Method and system for calculating transverse displacement of adjacent tunnel caused by uplift of pit bottom due to foundation pit excavation

Abstract

This invention discloses a method and system for calculating the lateral displacement of an adjacent tunnel caused by bottom heave during foundation pit excavation. The method first calculates the lateral displacement of the soil at any depth at the retaining structure caused by the unloading of the bottom heave, and then, based on the deformation coordination between the soil and the retaining structure, converts it into an equivalent displacement S of the retaining structure. z (z); then, based on the displacement S of the enclosure structure z (z) and the maximum displacement value S reached in the active state a The ratio η is used to obtain the cohesion utilization value, and from this, the non-limit active earth pressure p is obtained based on the theory of non-limit active earth pressure. a Thus, the horizontal unloading stress p1 is obtained, and finally, the additional horizontal stress σ in the tunnel direction is obtained. y Ultimately, the additional horizontal stress σ in the tunnel is... y The load P(x) is obtained, and the governing equation for the tunnel's lateral displacement ω(x) is derived based on the coordination between soil and tunnel displacement. This equation is then expressed in matrix form to calculate the tunnel's lateral displacement ω(x). This calculation method allows for a more accurate assessment of the impact of foundation pit construction on the tunnel structure in practice, providing guidance for foundation pit design and construction.

Description

Technical Field

[0001] This invention belongs to the field of underground engineering, specifically a method and system for calculating the lateral displacement of adjacent tunnels caused by the bottom heave of a foundation pit during excavation. Background Technology

[0002] Excavation of the foundation pit will cause disturbance to the surrounding soil, including an upward bulge at the bottom of the pit. This displacement will cause displacement of the surrounding soil and the shield tunnel.

[0003] At present, there is little research by domestic and foreign scholars on the lateral displacement of adjacent tunnels caused by pit heave. The main focus is on the vertical displacement of the tunnels below or beside the pit caused by pit heave. Chen Yu et al. (Chen Yu, Li Yongsheng. Calculation method of heave of the tunnel below caused by excavation and unloading of pit[J]. Journal of Underground Space and Engineering, 2005, (01): 91-94.) used a theoretical calculation method, regarded the load at the bottom of the pit as a uniformly distributed load, the magnitude of which is equivalent to the weight intensity of the excavated soil, and the direction is upward. Then, the vertical displacement generated by it acting on the tunnel below was calculated by Mindlin solution. Zhang Zhiguo et al. (Zhang Zhiguo, Zhang Mengxi, Wang Weidong. Two-stage analysis method for the impact of foundation pit excavation on adjacent subway tunnels[J]. Rock and Soil Mechanics, 2011, 32(07):2085-2092.DOI:10.16285 / j.rsm.2011.07.036.) regarded the unloading at the bottom of the pit as the weight of the original overlying soil, and calculated the vertical displacement deformation on the adjacent tunnel by combining the Mindlin basic solution and the unloading of the pit wall. Zhou Shunhua et al. (Zhou Shunhua, He Chao, Xiao Junhua. Energy calculation method for deformation of adjacent subway shield tunnel caused by foundation pit excavation under the effect of inter-ring misalignment[J]. China Railway Science, 2016, 37(03):53-60.) did not consider the plastic deformation of the soil in the calculation, took the stress release rate at the bottom of the pit as 100%, and did not consider the unloading of the pit wall, and calculated the horizontal and vertical displacement of the adjacent tunnel under this action. Xu Wenda et al. (Xu Wenda, Jiang Jun. Calculation method for longitudinal deformation of adjacent subway tunnels caused by foundation pit excavation [J]. Railway Construction, 2018, 58(09):63-67.) considered the plastic deformation of the soil in their calculations, introduced the initial residual stress coefficient when calculating the unloading at the bottom of the pit, reduced the unloading, and considered the friction between the retaining structure and the soil. Based on the released stress obtained from the calculation, the vertical displacement of the adjacent tunnel was calculated using the Mindlin solution.

