Foundation deformation calculation method based on numerical model stress extraction

Abstract

Disclosed in the present invention is a foundation deformation calculation method based on numerical model stress extraction. First, a numerical model is established to calculate the vertical additional stress distribution and horizontal additional stress distribution of foundation soil, wherein the elastic modulus of the foundation soil is selected within a range of two to five times the compression modulus on the basis of engineering experience; a layer-wise summation method is used, in which layered settlement is directly calculated for a natural foundation, settlement in a reinforced zone and settlement in an underlying layer are both calculated for a composite foundation, and layered settlement amounts are superimposed and multiplied by a settlement empirical correction coefficient to obtain a final settlement amount; the projection of a horizontal displacement calculation point on the ground and a vertical soil column below the horizontal displacement calculation point are taken as a vertically placed finite elastic long beam, the cross section of the soil column is square, the side length of the soil column is preferably 0.1 m or below, the modulus of the beam is the same as that of the soil, one end is located in a ground surface plane, and the other end is located in a plane where a calculation depth is located; and a distributed load is dispersed into several concentrated loads, a foundation bed coefficient is determined on the basis of a specification, and the horizontal displacement of the calculation point is obtained by means of a beam-on-elastic-foundation method.

Description

Calculation method of foundation deformation based on stress extraction of numerical model Technical Field

[0001] The present invention relates to the field of foundation deformation monitoring, and in particular to a foundation deformation calculation method based on numerical model stress extraction. Background Art

[0002] Foundation design is an important part of civil engineering, and the calculation of foundation vertical settlement and horizontal displacement is an important part of foundation design.

[0003] The most widely accepted method for calculating vertical settlement is the layered summation method, which can be used to calculate natural or composite foundations with layered strata. The key lies in the rational selection of soil parameters and the accuracy of the calculation of additional stresses.

[0004] The soil parameter most closely related to settlement is soil modulus. The modulus most commonly provided in geological survey reports is the compression modulus at different pressure ranges. It is also the easiest modulus to obtain from field or laboratory tests. Both the replacement ratio composite modulus method and the bearing ratio composite modulus method estimate the composite foundation modulus based on the compression modulus, and the layered summation method also uses the compression modulus. Therefore, in actual engineering, deformation calculations often require more than just the compression modulus.

[0005] The main methods for calculating additional stresses recommended in building and roadbed design codes include the Boussinesq method, the Mindlin method, the equivalent solid method, the L / 3 method, and the stress diffusion method. While the first two methods have a relatively sound theoretical foundation, the Boussinesq method is primarily applicable to homogeneous foundations. While the Mindlin method can account for the effects of piles, its calculations are complex and often require programming. While the latter three methods are computationally simple, their empirical nature significantly impacts the designer's choice of parameters, simplification of working conditions, and choice of calculation method. The technical approaches recommended by current codes provide widely accepted theoretical frameworks for settlement calculation and the selection of soil parameters. However, for structurally complex structures or composite foundations using piles, the calculation of additional stresses is more complex, and the applicable formulas cannot be applied under many conditions. Therefore, it is necessary to find a method for calculating additional stresses under complex conditions that is compatible with the layered summation method and the compression modulus. Together, these three methods would form a comprehensive set of settlement calculation methods.

[0006] In addition to the calculation methods recommended by the specifications, in engineering practice, deformation calculations for specific work points often utilize numerical simulation software such as finite element or finite difference methods. These software, with their comprehensive theoretical framework and powerful computing capabilities, have been widely used and recognized. Numerical modeling often utilizes the elastic modulus of soil. In scientific research, various physical and mechanical parameters of soil can be obtained through complex indoor tests. However, the elastic modulus is not directly reflected in geological survey reports. It is generally calculated by multiplying the compression modulus by a coefficient of 2 to 5. The coefficient has a wide range of values, lacks a unified implementation standard, and is significantly influenced by experience. Exponential changes in the elastic modulus can cause significant changes in the deformation obtained from numerical simulations. Therefore, many designers tend to only refer to the stress distribution and deformation trends obtained from numerical simulations, and are skeptical of the specific deformation values. This also limits the promotion and application of numerical simulation software in the design process.

