Calculation method for lateral deformation of asymmetric foundation pit diaphragm wall based on high-order plate theory

Abstract

The application relates to a kind of asymmetric foundation pit underground continuous wall lateral deformation calculation methods based on high-order plate theory, comprising: obtaining the parameter data of foundation pit, parameter data at least include underground continuous wall data, soil geological data, support data and foundation pit load calculation data;Establish a mechanical analysis model, and calculate the deformation generalized displacement field of continuous wall based on generalized third-order shear deformation plate theory, determine the displacement function of continuous wall;Calculate the total potential energy function of continuous wall, and the total potential energy includes continuous wall strain energy and the work of multiple external forces;Determine lateral deformation function, lateral deformation function meets total potential energy function minimum value;Determine the earth pressure distribution of continuous wall, and earth pressure distribution is obtained according to displacement function calculation;According to non-limiting soil pressure-displacement model and the earth pressure distribution, determine the three-dimensional earth pressure behind continuous wall;Iterative calculation of earth pressure distribution of continuous wall and the three-dimensional earth pressure behind the continuous wall, determine the lateral deformation of continuous wall.

Description

Technical Field

[0001] This invention relates to the field of earth pressure technology in civil engineering, and more specifically to a method for calculating the lateral deformation of an asymmetric foundation pit diaphragm wall based on higher-order plate theory. Background Technology

[0002] In urban underground space development, the size of foundation pits is constantly increasing, and there are significant differences in loads on both sides of the pit retaining structure. Internally braced diaphragm walls are a commonly used retaining structure for deep foundation pits. Related theoretical analysis methods often simplify the diaphragm wall to a plane strain state, neglecting the differences in stress and deformation along the wall's length. Furthermore, for wall deformation calculations under asymmetrical loads, the design is often based on the most unfavorable side of the retaining structure, leading to over-design on the side with less stress and resulting in economic losses.

[0003] To simplify the mechanical model, related calculation methods often treat the diaphragm wall as a rectangular thin plate and use classical plate theory for stress and deformation analysis. However, this model is not applicable to thick plate problems. Summary of the Invention

[0004] To address the aforementioned shortcomings, this invention provides a method for calculating the lateral deformation of an asymmetric diaphragm wall in an excavation pit based on higher-order plate theory. The method includes: acquiring parameter data of the excavation pit, including at least diaphragm wall data, soil geological data, support data, and excavation pit load calculation data; establishing a mechanical analysis model and calculating the generalized displacement field of the diaphragm wall based on the generalized third-order shear deformation plate theory to determine the displacement function of the diaphragm wall; calculating and determining the total potential energy function of the diaphragm wall, where the total potential energy includes the strain energy of the diaphragm wall and the work done by multiple external forces; determining the lateral deformation function, where the lateral deformation function satisfies the minimum value of the total potential energy function; determining the earth pressure distribution of the diaphragm wall, where the earth pressure distribution is calculated based on the displacement function; determining the three-dimensional earth pressure behind the diaphragm wall based on the non-limit earth pressure-displacement model and the earth pressure distribution; and iteratively calculating the earth pressure distribution of the diaphragm wall and the three-dimensional earth pressure behind the diaphragm wall to determine the lateral deformation of the diaphragm wall.

[0005] Optionally, the acquisition of the foundation pit parameter data includes at least the diaphragm wall data, soil geological data, support data, and foundation pit load calculation data, including: establishing Cartesian coordinate systems with the corner points of the two diaphragm walls as the origins, setting the displacement direction of the diaphragm wall into the foundation pit as positive; setting the support as an elastic rod, and continuously connecting the two ends of the support to the two diaphragm walls, setting the compression deformation of the support as positive; setting the external load of the foundation pit as a uniformly distributed load acting on the diaphragm wall.

[0006] Optionally, the establishment of a mechanical analysis model and the calculation of the generalized displacement field of the continuous wall based on the generalized third-order shear deformation plate theory, and the determination of the displacement function of the continuous wall, include: the generalized displacement field satisfying:

[0007]

[0008] Where u0(x,y), v0(x,y), and w0(x,y) are the displacements of the plate along the x-axis, y-axis, and z-axis, respectively, and φ is the displacement of the plate along the x-axis, y-axis, and z-axis, respectively. x (x,y), θ x (x,y), λ x (x,y) and φ y (x,y), θ y (x,y), λ y (x, y) are the rotation angles of the normal to the mid-surface of the plate along the x and y axes, respectively.

