Tunnel construction response calculation method for adjacent pile foundation, terminal device and storage medium

Abstract

The application discloses a tunnel construction adjacent pile foundation response calculation method, a terminal device and a storage medium, tunnel construction parameters, pile foundation parameters and stratum physical and mechanical parameters are determined; the free field displacement of the soil at the pile position is calculated; the additional load generated by the lateral deformation of the soil at the pile position is determined; the actual constraint state of the two ends of the pile foundation is determined; the control differential equation of the lateral deformation of the pile foundation is established; the independent equation is supplemented based on the finite difference principle and the internal force boundary condition of the two ends of the pile foundation; and the lateral deformation and internal force of the pile foundation are determined. The Vlasov-Timoshenko elastic foundation beam theory used in the application makes up for the shortcomings of the existing analytical calculation model, considers the actual constraint state of the two ends of the pile foundation, and gives a simplified calculation method for the constraints of the pile top and the pile end, so that the response characteristics of the adjacent existing pile foundation under the influence of the tunnel construction can be more accurately predicted, which has important guiding significance for the field construction.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of underground structure design, and particularly relates to a calculation method for response of adjacent pile foundation to tunnel construction considering actual constraints at both ends. BACKGROUND

[0002] When urban underground tunnels pass through densely built-up areas, they will inevitably affect adjacent existing pile foundations. Tunnel construction disturbs the surrounding soil, which in turn causes additional deformation and internal forces of adjacent pile foundations, and in severe cases, may affect the stability of the superstructure and endanger the safety of the superstructure. Therefore, how to accurately predict the response of pile foundations is of great significance to guide on-site construction, and has become a hot issue in urban underground engineering.

[0003] For the problem of response of adjacent pile foundations to tunnel construction, the existing research methods mainly include physical model test, numerical simulation and theoretical analysis. The physical model test is long in cycle and high in cost, and the numerical simulation is complex in modeling and time-consuming in calculation. Compared with the first two methods, the theoretical analysis has clear physical meaning and is convenient and fast in calculation, and is one of the effective means to solve the problem.

[0004] The two-stage analysis method is mainly used to analyze the problem of response of adjacent pile foundations to tunnel construction by analytical method, that is, first, the free field displacement of soil at the pile position caused by tunnel construction is calculated, then the soil displacement is applied to the pile foundation in the form of additional load, and the control differential equation of pile foundation deformation is established according to the beam theory of foundation, and then the analytical solution of the control equation is obtained based on the boundary conditions. The control equation of this problem is often a fourth-order non-homogeneous differential equation, which needs to be solved by finite difference method. In order to facilitate the solution of difference equation, the existing research often regards the pile foundation as a finite length beam with unconstrained top and free end. It is feasible to regard the end of friction pile as free boundary, but for end-bearing pile, especially rock-socketed pile, the constraint of rock layer on the end of pile cannot be ignored. In addition, except for some isolated piles, the top of pile is usually embedded in pile cap or raft foundation, which is inconsistent with the actual engineering problem to simplify it as free boundary. The solution of differential equation is essentially to deal with boundary value problem, and boundary condition is the decisive factor for solving differential equation. Therefore, it is necessary to consider the actual constraint state of both ends of pile foundation.

[0005] At present, the problem of pile-soil interaction is still dependent on the elastic foundation beam theory, that is, the pile foundation is regarded as a finite length beam in the elastic foundation, and a variety of analytical calculation models are established based on different foundation models and beam theories. Among the commonly used foundation models, the Winkler foundation model does not consider the shear effect between the foundation springs, although the Pasternak foundation model makes up for this deficiency, but the shear parameters of the soil in this model are mainly taken by experience; Compared with the first two kinds of foundation models, the Vlasov foundation model can reflect the shear properties of the soil, and the parameter selection has more theoretical basis. Compared with the Euler-Bernoulli beam, the Timoshenko beam can reflect the bending and shear characteristics at the same time, and obviously it is more reasonable to use the Vlasov-Timoshenko elastic foundation beam theory to establish the analytical model.

