Plastic drainage plate foundation equivalent plane strain simulation method

Abstract

The invention discloses a method for calculating bearing deformation of a plastic drainage plate foundation. The method includes the steps of setting the distance between drain boards in a plane strain model, selecting a proper unit type to simulate the drain boards, calculating and setting the equivalent width of the drain boards in the plane strain model, calculating and setting the equivalent horizontal permeability coefficient of foundation soil in the plane strain model, setting boundary conditions of the plane strain model and executing calculation. According to the method, the principle that the displacement per unit volume in a plane strain model and the displacement per unit volume in an axial symmetry model are equal is followed, the hydraulic gradient changing along with the consolidation process and the smearing effect and the well resistance effect of the drainage plate are considered, and a certain average consolidation degree does not need to be empirically selected in advance to serve as the requirement for matching conversion of the plane strain model; and a reasonable selection basis of the type of the drain board unit is given, modeling calculation of the drain board foundation can be rapidly completed, and a more accurate and reliable numerical simulation tool is provided for related design and calculation analysis of the drain board foundation.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology in civil engineering and geotechnical engineering, specifically relating to a method for calculating the bearing capacity and deformation of plastic drainage board foundations. Background Technology

[0002] Accurate prediction of the bearing-deformation behavior is crucial in the design, calculation, and construction of drainage board foundations. Numerical simulation, as an advanced and effective analytical tool, can simulate complex soil-structure interactions and time-varying loads, providing strong technical support for foundation settlement, lateral deformation, excess pore water pressure calculation, stress-strain analysis, stability evaluation, and optimization design. However, directly performing 3D solid modeling analysis presents several challenges: First, the cross-sectional dimensions of plastic drainage boards (e.g., a few millimeters thick, tens of millimeters wide) differ significantly from the scale of the foundation treatment area (tens or even hundreds of meters in length and width), resulting in substantial geometric scale differences in the model. Second, to accurately simulate seepage and stress fields around the drainage board, fine meshing is required near the drainage board, which not only easily leads to element mesh distortion but also significantly increases the likelihood of non-convergence in the calculation process. Third, even if successful modeling is achieved, the large number of elements consumes substantial computational resources (such as memory and CPU), resulting in excessively long calculation cycles that fail to meet the timeliness requirements of engineering design. Therefore, for linear or strip-shaped projects such as highways, railways, and dams, simplifying the three-dimensional problem into a two-dimensional plane strain problem for calculation and analysis is an important way to improve computational efficiency.

[0003] Therefore, various calculation methods have been developed in the existing technology to equate the three-dimensional drainage board foundation to a two-dimensional plane strain model. Although these methods have improved the calculation efficiency to a certain extent, they generally have the defects of incomplete theoretical assumptions and inadequate consideration of physical processes, resulting in the simulation accuracy still needing to be improved. Specifically, the following shortcomings exist: (1) Deviation in the equivalence principle: When converting from a three-dimensional model to a two-dimensional plane strain model, most methods fail to strictly ensure that the drainage volume per unit volume of soil remains consistent throughout the entire consolidation process before and after the conversion, which is one of the fundamental reasons for the calculation error. (2) Incomplete consideration of key physical factors: Existing methods fail to comprehensively and dynamically consider the key factors affecting the foundation consolidation process. For example, the dynamic changes in the hydraulic gradient caused by the dissipation of pore water pressure during the consolidation process are ignored; at the same time, the smearing effect of reduced permeability formed around the pile during the installation of the drainage board and the well resistance effect caused by the limited permeability of the drainage board itself are not adequately considered or are oversimplified, resulting in deviations from the actual engineering situation. (3) Reliance on empirical assumptions: Many equivalent methods require artificially setting an average degree of consolidation as the basis for parameter conversion based on experience. However, the degree of consolidation is the final result of the calculation, not the initial input condition. This approach makes the model construction dependent on subjective experience, inevitably introducing potential errors into the calculation results and affecting the reliability of the simulation results.

[0004] In conclusion, it is necessary to improve the existing methods. Summary of the Invention

[0005] Therefore, this invention provides a method for calculating the bearing deformation of plastic drainage board foundations. This method is based on three-dimensional foundations and plane strain theory, while taking into account both calculation efficiency and accuracy. It can comprehensively reflect the bearing deformation process of drainage board foundations and eliminates the reliance on empirical assumptions.