[0007] In terms of vertical settlement calculation, the specification provides several options, but the specification does not provide a clear method for calculating horizontal displacement. In actual engineering, calculations are generally performed through numerical simulation, but this still cannot avoid calculation differences caused by different designers' different values ​​of elastic modulus and Poisson's ratio.

[0008] Summary of the Invention

[0009] In order to solve the technical problems existing in the above-mentioned prior art, the present invention provides a method for calculating vertical settlement and horizontal displacement applicable to natural foundations or composite foundations. The method has high accuracy, low calculation difficulty, and is suitable for various working conditions.

[0010] To this end, the present invention adopts the following technical solutions:

[0011] A method for calculating foundation deformation based on stress extraction of a numerical model comprises the following steps:

[0012] S1, establish a numerical simulation model based on the on-site work points:

[0013] A numerical simulation model is established using soil parameters directly obtained from a geological survey report; after material properties, loads, contacts, and boundaries are set in the model, units other than the foundation soil are shielded using a birth-and-death unit method to obtain a foundation model;

[0014] S2, extract the horizontal and vertical additional stress distribution of the foundation:

[0015] Calculate the ground stress distribution under the deadweight load through the static general analysis step, and then import the calculated ground stress distribution into the foundation model obtained in S1 by importing the ODB file to perform ground stress balance;

[0016] When the foundation of the work site is a natural foundation, activating the embankment and the external load on the embankment in the model after the ground stress is balanced;

[0017] When the foundation of the work site is a composite foundation, first activate the piles, cushion layer or concrete slab structure in the model after the ground stress is balanced, then re-balance the ground stress, and finally activate the embankment and the external load on the embankment;

[0018] Using the model after activating the external load, the uniformly distributed load curve q(x) of the horizontal additional stress varying with depth and the vertical additional stress varying with depth were extracted;

[0019] S3, calculate the vertical settlement of the foundation:

[0020] The vertical settlement of the foundation s is calculated according to the following formula:

[0021] s=ψ s s′,

[0022] Where:

[0023] s′ is the total settlement of the foundation; ψ s Calculate empirical coefficients for settlement;

[0024] S4, calculate the horizontal displacement of the foundation:

[0025] The vertical soil column at the projection point of the test point on the ground surface and below is regarded as a finite length elastic foundation beam. The cross section of the soil column is square with a side length less than or equal to 0.1m. The deflection differential equation calculated by Winkel elastic foundation beam theory is the basis.

[0026] For the uniformly distributed load at any position u on the elastic foundation beam, the uniformly distributed load is discretized into several concentrated loads P(u) using the differential principle, and the horizontal displacement y caused by each concentrated load is calculated by the following formula: u (x):

[0027] Where λ is the flexibility coefficient of the elastic foundation beam, λ = (kb / 4EI) 0.25; E is the modulus of the elastic foundation beam; I is the section moment of inertia; b is the section width; k is the base coefficient; F1, F2, F3, F4 are Krylov functions; F1(λx)=ch(λx)cos(λx); F2(λx)=[ch(λx)sin(λx)+sh(λx)cos(λx)] / 2; F3(λx)=sh(λx)sin(λx) / 2; F4(λx=[c h(λx)sin(λx)-sh(λx)cos(λx)] / 4; y0 is the horizontal deformation of the measured point at the surface projection point; θ0 is the rotation angle of the measured point at the surface projection point; M0 is the bending moment of the measured point at the surface projection point; Q0 is the concentrated force of the measured point at the surface projection point; x and y are the coordinate values ​​of the point on the elastic foundation beam, the X-axis is the depth, and the Y-axis is the horizontal deformation of the elastic foundation beam.

[0028] The elastic foundation beam is divided into a micro-segment every α0.1m along the length direction of the beam, and the following formula is obtained:

[0029] P(u)=α·q(u),

[0030] Where q(u) is the value of the uniformly distributed load curve q(x) obtained by S2 at point u.

[0031] The displacement of the beam caused by each concentrated load varies as a function of depth y u (x) and the horizontal displacement y(x) at any position x on the beam under the uniformly distributed load can be calculated using the following formula:

[0032] y(x)=∑y u (x).

[0033] When the foundation described in S3 is a natural foundation, the total foundation settlement s′ is calculated by the following formula:

[0034] Where n is the number of soil layers divided within the depth range of foundation settlement calculation; E si is the average compression modulus of the i-th layer of soil; Δh i is the thickness of the i-th soil layer; p i is the average vertical additional stress of the i-th layer of soil in the natural foundation.

