Consideration of asymmetrically loaded foundation pit group retaining structure stress deformation determination and evaluation method

Abstract

The application provides a method for determining stress and deformation of a retaining structure of a group of asymmetrically loaded foundation pits, comprising: establishing an improved elastic foundation beam overall analysis model; determining calculation parameters and a coupling relationship between soil pressure and wall deformation based on the improved elastic foundation beam overall analysis model; changing boundary conditions to simulate foundation pit excavation, establishing a diaphragm wall stress balance equation set through the coupling relationship between soil pressure and wall deformation, and iteratively solving to determine the final deformation values of the two side walls. The method fully considers the influence of asymmetric loads on the deformation of the two side walls, can quickly solve the wall stress and deformation characteristics that are more in line with the actual situation, calculate the safety margin of the wall bending moment, and realize quantitative risk assessment, thereby providing theoretical support for engineering practice and design optimization.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering calculations, and more specifically, to a method for determining and evaluating the stress and deformation of retaining structures in foundation pit groups under asymmetric loading. Background Technology

[0002] Foundation pit engineering has played a crucial role in the rapid development of urban underground space. Determining the earth pressure load on the retaining structure is a key aspect of foundation pit engineering design. The value of the earth pressure load not only affects the safety of the entire foundation pit project but also plays a crucial role in controlling construction costs.

[0003] The elastic foundation beam method is a classic method for calculating the deformation of diaphragm walls. This method simplifies the diaphragm wall as an elastic beam, the supports as springs, and the soil in the pit as soil springs; it is also often called the "m-method." Asymmetric loading occurs when the soil widths on both sides are different, or when one side experiences surcharge. The traditional elastic foundation beam method treats the retaining wall with the calculated width as a vertical foundation beam, simplifies the supports (or anchors) as elastic bearings related to their cross-sectional area and elastic modulus, and simulates the reaction force of the soil in front of the wall below the excavation face on the foundation beam using soil springs. The calculated length of the supports is taken as half the distance between the pits, assuming the support center remains constant and compression is symmetrical on both sides. However, under asymmetric loading, the supports exhibit a displacement pattern of "translation + compression," requiring a comprehensive stress analysis of the support structure. The existing elastic foundation beam method is only a simplified model, only considering the stress and deformation of the pit under symmetrical loads, and cannot account for asymmetric loading.

[0004] Currently, most studies on earth pressure and deformation under asymmetric loading employ numerical methods, while theoretical solutions for the deformation of retaining structures under asymmetric loading are rarely proposed. Furthermore, stress-deformation analysis and risk assessment of retaining structures under asymmetric loading are crucial steps in ensuring safe construction. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method for determining and evaluating the stress and deformation of retaining structures in asymmetrically loaded foundation pit groups.

[0006] According to one aspect of the present invention, a method for determining the stress and deformation of the retaining structure considering asymmetric loading of a foundation pit group is provided, comprising:

[0007] An improved overall analysis model for elastic foundation beams was established.

[0008] Based on the improved overall analysis model of the elastic foundation beam, the calculation parameters and the coupling relationship between earth pressure and wall deformation are determined.

[0009] By changing the boundary conditions to simulate the excavation of the foundation pit, the force equilibrium equations of the diaphragm wall are established through the coupling relationship between the earth pressure and the wall deformation, and the final deformation values ​​of the walls on both sides are determined by iterative solution.

[0010] Preferably, the improved overall analysis model of the elastic foundation beam includes:

[0011] The diaphragm walls on both sides are treated as elastic beams, the supports as spring elements that can be freely compressed at both ends, and the soil inside the pit as soil spring elements. The earth pressure load behind the walls adopts a non-ultimate earth pressure model; wherein, the non-ultimate earth pressure model is...

[0012]

[0013]

[0014] Where, p z γ is the horizontal reaction force of the retaining wall; k is the active earth pressure lateral pressure coefficient; γ is the soil weight; H is the wall depth; z is the calculation depth; α is the angle between the slip surface and the horizontal plane. δ is the internal friction angle of the soil; δ is the friction angle between the wall and the soil.