[0006] A method for calculating the equivalent plane strain of a plastic drainage board foundation bearing deformation includes the following steps:

[0007] S1. Set the spacing of the drainage boards in the plane strain model.

[0008] The spacing between the drainage boards in the plane strain model is directly taken as the actual spacing s.

[0009] S2. Select and set the drainage board unit type.

[0010] Drainage boards can be simulated using drainage line units or solid units;

[0011] When the element type is a solid element, the equivalent diameter d of the drainage board is used. w The equivalent diameter d of the drainage board's affected area e The actual spacing s of the drainage boards is calculated using the following formula to determine the equivalent width b of the drainage boards in the plane strain model.w ;

[0012]

[0013] In the formula, a is the length of the drainage board cross-section, and b is the width of the drainage board cross-section.

[0014] S3. Calculate and set the equivalent horizontal permeability coefficient k of the foundation soil in the plane strain model. hp

[0015] Based on the actual spacing s of the drainage boards and the horizontal permeability coefficient k of the foundation soil h The equivalent diameter d of the drainage board's affected area e Based on the principle that the drainage volume is equal in the equivalent plane strain model and the axisymmetric model, the equivalent horizontal permeability coefficient k of the foundation soil is derived and established. hp ;

[0016]

[0017]

[0018] In the formula, d s k is the diameter of the smeared area. s q is the permeability coefficient of the coating area, l is the length of the drainage board, and q is the permeability coefficient of the coating area. w denoted as the drainage capacity of the drainage board, and μ as a dimensionless parameter related to the consolidation analysis of the drainage board foundation.

[0019] S4. Set boundary conditions and perform calculations.

[0020] Based on the actual engineering conditions, the displacement boundary and drainage boundary of the plane strain model are set, and simulation calculations are performed to obtain key data such as the surface settlement curve, the lateral deformation profile of the foundation, the excess pore water pressure dissipation curve in the foundation, and the stress and strain of the foundation soil.

[0021] Specifically, when selecting the drainage board unit type, the dimensionless well resistance factor μ' is calculated according to formula (6):

[0022] When μ'≤0.5, the drainage line element is used;

[0023] When μ'>0.5, solid elements are used.

[0024] Specifically, when using solid elements to simulate a drainage board, the equivalent permeability coefficient k of the drainage board needs to be calculated and set. wp The specific calculation is performed according to the following formula.

[0025]

[0026] In the formula, δ is k wpIn the derivation of the calculation formula, the virtual out-of-plane thickness of the plane strain model is used to ensure that the displacement of the plane strain model and the axisymmetric model are equal under the condition of equal volume.

[0027] Specifically, in the process of establishing the plane strain model, the change of the soil permeability coefficient with the void ratio is considered according to Taylor's formula. The exponent of the change in soil permeability coefficient with the void ratio is taken as 0.4-0.5 times the initial void ratio of the soil.

[0028] Specifically, displacement boundary conditions and drainage boundary conditions for the plane strain model are set according to the actual boundary conditions of the drainage board foundation.

[0029] Specifically, the equivalent width b of the drainage board in the plane strain model is calculated. w In both plane strain and axisymmetric models, the ratio of the cross-sectional area of ​​the drainage board to the area of ​​its influence zone remains constant.

[0030] Specifically, the equivalent horizontal permeability coefficient k of the foundation soil hp The specific solution process is as follows:

[0031] Based on the principle that the drainage volume is equal in the equivalent plane strain model and the axisymmetric model, the equivalent horizontal permeability coefficient k is derived and established. hp The calculation formula,

[0032] In an axisymmetric model, the drainage Δq of a saturated soil element of thickness dz within time dt. a It is equal to its change in volume, that is:

[0033]

[0034] In the formula, ε v Let z be the vertical strain, z be the depth, and t be the time.

