Building envelope displacement calculation method and system considering pit bottom upheaval caused by foundation pit excavation

Abstract

The invention discloses an enclosure structure displacement calculation method and system considering pit bottom upheaval caused by foundation pit excavation, and the calculation steps are as follows: taking the cross section of a foundation pit, taking the projection of the center of the foundation pit on the earth surface as the original point, taking the width direction of the foundation pit as the y axis, and taking the vertical direction as the z axis, and establishing a pit bottom upheaval curve function; based on an image source method and a pit bottom upheaval curve function, differentiating the pit bottom upheaval and enabling the differentiated pit bottom upheaval to be equivalent to a circular pore, and deducing to obtain soil body transverse displacement of any point on the enclosure structure; the method comprises the following steps of: applying a stress balance equation based on a rod system finite element method under the action of transverse displacement disturbance of a soil body to obtain a displacement vector of an end node of each beam unit, and obtaining a displacement field function in each beam unit through the vector; based on the displacement field function, obtaining an overall deformation curve of the enclosure structure considering the pit bottom upheaval, so as to obtain the displacement of any point on the enclosure structure; in the deep foundation pit, the method can accurately reflect the influence of the pit bottom upheaval on the displacement of the surrounding soil body and the enclosure structure.

Description

Technical Field

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

[0002] There has been a great deal of research on the calculation of the deformation of the retaining structure. Yang Yuwen et al. and Yang Zhiyong et al. used the limit equilibrium method when calculating the displacement of the retaining structure ([1] Yang Yuwen, Yuan Jianxin. Limit equilibrium analysis of soil nail support in deep foundation pit excavation [J]. Engineering Survey, 1998, (06): 11-13+17; [2] Yang Zhiyong, Pei Jingyou. Basic methods for strength and deformation analysis and calculation of foundation pit support structure [J]. Building Safety, 2007, (03): 48-49.). The calculation process of this method is simple and can obtain the stress characteristics of the retaining structure, but it cannot calculate the deformation of the structure. Lai Pengcheng et al. used the elastic foundation beam method to calculate the deformation and bending moment of the pile anchor support of a deep foundation pit and carried out deformation control design ([3] Lai Pengcheng. Application of the elastic foundation beam “m” method in deep foundation pit support structure [J]. China Water Transport (Theoretical Edition), 2006, 11: 61-63.). Liu Shehong et al. combined the finite element method of the rod system with the weighted residual method to solve the elastic foundation beam model and compared the results with numerical calculations. The results showed that both methods could obtain reasonable calculation results ([4] Liu Shehong, Yuan Juyun, Zhao Xin. Application of finite element method of elastic foundation beam in foundation pit support structure [J]. Industrial Construction, 2014, 44(S1): 840-846.). Yang Guanghua summarized the advantages and disadvantages of classical methods, elastic foundation beam method and other methods for calculating the deformation of retaining structure, and proposed an incremental calculation method that considers the construction process, takes into account the unsupported exposed state of the support structure during the excavation process, and successfully applied it in actual engineering ([5] Yang Guanghua. Practical calculation method and application of deep foundation pit support structure [J]. Rock and Soil Mechanics, 2004, (12): 1885-1896+1902). Based on the theory of elastic foundation beams, Lian Jing introduced the influencing factors of actual excavation conditions of foundation pits and proposed an incremental calculation method that can simulate the entire construction process. It fully considered the synergistic mechanism of soil, support piles and support system in the process of gradual support (or anchoring) and layer-by-layer excavation ([6] Lian Jing. Research on calculation model and method of foundation pit pile support structure based on elastic support method [D]. Southwest Jiaotong University, 2014.).

