A method for analyzing the density of a polymer impervious wall of a dam to be de-risked and reinforced

Abstract

A method for analyzing the density of a polymer impervious wall of a dam to be de-risked and reinforced is as follows: (1) Obtain the basic information of the dam to be de-risked and reinforced; (2) Use the basic information in step (1) to establish a finite element model and determine the evaluation index; (3) By analyzing the finite element model in step (2), obtain the functional relationship between the evaluation index and the density of the impervious wall; (4) Normalize the relationship between the evaluation index and the density of the impervious wall obtained in step (3) to obtain the efficacy function; (5) Determine the index weight, linearly add the efficacy functions obtained in step (4) according to the weight distribution scheme, construct an objective function regarding density, and determine the optimal density.

Description

Technical Field

[0001] The invention belongs to the field of dam risk removal and reinforcement, and in particular relates to a density analysis method of a polymer anti-seepage wall of a dam to be risk removed and reinforced. Background Art

[0002] Seepage problem is the key to dam safety. One of the most commonly used methods for dam anti-seepage is to build an anti-seepage wall. Concrete anti-seepage wall is a vertical anti-seepage measure widely used in earth-rock dam projects. It has a small permeability coefficient and good anti-seepage effect, so it is widely used in water conservancy project construction. However, concrete anti-seepage wall has exposed many disadvantages: large volume, heavy self-weight, large stress generated by itself, large elastic modulus, poor deformation coordination ability, etc. At present, polymer anti-seepage wall, as a new type of lightweight anti-seepage wall, has been widely recognized for its anti-seepage reinforcement performance. Polymer grouting material has many advantages such as light weight, early strength, large expansion force, no pollution, good anti-seepage performance, durability and excellent mechanical properties. After the polymer anti-seepage wall is completed, it has good coordination with the soil deformation and can adapt to large deformation of the dam without damage, so it has extremely high promotion value.

[0003] In recent years, theoretical research on polymer anti-seepage wall dams has mainly focused on the dynamic and static mechanical properties, stability and non-destructive testing of polymer anti-seepage walls, while little research has been done on the deformation coordination characteristics of polymer anti-seepage wall dams. Dam deformation coordination refers to the deformation coordination of different dam-building materials under load, which is increasingly receiving attention. There are many cases of dam dangers caused by uncoordinated deformation at home and abroad. The Iranian Masjid Suleiman core wall rockfill dam, built in 2000, is 177 meters high. Due to the uneven settlement caused by the difference in material density, the dam top is Longitudinal cracks appear, and separation occurs between the upstream of the core wall and the filter layer, and between the filter layer and the dam shell. Once the longitudinal cracks penetrate the upstream and downstream of the dam body, leakage channels will appear. The deformation coordination problem will not only pose a great threat to the dam body, but also run through the entire life cycle of the dam. Although people recognize the importance of deformation coordination, there is currently no strict definition and evaluation index for the deformation coordination of the dam body, and there are no relevant specifications or standards for reference. How to evaluate the impact of this deformation difference on the safety of the dam body and how to choose the optimal density of polymer materials are issues that need to be solved urgently. Summary of the invention

[0004] The purpose of the present invention is to address the problem that the current polymer anti-seepage wall density design method lacks comprehensive consideration of deformation coordination, strength reserve and economy, and proposes a polymer anti-seepage wall density analysis method for dams to be de-risked and reinforced.

[0005] A method for analyzing the density of a polymer anti-seepage wall of a dam to be reinforced, comprising the following steps:

[0006] (1) Obtain the modeling information of the dam to be reinforced against danger;

[0007] (2) Establish a finite element model and determine the evaluation index;

[0008] (3) By solving the finite element model in step (2), obtain the relationship between the evaluation index and the density;

[0009] (4) Obtain the efficacy function through normalizing the relationship between the evaluation index and the density obtained in step (3);

[0010] (5) Determine the index weight, linearly superimpose the efficacy function obtained in step (4) according to the weight distribution scheme, construct an objective function regarding the density, and determine the optimal density.

[0011] Furthermore, for the high polymer impervious wall density analysis method of the dam to be reinforced against danger, wherein: the modeling information of the dam to be reinforced against danger obtained in step (1) includes: the density ρ of the dam body soil bt , the elastic modulus E of the dam body soil bt , the Poisson's ratio μ of the dam body soil bt , the cohesion c of the dam body soil bt , the internal friction angle of the dam body soil and the permeability coefficient k of the dam body soil bt ; the density ρ of the dam foundation soil bj , the elastic modulus E of the dam foundation soil bj , the Poisson's ratio μ of the dam foundation soil bj , the cohesion c of the dam foundation soil bj , the internal friction angle of the dam foundation soil and the permeability coefficient k of the dam foundation soil bt ; the shape and size of the dam to be reinforced against danger; the construction depth l and construction thickness b of the high polymer impervious wall;

[0012] The density ρ of the dam body soil bt The unit is g / cm 3 , the elastic modulus E of the dam body soil bt The unit is kpa, the cohesion c of the dam body soil bt The unit is kpa, the internal friction angle of the dam body soil The unit is °, the permeability coefficient k of the dam body soil bt The unit is cm / s; the density ρ of the dam foundation soil bj The unit is g / cm 3 , the elastic modulus E of the dam foundation soil bj The unit is kpa, the cohesion c of the dam foundation soil bj The unit is kpa, the internal friction angle of the dam foundation soil The unit is °, the permeability coefficient k of the dam foundation soil btThe unit is cm / s; the construction depth l of the polymer impervious wall is in m, and the construction thickness b is in m.

[0013] To obtain the optimal polymer density, within the implementation range of the polymer density during construction: 0.1 g / cm 3 - 0.3 g / cm 3 select polymers with densities of 0.1 g / cm 3 、0.15 g / cm 3 、0.2 g / cm 3 、0.25 g / cm 3 、0.3 g / cm 3 respectively. Through laboratory tests, measure the elastic modulus E 3 、Poisson's ratio μ 3 、and permeability coefficient k 3 of the polymers with densities of 0.1 g / cm 3 、0.15 g / cm 3 、0.2 g / cm x 、0.25 g / cm x 、0.3 g / cm x . The unit of the obtained elastic modulus E x of the polymer is kPa, Poisson's ratio μ x , and the permeability coefficient k x is in cm / s.

[0014] Furthermore, for the method for analyzing the density of the polymer impervious wall of the dam to be de-risked and reinforced, where:

[0015] In step (2): Establish a finite element model of the dam using the information obtained in step (1). The geometric shape of this model is divided into two or more elements, and each element is connected through shared nodes; the density of the polymer grouting material is the sensitivity parameter, and the factors to be considered are the displacement difference, the length of the void area, the Mises stress of the impervious wall, the dam slope stability coefficient, and the construction cost.

