Method for predicting consolidation large deformation of soft soil foundation by vacuum preloading based on material point method

Abstract

This invention discloses a method for predicting large deformations of consolidation in vacuum-preloaded soft soil foundations based on the material point method, belonging to the field of soft soil foundation treatment and computational geotechnical mechanics. Addressing the problem that traditional grid-based numerical calculation methods are susceptible to grid distortion in large deformation analysis of geotechnical engineering, this invention discretizes the soft soil foundation into material points carrying material state variables and uses a background grid to solve the water-soil coupling control equations. Through information mapping between material points and the background grid, water-soil coupling solution of the background grid, and material point state updates, the method predicts the dissipation of pore water pressure, effective stress growth, and deformation within the soft soil foundation under negative pressure. This method improves the stability and applicability of large deformation analysis of vacuum-preloaded soft soil foundations, providing a technical basis for soft soil foundation reinforcement design, construction period assessment, and treatment effect evaluation.

Description

Technical Field

[0001] This invention belongs to the field of soft soil foundation treatment and computational geotechnical mechanics, specifically involving a method for predicting large deformation of consolidation in vacuum preloaded soft soil foundations based on the material point method. It can be used for predicting settlement and consolidation of vacuum preloaded soft soil foundations and evaluating the reinforcement effect of soft soil foundations. Background Technology

[0002] Under engineering loads and other conditions, soft soil foundations often experience significant consolidation settlement over a prolonged period. Accurately predicting the settlement development, pore pressure dissipation, and effective stress growth of soft soil foundations during the treatment process is crucial for determining the construction period for soft soil foundation treatment, evaluating treatment effectiveness, and optimizing reinforcement design.

[0003] Vacuum preloading is a common method for treating soft soil foundations. This method uses a sealing system, surface drainage layer, and vertical drainage bodies (i.e., plastic drainage boards) to transmit negative pressure into the soft soil foundation through vertical drainage channels. By reducing pore water pressure, it increases the effective stress level of the soil, accelerating the consolidation and settlement process. Currently, vacuum preloading consolidation analysis methods typically include Terzaghi's one-dimensional consolidation theory, radial consolidation theory, finite element method, and other empirical engineering methods. One-dimensional and radial consolidation theories are based on assumptions such as small deformation, ideal drainage boundaries, and linear elastic soil constitutive relations. Their computational accuracy is limited, making them suitable for preliminary estimations of soil drainage consolidation, but they struggle to accurately account for complex drainage arrangements, negative pressure loading processes, and consolidation settlement characteristics under conditions of large foundation settlement. Mesh-based numerical methods such as the finite element method can simulate pore pressure dissipation and settlement deformation to some extent, but their numerical stability is easily affected by mesh distortion and degraded mesh quality when dealing with large consolidation settlement in soft soil foundations.

[0004] The material point method is a numerical method that combines the advantages of Lagrangian description and Eulerian mesh computation. This method uses material points to carry state information such as material mass, volume, velocity, displacement, stress, and pore water pressure, while using a background mesh as a temporary solution carrier for the governing equations. Within each computation time step, the material point information is mapped to the background mesh, and the momentum equation and pore pressure governing equation are solved on the background mesh. The calculation results are then fed back to the material points, and the background mesh is reset. Because material history variables are stored on the material points, the background mesh only serves as a temporary solution carrier within each time step and is reset after the computation is complete. The material point method can reduce the numerical stability problems caused by mesh distortion in large deformation calculations using traditional mesh-based methods.

[0005] Therefore, this invention proposes a numerical analysis method for large deformation of vacuum preloading consolidation in soft soil foundations based on the material point method. This method integrates soil deformation, pore water pressure evolution, and stress state changes into the same large deformation calculation framework, enabling continuous simulation of the entire process of negative pressure transmission, pore water pressure dissipation, effective stress growth, and consolidation settlement. This provides a reliable theoretical basis and technical support for the design and evaluation of the treatment effect of soft soil foundation reinforcement. Summary of the Invention

[0006] (a) Technical problems to be solved

[0007] The technical problem to be solved by this invention is to provide a method for predicting large deformation of vacuum preloaded soft soil foundation consolidation based on the material point method. This method is used to solve the problems of insufficient calculation accuracy, grid distortion and inflexible handling of negative pressure boundaries in existing vacuum preloaded consolidation analysis methods when dealing with the coupled response of large deformation settlement, pore water pressure dissipation and soil skeleton deformation in soft soil foundations.