[0004] Existing calculations considering the impact of pit heave unloading on tunnel lateral deformation mainly focus on the vertical displacement of the underlying or adjacent tunnels, rarely considering the influence of pit heave on the lateral displacement of adjacent tunnels. In fact, pit heave causes horizontal displacement of the surrounding soil, which in turn causes lateral displacement of adjacent tunnels. Therefore, it is necessary to study methods for calculating the lateral displacement of adjacent tunnels caused by pit heave. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a method and system for calculating the lateral displacement of adjacent tunnels caused by pit bottom heave, filling the gap in existing methods for calculating the horizontal displacement of adjacent tunnels that ignore the influence of pit bottom heave.

[0006] The calculation method for the lateral displacement of the adjacent tunnel caused by the bottom heave due to foundation pit excavation includes the following steps:

[0007] Step 1: Take the center of the rectangular foundation pit as the origin of the coordinate axis, take the z-axis in the vertical direction, the x-axis in the length direction of the foundation pit, and the y-axis in the width direction of the foundation pit. Calculate the lateral displacement of the soil at any depth at the retaining structure caused by the unloading of the bottom of the pit, and convert it into the equivalent displacement S of the retaining structure based on the deformation compatibility between the soil and the retaining structure. z (z), where the lateral displacement is the displacement in the y-axis direction;

[0008] Step 2: Based on the displacement S of the enclosure structure z (z) and the maximum displacement value S reached in the active state a The ratio η yields the cohesive force utilization value. Based on this, the non-limit active earth pressure p is obtained from the theory of non-limit active earth pressure. a Thus, the horizontal unloading stress p1 at the corresponding depth of the retaining structure due to the heave of the pit bottom is obtained, and finally, the additional horizontal stress σ of the tunnel is obtained. y ;

[0009] Step 3: Apply additional horizontal stress σ through the tunnel y The load P(x) of the horizontal additional stress acting on the tunnel is obtained, and the governing equation of the tunnel lateral displacement ω(x) is obtained according to the coordination between the soil and the tunnel displacement. It is expressed in matrix form, and the matrix of undetermined coefficients A is calculated based on it. Finally, the lateral displacement function of the tunnel is obtained, and the lateral displacement ω(x) of the tunnel is calculated.

[0010] Furthermore, in step 1, the lateral displacement of the soil at any depth at the retaining structure is specifically as follows:

[0011] Based on the obtained pit bottom heave curve, the lateral displacement of the soil at any depth acting on the retaining structure is calculated using the image source method. Specifically, the image source method is as follows:

[0012] Obtain the soil deformation S at any point Q(y,z) in the retaining structure caused by soil loss at any point P(y0,d) at the bottom of the pit. y Then, by integrating along the width of the pit bottom, the lateral displacement S of the soil at any depth at the retaining structure is obtained. z (z):

[0013]

[0014] In the formula: B is the width of the foundation pit, d is the depth of the foundation pit, and z r The depth of the calculated point at the bottom of the foundation pit, r1 = [y 2 +(zd) 2 ] 1 / 2 r2 = [y 2 +(z+d) 2 ] 1 / 2 .

[0015] Furthermore, the depth z of the calculated point at the bottom of the foundation pit r Based on the curve of the pit bottom bulge:

[0016]

[0017] In the formula: S r S represents the amount of bulge at the center point. m This refers to the amount of heave on the sidewall of the foundation pit.

[0018] Furthermore, the center point bulge S r and the amount of heave on the sidewall of the foundation pit S m The calculation formula is:

[0019] S r =Y1Y2S0

[0020] S m =Y1Y2S1

[0021] S0=0.732Q(1-μ 2 ) / E0

[0022]

[0023] Where Y1 and Y2 are correction coefficients. Q is the total weight per unit thickness of the soil, Q = Bdγ, where γ is the weight of the soil within the excavation area; μ is the Poisson's ratio of the soil; E0 is the resilient modulus of the soil, and the empirical value of the resilient modulus E0 is (3~5)E s E s S1 is the soil compression modulus, S0 is the initial center point heave, and S1 is the initial pit sidewall heave.