[0016] The displacement difference is the absolute value of the vertical displacement value of point x on the impervious wall at time t minus the vertical displacement value of the corresponding point x on the dam body at time t; the length of the void area is the absolute value of the deflection of point x on the impervious wall at time t minus the displacement value of the corresponding point x on the dam body at time t in the normal direction of the impervious wall; the dam slope stability coefficient is the ratio between the maximum shear strength of the soil mass inside the slope and the actual shear stress generated by the external load inside the slope under the condition that the external load remains unchanged, and it is widely used as the standard for judging the critical failure of the dam slope in finite element analysis; the construction cost is the project cost corresponding to polymer materials with different densities; the Mises stress of the impervious wall is an equivalent stress based on the shear strain energy, and the value is:

[0017]

[0018] Among them, σ is the Mises stress of the impervious wall, σ1 represents the principal stress with the largest value, σ1≥σ2≥σ3, and the sorting takes into account the positive and negative signs. σ2 is the principal stress with a value in the middle of σ1~σ3, and σ3 represents the principal stress with the smallest value.

[0019] Furthermore, for the method for analyzing the density of the polymer impervious wall of the dam to be de-risked and reinforced, where:

[0020] In step (3), using the finite element model of the polymer impervious wall dam established in step (2), displacements in the x and y directions are imposed on the bottom of the model; displacements in the x direction are imposed on both sides, and no restrictions are imposed in the y direction. A water load is applied upstream of the dam, and the forces and displacements received by each node are analyzed; through the displacement difference in the x direction of the nodes corresponding to the impervious wall and the dam body, the displacement difference in the y direction of the nodes corresponding to the impervious wall and the dam body, and the maximum mises stress of each node of the impervious wall, the density of the polymer grouting material is obtained as 0.1 g / cm 3 、0.15 g / cm 3 、0.2 g / cm 3 、0.25 g / cm 3 、0.3 g / cm 3 Corresponding respectively to: the length of the void area, the displacement difference, the Mises stress of the impervious wall, and the dam slope stability coefficient; the length of the void area takes the maximum value of the absolute value of the displacement difference in the x direction of the nodes corresponding to the impervious wall and the dam body, the displacement difference takes the maximum value of the absolute value of the displacement difference in the y direction of the nodes corresponding to the impervious wall and the dam body, the Mises stress of the impervious wall takes the maximum mises stress among the nodes of the impervious wall, and the dam slope stability coefficient is calculated by the strength reduction method;

[0021] The functional relationship between the maximum displacement difference and the polymer density is obtained by quadratic function fitting:

[0022] F(H,ρ) = -0.00795ρ 2 -0.00482ρ + 0.00357

[0023] Taking the maximum displacement difference as the ordinate and the polymer density as the abscissa, a relationship diagram between the displacement difference and the polymer density is plotted;

[0024] The functional relationship between the maximum void length and the polymer density is obtained by quadratic function fitting:

[0025] F(h,ρ) = -0.001371ρ 2 -0.0077ρ + 0.004;

[0026] Taking the maximum void length as the ordinate and the polymer density as the abscissa, plot the relationship diagram between the maximum void length and the polymer density;

[0027] Through quadratic function fitting, the functional relationship between the maximum mises stress of the cutoff wall and the polymer density is obtained: F(σ,ρ) = 943223ρ 2 - 582488ρ + 144671

[0028] Taking the maximum mises stress of the cutoff wall as the ordinate and the polymer density as the abscissa, plot the relationship diagram between the maximum mises stress of the cutoff wall and the polymer density;

[0029] Since the above four indicators all belong to the smaller-the-better expectation, that is, the smaller the value, the more satisfactory the result, while the dam slope stability coefficient belongs to the larger-the-better expectation, that is, the larger the dam slope stability coefficient, the more stable the dam slope. Therefore, the reciprocal of the dam slope stability coefficient is used as the evaluation index. Through quadratic function fitting, the functional relationship between the reciprocal of the stability coefficient and the polymer density is obtained: F(K -1 ,ρ) = 0.07ρ 2 - 0.0296ρ + 0.54

[0030] Taking the reciprocal of the stability coefficient as the ordinate and the polymer density as the abscissa, plot the relationship diagram between the reciprocal of the stability coefficient and the polymer density;

[0031] The relationship between the construction cost and the polymer density F(S,ρ) is expressed by the following formula:

[0032] F(S,ρ) = (α + βρ)abd (3)

[0033] In the formula: α is the sum of the mechanical usage fee and labor cost required for the construction of the polymer cutoff wall per cubic meter, with the unit of yuan / m 3 ; β is the cost of the polymer grouting material per kilogram, with the unit of yuan / m 3 ; ρ is the polymer density, with the unit of kg / m 3 ; a is the width of the polymer cutoff wall, with the unit of m; b is the depth of the polymer cutoff wall, with the unit of m; d is the thickness of the polymer cutoff wall, with the unit of m.

[0034] Furthermore, in the above-mentioned polymer cutoff wall density analysis method for the dam to be reinforced against danger, where:

[0035] In step (4): The relationship F(X between the different evaluation indicators obtained in step (3) and the different polymer densities i, ρ) is normalized. For i = 1, 2, 3, 4, 5, X1 is the maximum displacement difference, X2 is the maximum void length, X3 is the maximum mises stress of the cut-off wall, X4 is the dam slope stability coefficient, and X5 is the construction cost, to obtain the efficacy function d[F(X i , ρ)]:

[0036] Since the function F(X i and density ρ, i.e., F(X i , ρ) is a dimensional function, it should be normalized first. The normalization method is as follows: i , ρ), and its normalization method is:

[0037]

[0038] s.t. ρ ∈ [ρ min , ρ max

[0039] In the formula, ρ min , ρ max represent the minimum polymer density and the maximum polymer density that can be implemented during the actual construction process, respectively. Among them, the minimum polymer density is 0.1 g / cm 3 , and the maximum polymer density is 0.3 g / cm 3 ;

[0040] s.t. ρ ∈ [ρ min , ρ max represents the boundary condition of the formula, that is, the density value range of the polymer is between 0.1 g / cm 3 and 0.3 g / cm 3 ;

[0041] After the function relationship F(H, ρ) between the maximum displacement difference and the polymer density is normalized, its efficacy function d[F(H, ρ)] can be obtained, and the expression is as follows: d[F(H, ρ)] = -4.9688ρ 2 - 3.0125ρ + 1.3509;

