A modeling method for layered soft soil subgrade reinforced by pile foundation under simulated earthquake action

Abstract

This invention discloses a modeling method for layered soft soil subgrades reinforced with pile foundations under simulated seismic loading, belonging to the field of seismic numerical simulation in geotechnical engineering. This method constructs a multi-field coupled numerical model based on a finite element platform, defines the contact mechanisms at the pile-soil and reinforced-subgrade interfaces, and completes the construction of in-situ stress equilibrium and initial pore water pressure fields. Static results are output through fill-consolidation coupling analysis. Distributed viscoelastic artificial boundaries are automatically constructed using Python scripts, and seismic waves are converted into equivalent nodal loads using wave theory. Multi-physics field connections between static and dynamic analysis boundaries are achieved, and core response parameters such as embankment settlement and pile-soil stress are output through implicit dynamic analysis. This invention considers the seismic wave propagation effect in layered soils, reduces spurious oscillations caused by the transformation of static and dynamic boundaries, and improves simulation accuracy and efficiency. It is suitable for seismic design and analysis of transportation infrastructure in soft soil areas.

Description

Technical Field

[0001] This invention belongs to the field of soft soil foundation reinforcement and geotechnical engineering numerical simulation technology, specifically involving a modeling method for layered soft soil subgrades under simulated earthquake loading and pile foundation reinforcement. Background Technology

[0002] In the construction of transportation infrastructure such as highways and railways in soft soil areas, pile-supported reinforced embankments have become a commonly used solution for soft soil foundation treatment due to their significant reinforcement effect. However, seismic activity in soft soil areas may lead to disasters such as excessive settlement, pile fracture, and embankment collapse in pile-supported reinforced embankments. Therefore, it is essential to conduct seismic dynamic response research on this type of structure.

[0003] Numerical simulation is an indispensable research tool in this field, but existing numerical simulation methods have many shortcomings in the study of seismic dynamic response of pile-supported reinforced embankments: 1) The conversion process between static and dynamic boundaries is complex, the setting of viscoelastic artificial boundaries is difficult, and the application of equivalent seismic loads is cumbersome and time-consuming; 2) In actual engineering, earthquakes mostly occur after the roadbed filling and consolidation are completed. Numerical simulation requires static analysis using fixed boundaries first, and then dynamic analysis using viscoelastic artificial boundaries. If fixed boundaries are directly deleted or used, oscillations and drifts are likely to occur, affecting the accuracy of the seismic response results; 3) There are differences in the parameters of each soil layer in stratified soft soil media. Seismic waves will have reflection and transmission effects at the interfaces of different soil layers. Existing methods are mostly for single-layer soil, and the efficiency of manual calculation is extremely low, making it difficult to guarantee the calculation accuracy.

[0004] Therefore, there is an urgent need for a numerical modeling method that can automatically set artificial boundaries for layered soft soil, convert seismic waves into equivalent nodal loads, and connect static and dynamic boundaries, so as to improve the accuracy and efficiency of seismic response simulation of pile-supported reinforced embankments. Summary of the Invention

[0005] To address the aforementioned shortcomings of existing technologies, the purpose of this invention is to provide a modeling method for layered soft soil subgrades under simulated seismic loading. By combining the collaborative application of a finite element platform and Python automated scripts, and integrating wave theory with the wave propagation laws of layered media, this method achieves automated construction of viscoelastic artificial boundaries, seismic wave conversion of layered soil, and connection of static and dynamic boundaries. Simultaneously, it incorporates the multi-field coupling effect of stress-seepage-dynamics, solving the problems of low accuracy and susceptibility to false oscillations in existing modeling methods.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for modeling layered soft soil subgrades under simulated seismic loading and pile foundation reinforcement includes the following steps: Step S1: Construct a multi-field coupled numerical model based on the finite element platform, including layered soft soil foundation, piles, pile top cushion, reinforced body and embankment fill, set the constitutive parameters of each component material and complete the mesh optimization.

[0007] Step S2: Define the contact interaction between the reinforced body and the cushion layer, and between the pile and the soil, set the boundary constraints of the model, and apply the global gravity load.

[0008] Step S3: Through the initial geostress field and geostress equilibrium analysis step, the geostress field of the model is balanced and the initial pore water pressure field is constructed.

[0009] Step S4: Construct the soil-consolidation coupled analysis process, activate the embankment soil, pile top cushion and reinforced body elements and corresponding gravity loads, enable the embankment center symmetric boundary constraints, and output the static calculation result set under the action of soil load, which contains the effect force field, pore water pressure field and boundary node reaction force data.

[0010] Step S5: Calibrate the node set, surface set, and geometric set of the bottom and two side boundaries of the model. Solve the boundary node control side length using the Python automated script embedded in the finite element platform. Calculate the spring stiffness coefficient and damping coefficient in combination with the physical and mechanical parameters of the soil layer to which the node belongs. Construct a viscoelastic artificial boundary using a distributed spring-damping element array. The physical and mechanical parameters include density, shear modulus, and wave velocity.

[0011] Step S6: Based on wave theory and the propagation law of layered media, the transmission and primary reflection effects of seismic waves at the soil interface are taken into account. The impedance ratio, reflection coefficient and transmission coefficient of adjacent soil layers are solved by Python script. The displacement time history and velocity time history of boundary nodes are calculated. The seismic waves are converted into equivalent nodal loads and applied to the model boundary.

[0012] Step S7: Use a Python script to perform multiphysics transformation of the static and dynamic analysis boundary.

[0013] Step S8: Solve the model using implicit dynamic analysis method to obtain the seismic dynamic response characteristic parameters of the pile-soil-reinforced embankment system.