[0015] Preferably, the determination of calculation parameters and the coupling relationship between earth pressure and wall deformation based on the improved elastic foundation beam overall analysis model includes:

[0016] Determine the calculation parameters, which include the stiffness matrix of the diaphragm walls on both sides, the stiffness matrix of the supports, and the stiffness matrix of the soil springs;

[0017] Based on the aforementioned wall stiffness matrix, support stiffness matrix, and soil spring stiffness matrix, and in conjunction with the improved overall analysis model of the elastic foundation beam, the coupling relationship between soil pressure and wall deformation is determined, namely, the coupling relationship between the wall-soil friction angle, the soil internal friction angle, and wall deformation.

[0018] Preferably, the process of obtaining the overall stiffness matrices [K1] and [K2] of the diaphragm walls on both sides includes:

[0019] Assuming the vertical stiffness of the wall is infinite, and ignoring the vertical compressive deformation of the wall, we only consider the relationship between the lateral displacement and rotation of the rod end and the force at the rod end;

[0020] Substituting the wall's elastic modulus, moment of inertia, and calculation element length into the matrix of the improved elastic foundation beam overall analysis model, the stiffness matrix of the diaphragm wall element is obtained:

[0021]

[0022] Among them, F Yi M represents the shear force at node i; i F is the bending moment at node i; YjM represents the shear force at node j; j Let E be the bending moment at node j; E be the elastic modulus of the wall; I be the moment of inertia of the wall; l be the length of the calculation element; and v be the bending moment at node j. i For the horizontal deformation of node i, θ i v is the turning angle of node i; j For the horizontal deformation of node j, θ j Let j be the corner of node j; the wall is divided into several bar elements, and the connection point between adjacent bar elements is called a node;

[0023] The stiffness matrices of the diaphragm wall units are superimposed one by one along the wall depth to obtain the overall stiffness matrices of the diaphragm walls on both sides, [K1] and [K2].

[0024] The support stiffness matrix [K] s The process of obtaining ] includes:

[0025] Treating the support as a spring element related to the support cross-sectional area, the elastic modulus of the wall, and the calculated length, the formula [K] is used. s =EA / LS calculates the stiffness of a single support, where E is the elastic modulus of the support, A is the cross-sectional area of ​​the support, L is the equivalent length of the support, and S is the equivalent spacing between supports;

[0026] Based on the number of supports corresponding to each construction stage, the support stiffness matrix [K] is obtained by superposition. s ];

[0027] The soil spring stiffness matrix [K] m The process of obtaining ] includes:

[0028] Based on the unit division and excavation depth, the corresponding soil spring stiffness is calculated. The soil spring stiffness is related to soil properties and burial depth, and is expressed by formula K. m =k h bh, k h =mz is obtained through calculation; K m For the stiffness of the earth spring, k h denoted as , b is the horizontal subgrade coefficient, h is the calculated width of the soil spring, m is the proportional coefficient of the subgrade coefficient, and z is the soil depth.

[0029] The individual soil spring stiffness values ​​are superimposed and integrated into a global soil spring stiffness matrix [K]. m ].

[0030] Preferably, the step of determining the friction angle δ and the internal friction angle of the soil based on the non-limit earth pressure model is described. The relationship with wall deformation s

[0031]

[0032] Where, δ mA modified friction angle that takes into account the coupling relationship between the friction angle and wall deformation; The modified internal friction angle of the soil is used to consider the coupling relationship between the internal friction angle of the soil and the deformation of the wall; s is the wall displacement, s c Let s be the ultimate displacement of the wall at the wall-soil friction angle. a The wall's ultimate displacement is the angle of internal friction within the soil.

[0033] Preferably, the step of simulating foundation pit excavation by changing boundary conditions, and establishing a set of force equilibrium equations for the diaphragm wall through the coupling relationship between earth pressure and wall deformation, includes:

[0034] Based on the soil spring stiffness matrix [K] for various working conditions m By establishing the coupling relationship between earth pressure and wall deformation, a set of force equilibrium equations for the diaphragm wall is constructed:

[0035]

[0036] Solving this system of equations yields the deformation matrix of the wall:

[0037]

[0038] Among them, [P] e1 ]、[P e2 [K1] and [K2] are the earth pressure load matrices acting on the two walls from outside the pit, [K1] and [K2] are the stiffness matrices of the two walls, and [Δ1] and [Δ2] are the overall displacement matrices of the two walls. m ] is the stiffness matrix of the soil spring, [Δ m1 ]、[Δ m2 [K]: Initial deformation matrix of the soil at the bottom of the pit before support installation; s [Δ] represents the support stiffness matrix. s1 ]、[Δ s2 [Δ′] refers to the overall deformation matrix supporting both ends; s1 ]、[Δ′ s2 [K] refers to the initial deformation matrix at both ends before installation. s ]·[Δ′ s1 ]、[K s ]·[Δ′ s2 To support the stress compensation matrix caused by construction delays, [Δ 10 ] = [P e1 ]·([K1]+[K m0 ]) -1 、[Δ 20 ] = [P e2 ]·([K2]+[K m0 ]) -1 For the initial equilibrium displacement before excavation, [K] m0 ] represents the initial support stiffness matrix.