[0035] When the foundation described in S3 is a composite foundation, the total foundation settlement s′ is calculated by the following formula:

[0036] s′=s1+s2,

[0037] Where, s1 is the soil settlement in the reinforcement area; s2 is the soil settlement in the underlying layer;

[0038] Let n1 be the number of soil layers divided within the reinforcement area, n2 be the number of soil layers divided within the underlying layer, n = n1 + n2, and s2 is obtained by the following formula:

[0039] Where:

[0040] E si is the average compression modulus of the i-th soil layer;

[0041] Δh i is the thickness of the i-th soil layer;

[0042] p i ′ is the average vertical additional stress of the i-th layer of soil in the composite foundation.

[0043] When the composite foundation is a flexible pile composite foundation, the following formula is obtained:

[0044] Where, E csi is the average compression modulus of the i-th layer of composite soil in the reinforcement area.

[0045] The E csi It can be calculated by the substitution rate complex modulus method:

[0046] E csi =mE p +(1-m)E si ,

[0047] m=A p / A 总 ,

[0048] Where m is the replacement rate of composite foundation area; A p is the area of ​​a single pile; A 总 is the unit area of ​​composite soil around the pile; E p is the compression modulus of the pile.

[0049] The E csi The E can also be calculated by the load-bearing capacity ratio composite modulus method. csi , we have the following formula:

[0050] E csi =ξE si ,

[0051] ξ=σ sp / σ0,

[0052] Where, σ0 is the basic bearing capacity of natural foundation; σ sp is the allowable bearing capacity of the composite foundation; ξ is the coefficient of increase in bearing capacity relative to the compression modulus.

[0053] When the composite foundation is a rigid pile composite foundation and the differential settlement of the pile and soil on the foundation surface cannot be ignored, the soil settlement s1 in the reinforcement area is calculated by the pile compression method, and the following formula is obtained:

[0054] s1=s p +Δ,

[0055] Where: Δ is the penetration amount of the pile; s p is the compression of the pile body, which can be obtained by the following formula:

[0056] Where, L is the pile length; E p is the pile modulus obtained in S1; p p (z) is the variation curve of pile stress along the depth, which is calculated by S2; the z is the depth of the pile.

[0057] When the composite foundation is a rigid pile composite foundation and the differential settlement of the pile and soil on the foundation surface can be ignored, the vertical settlement s of the foundation is calculated using the Mindlin method.

[0058] Preferably, the cross section of the soil column in S4 is a square, the side length of the square is ≤0.1m, and α is ≤0.1m; the undetermined parameters y0, θ0, M0, and Q0 are determined by known load conditions and boundary conditions.

[0059] Preferably, the boundary described in S1 is set to limit the horizontal displacement of the four peripheral interfaces of the model to zero, and limit the vertical displacement of the bottom boundary surface to zero; the load described in S1 is set to the downward gravitational acceleration and other additional loads (such as tracks, vehicles, awning columns and adjacent structure loads, etc.); the soil parameters include density, elastic modulus, cohesion and internal friction angle, and the elastic modulus value is taken in the range of 2 to 5 times the compression modulus based on engineering experience.

[0060] Research has shown that in finite element or finite difference calculations of foundation settlement, variations in the elastic modulus within a reasonable range can affect the settlement calculation results, but have little effect on the additional stress results. In other words, whether the elastic modulus of the soil is 2 or 5 times the compression modulus, the additional stress calculation results are reliable. Similar to vertical settlement, the values ​​of the elastic modulus and Poisson's ratio have a greater impact on horizontal displacement and a smaller impact on horizontal additional stress. This is based on the present invention.

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] 1. This method uses compression modulus and numerical models to calculate vertical additional stress, combined with standard algorithms to calculate vertical settlement. The soil column at the horizontal displacement calculation point is treated as a vertically placed finite-length beam. The horizontal additional stress distribution on the side of the soil column is extracted through numerical simulation, and the horizontal displacement is calculated using the elastic foundation beam method. This method can calculate complex working conditions and has a relatively common implementation standard and high recognition.