[0042] After the function relationship F(h, ρ) between the maximum void length and the polymer density is normalized, its efficacy function d[F(h, ρ)] can be obtained, and the expression is as follows:

[0043] d[F(h, ρ)] = -0.8311ρ 2 - 4.6676ρ + 1.475

[0044] After the function relationship F(σ, ρ) between the maximum Mises stress and the polymer density is normalized, its efficacy function d[F(σ, ρ)] can be obtained, and the expression is as follows: d[F(σ, ρ)] = 22.98ρ2 -14.19ρ + 2.19 The functional relationship F(K -1 , ρ) between the reciprocal of the dam slope stability coefficient and the polymer density can be normalized to obtain its efficacy function d[F(K -1 , ρ)], and the expression is as follows:

[0045] d[F(K -1 , ρ)] = 218.91ρ 2 - 92.5ρ - 8.0625

[0046] The functional relationship F(S, ρ) between the construction cost and the polymer density can be normalized to obtain its efficacy function d[F(S, ρ)], and the expression is as follows: d[F(S, ρ)] = 5ρ - 0.5;

[0047] Furthermore, for the polymer cutoff wall density analysis method of the dam to be reinforced against danger, where: in the step (5): for the efficacy functions d[F(H, ρ)], d[F(h, ρ)], d[F(σ, ρ)], d[F(K -1 , ρ)], d[F(S, ρ)] in step (4), weight coefficients are assigned according to their importance in the actual project: the weight coefficient of the maximum displacement difference is λ1, the weight coefficient of the maximum void area is λ2, the weight coefficient of the maximum Mises stress of the cutoff wall is λ3, the weight coefficient of the stability coefficient is λ4, and the weight coefficient of the construction cost is λ5, and the sum of the weight coefficients is 100%;

[0048] Determine 3 weight coefficient distribution schemes:

[0049] The first scheme is the equal weight scheme, that is, λ1 = λ2 = λ3 = λ4 = λ5 = 20%;

[0050] The second scheme is the partial strength control scheme, which increases the weights of the maximum Mises stress of the cutoff wall and the dam slope stability coefficient, that is, λ1 = λ2 = λ5 = 10%, λ3 = λ4 = 35%;

[0051] The third scheme is the partial deformation control scheme, which increases the proportions of the displacement difference and the void area length, that is, λ1 = λ2 = 35%, λ3 = λ4 = λ5 = 10%;

[0052] According to the basic principle of multi - objective optimization, construct the objective function about ρ as,

[0053]

[0054] s.t. ρ ∈ [ρ min , ρ max

[0055] ​Each index is assigned a proportion according to its importance in the actual project, that is, the weight coefficient;

[0056] In the formula: D[ρ] is the objective function, and the ρ corresponding to minD[ρ] is the optimal polymer density ρ of the coordinated deformation of the dam body; d[F(X i ,ρ)] is the efficacy function of each evaluation index. The evaluation indexes include: X1 represents the maximum displacement difference H, X2 represents the maximum void area h, X3 represents the Mises stress σ of the cutoff wall, X4 represents the dam stability coefficient Fv, X5 represents the construction cost S, and X i are the 5 evaluation indexes in step (3); where k = 5, and λ i is the set value of the importance of the 5 evaluation indexes, that is, the index weight: the weight coefficient λ1 of the maximum displacement difference, the weight coefficient λ2 of the maximum void area, the weight coefficient λ3 of the maximum Mises stress, the weight coefficient λ4 of the stability coefficient, and the weight coefficient λ5 of the construction cost. The sum of the index weights is 100%;

[0057] Obtain the objective function value of ρ: Just solve for the value of ρ.

[0058] The method of the present invention establishes a finite element model of a polymer cutoff wall dam, introduces the displacement difference, void area, maximum Mises stress of the cutoff wall, dam slope stability coefficient, and construction cost as evaluation indexes, and then through the method of multi-objective optimization, introduces index weights, and determines the most suitable polymer density according to different weight distribution schemes, which is convenient and efficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is the solution flow chart of the polymer cutoff wall density analysis method for the dam to be reinforced against danger and risk in the present invention;

[0060] Figure 2 is the dimension diagram of the dam to be reinforced against danger and risk by using polymer grouting in the embodiment of the present invention;

[0061] Figure 3 is the model component list of the embodiment of the present invention;

[0062] Figure 4 is the dam model diagram of the embodiment of the present invention;

[0063] Figure 5 is the material parameter table of the embodiment of the present invention;

[0064] Figure 6 is the dam body parameter setting diagram of the embodiment of the present invention;

[0065] Figure 7 is the cross-section management table of the embodiment of the present invention;

[0066] Figure 8 It is the model assembly setting diagram of the embodiment of the present invention;

[0067] Figure 9 It is the tangential behavior parameter setting diagram of the embodiment of the present invention;

[0068] Figure 10 It is the analysis step setting diagram of the embodiment of the present invention;

[0069] Figure 11 It is the field output setting diagram of the embodiment of the present invention;

[0070] Figure 12 It is the in-situ stress balance setting diagram of the embodiment of the present invention;

[0071] Figure 13 It is the load and boundary condition setting diagram of the embodiment of the present invention;

[0072] Figure 14 It is the strength reduction setting diagram of the embodiment of the present invention;

[0073] Figure 15 It is the schematic diagram of model mesh division of the embodiment of the present invention;

[0074] Figure 16 It is the maximum Mises stress diagram used in the present invention;

[0075] Figure 17 It is the maximum x-direction displacement nephogram used in the present invention;

[0076] Figure 18 It is the maximum y-direction displacement nephogram used in the present invention;

[0077] Figure 19 It is the safety factor calculation diagram used in the present invention;

[0078] Figure 20 It is the relationship diagram between the displacement difference and the polymer density in the embodiment of the present invention;

[0079] Figure 21 It is the relationship diagram between the maximum debonding zone length and the polymer density in the embodiment of the present invention;

[0080] Figure 22 It is the relationship diagram between the maximum Mises stress of the cutoff wall and the polymer density in the embodiment of the present invention;

[0081] Figure 23 It is the relationship diagram between the reciprocal of the stability coefficient and the polymer density in the embodiment of the present invention;

[0082] Figure 24 It is the schematic diagram for solving the optimal density of different weight schemes of Scheme 1, Scheme 2, and Scheme 3 shown in Table 3 of the embodiment of the present invention. Specific implementation mode

[0083] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with embodiments and the accompanying drawings. The illustrative implementation modes of the present invention and their descriptions are only used to explain the present invention and are not intended to limit the present invention.