[0009] Optionally, the establishment of a mechanical analysis model and the calculation of the generalized displacement field of the continuous wall based on the generalized third-order shear deformation plate theory, and the determination of the displacement function of the continuous wall, include: the displacement function satisfying:

[0010]

[0011] Where n, m, l, o, p, t, u, v, and w are the polynomial terms of each displacement function; a i b i c i d i e i f i g i h i and k i These are the undetermined coefficients of each displacement function; φ xi , φ yi φ zi , ψ xi , ψ yi , ζ xi , ζ yi ξ xi and ξ yi These are functions defined by the boundaries of the continuous wall.

[0012] Optionally, the calculation determines the total potential energy function of the diaphragm wall, the total potential energy including the strain energy of the diaphragm wall and the work done by multiple external forces, and the total potential energy function satisfies the following formula:

[0013]

[0014] Among them, U L U represents the strain energy function of the left wall of the continuous wall; RJ1 is the strain energy function of the right wall of the continuous wall; J2 is the support deformation energy. Work is done on the active lateral earth pressure on the left diaphragm wall; Work is done on the active lateral earth pressure on the right-side diaphragm wall; Work is done on the passive lateral earth pressure on the left diaphragm wall; Work is done on the passive lateral earth pressure on the right-side diaphragm wall.

[0015] Optionally, the lateral deformation function is determined, wherein the lateral deformation function satisfies the condition that the total potential energy function takes the minimum value, and also satisfies:

[0016]

[0017] The calculation yielded:

[0018]

[0019] Where {α} are the undetermined coefficients of the displacement function of the continuous wall; [K] is the material stiffness matrix of the continuous wall; {Q} is the function related to the work done by the earth pressure; the superscript L indicates that it is related to the left continuous wall; the superscript R indicates that it is related to the right continuous wall; and the superscript LR indicates that it is related to both walls.

[0020] Optionally, the earth pressure distribution of the continuous wall is determined based on the displacement function and satisfies the following formula:

[0021]

[0022] Where w(x,y) is the displacement function of the continuous wall; η a,max η is the coefficient of the active ultimate earth pressure; p,max η is the coefficient of passive ultimate earth pressure. m The coefficient for non-ultimate earth pressure; δ a and δ p These are the active and passive ultimate displacements of the soil, respectively; when the displacement of the continuous wall is less than the ultimate displacement δ of the soil... a and δ p At that time, η a,max =0, η p,max =0, η m =1, at this time the diaphragm wall is subjected to non-ultimate earth pressure; when the displacement of the diaphragm wall is greater than the ultimate displacement δ of the soil... a and δ p At that time, η a,max =1, η p,max =1, η m =0, at which point the continuous wall is subjected to active ultimate earth pressure or passive ultimate earth pressure.

[0023] Optionally, the three-dimensional earth pressure distribution behind the continuous wall is calculated based on the non-ultimate earth pressure-displacement model and the earth pressure distribution, wherein the non-ultimate earth pressure satisfies the following formula:

[0024]

[0025] The earth pressure-displacement function curve is divided into equal parts according to displacement intervals, and the relationship between earth pressure and displacement in each infinitesimal element is approximately reflected by straight line segments. m,i+1 and p m,i The displacements δ of the continuous wall are respectively i+1 δ i The corresponding non-ultimate earth pressure values, and satisfying that when the continuous wall displacement is in a static or ultimate state, the earth pressure values ​​are equal to the static earth pressure p0 and the active ultimate earth pressure p, respectively. a Or passive ultimate earth pressure p p Substitute η a,max η is the coefficient of the active ultimate earth pressure; p,max η is the coefficient of passive ultimate earth pressure. m Let be the coefficient for non-ultimate earth pressure. The distribution of three-dimensional earth pressure behind the wall satisfies the following formula:

[0026] P(x,y)=η a,max (x,y)p a (x,y)+η p,max (x,y)p p (x,y)+η m (x,y)p m (x,y).

