Foundation pit soil pressure calculation method for drum-shaped displacement and stress partition in limited space

Abstract

The invention discloses a foundation pit soil pressure calculation method for drum-shaped displacement and stress partitioning in a limited space, and belongs to the technical field of geotechnical engineering foundation pit supporting. The method comprises the following steps: S1, establishing a linear potential slip crack surface model; s2, a nonlinear soil internal friction angle and wall-soil interface friction angle exerting model is established by considering the drum-shaped displacement mode of the supporting structure and the difference of equivalent values of soil friction angles at different depths and different partitions; s3, stress deflection analysis is conducted on the two areas respectively, and a non-limit soil pressure control differential equation considering shear stress between the upper soil layer and the lower soil layer is established according to conditions based on a transverse stress infinitesimal method; and S4, solving the differential equation in different regions to obtain soil pressure distribution, and performing integral calculation on soil pressure resultant force and action point height. According to the method, the soil pressure calculation problem under the condition of coupling of the limited space and the asymmetric drum-shaped displacement is solved, and accurate theoretical support is provided for foundation pit supporting design in the sensitive environment.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering foundation pit support technology, specifically to a method for calculating the soil pressure of foundation pits in confined spaces based on drum-shaped displacement and stress zoning. Background Technology

[0002] With the continuous development of urban underground space, the construction of adjacent double and multiple foundation pits is becoming increasingly common. In such projects, the width of the soil behind the support structure is limited, rendering the traditional earth pressure theory based on the assumption of semi-infinite soil inapplicable. In actual engineering, flexible retaining walls under internal bracing or anchored support systems often exhibit a drum-shaped displacement pattern under limited spatial constraints, meaning that the top and bottom of the support structure displace relatively little, while the middle protrudes into the pit. This deformation pattern leads to a complex stress state in the limited soil behind the wall, exhibiting significant non-limit states and stress redistribution phenomena.

[0003] Existing research largely focuses on earth pressure calculations under translational or rotational modes around the wall top, with insufficient research on non-ultimate earth pressure under the drum-shaped displacement mode in finite spaces. Especially in practical engineering, when the support structure displacement has not reached its ultimate state, the soil shear strength is not fully utilized, and the earth pressure distribution exhibits significant nonlinear characteristics. Traditional Rankine or Coulomb theories cannot accurately reflect the true stress state. Furthermore, existing methods often fail to systematically consider the effects of relative displacement between upper and lower soil layers, soil arching effect, and stress deflection caused by drum-shaped deformation, leading to significant deviations between calculated results and actual conditions.

[0004] In summary, it is necessary to propose a calculation method that can accurately reflect the distribution of non-ultimate earth pressure under the drum-shaped displacement mode in a confined space, so as to provide a theoretical basis for the design of foundation pit support under similar working conditions. Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating the earth pressure in a foundation pit based on drum-shaped displacement and stress zoning in a confined space, thereby addressing the shortcomings of existing theories when considering complex displacement modes, confined soil spaces, and non-limit states.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for calculating earth pressure in a foundation pit based on drum-shaped displacement and stress zoning within a confined space, comprising the following steps: S1. Establish a potential slip surface model described by a straight line, divide the soil in the limited space behind the support structure into a rectangular main arch zone and a triangular passive wedge zone, and solve the soil height in the rectangular main arch zone and the soil height in the triangular passive wedge zone based on the force equilibrium condition of the slip wedge. S2. Considering the drum-shaped displacement mode of the support structure and the difference in the equivalent value of the soil friction angle at different depths, establish a model for the variation of the soil internal friction angle and the wall-soil interface friction angle with the displacement and depth of the support structure under non-limit conditions. S3. Perform stress deflection analysis on the rectangular main pressure arch area and the triangular passive wedge area respectively, and establish the expression for the distribution of non-limit earth pressure based on the transverse stress micro-element method. S4. Solve for the earth pressure coefficient and the height of the resultant force application point to complete the calculation of non-ultimate earth pressure under the drum-shaped displacement mode in finite space.

[0007] Furthermore, step S1 includes: like Figure 2 The potential slip surface is set as a plane with an angle of β with the horizontal plane. The slip surface divides the soil into a rectangular main arch region 1 and a triangular passive wedge region 2. Earth pressure is obtained from the overall force equilibrium condition of the sliding wedge. E a : ; Where n is the aspect ratio of the finite soil mass, H is the height of the flexible support structure, q is the soil surface load, γ is the soil weight, δ is the friction angle of the wall-soil interface, β is the angle between the sliding surface and the horizontal plane, and φ is the internal friction angle of the soil mass. Different β values ​​result in different failure surfaces and different Ea values. The maximum value of Ea is the ultimate earth pressure of the support structure. Solve for the β corresponding to the extreme value: ; Solve for the soil height H1 in the rectangular main arch zone and the soil height H2 in the triangular passive wedge zone: .