[0003] Through analysis, it was found that among existing calculation methods, the elastic foundation beam method considering incremental changes is more consistent with actual working conditions and has greater advantages. However, none of the above calculation methods consider the impact of pit bottom heave. In fact, pit heave causes horizontal displacement of the surrounding soil, which in turn causes lateral displacement of the retaining structure. Therefore, it is necessary to quantify the displacement of the retaining structure caused by pit bottom heave and improve the existing methods for calculating retaining structure deformation. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a method and system for calculating the displacement of retaining structures that considers the heave of the pit bottom caused by excavation. The calculated values ​​considering the heave more accurately reflect the actual situation. In deep pits, especially those with a large width, this invention can more accurately reflect the impact of the pit bottom heave on the displacement of the surrounding soil and retaining structure. This provides a method that is more in line with actual working conditions for the deformation calculation of retaining structures in underground engineering, making the distribution pattern of the calculation results closer to reality, improving the accuracy and reliability of the calculation, and having important guiding significance for engineering design.

[0005] The technical solution of the present invention is as follows:

[0006] A method for calculating the displacement of retaining structures considering the heave of the pit bottom caused by excavation, comprising the following steps:

[0007] S1. Take the cross-section of the foundation pit, with the projection of the center of the foundation pit onto the ground surface as the origin, the y-axis along the width of the foundation pit and the z-axis in the vertical direction. Based on the stress solution theory that the excavation section in the elastic half-space is a semi-circle, establish the bottom heave curve function.

[0008] S2. Based on the image source method and the pit bottom heave curve function, the pit bottom heave is differentiated and equivalent to a circular pore. The component of the total displacement along the y-axis generated by any point on the bottom of the pit and any point on the retaining structure is derived. Then, the lateral displacement of the soil at any point on the retaining structure is obtained by integrating along the width direction of the pit bottom. The lateral displacement is the displacement along the y-axis direction.

[0009] S3. The retaining structure is considered as an elastic foundation beam, which is vertically divided into several beam elements. The support of the retaining structure is simplified to the spring support of the retaining structure, and the passive zone soil below the bottom of the foundation pit is simplified to an equivalent stiffness soil spring. The water and soil pressure load is applied to the beam element. The overall stiffness matrix of the foundation beam, the support stiffness matrix, the soil spring stiffness matrix and the nodal load array are obtained by using the finite element method of the rod system. The force balance equation of the retaining structure is constructed to obtain the displacement vector of the end nodes of each beam element. Among them, the force generated by the lateral displacement of the soil at any point on the retaining structure is obtained by multiplying the lateral displacement of the soil at the corresponding position by the linear stiffness of the soil spring. This force is directly added to the nodal load array.

[0010] Based on the displacement vectors of the end nodes of each beam element, the displacement field function inside each beam element is obtained. By connecting the displacement field functions of each beam element end to end, the deformation curve of the entire retaining structure considering the bottom heave of the pit is obtained, thus obtaining the displacement of any point on the retaining structure.

[0011] Furthermore, in S1, the specific function for the bulge curve at the bottom of the pit is:

[0012]

[0013] Among them, z r S is the depth of the calculation point for the bottom heave of the pit, B is the width of the pit, and d is the depth of the pit; r S represents the maximum uplift of the foundation pit. m This refers to the uplift at the boundary of the foundation pit.

[0014] Furthermore, the maximum heave of the foundation pit is obtained by combining the width correction coefficient, the depth correction coefficient, and the heave at the initial center point of the foundation pit, and the heave at the boundary of the foundation pit is obtained by combining the width correction coefficient, the depth correction coefficient, and the heave at the initial sidewall of the foundation pit.

[0015] Furthermore, in S2, the component of the total displacement along the y-axis generated at any point on the retaining structure from any point on the bottom of the foundation pit is specifically as follows:

[0016] Based on the image source method, taking any point P(y0,z0) on the bottom of the foundation pit and any point Q1(y,z) on the retaining structure, the formula for the component of the total displacement along the y-axis is:

[0017]

[0018] Among them, S y1 Let S be the y-axis component of the displacement caused by a gap of radius a at any point P(y0,z0) on the bottom of the foundation pit at any point Q1(y,z) on the retaining structure. y2 Let P'(y0,-z0) be any point P(y0,z0) at the bottom of the foundation pit and mirror it along the y-axis. Then, let r1 be the displacement along the y-axis component of any point Q1(y,z) on the retaining structure caused by a gap of radius a at point P'(y0,-z0); r2 is the distance between point P and point Q1, and r2 is the distance between point P' and point Q1. d represents the depth of the foundation pit.