[0027] The method for calculating the lateral deformation of diaphragm walls in asymmetric foundation pits proposed in this invention can determine the lateral deformation of diaphragm walls on both sides with high accuracy, which is of great significance for foundation pit retaining design, ensuring construction safety, and increasing the overall economic benefits of foundation pit projects. This invention considers the actual working conditions of the diaphragm wall, releases the forced assumption of shear force along the thickness direction of the slab, and calculates the deformation of the retaining structure based on the generalized third-order shear deformation plate theory, thus exhibiting better universality and higher calculation accuracy. Attached Figure Description

[0028] The following figures illustrate exemplary embodiments of the present invention by way of example, and the same or similar reference numerals are used in the figures to denote the same or similar elements. In the figures:

[0029] Figure 1 A flowchart illustrating an exemplary embodiment of the present invention is provided, showing a method for calculating the lateral deformation of an asymmetric foundation pit diaphragm wall based on higher-order plate theory.

[0030] Figure 2A schematic diagram of a continuous wall stress model according to an exemplary embodiment of the present invention is shown.

[0031] Figure 3 A schematic diagram of continuous wall micro-element mesh generation, illustrating an exemplary embodiment of the present invention, is shown.

[0032] Figure 4 An earth pressure-displacement relationship diagram of an exemplary embodiment of the present invention is shown.

[0033] Figure 5a A three-dimensional deformation diagram of the left continuous wall of an exemplary embodiment of the present invention is shown.

[0034] Figure 5b A three-dimensional deformation diagram of the right-side continuous wall of an exemplary embodiment of the present invention is shown.

[0035] Figure 6 A schematic diagram showing the comparison between theoretical calculation results and field measurements of an exemplary embodiment of the present invention is provided. Detailed Implementation

[0036] To better explain and facilitate understanding of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] In this invention, the term "and / or" is intended to cover all possible combinations and sub-combinations of the listed elements, including any one, any sub-combination, or all of the elements listed individually, without necessarily excluding other elements. Unless otherwise stated, the terms "first," "second," etc., are used to describe various elements without intending to limit the positional, temporal, or importance relationships of these elements; such terms are merely used to distinguish one element from another. Unless otherwise stated, the orientations or positional relationships indicated by the terms "front," "back," "up," "down," "left," "right," etc., are generally based on the orientations or positional relationships shown in the accompanying drawings and are only for ease of description and simplification, and should not be construed as limiting the scope of protection of this invention.

[0038] Figure 1 A flowchart illustrating an exemplary embodiment of the present invention is provided, showing a method for calculating the lateral deformation of an asymmetric foundation pit diaphragm wall based on higher-order plate theory.

[0039] S102: Obtain parameter data of the foundation pit, the parameter data including at least diaphragm wall data, soil geological data, support data, and foundation pit load calculation data.

[0040] like Figure 2 As shown, the underground continuous walls on both sides are simplified into rectangular plates. A Cartesian coordinate system is established with one corner of the continuous wall as the coordinate center, and the displacement towards the pit is set as positive. Figure 1 H L LL t L These represent the depth, length, and thickness of the diaphragm wall on the left, H. R L R t R These are the depth, length, and thickness of the continuous wall on the right side, respectively. and The excavation depth is indicated on both the left and right sides.

[0041] Based on the site conditions, a rectangular slab with length L, width H, and thickness t of the diaphragm walls on both sides is obtained; the soil layer distribution of the diaphragm walls on both sides includes: the thickness h of each soil layer. i Severe V i internal friction angle Cohesion c i And set the active limit displacement value δ for each soil layer. a With the passive limit displacement value δ p Determine the excavation depth h on both sides of the foundation pit. d The value of the load q outside the pit and its distribution along the length of the continuous wall and its distance from the wall are determined. Further, a Cartesian coordinate system is established with one corner of each of the two continuous walls as the origin, and the displacement direction of the two continuous walls towards the pit is set as positive. Elastic members are assumed to be used for the support, and it is always assumed that the two ends of the support remain in contact with the two continuous walls during deformation, and the compression deformation of the support is set as positive. The soil layers behind the wall are uniformly distributed and layered. Combining the distance between the load outside the pit and the continuous wall and its distribution along the length of the wall, the load is simplified to a uniformly distributed load acting on the continuous wall according to the standard method.

[0042] S104: Establish a mechanical analysis model and calculate the deformation generalized displacement field of the continuous wall based on the generalized third-order shear deformation plate theory, and determine the displacement function of the continuous wall.