[0024] Furthermore, in step 2), the additional horizontal stress σ in the tunnel... y The calculation method is as follows:

[0025]

[0026] In the formula: let the coordinates of any point on the foundation pit wall near the tunnel be (ξ, B / 2, z), and take any point on the tunnel axis as (x1, L1, z0), p1 is the horizontal unloading stress, L1 is the distance from the tunnel axis to the center of the foundation pit; B is the width of the foundation pit; z is the non-ultimate active earth pressure p a The corresponding calculation depth; z0 is the depth from the ground surface to the tunnel axis, and μ is the Poisson's ratio of the soil.

[0027]

[0028] Furthermore, the calculation method for the horizontal unloading stress p1 is as follows:

[0029] p1=K0γz-p a

[0030] In the formula: K0 is the static lateral earth pressure coefficient, and z is the non-ultimate active earth pressure p. a The calculation depth, γ is the unit weight of soil, p a This refers to non-limiting active earth pressure.

[0031] Furthermore, the non-limit active earth pressure p a The calculation method is as follows:

[0032]

[0033] In the formula: γ is the unit weight of soil, q0 is the load outside the pit; θ is the soil cohesion; c m This is the value of the internal friction angle.

[0034] The cohesion performance value The calculation method is as follows:

[0035]

[0036] In the formula: R f The soil failure ratio, is the internal friction angle of the soil, and K0 is the coefficient of lateral earth pressure at rest.

[0037] Furthermore, the lateral displacement function of the tunnel is specifically as follows:

[0038] ω(x)=T n (x)A T

[0039] In the formula: A T The transpose of the matrix A with undetermined coefficients.

[0040] Where D t Where is the ring width of the tunnel segment ring, and N is the number of tunnel lining rings affected by the excavation of the foundation pit. The value of N is related to the range of influence of the excavation of the foundation pit.

[0041] Furthermore, the matrix form is specifically as follows:

[0042] ([K t ]+[K s ]){A} T ={P n} T

[0043] In the formula: [K t [K] represents the stiffness matrix between tunnel rings. s ] is the soil stiffness matrix, {P n} T This represents the interaction effect between the free soil displacement and the tunnel lining ring.

[0044] The governing equation for the tunnel's lateral displacement ω(x) is:

[0045]

[0046] In the formula: k t and k T Here, represents the inter-ring shear stiffness and inter-ring tensile stiffness of the tunnel, respectively; k is the subgrade coefficient of the soil; and m is the number of the lining ring. P(x) is the horizontal additional stress acting on the tunnel, P(x) = σ y D, where D is the outer diameter of the shield tunnel lining, and j is the proportionality coefficient for rigid body rotation effect; ξ i Let A be the elements of the undetermined coefficient matrix A, which are also the coefficients of the tunnel lateral displacement function polynomial. A = (a1, a2, a3, ..., a...). n ) T .

[0047] A calculation system for the lateral displacement of an adjacent tunnel caused by the bottom heave resulting from foundation pit excavation, used to implement the calculation method described in any one of the claims.

[0048] Beneficial effects:

[0049] This invention provides a method for calculating the lateral displacement of adjacent tunnels caused by the bottom heave of the foundation pit excavation. This method fills the gap in existing methods for calculating the horizontal displacement of adjacent tunnels, which ignores the influence of the bottom heave. This makes the current calculation method more scientific and comprehensive, and can more accurately assess the impact of foundation pit construction on tunnel structures in practice. It has guiding significance for foundation pit design and construction. Attached Figure Description

[0050] The accompanying drawings, which further illustrate the invention and constitute a part of it, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0051] Figure 1This is a simplified calculation diagram of soil displacement at the wall using the image source method in one embodiment of the present invention;