[0039] Preferably, the iterative solution includes:

[0040] Determine whether the deformation error between the two tests converges to the set value:

[0041]

[0042] Where [Δ1], [Δ2], [Δ′1], and [Δ′2] are the wall displacements in the two preceding and subsequent times, and β is the set error;

[0043] If the error requirement is not met, substitute ([Δ1]+[Δ′1]) / 2 and ([Δ2]+[Δ′2]) / 2 as new initial displacement matrices into [Δ 10 ]、[Δ 20 The iteration continues until the error requirement is met, and the final deformation values ​​of the two walls are obtained.

[0044] According to a second aspect of the present invention, a method for evaluating the stress and deformation of a retaining structure considering an asymmetricly loaded foundation pit group is provided, comprising:

[0045] The final deformation values ​​of the two side walls are obtained by using any one of the methods described.

[0046] The bending moment, shear force, and earth pressure distribution behind the wall are determined based on the final deformation values ​​of the two side walls.

[0047] Based on the bending moment, shear force, and earth pressure distribution behind the wall, the safety margin of the wall bending moment is determined, thereby achieving a quantitative assessment of wall safety during the excavation process.

[0048] Preferably, the bending moment and shear force of the wall are solved using interpolation.

[0049]

[0050] Among them, E w For the elastic modulus of the wall; I w [M] is the wall's moment of inertia; [Q] is the wall's bending moment matrix; [Q] is the wall's shear force matrix; k is the finite element number; Δl is the finite element length, i.e., the total wall length divided by the number of finite element divisions; [Δ] is the wall's shear force matrix. k+1 [Δ] k-1 [Δ] k These refer to the wall displacements at nodes k+1, k-1, and k, respectively; [M] k+1 [M] k These refer to the wall bending moments at nodes k+1 and k, respectively, which are obtained by solving the above formula [M].

[0051] The distribution of earth pressure behind the wall is obtained by substituting the final deformation values ​​of the two walls into the non-limit earth pressure formula.

[0052] Preferably, the safety margin for the bending moment of the wall is calculated as follows:

[0053] Where M is the maximum bending moment of the wall; Mu is the design limit value of the bending moment of the wall; and S is the safety margin of the bending moment of the wall.

[0054] When the wall bending moment safety margin S is lower than the set threshold, it is determined that the wall bending moment safety margin is insufficient and there is a risk.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] The method for determining and evaluating the stress and deformation of the retaining structure of the foundation pit group under asymmetric load in this embodiment of the invention fully considers the influence of asymmetric load on the deformation of the walls on both sides. It can quickly solve the stress and deformation characteristics of the walls that are more in line with the actual situation, calculate the safety margin of the bending moment of the walls and realize the quantitative assessment of risks, and provide theoretical support for engineering practice and design optimization. Attached Figure Description

[0057] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0058] Figure 1 This is a schematic diagram of a computational model according to a preferred embodiment of the present invention;

[0059] Figure 2 This is a flowchart of a preferred embodiment of the present invention for determining and evaluating the stress and deformation of the retaining structure of an asymmetricly loaded foundation pit group;

[0060] Figure 3 This is a comparison chart of the calculated wall deformation values ​​of another preferred embodiment of the present invention with the calculated values ​​of Qimingxing (a deep foundation pit excavation and support design software in the prior art) and the measured values ​​in engineering. Detailed Implementation

[0061] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0062] Please see Figure 1 and Figure 2 This invention provides an embodiment of a method for determining the stress and deformation of a retaining structure considering an asymmetrically loaded foundation pit group, comprising:

[0063] S100, Establish an improved overall analysis model for the elastic foundation beam. The parameters required for this model are obtained based on the actual engineering situation.

