Method for predicting mechanical response of confined space foundation pit coupled with enclosure-foundation-group pile

Abstract

The present application relates to a kind of enclosure-foundation-group pile coupling's confined space foundation pit mechanics response prediction method, belong to foundation pit engineering technical field.The method includes: input enclosure structure displacement, adjacent group pile design parameter and soil parameter;Establish adjacent single pile stress deformation control equation, consider the stiffness hardening characteristics of soil, determine foundation model parameter, generate model stiffness matrix;Additional displacement of soil is calculated, to determine the additional stress acting on single pile;The shear stress and shear strain of soil spring at different buried depths are calculated, and then the stiffness of soil is determined;Update model stiffness matrix, calculate the single pile displacement of each pile;Consider the shielding effect of group pile, calculate the lateral displacement of the pile body of rear row pile and the lateral displacement of the pile body of front row pile;Whether the error of lateral displacement of the pile body calculated in the last two iterations in iteration reaches the accuracy requirement is judged, yes, then output the lateral displacement of the pile body, otherwise continue iteration.The method can improve the prediction accuracy of the mechanics response of the confined space foundation pit of enclosure wall-foundation soil-group pile coupling.

Description

Technical Field

[0001] This invention belongs to the field of foundation pit engineering technology, specifically relating to a method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation, and pile groups. Background Technology

[0002] With the acceleration of urbanization and the increasing frequency of underground space development, foundation pit engineering in densely built-up areas often faces "confined space" conditions, meaning that there are existing buildings, underground pipelines, transportation facilities, and other important structures around the foundation pit, especially in cases where there are existing pile groups nearby. In such complex environments, foundation pit excavation will cause lateral displacement of the retaining structure, which in turn will transfer additional loads to the adjacent pile groups through the foundation soil, causing lateral displacement of the piles. In severe cases, this may threaten the safety and normal use of the existing pile groups.

[0003] Currently, the main analytical methods for analyzing the impact of foundation pit excavation on adjacent pile foundations include empirical formula methods, simplified analytical methods, and numerical simulation methods. Empirical formula methods rely on limited engineering cases, have a narrow scope of application, and struggle to reflect the coupling effect between the retaining wall, foundation soil, and pile group. Simplified analytical methods are often based on the Winkler foundation model or elastic half-space theory, failing to fully consider the nonlinearity of the soil and the shielding effect between pile groups. While numerical simulation methods (such as the finite element method) can describe the interaction mechanism in detail, they are complex in modeling, computationally expensive, and highly sensitive to parameters, making them unsuitable for rapid evaluation and iterative optimization during the engineering design phase. Especially under confined space conditions, a complex coupled mechanical system is formed between the confined space foundation pit retaining structure, foundation soil, and adjacent pile groups. Existing methods often neglect the stiffness decay characteristics of the soil under small strain conditions, the dynamic iterative coupling process of the retaining wall, foundation soil, and pile groups, and the mutual shielding effect between rows of piles, leading to significant deviations in the prediction of pile stress and deformation, making it difficult to meet the requirements of high-precision engineering design.

[0004] Therefore, it is necessary to develop an analytical method that can accurately predict the mechanical response of the retaining wall-foundation soil-pile system during the excavation of a confined space foundation pit, in order to make up for the shortcomings of existing technologies and provide a reliable basis for foundation pit design and protection of adjacent structures. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation soil, and pile groups. This method can improve the accuracy of predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation soil, and pile groups.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation, and pile groups, comprising the following steps:

[0007] Step S1: Input the displacement of the retaining structure of the confined space foundation pit, the design parameters of the adjacent pile group, and the soil parameters determined by the in-situ test of the SDMT lateral dilatation based on the seismic wave flat shovel.

[0008] Step S2: Based on the nonlinear elastic Kerr foundation model, establish the stress and deformation control equations of adjacent single piles, consider the stiffness hardening characteristics of soil, determine the Kerr foundation model parameters, and generate the model stiffness matrix;

[0009] Step S3: Calculate the additional soil displacement caused by the displacement of the retaining structure, and determine the additional stress acting on the single pile based on the additional soil displacement;

[0010] Step S4: Calculate the shear stress of the soil spring at different burial depths, then calculate the shear strain, determine the strain stage of the soil spring at different burial depths, and then determine the soil stiffness.

[0011] Step S5: Update the model stiffness matrix and calculate the spring deformation of the first layer of soil to obtain the displacement of each pile.

[0012] Step S6: Considering the shading effect of pile groups, calculate the shading displacement of the front piles to the rear piles, the shading matrix of the front piles to the rear piles, and then calculate the lateral displacement of the rear piles.