[0084] A method for analyzing the density of a polymer impervious wall of a dam to be reinforced against danger includes the following steps:

[0085] (1) Obtain the basic information of the dam to be reinforced against danger;

[0086] (2) Use the basic information of the dam obtained in step (1) to establish a finite element model and determine the evaluation indexes;

[0087] (3) By solving the finite element model in step (2), obtain the functional relationship between the evaluation indexes and the density of the impervious wall;

[0088] (4) Through normalizing the functional relationship between the evaluation indexes and the density of the impervious wall obtained in step (3), obtain the efficacy function;

[0089] (5) Introduce the index weights, linearly superimpose the efficacy function obtained in step (4) according to the weight distribution scheme, construct the objective function regarding the density, and determine the optimal density;

[0090] Furthermore, the information for modeling the dam to be reinforced against danger obtained in step (1) includes: polymer material properties, dam body material properties, dam foundation material properties, external loads, and the shape and size of the dam and the polymer impervious wall;

[0091] Measure the elastic modulus and Poisson's ratio of the polymer material at different densities through experiments; measure parameters such as the density, elastic modulus, Poisson's ratio, cohesion, and internal friction angle of the dam body and dam foundation materials through experiments; determine the water depth and the shape and size of the dam through on-site measurement;

[0092] Furthermore, step (2) is specifically as follows:

[0093] Establish a finite element model of the polymer impervious wall dam at different polymer densities. The density of the grouting material for the polymer impervious wall is the sensitive parameter, and the evaluation indexes are the displacement difference, the length of the void area, the Mises stress of the impervious wall, the dam slope stability coefficient, and the construction cost;

[0094] The differential displacement is the absolute value of the vertical displacement of point x on the cutoff wall at time t minus the vertical displacement of the corresponding point x on the dam body at time t; the length of the void area is the absolute value of the deflection of point x on the cutoff wall at time t minus the displacement of the corresponding point x on the dam body at time t in the normal direction of the cutoff wall; the dam slope stability coefficient, which is the ratio of the maximum shear strength of the soil mass inside the slope to the actual shear stress generated by the external load inside the slope under the condition that the external load remains unchanged, is widely used as the criterion for judging the critical failure of the dam slope in finite element analysis; the construction cost is the project cost corresponding to different density polymer materials; the Mises stress of the cutoff wall is an equivalent stress based on the shear strain energy, and its value is:

[0095]

[0096] where σ1, σ2, and σ3 respectively refer to the first, second, and third principal stresses;

[0097] Further, step (3) is specifically as follows:

[0098] Solve the finite element model of the polymer cutoff wall dam established in step (2), and obtain the functional relationship F(X i between different evaluation indexes X i and density ρ) through data fitting;

[0099] Further, in step (4), normalize the relationship F(X i , ρ) between different evaluation indexes and density obtained in step (3) to obtain the efficacy function d[F(X i , ρ)];

[0100] Since the function F(X i between the evaluation index X i and density ρ is a dimensional function, the efficacy functions should be normalized first. The normalization method is:

[0101]

[0102] s.t. ρ ∈ [ρ min , ρ max

[0103] In the formula, ρ min , ρ max respectively represent the minimum polymer density and the maximum polymer density that can be implemented in the actual construction process;

[0104] Further, in step (5), determine the index weights, linearly superimpose the normalized functions obtained in step (4) according to the weight distribution scheme, construct the objective function about the polymer density, and determine the optimal density; ​

[0105] According to the principle of multi-objective optimization, the objective function regarding ρ is constructed as follows:

[0106]

[0107] s.t. ρ ∈ [ρ min , ρ max

[0108] where: D[ρ] is the objective function, and the ρ corresponding to minD[ρ] is the optimal polymer density ρ of the coordinated deformation of the dam body; d[F(X i , ρ)] is the efficacy function represented by each evaluation index, and X i are the 5 evaluation indexes in step (3); λ i are determined respectively according to the importance of each objective

[0109] An example of the method for analyzing the density of the polymer impervious wall of a dam to be reinforced against danger: Taking a dam to be reinforced against danger by polymer grouting as an example:

[0110] (1) Obtain the modeling information of the dam to be reinforced against danger; the modeling information of the polymer impervious wall dam includes the density, elastic modulus, Poisson's ratio, and permeability coefficient of the polymer; the density, elastic modulus, Poisson's ratio, cohesion, internal friction angle, and permeability coefficient of the dam body soil; the density, elastic modulus, Poisson's ratio, cohesion, internal friction angle, and permeability coefficient of the dam foundation soil, as shown in Table 1; the depth of the water in front of the dam is 12 m; the shape and size of the dam to be reinforced against danger are shown in Figure 2 ; the construction depth of the polymer impervious wall is 17 m and the construction thickness is 0.02 m;

[0111] Table 1 Modeling information of polymer, dam body and dam foundation

[0112]

[0113] (2) Establish a finite element model and determine the evaluation indexes; specifically including the following sub-steps:

[0114] (2.1) Use the ABAQUS software to establish a finite element model of the dam, and the external dimensions of the dam are as shown in Figure 2 ; the polymer impervious wall is located in the middle of the dam body, with a construction depth of 17 m and a construction thickness of 0.02 m; in this embodiment, 5 models are established, corresponding to the polymer impervious wall dams under 5 kinds of polymer densities;

[0115] The operations in the ABAQUS software are as follows:

[0116] ​Step 1: Establish model components according to specific implementation working conditions. The models to be established in the present invention include a dam and a cutoff wall. The specific operation is to execute the [Component] / [Create] command in the "Component" module, and establish a component named dam and a component named qiang according to the model size, as Figure 3 shown; Figure 4 is the embankment model diagram of the established finite element model;

[0117] Step 2: Set different material properties and assign them to the corresponding model components. This work enables the model components in Step 1 to have the physical properties required for simulation, so that the results can be obtained through the simulation calculation of the software. The specific steps are as follows:

[0118] Step 2.1: Set the parameters of the polymer material, as Figure 5 shown, specifically including the density, elastic modulus, Poisson's ratio, etc. of the polymer;

[0119] Step 2.2: Set the material parameters of the dam body and the dam foundation, as Figure 6 shown, specifically including the density, elastic modulus, Poisson's ratio and plastic-related parameters of the dam body and the dam foundation materials, etc. The main difference lies in that the Mohr-Coulomb model is selected for the plastic parameters of the surrounding rock. This constitutive relationship has good practicability for both rock and soil masses. In the ABAQUS software, the material characteristics of rock and soil masses are mainly described by setting four parameters: friction angle, dilation angle, cohesion and plastic strain;

[0120] Step 2.2: Assign the set material parameters to the corresponding models. The specific operation is as follows: execute the [Section] / [Create] command, set the corresponding sections based on the defined materials bati, baji, and qiang, and execute the [Assign Section] command to assign them to the corresponding regions, as Figure 7 shown;

[0121] Step 3: Assemble the model components into a whole according to the actual working conditions; as Figure 8 shown, the specific steps are as follows:

[0122] Step 3.1: Adjust the model components to the corresponding positions according to the mutual relationship between the model components;

[0123] Step 3.2: Establish a contact relationship that conforms to the actual situation for the contact surface between the cutoff wall and the dam body. The present invention describes the contact between the cutoff wall and the dam body mainly by defining the Goodman element. The relevant settings of the Goodman element are described as follows:

[0124] Firstly: Select user-defined for the tangential friction formula, and the relevant parameter setting interface is as Figure 9 shown;

[0125] Second, the slip formula selects finite slip. This slip formula is more suitable for cases with small relative sliding or rotation compared to small slip, which is in line with the actual engineering situation.