[0043] Based on the deformation characteristics of continuous walls and the generalized third-order shear deformation plate theory, the normal strain in the direction of the surface normal of the plate (physically rectangular plate, non-shear deformation) is set to zero, that is, the displacement function w(x,y) in the z direction is independent of z. The generalized displacement field of the continuous wall deformation is calculated and satisfies the following formula (1):

[0044]

[0045] Where u0(x,y), v0(x,y), and w0(x,y) are the displacements of the plate along the x-axis, y-axis, and z-axis, respectively, and φ is the displacement of the plate along the x-axis, y-axis, and z-axis, respectively. x (x,y), θ x (x,y), λ x (x,y) and φ y (x,y), θ y (x,y), λy (x, y) are the rotation angles of the normal to the mid-surface of the plate along the x and y axes, respectively.

[0046] Based on the working environment of the diaphragm wall, the boundary condition assumptions of the diaphragm wall are adjusted, and the displacement and rotation angles of the two diaphragm walls are set using the pb-2 Rayleigh Ritz method to obtain the displacement function, which satisfies the following formula (2):

[0047]

[0048] Where n, m, l, o, p, t, u, v, and w are the polynomial terms of each displacement function; a i b i c i d i e i f i g i h i and k i These are the undetermined coefficients (variables to be solved) of each displacement function; φ xi φ yi φ zi , ψ xi , ψ yi , ζ xi , ζ yi ξ xi and ξ yi These are functions related to the boundary of the continuous wall. Let φ be an example. xi For example, Among them, Ω1, Ω2, Ω3, and Ω4 are determined according to the boundary conditions of the top, bottom, left, and right sides of the continuous wall; when it is a free boundary, Ω i =0; Ω when it is a simply supported boundary i =1; when it is a fixed boundary, Ω i =2.

[0049] In some embodiments, the number of undetermined coefficients is equal to the number of terms in the polynomial, and the more terms in the polynomial, the more accurate the theoretical calculation results.

[0050] S106: Calculate and determine the total potential energy function of the continuous wall, wherein the total potential energy includes the strain energy of the continuous wall and the work done by multiple external forces.

[0051] Based on the generalized displacement field equation of the continuous wall deformation, and combined with the established continuous wall displacement function, the strain energy function U of the continuous wall is calculated. Each support is set as an elastic rod, and both ends of the support are fixed to the wall. At this point, the support deformation value is the relative displacement w between the two walls. L (x,y)+w R(x,y), calculate the support deformation energy J1; assume that the displacement of the soil behind the wall is the same as that of the continuous wall, that is, the non-ultimate earth pressure is linearly related to the wall displacement, and set that when the displacement of the continuous wall reaches or exceeds the ultimate displacement of the soil, the earth pressure is in the ultimate earth pressure state, and the relationship between the magnitude of the non-ultimate earth pressure and the lateral deformation of the wall satisfies the following formula (3):

[0052]

[0053] In the formula, w is the lateral deformation value of the wall, and P m P is the non-ultimate earth pressure, P0 is the at-rest earth pressure, and P a This refers to the active ultimate earth pressure.

[0054] like Figure 3 As shown, by dividing the underground continuous wall into high-precision micro-element meshes (d... x d y ), set the earth pressure values ​​in each grid to be the same, and calculate the work done by the active lateral earth pressure J2; calculate the weighted average of the unit weight, internal friction angle and thickness of each soil layer in the foundation pit, and calculate the work done by the passive lateral earth pressure J3 using the linear elastic m method (refer to the Technical Specification for Foundation Pit Support JGJ120-2012). Taking into account the total strain energy and the work done by the external forces, establish the total potential energy function of the continuous wall, which satisfies the following formula (4):

[0055]

[0056] Among them, the superscripts L and R indicate that they are related to the left and right diaphragm walls, respectively; U L U represents the strain energy function of the left wall of the continuous wall; R J1 is the strain energy function of the right wall of the continuous wall; J2 is the support deformation energy. Work is done on the active lateral earth pressure on the left diaphragm wall; Work is done on the active lateral earth pressure on the right-side diaphragm wall; Work is done on the passive lateral earth pressure on the left diaphragm wall; Work is done on the passive lateral earth pressure on the right-side diaphragm wall.

[0057] S108: Determine the lateral deformation function, wherein the lateral deformation function satisfies the condition that the total potential energy function takes the minimum value.