[0019] Furthermore, in S2, the lateral displacement of the soil at any point on the retaining structure is specifically as follows:

[0020]

[0021] Among them, S z (z) represents the lateral displacement of the soil at any point on the retaining structure.

[0022] Furthermore, the force balance equation is as follows:

[0023] [P]=([K]+[K R ]+[K H ])·[S T ]

[0024] In the formula, [P] represents the nodal load array generated by the horizontal load acting on the beam, which is composed of the nodal load array P of each beam element. e The assembly yields [K], which is the overall stiffness matrix of the foundation beam, derived from the stiffness matrix K of each beam element. e Assembled;

[0025] [K R [This is the support stiffness matrix, consisting of the stiffness k of each support.] R Assembled; [K] H [ ] represents the soil spring stiffness matrix, derived from the soil spring stiffness k at each depth. H Assembled; [S T [ ] represents the displacement vector of each beam element's end nodes, derived from the displacement q of each beam element's nodes. e It was assembled.

[0026] Furthermore, the process of obtaining the displacement field function inside each beam element based on the displacement vector of each beam element end node is as follows:

[0027] v(x)=N(ξ)q e

[0028] Where v(x) is the displacement field function, q e Let N(ξ) be the nodal displacement of each beam element, and N(ξ) be the element shape function, N(ξ) = [1-3ξ]. 2 +2ξ 3 l(ξ-2ξ 2 +ξ 3 )3ξ 2 -2ξ 3 l(ξ 3 -ξ 2 )], x is the distance from the calculation point to the end of the beam element, and l is the length of the beam element.

[0029] Furthermore, the retaining structure is specifically either a retaining wall or retaining piles.

[0030] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for calculating the displacement of a retaining structure considering the heave of the pit bottom caused by excavation, as described in any one of the claims.

[0031] A system for calculating the displacement of retaining structures considering the heave of the pit bottom caused by excavation, the system comprising:

[0032] One or more processors;

[0033] Memory, used to store one or more programs;

[0034] When the one or more programs are executed by the one or more processors, the one or more processors implement any of the methods described above for calculating the displacement of the retaining structure considering the bottom heave caused by foundation pit excavation.

[0035] Beneficial effects:

[0036] Compared to calculation models that only consider horizontal soil and water pressure, this invention improves the theoretical level by introducing the effect of pit bottom heave to correct the calculation results. Specifically, it calculates the pit bottom heave curve caused by excavation and the soil displacement at the retaining structure due to the effect of pit bottom heave. Based on the Winkler foundation model, it derives the displacement of the retaining structure caused by soil displacement and solves the deformation calculation method using the finite element method. The calculation results are in better agreement with actual measurements, especially in the area at and below the bottom of the pit. By considering the heave effect and superimposing the results of existing calculation methods, the displacement of the retaining structure caused by pit bottom heave is quantified, thus improving existing retaining structure calculation methods. The calculation values ​​considering heave in this invention can more realistically reflect the actual situation. In deep pits, especially those with large widths, it can more accurately reflect the impact of pit bottom heave on the displacement of the surrounding soil and retaining structure. This provides a method that is more in line with actual working conditions for the deformation calculation of retaining structures in underground engineering, making the distribution law of the calculation results closer to reality, improving the accuracy and reliability of the calculation, and has important guiding significance for engineering design. Attached Figure Description

[0037] The accompanying drawings, which serve to further explain the invention and constitute a part of this invention, illustrate exemplary examples and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0038] Figure 1 A schematic diagram showing the displacement of the retaining structure caused by the heave of the pit bottom.