[0126] Third, the normal contact behavior is defined as "hard" contact, which means there is no limit to the magnitude of the contact pressure that can be transmitted between two contact surfaces; when the contact pressure between the contact surfaces becomes 0 or negative, the two contact surfaces separate, and the contact constraints on the corresponding nodes are released simultaneously.

[0127] Step 4: Set the analysis step parameters and check the required field output variables and history output variables; this step is related to the workflow of the ABAQUS software. The analysis work of the software is based on certain analysis steps, and the results of the software simulation analysis are reflected by the output variable values.

[0128] Step 4.1 Set the analysis step parameters; this invention sets a total of two analysis steps. The first analysis step is the in-situ stress balance analysis step, the second analysis step is the load application analysis step, and the third analysis step is the strength reduction analysis step, as Figure 10 shown.

[0129] Step 4.2: Check the required field output variables and history output variables; the ABAQUS software can set the calculation result items required for the simulation analysis in the analysis step module, which are mainly divided into field output variables and history output variables; among them, the field variable output is used to describe the change of a certain quantity with spatial position, and the history output variable is used to describe the change of a certain quantity with time; this invention mainly focuses on the following calculation results: the stress, strain, predefined field variables, and displacement of the structure, as Figure 11 shown.

[0130] Step 5: Define the loads and boundary conditions; when applying loads, mainly consider the influence of other actions except water pressure on the structure, and when applying boundary conditions, mainly reflect the relationship between various model components; the specific steps are as follows:

[0131] Step 5.1: Apply the gravity load to the model; this step considers the influence of gravity on the cutoff wall and the dam.

[0132] Step 5.2: Conduct in-situ stress balance on the model in the first analysis step, as Figure 12 shown. If the in-situ stress balance is not carried out and only gravity is applied, the model will deform under the action of gravity. In actual engineering, when we apply loads, the deformation caused by gravity has already occurred, and actually, what we get is the deformation caused by the additional stress. When implementing specifically, the odb file method is used. Its principle is to simulate and analyze the stress-strain state of the model under the action of overlying rock and soil stress and use it as the initial state of the model for stress analysis.

[0133] Step 5.3: Apply boundary conditions in the initial analysis step. Apply constraints in the x and y directions to the bottom boundary of the model, and apply constraints in the y direction to the two side boundaries of the dam body; Apply water pressure load to the model in the second analysis step, as Figure 13 shown;

[0134] Step 5.4: Perform strength reduction calculation to obtain the safety factor in the third analysis step; The safety factor refers to the ratio between the maximum shear strength of the soil mass inside the slope and the actual shear stress generated by the external load inside the slope under the condition that the external load remains unchanged, and is widely used as a criterion for judging the critical failure of the dam slope in finite element analysis, as Figure 14 shown;

[0135] Step 6: Divide the mesh for the model and set the cell attributes; This step is based on the principle of the finite element simulation method, that is: divide the model into a finite number of sub-regions with certain attributes for solution, and the schematic diagram of the mesh division is shown as Figure 15 shown;

[0136] In finite element numerical simulation analysis, the size of the mesh division is a relatively important issue; Generally speaking, the finer the mesh division, the more accurate the calculation result. Relatively, the calculation amount is also larger and the computer time is longer; The present invention divides the mesh of different model components according to different scales according to the required accuracy of the results. Among them, the dam foundation and the dam body are divided into meshes with a spacing of 1000 mm, and the high-polymer impervious wall is divided into meshes with a spacing of 50 mm. This method of dividing the mesh according to the specific situation of the research problem takes into account both the calculation accuracy and the calculation amount;

[0137] Step 8: Submit the model to the software for operation; In the [Job] module, execute the [Create Job] command to establish a task named job-1 and submit the calculation;

[0138] Step 9: Obtain and organize the required structural simulation analysis results through software post-processing; For the maximum mises stress contour map obtained from the simulation analysis corresponding to Working Condition 1 of the present invention, see Appendix Figure 16 , the maximum x-direction displacement contour map is shown in Figure 17 , the maximum y-direction displacement contour map is shown in Figure 18 , and the relationship diagram between displacement and predefined field variables is shown in Figure 19 ;

[0139] Step 10: Repeat the above steps, each time changing the parameters of the high-polymer material in Step 2.1, and calculate the models under the high-polymer densities of 0.1 g / cm 3 , 0.15 g / cm 3 , 0.2 g / cm 3 , 0.25 g / cm 3 , 0.3 g / cm 3 respectively;

[0140] (2.2) The evaluation indicators are the maximum displacement difference H, the maximum void h, the Mises stress σ of the cutoff wall, the dam stability coefficient Fv, and the construction cost S;

[0141] The maximum displacement difference H describes the vertical deformation coordination between the cutoff wall and the dam body, and the expression is:

[0142]

[0143] In the formula: is the vertical displacement at point i on the cutoff wall; is the vertical displacement of the dam body corresponding to point i;

[0144] The maximum void h describes the deformation coordination between the normal direction of the cutoff wall and the dam body, and the expression is:

[0145]

[0146] In the formula: is the normal displacement at point i on the cutoff wall; is the displacement of the dam body corresponding to point i in the normal direction of the cutoff wall;

[0147] When the density of the polymer increases, the construction cost increases accordingly. The relationship F(S, ρ) between the construction cost and the polymer density is expressed by the following formula: F(S, ρ) = (α + βρ)abd (3)

[0148] In the formula: α is the sum of the mechanical usage fee and labor cost required for the construction of the polymer cutoff wall per cubic meter (yuan / m 3 ); β is the cost of the polymer grouting material per kilogram; ρ is the polymer density (kg / m 3 ); a is the width (m) of the polymer cutoff wall; b is the depth (m) of the polymer cutoff wall; d is the thickness (m) of the polymer cutoff wall;