[0013] Step S7: Considering the shading effect of pile groups, calculate the shading displacement of the rear piles on the front piles and the shading matrix of the rear piles on the front piles, and then calculate the lateral displacement of the front piles.

[0014] Step S8: Determine whether the lateral displacement error of the front row piles and the lateral displacement error of the rear row piles between two consecutive calculations during the iterative calculation process meet the accuracy requirements. If yes, output the lateral displacement of the front row piles and the lateral displacement of the rear row piles. Otherwise, return to step S6 to continue the iterative calculation until the accuracy requirements are met.

[0015] Further, in step S1, the displacement u of the retaining structure is obtained through on-site monitoring data; the design parameters of the adjacent pile group include pile diameter D, pile length L, pile spacing L0, and Young's modulus E of the pile body; the soil parameters determined based on SDMT in-situ testing include:

[0016]

[0017] in, Effective cohesion of the soil; This represents the effective overburden stress of the soil. K is the effective internal friction angle of the soil. D K0 is the horizontal stress index; K0 is the lateral earth pressure coefficient. To be with K D Correlation coefficient; For soil reference unloading-reloading Young's modulus; E D This refers to the modulus of pressure on the soil side. For soil with small strain stiffness; This refers to the soil density. The shear wave velocity of the soil; is the soil shear strain level; c is the soil cohesion. This represents the effective principal stress of the soil.

[0018] Further, in step S2, the force-deformation control equation of the adjacent single pile is:

[0019]

[0020] Where EI is the bending stiffness of the pile; D is the pile diameter; p is the additional stress on the pile due to the excavation of the foundation pit; w1 is the deformation of the first layer of soil springs; z is the ordinate of any point in the soil when a coordinate system is established with the horizontal direction of the ground as the X-axis and the direction of the retaining structure as the Z-axis; k, f, and G are the stiffness of the first layer of soil springs on the side away from the pile, the stiffness of the second layer of soil springs on the side closer to the pile, and the stiffness of the shear layer between the first and second layers of soil springs, respectively, which are determined by the following formula:

[0021]

[0022] Among them, E t t is the Young's modulus of the soil; v is the thickness of the shear layer; t a1 and a2 are Poisson's ratios of the soil; a1 and a2 are set coefficients.

[0023] Young's modulus of soil E t The following formula is used to determine the soil stiffness hardening:

[0024]

[0025] in, For reference confining pressure; denoted as the effective minor principal stress of the soil; m is a parameter characterizing the dependence of stiffness on stress level. For soil unloading and reloading, Young's modulus is applied. For soil reference unloading-reloading Young's modulus;

[0026] Model stiffness matrix for:

[0027]

[0028] in, , L is the pile length.

[0029] Furthermore, in step S3, the additional soil displacement S x (z) Calculated using the following formula:

[0030]

[0031] in, ; x and z are the x and y coordinates of any point in the soil when a coordinate system is established with the horizontal direction of the ground as the X-axis and the direction of the retaining structure as the Z-axis; x0 and z0 are the x and y coordinates of any point on the retaining structure based on the aforementioned coordinate system; u is the lateral displacement of point (x0, z0); H is the vertical length of the retaining structure.

[0032] The additional stress p(z) acting on the pile is calculated by the following formula:

[0033]

[0034] in, for The second derivative of .

[0035] Furthermore, in step S4, the soil spring shear stress τ at different burial depths of the pile is calculated using the following formula:

[0036]

[0037] Where P is the equivalent concentrated force of the additional stress p(z) acting on the pile;

[0038] Soil spring shear strain at different burial depths of piles Calculated using the following formula:

[0039]

[0040] Cutoff strain Size:

[0041]

[0042] Among them, G ur For soil unloading-reloading stiffness, ;v ur For soil unloading and reloading, Poisson's ratio is applied.

[0043] when At that time, the soil is considered to be in a small strain stage, and the soil stiffness G is calculated using the following formula. t :

[0044]

[0045] when At this point, the soil is considered to have exceeded the small strain stage, and the soil stiffness G is taken as... t = G ur .

[0046] Furthermore, in step S5, the Young's modulus of the soil is updated using the following formula:

[0047]

[0048] This leads to the updating of the first-layer soil spring stiffness k, the second-layer soil spring stiffness f, and the shear layer stiffness G, thereby updating the model stiffness matrix. ;

[0049] The finite difference method is used to solve for the lateral displacement of the pile. The pile is discretized into n segments from top to bottom using n+1 nodes, and a virtual node is introduced on each side. The spring deformation w1 of the first layer of soil is calculated using a matrix in a difference form. express, Calculated using the following formula:

[0050]

[0051] in, (w1) n The first-layer soil spring deformation is represented by node n, and the additional stress matrix consists of the additional stresses of the n+1 nodes. p n The magnitude of the additional stress at node n;

[0052] Single pile displacement Using matrices It means that among them Calculated using the following formula:

[0053]

[0054] in, Let represent the lateral displacement of node i, where i = 0, 1, ..., n; and l represent the discrete node spacing, where l = L / n.