[0039] Figure 2 A model for calculating soil displacement using the image source method;

[0040] Figure 3 This is a schematic diagram of the image source method mirroring process;

[0041] Figure 4 This is the Winkler foundation pile-soil interaction model;

[0042] Figure 5 This is to compare the measured and calculated displacement results of the enclosure structure. Detailed Implementation

[0043] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The purpose and effects of the present invention will become clearer. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0044] The following examples use names for the enclosure structure, including but not limited to enclosure wall, enclosure pile, and diaphragm wall;

[0045] The displacement calculation method for the retaining structure considering the bottom heave of the pit in this embodiment specifically includes the following steps:

[0046] Step 1: Analyze the model

[0047] To analyze its impact on the lateral displacement of the adjacent diaphragm wall, this invention, based on the image source method, treats the heaving deformation (soil relaxation caused by unloading) as pores. The surrounding soil will inevitably displace towards these pores, leading to the following derivation: Figure 1 As shown, the raised bottom of the pit is divided into units and equivalent to circular pores. The surrounding soil will displace towards point P. The soil Q1 at a certain depth of the diaphragm wall will have a displacement component to the left. The diaphragm wall at this location will be subjected to a component force into the pit, which will then cause displacement. Take the cross-section of the pit, with the projection of the pit center onto the ground surface as the origin, the y-axis along the width of the pit, and the z-axis in the vertical direction.

[0048] Step 2: Calculate the bottom heave curve

[0049] Based on the calculation method proposed by Wei Gang (Wei Gang, Guo Binglai, Wang Zhe, et al. Calculation of deformation of the underlying shield tunnel caused by unloading of the foundation pit considering the excavation width [J]. Chinese Journal of Rock Mechanics and Engineering, 2023, 42: 1019-1030) and other scholars, which is based on the stress solution of the excavation section being a semicircle in an elastic half-space, the curve expression of the bottom heave is as follows:

[0050]

[0051] Where B is the width of the excavation pit, d is the depth of the excavation pit; S r S represents the maximum uplift of the foundation pit. m The uplift at the boundary of the foundation pit can be calculated using the stress solution based on a rectangular excavation section within an elastic half-space. The calculation method is as follows:

[0052] S r =Y1Y2S0

[0053] S m =Y1Y2S1

[0054] S0=0.732Q(1-μ2 ) / E0

[0055]

[0056] Where S0 is the initial center point heave, S1 is the initial pit sidewall heave, and Y1 and Y2 are width and depth correction coefficients. Q is the total weight per unit thickness of soil, Q = Bdγ; γ is the weight of 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 in soft soil areas is (3~5)E s E s For non-uniform layered soils, the equivalent confined compression modulus E can be obtained by weighting the thickness of each soil layer within a depth range of 3.16R. s .

[0057] Step 3: Calculate the horizontal displacement of the soil at the retaining structure using the image source method.

[0058] The derivation is based on the image source method, such as Figure 2 As shown, the displacement along the y-axis produced by the gap of radius a at point P(y0,z0) at point Q1(y,z) on the axis of the enclosure structure is:

[0059]

[0060] in,

[0061] r1 = [y 2 +(zd) 2 ] 1 / 2

[0062] In the formula: r1 is the distance between point P and point Q1.

[0063] The above formula is based on the condition of a full space, while in reality it is a half-space volume. Therefore, the point P(y0,z0) is mirrored as P'(y0,-z0), as follows. Figure 3 As shown, the displacement along the y-axis produced by P'(y0,-z0) at point Q1(y,z) is:

[0064]

[0065] in,

[0066] r2=[y 2 +(z+d) 2 ] 1 / 2

[0067] In the process of transforming into a half-space problem, shear strain will occur on the ground surface. Since this paper assumes that the soil is not under compression, it is assumed that the additional shear stress field does not affect the deformation of the soil. Therefore, the total displacement along the y-axis of the gap of radius a at point P(y0,z0) at any point Q1(y,z) is:

[0068]

[0069] Based on the principle of area equivalence, the bulge deformation at the bottom of the pit is divided into n small rectangles. The area of ​​each rectangle is converted into a circle, and the equivalent radius is:

[0070]

[0071] After obtaining the soil deformation at any point along the diaphragm wall caused by soil loss at any point at the bottom of the pit, integrating along the width of the pit bottom will yield the lateral displacement of the soil at any point along the diaphragm wall.