[0063] 2. This method avoids the disadvantage of large differences in deformation calculation results caused by different elastic modulus values ​​in numerical simulation;

[0064] 3. All calculation parameters required by this method can be obtained from geological survey reports or standard tables;

[0065] 4. This method reduces the computational difficulty and does not require programming. The additional stress can be obtained through numerical simulation using commercial software.

[0066] 5. This method has a wide range of applications. It is not only applicable to natural foundations, but also to composite foundations such as pile nets, pile rafts, and pile boards; it is not only applicable to building foundations, but also to highway and railway subgrades; it is also applicable to working conditions with adjacent structures and ancillary structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] FIG1 is a schematic flow chart of the calculation method of the present invention;

[0068] FIG2 is a schematic diagram of a finite element model of a double-track railway subgrade established in Example 1 of the present invention;

[0069] FIG3 is a schematic diagram of a finite element model of a pile-plate structure;

[0070] FIG4 is a schematic diagram of the calculation point positions of the implementation case 1;

[0071] FIG5 is a vertical additional stress distribution curve in Example 1;

[0072] FIG6 is a horizontal additional stress distribution curve in Example 1;

[0073] Figure 7 is a schematic diagram of the Winkel elastic foundation beam calculation. DETAILED DESCRIPTION

[0074] The calculation method of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0075] Example 1

[0076] The composite foundation model of a double-track railway subgrade is taken as an example to illustrate the composite foundation in the foundation deformation calculation method based on numerical model stress extraction of the present invention.

[0077] Referring to FIG1 , the method includes the following steps:

[0078] S1, establish a numerical simulation model based on the on-site work points:

[0079] Taking the ABAQUS commercial finite element software as an example, a railway double-line subgrade composite foundation model was established based on reasonable simplification according to a certain on-site work site and engineering experience, as shown in Figures 2 and 3.

[0080] The embankment has a top width of 13.6m and a bottom width of 28.6m, a height of 5m, a foundation width of 88.6m and a depth of 50m, and a model length of 10m along the route. The foundation soil, from top to bottom, consists of 3m thick clay (soft plastic), 9m thick silty soil, 6m thick silty clay (soft plastic), 2m thick silt (dense), and below that, silty clay (hard plastic). The properties of the foundation soil and other materials are shown in Tables 1 and 2, respectively. The elastic modulus of the foundation soil can be 2-5 times the compression modulus, but in this example, 2 times is used.

[0081] Table 1

[0082] Table 2

[0083] The groundwater level is at the surface, and the weight of the soil is the floating weight. The foundation is reinforced with a pile-slab structure. The length of the pipe pile is 20m, the pile diameter is 0.5m, the pile spacing is 2.5m, the concrete slab thickness is 0.5m, the pile top is bound to the concrete slab, and the other components are in friction contact with a friction coefficient of 0.3. The base bed coefficient is determined according to the specification. In the boundary setting, the horizontal displacement of the four peripheral interfaces of the model is limited to zero, and the vertical displacement of the bottom boundary surface is limited to zero. In the load setting, a downward gravity acceleration is applied to the model, and two tracks with a width of 3.1m and a size of 54.1kN / m are applied to the top surface of the roadbed, and train loads. The elements other than the foundation soil are shielded by the method of life and death elements (that is, the method of temporarily shielding elements that are not related to a certain analysis step in ABAQUS and activating them when needed).

[0084] S2, extract the horizontal and vertical additional stress distribution of the foundation:

[0085] Based on the composite foundation model established in S1, the ground stress distribution under the self-weight load is calculated through the static general analysis step, and then the ground stress equilibrium is performed by importing the ODB file (the ground stress result of the last incremental step under the self-weight load is set as the initial ground stress, and the static calculation is repeated to extract the maximum displacement or maximum strain. If the magnitude of the displacement or strain meets the calculation accuracy, the ground stress equilibrium is considered to be completed, otherwise repeat the above steps).

[0086] Next, the pile-slab structure (i.e., the pipe piles and concrete slab) is activated using the birth-and-death element method, and the in-situ stress balance is performed again. Finally, the embankment and the external loads on it are activated. If there are many components or ancillary structures, multiple in-situ stress balance and element activation cycles may be performed as needed.

