Method and system for calculating lateral displacement of adjacent tunnel caused by pit bottom upheaval caused by foundation pit excavation

Abstract

The invention discloses a method and a system for calculating lateral displacement of an adjacent tunnel caused by pit bottom upheaval due to excavation of a foundation pit, and the method comprises the following steps: firstly, calculating the lateral displacement of a soil body at any depth at a retaining structure caused by unloading of the pit bottom upheaval, and enabling the lateral displacement to be equivalent to the displacement Sz (z) of the retaining structure according to deformation coordination between the soil body and the retaining structure; then, according to the ratio eta of the displacement Sz (z) of the retaining structure to the maximum displacement value Sa in the active state, a cohesive force exerting value # imgabs0 # is obtained, non-limit active soil pressure pa is obtained on the basis of the non-limit active soil pressure theory, and therefore horizontal unloading stress p1 is obtained, and finally additional stress sigma y in the horizontal direction of the tunnel is obtained; and finally, obtaining a load P (x) through the additional stress sigma y in the horizontal direction of the tunnel, obtaining a control equation of the transverse displacement omega (x) of the tunnel according to the coordination of the soil body and the tunnel displacement, and then expressing the control equation as a matrix form so as to calculate the transverse displacement omega (x) of the tunnel. Through the calculation method, the influence of foundation pit construction on the tunnel structure is evaluated more accurately in practice, and guiding significance is achieved for foundation pit design and construction.

Description

Technical Field

[0001] The invention belongs to the field of underground engineering, and in particular relates to a method and system for calculating lateral displacement of an adjacent tunnel caused by pit bottom uplift due to foundation pit excavation. Background Art

[0002] The excavation of foundation pit will cause disturbance of nearby soil, among which the bottom of foundation pit will produce upward bulge. This displacement will cause displacement of surrounding soil and shield tunnel.

[0003] At present, domestic and foreign scholars have conducted little research on the lateral displacement of adjacent tunnels caused by foundation pit uplift, and mainly focus on the vertical displacement of the underlying or side tunnels. Chen Yu et al. (Chen Yu, Li Yongsheng. Calculation method of underlying tunnel uplift caused by foundation pit excavation unloading [J]. Journal of Underground Space and Engineering, 2005, (01): 91-94.) used a theoretical calculation method, treating the pit bottom load as a uniformly distributed load, whose size is equivalent to the gravity strength of the excavated soil, and whose direction is upward. The Mindlin solution was then used to calculate the vertical displacement caused by its action on the underlying tunnel. Zhang Zhiguo et al. (Zhang Zhiguo, Zhang Mengxi, Wang Weidong. Two-stage analysis method for the effect 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 of the pit bottom as the weight of the original overlying soil, and calculated the vertical displacement deformation of the adjacent tunnel by combining the unloading of the pit wall with the Mindlin fundamental solution. 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 of the pit bottom as 100%, and did not consider the unloading of the pit wall, and calculated the horizontal and vertical displacements of the adjacent tunnel under this effect. Xu Wenda et al. (Xu Wenda, Jiang Jun. Calculation method of longitudinal deformation of adjacent subway tunnels caused by foundation pit excavation [J]. Railway Construction, 2018, 58(09): 63-67.) took into account the plastic deformation of the soil in the calculation, introduced the initial residual stress coefficient when calculating the pit bottom unloading, reduced the unloading, and considered the friction between the retaining structure and the soil. Based on the calculated released stress, the vertical displacement of the adjacent tunnel was calculated by the Mindlin solution.

[0004] The existing calculation of the lateral deformation of the tunnel due to the unloading of the pit bottom uplift mainly focuses on the vertical displacement of the underlying or adjacent tunnels, and rarely considers the influence of the pit bottom uplift on the lateral displacement of the adjacent tunnels. In fact, the uplift of the pit will cause the surrounding soil to also displace in the horizontal direction, and this part of the displacement will cause a part of the lateral displacement of the adjacent tunnels. Therefore, it is necessary to study the calculation method of the lateral displacement of the adjacent tunnel caused by the pit bottom uplift. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention proposes a method and system for calculating the lateral displacement of adjacent tunnels caused by pit bottom heave, filling the gap in the existing method for calculating the horizontal displacement of adjacent tunnels that ignores the influence of pit bottom heave.