[0072]

[0073] Step 4: Calculation of retaining structure displacement caused by soil displacement based on the bar-system finite element method

[0074] To solve for the deformation of the retaining structure, the diaphragm wall is considered as an elastic foundation beam, vertically divided into several beam elements. The support of the diaphragm wall can be simplified as the spring supports of the retaining structure. The passive zone soil below the bottom of the foundation pit is simplified as an equivalent stiffness soil spring. Then, loads such as water and soil pressure are applied to the beam. For solving this model, the finite element method of the rod system is generally used. By simplification, the overall stiffness matrix of the foundation beam, the support stiffness matrix, the soil spring stiffness matrix, and the nodal load matrix can be obtained. Thus, the force balance equation of the retaining structure can be obtained as follows:

[0075] [P]=([K]+[K R ]+[K H ])·[S T ]

[0076] In the formula, [P] represents the nodal load array generated by the horizontal load acting on the beam, which is composed of the nodal load array P of each beam element. e The assembly yields [K], which is the overall stiffness matrix of the foundation beam, derived from the stiffness matrix K of each beam element. e Assembled; [K] R [This is the support stiffness matrix, consisting of the stiffness k of each support.] R Assembled; [K] H [ ] represents the soil spring stiffness matrix, derived from the soil spring stiffness k at each depth. H Assembled; [S T [ ] represents the displacement vector of each beam element's end nodes, derived from the displacement q of each element's nodes. eThe assembly is complete. This step is a relatively basic part of the finite element method and structural mechanics, and it is also described in many documents (Song Gonghe, Wu Minghao. MATLAB programming algorithm for finite element method of deep foundation pit support structure bar system [J]. Construction Engineering, 2010, 32(04):339-342.) or specifications, so it will not be repeated here.

[0077] In this process, the force exerted on the diaphragm wall by the soil deformation caused by the heave at the bottom of the pit in step two must be considered (see schematic diagram). Figure 4 As shown), first calculate the soil displacement at each node of the diaphragm wall using the formula derived in step 3, and then compare it with the corresponding soil spring stiffness k. H Multiplying these gives the force exerted by the soil displacement on the diaphragm wall. Where:

[0078] k H =m(z-h0)b0

[0079] z is the depth of the calculation point from the ground; h0 is the excavation depth of the foundation pit; m is the proportional coefficient of the horizontal reaction force of the soil, which is taken according to the specification; b0 is the calculation width of the diaphragm wall unit.

[0080] By directly applying the forces at each location to the nodal load array [P], the displacement of the diaphragm wall caused by the soil displacement at the diaphragm wall due to the bottom heave can be taken into account.

[0081] Therefore, the final deformation of the diaphragm wall should be expressed as:

[0082] [S T ]=[P]·([K]+[K R ]+[K H ]) -1

[0083] Solving the above matrix equations yields the displacements [S] of the end nodes of each beam element. T ].

[0084] The displacement field function v(x) inside each beam element can be obtained by the following formula, where x is the distance from the calculation point to the end of the left beam element.

[0085] v(x)=N(ξ)q e

[0086] Where N(ξ) is the element shape function, expressed as follows:

[0087] N(ξ)=[1-3ξ 2 +2ξ 3 l(ξ-2ξ 2 +ξ 3 )3ξ 2 -2ξ 3 l(ξ 3 -ξ2 )]

[0088] in:

[0089]

[0090] At this point, by connecting the displacement field functions v(x) of each unit end to end, we obtain the overall deformation curve of the retaining structure considering the bottom heave of the pit. Through this curve, we can obtain the displacement of any point on the retaining structure considering the bottom heave caused by the excavation of the foundation pit.