[0058] According to the principle of minimum potential energy, Further calculations yielded the following matrix equation:

[0059]

[0060] Where {α} are the undetermined coefficients of the displacement function of the continuous wall; [K] is the material stiffness matrix of the continuous wall; {Q} is the function related to the work done by the earth pressure; the superscript L indicates that it is related to the left continuous wall; the superscript R indicates that it is related to the right continuous wall; and the superscript LR indicates that it is related to both walls.

[0061] Solve for α L α R Substituting this into the formula for the displacement function, we can obtain the lateral deformation function w of the continuous walls on both sides. L (x,y) and w R (x,y).

[0062] S110: Determine the earth pressure distribution of the continuous wall, wherein the earth pressure distribution is calculated based on the displacement function.

[0063] Based on the calculated lateral deformation values ​​of the diaphragm walls on both sides and the ultimate displacement δ of the active side soil... a and δ p The relationship between the earth pressure and the soil pressure pattern of each continuous wall micro-element mesh is determined, satisfying the following formula (6):

[0064]

[0065] Where w(x,y) is the displacement function of the continuous wall; η a,max η is the coefficient of the active ultimate earth pressure; p,max η is the coefficient of passive ultimate earth pressure. m δ is the coefficient for non-ultimate earth pressure; a and δ p These are the active and passive ultimate displacements of the soil, respectively; when the displacement of the continuous wall is less than the ultimate displacement δ of the soil... a and δ p At that time, η a,max =0, η p,max =0, η m =1, at this time the diaphragm wall is subjected to non-ultimate earth pressure; when the displacement of the diaphragm wall is greater than the ultimate displacement δ of the soil... a and δ p At that time, η a,max =1, η p,max =1, η m =0, at which point the continuous wall is subjected to active ultimate earth pressure or passive ultimate earth pressure.

[0066] S112: Calculate the three-dimensional earth pressure behind the continuous wall based on the non-ultimate earth pressure-displacement model and the earth pressure distribution.

[0067] like Figure 4As shown, a non-ultimate earth pressure-displacement model is introduced. Considering the problem of solving the theoretical model, the embodiment of this invention divides the earth pressure-displacement function curve into equal parts according to displacement intervals, and uses straight line segments to approximately reflect the relationship between earth pressure and displacement in each infinitesimal segment. Non-ultimate earth pressure p m It satisfies the following formula (7):

[0068]

[0069] Where, p m,i+1 and p m,i The displacements δ of the continuous wall are respectively i+1 δ i The corresponding non-ultimate earth pressure values, and satisfying that when the continuous wall displacement is in a static state or an ultimate state, the earth pressure is equal to the static earth pressure p0 and the active ultimate earth pressure p, respectively. a Or passive ultimate earth pressure p p .

[0070] The accuracy of the earth pressure model can be improved by adjusting the number of infinitesimal segments in the earth pressure-displacement relationship curve. Substitute the earth pressure-displacement mode coefficient η from step S110... a,max η p,max η m The earth pressure P behind the wall satisfies the following formula (8):

[0071] P(x,y)=η a,max (x,y)p a (x,y)+η p,max P(x,y)p p (x,y)+η m (x,y)p m (x,y) (8);

[0072] The non-ultimate earth pressure calculation method provided by the embodiments of the present invention can be combined with different earth pressure-displacement relationship curves to calculate p. m,i+1 and p m,i Adjustments were made, and the accuracy of the earth pressure model was improved by increasing the number of micro-segments, making it more closely resemble actual working conditions.

[0073] S114: Iteratively calculate the earth pressure distribution of the continuous wall and the three-dimensional earth pressure distribution behind the continuous wall to determine the lateral deformation of the continuous wall.

[0074] Repeat steps S110 and S112 to iteratively calculate the lateral deformation function of the wall. Considering computational efficiency and accuracy, set the number of undetermined coefficients n, m, l, o, p, t, u, v, and w, along with the convergence criterion for iterative deformation, to accurately calculate the lateral deformation of the continuous walls on both sides. Specifically, calculate the earth pressure p of the active side continuous wall based on the earth pressure distribution, then repeatedly calculate the work J2 done by the earth pressure on the active side, and obtain the lateral deformation function w and the earth pressure distribution on the active side. Iterate until the lateral deformation result converges.

[0075] In some embodiments, such as using MATLAB software, a system for calculating the lateral deformation of diaphragm walls in asymmetric foundation pits was developed. This system allows for quick and convenient calculation results with only input parameters, thus better serving practical engineering applications. To further illustrate the calculation method proposed in the embodiments of the present invention, the calculation results of the embodiments were compared with measured data from a foundation pit project to verify the accuracy of the calculation method of the present invention.