[0014] Further optimization, step S1 specifically includes: Step S1.1: Utilizing the left-right symmetry of the pile-supported reinforced embankment, a two-dimensional simplified model is constructed by selecting one side of the embankment center and assigning values ​​according to the preset material parameter table. The embankment soil, pile top cushion layer and foundation soil adopt the Mohr-Coulomb strength criterion, and the pile body and reinforced body adopt a linear elastic constitutive model. Step S1.2: The pile body, embankment fill and pile top cushion layer adopt CPE4 four-node plane strain element, the soft soil of the foundation adopts CPE4P four-node pore water pressure element, and the reinforcement adopts T2D2 two-node truss element. Step S1.3: Mesh cell feature size Δ x The following relationship (1) is satisfied, and the pile-soil contact surface and the distribution area of ​​the reinforced body are subjected to mesh densification. (1); In the formula a λ is the coefficient for taking values. min This is the minimum wavelength of a seismic wave.

[0015] Further optimization, in step S2, the method for defining the contact action mechanism and setting the boundary load includes: Step S2.1: Define the contact mode according to the interaction characteristics of the components: the reinforced body and the pile top cushion layer adopt embedded constraint, the pile top and the embankment soil and the pile side and the foundation soil adopt surface contact, and the pile bottom and the foundation soil adopt bonded contact.

[0016] Step S2.2: In the face-to-face contact between the pile and the soil, the penalty function algorithm is used in the tangential direction and the hard contact algorithm is used in the normal direction to simulate the nonlinear effect of the pile-soil interface.

[0017] Step S2.3: Set boundary constraints: Apply normal displacement constraints to the left and right sides of the model foundation, and apply X and Y bidirectional displacement constraints to the bottom of the foundation. Where X and Y are the orthogonal directions of the global Cartesian coordinate system defined by the model; X is the horizontal coordinate axis of the model, parallel to the soft soil foundation surface; Y is the vertical coordinate axis of the model, perpendicular to the soft soil foundation surface, with upward as the positive direction.

[0018] Step S2.4: Apply a global gravity load to the model to ensure that the load covers all components and conforms to the actual stress state of the project.

[0019] Further optimization, in step S3, the method for constructing the geostress field equilibrium and the initial pore water pressure field includes: Step S3.1: Apply an initial geostress field to the model. This geostress field is set based on the natural stress distribution law of soft soil foundation and matches the initial stress state of the actual strata.

[0020] Step S3.2: Activate the geostress equilibrium analysis step of the finite element platform and achieve self-equilibrium of the geostress field of the model through iterative calculation.

[0021] Step S3.3: Based on the groundwater level, soil unit weight and seepage conditions, simultaneously construct the initial pore water pressure field to ensure that the initial field parameters are consistent with the actual engineering conditions.

[0022] Further optimization is achieved by implementing the soil-consolidation coupling analysis process in step S4, which includes: Step S4.1: Create a soil filling-consolidation coupled analysis step in the finite element platform and specify the analysis step duration, such as setting the soil filling stage to 55 days and the consolidation stage to 400 days, in line with the engineering construction and consolidation time.

[0023] Step S4.2: In this analysis step, activate the embankment fill, pile top cushion and reinforced body units, and apply the corresponding gravity loads to each component simultaneously.

[0024] Step S4.3: Enable the embankment center symmetric boundary constraint and apply normal displacement constraint to the center of the embankment to ensure that the model is subjected to symmetrical forces.

[0025] Step S4.4: Simultaneously activate the embedding constraint between the reinforced body and the pile top cushion layer, and the surface contact relationship between the pile top and the embankment soil to ensure that the contact effect continues to be effective during the consolidation process.

[0026] Step S4.5: After the analysis is completed, output a set of static calculation results containing effective stress field, pore water pressure field and boundary node reaction force data, to provide initial parameters for subsequent dynamic analysis.

[0027] Further optimization is achieved by the method for constructing the viscoelastic artificial boundary in step S5, which includes: Step S5.1: After the mesh is generated, create boundary sets in the finite element platform, including the node sets (Set-X0, Set-X1, Set-Y0) of the bottom boundary (Y0) and the two side boundaries (X0, X1), the surface sets (Surf-X0, Surf-X1, Surf-Y0), and the geometry sets (Geom-X0, Geom-X1, Geom-Y0). Step S5.2: Copy the model after static calculation, delete the in-situ stress equilibrium analysis step, the fill-consolidation coupling analysis step, and the static general analysis step, and add a dynamic implicit solution analysis; Step S5.3: Automatically generate three boundary node reaction force calculation sub-models (Submodel-X0, Submodel-X1, Submodel-Y0) using Python scripts. Apply the corresponding boundary normal displacement constraints and unit uniformly distributed loads to each sub-model, extract the node reaction forces, and use their absolute values ​​as the boundary node control side length A. Step S5.4: Determine the soft soil layer to which each boundary node belongs based on the soil layer thickness and node coordinates. Combining soil density, shear modulus, shear wave velocity, longitudinal wave velocity, and node control side length, calculate the tangential / normal spring stiffness coefficient and tangential / normal damping coefficient of each node using the following formulas: ; In the formulaK T , K N These are the tangential stiffness coefficient and the normal stiffness coefficient of the spring, respectively. C T , C N These are the tangential damping coefficient and the normal damping coefficient of the damper, respectively; α T and α N These are the tangential and normal correction factors for the viscoelastic artificial boundary, respectively. G Shear modulus of the foundation soil layer; R This represents the distance from the wave source to the artificial boundary node. ρ This refers to the density of the foundation soil layer; V S and V P These are the shear wave velocity and longitudinal wave velocity of the soil layer, respectively. A Control the edge length for boundary nodes; Step S5.5: Traverse all nodes at the bottom and side boundaries of the model, and apply the corresponding spring-damping elements one by one to form a distributed viscoelastic artificial boundary, thereby improving the accuracy of simulating the infinite domain effect of the foundation and mitigating the influence of boundary reflections. Further optimization is achieved by including the following method for calculating and applying the equivalent nodal load in step S6: Step S6.1: Based on the density of adjacent soil layers ρ With shear wave velocity V S Calculate wave impedance Z = ρ × V S The reflection coefficient β is derived from the amplitude ratio relationship. (L-1)L With transmission coefficient γ (L-1)L Soil layers are numbered from bottom to top, with the bottom layer defined as layer 1. Therefore: ; In the formula Z L-1 , Z L They represent the first L -1st floor, No. L The wave impedance of the soil medium in the layer.