[0064] S200, based on the improved elastic foundation beam overall analysis model established in S100, determines the calculation parameters and the coupling relationship between earth pressure and wall deformation;

[0065] S300: Simulate foundation pit excavation by changing boundary conditions. Establish the diaphragm wall force equilibrium equations by using the parameters in S200 and the coupling relationship between earth pressure and wall deformation, and solve them iteratively to obtain the final deformation values ​​of the walls on both sides.

[0066] This embodiment is based on an improved overall analysis model of elastic foundation beams and combines the research results of finite element method and non-ultimate earth pressure. It fully considers the influence of asymmetric loads on the deformation of the walls on both sides, and quickly solves the stress and deformation characteristics of the walls that are more in line with the actual situation. It can be applied to the quantitative assessment of bending moment risk of retaining structures and provides theoretical support for engineering practice and design optimization.

[0067] In a preferred embodiment of the present invention, step S100 is implemented, and an improved overall analysis model of the elastic foundation beam is established based on actual working conditions. The diaphragm walls on both sides are simplified to elastic beams, the supports are simplified to spring elements with free compression at both ends, the soil in the pit is simplified to soil spring elements, and the earth pressure load behind the walls is simulated using a non-ultimate earth pressure model. The formula for solving the earth pressure is:

[0068]

[0069] in,

[0070] The improved elastic foundation beam analysis model takes into account the stress and deformation of the foundation pit under asymmetric loads, and uses a non-ultimate earth pressure model to calculate the soil pressure behind the wall.

[0071] Where, p z The horizontal reaction force of the retaining wall needs to be calculated using the above formula; k is the active earth pressure lateral pressure coefficient, obtained through direct shear test; γ is the soil weight, obtained by measuring the mass and volume of the soil block; H is the wall depth, which is known from the design; z is the calculation depth, obtained according to the calculation conditions; α is the angle between the slip surface and the horizontal plane. δ is the internal friction angle of the soil; δ is the wall-soil friction angle, obtained through the corrected formulas for the wall-soil friction angle and the internal friction angle of the soil.

[0072] This embodiment defines a method for determining and evaluating the stress and deformation of the retaining structure of an asymmetricly loaded foundation pit group. It fully considers the wall-soil coupling theory and the influence of asymmetric loads on the deformation of the walls on both sides, and can quickly solve for the stress and deformation characteristics of the walls that are more in line with the actual situation, providing theoretical support for engineering practice and design optimization.

[0073] In another preferred embodiment of the present invention, S200 is implemented based on the improved overall analysis model of the elastic foundation beam established in S100. Specifically, it includes:

[0074] S201, assuming the vertical stiffness of the wall is infinite, neglecting the vertical compressive deformation of the wall, only considering the relationship between the lateral displacement and rotation angle of the rod end and the force at the rod end. Substituting the relevant data of S100, namely the elastic modulus of the wall, moment of inertia and the length of the calculation unit, the stiffness matrix of the diaphragm wall unit can be obtained as follows. Then, the unit elements are superimposed one by one along the wall depth to obtain the overall stiffness matrix of the diaphragm wall [K1] and [K2].

[0075]

[0076] Among them, the elastic modulus, moment of inertia, and length of the computational element are inherent properties of the elastic foundation beam analysis model, related to the wall material, and do not need to be obtained through calculation. E is the elastic modulus of the wall; I is the moment of inertia of the wall; l is the length of the computational element; v i For the horizontal deformation of node i, θ i v is the turning angle of node i; j For the horizontal deformation of node j, θ j F is the rotation angle of node j; Yi M represents the shear force at node i; i F is the bending moment at node i; Yj M represents the shear force at node j; j Let j be the bending moment at node j; a node refers to the connection point between adjacent bar elements when the wall is divided into several bar elements.

[0077] S202 simplifies the support into a spring element related to the cross-sectional area, elastic modulus, and calculated length, using formula [K] s The stiffness of a single support is calculated using EA / LS. Then, based on the number of supports at each construction stage, these are combined to form a support stiffness matrix [K]. s ]. Among them, [K s ] is the support stiffness matrix; E is the support elastic modulus; A is the support cross-sectional area; L is the support equivalent length; S is the support equivalent spacing.