[0055] Furthermore, in step S6, the shielding displacement of point j in the front row of piles near the foundation pit relative to point i in the rear row of piles... This can be expressed by the following formula:

[0056]

[0057] in, Let be the lateral displacement of point j in the front row of piles; The lateral displacement of the soil at point j caused by the excavation of the foundation pit; The lateral displacement influence factor of the front row of piles on the rear row of piles is expressed by the following formula:

[0058]

[0059] In the formula, k zj Let L1 be the spring stiffness of the first layer of soil at point j in the front row of piles; L1 be the pile length of the front row of piles; and R3 be the actual distance between point j and point i. R4 is the equivalent distance between point j and point i. L0 represents the pile spacing; x1 represents the x-coordinate of the front row of piles; z i and z j These are the ordinates of points i and j, respectively;

[0060] Under the shielding effect of the front row of piles, the lateral displacement w of the rear row of piles 22 Using matrices Representation, matrix Including the shielding effect of the front row of piles, the lateral displacement of n+1 nodes in the rear row of piles:

[0061]

[0062] Where {K2} is the model stiffness matrix of the rear piles; This is the additional stress matrix for the rear piles; This represents the additional stress matrix exerted by the front row of piles on the rear row of piles. ,in for The second derivative of .

[0063] Furthermore, in step S7, the shielding displacement of point i in the rear row of piles away from the foundation pit relative to point j in the front row of piles... This can be expressed by the following formula:

[0064]

[0065] in, Let i be the lateral displacement of a point i in the rear row of piles; The lateral displacement of the soil at point i caused by the excavation of the foundation pit; The lateral displacement influence factor of the rear piles on the front piles is expressed by the following formula:

[0066]

[0067] In the formula, k zi Let L1 be the spring stiffness of the first layer of soil at point i in the rear row of piles; L2 be the pile length of the rear row of piles; and x2 be the abscissa of the rear row of piles.

[0068] Under the shielding effect of the rear piles, the lateral displacement w of the front pile body 11Using matrices Representation, matrix Including the shielding effect of the rear piles, the lateral displacement of n+1 nodes in the front piles:

[0069]

[0070] Where {K1} is the model stiffness matrix of the front piles; This is the additional stress matrix for the front row of piles; This represents the additional stress matrix exerted by the rear row of piles on the front row of piles. ,in for The second derivative of .

[0071] Furthermore, in step S8, the accuracy requirement for the lateral displacement error of the pile between the two calculations is as follows:

[0072]

[0073] in, The error in the lateral displacement of the front row of piles is the difference between the (k-1)th and kth iterations. and These represent the lateral displacements of the front row of piles in the (k-1)th and kth iterations, respectively. The error in the lateral displacement of the rear pile body between the (k-1)th and kth iterations; and These are the lateral displacements of the rear piles in the (k-1)th and kth iterations, respectively. This is the preset accuracy threshold.

[0074] The present invention also provides a confined space foundation pit mechanical response prediction system coupled with retaining wall-foundation-pile group, including a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, it can implement the above-mentioned method.

[0075] Compared with existing technologies, this invention has the following advantages: This invention provides a method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation soil, and pile groups. This method obtains soil parameters based on in-situ seismic wave dilatational lateral expansion (SDMT) testing, combines a nonlinear Kerr foundation beam model, constructs the pile stress-deformation control equation, establishes an additional stress transfer model based on additional soil displacement, introduces a soil nonlinearity and strain stage discrimination mechanism, and identifies the soil stiffness state in real time by combining shear stiffness-shear strain relationship. This effectively captures stiffness attenuation and hardening behavior in the small strain stage, dynamically updates foundation model parameters and stiffness matrix, and achieves refined modeling of the retaining wall-foundation soil-pile group coupled system. This invention proposes an iterative algorithm for pile group shielding effect based on displacement influence factors, calculates the mutual shielding displacement and shielding matrix between the front and rear piles respectively, and accurately reflects the collaborative working mechanism of the pile group through bidirectional iterative correction of the front and rear pile displacements. It achieves iterative stable solution throughout the entire process through displacement error convergence control, outputting the pile displacement response results. This invention fully considers key factors such as the displacement transfer of retaining walls, nonlinear stiffness of soil, and the shielding effect of pile groups under confined space conditions, significantly improving the accuracy and reliability of predicting the mechanical response of foundation pit excavation to adjacent pile groups. It is suitable for foundation pit engineering design and safety assessment in complex environments of dense urban areas. Attached Figure Description

[0076] Figure 1 This is a flowchart illustrating the implementation of the confined space foundation pit mechanical response prediction method coupled with retaining wall, foundation, and pile group provided in this embodiment of the invention.