[0052] Figure 2 This is a schematic diagram of a calculation model for pit heave and tunnel displacement in one embodiment of the present invention, wherein (a) is a top view, (b) is a front view, and (c) is an axis view;

[0053] Figure 3 This is a flowchart illustrating the method for calculating the lateral displacement of an adjacent tunnel caused by the bottom heave resulting from foundation pit excavation, as described in this invention. Detailed Implementation

[0054] The present invention will be described in detail below with reference to the accompanying drawings. The purpose and effects of the present invention will become clearer. It should be understood that the accompanying drawings are only used to explain the present invention and are not intended to limit the present invention.

[0055] like Figure 1 There is an existing shield tunnel next to a rectangular foundation pit. The excavation of the foundation pit caused the bottom of the pit to bulge. This bulge will cause the soil at the retaining structure to shift laterally, which will affect the deformation of the adjacent existing shield tunnel.

[0056] Step 1: Take the center of the rectangular foundation pit as the origin of the coordinate axes. Take the z-axis vertically, the x-axis along the length of the foundation pit, and the y-axis along the width of the foundation pit. The horizontal direction mentioned in this invention refers to the y-axis direction. Calculate the displacement S of the retaining structure caused by the unloading of the pit bottom heave. z (z);

[0057] The bulge at the bottom of the pit exhibits a parabolic shape, and the curve of the bulge is as follows:

[0058]

[0059] In the formula z r S is the depth of the calculated point at the bottom of the foundation pit, y is the horizontal distance from the calculated point to the z-axis, and S is the depth of the calculated point at the bottom of the foundation pit. r S represents the amount of bulge at the center point. m The amount of heave on the sidewall of the foundation pit

[0060] The center point bulge S r and the amount of heave on the sidewall of the foundation pit S m The calculation formula is as follows:

[0061] S r =Y1Y2S0

[0062] S m =Y1Y2S1

[0063] S0=0.732Q(1-μ 2 ) / E0

[0064]

[0065] Where Y1 and Y2 are correction coefficients. B is the width of the excavation pit, d is the depth of the excavation pit (i.e., the initial depth before uplift occurs); Q is the total weight per unit thickness of the soil, Q = Bdγ; γ is the weight of the soil within the excavation area; μ is the Poisson's ratio of the soil; E0 is the resilient modulus of the soil, and the empirical value of the resilient modulus E0 is (3~5)E s E s S1 is the soil compression modulus, S0 is the initial center point heave, and S1 is the initial pit sidewall heave.

[0066] After obtaining the bottom heave curve, the lateral displacement of the soil at any depth acting on the retaining structure is calculated using the image source method. The calculation model is attached. Figure 1 ;

[0067] Image source method:

[0068] The total displacement along the y-axis produced by a gap of radius a at any point P(y0,d) at the bottom of the pit at any point Q(y,z) on the sidewall of the pit, i.e., the retaining structure, is as follows:

[0069]

[0070] in:

[0071]

[0072] r1 = [y 2 +(zd) 2 ] 1 / 2

[0073] r2=[y 2 +(z+d) 2 ] 1 / 2

[0074] Obtain the soil deformation S at any point Q(y,z) in the retaining structure caused by soil loss at any point P(y0,d) at the bottom of the pit. y Then, by integrating along the width of the pit bottom, i.e., the y-axis direction, the lateral displacement S of the soil at any depth corresponding to the retaining structure can be obtained. z (z):

[0075]

[0076] Due to the deformation coordination between the soil and the retaining structure, the lateral displacement S of the soil at any depth at the retaining structure is hereby defined. z (z) is equivalent to the displacement of the enclosure structure, in order to perform subsequent unloading calculations.