[0035] When establishing a plane strain model, it is essential to ensure that the displacement of the plane strain model and the axisymmetric model are equal under the condition of equal volume. Therefore, a virtual out-of-plane thickness δ is introduced into the plane strain model to ensure that its volume is consistent with the corresponding axisymmetric model. Based on the above principle of equal volume, the formula for calculating δ is derived as follows:

[0036]

[0037] Furthermore, by replacing the initial excess pore water pressure u0 used in the original framework with the time-varying average excess pore water pressure ū, a displacement Δq in the equivalent plane strain model considering the dynamic changes of the hydraulic gradient and the principle of equal volume is derived. hp The expression is as follows:

[0038]

[0039] In the formula, γ w The specific gravity of water;

[0040] Let the displacement be equal in the plane strain model and the axisymmetric model, i.e., Δq. hp =Δq a And establish the vertical strain rate based on the effective stress principle. Relationship with average excess pore water pressure ū:

[0041]

[0042] In the formula, For the average effective stress, m v The volume compressibility factor;

[0043] From the above, we can obtain the approximate differential equation for the average excess pore water pressure ū:

[0044]

[0045] Solving the differential equation described in equation (13), and based on the initial condition ū(t=0)=u0, we can derive:

[0046]

[0047] Based on soil parameter relationships and average degree of consolidation The relationship between the average excess pore water pressure ū and equation (14) can be rewritten as equation (18):

[0048]

[0049] In the formula, T h c is the time factor for the horizontal consolidation of the soil. h and k h These are the horizontal consolidation coefficient and horizontal permeability coefficient of the soil, respectively.

[0050] Furthermore, according to Hansbo's radial consolidation theory:

[0051]

[0052] Substituting equations (9) and (19) into equation (18) yields the equivalent horizontal permeability coefficient k of the foundation soil. hp The calculation formula:

[0053]

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] 1. The principle is more scientific, and the accuracy is effectively improved.

[0056] This approach abandons the existing method of empirically selecting the degree of consolidation as the basis for conversion, eliminating the source of error caused by subjective selection. It strictly follows the core physical principle of "equal drainage per unit volume" for equivalent conversion, ensuring that the plane strain model and the actual three-dimensional model have consistent drainage behavior during the consolidation process, thus theoretically guaranteeing the simulation accuracy.

[0057] 2. It considers more comprehensive factors and the simulation is closer to reality.

[0058] Instead of using a fixed value, the dynamic hydraulic gradient that changes with the dissipation of pore water pressure during the consolidation process is considered. This eliminates the need to empirically select a certain average degree of consolidation as the basis for plane strain model matching and transformation, reducing potential errors that rely on user choice subjectivity and experience. The model systematically and quantitatively considers the two key factors affecting the consolidation rate, namely the smearing effect and the well resistance effect, making the model more reflective of engineering practice.

[0059] 3. Innovatively, a dimensionless well resistance factor μ' is introduced as a decision indicator, providing a clear and quantitative selection threshold (μ'≤0.5 or >0.5) to guide users in choosing between the computationally efficient "drain line element" or the more accurate "solid element". This overcomes the blind reliance on experience in the past and achieves the best balance between efficiency and accuracy.

[0060] 4. By transforming complex three-dimensional problems into two-dimensional plane strain problems, the number of computational units is greatly reduced, saving computational resources. Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1 This invention relates to schematic diagrams of an axisymmetric model and an equivalent plane strain model of a drainage board foundation;

[0063] Figure 2 This is a cross-sectional view of soft soil foundation and surcharge fill in an engineering case study;

[0064] Figure 3 This is a comparison chart of surface settlement calculation results in engineering cases;

[0065] Figure 4 This is a comparison chart of the calculation results of excess pore pressure in engineering cases. Detailed Implementation

[0066] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] See Figure 1 A method for calculating the bearing capacity and deformation of a plastic drainage board foundation includes the following steps:

[0068] S1. Set the spacing of the drainage boards in the plane strain model.

[0069] When establishing the plane strain model, the spacing of the plastic drainage boards (hereinafter referred to as drainage boards) (i.e. the influence width of a single drainage board) is taken as the actual spacing s of the drainage boards. This design can make the distribution of excess pore water pressure between adjacent drainage boards closer to the actual situation.

[0070] S2. Select and set the drainage board unit type.