[0078] S203, based on the element division (e.g., dividing the wall into several elements along the depth direction, each element being called a finite element member; the stiffness of each member element is calculated using the matrix formula above, and then superimposed to obtain the stiffness matrix of the entire wall) and the excavation depth, calculate the corresponding soil spring stiffness. Its elastic compressive stiffness is related to soil properties and burial depth, and can be calculated using formula K. m =k h bh, k h =mz is calculated. Then, the calculated individual soil spring stiffnesses are integrated into the overall soil spring stiffness matrix [K]. m ]. Among them, K m For earth spring stiffness; k h denoted as σa, where σb is the calculated width of the soil spring; σh is the calculated width of the soil spring; σm is the proportional coefficient of the subgrade coefficient; and σz is the soil depth.

[0079] S204, based on the non-ultimate earth pressure model in S100, determine the friction angle δ and the soil internal friction angle. The relationship between the wall deformation s and the wall deformation s is as follows:

[0080]

[0081] Where s is the wall displacement, s c Let s be the ultimate displacement of the wall at the wall-soil friction angle. a The wall's ultimate displacement is the angle of internal friction within the soil.

[0082] In this embodiment, during implementation S201, the wall is discretized into multiple rod sub-elements using the finite element method. Structural mechanics is then used to solve the force and displacement relationships of each element, which are then superimposed to obtain the stiffness matrix of the entire wall. This method offers higher calculation accuracy and faster efficiency. During implementation S202, the individual support members acting on the wall are superimposed to form an overall support stiffness matrix, facilitating the calculation of the wall's stress and deformation. During implementation S203, the earth pressure at the bottom of the pit acting on the wall is converted into an overall soil spring stiffness matrix. This reflects the resistance of the soil at the bottom of the pit to the wall's deformation, and the use of an overall soil spring stiffness matrix allows for more efficient matrix calculations to obtain the wall's stress and deformation. During implementation S204, considering that the development process of non-ultimate earth pressure is related to the wall-soil friction angle and the internal soil friction angle as the wall deforms, correction formulas for the friction angle and internal soil friction angle based on wall-soil coupling are established. This calculation method better reflects the actual stress and deformation characteristics of the wall, providing theoretical support for engineering practice and design optimization.

[0083] In another preferred embodiment of the present invention, based on the friction angle δ in S200 and the soil internal friction angle The relationship between the wall deformation s and the boundary conditions was simulated by implementing S300 and changing the boundary conditions to examine the excavation of the foundation pit. This was achieved through the coupling relationship between the axial force of the supports and the deformation of the walls on both sides (i.e., the friction angle δ and the internal friction angle of the soil). (Relationship with wall deformation s) Establish a set of force equilibrium equations for the diaphragm wall and solve iteratively. When the two deformation calculations converge to the error set value, the final deformation values ​​of the walls on both sides are obtained. Here, changing the boundary conditions means considering the force conditions of asymmetric loads. Under conventional symmetrical conditions, it is only necessary to establish a force equilibrium equation using a half-model to calculate the force deformation. When considering asymmetric conditions, it is not possible to choose a symmetrical model for calculation. It is necessary to consider the force boundaries on both sides of the foundation pit separately and jointly establish the following force equilibrium equations for the diaphragm wall. The specific implementation process of S300 includes:

[0084] S301, based on the formula in S203, determines the soil spring stiffness matrix under various excavation conditions.

[0085] S302, based on the formula in S200, solve for the earth pressure load matrix. If this is the first solution, the wall deformation can be assumed to be zero. Establish the force equilibrium equations for the diaphragm wall through the coupling relationship between the axial force of the support and the deformation of the walls on both sides:

[0086]

[0087] S303, Solve for the deformation of the wall in step S302:

[0088]

[0089] Among them, [P] e1 ]、[P e2 [K1] and [K2] are the earth pressure load matrices acting on the two walls from outside the pit, [K1] and [K2] are the stiffness matrices of the two walls, and [Δ1] and [Δ2] are the overall displacement matrices of the two walls. m ] is the stiffness matrix of the soil spring, [Δ m1 ]、[Δ m2 [K]: Initial deformation matrix of the soil at the bottom of the pit before support installation; s [Δ] represents the support stiffness matrix. s1 ]、[Δ s2 [Δ′] refers to the overall deformation matrix supporting both ends; s1 ]、[Δ′ s2 [K] refers to the initial deformation matrix at both ends before installation. s ]·[Δ′ s1 ]、[K s ]·[Δ′ s2 To support the stress compensation matrix caused by construction delays, [Δ 10 ] = [P e1]·([K1]+[K m0 ]) -1 、[Δ 20 ] = [P e2 ]·([K2]+[K m0 ]) -1 For the initial equilibrium displacement before excavation, [K] m0 ] represents the initial support stiffness matrix.