[0028] Step S6.2: Calculate the displacement time history of the vertically incident seismic wave using the following formula: ; The formula for calculating the arrival time of the incident wave is: ; The formula for calculating the arrival time of the reflected wave is: ; In the formula u 0( t Let t be the magnitude of the displacement at time t. h i For the first i Soil layer thickness, d This represents the vertical distance from the node to the bottom of its layer. V For wave speed, h j The node is located at the 1st j The thickness of the soil layer.

[0029] Step S6.3: Based on the derivation logic of the displacement time history of each boundary node, obtain the velocity time history of the corresponding boundary node through the time derivative. .

[0030] Step S6.4: The equivalent nodal load is calculated using the displacement and velocity time history data obtained through the following formula: ; in C and K These are the damping coefficient and spring stiffness coefficient of the boundary node, respectively; u ff ( t )and These are displacement data and velocity data, respectively. The stress tensor generated by the free field; n It is the cosine vector of the direction of the outer normal to the boundary; A The node controls the edge length; Step S6.5: Apply the equivalent nodal load in the form of an amplitude curve to the bottom and side boundaries of the model to improve the accuracy of seismic wave load application.

[0031] Further optimization, in step S7, the multiphysics field connection and transformation method for the static and dynamic analysis boundary includes: Step S7.1: After completing the construction of the viscoelastic artificial boundary and the application of the equivalent nodal load, remove the original fixed constraints of the bottom boundary and the two side boundaries in the dynamic analysis step, and retain the gravity load and initial geostress field settings from the static analysis stage. Step S7.2: Read the static ODB result file generated by the soil-consolidation coupling analysis using a Python script, and import the consolidated effective stress field and pore water pressure field into the seismic dynamic model as the initial predefined field; Step S7.3: Extract the reaction force Fstatic at the boundary nodes of the static model, convert it into an equivalent reverse node force, and apply it to the corresponding node of the dynamic model to achieve the balance between gravity and initial ground stress.

[0032] Step S7.4: Verify the initial stress equilibrium state to ensure that the model has no spurious oscillations at the initial moment of dynamic analysis, and complete the transformation of static and dynamic analysis boundary conditions.

[0033] Further optimization is achieved by using the following method to solve for and output the seismic dynamic response in step S8: Step S8.1: Solve using the implicit dynamic analysis step of the finite element platform, setting the preset incremental step size of the analysis step to 0.01s to ensure the time accuracy of the dynamic response calculation.

[0034] Step S8.2: Output core response parameters: embankment settlement, vertical stress distribution of pile and soil, stress change data of pile body and strain distribution of reinforced body.

[0035] Step S8.3: Conduct seismic dynamic response characteristic evaluation of pile-supported reinforced embankments based on output parameters to provide data support for structural seismic design optimization.

[0036] Compared with the prior art, the present invention has the following beneficial effects: 1) This invention breaks through the assumption of single-layer soft soil, fully considers the parameter differences of layered soft soil foundations, calculates the transmission and reflection coefficients of seismic waves at the soil interface based on wave theory, and transforms seismic waves into equivalent nodal loads instead of direct acceleration loading. At the same time, it constructs a distributed viscoelastic artificial boundary to improve the accuracy of simulating the infinite domain effect of the foundation and mitigate the influence of boundary reflection. Furthermore, by inheriting the static field quantity across the analysis step and balancing the initial geostress, it reduces the spurious oscillations in the static-dynamic conversion. The simulation results are highly consistent with the actual seismic dynamic response law in engineering. Numerical verification shows that the numerical simulation solution and analytical solution of the bottom boundary and the top free surface of the model have small errors.

[0037] 2) This invention uses Python automated scripts to connect key steps such as boundary node control side length calculation, viscoelastic artificial boundary parameter solution, seismic wave equivalent load conversion, static and dynamic boundary condition adjustment, and field quantity data transmission. It replaces traditional manual calculation and manual operation, greatly reduces human error, shortens the modeling cycle from several days to hours, and significantly improves the efficiency of seismic modeling of layered soft soil-pile foundation-reinforced embankment system.

[0038] 3) This invention constructs a multi-field coupled analysis system of stress-seepage-dynamics, which simultaneously considers the dissipation of pore water pressure and the increase of effective stress during the filling-consolidation stage, simulates the consolidation deformation law of layered soft soil, and outputs a static result set containing a complete effective stress field and pore water pressure field, providing initial field parameters consistent with engineering reality for dynamic analysis, and solving the problem of initial field distortion in existing technologies.

[0039] 4) This invention forms an integrated modeling system of "model construction - static consolidation - artificial boundary construction - seismic wave application - static-dynamic conversion - dynamic solution", covering all key components and core technologies of the layered soft soil-pile foundation-reinforced embankment system. It can be directly adapted to pile-supported reinforced embankment projects with different soft soil areas, different embankment sizes, and different pile types. At the same time, the output parameters such as embankment settlement, pile-soil stress, and reinforced body strain can be directly used for seismic design and structural optimization of engineering projects, and have broad engineering application value.