[0008] Furthermore, step S2 includes: The displacement at the midpoint of the support structure in the drum-shaped displacement mode is S. a The displacement required to reach the active ultimate failure is S. max Where z is the depth, Δz is the soil element thickness, and φ is the equivalent value of the internal friction angle affected by the depth of the support structure. m Equivalent value of the friction angle at the wall-soil interface δ m As shown in the following formula: When the displacement at the midpoint of the support structure in the drum-shaped displacement mode is greater than the displacement required for active ultimate failure... ; ; When the displacement at the midpoint of the support structure in the drum-shaped displacement mode is less than the displacement required for active ultimate failure: ; .

[0009] Furthermore, step S3 includes: In the drum-shaped displacement mode, the flexible support structure is considered to rotate around the top of the support structure at the top and around the bottom of the support structure at the bottom. Each soil layer will undergo relative motion with respect to the lower soil layer in the direction of rotation. By introducing the transverse stress infinitesimal element method and comparing the magnitudes of H and H1, the differential equations of earth pressure in the non-limit state are calculated for both cases: When H1 > H / 2, the horizontal earth pressure σ acting on the soil in the finite space behind the support structure can be obtained according to the mechanical equilibrium condition of the differential element. w for: ; Where k is the principal stress ratio, q is the soil surface load, l is the width of the soil in the finite space, γ is the soil weight, and φ is the equivalent value of the internal friction angle. m The equivalent value of the friction angle at the wall-soil interface is δ m Undetermined coefficients , , , , , , ; When H1 < H / 2, the horizontal earth pressure σ acting on the soil in the finite space behind the support structure can be obtained according to the mechanical equilibrium condition of the differential element. w for: ; Where k is the principal stress ratio, q is the soil surface load, l is the width of the soil in the finite space, γ is the soil weight, and φ is the equivalent value of the internal friction angle. m The equivalent value of the friction angle at the wall-soil interface is δ m Undetermined coefficients , , , , , , .

[0010] Furthermore, step S4 includes: When H1 > H / 2, the resultant horizontal earth pressure is obtained by integrating along the height of the support structure: ; When H1 < H / 2, the resultant horizontal earth pressure is obtained by integrating along the height of the support structure: ; The expression for the resultant force is:

[0011] When H1 > H / 2, the moment of the horizontal earth pressure about the bottom of the support structure is: ; When H1 is less than H / 2, the moment of the horizontal earth pressure about the bottom of the support structure is: ; The relative height of the point of application of the resultant horizontal earth pressure is: .

[0012] Furthermore, in step S1, the potential slip surface is a plane with an included angle. β Using the extreme value method, the sliding wedge is divided into two regions for force analysis: a rectangular main pressure arch region and a triangular passive wedge region.

[0013] Furthermore, in step S2, the equivalent value of the friction angle adopts a piecewise linear model, comprehensively considering the influence of the displacement and depth of the midpoint of the support structure on the degree of friction angle utilization.

[0014] Furthermore, in step S3, the transverse stress infinitesimal method is used to establish differential equations for two cases based on the location of the maximum displacement point, and the earth pressure distribution is solved iteratively through boundary conditions.

[0015] Furthermore, in step S4, the calculation of the resultant force and the point of application is based on the integration of the earth pressure distribution curve, thus obtaining the nonlinear distribution characteristics of earth pressure under the drum-shaped displacement mode.

[0016] As can be seen from the above technical solution, the present invention has the following beneficial effects: This method establishes a friction angle utilization model considering the non-uniform deformation under the drum-shaped displacement mode, more realistically reflecting the degree of utilization of the shear strength of soil in a finite space under non-limit conditions. The method clarifies the development law of the slip surface and the basis for regional division of finite soil under the drum-shaped displacement mode. Employing the transverse stress micro-element method, this method establishes a non-limit earth pressure calculation model considering the influence of shear stress in upper and lower layers, accurately reflecting the nonlinear distribution characteristics of earth pressure, and providing a theoretical basis and practical method for the design of foundation pit support under similar engineering conditions. Attached Figure Description