[0077] Figure 2 This is a plan view of the confined space foundation pit and adjacent pile groups in an embodiment of the present invention;

[0078] Figure 3 This is a schematic diagram of the Kerr foundation beam model construction in an embodiment of the present invention;

[0079] Figure 4 This is a schematic diagram of soil shear stiffness attenuation in an embodiment of the present invention;

[0080] Figure 5 This is a schematic diagram of the shielding effect of pile groups in an embodiment of the present invention;

[0081] Figure 6 This is a comparison chart of the predicted and monitored values ​​of the lateral displacement of the pile body in an embodiment of the present invention. Detailed Implementation

[0082] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0083] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0084] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0085] like Figure 1 As shown in the figure, this embodiment provides a method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation and pile group, and its implementation steps are as follows.

[0086] Step S1: Input the displacement u of the confined space foundation pit retaining structure, the design parameters of the adjacent pile group (pile diameter D, pile length L, pile spacing L0, pile Young's modulus E), and the soil parameters determined based on the in-situ test of seismic wave flat shovel dilatation (SDMT).

[0087] The displacement u of the retaining structure can be obtained through on-site monitoring data. Soil parameters determined based on SDMT in-situ testing include:

[0088]

[0089] in, Effective cohesion of the soil; The effective overburden stress of the soil is determined by the formula. We find that z is the depth of any point on the soil. The effective unit weight of the soil at this point is given by the formula. Seeking, The soil weight, The specific weight of water is taken as 10 kN / m³. 3 ; K is the effective internal friction angle of the soil. D K0 is the horizontal stress index; K0 is the lateral earth pressure coefficient. To be with K D Correlation coefficient; For soil reference unloading-reloading Young's modulus; E D This refers to the modulus of pressure on the soil side. For soil with small strain stiffness; This refers to the soil density. The shear wave velocity of the soil; is the soil shear strain level; c is the soil cohesion. K represents the effective principal stress of the soil. D , E D All were obtained through in-situ SDMT testing.

[0090] Step S2: Based on the nonlinear elastic Kerr foundation model, establish the stress-deformation control equations for adjacent single piles, consider the stiffness hardening characteristics of the soil, determine the Kerr foundation model parameters f, G, and k, and generate the model stiffness matrix. .

[0091] Specifically, the governing equation for the stress and deformation of the adjacent single pile is:

[0092]

[0093] Where EI is the bending stiffness of the pile; D is the pile diameter; p is the additional stress on the pile due to the excavation of the foundation pit; w1 is the spring deformation of the first layer of soil; z is the coordinate system established with the horizontal direction of the ground as the X-axis (positive to the right) and the direction of the retaining structure as the Z-axis (positive downward) (the specific coordinate system is as follows). Figure 4 As shown, the ordinate of any point within the soil; k, f, and G are the stiffness of the first layer of soil springs (away from the pile), the second layer of soil springs (closer to the pile), and the shear layer (between the first and second layers of soil springs), respectively, determined by the following formula:

[0094]

[0095] in, To set coefficients; preferably, Take 3, that is E t v is the Young's modulus of the soil. t For soil with a Poisson's ratio, the best location is v. t Take 0.3; t is the shear layer thickness; To set coefficients; preferably, Take 11, that is That is, the shear layer thickness t is taken as 11 times the pile diameter.

[0096] Young's modulus of soil E t It can be determined by the following formula, taking into account soil stiffness hardening:

[0097]

[0098] in, For soil unloading and reloading, Young's modulus is applied. For soil reference unloading-reloading Young's modulus; For reference confining pressure, take 100 kPa; denoted as the effective minor principal stress of the soil; m is a parameter characterizing the dependence of stiffness on stress level, taken as 0.5 for sand and 1.0 for clay.

[0099] Model stiffness matrix for:

[0100]

[0101] in, , L is the pile length.

[0102] Step S3: Calculate the additional soil displacement S caused by the displacement u of the retaining structure. x (z), and based on the additional soil displacement S x (z) Determine the additional stress p(z) acting on a single pile.