[0071] Drainage boards can be simulated using drainage line units or solid units;

[0072] When the element type is a solid element, the equivalent diameter d of the drainage board is used. w The equivalent diameter d of the drainage board's affected area e The spacing s of the drainage boards is calculated using the following formula to determine the equivalent width b of the drainage boards in the plane strain model. w .

[0073]

[0074]

[0075] In the formula, a is the length of the drainage board cross-section, and b is the width of the drainage board cross-section.

[0076] S3. Calculate and set the equivalent horizontal permeability coefficient k of the foundation soil in the plane strain model. hp

[0077] Based on the actual spacing s of the drainage boards and the horizontal permeability coefficient k of the foundation soil h The equivalent diameter d of the drainage board's affected area e Based on the principle that the equivalent plane strain model and the axisymmetric model have equal drainage volumes, the equivalent horizontal permeability coefficient k in the plane strain model is derived and established. hp The calculation formula,

[0078]

[0079] In the formula, d s k is the diameter of the smeared area.s q is the permeability coefficient of the coating area, l is the length of the drainage board, and q is the permeability coefficient of the coating area. w denoted as the drainage capacity of the drainage board, and μ as a dimensionless parameter related to the consolidation analysis of the drainage board foundation.

[0080] S4. Set boundary conditions and perform calculations.

[0081] Based on the actual engineering conditions, the displacement boundary and drainage boundary of the plane strain model are set, and simulation calculations are performed using numerical simulation software such as Plaxis and Abaqus. This yields key data such as the surface settlement curve, the lateral deformation profile of the foundation, the excess pore water pressure dissipation curve in the foundation, and the stress and strain of the foundation soil.

[0082] This embodiment abandons the method of empirically selecting the degree of consolidation as the basis for conversion in the prior art, eliminates the source of error caused by subjective selection, and strictly follows the core physical principle of "equal drainage per unit volume" for equivalent conversion, ensuring that the plane strain model and the actual three-dimensional model have consistent drainage behavior during the consolidation process, thus theoretically guaranteeing the simulation accuracy.

[0083] In some embodiments, drainage board element types are divided into ideal drainage line elements with infinite drainage capacity and solid elements with drainage capacity consistent with actual drainage boards. Due to the influence of well resistance effect, different drainage board element types may lead to different simulation results. Inappropriate element type selection will result in problems such as insufficient accuracy of simulation calculation results or excessive computation time cost. This invention introduces a dimensionless well resistance factor μ' to consider the salience of well resistance effect, and selects an appropriate drainage board element type accordingly. The calculation formula for μ' is as follows.

[0084]

[0085] Research has shown that when μ' ≤ 0.5, drainage line elements, which offer simpler meshing and higher simulation efficiency, can achieve the required simulation accuracy for engineering applications. When μ' > 0.5, solid elements with finer meshing and a larger number of elements should be used to simulate the drainage board to ensure the accuracy of the simulation calculation. In practical applications, the dimensionless well resistance factor μ' for each soil layer should be calculated first, and the weighted average of μ' based on the soil layer thickness should be calculated. Then, based on this weighted average, the appropriate drainage board element type should be selected according to the principles mentioned above.

[0086] In this embodiment, a dimensionless well resistance factor μ' is innovatively introduced as a decision index, providing a clear and quantitative selection threshold (μ'≤0.5 or >0.5) to guide users on whether to choose the computationally efficient "drain line unit" or the more accurate "solid unit". This overcomes the blindness of relying on experience in the past and achieves the best balance between efficiency and accuracy.

[0087] Specifically, the equivalent horizontal permeability coefficient k of the foundation soil hp The specific solution process is as follows;

[0088] In an axisymmetric model, the drainage Δq of a saturated soil element of thickness dz within time dt. a It is equal to its change in volume, that is:

[0089]

[0090] In the formula, ε v Let z be the vertical strain, z be the depth, and t be the time.