[0040] 5) The modeling method of the present invention is based on a general finite element platform. The Python script is highly compatible with the finite element platform. The parameter calculation and operation process of each step have clear formulas and specifications. Those skilled in the art can directly reproduce the modeling process according to the actual parameters of the project. Moreover, the parameter settings and result output of the model solution are unified, which ensures the repeatability and scalability of the method. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the finite element model of the layered soft soil-pile foundation-reinforced embankment system in an embodiment of the present invention; Figure 2 This is a comparison diagram showing the verification of the viscoelastic artificial boundary and the application of equivalent seismic wave load in this invention; Figure 3 This is a comparison diagram of the vertical stress between the soil between piles and the soil on top of piles under static load and seismic action in an embodiment of the present invention. Figure 4 This is a strain distribution diagram of the reinforced body under seismic loading in an embodiment of the present invention; Figure 5 This is a curve showing the variation of settlement of soil between piles and soil on top of piles with embankment height under static load and seismic action in an embodiment of the present invention. Figure 6 This is a comparison diagram of the differential settlement between the soil on the pile and the soil between the piles at different pile locations under static load and seismic action in an embodiment of the present invention. Figure 7 This is an enlarged cloud map showing the deformation of the embankment in the U2 direction under seismic loading in an embodiment of the present invention. Figure 8 This is a curve showing the stress variation of pile #7 at the shoulder with pile depth under static load and seismic action in an embodiment of the present invention. Detailed Implementation

[0042] The following detailed description of the multi-field coupled numerical modeling method for seismic dynamic response of the layered soft soil-pile foundation-reinforced embankment system of the present invention, with reference to specific embodiments and accompanying drawings, is presented in this embodiment. The modeling is based on the ABAQUS finite element platform, and all Python automated scripts are embedded in the ABAQUS environment. Those skilled in the art can adjust the model size, material parameters, analysis step time and other indicators according to the actual engineering parameters.

[0043] A method for modeling layered soft soil subgrades under simulated seismic loading and pile foundation reinforcement is described below: Step S1: Construction of multi-field coupled numerical model and mesh optimization, specifically including: Step S11: Establish a multi-field coupled numerical model in Abaqus. This model includes five major components: layered soft soil foundation, piles, pile top cushion, reinforced body, and embankment fill.

[0044] To minimize computational workload and considering the bilateral symmetry of pile-supported reinforced embankments, a simplified two-dimensional model was constructed on one side of the embankment's center. Specific model dimensions are referenced. Figure 1 The model has a total length of 78.0m, an embankment fill height of 5.6m, a pile top cushion layer thickness of 0.5m, and a reinforcement body (geogrid) embedded in the middle of the cushion layer. The groundwater level is 1.5m below the ground surface. The foundation soil layers from top to bottom are: a 1.5m thick coarse-grained fill layer, a 2.3m thick silty clay layer, a 10.2m thick silty clay layer, a 3.0m thick silt layer, and a 9.0m thick silty sand layer. The piles are reinforced concrete piles embedded in the silty sand layer, with a pile diameter of 1.0m and a pile spacing of 3.0m.

[0045] Material constitutive parameters are set according to the engineering characteristics of the components. The embankment soil, pile top cushion layer and each layer of foundation soil adopt the Mohr-Coulomb strength criterion to consider the elastic-plastic deformation of the soil. The pile body and the reinforced body adopt the linear elastic constitutive model, which conforms to the mechanical characteristics of reinforced concrete piles and geogrids. The specific material parameters of each component are shown in Table 1.

[0046] Table 1 Material Parameters of the Example Model ; Step S12: The pile body, embankment fill and pile top cushion layer adopt CPE4 four-node plane strain element, which is suitable for elastic-plastic solid deformation analysis; the soft soil of the foundation adopts CPE4P four-node pore water pressure element to realize stress-seepage coupling analysis; the reinforced body adopts T2D2 two-node truss element, which only considers axial tensile deformation and fits the stress characteristics of geogrid.

[0047] Step S13: Perform mesh optimization subdivision, with mesh cell feature size Δ x The relationship of equation (1) is satisfied. At the same time, the grid is densified in key areas where stress and strain are concentrated, such as the pile-soil contact surface and the distribution area of ​​the reinforced body. Gradual grids are used in non-critical areas to reduce the computational complexity while ensuring the accuracy of the calculation.

[0048] Step S2: Define the contact action mechanism and set the boundary loads, specifically including: Step S21: Define the contact mechanism between each component, which conforms to the actual interaction law of components in engineering: The reinforced body and the pile top cushion layer adopt embedded constraint, embedding the reinforced body into the cushion layer to simulate the coordinated deformation of the two; the pile top and the embankment soil, and the pile side and the foundation soil adopt surface contact, considering the relative slippage of the pile-soil interface; the pile bottom and the foundation soil adopt bound contact, simulating the rigid connection between the pile bottom and the bearing layer, without relative deformation.

[0049] Step S22: Set the surface contact between the pile and the soil: the penalty function algorithm is used in the tangential direction, and the friction coefficient is set to 0.3 to match the interface friction characteristics of soft soil and reinforced concrete pile; the hard contact algorithm is used in the normal direction to allow the separation and contact of the pile and soil interface, which conforms to the actual mechanical behavior of pile-soil interaction.

[0050] Step S23: Set boundary constraints for the static analysis stage: For Figure 1 Apply normal displacement constraints (U1=0, X direction, horizontal transverse) to the left and right sides of the foundation of the model to restrict horizontal displacement; Figure 1 A bidirectional displacement constraint (U1=0, U2=0, Y direction is vertical) is applied to the bottom of the foundation of the model to restrict horizontal and vertical displacement.

[0051] Step S24: Apply a global gravity load to the model, covering the entire area. Figure 1 All components are simulated to mimic the actual gravitational field action in engineering.

[0052] Step S3: Equilibrium of the geostress field and construction of the initial pore water pressure field, specifically including: Step S31: Apply an initial geostress field to the model. This geostress field is set based on the natural self-weight stress distribution law of layered soft soil foundations, according to... Figure 1 The unit weight and burial depth of each soil layer are used to calculate the self-weight stress, which is matched to the actual initial stress state of the strata in the project.