[0076] A foundation pit project is located near buildings and a subway tunnel. The project uses internally supported diaphragm walls as the main retaining structure, constructed using the open-cut method. The foundation pit is 46.9m long, 7m wide, and 12.35–19.05m deep. The left side of the pit is subjected to a load of 20kPa. The diaphragm walls on both sides are 24.5m and 33.2m deep respectively, with a wall thickness of 800mm. The concrete used is of grade C35. The support system consists of one 0.8×0.6m square support and three H400×400×13×21 steel composite supports. The concrete supports are spaced approximately 6m apart, and the steel supports are spaced approximately 3m apart. (Refer to Figure 5 and...) Figure 6 As shown, Figure 5 is a three-dimensional deformation diagram of a continuous wall obtained by the calculation method proposed in the embodiment of the present invention. Figure 6 This image shows a comparison between the theoretically calculated values ​​and the actual measured values ​​at monitoring points in a foundation pit project. By comparing these values ​​with a real-world engineering case, the accuracy of the calculation method presented in this invention is verified. It reflects the overall deformation of the diaphragm walls on both sides under asymmetric loads, and can provide theoretical guidance for the safety and design optimization of asymmetric foundation pit construction.

[0077] The method for calculating the lateral deformation of diaphragm walls in asymmetric foundation pits proposed in this invention can determine the lateral deformation of diaphragm walls on both sides with high accuracy, which is of great significance for foundation pit retaining design, ensuring construction safety, and increasing the overall economic benefits of foundation pit projects. This invention considers the actual working conditions of the diaphragm wall, releases the forced assumption of shear force along the thickness direction of the slab, and calculates the deformation of the retaining structure based on the generalized third-order shear deformation plate theory, thus exhibiting better universality and higher calculation accuracy.

[0078] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method for calculating the lateral deformation of an asymmetric underground continuous wall in an excavation pit based on higher-order plate theory, characterized in that, include: Obtain parameter data for the foundation pit, including at least diaphragm wall data, soil geological data, support data, and foundation pit load calculation data; A mechanical analysis model was established, and the deformation generalized displacement field of the continuous wall was calculated based on the generalized third-order shear deformation plate theory to determine the displacement function of the continuous wall. The total potential energy function of the continuous wall is calculated and determined, wherein the total potential energy includes the strain energy of the continuous wall and the work done by multiple external forces; Determine the lateral deformation function, wherein the lateral deformation function satisfies the condition that the total potential energy function takes the minimum value; The earth pressure distribution of the continuous wall is determined, and the earth pressure distribution is calculated based on the displacement function, satisfying the following formula: ； in, Let be the displacement function of the continuous wall; This is the coefficient of the active ultimate earth pressure. This is the coefficient of the passive ultimate earth pressure; This is the coefficient for non-ultimate earth pressure; and These are the active and passive ultimate displacements of the soil, respectively; when the displacement of the continuous wall is less than the ultimate displacement of the soil... and hour, , , At this point, the diaphragm wall is subjected to non-ultimate earth pressure; when the displacement of the diaphragm wall exceeds the ultimate displacement of the soil... and hour, , , At this time, the continuous wall is subjected to active ultimate earth pressure or passive ultimate earth pressure. Based on the non-ultimate earth pressure-displacement model and the earth pressure distribution, the three-dimensional earth pressure behind the continuous wall is determined. The non-ultimate earth pressure satisfies the following formula: ； The earth pressure-displacement function curve is divided into equal parts according to the displacement interval, and the relationship between earth pressure and displacement in each infinitesimal element is approximately reflected by straight line segments. and These are the displacements of the continuous wall. , The corresponding non-ultimate earth pressure value, and satisfying that when the continuous wall displacement is in a static or ultimate state, the earth pressure value is equal to the at-rest earth pressure. Active ultimate earth pressure Or passive ultimate earth pressure Substitute This is the coefficient of the active ultimate earth pressure. This is the coefficient of the passive ultimate earth pressure; Let be the coefficient for non-ultimate earth pressure. The distribution of three-dimensional earth pressure behind the wall satisfies the following formula: ;as well as The earth pressure distribution of the continuous wall and the three-dimensional earth pressure behind the continuous wall are calculated iteratively to determine the lateral deformation of the continuous wall.

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