[0006] The calculation method of the lateral displacement of the adjacent tunnel caused by the uplift of the pit bottom 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 along the vertical direction, the x axis along the length of the foundation pit, and the y axis along the width of the foundation pit, calculate the lateral displacement of the soil at any depth at the retaining structure caused by the unloading of the pit bottom, and equate it to the displacement of the retaining structure S according to the deformation coordination between the soil and the retaining structure z (z), the lateral displacement is the displacement in the y-axis direction;

[0008] Step 2: According to the displacement S of the enclosure structure z (z) and the maximum displacement value S in the active state a The ratio η of the cohesion is obtained Based on the non-limit active earth pressure theory, the non-limit active earth pressure p is obtained. a , thus obtaining the horizontal unloading stress p1 generated by the uplift of the pit bottom at the corresponding depth calculated by the retaining structure, and finally obtaining the additional stress σ in the horizontal direction of the tunnel y ;

[0009] Step 3: Add stress σ in the horizontal direction through the tunnel y The load P(x) of the horizontal additional stress acting on the tunnel is obtained, and the control 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 unknown coefficient matrix 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:

[0011] According to the obtained pit bottom uplift curve, the lateral displacement of the soil at any depth acting on the retaining structure is calculated by the image source method. The image source method is specifically as follows:

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

[0013]

[0014] Where: B is the width of the foundation pit, d is the depth of the foundation pit, z r is 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 According to the pit bottom uplift curve, we can get:

[0016]

[0017] Where: S r is the center point uplift, S m It is the uplift of the side wall of the foundation pit.

[0018] Furthermore, the center point uplift S r and the uplift of the foundation pit side wall S m The calculation formula is:

[0019] S r =Y1Y2S0

[0020] S m =Y1Y2S1

[0021] S0=0.732Q(1-μ 2 ) / E0

[0022]

[0023] Among them, Y1 and Y2 are correction coefficients. Q is the total weight of soil per unit thickness, Q = Bdγ, γ is the weight of soil within the excavation range; μ is the Poisson's ratio of soil; E0 is the soil rebound modulus, and the empirical value of the soil rebound modulus E0 is (3-5)E s , E s is the soil compression modulus, S0 is the initial center point uplift, and S1 is the initial pit side wall uplift.

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

[0025]

[0026] Where: Let the coordinates of any point on the foundation pit wall close to the tunnel side be (ξ, B / 2, z), take any point on the tunnel axis (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-limiting active earth pressure p a The corresponding calculation depth; z0 is the depth from the surface to the tunnel axis, μ is the Poisson's ratio of the soil,

[0027]

[0028] Furthermore, the calculation method of the horizontal unloading stress p1 is:

[0029] p1=K0γz-p a

[0030] Where: K0 is the static lateral earth pressure coefficient, z is the non-limiting active earth pressure p a The calculation depth of the soil is γ, p is the soil density, a is the non-limit active earth pressure.

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

[0032]

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

[0034] The cohesion exertion value The calculation method is:

[0035]

[0036] Where: R f is the soil damage ratio, is the internal friction angle of soil, and K0 is the static lateral earth pressure coefficient.

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

[0038] ω(x)=T n (x)A T

[0039] Where: A T is the transpose of the unknown coefficient matrix A,

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

[0041] Furthermore, the matrix form is specifically:

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

[0043] Where: [K t ] is the tunnel ring stiffness matrix, [K s ] is the soil stiffness matrix, {P n} T Represents the mutual effect of free soil displacement and tunnel lining ring;

[0044] The control equation of the tunnel lateral displacement ω(x) is:

[0045]

[0046] Where: k t and k T are the inter-ring shear stiffness and inter-ring tensile stiffness of the tunnel, k is the soil base coefficient, and 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 proportional coefficient of the rigid body rotation effect; ξ i are the elements in the undetermined coefficient matrix A, i.e., 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 uplift of a pit bottom due to foundation pit excavation, used to implement any of the calculation methods described above.