[0103] Specifically, the additional displacement S of the soil x (z) Calculated using the following formula:

[0104]

[0105] in, ; x and z are the x and y coordinates of any point in the soil when a coordinate system is established with the horizontal direction of the ground as the X-axis and the direction of the retaining structure as the Z-axis; x0 and z0 are the x and y coordinates of any point on the retaining structure based on the aforementioned coordinate system; u is the lateral displacement of point (x0, z0); and H is the vertical length of the retaining structure.

[0106] The additional stress p(z) acting on the pile is calculated by the following formula:

[0107]

[0108] in, for The second derivative of .

[0109] Step S4: Calculate the shear stress τ of the soil spring at different burial depths, then calculate the shear strain γ, determine the strain stage of the soil spring at different burial depths, and then determine the soil stiffness G. t .

[0110] Specifically, the soil spring shear stress τ at different burial depths of the pile is calculated using the following formula:

[0111]

[0112] Where P is the equivalent concentrated force of the additional stress p(z) acting on the pile, which can be calculated by the following formula:

[0113] .

[0114] Soil spring shear strain at different burial depths of piles Calculated using the following formula:

[0115]

[0116] Cutoff strain Size:

[0117]

[0118] Among them, G ur For soil unloading-reloading stiffness, ;v ur The Poisson's ratio for soil unloading-reloading is set to 0.2.

[0119] when At that time, the soil is considered to be in a small strain stage, and the soil stiffness G is calculated using the following formula. t :

[0120]

[0121] when At this point, the soil is considered to have exceeded the small strain stage, and the soil stiffness G is taken as... t = G ur .

[0122] Step S5: Update the model stiffness matrix The deformation of the first layer of soil spring, w1, was calculated to obtain the displacement of each pile. .

[0123] Specifically, the Young's modulus of the soil is updated using the following formula:

[0124]

[0125] This leads to the updating of the first-layer soil spring stiffness k, the second-layer soil spring stiffness f, and the shear layer stiffness G, thereby updating the model stiffness matrix. .

[0126] The finite difference method is used to solve for the lateral displacement of the pile. The pile is discretized into n segments from top to bottom using n+1 nodes (the nodes are numbered sequentially from top to bottom, i.e., the node at the top of the pile is numbered 0 and the node at the bottom of the pile is numbered n). A virtual node is introduced on each side. We solve for the first layer of soil spring deformation of each node and connect them to form a curve, which is the first layer of soil spring deformation curve of the pile.

[0127] The deformation w1 of the first layer of soil spring is expressed in a difference form using a matrix. express, Calculated using the following formula:

[0128]

[0129] in, (w1) n The first-layer soil spring deformation is represented by node n, and the additional stress matrix consists of the additional stresses of the n+1 nodes. p n The magnitude of the additional stress at node n;

[0130] Single pile displacement Using matrices It means that among them Calculated using the following formula:

[0131]

[0132] in, Let be the lateral displacement of node i, where i = 0, 1, ..., n; and l be the discretized node spacing, l = L / n. When calculating... and When, the formula appears , The first-layer soil spring deformation of the two virtual nodes is calculated using the following formula:

[0133]

[0134] .

[0135] Step S6: Considering the shielding effect of pile groups, calculate the shielding displacement of the front row of piles on the rear row of piles. Shielding matrix of front row piles to rear row piles Then, the lateral displacement w of the rear pile body is calculated. 22 .

[0136] Specifically, the shielding displacement of point j in the front row of piles (on the side closest to the foundation pit) relative to point i in the rear row of piles. This can be expressed by the following formula:

[0137]

[0138] in, Let be the lateral displacement of point j in the front row of piles; The lateral displacement of the soil at point j caused by the excavation of the foundation pit; The lateral displacement influence factor of the front row of piles on the rear row of piles is expressed by the following formula:

[0139]

[0140] In the formula, k zj Let L1 be the spring stiffness of the first layer of soil at point j in the front row of piles; L1 be the pile length of the front row of piles; and R3 be the actual distance between point j and point i. R4 is the equivalent distance between point j and point i. L0 represents the pile spacing; x1 represents the x-coordinate of the front row of piles; z i and z j These are the ordinates of points i and j, respectively.

[0141] Under the shielding effect of the front row of piles, the lateral displacement w of the rear row of piles 22 Using matrices Representation, matrix Including the shielding effect of the front row of piles, the lateral displacement of n+1 nodes in the rear row of piles:

[0142]

[0143] Where {K2} is the model stiffness matrix of the rear piles, based on the above model stiffness matrix. The calculation method is used for calculation; This is the additional stress matrix for the rear piles; This represents the additional stress matrix exerted by the front row of piles on the rear row of piles. ,in for The second derivative of .