[0006] In summary, the existing research on the boundary conditions of pile foundation does not conform to the actual engineering problems, and the analytical calculation model still has certain theoretical defects, which cannot truly meet the engineering needs. In view of the deficiencies in the research on the response of adjacent pile foundation induced by tunnel adjacent construction, it is urgent to establish a reliable and simple calculation method, which can accurately predict the influence of tunnel construction on adjacent existing pile foundation and maximize the safety of construction. SUMMARY

[0007] The technical problem to be solved by the present application is to provide a tunnel construction adjacent pile foundation response calculation method, terminal equipment and storage medium, which can accurately predict the influence of tunnel construction on adjacent existing pile foundation and maximize the safety of construction.

[0008] To solve the above technical problems, the technical scheme adopted by the present application is: a tunnel construction adjacent pile foundation response calculation method considering the actual constraints at both ends, comprising the following steps:

[0009] S1, according to the Vlasov-Timoshenko elastic foundation beam theory and the stress balance of the pile micro-section unit, the control differential equation of the lateral deformation w of the pile foundation is established:

[0010]

[0011] wherein (EI) p and χGA respectively represent the bending stiffness and shear stiffness of the pile section, χ is the shear correction coefficient, k and t respectively represent the foundation reaction coefficient and the load transfer rate, D p is the pile diameter, q(z) is the additional load generated by the lateral deformation of the soil at the pile position, and z is the calculation point depth;

[0012] S2, the pile foundation is discretized into n beam units with a length of l along the axial direction, two virtual nodes are added at both ends of the pile foundation, C=χGA, D=(EI) p, K i = k i D p , T i = 2t i D p , the finite difference expression of the lateral deformation w and the bending moment M of the pile foundation is obtained:

[0013]

[0014] wherein w i and M i respectively represent the lateral deformation and the bending moment of the pile foundation at the node i, k i and t i respectively represent the ground reaction coefficient and the load transfer rate at the node i, l is the length of the discrete beam element, q i is the additional load generated by the lateral deformation of the soil at the node i; i = -2, -1, 0, 1, …, n+2;

[0015] S3, the finite difference expression of the lateral deformation w of the pile foundation is expressed in the following matrix form: (K1-K2+K3)·w=(Q1-Q2-Q3), the lateral deformation w and the bending moment M of the adjacent existing pile foundation after the completion of the tunnel construction are calculated by using the matrix form; wherein,

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] wherein,

[0022] A1=c0c7+c8-4c0+6;A2=c1c7+c9-4c1-4;A3=c2c7+c 10 -4c2+1;A4=c3c7+c 11 -4c3;

[0023] A5=c0-4;A6=c1+6;A7=c2-4;A8=c3+1;A9=c0-2;A 10 =c1+1;

[0024]

[0025]

[0026] A1' = c0'c7' + c8' - 4c0' + 6; A2' = c1'c7' + c9' - 4c1' - 4; A3' = c2'c7' + c 10 ' - 4c2' + 1; A4' = c3'c7' + c 11 ' - 4c3' ;

[0027] A5' = c0' - 4; A6' = c1' + 6; A7' = c2' - 4; A8' = c3' + 1; A9' = c0' - 2; A 10 ' = c1' + 1;

[0028]

[0029]

[0030]

[0031]

[0032] β = 30αD 2 (C + T1)[1 + (δ 11 - lδ 12 )K t0 + αC 2 l 4 T0[5 + (5δ 11 - 4lδ 12 )K t0 ] - 60CD 2 lK t0 (C + T0);

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045] β' = -30α' D 2 (C + T n-1 )[1 + (δ 11 - lδ 12 )K tn ]+ α' C 2 l 4 T n [5 + (5δ 11 - 4lδ 12 )K tn ]- 60CD 2 lK tn (C + T n );

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] K t0 and K θ0 are the horizontal and rotational spring stiffness of the pile top, respectively; K tn and K θn are the horizontal and rotational spring stiffness of the pile tip, respectively; δ 11 and δ 12 are the displacements at node i = 0 due to unit load acting alone; δ 21 and δ 22 are the displacements at node i = 1 due to unit load acting alone.