[0087] The method described in the present invention can solve the vertical settlement and horizontal displacement at any position in the foundation. This example takes the calculation of the vertical settlement of the foundation surface below the center of the embankment and the horizontal displacement of the surface 5m outside the slope foot as an example. Set the data extraction path in the ODB file. As shown in Figure 5, the vertical additional stress variation curve caused by the embankment load in the foundation soil at the center point below the embankment (point D in Figure 4) and below is extracted. The additional stress can be obtained by subtracting the stress result before the embankment load is applied from the stress result after the embankment load is applied. If the pile body compression method is required to calculate the settlement of the reinforced area, the curve of the variation of the pile body additional stress along the depth of the pile closest to the calculation point is extracted. According to the principle that the vertical additional stress is equal to 10% of the effective deadweight stress, the calculation depth is determined to be 35m. As shown in Figure 6, the curve of the variation of the horizontal additional stress along the depth at 5m outside the slope foot (point A in Figure 4) and below is extracted, as shown in Figure 6.

[0088] S3, calculate the vertical settlement of the foundation surface:

[0089] According to the building foundation design specifications, the natural foundation settlement can be calculated as follows:

[0090] Where:

[0091] s is the vertical settlement of the foundation;

[0092] s′ is the total settlement of the foundation;

[0093] ψ s Calculate empirical coefficients for settlement;

[0094] n is the number of soil layers divided within the depth range of foundation settlement calculation;

[0095] E si is the average compression modulus of the i-th soil layer;

[0096] Δh i is the thickness of the i-th soil layer;

[0097] p i is the average vertical additional stress of the i-th layer of soil in the natural foundation calculated by S2.

[0098] For composite foundations, there are:

[0099] s′=s1+s2 (2)

[0100] Among them, s1 is the soil settlement in the reinforcement area; s2 is the settlement of the underlying soil.

[0101] Let n1 be the number of soil layers divided within the reinforcement area, and n2 be the number of soil layers divided within the underlying layer, then n = n1 + n2. The underlying layer settlement can be calculated using the following formula:

[0102] Where, E si is the average compression modulus of the i-th layer of soil; Δh i is the thickness of the i-th soil layer; p i ′ is the average vertical additional stress in the i-th layer of soil in the composite foundation. Composite foundations are categorized as flexible pile composite foundations and rigid pile composite foundations. Rigid pile composite foundations can be further categorized based on engineering experience to determine whether the differential settlement of the piles and soil at the foundation surface can be ignored.

[0103] For flexible pile composite foundations, the settlement of the reinforced area can be calculated using the replacement ratio composite modulus method or the bearing ratio composite modulus method. The underlying layer settlement can then be calculated using Equation (3). The total settlement is obtained by summing the settlement of the reinforced area and the underlying layer. The replacement ratio composite modulus method is a common method for calculating the settlement of flexible pile composite foundations. If on-site bearing capacity data for natural and composite foundations are available, the bearing capacity ratio composite modulus method can be used. The calculation formulas for both methods are as follows.

[0104] 1) Substitution rate composite modulus method:

[0105] Assume that the average modulus of the composite soil in each reinforced area is E csi , then the soil settlement s1 in the reinforcement area is:

[0106] Where, E csi is the average compression modulus of the i-th layer of composite soil in the reinforcement area, and its value can be obtained by the area-weighted average method:

[0107] E csi =mE p +(1-m)E si (5)

[0108] m=A p / A 总 (6)

[0109] Where m is the composite foundation area replacement rate;

[0110] A p is the area of ​​a single pile;

[0111] A 总 is the unit area of ​​composite soil around the pile;

[0112] E p is the compression modulus of the pile.

[0113] 2) Bearing capacity ratio composite modulus method:

[0114] The bearing capacity ratio method is to determine the E of each layer of soil in the reinforced area by the modulus improvement coefficient ξ of the soil in the reinforced area. csi :

[0115] E csi =ξE si (7)

[0116] ξ=σ sp / σ0 (8)

[0117] Where, σ0 is the basic bearing capacity of natural foundation;

[0118] σ sp is the allowable bearing capacity of the composite foundation;

[0119] ξ is the coefficient of increase in bearing capacity relative to compression modulus.