[0077] Step 2: Additional horizontal stress σ in the tunnely calculate

[0078] Based on the theory of non-limit active earth pressure, the relationship between the deformation of the retaining structure and the earth pressure is shown in the following equation:

[0079]

[0080] Where γ is the unit weight of soil; z is the non-ultimate active earth pressure p. a The calculation depth; q0 is the load outside the pit; θ is the soil cohesion; p a For non-limit active earth pressure, c m This is the value of the internal friction angle. Cohesion performance value

[0081] The calculation method is as follows:

[0082]

[0083] In the formula: R f Let η be the soil failure ratio, and η be the displacement S of the retaining structure. z (z) and the maximum displacement value S reached in the active state a The ratio, i.e. K0 is the coefficient of lateral earth pressure at rest; The friction angle within the soil.

[0084] Therefore, the horizontal unloading stress p1 at the corresponding depth of the retaining structure due to the heave of the pit bottom is expressed by the following formula:

[0085] p1=K0γz-p a .

[0086] Let the coordinates of any point on the tunnel wall near the tunnel side be (ξ, B / 2, z). The calculation model is shown in the appendix. Figure 2 The horizontal additional stress σ at any point (x1, L1, z0) on the tunnel axis y The solution is obtained using the Mindlin formula.

[0087]

[0088] in:

[0089]

[0090] L1 is the distance from the tunnel axis to the center of the pit ground; B is the width of the pit; z is the calculation depth of non-ultimate active earth pressure; z0 is the depth from the ground surface to the tunnel axis; and μ is the Poisson's ratio of the soil.

[0091] Step 3: Calculation of lateral displacement of the tunnel

[0092] A calculation model for tunnel rotation misalignment is introduced;

[0093] Let the lateral displacement of the tunnel be ω(x). Based on the coordination between the soil and tunnel displacement, the governing equation for the lateral displacement ω(x) of the tunnel is obtained as follows:

[0094]

[0095] in:

[0096] ω(x)=T n (x)A T

[0097]

[0098] In the formula: k t and k T Here, represents the inter-ring shear stiffness and inter-ring tensile stiffness of the tunnel, respectively; k is the subgrade coefficient of the soil; m is the number of the lining ring; N is the number of calculated tunnel lining rings affected by the excavation, and its value is related to the influence range of the excavation; P(x) is the load of horizontal additional stress acting on the tunnel, P(x) = σ y D, where D is the outer diameter of the shield tunnel lining; k t and k T These are the inter-ring shear stiffness and inter-ring tensile stiffness of the tunnel, respectively. The method for determining their values ​​can be found in the research of Guo Le et al. (Guo Le, Yang Xin'an, Qiu Yan. Longitudinal heterogeneous equivalent continuous model of shield tunnel segment lining [J]. Urban Rail Transit Research, 2017, 20(4): 17–22.).

[0099] j is the proportionality coefficient for rigid body rotation effect; D t ξ is the ring width of the segment ring; i Let A be the elements of the undetermined coefficient matrix A, which are also the coefficients of the tunnel lateral displacement function polynomial. A = (a1, a2, a3, ..., a...). n ) T .

[0100] k is the subgrade coefficient of the soil, calculated using the Vesic formula. Where μ is the Poisson's ratio of the soil; E0 is the compression modulus of the soil; E t I t The equivalent bending stiffness of the tunnel can be determined using the following formula:

[0101]

[0102] In the formula, E c The elastic modulus of the tunnel segment; n is the number of bolts in the tunnel axial direction (x-axis); K b A represents the average linear stiffness of the joint bolts. sLet λ1 be the cross-sectional area of ​​the tunnel; without considering changes in the horizontal and vertical diameters of the tunnel, λ1 = tD(A1 + A2 - A3 - A4 - A5); λ2 = tD(A1 + A2 + A3 + A4 + A5); A1 = πD 2 / 16;A2=πD 2 sin 2 ψ / 8; A3 = D 2 ψ / 8; A4 = D 2 ψsin 2 ψ / 4; A5 = 3D 2 sinψcosψ / 8; where ψ is the position parameter of the central axis of the segment ring, and the method of taking the value can refer to the research of Ye Fei et al. (Ye Fei, He Chuan, Zhu Hehua, et al. Analysis of longitudinal equivalent stiffness of shield tunnel considering lateral performance [J]. Chinese Journal of Geotechnical Engineering, 2011, 33(12): 1870–1876.); t is the thickness of the segment; D is the outer diameter of the tunnel. The governing equation of the tunnel lateral displacement ω(x) is expressed in matrix form:

[0103] ([K t ]+[K s ]){A} T ={P n} T

[0104] In the formula: [K t [ ] represents the stiffness matrix between tunnel rings.

[0105]

[0106] [K s [ ] represents the soil stiffness matrix.

[0107]

[0108] {P n} T This represents the interaction effect between free soil displacement and tunnel lining ring:

[0109]

[0110] The matrix of undetermined coefficients A is obtained by calculating the matrix form of the governing equations;

[0111] Finally, the lateral displacement function of the tunnel is obtained as ω(x) = T. n (x)A T .

[0112] When considering the effect of pit heave, this invention, because the soil and retaining structure are coordinated, uses the image source method in step 1 to calculate the soil displacement at the location of the retaining structure to equivalently represent the retaining structure displacement. This allows for the calculation of the effect and displacement on the adjacent tunnel. This solves the problem that existing methods cannot consider the effect of soil heave on the lateral displacement of the adjacent tunnel.

[0113] The calculation method of this invention can be implemented numerically using Matlab programming. The integration operation utilizes the composite Simpson's quadrature formula and employs an integration step size that meets the accuracy requirements for numerical integration.

[0114] The above is a detailed description of the invention. Any modifications or equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method of calculating lateral displacement of a tunnel caused by a tunnel bottom heave resulting from excavation of a foundation pit, characterized by, The method comprises the following steps: Step 1: Take the center of the rectangular foundation pit ground surface as the coordinate axis origin, take z axis in the vertical direction, take x axis in the length direction of the foundation pit, and take y axis in the width direction of the foundation pit, calculate the lateral displacement of the soil at any depth of the enclosure structure caused by the uplift unloading of the pit bottom, and equivalent it to the enclosure structure displacement S according to the deformation coordination between the soil and the enclosure structure z (z), the lateral displacement is the displacement in the y axis direction; Step 2: According to the displacement S of the enclosure z (z) and the ratio η of the maximum displacement value S reached in the active state a , the cohesion exertion value is obtained, and the non-limiting active earth pressure p a is obtained based on the non-limiting active earth pressure theory, so as to obtain the horizontal unloading stress p1 at the corresponding depth of the enclosure due to the heave of the pit bottom, and finally obtain the additional stress σ y in the horizontal direction of the tunnel; Step 3: Additional stress σ in horizontal direction by tunnel y The load P(x) acting on the tunnel by the additional stress in horizontal direction is obtained, and the governing equation of the tunnel transverse displacement ω(x) is obtained according to the displacement coordination of the soil and the tunnel. The governing equation is expressed in matrix form, and the undetermined coefficient matrix A is calculated. Finally, the transverse displacement function of the tunnel is obtained, and the transverse displacement ω(x) of the tunnel is calculated.

2. The computational method of claim 1, wherein, In step 1, the lateral displacement of the soil at any depth of the enclosure is specifically as follows: According to the obtained bottom heave curve, the lateral displacement of the soil at any depth of the enclosure is calculated by an image source method, and the image source method is specifically as follows: Obtain the soil deformation S at any point Q(y, z) of the enclosure caused by the soil loss at any point P(y0, d) of the pit bottom y Then, integrate along the pit bottom width direction to obtain the lateral displacement S of the soil at any depth of the enclosure z (z): where B is the width of the excavation, d is the depth of the excavation, z r is the depth of the calculated point at the bottom of the excavation, r1 = [y 2 +(z-d) 2 ] 1 / 2 , r2 = [y 2 +(z+d) 2 ] 1 / 2 .