[0090] S304, comparing the error in wall deformation between the two tests:

[0091]

[0092] Where [Δ1], [Δ2], [Δ′1], and [Δ′2] represent the wall displacements in the two preceding and subsequent operations, and β represents the set error.

[0093] If the error requirement is not met, in order to ensure the convergence of the calculation results, ([Δ1]+[Δ′1]) / 2 and ([Δ2]+[Δ′2]) / 2 are used as new initial displacement matrices and substituted into the relationship between the friction angle and displacement in S204. The distribution value of the earth pressure under this displacement is solved, and the solution process from S200 to S300 is repeated until the displacement of the wall in the two solutions is less than the set error.

[0094] In another embodiment of the present invention, a method for evaluating the stress and deformation of the retaining structure of an asymmetricly loaded foundation pit group is also provided, specifically including the following steps:

[0095] (1) Based on the actual parameters of the project, the final deformation values ​​of the two walls can be obtained. Specifically, the method for determining the stress and deformation of the retaining structure of the pit group under asymmetric load in any of the above embodiments can be used.

[0096] (2) Determine the bending moment, shear force and earth pressure distribution behind the wall based on the final deformation values ​​of the two walls;

[0097] (3) Based on the bending moment, shear force and earth pressure distribution of the wall, the safety margin of the bending moment of the wall is determined, so as to realize the quantitative assessment of the wall safety during the excavation process.

[0098] In this embodiment, the obtained final deformation value is applied to engineering safety assessment, which can realize early warning of engineering safety.

[0099] In a preferred embodiment, the bending moment and shear force of the wall can be solved using the following formula:

[0100]

[0101] Among them, E w The elastic modulus of the wall is provided by the design unit; I w[M] is the wall's moment of inertia, provided by the design unit; [Q] is the wall's bending moment matrix; [Q] is the wall's shear force matrix; k is the finite element element designation; Δl is the finite element element length, i.e., the total wall length divided by the number of finite element divisions (a finite element element refers to dividing the entire foundation pit retaining wall along the depth direction into several elements, each wall element being called a member finite element); [Δl] is the wall's moment of inertia, provided by the design unit; [M] is the wall's bending moment matrix; [Q] is the wall's shear force matrix; k is the finite element element designation; Δl is the finite element element length, i.e., the total wall length divided by the number of finite element divisions (a finite element element refers to dividing the entire foundation pit retaining wall into several elements along the depth direction, each wall element being called a member finite element); [Δl] k+1 [Δ] k-1 [Δ] k These refer to the wall displacements at nodes k+1, k-1, and k, respectively, [Δ]. k+1 [Δ] k-1 [Δ] k These refer to the wall displacements at nodes k+1, k-1, and k, respectively; where [Δ] is the final deformation matrix of the wall, and the displacement values ​​at the nodes are extracted from this matrix; [M] k+1 [M] k These refer to the wall bending moments at nodes k+1 and k, respectively, which are obtained by solving the above formula [M].

[0102] The distribution of earth pressure behind the wall is obtained by substituting the final deformation values ​​of the two walls into the non-ultimate earth pressure formula. Specifically, the calculated wall deformation values ​​(displacement matrix [Δ]) are substituted into the friction angle δ and the soil internal friction angle. From the two formulas relating to wall deformation s, the corrected friction angle and the internal friction angle δ of the soil are calculated. m , Then δ m , Substitute these values ​​into the equations and solve for Pz, C1, and C2 to obtain the final non-limit earth pressure.

[0103] In a preferred embodiment, the formula for determining the safety margin of the wall bending moment is:

[0104]

[0105] Where M is the maximum bending moment of the wall; M u S represents the design limit value of the wall bending moment; S represents the safety margin of the wall bending moment.

[0106] Specifically, when quantitatively assessing the safety of the wall during the excavation process, the obtained wall bending moment safety margin can be compared with a set safety threshold. If it is less than the set safety threshold, a risk is assessed, and an alarm or action can be taken. For example, in one embodiment, the safety threshold is set to 0.3. When S≤0.3, the wall bending moment safety margin is assessed as insufficient, indicating a risk, and optimization measures should be taken.