[0053] Step S32: Create a geostatic stress equilibrium analysis step in ABAQUS. Achieve self-equilibrium of the model's geostress field through iterative calculation, eliminate the initial unbalanced stress generated during model construction, and ensure that the initial stress state of the static analysis is consistent with the actual engineering situation.

[0054] Step S33: Combining the groundwater level (1.5m below the surface) of the stratified soft soil foundation with the unit weight and seepage conditions of each soil layer, an initial pore water pressure field is constructed in ABAQUS using the Predefined Field function. The pore water pressure of the soil layer below the groundwater level is calculated based on hydrostatic pressure, while the pore water pressure of the soil layer above the groundwater level is 0, thus realizing the initial field coupling of stress and seepage.

[0055] Step S4: Soil-consolidation coupling analysis and static result output, specifically including: Step S41: Create fill-consolidation coupled analysis steps (Soils) in ABAQUS, and set the analysis step duration according to the actual construction project: 55 days for the fill stage and 400 days for the consolidation stage, and simulate... Figure 1 The construction process of the embankment fill and the subsequent consolidation deformation of the soft soil foundation.

[0056] Step S42: In this analysis step, activate the embankment fill, pile top cushion and reinforced body units, and simultaneously apply the corresponding gravity loads to each component to simulate the layered construction process of the embankment fill.

[0057] Step S43: Enable the symmetric boundary constraint at the center of the embankment and apply a normal displacement constraint (U1=0) to the center of the embankment to ensure the symmetric force characteristics of the model; simultaneously activate the embedding constraint between the reinforced body and the pile top cushion layer, and the surface contact relationship between the pile top and the embankment soil to ensure that the contact action of each component continues to be effective during the filling-consolidation process.

[0058] Step S44: Submit the calculation task for the soil-consolidation coupling analysis. After the calculation is completed, output the static calculation result set. The result set is stored in ODB file format and contains the effective stress field, pore water pressure field, displacement field and nodal reaction force data of each component of the model, as well as the bottom and side boundary nodal reaction force data of the model, providing complete static field parameters for subsequent dynamic analysis.

[0059] Step S5: Automated construction of distributed viscoelastic artificial boundaries, specifically including: Step S51: After the mesh is generated, create different types of meshes in ABAQUS using the Set and Surface functions. Figure 1 The set of model boundaries includes the node set (Set-X0, Set-X1, Set-Y0), surface set (Surf-X0, Surf-X1, Surf-Y0), and geometry set (Geom-X0, Geom-X1, Geom-Y0) of the bottom boundary (Y0) and the two side boundaries (X0, X1), which provides a calibration basis for subsequent boundary parameter calculations.

[0060] Step S52: Copy the model after static calculation, delete the geostress equilibrium analysis step, the fill-consolidation coupling analysis step and other static general analysis steps in the model, create a dynamic implicit solution analysis step in ABAQUS, and set the time domain and time increment step size for dynamic analysis.

[0061] Step S53: Run the embedded Python automation script. The script automatically generates three boundary node reaction force calculation sub-models (Submodel-X0, Submodel-X1, Submodel-Y0). In each sub-model, the normal displacement constraint of the corresponding boundary and a unit uniformly distributed load of 1 kPa are applied. The script automatically extracts the reaction force of each boundary node and uses its absolute value as the control side length of the node.

[0062] Step S54: Based on the soil layer thickness and node coordinates, determine the soft soil layer to which each boundary node belongs. Combine the soil layer density, shear modulus, shear wave velocity, longitudinal wave velocity and node control side length, and calculate the tangential / normal spring stiffness coefficient and tangential / normal damping coefficient of each node using formula (2).

[0063] In this embodiment, take α T =0.5、 α N =1.0.

[0064] Step S55: The Python script automatically traverses all nodes at the bottom and sides of the model, and applies the corresponding spring-damping element to each node to form a distributed viscoelastic artificial boundary, which improves the accuracy of simulating the infinite domain effect of the foundation and reduces the reflection distortion of seismic waves at the model boundary.

[0065] Step S6: Calculation and application of equivalent nodal loads for seismic waves in layered soil. In this embodiment, taking the bottom-incident Kobe wave as an example, the calculation and application of equivalent nodal loads for seismic waves are carried out, specifically including: Based on wave theory, considering transmission and primary reflection of each soil layer, the wave impedance ratio, reflection coefficient, and transmission coefficient between adjacent soil layers are calculated using Python scripts. The displacement and velocity time histories of each boundary node are also calculated. The seismic waves are converted into equivalent nodal loads and applied to the bottom and side boundaries in the form of amplitude curves. The specific steps include: Step S61: Run a Python automation script based on the density of adjacent soil layers. ρ With shear wave velocity V S Calculate wave impedance Z = ρ × V SThe reflection coefficient β is derived from the amplitude ratio relationship in formula (3). (L-1)L With transmission coefficient γ (L-1)L The soil layers are numbered from bottom to top, with the bottom layer defined as layer 1.

[0066] Step S62: Calculate the displacement time history of the vertically incident seismic wave using formula (4). In this embodiment, the incident wave is a shear wave velocity, therefore, the velocity here is... V S .

[0067] Step S63: Based on the derivation logic of the displacement time history, the script obtains the corresponding seismic wave velocity time history of the boundary node by performing time derivative on the displacement time history of the boundary node.

[0068] Step S64: The script combines the damping system of the boundary nodes, spring stiffness coefficient, displacement time history, velocity time history, free field stress tensor, cosine vector of the outer normal direction of the boundary and the control side length of the nodes to automatically solve the equivalent nodal load according to formula (7).

[0069] Step S65: The script automatically applies the calculated equivalent nodal loads as amplitude curves to the... Figure 1 The bottom and side boundaries of the model are used to load seismic waves, and the load and the distributed viscoelastic artificial boundary work together to match the propagation law of seismic waves in the layered soft soil foundation.