[0144] Step S7: Considering the shielding effect of pile groups, calculate the shielding displacement of the rear piles on the front piles. The shielding matrix of the rear piles to the front piles Then, the lateral displacement w of the front row of piles is calculated. 11 .

[0145] Specifically, the shielding displacement of point i in the rear row of piles (on the side furthest from the foundation pit) relative to point j in the front row of piles. This can be expressed by the following formula:

[0146]

[0147] in, Let i be the lateral displacement of a point i in the rear row of piles; The lateral displacement of the soil at point i caused by the excavation of the foundation pit; The lateral displacement influence factor of the rear piles on the front piles is expressed by the following formula:

[0148]

[0149] In the formula, k ziL1 represents the spring stiffness of the first layer of soil at point i in the rear row of piles; L2 represents the pile length of the rear row of piles; and x2 represents the abscissa of the rear row of piles.

[0150] Under the shielding effect of the rear piles, the lateral displacement w of the front pile body 11 Using matrices Representation, matrix Including the shielding effect of the rear piles, the lateral displacement of n+1 nodes in the front piles:

[0151]

[0152] Where {K1} is the model stiffness matrix of the front row of piles, based on the above model stiffness matrix. The calculation method is used for calculation; This is the additional stress matrix for the front row of piles; This represents the additional stress matrix exerted by the rear row of piles on the front row of piles. ,in for The second derivative of .

[0153] Step S8: Determine the lateral displacement error Δw of the front row of piles between two consecutive calculations during the iterative calculation process. 11 Lateral displacement error Δw of the pile body of the rear row of piles 22 If the accuracy requirement is met, output the lateral displacement w of the front row of piles. 11 and the lateral displacement w of the rear pile body 22 Otherwise, return to step S6 to continue iterative calculation until the required accuracy is achieved.

[0154] When the shielding effect is considered, compared to the case where the shielding effect is not considered, changes in pile displacement will lead to changes in shielding displacement, which in turn will lead to changes in additional stress. Changes in additional stress will in turn lead to changes in pile displacement, thus forming an iterative mechanism.

[0155] Specifically, the accuracy requirement for the lateral displacement error of the pile between the two calculations is as follows:

[0156]

[0157] in, The error in the lateral displacement of the front row of piles is the difference between the (k-1)th and kth iterations. and These represent the lateral displacements of the front row of piles in the (k-1)th and kth iterations, respectively. The error in the lateral displacement of the rear pile body between the (k-1)th and kth iterations; and These are the lateral displacements of the rear piles in the (k-1)th and kth iterations, respectively. The preset accuracy threshold can be 0.1mm.

[0158] The implementation process of this method is further illustrated below with a specific embodiment.

[0159] Taking an existing pile group project adjacent to a confined space foundation pit as the research object, such as Figure 2 As shown. A Kerr foundation beam model is established for the pile body under the combined action of additional load and soil spring, as follows. Figure 3 As shown. Considering the nonlinear decay characteristic of soil shear stiffness with shear strain, such as... Figure 4 As shown. Further consideration should be given to the shielding effect of pile groups, such as... Figure 5 As shown. The lateral deformation of the pile is monitored in real time, and the calculation results of the proposed prediction method are compared with the monitored values, as shown. Figure 6 As shown. The specific implementation steps are as follows:

[0160] Step 1: Before the foundation pit is excavated, based on the SDMT in-situ test and the above calculation formula, the soil parameters and the design parameters of the adjacent pile group are obtained, as shown in Table 1.

[0161] Step 2: During the excavation of the foundation pit, monitor the deformation of the retaining structure and the lateral displacement of the adjacent pile groups in real time.

[0162] Step 3: After the foundation pit is excavated, the monitoring values ​​of the foundation pit retaining structure are substituted into the proposed prediction method as input. Considering the small strain characteristics of the soil and the shielding effect of the pile group, the lateral displacement of the piles is calculated iteratively, and the prediction results are compared with the monitoring data of the lateral displacement of the adjacent pile group. The comparison results are as follows: Figure 6 As shown, the prediction results and monitoring data are in good agreement, indicating that the present invention couples the small strain characteristics of the soil and the shielding effect of the pile group, and can accurately predict the mechanical response of the confined space foundation pit coupled with the retaining wall-foundation soil-pile group.

[0163] Table 1 Soil parameters and design parameters of adjacent pile groups

[0164]

[0165] This embodiment also provides a confined space foundation pit mechanical response prediction system coupled with retaining wall, foundation and pile group, including a memory, a processor and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, it can implement the above-mentioned method.