[0008] (II) Technical Solution

[0009] To solve the above-mentioned technical problems, the present invention adopts the following technical solution.

[0010] A method for predicting large consolidation deformation of vacuum preloaded soft soil foundation based on the material point method includes the following steps:

[0011] Step S1: Obtain the model parameters of the soft soil foundation to be treated. The model parameters include geometric parameters, plastic drainage board layout parameters, soil physical and mechanical parameters, initial stress state, and vacuum preloading conditions.

[0012] Step S2: Based on the model parameters obtained in step S1, establish a water-soil coupling analysis model for soft soil foundation under vacuum preloading, including the momentum balance equation of the soil skeleton and the mass conservation equation of pore water.

[0013] The momentum balance equation of the soil skeleton is:

[0014]

[0015]

[0016] in, This represents the total density of saturated soil. Porosity For soil particle density, The density of pore water, For the velocity of the soil skeleton, To calculate time, For the total stress tensor, This is the vector of gravitational acceleration.

[0017] The pore water pressure control equation is as follows:

[0018]

[0019] in, The water storage coefficient, Pore ​​water pressure, The velocity vector of the soil skeleton. Permeability coefficient, The density of water, Equivalent source and sink terms caused by drainage boundaries, negative pressure, or external source and sink effects.

[0020] Step S3: Establish a material point method discretization model, discretizing the soft soil foundation computational domain into material points and a background grid. The material points carry soil mass, volume, velocity, displacement, stress, pore water pressure, void ratio, and internal variables of the soil constitutive model; the background grid is used to solve the water-soil coupling control equations in each computational time step.

[0021] Material points serve as Lagrangian description points, used to store the soil motion state, pore water pressure state, and internal variables of the soil constitutive model. The background mesh serves as a temporary computational mesh, used to calculate nodal mass, nodal momentum, nodal internal forces, nodal external forces, nodal pore water pressure increments, and pore pressure gradients. After each computational time step, the background mesh is reset or cleared, while the state variables at the material points are retained and carried over to the next computational time step.

[0022] Step S4: Initialize the state information of the material point, including the position, mass, volume, velocity, displacement, initial stress, initial strain, initial pore water pressure, initial void ratio, and internal variables of the soil constitutive model.

[0023] For any matter point p, initialize its mass. ,volume ,Location ,speed Displacement ,stress pore water pressure Porosity .

[0024] Step S5: Set boundaries and loading conditions, including displacement boundaries, drainage boundaries and vacuum pre-compression loading conditions, wherein the vacuum pre-compression loading conditions are used to describe the magnitude of the negative pressure inside the plastic drainage board, the holding time and its decay mode along the depth.

[0025] The drainage boundary described in step S5 satisfies:

[0026]

[0027] in, The corrected pore water pressure applied to the drainage boundary. The target negative pressure provided to the vacuum pump This is the negative pressure correction factor; when the attenuation of negative pressure along the depth is not considered, take... =1; when considering the attenuation of negative pressure along the depth, Use a linear decay function, an exponential decay function, or a piecewise function.

[0028] Step S6: Perform information mapping from material points to the background mesh. Initialize the time steps and, within each computation time step, map the material point information to the background mesh nodes to obtain the mass, momentum, stress, pore water pressure, and constitutive model parameters of the soft soil foundation on the background mesh nodes.

[0029] The mass-momentum mapping relationship from material point p to background mesh node i is as follows:

[0030]

[0031]

[0032] The internal forces at the nodes are:

[0033]

[0034] in, The node quality of background mesh node i, Let i be the momentum of the background mesh node i. Let p be the shape function value of the material point p with respect to the background mesh node i. Let p be the mass of the substance point. Let p be the velocity of the substance point. Let p be the volume of the substance point. Let p be the stress tensor of the material point.

[0035] Furthermore, when the stress, pore water pressure, and material parameters carried by the material points are mapped to the background mesh nodes, a shape function weighted average method is used, the expression of which is:

[0036]

[0037]

[0038] in, Let i be the stress tensor at node i of the background mesh. Let p be the stress tensor carried by the material point p; The pore water pressure at node i of the background mesh. Let p be the pore water pressure carried by the material point; Let p be the volume of the substance point.