[0120] For the above two situations of rigid pile composite foundation, the following two methods can be adopted respectively:

[0121] 1) Pile compression method:

[0122] For situations where the differential settlement of piles and soil on the foundation surface cannot be ignored (such as pile-net structures), the pile body compression method can be used to calculate the settlement of the reinforced area. This method calculates the compression of the reinforced area by calculating the compression of the pile body. Let the pile penetration be Δ and the pile body compression be s p , then the settlement of the soil in the reinforced area of ​​the composite foundation s1 can be calculated by the following formula:

[0123] s1=s p +Δ (9)

[0124] The compression of the pile body can be obtained from the pile body stress and pile body modulus:

[0125] Where, L is the pile length; E p is the pile modulus; p p (z) is the expression of the variation of pile stress along the depth. Among them, the pile penetration Δ is taken according to the standard, and the pile modulus E p See S1, pile stress distribution p p (z) is calculated by S2, where z is the depth.

[0126] 2) Mindlin method:

[0127] For situations where differential settlement between the pile and soil on the foundation surface can be ignored (such as in the pile-slab structure in this example), the Mindlin method, as specified in the code, can be used to calculate vertical settlement. The Mindlin method uses a table to calculate the additional stress in the foundation soil caused by the superposition of the pile side and pile end loads, and then applies the layer-wise summation method to the calculation.

[0128] The additional stress calculation has been completed in the finite element method, and there is no need to look up the table. Therefore, similar to the natural foundation, there is no need to distinguish between the reinforced area and the underlying layer. The additional stress extracted from S2 is brought into the formula (1) for calculation. Assuming that the number of soil layers n is 70, the thickness of each soil layer Δh i 0.5m, p i Calculated from S2, the additional settlement of the foundation surface at the center below the embankment can be obtained as 8.0 cm using the material parameters in Tables 1 and 2, Figure 5, and Equation (1).

[0129] S4, calculate the horizontal displacement of the foundation:

[0130] The vertical soil column 5 m outside the slope toe (point A) and below it is considered a finite-length beam with a length of 35 m and a square cross-section of 0.1 m. The soil outside the soil column is considered the foundation. The deformation is calculated using the Winkel elastic foundation beam theory, as shown in Figure 7. Based on the basic assumptions of the elastic foundation beam and the deformation coordination conditions of the foundation beam and the soil below the beam, and considering the force equilibrium conditions of the elastic foundation beam micro-segment, the deflection differential equation is obtained:

[0131] Where:

[0132] E is the modulus of the elastic foundation beam;

[0133] I is the moment of inertia of the section;

[0134] b is the cross-section width;

[0135] k is the base bed coefficient;

[0136] x and y are the coordinate values ​​of the point on the elastic foundation beam in Figure 7, the X-axis is the depth, and the Y-axis is the horizontal deformation of the elastic foundation beam; q(x) is the uniformly distributed load curve of the horizontal additional stress varying with depth as described in S2.

[0137] When a uniformly distributed load q is applied to any position u on an elastic foundation beam, the displacement of any section on the beam (the section at a distance x from the origin O) is:

[0138] Where:

[0139] λ is the flexibility coefficient of the elastic foundation beam, λ=(kb / 4EI) 0.25 ;

[0140] F1, F2, F3, and F4 are Krylov functions;

[0141] F1(λx)=ch(λx)cos(λx);

[0142] F2(λx)=[ch(λx)sin(λx)+sh(λx)cos(λx)] / 2;

[0143] F3(λx)=sh(λx)sin(λx) / 2;

[0144] F4(λx)=[ch(λx)sin(λx)-sh(λx)cos(λx)] / 4;

[0145] y0 is the horizontal deformation of point A;

[0146] θ0 is the rotation angle of point A;

[0147] M0 is the bending moment at point A;

[0148] Q0 is the concentrated force at point A;

[0149] u is the position of the load center point;

[0150] c is the position of the end point of the uniformly distributed load close to the origin O;

[0151] B is the end point of the foundation beam (located at the calculation depth plane).

[0152] However, the integral of the uniformly distributed load in formula (12) is difficult to calculate. It is necessary to use the principle of differentiation to discretize the uniformly distributed load into several concentrated loads P(u), and finally superimpose the effects of these loads. The displacement caused by each concentrated load is:

[0153] The beam is divided into micro-segments every 0.1m along its length. Taking every 0.1m as an example, since the beam is 35m long, the horizontal additional stress on the beam can be converted into 350 concentrated loads P(u):

[0154] P(u)=0.1q(u) (14)

[0155] Where:

[0156] q(u) is the value of the uniformly distributed load curve q(x) at point u.