3. The computational method of claim 2, wherein, Depth z of the calculated point of the pit bottom r According to the pit bottom uplift curve: In the formula: S r is the amount of central point heave, S m is the amount of side wall heave.

4. The computational method of claim 3, wherein, The center point bulging amount S r And the foundation pit side wall bulging amount S m The calculation formula is: S r =Y1Y2S0 S m = Y1Y2S1 S0 = 0.732 Q (1 - μ 2 ) / E0 wherein Y1, Y2 are correction factors, Q is the total weight per unit thickness of the soil, Q = Bdγ, γ is the weight of the soil in the excavation range; μ is the Poisson's ratio of the soil; E0 is the resilient modulus of the soil, the empirical value of the resilient modulus of the soil E0 is (3-5)E s , E s is the compression modulus of the soil, S0 is the initial central point heave, S1 is the initial side wall heave of the foundation pit.

5. The computational method of claim 1, wherein, Step 2) In the formula, the tunnel horizontal direction additional stress σ y The calculation method is as follows: wherein: let the coordinates of an arbitrary point on the side of the foundation pit near the tunnel be (ξ, B / 2, z), take an arbitrary point (x1, L1, z0) on the tunnel axis, p1 be the horizontal unloading stress, L1 be the distance from the tunnel axis to the center of the foundation pit; B be the width of the foundation pit; z be the non-limiting active earth pressure p a corresponding to the calculated depth; z0 be the depth from the ground surface to the tunnel axis, and μ be the Poisson's ratio of the soil.

6. The computational method of claim 1, wherein, The calculation method of the horizontal unloading stress p1 is as follows: p1= K0y2- p a where: K0 is the coefficient of static lateral earth pressure, z is the calculated depth of the non-limiting active earth pressure p a γ is the unit weight of the soil, and p a is the non-limiting active earth pressure.

7. The computational method of claim 1, wherein, The non-limiting active earth pressure p a The calculation method is: where: γ is the soil unit weight, q0 is the surcharge load outside the pit; θ is the soil cohesion; c m is the internal friction angle. the cohesion exertion value is calculated as follows: wherein R f is the ratio of soil failure, is the internal friction angle of the soil, and K0is the coefficient of static lateral earth pressure.

8. The computational method of claim 1, wherein, The lateral displacement function of the tunnel is specifically as follows: ω(x) = T n (x) A T where: A T is the transpose of the pending coefficient matrix A, where D t is the ring width of the segment ring, N is the number of tunnel lining calculation rings affected by the foundation pit excavation, which is related to the influence range of the foundation pit excavation.

9. The computational method of claim 8, wherein, The matrix form is specifically as follows: ([K t ]+[K s ]){A} T ={P n} T where: [K t ] is the inter-tunnel ring stiffness matrix, [K s ] is the soil stiffness matrix, {P n} T represents the interaction effect of free soil displacement and tunnel lining ring. The control equation of the lateral displacement ω(x) of the tunnel is as follows: wherein: k t and k T are the inter-ring shear stiffness and the inter-ring tensile stiffness of the tunnel, respectively, k is the bedding coefficient of the soil, m is the number of the lining ring; P(x) is the load of the horizontal additional stress acting on the tunnel, P(x) = σ y D, D is the outer diameter of the shield tunnel lining, j is the proportionality coefficient of the rigid body rotation effect; ξ i is each element in the undetermined coefficient matrix A, that is, the coefficient of the polynomial of the tunnel transverse displacement function, A = (a1, a2, a3, …, a n ) T .

10. A system for calculating lateral displacement of a tunnel caused by a tunnel bottom heave resulting from excavation of a foundation pit, characterized by, A computer program product for implementing the calculation method according to any one of claims 1-9.

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