[0058] The formula for calculating the additional load q(z) caused by the lateral deformation of the soil at the pile location is: Where u(z) is the free field displacement of the soil at the pile location.

[0059] The formula for calculating the free field displacement u(z) of the soil at the pile location is as follows:

[0060]

[0061] Where ε is the equivalent formation loss rate, y is the horizontal distance from the calculation point to the tunnel axis, R is the tunnel radius, H is the tunnel axis burial depth, and μ s The Poisson's ratio of the soil.

[0062] For a circular cross-section, χ = 0.89; for a rectangular cross-section, χ = 0.83.

[0063] Horizontal spring stiffness K at the pile top t0 The calculation formula is: K t0 =(C z ·S 侧 +μ·P c ) / m; where C z S is the horizontal resistance coefficient of the foundation; 侧 P is the lateral area of ​​the foundation embedded in the soil; μ is the coefficient of friction between the bottom of the foundation and the foundation soil; P c is the vertical load borne by the soil beneath the pile cap; m is the number of piles.

[0064] Stiffness K of the rotating spring at the pile top θ0 The calculation formula is: K θ0 =(EI) c / m; m is the number of piles; (EI) c This refers to the bending stiffness of the foundation.

[0065] Pile end horizontal spring stiffness K tn The calculation formula is: K tn =C x A; C z denoted as the horizontal resistance coefficient of the foundation, and A is the area of ​​the pile bottom.

[0066] Stiffness K of the rotating spring at the pile end θn The calculation formula is: is the bending stiffness coefficient, and I is the moment of inertia of the pile end section.

[0067] As an inventive concept, the present invention also provides a terminal device, including a memory, a processor, and a computer program stored in the memory; the processor executes the computer program to implement the steps of the method described above.

[0068] As an inventive concept, the present application also provides a computer readable storage medium, which stores computer programs / instructions; the computer programs / instructions are executed by a processor to realize the steps of the method of the present application.

[0069] Compared with the prior art, the present application has the beneficial effects that:

[0070] 1) The pile-soil interaction problem is constructed by relying on the elastic foundation beam theory, and based on different foundation models and beam theories, a variety of analytical calculation models can be established, and the elastic foundation beam theory is the basis for solving the problem, and the selection of the elastic foundation beam theory will affect the accuracy of the results. Compared with the Winkler foundation model and the Pasternak foundation model, the Vlasov foundation model considers the shear effect between the foundation springs, and the parameter values are more theoretically based; compared with the Euler-Bernoulli beam, the Timoshenko beam can reflect the bending and shear characteristics at the same time, obviously, it is more reasonable to construct an analytical model by using the Vlasov-Timoshenko elastic foundation beam theory. The elastic foundation beam theory used in the present application is more theoretically based, and the actual constraint state of the pile foundation at both ends is considered, which is more in line with the engineering practice, and thus the response characteristics of the adjacent existing pile foundation under the influence of tunnel construction can be more accurately predicted.

[0071] 2) The calculation method proposed in the present application considers the actual constraint state of the pile foundation at both ends, and gives a simplified calculation method for the constraints at the top and the end of the pile, which can more accurately predict the response characteristics of the adjacent existing pile foundation under the influence of tunnel construction, and has important guiding significance for field construction. BRIEF DESCRIPTION OF DRAWINGS

[0072] Figure 1 The flow chart of the calculation method for the response of the adjacent pile foundation considering the actual constraints at both ends of the tunnel construction of the embodiment of the present application;

[0073] Figure 2 The schematic diagram of the tunnel-soil-pile foundation interaction model of the embodiment of the present application;

[0074] Figure 3 The schematic diagram of the simplified calculation model of the pile foundation of the embodiment of the present application;