[0070] The application of viscoelastic artificial boundaries and equivalent seismic wave loads in Python scripts was verified, and the verification results are as follows: Figure 2 As shown, where Figure 2 (a) shows the comparison between the numerical simulation solution and the theoretical value of the horizontal displacement at the bottom boundary, and (b) shows the comparison between the numerical simulation solution and the theoretical value of the horizontal displacement at the top free surface. Figure 2 It can be seen that the numerical simulation solution of the horizontal displacement of the bottom boundary and the top free surface is consistent with the theoretical value and has a small error, which verifies the effectiveness and accuracy of the viscoelastic artificial boundary construction and equivalent seismic wave load application method of the present invention.

[0071] Step S7: Perform static and dynamic analysis boundary transformation using a Python script, specifically including: Step S71: After completing the construction of the viscoelastic artificial boundary and the application of the equivalent nodal load, in the dynamic implicit analysis step, the original static fixed constraints of the bottom boundary and the two side boundaries of the model are automatically removed by the Python script, while the gravity load and initial stress field settings of the static analysis stage are retained to ensure the continuity of the gravity field and the initial stress field of the dynamic analysis.

[0072] Step S72: Read the static ODB result file generated in step S4 through the script, and input the consolidated effective stress field and pore water pressure field into the seismic dynamic model as the initial predefined field to realize the cross-analysis step inheritance of static and dynamic field quantities.

[0073] Step S73: The script automatically extracts the reaction forces at the boundary nodes of the static model, converts them into equivalent reverse node forces, and applies them to the corresponding nodes of the seismic dynamic model to balance gravity and initial ground stress.

[0074] Step S74: Automatically verify the initial stress equilibrium state of the model through the script to ensure that there are no spurious oscillations in the model at the initial moment of dynamic analysis, and complete the multi-physics field connection and transformation of the static and dynamic analysis boundary.

[0075] Step S8: Seismic dynamic response solution and characteristic parameter output, specifically including: Step S81: Submit the dynamic implicit analysis calculation task in ABAQUS, and set the preset increment step size of the analysis step to 0.01s to ensure the time accuracy of the seismic dynamic response calculation.

[0076] Step S82: After the calculation is completed, extract and output the core seismic dynamic response characteristic parameters of the model, specifically including: Embankment settlement: The output results are plotted as follows Figure 5 , Figure 6 and Figure 7 .in Figure 5 The curves show the settlement of the soil between piles and the soil on top of piles under static load and seismic action as a function of embankment height. Figure 6 This is a comparison diagram of the differential settlement between the soil on and between piles at different pile locations under static load and seismic action. Figure 7 This is an enlarged cloud map showing the deformation of the embankment in the U2 direction under seismic loading. Unit: m.

[0077] Vertical stress distribution law of pile and soil: The output result is plotted as follows Figure 3 A comparison diagram of vertical stress between soil between piles and soil on top of piles under static load and seismic action.

[0078] Pile stress (lateral earth pressure, vertical stress) variation data: Output results plotted as follows Figure 8 The stress variation curve of pile #7 at the shoulder under static load and seismic action with pile depth, among which... Figure 8 (a) shows the variation curve of the lateral earth pressure S11 on the pile side, and (b) shows the variation curve of the vertical stress S22 at the pile center.

[0079] Stiffened body strain distribution: The output results are plotted as follows Figure 4 Strain distribution diagram of a reinforced body under seismic loading.

[0080] Step S83: Based on the output feature parameters and appended parameters Figure 3-8Evaluation of the seismic dynamic response characteristics of pile-supported reinforced embankments: from Figure 3 It can be seen that under static load of self-weight, the vertical stress of the soil on the pile is significantly greater than that of the soil between the piles, and there is a significant soil arching effect in the embankment. The load is transferred to the piles, and stress redistribution occurs. Under seismic load, the static soil arching effect of the embankment is significantly weakened, the stress of the soil on the pile decreases, and the soil between the piles begins to share more of the load.

[0081] from Figure 4 It can be seen that under seismic loading, the reinforced body exhibits local strain peaks near the pile edge, and this area is a critical location where the reinforced body is prone to tensile cracking. It was also found that the tensile membrane effect still exists under seismic loading, and the geogrid transfers the load of the soil between piles to the pile top through the tensile membrane effect, with local peaks appearing near the pile edge.

[0082] from Figure 5 , Figure 6 It can be seen that under static load, there is differential settlement between the soil between the piles and the soil on top of the piles at the bottom of the embankment, but an isostatic surface appears at approximately 2m of the embankment. Under seismic loading, the differential settlement between the piles and soil is amplified, and the isostatic surface essentially disappears. Near the center of the embankment, the differential settlement of the upper part of the embankment is significant, and there are local areas of concentrated settlement. Further amplification of embankment settlement deformation is shown in the figure. Figure 7 It can be observed that the embankment surface exhibits unevenness and localized collapse under seismic action.

[0083] from Figure 8 It can be seen that under earthquake loading, the lateral earth pressure on the pile increases significantly, with a peak value appearing in the middle of the pile, making it prone to fracture failure; from Figure 8 As can be seen in (a), under static load, the lateral earth pressure on the pile increases with the increase of pile depth; under seismic load, the trend is similar to that under static load, but the lateral earth pressure increases significantly, the peak value appears in the middle of the pile, the bending moment is the largest, and the pile body is prone to fracture. Figure 8 As can be seen from (b), the vertical stress of the pile under static load gradually increases with depth; under seismic action, the vertical stress in the middle of the upper part of the pile is less than that under static load, while that at the bottom is greater than that under static load.

[0084] The above analysis results can provide relatively accurate data support for seismic design and structural optimization in engineering projects, such as according to Figure 8 Optimize pile reinforcement based on the location of peak stress in the middle pile body. Figure 4 Optimization of geogrid layout in the strain peak region of reinforced concrete, etc.