[0039] Step S7: Assemble and solve the water-soil coupling control equations under vacuum preloading on the background grid to obtain the velocity, displacement increment, acceleration, internal force, external force, pore water pressure increment, and pore pressure gradient on the background grid nodes.

[0040] The internal and external forces on the background mesh nodes are as follows:

[0041]

[0042]

[0043] in, For nodal internal forces, For nodal external forces, The vector of gravitational acceleration. Equivalent nodal force obtained from the transformation of external mechanical surface force boundary.

[0044] The nodal acceleration is determined by the following formula:

[0045]

[0046] in, Let be the nodal acceleration of node i in the background mesh. Based on the nodal acceleration, the nodal velocity and nodal displacement increments can be further updated, serving as the basis for subsequent material point propagation. The nodal velocity and material point motion state are also updated based on the nodal acceleration.

[0047] Step S8: Perform the calculation results from the background mesh to the material points and send them back.

[0048] The calculation results from the background mesh nodes are fed back to the material points to update their position, velocity, displacement, deformation gradient, stress state, and pore water pressure. Specifically, the position, velocity, and displacement of the material points are updated based on the velocity, acceleration, and displacement increments of the background mesh nodes; the pore water pressure of the material points is updated based on the pore water pressure increments and pore pressure gradients of the background mesh nodes; the deformation gradient of the material points is updated based on their velocity or displacement gradients; and the stress state of the material points and the internal variables of the soil constitutive model are updated based on the strain increments and soil constitutive relations.

[0049] Step S9: Calculate the current time step prediction and reset the background grid information.

[0050] Based on the updated material point states, the calculation results of the current time step are extracted and saved, and time history data is output. The calculation results include surface subsidence, pore water pressure dissipation, stress state change, and degree of consolidation. Subsequently, the background mesh information is reset to prepare for the calculation of the next time step. The background mesh information includes nodal mass, momentum, velocity, acceleration, internal force, external force, pore water pressure increment, and pore pressure gradient.

[0051] (III) Beneficial Effects

[0052] Compared with existing technologies, the present invention designs a method for predicting large deformations of consolidation in vacuum preloaded soft soil foundations based on the material point method, which has the following advantages:

[0053] (1) This invention employs the material point method for numerical analysis of vacuum preloaded soft soil foundations. Material points carry state information such as the mass, volume, velocity, displacement, stress, and pore water pressure of the soil, and the background grid serves as a temporary solution carrier for the governing equations. The background grid is reset after each calculation time step, which can mitigate the decrease in calculation accuracy and numerical stability caused by grid distortion under large consolidation deformation conditions in traditional fixed grid methods, and improve the adaptability to the large deformation consolidation process of soft soil foundations.

[0054] (2) Under the framework of the material point method, this invention simultaneously considers the movement of the soil skeleton and the evolution of pore water pressure. Through the information mapping between the material point and the background grid, the water-soil coupling solution on the background grid, and the back transmission of the calculation results to the material point, the unified calculation of the pore water pressure dissipation and soil settlement deformation process can be realized, which can describe the consolidation response of soft soil foundation under vacuum preloading in a relatively complete way.

[0055] (3) In view of the characteristics of the role of plastic drainage board in vacuum preloading project, the present invention characterizes the role area of ​​drainage board through equivalent negative pressure boundary, and can set different distribution or attenuation modes of vacuum negative pressure along the depth direction of drainage board, thereby reflecting the influence of vacuum negative pressure transmission loss in drainage board on pore water pressure distribution and foundation settlement response, and improving the rationality and engineering applicability of vacuum preloading boundary condition description.

[0056] (4) This invention can calculate and analyze the consolidation process of soft soil foundation under different drainage board spacing, different vacuum negative pressure magnitude and different negative pressure distribution patterns along the depth, and obtain prediction results such as surface settlement, settlement time history, pore water pressure dissipation process, pore water pressure distribution at different depths and material point displacement field, which can provide technical basis for the comparison of vacuum preloading soft soil foundation treatment schemes, drainage board layout design and treatment effect analysis. Attached Figure Description

[0057] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0058] Figure 1 This is a flowchart illustrating the overall process of the method for predicting large consolidation deformation of vacuum preloaded soft soil foundation based on the material point method in this application.

[0059] Figure 2 This is a schematic diagram of the material point discretization and mapping of the vacuum preloaded soft soil foundation consolidation large deformation prediction method based on the material point method of this application.