[0048] Beneficial effects:

[0049] The present invention provides a method for calculating the lateral displacement of an adjacent tunnel caused by the uplift of a pit bottom due to foundation pit excavation, which fills the gap of ignoring the influence of the uplift of the pit bottom in the existing method for calculating the horizontal displacement of an adjacent tunnel, making the current relevant calculation method more scientific and comprehensive, and being able to more accurately evaluate the influence of foundation pit construction on the tunnel structure in practice, which has guiding significance for foundation pit design and construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The accompanying drawings described herein further explain the present invention and constitute a part of the present invention. The illustrative examples of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations of the present invention. In the accompanying drawings:

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

[0052] Figure 2 Schematic diagram of a calculation model for foundation pit uplift 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 axial view;

[0053] Figure 3 The present invention is a flow chart of a method for calculating the lateral displacement of an adjacent tunnel due to pit bottom uplift caused by foundation pit excavation. DETAILED DESCRIPTION

[0054] The present invention will be described in detail below with reference to the accompanying drawings, and the purpose and effects of the present invention will become more apparent. It should be understood that the accompanying drawings are only used to explain the present invention and are not used 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 causes the bottom of the pit to bulge, which will cause lateral displacement of the soil at the retaining structure, which will cause deformation of the adjacent existing shield tunnel.

[0056] Step 1: Take the center of the rectangular foundation pit surface as the origin of the coordinate axis, take the z axis along the vertical direction, take the x axis along the length direction of the foundation pit, and take the y axis along the width direction 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 uplift. z (z);

[0057] The pit bottom bulge is parabolic, and the pit bottom bulge curve is:

[0058]

[0059] Where z r 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, S r is the center point uplift, S m is the uplift of the foundation pit side wall

[0060] The center point uplift S r and the uplift of the foundation pit side wall 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] Among them, Y1 and Y2 are correction coefficients. B is the width of the foundation pit, d is the depth of the foundation pit, that is, the initial depth of the foundation pit when no uplift occurs; Q is the total weight of the soil per unit thickness, Q = Bdγ; γ is the weight of the soil within the excavation range; μ is the Poisson's ratio of the soil; E0 is the soil rebound modulus, and the empirical value of the soil rebound modulus E0 is (3~5)E s , E s is the soil compression modulus, S0 is the initial center point uplift, S1 is the initial foundation pit side wall uplift;

[0066] After obtaining the pit bottom uplift curve, the image source method is used to calculate the lateral displacement of the soil at any depth at the retaining structure. The calculation model is shown in the attached Figure 1 ;

[0067] Image source method:

[0068] The total displacement component along the y-axis generated by the gap with a radius of a at any point P (y0, d) at the bottom of the pit at any point Q (y, z) on the side wall of the foundation pit, i.e., the retaining structure, is:

[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) on 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 direction 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 surrounding structure, the lateral displacement S of the soil at any depth at the surrounding structure is calculated as z (z) is equivalent to the displacement of the retaining structure for subsequent unloading calculations.

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

[0078] Based on the non-limit active earth pressure theory, the relationship between the deformation of the retaining structure and the earth pressure is as follows:

[0079]

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

[0081] The calculation method is as follows:

[0082]

[0083] Where: R f is the soil damage ratio, η is the displacement of the surrounding structure S z (z) and the maximum displacement value S in the active state a The ratio of K0 is the static lateral earth pressure coefficient; is the internal friction angle of soil.

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

[0085] p1=K0γz-p a .