[0091] Example 1:

[0092] The basic parameters of a sub-pit for a subway station in Hangzhou are as follows: excavation dimensions: length L = 38m, width B = 23.7m, excavation depth d = 18.01m, diaphragm wall embedment depth H = 28.79m, wall thickness 1m, surface surcharge outside the pit 20kPa, groundwater depth 2.2m, Poisson's ratio of the soil 0.324, soil compression modulus 13.87MPa, other basic soil parameters are shown in Table 1, and basic support parameters are shown in Table 2.

[0093] Table 1. Main physical and mechanical properties of bedrock and soil in various regions

[0094]

[0095]

[0096] Table 2 Supporting Basic Parameters

[0097]

[0098] After the foundation pit excavation is completed, the measured displacement results of the diaphragm wall are compared with the calculation results of this invention considering pit bottom heave, and with the calculation results not considering pit bottom heave. Figure 5 As shown.

[0099] Analysis shows that in shallow areas, the calculation method considering pit bottom heave is largely consistent with the traditional method. However, in the area below the bottom of the pit, the calculated values ​​without considering heave begin to converge, while the calculated values ​​considering heave continue to increase, reaching a maximum of approximately 14.5 mm at a depth of about 25 m. Compared with the measured values, the overall trend of the calculated values ​​considering heave, as well as the depth and size of the maximum value, are more consistent with the measured values. This indicates that in deep foundation pits, especially those with a large width, the impact of pit bottom heave on the lateral displacement of the surrounding soil and retaining structure should be taken seriously.

[0100] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and 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 for calculating displacement of a retaining structure considering heave of a pit bottom caused by excavation of the pit, characterized by the steps of The method comprises the following steps: S1, taking a foundation pit cross section, taking the projection of the foundation pit center on the ground surface as the origin, taking the direction along the foundation pit width as the y-axis, and taking the vertical direction as the z-axis, a pit bottom heave curve function is established based on the stress solution theory of the excavation section being a semicircle in an elastic half space; S2, based on the image source method and the pit bottom heave curve function, the pit bottom heave is differentiated and equivalent to a circular pore, the total displacement of an arbitrary point on the pit bottom along the y-axis generated by an arbitrary point on the retaining structure is derived, and then the soil body transverse displacement of an arbitrary point on the retaining structure is obtained by integrating along the pit bottom width direction, the transverse displacement is the displacement along the y-axis direction; S3, the retaining structure is regarded as an elastic foundation beam, the elastic foundation beam is vertically divided into a plurality of beam units, the support of the retaining structure is simplified as a spring support of the retaining structure, and the passive zone soil body below the pit bottom surface is simplified as an equivalent stiffness soil spring, the water and soil pressure load is applied to the beam unit, the overall stiffness matrix of the foundation beam, the support stiffness matrix, the soil spring stiffness matrix and the node load column array are obtained by using the truss finite element method, and the stress balance equation of the retaining structure is constructed to obtain the displacement vector of each beam unit end node; wherein, based on the soil body transverse displacement of an arbitrary point on the retaining structure multiplied by the soil spring linear stiffness at the corresponding position, the force generated by the soil body transverse displacement on the retaining structure is obtained, and the force is directly added to the node load column array; the displacement field function of each beam unit is obtained based on the displacement vector of each beam unit end node, the displacement field functions of the beam units are connected in sequence, the deformation curve of the overall retaining structure considering the pit bottom heave is obtained, and thus the displacement of any point on the retaining structure is obtained.