[0085] The simulation results obtained in this embodiment using the above modeling method (such as...) Figure 3-8 The characteristics of the soil arching effect under static load, the weakening of the soil arching effect under earthquake, the peak stress in the pile body appearing in the middle, and the amplification of differential settlement are all consistent with the seismic failure characteristics of pile-supported reinforced embankments in soft soil areas. Figure 2 The small error between the numerical simulation solution and the theoretical solution verifies the effectiveness of the viscoelastic artificial boundary construction and seismic wave load application method of the present invention, and proves that the modeling method of the present invention has the technical advantages of high precision and high reliability.

[0086] As described above, although the invention has been illustrated and described with reference to specific embodiments, it should not be construed as limiting the invention itself. Various changes in form and detail may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A method for modeling layered soft soil subgrades under simulated seismic loading and pile foundation reinforcement, characterized in that, Includes the following steps: Step S1: Construct a multi-field coupled numerical model based on the finite element platform, including layered soft soil foundation, piles, pile top cushion, reinforced body and embankment fill, set the constitutive parameters of each component material and complete the mesh optimization; Step S2: Define the contact interaction between the reinforced body and the cushion layer, and between the pile and the soil; set the boundary constraints of the model and apply the global gravity load. Step S3: By adopting the initial geostress field and geostress equilibrium analysis step, the geostress field of the model is balanced and the initial pore water pressure field is constructed; Step S4: Construct the soil-consolidation coupled analysis process, activate the embankment soil, pile top cushion and reinforced body elements and corresponding gravity loads, enable the embankment center symmetric boundary constraints, and output the static calculation results under the action of soil load; Step S5: Calibrate the node set, surface set and geometric set of the bottom and two side boundaries of the model. Solve the boundary node control side length through the Python automated script embedded in the finite element platform. Calculate the spring stiffness coefficient and damping coefficient in combination with the physical and mechanical parameters of the soil layer to which the node belongs. Construct a viscoelastic artificial boundary through a distributed spring-damping element array. Step S6: Based on wave theory and the propagation law of layered media, calculate the transmission and primary reflection effects of seismic waves at the soil interface, solve the wave impedance ratio, reflection coefficient and transmission coefficient of adjacent soil layers through Python script, calculate the displacement time history and velocity time history of boundary nodes, and convert the seismic waves into equivalent nodal loads and apply them to the model boundary. Step S7: Use Python scripts to perform multiphysics transformation of the static and dynamic analysis boundary; Step S8: Solve the model using implicit dynamic analysis to obtain the seismic dynamic response characteristic parameters of the pile-soil-reinforced embankment system.

2. The method for modeling layered soft soil subgrades under simulated seismic loading as described in claim 1, characterized in that, Step S1 specifically includes: Step S1.1: Utilizing the left-right symmetry of the pile-supported reinforced embankment, a two-dimensional simplified model is constructed by selecting one side of the embankment center and assigning values ​​according to the preset material parameter table. The embankment soil, pile top cushion layer and foundation soil adopt the Mohr-Coulomb strength criterion, and the pile body and reinforced body adopt a linear elastic constitutive model. Step S1.2: The pile body, embankment fill and pile top cushion layer adopt CPE4 four-node plane strain element, the soft soil of the foundation adopts CPE4P four-node pore water pressure element, and the reinforcement adopts T2D2 two-node truss element. Step S1.3: Mesh cell feature size Δ x The following relationship (1) is satisfied, and the pile-soil contact surface and the distribution area of ​​the reinforced body are subjected to mesh densification. ; In the formula a λ is the coefficient for taking values. min This is the minimum wavelength of a seismic wave.

3. The method for modeling layered soft soil subgrades under simulated seismic loading as described in claim 1, characterized in that, In step S2, the methods for defining the contact action mechanism and setting the boundary load include: Step S2.1: Define the contact mode according to the interaction characteristics of the components: the reinforced body and the pile top cushion layer adopt embedded constraint, the pile top and the embankment soil and the pile side and the foundation soil adopt surface contact, and the pile bottom and the foundation soil adopt bonded contact. Step S2.2: In the face-to-face contact between the pile and the soil, the penalty function algorithm is used in the tangential direction and the hard contact algorithm is used in the normal direction to simulate the nonlinear effect of the pile-soil interface; Step S2.3: Set boundary constraints: Apply normal displacement constraints to the left and right sides of the model foundation, and apply bidirectional X and Y displacement constraints to the bottom of the foundation; Step S2.4: Apply a global gravity load to the model to ensure that the load covers all components and conforms to the actual stress state of the project.

4. The method for modeling layered soft soil subgrades under simulated seismic loading as described in claim 3, characterized in that, In step S3, the method for balancing the geostress field and constructing the initial pore water pressure field includes: Step S3.1: Apply an initial geostress field to the model. This geostress field is set based on the natural stress distribution law of soft soil foundation and matches the initial stress state of the actual strata. Step S3.2: Activate the geostress equilibrium analysis step of the finite element platform and achieve self-equilibrium of the geostress field of the model through iterative calculation; Step S3.3: Based on the groundwater level, soil unit weight and seepage conditions, simultaneously construct the initial pore water pressure field to ensure that the initial field parameters are consistent with the actual engineering conditions.

5. The method for modeling layered soft soil subgrades under simulated seismic loading as described in claim 4, characterized in that, In step S4, the implementation method of the soil-consolidation coupling analysis process includes: Step S4.1: Create a soil-consolidation coupling analysis step in the finite element platform and specify the analysis step duration; Step S4.2: In this analysis step, activate the embankment fill, pile top cushion and reinforced body units, and apply the corresponding gravity loads to each component simultaneously; Step S4.3: Enable the embankment center symmetric boundary constraint and apply a normal displacement constraint to the center of the embankment to ensure that the model is subjected to symmetrical forces; Step S4.4: Simultaneously activate the embedding constraint between the reinforced body and the pile top cushion, and the surface contact relationship between the pile top and the embankment soil to ensure that the contact effect continues to be effective during the consolidation process; Step S4.5: After the analysis is completed, output a set of static calculation results containing effective stress field, pore water pressure field and boundary node reaction force data, to provide initial parameters for subsequent dynamic analysis.