[0091] When establishing a plane strain model, it is essential to ensure that the displacement of the plane strain model and the axisymmetric model are equal under the condition of equal volume. Therefore, a virtual out-of-plane thickness δ is introduced into the plane strain model to ensure that its volume is consistent with the corresponding axisymmetric model. Based on the above principle of equal volume, the formula for calculating δ is derived as follows:

[0092]

[0093] Furthermore, building upon the research framework of Kim and Lee, as well as Nguyen et al., this paper proposes a time-varying average excess porosity pressure ū instead of the initial excess porosity pressure u0 used in the original framework. This leads to the decomposition Δq in an equivalent plane strain model that considers the dynamic changes in the hydraulic gradient and the principle of equal volume. hp The expression is as follows:

[0094]

[0095] In the formula, γ w It is the density of water.

[0096] Let the displacement be equal in the plane strain model and the axisymmetric model, i.e., Δq. hp =Δq a And establish the vertical strain rate based on the effective stress principle. Relationship with average excess pore water pressure ū:

[0097]

[0098] In the formula, For the average effective stress, m v is the volume compressibility factor.

[0099] From the above, we can obtain the approximate differential equation for the average excess pore water pressure ū:

[0100]

[0101] Solving the differential equation described in equation (12), and based on the initial condition ū(t=0)=u0, we can derive:

[0102]

[0103] Based on the soil parameter relationships (Equations (14) and (15)) and the average degree of consolidation The relationship between the average excess pore water pressure ū (Equation (16)) can be used to rewrite Equation (14) as Equation (17):

[0104]

[0105] In the formula, T h c is the time factor for the horizontal consolidation of the soil. h and k h These are the horizontal consolidation coefficient and horizontal permeability coefficient of the soil, respectively.

[0106] Furthermore, according to Hansbo's radial consolidation theory:

[0107]

[0108] In the formula, μ is a dimensionless parameter related to the consolidation analysis of the drainage board foundation, and its calculation formula is as follows:

[0109]

[0110] In the formula, d s k is the diameter of the smeared area. s q is the permeability coefficient of the coating area, l is the length of the drainage board, and q is the permeability coefficient of the coating area. w This represents the drainage capacity of the drainage board.

[0111] Substituting equations (9) and (19) into equation (18), we obtain the equivalent horizontal permeability coefficient k of the foundation soil. hp The calculation formula is as follows:

[0112]

[0113] In this embodiment, the equivalent horizontal permeability coefficient k is described above. hp The calculation expression is derived based on the principle that the drainage volume of the equivalent plane strain model and the axisymmetric model are equal. It considers the dynamically changing hydraulic gradient, smearing effect, and well resistance effect during the consolidation process. Furthermore, it eliminates the need for existing plane strain simulation methods to empirically pre-select a certain average degree of consolidation as the model matching conversion, reducing potential errors caused by reliance on user subjectivity and experience. The equivalent horizontal permeability coefficient k of the foundation soil in the plane strain model is calculated. hp The dimensionless factor μ involved was analyzed using the calculation formula of Hansbo's radial seepage consolidation theory. This dimensionless factor takes into account the effects of smearing effect and well resistance effect.

[0114] Specifically, the equivalent width b of the drainage board in the plane strain model is calculated. w At the same time, following the principle that the ratio of the cross-sectional area of ​​the drainage board to the area of ​​its influence zone remains unchanged in the plane strain model and axisymmetric model, the displacement boundary conditions and drainage boundary conditions of the plane strain model are set according to the actual boundary conditions of the drainage board foundation.

[0115] When using solid elements to simulate a drainage board, the equivalent permeability coefficient k of the drainage board needs to be calculated and set. wp The specific calculation is performed according to the following formula.

[0116]

[0117] To make the simulation results of the model more realistic, the change of the soil permeability coefficient with the void ratio was considered in the process of establishing the plane strain model according to Taylor's formula. The exponent of the change of soil permeability coefficient with the void ratio was taken as 0.4-0.5 times the initial void ratio of the soil.