[0075] Figure 4 The schematic diagram of the discrete pile foundation of the embodiment of the present application. DETAILED DESCRIPTION

[0076] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the following will clearly and completely explain the technical solutions in the embodiments of the present application with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0077] In this document, the terms "first", "second", and other similar terms are not intended to imply any order, quantity, and importance, but are merely used to distinguish different elements. In this document, the terms "one", "a", and other similar terms are not intended to mean that there is only one of the described things, but that the description is directed to only one of the described things, which can have one or more. In this document, the terms "include", "comprise", and other similar terms are intended to mean logical relationships, and cannot be regarded as indicating spatial structural relationships. For example, "A includes B" is intended to mean that B logically belongs to A, and does not mean that B is located inside A in space. In addition, the meaning of the terms "include", "comprise", and other similar terms should be regarded as open, rather than closed. For example, "A includes B" is intended to mean that B belongs to A, but B does not necessarily constitute all of A, and A can also include C, D, E, and other elements.

[0078] Embodiment 1

[0079] Embodiment 1 of the present application provides a calculation method for the response of adjacent pile foundation to tunnel construction considering actual constraints at both ends, comprising the following steps:

[0080] Step 1: Determine the tunnel construction parameters, pile foundation parameters, and stratum physical and mechanical parameters; wherein the tunnel construction parameters: R is the tunnel radius, and H is the tunnel axis burial depth; the pile foundation parameters: E p is the pile foundation elastic modulus, and μ p is the pile foundation Poisson's ratio, L p is the pile length, and D p is the pile diameter, and y0 is the horizontal distance between the tunnel axis and the pile foundation; the stratum physical and mechanical parameters: H n is the thickness of the nth layer of soil, E sn and μ sn are the elastic modulus and Poisson's ratio of the nth layer of soil, respectively;

[0081] As shown in FIG. 1, the tunnel construction parameters, pile foundation parameters, and stratum physical and mechanical parameters are as follows: Figure 2

[0082] The tunnel construction parameters: the tunnel radius R = 3 m, and the tunnel axis burial depth H = 20 m; the pile foundation parameters: the pile foundation elastic modulus E p ​= 30 GPa, pile foundation Poisson's ratio μ p = 0.2, pile length L p = 25 m, pile diameter D p = 0.5 m, horizontal distance y0 between tunnel axis and pile foundation = 4.5 m; physical and mechanical parameters of stratum: soil in the range of pile foundation depth is simplified as two layers, thickness of upper layer soil H1 = 10 m, elastic modulus E s1 = 12 MPa, thickness of lower layer soil H2 = 15 m, elastic modulus E s2 = 24 MPa, Poisson's ratio μ of soil s1 = μ s2 = 0.4;

[0083] Step two: calculate soil free field displacement u(z) at pile position, the calculation formula is as follows:

[0084]

[0085] In the above formula, ε is equivalent stratum loss rate, y is horizontal distance of calculation point to tunnel axis, z is depth of calculation point;

[0086] Equivalent stratum loss rate ε = 1%, horizontal distance of calculation point to tunnel axis y = y0 = 4.5 m, calculation results of soil free field displacement u(z) at pile position are shown in Table 1;

[0087] Step three: the soil free field displacement acts on the pile foundation in the form of additional load, and the additional load q(z) generated by the lateral deformation of the soil at the pile position is determined, the calculation formula is as follows:

[0088]

[0089] In the formula, k and t are respectively the foundation reaction coefficient and the load transmission rate, which can be calculated and determined according to the following formula:

[0090]

[0091] Wherein, H e is the thickness of the elastic layer of foundation, which can be taken as H e = 2.5D p ; h = h(z) is a function describing the vertical variation of displacement, for the convenience of calculation, the following linear function form is used to represent:

[0092]