[0149] In the embodiment of the present invention, the value of α is taken as 2000 yuan / m 3 , the value of β is taken as 160 yuan, a is 100 m, b is 17 m, and d is 0.02 m; substituting into formula (10), the relationship between the construction cost and the polymer density can be obtained as:

[0150] F(S, ρ) = 4080ρ + 51000 (4)

[0151] (3) By performing data processing on the result file of step (2), the functional relationship F(X i between different evaluation indicators X i, ρ) (i = 1, 2, 3, 4, 5), where X1 is the maximum displacement difference H, X2 is the maximum void area h, X3 is the Mises stress σ of the cutoff wall, X4 is the dam stability coefficient Fv, and X5 is the construction cost S; specifically, it includes the following sub-steps:

[0152] (3.1) Read the result file to obtain the maximum displacement difference H, the maximum void area h, the Mises stress σ of the cutoff wall, and the dam stability coefficient Fv, including the following steps:

[0153] 1. Read Figure 17 information to obtain the maximum displacement difference as shown in the following table:

[0154]

[0155] 2. Read Figure 16 information to obtain the maximum void area as shown in the following table:

[0156]

[0157] 3. Read Figure 15 information to obtain the maximum mises stress as shown in the following table:

[0158]

[0159] 3. Read Figure 19 information to obtain the reciprocal of the most stable coefficient as shown in the following table:

[0160] Model Model-1 Model-2 Model-3 Model-4 Model-5 Stability coefficient 0.53855 0.5375 0.53717 0.5369 0.5368

[0161] (3.2) According to step (3.1), draw the images of the maximum displacement difference H, the maximum void area h, the Mises stress σ of the cutoff wall, and the dam stability coefficient Fv corresponding to different polymer densities, and through quadratic function fitting (as Figure 20 shown), obtain the functional relationship between the maximum displacement difference H and the polymer density ρ as shown in equation (5)

[0162] F(H, ρ) = -0.00795ρ 2 -0.00482ρ + 0.00357 (5)

[0163] Through quadratic function (as Figure 21 shown) fitting, obtain the functional relationship between the maximum void area h and the polymer density ρ as shown in equation (6)

[0164] F(h, ρ) = -0.001371ρ 2 -0.0077ρ + 0.004 (6)

[0165] Through quadratic function (as Figure 22The functional relationship between the Mises stress σ of the cutoff wall and the density ρ of the polymer obtained by fitting (as shown in the figure) is as shown in Equation (7).

[0166] F(σ,ρ) = 943223ρ 2 -582488ρ + 144671 (8)

[0167] The larger the slope stability coefficient, the more beneficial it is to the safety of the dam embankment. And the smaller the other indicators, the more beneficial it is to the safety of the dam embankment. The reciprocal K of the stability coefficient is used -1 to represent the contribution of the stability coefficient to the objective function; A quadratic function (such as Figure 23 shown in the figure) is used to fit the relationship between the reciprocal of the stability coefficient and the density of the polymer to obtain Equation (9):

[0168] F(K -1 ,ρ) = 0.07ρ 2 -0.0296ρ + 0.54 (9)

[0169] (4) By normalizing the functional relationship F(X i ,ρ) obtained in step (3), the efficacy function d[F(X i ,ρ)] is obtained. The method of normalization is as follows:

[0170]

[0171] In the formula: ρ min ,ρ max respectively represent the minimum density of the polymer and the maximum density of the polymer that can be implemented during the actual construction process;

[0172] In this embodiment, ρ min is 0.1 g / cm 3 , and ρ max is 0.3 g / cm 3 ; The d[F(X i ,ρ)] obtained by normalization is shown in Table 2:

[0173] Table 2 Efficacy Function

[0174]

[0175]

[0176] (5) Determine the index weights, and linearly add the efficacy function d[F(X i ,ρ)] obtained in step (4) according to the three weight distribution schemes of equal weight, partial strength control, and partial deformation control (as shown in Table 3), construct the objective function D[ρ] about the density, and determine the optimal density minD[ρ]; where the objective function D[ρ] is calculated according to the following formula:

[0177]

[0178] In the formula: D[ρ] is the objective function, and the ρ corresponding to minD[ρ] is the optimal polymer density ρ for the coordinated deformation of the dam body; ρ min , ρ max respectively represent the minimum polymer density and the maximum polymer density that can be implemented during the actual construction process. In this embodiment, ρ min is 0.1 g / cm 3 , ρ max is 0.3 g / cm 3 ;; d[F(X i , ρ)] is the efficacy function represented by each evaluation index. In this embodiment, X1 is the maximum displacement difference H, X2 is the maximum void area h, X3 is the Mises stress σ of the cut-off wall, X4 is the dam stability coefficient Fv, and X5 is the construction cost S; λ i are determined according to the importance of each evaluation index respectively, in this embodiment, k = 5, λ1 is the weight coefficient of the maximum displacement difference H, λ2 is the weight coefficient of the maximum void area h, λ3 is the weight coefficient of the Mises stress σ of the cut-off wall, λ4 is the weight coefficient of the dam stability coefficient Fv, and λ5 is the weight coefficient of the construction cost S;

[0179] Among them, d[F(H, ρ)] describes the displacement difference, d[F(h, ρ)] describes the void area, and d[F(H, ρ)], d[F(h, ρ)] belong to the indexes related to the deformation coordination property; d[F(σ, ρ)] describes the Mises stress of the polymer cut-off wall, d[F(Fv, ρ)] describes the slope stability coefficient of the dam, and d[F(σ, ρ)], d[F(Fv, ρ)] belong to the indexes related to the strength property; d[F(S, ρ)] describes the construction cost and belongs to the index related to the cost;

[0180] Considering various factors, the 3 weight allocation schemes adopted in this example are shown in Table 3;

[0181] Table 3 Weight Allocation Scheme

[0182]

[0183] Substituting Table 3 into Equation (11), we can obtain:

[0184] The objective function of Scheme 1 is: D[ρ] = -21.87ρ 2 + 47.18ρ + 2.51 (12)

[0185] The objective function of Scheme 2 is: D[ρ] = -37.61ρ 2 + 84ρ + 3.82 (13)

[0186] The objective function of Scheme 3 is: D[ρ] = -12.85ρ 2 +22.14ρ + 0.29(14)

[0187] Taking the minimum value of Equation (12) in the interval [0.1, 0.3], the optimal polymer density ρ under the equal - weight allocation scheme is 0.232 g / cm 3 ; taking the minimum value of Equation (13) in the interval [0.1, 0.3], the optimal polymer density ρ under the partial strength reserve allocation scheme is 0.223 g / cm 3 ; taking the minimum value of Equation (14) in the interval [0.1, 0.3], the optimal polymer ρ under partial deformation control is 0.29 g / cm 3 , as Figure 24 shown.