[0118] The following is a brief explanation using one of the engineering cases as an example: This engineering case is a soft soil foundation preloading treatment project located in the western suburbs of Shanghai. Figure 2 This is a cross-section of the soft soil foundation and surcharge fill. The preloading zone is 60m wide and the fill height is 6m. The fill unit weight is γ. em Approximately 16.5 kN / m 3 The geological strata are mainly composed of clay. The plastic drainage board has a cross-sectional dimension of 4mm × 100mm and an equivalent diameter d. w =0.052m, drainage capacity q w =100m 3 / year, the drainage boards are arranged in a quincunx pattern at 1.1m intervals in the foundation, with a driving depth of 20m. The equivalent diameter d of the drainage board's influence zone. e =1.155m. Based on the compilation of a series of field test data, the diameter d of the coating area is... s Generally 4 to 6 times the d w (i.e., 0.2m~0.3m), the permeability coefficient k of the coated area s Generally 1 / 2 to 1 / 10k h compromise and take d s =0.25m, k s =1 / 5k h Other parameters are shown in Tables 1 and 2. Among them, k v Let e0 be the vertical permeability coefficient of the soil, e0 be the initial void ratio of the soil, and c be the vertical permeability coefficient of the soil. k C is the exponent for the change in soil permeability coefficient with varying void ratio. c and C sThese are the compression index and expansion index of the soil, respectively; M is the slope of the critical state line of the soil; OCR is the overconsolidation ratio of the soil; MCC represents the modified Cambridge model; and MC represents the Mohr-Coulomb model.

[0119] Table 1. Soil permeability coefficient in the case study.

[0120]

[0121] Table 2 Physical and mechanical parameters of soil

[0122]

[0123] According to equation (6), the dimensionless well resistance factor μ' = 0.336 < 0.5. Therefore, the drainage line unit is preferred to simulate the drainage board. According to equation (7), the permeability coefficient k of the drainage board solid unit is calculated. wp =129 m / day. An equivalent plane strain model of the drainage board foundation was established according to the invention method, and simulation calculations were performed. The obtained surface settlement curve and excess pore water pressure dissipation curve in the foundation showed good agreement with the measured values ​​(see...). Figure 3 and Figure 4 ).

[0124] This invention adheres to the principle that the unit volume drainage capacity of the plane strain model and the actual drainage board foundation model are equal; it comprehensively considers the hydraulic gradient, the smearing effect of the drainage board, and the well resistance effect that change with the consolidation process; it eliminates the need for empirically pre-selecting a certain average degree of consolidation as the basis for matching and transforming the plane strain model, reducing potential errors that rely on the subjectivity and experience of user selection; it introduces a dimensionless well resistance factor to consider the prominence of the well resistance effect of the drainage board, and provides a reasonable basis for selecting the drainage board element type; the drainage board foundation bearing deformation calculation method provided by this invention can quickly complete the calculation and analysis of the drainage board foundation, improve the accuracy of simulation calculation, and obtain key data such as settlement, lateral deformation, excess pore water pressure, stress, and strain throughout the entire process of drainage board foundation bearing consolidation, providing a reference for the relevant design and calculation analysis of drainage board foundations.

[0125] The above embodiments are merely illustrative examples to clearly illustrate the present invention and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all embodiments here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for calculating the bearing capacity and deformation of a plastic drainage board foundation, characterized in that, Includes the following steps: S1. Set the spacing of the drainage boards in the plane strain model. The spacing between the drainage boards in the plane strain model is directly taken as the actual spacing s. S2. Select and set the drainage board unit type. Drainage boards can be simulated using drainage line units or solid units; When the element type is a solid element, the equivalent diameter d of the drainage board is used. w The equivalent diameter d of the drainage board's affected area e The actual spacing s of the drainage boards is calculated using the following formula to determine the equivalent width b of the drainage boards in the plane strain model. w ; In the formula, a is the length of the drainage board cross-section, and b is the width of the drainage board cross-section. S3. Calculate and set the equivalent horizontal permeability coefficient k of the foundation soil in the plane strain model. hp Based on the actual spacing s of the drainage boards and the horizontal permeability coefficient k of the foundation soil h The equivalent diameter d of the drainage board's affected area e Based on the principle that the drainage volume is equal in the equivalent plane strain model and the axisymmetric model, the equivalent horizontal permeability coefficient k of the foundation soil is derived and established. hp ; In the formula, d s k is the diameter of the smeared area. s q is the permeability coefficient of the coating area, l is the length of the drainage board, and q is the permeability coefficient of the coating area. w denoted as the drainage capacity of the drainage board, and μ as a dimensionless parameter related to the consolidation analysis of the drainage board foundation. S4. Set boundary conditions and perform calculations. Based on the actual engineering conditions, the displacement boundary and drainage boundary of the plane strain model are set, and simulation calculations are performed to obtain key data such as the surface settlement curve, the lateral deformation profile of the foundation, the excess pore water pressure dissipation curve in the foundation, and the stress and strain of the foundation soil.