[0157] Assuming the constraints at both ends of the beam are free, the unknown parameters y0, θ0, M0, and Q0 are determined using the known load and boundary conditions. Substituting these four parameters into Equation (13), the displacements caused by each concentrated load can be superimposed using Equation (15) to obtain the displacement y(x) at any position x on the beam under the uniformly distributed load. If x is set to zero, the horizontal displacement y(0) at the ground surface is 6.5 cm.

[0158] y(x)=∑y u (x) (15)

[0159] According to the on-site monitoring results, the vertical settlement of the foundation surface at the center of the roadbed after construction was 8.6 cm, and the horizontal displacement 5 m outside the slope toe was 7.2 cm. The calculation results were consistent with the test results.

[0160] Example 2

[0161] This embodiment takes a natural foundation model of a double-track railway subgrade as an example to illustrate the situation of a natural foundation in the foundation deformation calculation method based on numerical model stress extraction of the present invention.

[0162] The main differences between the natural foundation calculation and the composite foundation calculation in Example 1 are:

[0163] In S1, a natural foundation model is established, and there is no need to construct the pile-slab structure (i.e., pipe piles and concrete slabs) and set related contacts.

[0164] In S2, based on the natural foundation model established in S1, after the first ground stress balance is completed, there is no need to activate the pipe piles and concrete slabs through the birth-death unit method, and the embankment and corresponding loads can be directly activated; the calculation depth determination standard is the same as that of the composite foundation, but due to the lack of the influence of piles, the value of the calculated depth may change.

[0165] In S3, there is no need to distinguish between the reinforced area and the underlying layer, and the vertical settlement of the foundation can be calculated directly using formula (1).

[0166] The calculation method in S4 is the same as that for composite foundation.

Claims

1. A method for calculating foundation deformation based on numerical model stress extraction, characterized in that: The following steps are involved: S1, establish a numerical simulation model based on the on-site work points: A numerical simulation model is established using soil parameters directly obtained from a geological survey report; after material properties, loads, contacts and boundaries are set in the model, units other than the foundation soil are shielded by a birth-and-death unit method to obtain a foundation model; S2, extract the horizontal and vertical additional stress distribution of the foundation: Calculate the ground stress distribution under the deadweight load through the static general analysis step, and then import the calculated ground stress distribution into the foundation model obtained in S1 by importing the ODB file to balance the ground stress; When the foundation of the work site is a natural foundation, activating the embankment and the external load on the embankment in the model after the ground stress is balanced; When the foundation of the work site is a composite foundation, the pile, cushion or concrete slab structure is first activated in the model after the ground stress is balanced, and then the ground stress is balanced again, and finally the embankment and the external load on the embankment are activated; Using the model after activating the external load, the uniformly distributed load curve q(x) of the horizontal additional stress varying with depth and the curve of the vertical additional stress varying with depth are extracted; S3, calculate the vertical settlement of the foundation: The vertical settlement of the foundation s is calculated according to the following formula: s=ψ s s′, Where: s′ is the total settlement of the foundation; ψ s Calculate empirical coefficients for settlement; S4, calculate the horizontal displacement of the foundation: The vertical soil column at the projection point of the test point on the ground surface and below is regarded as a finite length elastic foundation beam, and the deflection differential equation calculated by Winkel elastic foundation beam theory is used as the basis; For the uniformly distributed load at any position u on the elastic foundation beam, the uniformly distributed load is discretized into several concentrated loads P(u) using the differential principle, and the horizontal displacement y caused by each concentrated load is calculated by the following formula: u (x): Where: λ is the flexibility coefficient of the elastic foundation beam, λ=(kb / 4EI) 0.25 ; E is the modulus of the elastic foundation beam; I is Section inertia moment; b is the section width; k is the base coefficient; F1, F2, F3, F4 are Krylov functions; F1(λx)=ch(λx)cos(λx); F2(λx)=[ch(λx)sin(λx)+sh(λx)cos(λx)] / 2; F3(λx)=sh(λx)sin(λx) / 2; F4(λx)=[ch(λx)sin(λx)-sh(λx)cos(λx)] / 4; y0 is the horizontal deformation of the point to be measured at the projection point on the ground surface; θ0 is the rotation angle of the point to be measured at the projection point on the ground surface; M0 is the bending moment of the point to be measured at the projection point on the ground surface; Q0 is the concentrated force of the point to be measured at the projection point on the ground surface; x and y are the coordinate values ​​of the point on the elastic foundation beam, the X axis is the depth, and the Y axis is the horizontal deformation of the elastic foundation beam; Divide the elastic foundation beam into a micro-segment every αm along the length direction of the beam, and then we have the following formula: P(u)=α·q(u), Where q(u) is the value of the uniform load curve q(x) obtained by S2 at position u; The displacement of the beam caused by each concentrated load varies as a function of depth y u (x) and the horizontal displacement y(x) at any position x on the beam under the uniformly distributed load is calculated by the following formula: y(x)=∑y u (x)。 2. The method according to claim 1, characterized in that: When the foundation described in S3 is a natural foundation, the total settlement s′ of the foundation is calculated by the following formula: Where: n is the number of soil layers divided within the depth range of foundation settlement calculation; E si is the average compression modulus of the i-th layer of soil; Δh i is the thickness of the i-th soil layer; p i is the average vertical additional stress of the i-th soil layer in the natural foundation.