[0017] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram illustrating the soil destruction process described in this invention. Figure 3 This is a diagram showing the relationship between the friction angle and the depth of the support structure in this invention. Figure 4 This is a schematic diagram of the horizontal differential calculation unit for damaged soil in this invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] like Figures 1-4 As shown, this invention provides a technical solution: a method for calculating earth pressure in a foundation pit based on drum-shaped displacement and stress zoning within a confined space, the method comprising: S1. Establish a potential slip surface model described by a straight line, divide the soil in the limited space behind the support structure into a rectangular main arch area and a triangular passive wedge area, and solve the soil height in the rectangular main arch area and the soil height in the triangular passive wedge area based on the force equilibrium condition of the slip wedge. S2. Considering the drum-shaped displacement mode of the support structure and the difference in the equivalent value of the soil friction angle at different depths, a linear relationship model is established between the soil internal friction angle and the wall-soil interface friction angle as a function of the support structure displacement and depth. S3. Perform stress deflection analysis on the rectangular main pressure arch area and the triangular passive wedge area respectively, and establish the non-limit earth pressure distribution expression based on the transverse stress micro-element method for different cases. S4. Solve for the earth pressure coefficient and the height of the resultant force application point in different cases to complete the calculation of non-ultimate earth pressure.

[0020] The method for calculating non-ultimate earth pressure in finite soil under the drum-shaped displacement mode provided by this invention aims to more realistically reflect the actual stress distribution of the soil behind the flexible support structure during drum-shaped deformation. Its core principle is to combine the asymmetric deformation characteristics of soil under the drum-shaped displacement mode with the soil arching effect mechanism, overcoming the shortcomings of traditional Rankine or Coulomb theories in handling finite soil, non-ultimate states, and complex displacement modes. During foundation pit excavation, due to the drum-shaped displacement mode of the support structure, the soil displacement is large in the middle and small at the top and bottom, resulting in different degrees of soil friction angle development and a significant nonlinear and asymmetric stress distribution. Especially in the areas near the top and bottom of the support structure, the soil arching effect is significant, and stress redistribution is prominent. Therefore, in this invention, the failure mode and stress state of the soil under the drum-shaped displacement mode are first simulated using finite element software to identify the slip surface morphology and stress deflection law. Subsequently, the slip wedge is divided into rectangular and triangular regions, and soil arching calculation models considering principal stress deflection are established for each region. The stress state in each region is analyzed, and static equilibrium equations are constructed based on soil strength theory. To improve computational accuracy and applicability, this invention further considers the influence of the displacement and depth of the support structure on the equivalent value of the friction angle, and establishes a linear friction angle model under non-limit states. Using the transverse stress infinitesimal element method, force analysis is performed on four different differential element bodies, and the governing differential equations are established and solved to obtain the earth pressure distribution on the support structure. Finally, the resultant earth pressure, earth pressure coefficient, and the location of the resultant force's point of application are obtained through integration, providing a more scientific and accurate theoretical basis for the design of foundation pit support structures.

[0021] S1 includes: defining the potential slip surface as a plane with an angle β to the horizontal plane, the slip surface dividing the soil into a rectangular main arch zone ① and a triangular passive wedge zone ②; Earth pressure is obtained from the overall force equilibrium condition of the sliding wedge. E a : ; Where n is the aspect ratio of the finite soil mass, H is the height of the flexible support structure, q is the soil surface load, γ is the soil weight, δ is the friction angle at the wall-soil interface, β is the angle between the sliding surface and the horizontal plane, and φ is the internal friction angle of the soil mass.

[0022] Different values ​​of β result in different failure surfaces and different values ​​of Ea. The maximum value of Ea is the ultimate earth pressure on the support structure. Solve for the β corresponding to the extreme value: ; Solve for the soil height H1 in the rectangular main arch region and the soil height H2 in the triangular passive wedge region: ; This implementation details the construction steps of a linear slip surface model. Its working principle is first reflected in dividing a finite soil mass into a rectangular main arch zone and a triangular passive wedge zone using a linear slip surface, thereby achieving a quantitative description of the soil failure mechanism. Specifically, the method first determines the angle β between the slip surface and the horizontal plane based on the soil's physical and mechanical parameters and boundary conditions. This angle is jointly determined by the soil's internal friction angle φ and the wall-soil interface friction angle δ. Subsequently, based on the force equilibrium conditions of the slip wedge, the soil height H1 in the rectangular main arch zone and the soil height H2 in the triangular passive wedge zone are solved, ensuring the rationality of the zoning and the clarity of the calculation boundaries. Through this series of rigorous, continuous, and analytical geometric derivation steps, this invention transforms the abstract slip surface mechanism into a quantifiable geometric parameter system, providing boundary support and initial conditions for subsequent stress deflection analysis and earth pressure numerical iteration, ensuring the consistency, accuracy, and engineering practicality of the earth pressure calculation process in terms of physical logic and mathematical expression.