[0188] A method for optimizing the density of a polymer cutoff wall dam based on multi - objective optimization proposed by the present invention performs finite - element calculations on the polymer cutoff wall dam. On the premise that the dam body material and the dam foundation material are consistent with the actual situation, the density of the polymer material is changed, and the influence of polymer materials with different densities on the working state of the dam body is calculated; and five specific evaluation indicators are proposed from aspects such as displacement difference, length of the void area, Mises stress of the cutoff wall, dam slope stability coefficient, and construction cost. Through multi - objective optimization, the calculation is more concise and efficient. The above - described specific content in this specification is only an example of the present invention and is not used to limit the present invention; for those of ordinary skill in the art, equivalent substitutions or changes can be made according to the technical solution and its concept of the present invention; any modification made within the scope of the thought and principle of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analyzing the density of a polymer impervious wall of a dam to be de-risked and reinforced, characterized in that It includes the following steps: Step 1: Obtain the modeling information of the dam to be reinforced against risks. Step 2: Establish a finite element model and determine the evaluation indexes. Step 3: By solving the finite element model in Step 2, obtain the relationship between the evaluation indexes and the density. Step 4: Through normalizing the relationship between the evaluation indexes and the density obtained in Step 3, obtain the efficacy function. Step 5: Determine the index weights, linearly superimpose the efficacy function obtained in Step 4 according to the weight distribution scheme, construct an objective function regarding the density, and determine the optimal density. In Step 2: Use the information obtained in Step 1 to establish a finite element model of the dam. The geometric shape of this finite element model is divided into two or more elements, and each element is connected by shared nodes. The density of the polymer grouting material is a sensitivity parameter, and the factors to be considered are the displacement difference, the length of the void area, the Mises stress of the cut-off wall, the dam slope stability coefficient, and the construction cost. The displacement difference is the absolute value of the vertical displacement value of point x on the cut-off wall at time t minus the vertical displacement value of the corresponding point x on the dam body at time t. The length of the void area is the absolute value of the deflection of point x on the cut-off wall at time t minus the displacement value of the corresponding point x on the dam body at time t in the normal direction of the cut-off wall. The dam slope stability coefficient refers to the ratio between the maximum shear strength of the soil mass inside the slope and the actual shear stress generated by the external load inside the slope under the condition that the external load remains unchanged, and it is widely used as a criterion for judging the critical failure of the dam slope in finite element analysis. The construction cost is the project cost corresponding to polymer materials with different densities. The Mises stress of the cut-off wall is an equivalent stress based on the shear strain energy, and its value is: where σ is the Mises stress of the cut-off wall, σ1 represents the principal stress with the largest value, σ1≥σ2≥σ3, and the sorting considers the positive and negative signs. σ2 is the principal stress with a value between σ1 and σ3, and σ3 represents the principal stress with the smallest value.

2. The method for analyzing the density of the polymer impervious wall of the dam to be reinforced against danger according to claim 1, wherein: The modeling information of the dam to be reinforced against risks obtained in the step 1 includes: the density ρ of the dam body soil bt , the elastic modulus E of the dam body soil bt , the Poisson's ratio μ of the dam body soil bt , the cohesion c of the dam body soil bt , the internal friction angle of the dam body soil and the permeability coefficient k of the dam body soil bt ; the density ρ of the dam foundation soil bj , the elastic modulus E of the dam foundation soil bj , the Poisson's ratio μ of the dam foundation soil bj , the cohesion c of the dam foundation soil bj , the internal friction angle of the dam foundation soil and the permeability coefficient k of the dam foundation soil bt ; the shape and size of the dam to be reinforced against risks; the construction depth l and construction thickness b of the polymer impervious wall To obtain the optimal polymer density, within the implementation range of the polymer density during construction: 0.1 g / cm 3 - 0.3 g / cm 3 , polymers with densities of 0.1 g / cm 3 , 0.15 g / cm 3 , 0.2 g / cm 3 , 0.25 g / cm 3 , and 0.3 g / cm 3 are selected. Through indoor tests, the elastic modulus E 3 , Poisson's ratio μ 3 , and permeability coefficient k 3 of polymers with densities of 0.1 g / cm 3 , 0.15 g / cm 3 are measured. x , Poisson's ratio μ x , and permeability coefficient k x .

3. The method for analyzing the density of the polymer impervious wall of the dam to be reinforced against risks according to claim 2, characterized in that: In Step 3, using the finite element model of the polymer impervious wall dam established in Step 2, displacement constraints in the x and y directions are imposed on the bottom of the finite element model; displacement constraints in the x direction are imposed on both sides, and no constraint is imposed in the y direction. A water load is applied upstream of the dam to analyze the forces and displacements received by each node; through the x-direction displacement difference between the nodes corresponding to the impervious wall and the dam body, the y-direction displacement difference between the nodes corresponding to the impervious wall and the dam body, and the maximum Mises stress of each node of the impervious wall, the density of the polymer grouting material is obtained as 0.1 g / cm 3 , 0.15 g / cm 3 , 0.2 g / cm 3 , 0.25 g / cm 3 , 0.3 g / cm 3 respectively corresponding to: the length of the void area, the displacement difference, the Mises stress of the impervious wall, and the dam slope stability coefficient; the length of the void area is taken as the maximum value of the absolute value of the x-direction displacement difference between the nodes corresponding to the impervious wall and the dam body, the displacement difference is taken as the maximum value of the absolute value of the y-direction displacement difference between the nodes corresponding to the impervious wall and the dam body, the Mises stress of the impervious wall is taken as the maximum Mises stress among the nodes of the impervious wall, and the dam slope stability coefficient is calculated by the strength reduction method; Obtain the functional relationship between the maximum displacement difference H and the polymer density ρ through quadratic function fitting: F(H,ρ) = -0.00795ρ 2 -0.00482ρ + 0.00357; Taking the maximum displacement difference as the vertical coordinate and the polymer density as the horizontal coordinate, draw the relationship diagram between the displacement difference and the polymer density. Obtain the functional relationship between the maximum length of the void area h and the polymer density ρ through quadratic function fitting: F(h,ρ) = -0.001371ρ 2 -0.0077ρ + 0.004; Taking the maximum length of the void area as the vertical coordinate and the polymer density as the horizontal coordinate, draw the relationship diagram between the maximum length of the void area and the polymer density. The functional relationship between the maximum Mises stress σ of the cut-off wall and the density ρ of the polymer is obtained by fitting with a quadratic function: F(σ,ρ) = 943223ρ 2 - 582488ρ + 144671; Taking the maximum Mises stress of the cut-off wall as the vertical coordinate and the polymer density as the horizontal coordinate, draw the relationship diagram between the maximum Mises stress of the cut-off wall and the polymer density. Since the lengths of the void areas, displacement differences, and Mises stresses of the cutoff walls all belong to the smaller-the-better expectations, that is, the smaller the values, the more satisfactory the results, while the dam slope stability coefficient belongs to the larger-the-better expectation, that is, the larger the dam slope stability coefficient, the more stable the dam slope. Therefore, the reciprocal of the dam slope stability coefficient is used as the evaluation index; the reciprocal K of the stability coefficient is obtained by fitting with a quadratic function. -1 The functional relationship between F(K -1 ,ρ) = 0.07ρ 2 - 0.0296ρ + 0.54; Taking the reciprocal of the stability coefficient as the vertical coordinate and the polymer density as the horizontal coordinate, draw the relationship diagram between the reciprocal of the stability coefficient and the polymer density. The relationship F(S,ρ) between the construction cost S and the polymer density ρ is expressed by the following formula: F(S,ρ)=(α+βρ)abd Where: α is the sum of the mechanical usage fee and labor cost required for the construction of each cubic meter of the polymer impervious wall, with the unit of yuan / m 3 ; β is the cost of each kilogram of the polymer grouting material, with the unit of yuan / m 3 ; ρ is the polymer density, with the unit of kg / m 3 ; a is the width of the polymer impervious wall, with the unit of m; b is the depth of the polymer impervious wall, with the unit of m; d is the thickness of the polymer cut-off wall, with the unit of m.