2. The retaining structure displacement calculation method considering the pit bottom heave caused by the foundation pit excavation according to claim 1, characterized in that, In S1, the pit bottom heave curve function is specifically: wherein z r is the depth of the calculation point of the pit bottom heave, B is the foundation pit width, d is the foundation pit depth; S r is the maximum heave of the foundation pit, S m is the heave at the boundary of the foundation pit.

3. The retaining structure displacement calculation method considering the pit bottom heave caused by the foundation pit excavation according to claim 2, characterized in that, The maximum heave amount of the foundation pit is obtained by combining the initial foundation pit center point heave amount with the width correction coefficient and the depth correction coefficient, and the heave amount at the boundary of the foundation pit is obtained by combining the initial foundation pit side wall heave amount with the width correction coefficient and the depth correction coefficient.

4. The retaining structure displacement calculation method considering the pit bottom heave caused by the foundation pit excavation according to claim 2, characterized in that, In S2, the component of the total displacement along the y-axis of an arbitrary point on the pit bottom at an arbitrary point on the retaining structure is specifically: Based on the image source method, taking an arbitrary point P(y0, z0) on the pit bottom and an arbitrary point Q1(y, z) on the retaining structure, the formula of the component of the total displacement along the y-axis is: wherein S y1 is the displacement along the y-axis component of the gap of radius a at any point P(y0, z0) on the bottom of the foundation pit at any point Q1(y, z) on the enclosure structure; S y2 is the displacement along the y-axis component of the gap of radius a at any point P'(y0, -z0) obtained by mirroring any point P(y0, z0) on the bottom of the foundation pit along the y-axis at any point Q1(y, z) on the enclosure structure; r1 is the distance between point P and point Q1, and r2 is the distance between point P' and point Q1. d is the depth of the excavation.

5. The method for calculating displacement of the retaining structure considering the uplift of the pit bottom caused by the excavation of the pit according to claim 4, characterized in that, In S2, the soil body transverse displacement of an arbitrary point on the retaining structure is specifically: where S z (z) is the lateral displacement of the soil at any point on the envelope.

6. The retaining structure displacement calculation method considering the pit bottom heave caused by foundation pit excavation according to claim 1, characterized in that, In S3, the stress balance equation is: [P] = ([K] + [K R ] + [K H ]) · [S T ] where [P] is the nodal load array due to the horizontal load acting on the beam, which is assembled from the nodal load array P e of each beam element; [K] is the global stiffness matrix of the foundation beam, which is assembled from the stiffness matrix K e of each beam element. [K R ] is the support stiffness matrix, assembled from the stiffness k R of each support;[K H ] is the soil spring stiffness matrix, assembled from the soil spring stiffness k H of each depth;[S T ] is the displacement vector of the end nodes of each beam element, assembled from the beam element node displacements q e of each beam element.

7. The retaining structure displacement calculation method considering the pit bottom heave caused by foundation pit excavation according to claim 1, characterized in that, The process of obtaining the displacement field function of each beam unit based on the displacement vector of each beam unit end node is: v(x) = N(ξ)q e where v(x) is the displacement field function, q e is the nodal displacement of each beam element, N(ξ) is the element shape function, N(ξ) = [1-3ξ 2 +2ξ 3 l(ξ-2ξ 2 +ξ 3 )3ξ 2 -2ξ 3 l(ξ 3 -ξ 2 )], x is the distance from the calculation point to the end of the beam element, and l is the length of the beam element.

8. The retaining structure displacement calculation method considering the pit bottom heave caused by foundation pit excavation according to claim 1, characterized in that, The retaining structure is specifically any one of a retaining wall and a retaining pile.

9. A computer readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the method for calculating the displacement of the retaining structure considering the pit bottom heave caused by the foundation pit excavation according to any one of claims 1-8.

10. A retaining structure displacement calculation system that takes into account a pit bottom heave caused by excavation of a foundation pit, characterized by, The system comprises: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the method for calculating the displacement of the retaining structure considering the pit bottom heave caused by the foundation pit excavation according to any one of claims 1-8.

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