[0093] Corresponding Figure 2 , in the embodiment, the thickness of the elastic layer of foundation H e is taken as 1.25 m; the foundation reaction coefficient k1 of the upper layer soil is k1 = 20.57 × 10 3 kN / m 3 , and the load transmission rate t1 is t1 = 8.93 × 102 kN / m; the foundation reaction coefficient k2 of the underlying soil = 41.14 x 10 3 kN / m 3 , the load transfer rate t2 = 1.79 x 10 3 kN / m; the additional load q(z) generated by the lateral deformation of the soil at the pile position is shown in Table 1;

[0094] Table 1: soil free field displacement at the pile position and additional load generated by the lateral deformation of the soil at the pile position

[0095]

[0096] Step four: determine the actual constraint state of the pile top and pile end. The simplified calculation formulae of the horizontal spring stiffness (K t0 and K tn ) and the rotational spring stiffness (K θ0 and K θn ) of the two ends of the pile foundation are as follows:

[0097] K t0 = (C z · S 侧 + μ· P c ) / m;

[0098] K θ0 = (EI) c / m;

[0099] K tn = C x A;

[0100]

[0101] In the formula, C z is the horizontal resistance coefficient of the foundation; S 侧 is the side area of the pile cap embedded in the soil; μ is the friction coefficient between the bottom of the pile cap and the foundation soil; P c is the vertical load borne by the soil at the bottom of the pile cap; m is the number of piles; (EI) c is the bending stiffness of the pile cap; C x and are the shear and bending stiffness coefficients of the foundation, respectively; A is the bottom area of the pile foundation; I is the sectional moment of inertia of the pile end;

[0102] It is assumed that the horizontal spring stiffness of the pile top and pile end in this embodiment is K t0 = K tn = 10 8 kN / m, and the rotational spring stiffness is K θ0 = K θn = 10 7 kN·m / rad;

[0103] Step five: according to the Vlasov-Timoshenko elastic foundation beam theory and stress balance of the pile micro-section unit, a control differential equation of the lateral deformation w of the pile foundation is established, and the balance differential equation is as follows:

[0104]

[0105] wherein (EI) p and χGA respectively represent the bending stiffness and shear stiffness of the pile foundation section, χ is a shear correction coefficient, and χ = 0.89 is taken for a circular section, and χ = 0.83 is taken for a rectangular section.

[0106] In the embodiment, the shear correction coefficient χ is taken as 0.89; the bending stiffness (EI) p of the pile foundation section is 92.0 x 10 3 kN·m 2 ; and the shear stiffness χGA is 2.18 x 10 6 kN.

[0107] Step six: based on the finite difference principle and the internal force boundary conditions of the two ends of the pile foundation, independent equations are supplemented. The pile foundation is discretized into n (in the embodiment, n is set as 25) beam units with a length of l (in the embodiment, l is set as 1 m) along the axial direction, two virtual nodes are added to each end of the pile foundation, C = χGA, D = (EI) p , K i = k i D p , T i = 2t i D p , and the finite difference expressions of the lateral deformation w and the bending moment M of the pile foundation are obtained, and the finite difference expressions are respectively as follows:

[0108]

[0109]

[0110] When i = 0, the finite difference expression is as follows:

[0111]

[0112] From the finite difference expression of the lateral deformation of the pile foundation, n+1 independent equations are obtained, but there are n+5 unknown quantities, and 4 independent equations need to be supplemented according to the internal force boundary conditions of the two ends of the pile foundation. Taking the pile top as an example, the node 0-1 isolation body micro-section unit is taken as the analysis object, and the virtual node displacement w -1 and w -2 of the pile top are obtained by combining the force method equation and the finite difference expression:

[0113]

[0114] In this embodiment,

[0115] Step seven: the finite difference expression of the lateral deformation w of the pile foundation is expressed in the following matrix form, and the lateral deformation and internal force of the adjacent existing pile foundation after the completion of the tunnel construction are calculated by means of MATLAB mathematical software:

[0116] (K1-K2+K3)·w=(Q1-Q2-Q3);

[0117] In the formula,

[0118]

[0119]

[0120]

[0121]

[0122]

[0123] Wherein, In this embodiment,

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] The calculation results of the lateral deformation w and the bending moment M of the pile foundation after the completion of the tunnel construction in this embodiment are shown in Table 2.