[0060] Figure 3 This is a pore pressure comparison diagram showing the comparison between the analytical solution of the one-dimensional vacuum pre-consolidation large deformation in Example 1 and the MPM simulation results;

[0061] Figure 4 A settlement comparison diagram showing the one-dimensional vacuum preloaded consolidation large deformation analytical solution and MPM simulation results from Example 1;

[0062] Figure 5 This is a cloud map showing the distribution of pore water pressure in soil under different drainage board spacings and vacuum pressure transmission conditions in Example 2.

[0063] Figure 6 This is a cloud map showing the vertical settlement distribution of soil under different drainage board spacings and vacuum pressure transmission conditions in Example 2. Detailed Implementation

[0064] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and should not be construed as limiting the scope of the invention.

[0065] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0066] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0067] It should be noted that the following description covers various aspects of embodiments within the scope of the appended claims. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number and aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0068] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The drawings only show the components related to this application and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0069] Additionally, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that practice can be carried out without these specific details.

[0070] The technical solutions provided by various embodiments of this application are described below with reference to the accompanying drawings. It should be noted that: (The accompanying drawings are attached.) Figure 3In the diagram, Xie-Leo represents the pore water pressure distribution calculated using the analytical solution for large deformation under one-dimensional vacuum preloading consolidation, serving as a theoretical reference solution; GeoTaichi MPM represents the pore water pressure distribution calculated using the material point method model in the GeoTaichi program, used to characterize the simulation results of the numerical method of this invention. By comparing the pore pressure distribution along the height of the soil column at different consolidation stages, the simulation accuracy of the material point method model for the vacuum negative pressure transmission and pore pressure dissipation process can be verified. (Appendix) Figure 4 In this context, "Xie-Leo settlement" represents the settlement at the top of the soil column calculated using the analytical solution of large deformation under one-dimensional vacuum preloading, serving as a theoretical reference for the settlement development process; "GeoTaichi MPM" represents the settlement at the top of the soil column calculated using the GeoTaichi material point method model, serving as the simulation result of the numerical method of this invention. By comparing the relationship between the two and the consolidation time factor, the predictive ability of the method of this invention for the large deformation settlement development of soil under vacuum preloading can be verified.

[0071] Example 1: Comparison of analytical solution and MPM results for large deformation under one-dimensional vacuum preloading consolidation

[0072] like Figures 1-4 As shown, this embodiment illustrates the applicability and computational accuracy of the method of the present invention in large deformation problems under one-dimensional vacuum preloading consolidation. The computational object is a saturated soil column with an initial height of 1.00 m and a width of 0.05 m, using a linear elastic constitutive model. A negative pressure of -80.0 kPa is applied to the top of the soil column, and the bottom is set as an undrained boundary, with lateral constraints on horizontal displacement.

[0073] In this embodiment, the soil permeability coefficient A constant is set to be used to construct a one-dimensional verification example of large deformation under vacuum preloading consolidation. By comparing the simulation results of the material point method with the analytical solution, the reliability of the method in calculating the pore water pressure dissipation process and the large deformation settlement response of soil under vacuum preloading is verified.

[0074] The specific calculation steps are as follows:

[0075] Step S1: Establish a one-dimensional soil column material point model, and input the geometric dimensions of the soil column, soil elastic parameters, and permeability coefficient. Initial pore pressure state and top negative pressure;

[0076] Table 1. Parameter List of One-Dimensional Vacuum Pre-compression Consolidation Model

[0077] Step S2: Discretize the soil column into material points and background mesh, and initialize the mass, volume, velocity, stress, pore water pressure, and porosity of the material points. ;

[0078] Step S3: In each computation time step, perform information mapping from material points to the background mesh to obtain the mass, momentum, internal force and pore pressure of the background mesh nodes.

[0079] Step S4: Apply pore water pressure boundary conditions and displacement boundary conditions to the background mesh, and solve the pore water pressure governing equation and the soil skeleton motion equation. The pore water pressure boundary conditions are set as follows: the top surface is a drained boundary with a vacuum negative pressure applied; the two side boundaries and the bottom boundary are set as undrained boundaries. The displacement boundary conditions are set as follows: the two side boundaries use roller boundary conditions, i.e., restricting lateral normal displacement but allowing vertical displacement; the bottom boundary uses a fully fixed constraint, i.e., restricting both horizontal and vertical displacement.