6. The method for modeling layered soft soil subgrades under simulated seismic loading as described in claim 5, characterized in that, In step S5, the method for constructing the viscoelastic artificial boundary includes: Step S5.1: After meshing is completed, create boundary sets in the finite element platform, including the node sets (Set-X0, Set-X1, Set-Y0) of the bottom boundary (Y0) and the two side boundaries (X0, X1), the surface sets (Surf-X0, Surf-X1, Surf-Y0), and the geometry sets (Geom-X0, Geom-X1, Geom-Y0). Step S5.2: Copy the model after static calculation, delete the in-situ stress equilibrium analysis step, the fill-consolidation coupling analysis step, and the static general analysis step, and add a dynamic implicit solution analysis; Step S5.3: Automatically generate three boundary node reaction force calculation sub-models (Submodel-X0, Submodel-X1, Submodel-Y0) using Python scripts. Apply the corresponding boundary normal displacement constraints and unit uniformly distributed loads to each sub-model, extract the node reaction forces, and use their absolute values ​​as the boundary node control side length A. Step S5.4: Based on the soil layer thickness and node coordinates, determine the soft soil layer to which each boundary node belongs. Combining the soil layer density, shear modulus, shear wave velocity, longitudinal wave velocity, and node control side length, calculate the tangential / normal spring stiffness coefficient and tangential / normal damping coefficient of each node using the following formula (2): ; In the formula K T , K N These are the tangential stiffness coefficient and the normal stiffness coefficient of the spring, respectively. C T , C N These are the tangential damping coefficient and the normal damping coefficient of the damper, respectively; α T and α N These are the tangential and normal correction factors for the viscoelastic artificial boundary, respectively. G Shear modulus of the foundation soil layer; R This represents the distance from the wave source to the artificial boundary node. ρ This refers to the density of the foundation soil layer; V S and V P These are the shear wave velocity and longitudinal wave velocity of the soil layer, respectively. A Control the edge length for boundary nodes; Step S5.5: Traverse all nodes at the bottom and side boundaries of the model and apply the corresponding spring-damping elements one by one to form a distributed viscoelastic artificial boundary.

7. The method for modeling layered soft soil subgrades under simulated seismic loading as described in claim 6, characterized in that, In step S6, the method for calculating and applying the equivalent nodal load includes: Step S6.1: Based on the density of adjacent soil layers ρ With shear wave velocity V S Calculate wave impedance Z = ρ × V S The reflection coefficient β is derived from the amplitude ratio relationship in the following formula (3). (L-1)L With transmission coefficient γ (L-1)L Soil layers are numbered from bottom to top, with the bottom layer defined as layer 1. Therefore: ; In the formula Z L-1 , Z L They represent the first L -1st floor, No. L The wave impedance of the soil medium in the layer; Step S6.2: Calculate the displacement time history of the vertically incident seismic wave using the following formula (4): ； The arrival time of the incident wave t t The calculation formula is: ； Time of arrival of reflected wave t r The calculation formula is: ； In the formula u 0( t Let t be the original displacement time history of the incident wave at time t. h i For the first i Soil layer thickness, d This represents the vertical distance from the node to the bottom of its layer. V For wave speed, h j The node is located at the 1st j The thickness of the soil layer; Step S6.3: Based on the derivation logic of the boundary node displacement time history, obtain the corresponding boundary node velocity time history through the time derivative. ; Step S6.4: The equivalent nodal load is calculated using the displacement and velocity time history data obtained through the following formula (7): ； in C and K These are the damping coefficient and spring stiffness coefficient of the boundary node, respectively; u ff ( t )and These are displacement data and velocity data, respectively. The stress tensor generated by the free field; n It is the cosine vector of the direction of the outer normal to the boundary; A The node controls the edge length; Step S6.5: Apply the equivalent nodal loads as amplitude curves to the bottom and side boundaries of the model.

8. The method for modeling layered soft soil subgrades under simulated seismic loading as described in claim 7, characterized in that, In step S7, the multiphysics field connection and transformation method for the static and dynamic analysis boundary includes: Step S7.1: After completing the construction of the viscoelastic artificial boundary and the application of the equivalent nodal load, remove the original fixed constraints of the bottom boundary and the two side boundaries in the dynamic analysis step, and retain the gravity load and initial geostress field settings from the static analysis stage. Step S7.2: Read the static ODB result file generated by the soil-consolidation coupling analysis using a Python script, and import the consolidated effective stress field and pore water pressure field into the seismic dynamic model as the initial predefined field; Step S7.3: Extract the reaction forces at the boundary nodes of the static model, convert them into equivalent reverse node forces, and apply them to the corresponding nodes of the dynamic model to achieve a balance between gravity and initial ground stress; Step S7.4: Verify the initial stress equilibrium state to ensure that the model has no spurious oscillations at the initial moment of dynamic analysis, and complete the transformation of static and dynamic analysis boundary conditions.

9. The method for modeling layered soft soil subgrades under simulated seismic loading as described in claim 8, characterized in that, In step S8, the method for solving and outputting the seismic dynamic response is as follows: Step S8.1: Solve using the implicit dynamic analysis step of the finite element platform, setting the preset incremental step size of the analysis step to 0.01s to ensure the time accuracy of the dynamic response calculation; Step S8.2: Output core response parameters: embankment settlement, vertical stress distribution of pile and soil, stress variation data of pile body and strain distribution of reinforced body; Step S8.3: Conduct seismic dynamic response characteristic evaluation of pile-supported reinforced embankments based on output parameters to provide data support for structural seismic design optimization.

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