[0166] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0167] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0168] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0169] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0170] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation, and pile groups, characterized in that, Includes the following steps: Step S1: Input the displacement of the retaining structure of the confined space foundation pit, the design parameters of the adjacent pile group, and the soil parameters determined by the in-situ test of the SDMT lateral dilatation based on the seismic wave flat shovel. Step S2: Based on the nonlinear elastic Kerr foundation model, establish the stress and deformation control equations of adjacent single piles, consider the stiffness hardening characteristics of soil, determine the Kerr foundation model parameters, and generate the model stiffness matrix; Step S3: Calculate the additional soil displacement caused by the displacement of the retaining structure, and determine the additional stress acting on the single pile based on the additional soil displacement; Step S4: Calculate the shear stress of the soil spring at different burial depths, then calculate the shear strain, determine the strain stage of the soil spring at different burial depths, and then determine the soil stiffness. Step S5: Update the model stiffness matrix and calculate the spring deformation of the first layer of soil to obtain the displacement of each pile. Step S6: Considering the shading effect of pile groups, calculate the shading displacement of the front piles to the rear piles, the shading matrix of the front piles to the rear piles, and then calculate the lateral displacement of the rear piles. Step S7: Considering the shading effect of pile groups, calculate the shading displacement of the rear piles on the front piles and the shading matrix of the rear piles on the front piles, and then calculate the lateral displacement of the front piles. Step S8: Determine whether the lateral displacement error of the front row piles and the lateral displacement error of the rear row piles between two consecutive calculations during the iterative calculation process meet the accuracy requirements. If yes, output the lateral displacement of the front row piles and the lateral displacement of the rear row piles. Otherwise, return to step S6 to continue the iterative calculation until the accuracy requirements are met.

2. The method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation, and pile groups as described in claim 1, is characterized in that... In step S1, the displacement u of the retaining structure is obtained through on-site monitoring data; the design parameters of the adjacent pile group include pile diameter D, pile length L, pile spacing L0, and Young's modulus E of the pile body; the soil parameters determined based on SDMT in-situ testing include: in, This represents the effective cohesion of the soil. This represents the effective overburden stress of the soil. K is the effective internal friction angle of the soil. D K0 is the horizontal stress index; K0 is the lateral earth pressure coefficient. To be with K D Correlation coefficient; For soil reference unloading-reloading Young's modulus; E D This refers to the modulus of soil pressure. For soil with small strain stiffness; This refers to the soil density. The shear wave velocity of the soil; is the soil shear strain level; c is the soil cohesion. This represents the effective principal stress of the soil.

3. The method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation, and pile groups as described in claim 1, is characterized in that... In step S2, the force-deformation control equation of the adjacent single pile is: Where EI is the bending stiffness of the pile; D is the pile diameter; p is the additional stress on the pile due to the excavation of the foundation pit; w1 is the deformation of the first layer of soil springs; z is the ordinate of any point in the soil when a coordinate system is established with the horizontal direction of the ground as the X-axis and the direction of the retaining structure as the Z-axis; k, f, and G are the stiffness of the first layer of soil springs on the side away from the pile, the stiffness of the second layer of soil springs on the side closer to the pile, and the stiffness of the shear layer between the first and second layers of soil springs, respectively, which are determined by the following formula: Among them, E t t is the Young's modulus of the soil; v is the thickness of the shear layer; t a1 and a2 are Poisson's ratios of the soil; a1 and a2 are set coefficients. Young's modulus of soil E t The following formula is used to determine the soil stiffness hardening: in, For reference confining pressure; denoted as the effective minor principal stress of the soil; m is a parameter characterizing the dependence of stiffness on stress level. For soil unloading and reloading, Young's modulus is applied. For soil reference unloading-reloading, Young's modulus is used. Model stiffness matrix for: in, , L is the pile length.

4. The method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation, and pile groups as described in claim 1, is characterized in that... In step S3, the additional displacement S of the soil x (z) Calculated using the following formula: in, ; x and z are the x and y coordinates of any point in the soil when a coordinate system is established with the horizontal direction of the ground as the X-axis and the direction of the retaining structure as the Z-axis; x0 and z0 are the x and y coordinates of any point on the retaining structure based on the aforementioned coordinate system; u is the lateral displacement of point (x0, z0); H is the vertical length of the retaining structure. The additional stress p(z) acting on the pile is calculated by the following formula: in, for The second derivative of .