[0080] Step S5: Transfer the velocity, displacement, pore pressure increment, and stress increment on the background mesh nodes back to the material point to update the material point's position, volume, pore water pressure, and stress state.

[0081] Step S6: Repeat steps S3 to S5 until the set calculation time is reached;

[0082] Step S7: Output the time history curves of pore water pressure distribution and surface settlement of the soil column, and compare them with the one-dimensional large deformation consolidation analytical solution.

[0083] like Figures 3-4 As shown, the MPM simulation results can reflect the process of negative pressure being transferred from the top to the interior of the soil, and quantitatively predict the development of settlement due to the dissipation of pore water pressure. The calculation results show that at t=4.0 s, the top settlement obtained by the MPM simulation is approximately 189.84 mm, while the analytical solution corresponds to a settlement of approximately 195.29 mm; the numerical solution of the MPM pore pressure is in good agreement with the analytical solution.

[0084] Example 2: Analysis of the Vacuum Preloading Consolidation Process in Two-Dimensional Soft Soil Foundation

[0085] like Figures 1-2 , Figures 5-6 As shown, this embodiment illustrates the application of the method of the present invention in the vacuum preloading consolidation analysis of two-dimensional soft soil foundations. The calculation object is a soft soil foundation with vertical drainage boards, considering the influence of different drainage board spacing and the attenuation mode of negative pressure along the depth inside the drainage boards on the final pore water pressure distribution and soil displacement distribution.

[0086] In this embodiment, the effective area of ​​the drainage board is represented by an equivalent negative pressure boundary, and different attenuation modes are used to describe the distribution of negative pressure along the depth. A modified Cambridge model is used to describe the nonlinear elastoplastic constitutive response of the soft soil. To analyze the influence of drainage board density and negative pressure transfer loss within the drainage boards on the consolidation effect of the soft soil foundation, this embodiment selects two drainage board spacings and two negative pressure distributions along the depth direction of the drainage boards for combined calculations to analyze the influence of drainage board density and vacuum pressure loss within the drainage boards on the consolidation effect of the soft soil foundation. The drainage board spacing is 0.20 m and 0.50 m, respectively; the vacuum pressure transfer modes are the no-attenuation condition and the linear attenuation condition along the depth, respectively. Under the no-attenuation condition, a negative pressure of -80 kPa is applied throughout the entire depth of the drainage board to characterize the ideal state where there is basically no loss in the transmission of vacuum pressure along the drainage board; under the linear attenuation condition, the negative pressure at the top of the drainage board is -80 kPa and the negative pressure at the bottom is -20 kPa. The vacuum pressure gradually decreases from the top to the bottom of the drainage board along the depth direction to characterize the engineering state where there is significant transmission loss of vacuum pressure in the drainage board.

[0087] The specific calculation steps are as follows:

[0088] Step S1: Establish a two-dimensional vacuum preloaded soft soil foundation model, and input the soil layer dimensions, drainage board spacing, drainage boundary location, negative pressure magnitude, negative pressure attenuation mode along depth, and corrected Cambridge model parameters.

[0089] Table 2. Parameter List of Two-Dimensional Vacuum Pre-compression Consolidation Model

[0090] Step S2: Discretize the soft soil foundation into material points and background mesh, and initialize the mass, volume, velocity, stress, pore water pressure of the material points and the internal variables of the soil constitutive model;

[0091] Step S3: Determine the drainage boundary or drainage body action area based on the spacing of the drainage boards, and apply depth-related negative pressure according to the no-attenuation working condition and the linear attenuation working condition modes.

[0092] Step S4: In each computation time step, perform information mapping from material points to the background grid, assemble and solve the soil skeleton momentum balance equation and pore water pressure control equation on the background grid.

[0093] Step S5: Feed back the background mesh solution results to the material points and update the material point positions, displacements, stresses, pore water pressures, and constitutive states.

[0094] Step S6: Repeat the above calculation process until the set calculation time is reached;

[0095] Step S7: Output the final pore water pressure cloud map and vertical displacement cloud map, and compare the differences in consolidation large deformation under different drainage plate spacing and vacuum pressure transmission conditions.