2. The equivalent plane strain calculation method according to claim 1, characterized in that: When selecting the drainage board unit type, the dimensionless well resistance factor μ' is calculated according to formula (6): When μ'≤0.5, the drainage line element is used; When μ'>0.5, solid elements are used.

3. The equivalent plane strain calculation method according to claim 1 or 2, characterized in that: When using solid elements to simulate a drainage board during the plane strain model establishment process, the equivalent permeability coefficient k of the drainage board needs to be calculated and set. wp The specific calculation is performed according to the following formula. In the formula, δ is k wp In the derivation of the calculation formula, the virtual out-of-plane thickness of the plane strain model is used to ensure that the displacement of the plane strain model and the axisymmetric model are equal under the condition of equal volume.

4. The equivalent plane strain calculation method according to claim 1 or 2, characterized in that: In the process of establishing the plane strain model, the change of soil permeability coefficient with void ratio is considered according to Taylor's formula. The exponent of soil permeability coefficient change with void ratio is taken as 0.4-0.5 times the initial void ratio of soil.

5. The equivalent plane strain calculation method according to claim 1 or 2, characterized in that: Based on the actual boundary conditions of the drainage board foundation, set the displacement boundary conditions and drainage boundary conditions for the plane strain model in all directions.

6. The equivalent plane strain calculation method according to claim 1 or 2, characterized in that: The equivalent width b of the drainage board in the plane strain model is calculated. w In both plane strain and axisymmetric models, the ratio of the cross-sectional area of ​​the drainage board to the area of ​​its influence zone remains constant.

7. The equivalent plane strain calculation method according to claim 1 or 2, characterized in that: Equivalent horizontal permeability coefficient k of foundation soil hp The specific solution process is as follows: Based on the principle that the drainage volume is equal in the equivalent plane strain model and the axisymmetric model, the equivalent horizontal permeability coefficient k is derived and established. hp The calculation formula, In an axisymmetric model, the drainage Δq of a saturated soil element of thickness dz within time dt. a It is equal to its change in volume, that is: In the formula, ε v Let z be the vertical strain, z be the depth, and t be the time. When establishing a plane strain model, it is essential to ensure that the displacement of the plane strain model and the axisymmetric model are equal under the condition of equal volume. Therefore, a virtual out-of-plane thickness δ is introduced into the plane strain model to ensure that its volume is consistent with the corresponding axisymmetric model. Based on the above principle of equal volume, the formula for calculating δ is derived as follows: Furthermore, by replacing the initial excess pore water pressure u0 used in the original framework with the time-varying average excess pore water pressure ū, a displacement Δq in the equivalent plane strain model considering the dynamic changes of the hydraulic gradient and the principle of equal volume is derived. hp The expression is as follows: In the formula, γ w The specific gravity of water; Let the displacement be equal in the plane strain model and the axisymmetric model, i.e., Δq. hp =Δq a And establish the vertical strain rate based on the effective stress principle. Relationship with average excess pore water pressure ū: In the formula, For the average effective stress, m v The volume compressibility factor; From the above, we can obtain the approximate differential equation for the average excess pore water pressure ū: Solving the differential equation described in equation (13), and based on the initial condition ū(t=0)=u0, we can derive: Based on soil parameter relationships and average degree of consolidation The relationship between the average excess pore water pressure ū and equation (14) can be rewritten as equation (18): In the formula, T h c is the time factor for the horizontal consolidation of the soil. h and k h These are the horizontal consolidation coefficient and horizontal permeability coefficient of the soil, respectively. Furthermore, according to Hansbo's radial consolidation theory: Substituting equations (9) and (19) into equation (18) yields the equivalent horizontal permeability coefficient k of the foundation soil. hp The calculation formula:

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