[0107] Due to the large amount of computation involved, this embodiment of the invention is suitable for implementation using software programming. Next, a case study from a real-world engineering project will be used to demonstrate the comparison between the diaphragm wall deformation and stress values ​​calculated by this embodiment and the measured values ​​from an actual project. This case study involves a foundation pit project on a certain plot of land, and the on-site measured data includes the deformation of the diaphragm walls on both sides under different excavation conditions. Figure 3 The figure shows the calculation results for conditions three, four, and five. As shown in the figure, compared with the traditional elastic foundation beam solution (Morning Star), the displacement calculation value of the diaphragm wall obtained by the embodiment of the present invention matches the measured value better, and has accurate calculation results. It can be seen that the calculation results of the embodiment of the present invention can fully consider the influence of asymmetric loads on wall deformation, and provide theoretical support for engineering practice and design optimization.

[0108] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention. The above preferred features can be used in any combination without conflict.

Claims

1. A method for determining the stress and deformation of the retaining structure of an asymmetrically loaded foundation pit group, characterized in that, include: An improved overall analysis model for elastic foundation beams was established. Based on the improved overall analysis model of the elastic foundation beam, the calculation parameters and the coupling relationship between earth pressure and wall deformation are determined. By changing the boundary conditions to simulate the excavation of the foundation pit, the force equilibrium equations of the diaphragm wall are established through the coupling relationship between the earth pressure and the wall deformation, and the final deformation values ​​of the two walls are determined by iterative solution. The improved overall analysis model for elastic foundation beams includes: The diaphragm walls on both sides are treated as elastic beams, the supports as spring elements that can be freely compressed at both ends, and the soil inside the pit as soil spring elements. The earth pressure load behind the walls adopts a non-ultimate earth pressure model; wherein, the non-ultimate earth pressure model is... ， ， ， in, The horizontal reaction force of the retaining wall; This is the coefficient of active earth pressure lateral pressure. The soil weight; The depth of the wall; To calculate depth; The angle between the slip surface and the horizontal plane; The internal friction angle of the soil; The angle of friction between the wall and the soil; The improved overall analysis model for elastic foundation beams determines the calculation parameters and the coupling relationship between earth pressure and wall deformation, including: Determine the calculation parameters, which include the stiffness matrix of the diaphragm walls on both sides, the stiffness matrix of the supports, and the stiffness matrix of the soil springs; Based on the aforementioned wall stiffness matrix, support stiffness matrix, and soil spring stiffness matrix, and in conjunction with the improved overall analysis model of elastic foundation beam, the coupling relationship between earth pressure and wall deformation is determined, namely, the coupling relationship between wall-soil friction angle, soil internal friction angle, and wall deformation. The overall stiffness matrix of the diaphragm walls on both sides , The acquisition process includes: Assuming the vertical stiffness of the wall is infinite, and ignoring the vertical compressive deformation of the wall, we only consider the relationship between the lateral displacement and rotation of the rod end and the force at the rod end; Substituting the wall's elastic modulus, moment of inertia, and calculation element length into the matrix of the improved elastic foundation beam overall analysis model, the stiffness matrix of the diaphragm wall element is obtained: ； in, F Yi The shear force at node i; M i Let i be the bending moment at node i; F Yj The shear force at node j; M j Let J be the bending moment at node j; E is the elastic modulus of the wall, I is the moment of inertia of the wall, and l is the length of the calculation element. For the horizontal deformation of node i, Let be the angle of node i; v j For the horizontal deformation of node j, θ j Let j be the corner of node j; the wall is divided into several bar elements, and the connection point between adjacent bar elements is called a node; The stiffness matrix of the diaphragm wall unit is superimposed along the wall depth to obtain the overall stiffness matrix of the diaphragm walls on both sides. , ; The process of obtaining the support stiffness matrix includes: Treating the support as a spring element related to the support cross-sectional area, the wall's elastic modulus, and the calculated length, the formula is used... Calculate the stiffness of a single support, where, To support the elastic modulus, To support the cross-sectional area, To support the equivalent length, To support the equivalent spacing; The support stiffness matrix is ​​obtained by superimposing the support stiffness matrix according to the number of supports corresponding to each construction stage. ; The process of obtaining the soil spring stiffness matrix includes: Based on the unit division and excavation depth, the corresponding soil spring stiffness is calculated. The soil spring stiffness is related to soil properties and burial depth, and is expressed by the formula... , Calculated; For the stiffness of the earth spring, The horizontal subgrade coefficient, Calculate the width of the soil spring. Calculate the width of the soil spring. The proportionality coefficient of the bed base coefficient. For the depth of soil burial; The individual soil spring stiffness values ​​are superimposed and integrated into a soil spring stiffness matrix. ; The method of simulating foundation pit excavation by changing boundary conditions establishes a set of force equilibrium equations for the diaphragm wall through the coupling relationship between earth pressure and wall deformation, including: Based on the soil spring stiffness matrix under various working conditions By establishing the coupling relationship between earth pressure and wall deformation, a set of force equilibrium equations for the diaphragm wall is constructed: ； Solving this system of equations yields the deformation matrix of the wall: ； in, , This is the matrix of external earth pressure loads acting on the two side walls. , Here is the stiffness matrix of the two side walls. , Refers to the overall displacement matrix of the two side walls. Here is the stiffness matrix of the soil spring. , : Initial deformation matrix of the soil at the bottom of the pit before support installation; To support the stiffness matrix, , Refers to the overall deformation matrix supporting both ends; , This refers to the initial deformation matrix at both ends before installation. , To support the stress compensation matrix caused by construction delays, , This represents the initial equilibrium displacement before excavation. This is the initial support stiffness matrix.