[0096] Figure 5 Cloud maps showing the distribution of pore water pressure in soil under different drainage board spacing and vacuum pressure transmission conditions. Figure 6 This is a cloud map showing the vertical settlement distribution of the soil under the corresponding working conditions. (From...) Figure 5 It is evident that the loss of vacuum pressure within the drainage board along its depth has a significant impact on the distribution of pore water pressure in the soil. Under the condition of no vacuum pressure decay, the drainage board maintains a negative pressure of -80 kPa throughout its entire depth range, and the average pore water pressure in the soil at the end of the calculation is approximately -79 kPa, indicating that the negative pressure can be fully transmitted within the soil. Under the condition of strong linear decay, the negative pressure at the top of the drainage board is -80 kPa, decaying to -20 kPa at the bottom, and the average pore water pressure in the soil at the end of the calculation is approximately -48 kPa, indicating that the loss of vacuum pressure at the depth of the drainage board significantly weakens the negative pressure level inside the soil and slows down the dissipation of pore pressure in the deep soil.

[0097] from Figure 6 The settlement results show that both the spacing between drainage boards and the loss of vacuum pressure affect soil consolidation deformation. Under no attenuation conditions, when the spacing between drainage boards increases from 0.20 m to 0.50 m, the average surface settlement decreases from approximately 95.01 mm to approximately 48.75 mm, indicating that a smaller spacing between drainage boards can shorten the drainage path, enhance negative pressure transmission, and improve the consolidation settlement response. Under linear strong attenuation conditions, the average surface settlement at drainage board spacings of 0.20 m and 0.50 m is approximately 46.11 mm and 40.54 mm, respectively. The overall settlement level is significantly lower than that under the no-attenuation condition, indicating that even with a small spacing, the consolidation effect is weakened after the vacuum pressure within the drainage boards is lost along the depth.

[0098] Further comparison reveals that, under the same drainage board spacing, the pore pressure dissipation and surface settlement under the no-attenuation condition are greater than those under the linear strong attenuation condition; while under the same vacuum pressure transmission conditions, a smaller drainage board spacing corresponds to a more pronounced settlement response. These results indicate that the drainage board spacing and the vacuum pressure transmission loss within the drainage boards are two key factors affecting the vacuum preloading consolidation effect: the drainage board spacing mainly controls the horizontal drainage path and the range of negative pressure, while the vacuum pressure loss along depth directly weakens the deep negative pressure level and the overall consolidation driving force.

[0099] In summary, Example 1 verified the computational accuracy of the method of the present invention in the large deformation consolidation problem of one-dimensional vacuum preloading, and Example 2 demonstrated the application capability of the method of the present invention in the vacuum preloading consolidation analysis of two-dimensional soft soil foundations. Both examples together illustrate that the calculation method proposed in this invention can effectively predict the pore pressure-deformation of soft soil foundations during vacuum preloading, providing a technical basis for the design of soft soil foundation reinforcement, the judgment of construction period, and the evaluation of treatment effects.

[0100] The same or similar parts between the various embodiments in this specification can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments.

[0101] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for predicting large consolidation deformation of vacuum preloaded soft soil foundation based on the material point method, characterized in that: Includes the following steps: Step S1: Obtain the model parameters of the soft soil foundation to be treated. The model parameters include geometric parameters, plastic drainage board layout parameters, soil physical and mechanical parameters, initial stress state and vacuum preloading conditions. Step S2: Based on the relevant parameters obtained in step S1, establish a water-soil coupling analysis model for soft soil foundation under vacuum preloading. The water-soil coupling analysis model includes the soil skeleton momentum balance equation, the pore water pressure control equation, and the soil constitutive relationship. Step S3: Establish a material point method discretization model, and discretize the soft soil foundation computational domain into material points and background grids. The material points carry soil mass, volume, velocity, displacement, stress, pore water pressure, void ratio and internal variables of the soil constitutive model. The background grid is used to solve the water-soil coupling control equations in each computation time step. Step S4: Initialize the state information of the material point, including the position, mass, volume, velocity, displacement, initial stress, initial strain, initial pore water pressure, initial void ratio, and internal variables of the soil constitutive model. Step S5: Set boundaries and loading conditions, including displacement boundaries, drainage boundaries and vacuum pre-compression loading conditions, wherein the vacuum pre-compression loading conditions are used to describe the magnitude of the negative pressure inside the plastic drainage board, the holding time and its decay mode along the depth. Step S6: Initialize the time step and map the material point information to the background grid nodes in each calculation time step to obtain the mass, momentum, stress, pore water pressure, void ratio and constitutive model parameters of the soft soil foundation on the background grid nodes. Step S7: Assemble and solve the water-soil coupling control equations for soft soil foundation under vacuum preloading on the background grid to obtain the velocity, displacement increment, acceleration, internal force, external force, pore water pressure increment and pore pressure gradient on the background grid nodes. Step S8: Transfer the calculation results from the background mesh nodes back to the material points, and update the position, velocity, displacement, deformation gradient, stress state, pore water pressure, void ratio, and internal variables of the soil constitutive model of the material points. Step S9: Calculate the key indicators in the consolidation process based on the current material point state and output the time history data. Then clear the background grid information to advance the next calculation. The key indicators include surface subsidence, pore pressure dissipation, effective stress increase and degree of consolidation.

