the optimization judgment condition, the optimization is terminated. If it does not meet the optimization judgment condition, the optimization is continued back to step 4 until the optimization judgment condition is met and the optimization is terminated.

2. The topological optimization method for supporting arrangement in a foundation pit according to claim 1 is characterized in that: In step 1, three types of built-in support structures for foundation pits are selected for modeling in ABAQUS. The three built-in structures for foundation pits include full support, circular support and full-plane support for special-shaped foundation pits. The supporting material for full support is Q235 steel support, the supporting material for circular support is Q235 steel, and the full-plane support for special-shaped foundation pits is C30 concrete.

3. The topological optimization method for supporting arrangement in a foundation pit according to claim 2 is characterized in that: In step 2, according to the three foundation pit models selected in step 1, the design area directly selects the entire area of ​​the model, and divides the entire area of ​​the model into multiple grid units; Define the design variables, define the mesh unit strain energy density as the design variable, and assign a unit strain energy density value to each unit according to whether the material of each mesh unit exists and the degree of existence; The relationship between the physical properties of the material and the strain energy density of the mesh unit is defined by the interpolation method. The value range of the strain energy density of the mesh unit is [0 1]. When the unit density is 1, the mesh unit has the complete physical properties of the material. When the mesh unit density is 0, the physical properties of the unit are close to the state without material.

4. The topological optimization method for supporting arrangement in a foundation pit according to claim 3 is characterized in that: The objective function in step 3 is, (1) Strain energy density of grid cells: u=∑(0.5×σ×ε×V)where, Σ represents the summation of each unit, σ is the grid unit stress, ε is the grid unit displacement, V is the grid unit volume, u represents the strain energy density of the grid element; (2) Grid unit strain energy: E i =∫u dv Where ∫ represents the integration of the volume of the entire unit, dV represents the volume of the microelement, u represents the strain energy density of the grid unit, and E i represents the strain energy of the mesh element; (3) Overall strain energy of foundation pit: Among them, E i represents the strain energy of the grid unit, and E represents the overall strain energy of the foundation pit.

5. The topological optimization method for supporting arrangement in a foundation pit according to claim 4 is characterized in that: In step 3, the constraints include volume constraint, limit on the number of iterations, design variable stability and convergence test; the volume constraint is the proportion of the optimized volume in the total volume of the foundation pit, the limit on the number of iterations is less than or equal to 50 times, the design variable stability is to monitor the strain energy density of the grid unit and not change much in several consecutive iterations to achieve the stability of the design variables, and the convergence test is to monitor the numerical change of the overall strain energy of the target foundation pit.

6. The topological optimization method for supporting arrangement in a foundation pit according to claim 5, characterized in that: In step 4, the load is a uniformly distributed load applied vertically toward the inside of the foundation pit around the foundation pit structure, and the load value is 180 kN / m.

7. The topological optimization method for supporting arrangement in a foundation pit according to claim 6, characterized in that: The iterative optimization in step 4 includes the following steps: Step 4.1, input the load value into Abaqus finite element software; Step 4.2: Set the constraint conditions, use the TOSCA topology optimization algorithm to minimize the solution, and perform iterative optimization.

8. The topological optimization method for supporting arrangement in a foundation pit according to claim 7, characterized in that: The substitution constraints are volume constraints and the number of iterations.

9. The topological optimization method for supporting arrangement in a foundation pit according to claim 8, characterized in that: In step 5, the optimization judgment condition is that after iterative optimization, the mesh cells with a strain energy density value of 0.5 account for the majority, and the overall strain energy of the foundation pit has no significant change.

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