[0086] Assume that the coordinates of any point on the pit wall near one side of the tunnel are (ξ, B / 2, z), and the calculation model is shown in the attached Figure 2 ; Horizontal additional stress σ at any point (x1, L1, z0) on the tunnel axis y Solved using Mindlin's formula.

[0087]

[0088] in:

[0089]

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

[0091] Step 3: Calculation of tunnel lateral displacement

[0092] Introducing a tunnel rotation misalignment calculation model;

[0093] Let the lateral displacement of the tunnel be ω(x). According to the coordination between soil and tunnel displacement, the control equation of the lateral displacement of the tunnel ω(x) is as follows:

[0094]

[0095] in:

[0096] ω(x)=T n (x)A T

[0097]

[0098] Where: k t and k T are the inter-ring shear stiffness and inter-ring tensile stiffness of the tunnel, k is the soil base coefficient, and m is the number of the lining ring; N is the number of tunnel lining calculation rings affected by the foundation pit excavation, and its value is related to the influence range of the foundation pit excavation; 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; k t and k T They are the inter-ring shear stiffness and inter-ring tensile stiffness of the tunnel, respectively. The value selection method can refer to the research of Guo Le et al. (Guo Le, Yang Xin'an, Qiu Yan. Longitudinal non-homogeneous equivalent continuous model of shield segment lining [J]. Urban Rail Transit Research, 2017, 20(4): 17–22.).

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

[0100] k is the soil base coefficient, 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 is the equivalent bending stiffness of the tunnel, which can be determined according to the following formula:

[0101]

[0102] In the formula, E c is the elastic modulus of the segment; n is the number of bolts in the tunnel axial direction, i.e., the x-axis direction; K b is the average linear stiffness of the joint bolts; A sis the cross-sectional area 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. The value method 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 control equation of the tunnel lateral displacement ω(x) is expressed in matrix form:

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

[0104] Where: [K t ] is the tunnel ring stiffness matrix,

[0105]

[0106] [K s ] is the soil stiffness matrix,

[0107]

[0108] {P n} T Represents the mutual effect of free soil displacement and tunnel lining ring:

[0109]

[0110] The undetermined coefficient matrix A is calculated from the matrix form of the control equation;

[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 foundation pit uplift, the present invention uses the image source method in step 1 to calculate the soil displacement acting on the retaining structure position to equal the retaining structure displacement, and then calculates the effect and displacement on the adjacent tunnel. This solves the problem that the existing method cannot consider the effect of soil uplift on the lateral displacement of the adjacent tunnel.

[0113] The calculation method of the present invention can realize numerical calculation through Matlab programming. The composite Simpson quadrature formula is used in the integral calculation, and the integral step length that meets the accuracy requirement is used for numerical integration.

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

Claims

1. A method for calculating the lateral displacement of adjacent tunnels caused by the uplift of the pit bottom due to foundation pit excavation, characterized in that: The following steps are involved: Step 1: Take the center of the rectangular foundation pit as the origin of the coordinate axis, take the z axis along the vertical direction, the x axis along the length of the foundation pit, and the y axis along the width of the foundation pit, calculate the lateral displacement of the soil at any depth at the retaining structure caused by the unloading of the pit bottom, and equate it to the displacement of the retaining structure S according to the deformation coordination between the soil and the retaining structure z (z), the lateral displacement is the displacement in the y-axis direction; Step 2: According to the displacement S of the enclosure structure z (z) and the maximum displacement value S in the active state a The ratio η of the cohesion is obtained Based on the non-limit active earth pressure theory, the non-limit active earth pressure p is obtained. a , thus obtaining the horizontal unloading stress p1 generated by the uplift of the pit bottom at the corresponding depth calculated by the retaining structure, and finally obtaining the additional stress σ in the horizontal direction of the tunnel y ; Step 3: Add stress σ in the horizontal direction through the tunnel y The load P(x) of the horizontal additional stress acting on the tunnel is obtained, and the control 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 unknown coefficient matrix 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.