3. The method according to claim 1, characterized in that: When the foundation described in S3 is a composite foundation, the total settlement s′ of the foundation is calculated by the following formula: s′=s1+s2, Where, s1 is the soil settlement in the reinforcement area; s2 is the soil settlement in the underlying layer; Let n1 be the number of soil layers divided within the reinforcement area, n2 be the number of soil layers divided within the underlying layer, n = n1 + n2, and s2 is obtained by the following formula: In the formula, E si is the average compression modulus of the i-th layer of soil; Δh i is the thickness of the i-th soil layer; p i ′ is the average vertical additional stress of the i-th soil layer in the composite foundation.

4. The method according to claim 3, characterized in that: When the composite foundation is a flexible pile composite foundation, the following formula is available: In the formula, E csi is the average compression modulus of the i-th layer of composite soil in the reinforcement area.

5. The method according to claim 4, characterized in that: The E was calculated by the substitution ratio complex modulus method. csi , the following formula: E csi =mE p +(1-m)E si , m=A p / A 总 , Where m is the replacement rate of composite foundation area; A p is the area of ​​a single pile; A 总 is the unit area of ​​composite soil around the pile; E p is the compression modulus of the pile.

6. The method according to claim 4, characterized in that: The E is calculated by the load-bearing capacity ratio composite modulus method. csi , the following formula: E csi =ξE si , ξ=σ sp / σ0, Where, σ0 is the basic bearing capacity of natural foundation; σ sp is the allowable bearing capacity of the composite foundation; ξ is the coefficient of increase in bearing capacity compared to the compression modulus.

7. The method according to claim 3, characterized in that: When the composite foundation is a rigid pile composite foundation and the differential settlement of the pile and soil on the foundation surface cannot be ignored, the soil settlement s1 in the reinforcement area is calculated by the pile body compression method, and the following formula is obtained: s1 = s p +Δ, Where Δ is the pile penetration; s p is the compression of the pile body; The compression amount s of the pile body p Obtained by the following formula: Where, L is the pile length; E p is the pile modulus obtained in S1; p p (z) is the variation curve of pile body stress along the depth, which is calculated by S2; and z is the depth of the pile body.

8. The method according to claim 3, characterized in that: When the composite foundation is a rigid pile composite foundation and the differential settlement of the pile and soil on the foundation surface can be ignored, the vertical settlement s of the foundation is calculated by the Mindlin method.

9. The method according to claim 1, characterized in that: The cross section of the soil column in S4 is a square, and the side length of the square is ≤0.1m; the α is ≤0.1m; and the undetermined parameters y0, θ0, M0, Q0 are determined by known load conditions and boundary conditions.

10. The method according to claim 1, characterized in that: The boundary settings described in S1 are to limit the horizontal displacement of the interfaces around the model to zero, and to limit the vertical displacement of the bottom boundary surface to zero; the loads described in S1 are set to downward gravity acceleration and other additional loads; the soil parameters include density, elastic modulus, cohesion and internal friction angle, and the elastic modulus is taken in the range of 2 to 5 times the compression modulus based on engineering experience.

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