4. The method for analyzing the density of the polymer cut-off wall of the dam to be reinforced against risks according to claim 3, wherein: In Step 4: The relationship F(X i , ρ) between different evaluation indices obtained in Step 3 and different densities of the polymer is normalized. For i = 1 to 5: X1 is the maximum displacement difference, X2 is the maximum void length, X3 is the maximum Mises stress of the cutoff wall, X4 is the dam slope stability factor, and X5 is the construction cost, to obtain the efficacy function d[F(X i , ρ)]: Due to the evaluation index X i and the function F(X i , ρ) between the density ρ is a dimensional function, so the normalization process should be carried out on F(X i , ρ) first. The normalization method is as follows: s.t. ρ ∈ [ρ min , ρ max ​ where ρ min , ρ max represent the minimum polymer density and the maximum polymer density that can be implemented during the actual construction process, respectively. Among them, the minimum polymer density is 0.1 g / cm 3 , and the maximum polymer density is 0.3 g / cm 3 ; s.t. ρ ∈ [ρ min , ρ max represents the boundary condition of the formula, that is, the density value range of the polymer is between 0.1 g / cm 3 and 0.3 g / cm 3 ; The functional relationship F(H,ρ) between the maximum displacement difference H and the polymer density ρ can be normalized to obtain its efficacy function d[F(H,ρ)], and the expression is as follows: d[F(H,ρ)] = -4.9688ρ 2 -3.0125ρ + 1.3509; The functional relationship F(h,ρ) between the maximum void length h and the polymer density ρ can be normalized to obtain its efficacy function d[F(h,ρ)], and the expression is as follows: d[F(h,ρ)] = -0.8311ρ 2 -4.6676ρ + 1.475; The functional relationship F(σ,ρ) between the maximum Mises stress σ and the polymer density ρ can be normalized to obtain its efficacy function d[F(σ,ρ)], and the expression is as follows: d[F(σ,ρ)] = 22.98ρ 2 -14.19ρ + 2.19; The reciprocal K of the dam slope stability coefficient - 1 The functional relationship F(K -1 , ρ) between the polymer density ρ can be normalized to obtain its efficacy function d[F(K -1 , ρ)], and the expression is as follows: d[F(K -1 ,ρ)] = 218.91ρ 2 - 92.5ρ - 8.0625; The functional relationship F(S,ρ) between the construction cost S and the polymer density ρ can be normalized to obtain its efficacy function d[F(S,ρ)], and the expression is as follows: d[F(S,ρ)] = 5ρ - 0.

5.

5. The method for analyzing the density of the high-polymer impervious wall of the dam to be reinforced against risks according to claim 4, characterized in that In step 5: The effectiveness functions d[F(H,ρ)], d[F(h,ρ)], d[F(σ,ρ)], d[F(K -1 ,ρ)], d[F(S,ρ)] in step 4 are assigned weight coefficients according to their importance in the actual project: the weight coefficient of the maximum displacement difference is λ1, the weight coefficient of the maximum length of the void area is λ2, the weight coefficient of the maximum Mises stress of the cut-off wall is λ3, the weight coefficient of the stability coefficient is λ4, and the weight coefficient of the construction cost is λ5. The sum of the weight coefficients is 100%; Determine three weight coefficient distribution schemes: The first scheme is the equal weight scheme, that is, λ1 = λ2 = λ3 = λ4 = λ5 = 20%; The second scheme is the partial strength control scheme, which increases the weights of the maximum Mises stress of the cutoff wall and the slope stability coefficient, that is, λ1 = λ2 = λ5 = 10%, λ3 = λ4 = 35%; The third scheme is the partial deformation control scheme, which increases the weights of the displacement difference and the void length, that is, λ1 = λ2 = 35%, λ3 = λ4 = λ5 = 10%; According to the basic principle of multi-objective optimization, the objective function about ρ is constructed as s.t. ρ ∈ [ρ min , ρ max ​ Each index is assigned a proportion according to its importance in the actual project, that is, the weight coefficient; where: D[ρ] is the objective function, and the ρ corresponding to minD[ρ] is the optimal polymer density ρ for the coordinated deformation of the dam body; d[F(X i ,ρ)] is the efficacy function of each evaluation index. The evaluation indexes include: X1 represents the maximum displacement difference H, X2 represents the maximum length of the void area h, X3 represents the Mises stress σ of the cutoff wall, X4 represents the dam stability coefficient K, X5 represents the construction cost S, and X i are the 5 evaluation indexes in Step 3; where k = 5, and λ i is the set value of the importance of the 5 evaluation indexes, that is, the index weight: the weight coefficient λ1 of the maximum displacement difference, the weight coefficient λ2 of the maximum length of the void area, the weight coefficient λ3 of the maximum Mises stress, the weight coefficient λ4 of the stability coefficient, and the weight coefficient λ5 of the construction cost. The sum of the index weights is 100%; Obtain the objective function value of ρ: Just solve for the value of ρ.

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