2. The method for predicting large deformation of consolidation in vacuum preloaded soft soil foundation based on the material point method according to claim 1, characterized in that: The geometric parameters in step S1 include the soft soil foundation treatment depth, calculation area size, soil layer thickness, and drainage boundary location; the plastic drainage board layout parameters include the plastic drainage board driving depth, drainage board spacing, drainage board layout form, and drainage board boundary location; the soil physical and mechanical parameters include soil particle density. pore water density Initial porosity Permeability coefficient The parameters of the soil constitutive model include the magnitude of the negative pressure inside the plastic drainage board, the holding time, and its decay mode along the depth.

3. The method for predicting large consolidation deformation of vacuum preloaded soft soil foundation based on the material point method according to claim 1, characterized in that: The momentum balance equation of the soil skeleton in step S2 is: in, This represents the total density of saturated soil. Porosity For soil particle density, The density of pore water, The velocity vector of the soil skeleton. To calculate time, For the total stress tensor, This is the vector of gravitational acceleration; The pore water pressure control equation in step S2 is: in, The water storage coefficient, Pore ​​water pressure, The velocity vector of the soil skeleton. Permeability coefficient, The density of water, Equivalent source and sink terms caused by drainage boundaries, negative pressure, or external source and sink effects.

4. The method for predicting large deformation of consolidation in vacuum preloaded soft soil foundation based on the material point method according to claim 1, characterized in that: The material point method discretization process in step S3 includes determining the mass of material point p. ,speed ,volume ,stress pore water pressure Porosity and permeability coefficient Mapped to background grid node i, the mapping relationship between the mass and momentum of material point p and background grid node i is as follows: in, For background mesh node quality, For the momentum of the background mesh nodes, Let p be the shape function from the material point p to the background mesh node i. For the mass of a substance point, Let V be the velocity vector of the material point. Let V be the volume of a point mass. Let be the point stress tensor of the material.

5. The method for predicting large consolidation deformation of vacuum preloaded soft soil foundation based on the material point method according to claim 1, characterized in that: In step S7, the internal and external forces on the background mesh nodes are as follows: in, Let i be the internal force at node i. For the external force at node i, Equivalent nodal forces obtained from the transformation of external mechanical surface force boundaries; The nodal acceleration is: in, Let be the acceleration of background grid node i.

6. The method for predicting large consolidation deformation of vacuum preloaded soft soil foundation based on the material point method according to claim 1, characterized in that: The drainage boundary correction described in step S5 satisfies: in, The corrected pore water pressure applied to the drainage boundary. The target negative pressure provided to the vacuum pump This is the negative pressure correction factor; when the attenuation of negative pressure along the depth is not considered, take... =1; when considering the attenuation of negative pressure along the depth, Use a linear decay function, an exponential decay function, or a piecewise function.

7. The method for predicting large consolidation deformation of vacuum preloaded soft soil foundation based on the material point method according to claim 1, characterized in that: In step S6, the stress and pore water pressure carried by the material points are mapped to the background mesh nodes using a shape function weighted average method. The expression is as follows: in, Let i be the stress tensor at node i of the background mesh. Let p be the stress tensor carried by the material point p; The pore water pressure at node i of the background mesh. Let p be the pore water pressure carried by the material point; Let p be the volume of the substance point.

8. The method for predicting large consolidation deformation of vacuum preloaded soft soil foundation based on the material point method according to claim 1, characterized in that: The soil constitutive relation described in step S2 is used to quantitatively characterize the stress-strain relationship of soft soil foundations, and the updated stress increment is calculated based on the strain increment of the material point during the material point state update process. Its expression is: in, For stress increment, For the strain increment, This is the soil stiffness matrix.

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