[0131] Table 2 Calculation results of lateral deformation w and bending moment M

[0132]

[0133] Embodiment 2

[0134] Embodiment 2 of the present application provides a terminal device corresponding to the above-mentioned embodiment 1, which can be a processing device for a client, such as a mobile phone, a notebook computer, a tablet computer, a desktop computer, etc., to execute the method of the above-mentioned embodiment.

[0135] The terminal device of the embodiment includes a memory, a processor, and a computer program stored in the memory; the processor executes the computer program stored in the memory to implement the steps of the method of embodiment 1.

[0136] In some implementations, the memory can be a high-speed random access memory (RAM), and can also include a non-volatile memory, such as at least one disk memory.

[0137] In some implementations, the processor can be a central processing unit (CPU), a digital signal processor (DSP), or various types of general-purpose processors, without limitation.

[0138] Embodiment 3

[0139] Embodiment 3 of the present application provides a computer-readable storage medium corresponding to the above-mentioned embodiment 1, which stores a computer program / instruction. The computer program / instruction is executed by the processor to implement the steps of the method of embodiment 1.

[0140] The computer-readable storage medium can be a tangible device that maintains and stores instructions for use by an instruction execution device. The computer-readable storage medium can be, for example but not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof.

[0141] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROMs, optical storage devices, etc.) containing computer-usable program code. The solutions in the embodiments of the present application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0142] The present application is described with reference to flowcharts and / or block diagrams according to the methods, devices (systems), and computer program products of the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to produce a machine, so that the instructions executed by the computer or other programmable data processing devices produce a device that implements the functions described in the flowcharts and / or block diagrams.Figure 1 apparatuses that implement functions specified in one or more flowcharts and / or blocks. Figure 1

[0143] These computer program instructions can also be loaded into computer or other programmable data processing devices, so that a series of operation steps are performed on the computer or other programmable data processing devices to generate computer-implemented processes, thus the instructions executed on the computer or other programmable data processing devices provide a process for implementing the functions specified in the flowcharts Figure 1 apparatuses that implement functions specified in one or more flowcharts and / or blocks. Figure 1

[0144] Although the preferred embodiments of the application have been described, those skilled in the art will be able to make additional modifications and variations to these embodiments without departing from the spirit and scope of the application. Accordingly, it is intended that the appended claims be construed to include all such modifications and variations as fall within the scope of the application.

[0145] Obviously, various modifications and changes can be made to the present application by those skilled in the art without departing from the spirit and scope of the present application. Thus, it is intended that the present application encompass all such modifications and changes as fall within the scope of the claims and their equivalents.​​