2. The calculation method according to claim 1, characterized in that: In step 1, the lateral displacement of the soil at any depth at the retaining structure is specifically: According to the obtained pit bottom uplift curve, the lateral displacement of the soil at any depth acting on the retaining structure is calculated by the image source method. The image source method is specifically as follows: Obtain the soil deformation S at any point Q(y,z) on the retaining structure caused by soil loss at any point P(y0,d) at the bottom of the pit y Then, the lateral displacement S of the soil at any depth at the retaining structure is obtained by integrating along the width direction of the pit bottom. z (z): Where: B is the width of the foundation pit, d is the depth of the foundation pit, z r is 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 .

3. The calculation method according to claim 2, characterized in that: The depth z of the calculated point at the bottom of the foundation pit r According to the pit bottom uplift curve, we can get: Where: S r is the center point uplift, S m It is the uplift of the side wall of the foundation pit.

4. The calculation method according to claim 3, characterized in that: The center point uplift S r and the uplift of the foundation pit side wall S m The calculation formula is: S r =Y1Y2S0 S m =Y1Y2S1 S0=0.732Q(1-μ 2 ) / E0 Among them, Y1 and Y2 are correction coefficients. Q is the total weight of soil per unit thickness, Q = Bdγ, γ is the weight of soil within the excavation range; μ is the Poisson's ratio of soil; E0 is the soil rebound modulus, and the empirical value of the soil rebound modulus E0 is (3-5)E s , E s is the soil compression modulus, S0 is the initial center point uplift, and S1 is the initial pit side wall uplift.

5. The calculation method according to claim 1, characterized in that: Step 2) The additional stress σ in the horizontal direction of the tunnel is y The calculation method is: Where: Let the coordinates of any point on the foundation pit wall close to the tunnel side be (ξ, B / 2, z), take any point on the tunnel axis (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-limiting active earth pressure p a The corresponding calculation depth; z0 is the depth from the surface to the tunnel axis, μ is the Poisson's ratio of the soil, 6. The calculation method according to claim 1, characterized in that: The calculation method of the horizontal unloading stress p1 is: p1=K0γz-p a Where: K0 is the static lateral earth pressure coefficient, z is the non-limiting active earth pressure p a The calculation depth of the soil is γ, p is the soil density, a is the non-limit active earth pressure.

7. The calculation method according to claim 1, characterized in that: The non-limit active earth pressure p a The calculation method is: Where: γ is the soil weight, q0 is the load outside the pit; θ is the soil cohesion; c m is the value of the internal friction angle; The cohesion exertion value The calculation method is: Where: R f is the soil damage ratio, is the internal friction angle of soil, and K0 is the static lateral earth pressure coefficient.

8. The calculation method according to claim 1, characterized in that: The lateral displacement function of the tunnel is specifically: ω(x)=T n (x)A T Where: A T is the transpose of the unknown coefficient matrix A, Where D t is the ring width of the segment ring, N is the number of calculated rings of the tunnel lining affected by the foundation pit excavation, and its value is related to the influence range of the foundation pit excavation.

9. The calculation method according to claim 8, characterized in that: The matrix form is specifically: ([K t ]+[K s ]){A} T ={P n } T Where: [K t ] is the tunnel ring stiffness matrix, [K s ] is the soil stiffness matrix, {P n } T Represents the mutual effect of free soil displacement and tunnel lining ring; The control equation of the tunnel lateral displacement ω(x) is: Where: k t and k T are the inter-ring shear stiffness and inter-ring tensile stiffness of the tunnel, k is the soil base coefficient, and 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 proportional coefficient of the rigid body rotation effect; ξ i are the elements in the undetermined coefficient matrix A, i.e., the coefficients of the tunnel lateral displacement function polynomial, A = (a1, a2, a3, ..., a n ) T .

10. A calculation system for the lateral displacement of adjacent tunnels caused by the uplift of the pit bottom due to foundation pit excavation, characterized in that: Used to implement the calculation method as described in any one of claims 1 to 9.

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