5. The method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation, and pile groups as described in claim 1, is characterized in that... In step S4, the soil spring shear stress τ at different burial depths of the pile is calculated using the following formula: Where P is the equivalent concentrated force of the additional stress p(z) acting on the pile; Soil spring shear strain at different burial depths of piles Calculated using the following formula: Cutoff strain Size: Among them, G ur For soil unloading-reloading stiffness, ;v ur For soil unloading and reloading, Poisson's ratio is applied. when At that time, the soil is considered to be in a small strain stage, and the soil stiffness G is calculated using the following formula. t : when At this point, the soil is considered to have exceeded the small strain stage, and the soil stiffness G is taken as... t = G ur .

6. The method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation, and pile groups according to claim 1, characterized in that, In step S5, the Young's modulus of the soil is updated using the following formula: This leads to the updating of the first-layer soil spring stiffness k, the second-layer soil spring stiffness f, and the shear layer stiffness G, thereby updating the model stiffness matrix. ; The finite difference method is used to solve for the lateral displacement of the pile. The pile is discretized into n segments from top to bottom using n+1 nodes, and a virtual node is introduced on each side. The spring deformation w1 of the first layer of soil is calculated using a matrix in a difference form. express, Calculated using the following formula: in, (w1) n The first-layer soil spring deformation is represented by node n, and the additional stress matrix consists of the additional stresses of the n+1 nodes. p n The magnitude of the additional stress at node n; Single pile displacement Using matrices It means that among them Calculated using the following formula: in, Let represent the lateral displacement of node i, where i = 0, 1, ..., n; and l represent the discrete node spacing, where l = L / n.

7. The method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation, and pile groups as described in claim 6, is characterized in that... In step S6, the shielding displacement of point j in the front row of piles near the foundation pit relative to point i in the rear row of piles. This can be expressed by the following formula: in, Let be the lateral displacement of point j in the front row of piles; The lateral displacement of the soil at point j caused by the excavation of the foundation pit; The lateral displacement influence factor of the front row of piles on the rear row of piles is expressed by the following formula: In the formula, k zj Let L1 be the spring stiffness of the first layer of soil at point j in the front row of piles; L1 be the pile length of the front row of piles; and R3 be the actual distance between point j and point i. R4 is the equivalent distance between point j and point i. L0 represents the pile spacing; x1 represents the x-coordinate of the front row of piles; z i and z j These are the ordinates of points i and j, respectively; Under the shielding effect of the front row of piles, the lateral displacement w of the rear row of piles 22 Using matrices Representation, matrix Including the shielding effect of the front row of piles, the lateral displacement of n+1 nodes in the rear row of piles: Where {K2} is the model stiffness matrix of the rear piles; This is the additional stress matrix for the rear piles; This represents the additional stress matrix exerted by the front row of piles on the rear row of piles. ,in for The second derivative of .

8. The method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation, and pile groups as described in claim 6, is characterized in that... In step S7, the shielding displacement of point i in the rear row of piles on the side away from the foundation pit relative to point j in the front row of piles. This can be expressed by the following formula: in, Let i be the lateral displacement of a point i in the rear row of piles; The lateral displacement of the soil at point i caused by the excavation of the foundation pit; The lateral displacement influence factor of the rear piles on the front piles is expressed by the following formula: In the formula, k zi Let L1 be the spring stiffness of the first layer of soil at point i in the rear row of piles; L2 be the pile length of the rear row of piles; and x2 be the abscissa of the rear row of piles. Under the shielding effect of the rear piles, the lateral displacement w of the front pile body 11 Using matrices Representation, matrix Including the shielding effect of the rear piles, the lateral displacement of n+1 nodes in the front piles: Where {K1} is the model stiffness matrix of the front piles; This is the additional stress matrix for the front row of piles; This represents the additional stress matrix exerted by the rear row of piles on the front row of piles. ,in for The second derivative of .

9. The method for predicting the mechanical response of a confined space foundation pit coupled with retaining wall, foundation, and pile groups according to claim 1, characterized in that, In step S8, the accuracy requirement for the lateral displacement error of the pile between the two calculations is as follows: in, The error in the lateral displacement of the front row of piles is the difference between the (k-1)th and kth iterations. and These represent the lateral displacements of the front row of piles in the (k-1)th and kth iterations, respectively. The error in the lateral displacement of the rear pile body between the (k-1)th and kth iterations; and These are the lateral displacements of the rear piles in the (k-1)th and kth iterations, respectively. This is the preset accuracy threshold.

10. A confined space foundation pit mechanical response prediction system coupled with retaining wall, foundation, and pile group, characterized in that, It includes a memory, a processor, and computer program instructions stored in the memory and executable by the processor, wherein when the processor executes the computer program instructions, it can implement the method as described in any one of claims 1-9.

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