Claims

1. A method for calculating the response of a neighboring pile foundation to tunnel construction considering actual constraints at both ends, characterized by, The method comprises the following steps: S1, establishing a control differential equation of lateral deformation w of the pile foundation according to a Vlasov-Timoshenko elastic foundation beam theory and stress balance of a pile micro-unit: wherein (EI) p and χ GA represent the bending stiffness and shear stiffness of the pile section, respectively, χ is a shear correction factor, k and t represent the subsoil reaction coefficient and load transfer rate, respectively, D p is the pile diameter, and q(z) is the additional load due to lateral deformation of the soil at the pile location, and z is the depth of the calculation point. S2, discretize the pile foundation into n beam elements with length l along the axial direction, add two virtual nodes at each end of the pile foundation, let C = χGA, D = (EI) p , K i = k i D p , T i = 2t i D p , get the finite difference expression of the lateral deformation w and the bending moment M of the pile foundation where w i and M i denote the lateral deformation and bending moment of the pile at node i, k i and t i denote the subgrade reaction coefficient and load transfer ratio at node i, l is the length of the discrete beam element, q i is the additional load due to the lateral deformation of the soil at node i; i = -2, -1, 0, 1, …, n+2; y S3, expressing a finite difference expression of the lateral deformation w of the pile foundation in a matrix form as follows: (K1-K2+K3)·w=(Q1-Q2-Q3), and using the matrix form to calculate the lateral deformation w and the bending moment M of the adjacent existing pile foundation after the tunnel construction is completed; wherein, wherein, A1 = c0c7 + c8 - 4c0 + 6; A2 = clc7 + c9 - 4cl - 4; A3 = c2c7 + c 10 -4c2 + 1; A4 = c3c7 + c 11 -4c3; A5 = c0 - 4; A6 = cl + 6; A7 = c2 - 4; A8 = c3 + 1; A9 = c0 - 2; A 10 = cl + 1; A1' = cO'c7' + c8' - 4cO' + 6; A2' = cl'c7' + c9' - 4cl' - 4; A3' = c2'c7' + c 10 ' - 4c2' + 1; A4' = c3'c7' + c 11 ' - 4c3'. A5' = c0' - 4; A6' = c1' + 6; A7' = c2' - 4; A8' = c3' + 1; A9' = c0' - 2; A 10 ' = c1' + 1; β = 30 αD 2 (C + T1) [1 + (δ 11 - lδ 12 )K t0 ]+ αC 2 l 4 T0[5 + (5δ 11 - 4lδ 12 )K t0 ]- 60CD 2 lK t0 (C + T0); β' = -30α' D 2 (C + T n-1 ) + α' C 11 [1 + (δ 12 )K tn ] + α' C 2 l 4 T n [5 + (5δ 11 - 4lδ 12 )K tn ] - 60CD 2 lK tn (C + T n ) K t0 and K θ0 are the horizontal and rotational spring stiffness of the pile top, respectively; K tn and K θn are the horizontal and rotational spring stiffness of the pile tip, respectively; δ 11 and δ 12 are the displacements at node i = 0 due to unit load acting alone; δ 21 and δ 22 are the displacements at node i = 1 due to unit load acting alone.

2. The method of claim 1, wherein the method is characterized by, The formula for calculating the additional load q(z) caused by the lateral deformation of the soil at the pile position is where u(z) is the free-field displacement of the soil at the pile position.

3. The method of claim 2, wherein the method is characterized by, A calculation formula of a free field displacement u(z) of the soil at the pile position is as follows: where ε is the equivalent strata loss rate, y is the horizontal distance from the calculation point to the tunnel axis, R is the tunnel radius, H is the depth of the tunnel axis, μ s is the Poisson's ratio of the soil.

4. The method of claim 1, wherein the method is characterized by, For a circular section, χ=0.89, and for a rectangular section, χ=0.

83. 5.The method of claim 1, wherein, Pile top horizontal spring stiffness K t0 The calculation formula is: K t0 = (C z ·S 侧 + μ·P c ) / m; wherein C z is the horizontal resistance coefficient of the foundation; S 侧 is the side area of the pile cap embedded in the soil body; μ is the friction coefficient between the bottom of the pile cap and the soil; P c is the vertical load borne by the soil body under the pile cap; m is the number of piles.

6. The method of claim 1, wherein the method is characterized by: Rotational spring stiffness K θ0 The calculation formula is: K θ0 = (EI) c / m; m is the number of piles; (EI) c is the bending stiffness of the pile cap.

7. The method of claim 1, wherein the method is characterized by: K = K0 + K1 tn The calculation formula is: K tn = C x A; C z is the horizontal resistance coefficient of the foundation, and A is the base pile bottom area. 8.The method of claim 1, wherein, K = 2.5 (D - d) / d θn The formula for calculating K is: EI is the bending stiffness coefficient, and I is the cross-sectional moment of inertia of the pile tip.

9. A terminal device comprising a memory, a processor, and a computer program stored on the memory; characterized in that, The processor executes the computer program to implement the steps of the method of any one of claims 1-8.

10. A computer readable storage medium having stored thereon computer programs / instructions; characterized in that, The computer program / instruction is executed by the processor to implement the steps of the method of any one of claims 1-8.

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