2. The method for determining the stress and deformation of the retaining structure considering asymmetric loading of a foundation pit group according to claim 1, characterized in that, The friction angle is determined based on the non-limit earth pressure model. , soil internal friction angle With wall deformation Relationship, ； ； in, A modified friction angle that takes into account the coupling relationship between the friction angle and wall deformation; The modified internal friction angle of soil is designed to consider the coupling relationship between the internal friction angle of soil and the deformation of the wall. This is for wall displacement. This represents the ultimate displacement of the wall at the wall-soil friction angle. The wall's ultimate displacement is the angle of internal friction within the soil. , .

3. The method for determining the stress and deformation of the retaining structure considering asymmetric loading of a foundation pit group according to claim 1, characterized in that, The iterative solution includes: Determine whether the deformation error between the two tests converges to the set value: ； in , , , This refers to two separate wall displacements. To set the error; If the error requirement is not met, and Substitute as the new initial displacement matrix , The iteration continues until the error requirement is met, and the final deformation values ​​of the two walls are obtained.

4. A method for evaluating the stress and deformation of retaining structures in foundation pit groups under asymmetric loading, characterized in that, include: The final deformation values ​​of the two side walls are obtained by using the method described in any one of claims 1-3; The bending moment, shear force, and earth pressure distribution behind the wall are determined based on the final deformation values ​​of the two side walls. Based on the bending moment, shear force, and earth pressure distribution behind the wall, the safety margin of the wall bending moment is determined, thereby achieving a quantitative assessment of wall safety during the excavation process.

5. The method for evaluating the stress and deformation of a retaining structure considering asymmetric loading of a foundation pit group according to claim 4, characterized in that, The bending moment and shear force of the wall are solved using interpolation. ； ； in, The elastic modulus of the wall; Let the moment of inertia of the wall be denoted as . Here is the bending moment matrix of the wall; Here, k represents the shear force matrix of the wall; k is the finite element number. The length of the finite element is the total length of the wall divided by the number of finite element divisions. , , These refer to the wall displacements at nodes k+1, k-1, and k, respectively. , These refer to the wall bending moments at nodes k+1 and k, respectively, which are obtained by solving the above formula [M]. The distribution of earth pressure behind the wall is obtained by substituting the final deformation values ​​of the two walls into the non-ultimate earth pressure formula.

6. The method for evaluating the stress and deformation of a retaining structure considering asymmetric loading of a foundation pit group according to claim 5, characterized in that, The safety margin for the bending moment of the wall is calculated as follows: ; Where M is the maximum bending moment of the wall; Mu is the design limit value of the bending moment of the wall; and S is the safety margin of the bending moment of the wall. When the wall bending moment safety margin S is lower than the set threshold, it is determined that the wall bending moment safety margin is insufficient and there is a risk.

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