[0023] Step S2 includes: In the non-limit state, the process in which the support structure undergoes displacement, causing the internal friction angle of the soil behind it to gradually develop. The displacement of the support structure at the midpoint in the drum-shaped displacement mode is S. a The displacement required to reach the active ultimate failure is S. max z represents the depth, and Δz represents the thickness of the soil element.

[0024] Equivalent value of internal friction angle φ considering the influence of support structure depth m Equivalent value of the friction angle at the wall-soil interface δ m As shown in the following formula: When the displacement at the midpoint of the support structure in the drum-shaped displacement mode is greater than the displacement required for active ultimate failure... When the displacement at the midpoint of the support structure in the drum-shaped displacement mode is less than the displacement required for active ultimate failure... This implementation method constructs a refined calculation system for the equivalent value of soil friction angle, which is based on the introduction of a drum-shaped displacement mode to establish the soil internal friction angle φ. m Friction angle δ at the wall-soil interface m A linear relationship model of soil shear strength variation with displacement and depth of the supporting structure was established to reveal the mechanism of soil shear strength utilization under non-limit states. m and δ mA model is proposed that the friction angle increases linearly with the horizontal displacement of the support structure, taking into account the influence of the support structure depth. Formulas for calculating the equivalent friction angle at different depths are given. This model can accurately reflect the extent to which the soil shear strength is utilized under non-limit conditions, providing accurate parameter inputs for subsequent stress deflection analysis and earth pressure distribution calculations.

[0025] Step S3 includes: In the drum-shaped displacement mode, the flexible support structure can be considered as the upper part rotating around the top (RT) of the support structure and the lower part rotating around the bottom (RB) of the support structure. Each soil layer will undergo relative motion with respect to the lower soil layer in the direction of rotation, and the influence of shear stress between the upper and lower soil layers needs to be considered. The transverse stress infinitesimal element method is introduced, and by comparing the magnitudes of H and H1, the differential equations of earth pressure in the non-limit state are calculated for both cases, and their distribution is discussed.

[0026] When H1 > H / 2, the horizontal earth pressure σ acting on the soil in the finite space behind the support structure can be obtained according to the mechanical equilibrium condition of the differential element. w for: ; Where k is the principal stress ratio, q is the soil surface load, l is the width of the soil in the finite space, γ is the soil weight, and φ is the equivalent value of the internal friction angle. m The equivalent value of the friction angle at the wall-soil interface is δ m Undetermined coefficients , , , , , , .

[0027] When H1 < H / 2, the horizontal earth pressure σ acting on the soil in the finite space behind the support structure can be obtained according to the mechanical equilibrium condition of the differential element. w for: ; Where k is the principal stress ratio, q is the soil surface load, l is the width of the soil in the finite space, γ is the soil weight, and φ is the equivalent value of the internal friction angle. m The equivalent value of the friction angle at the wall-soil interface is δ m Undetermined coefficients , , , , , , .

[0028] This implementation simulates the stress redistribution phenomenon in actual soil under the drum-shaped displacement mode by performing stress deflection analysis on the rectangular main arch region and the triangular passive wedge region respectively. These analyses, based on local stress states, reflect the shift in soil stress transmission paths caused by drum-shaped displacement, resulting in a non-uniform distribution of earth pressure. Based on the transverse stress micro-element method, expressions for the non-limit earth pressure distribution are established for different cases. This method fully considers the relative motion trend and the influence of the soil arching effect under the drum-shaped displacement mode, accurately describing key mechanical behaviors such as soil stress concentration areas, arch foot supports, and force transmission paths at the arch crown, thus revealing the specific impact of the spatial distribution of earth pressure under non-limit states. This method not only improves the accuracy of earth pressure calculation but also makes the model more adaptable and provides engineering guidance when simulating the mechanical response under complex foundation pit conditions.

[0029] Step S4 includes: When H1 > H / 2, the resultant horizontal earth pressure can be obtained by integrating along the height of the support structure as follows:

[0030] When H1 < H / 2, the resultant horizontal earth pressure can be obtained by integrating along the height of the support structure:

[0031] The expression for the resultant force is: ; When H1 > H / 2, the moment of the horizontal earth pressure about the bottom of the support structure is:

[0032] When H1 is less than H / 2, the moment of the horizontal earth pressure about the bottom of the support structure is:

[0033] The relative height of the point of application of the resultant horizontal earth pressure is: ; This implementation method constructs a mathematical model of the resultant earth pressure force and its point of application by performing integral analysis on the expression for the distribution of non-ultimate earth pressure, thereby achieving accurate assessment of the stress distribution on the support structure. Specifically, based on the stress distribution law within the soil depth range, the method divides the lateral earth pressure into different segments, calculates the stress borne by the support structure per unit width within each segment, and obtains the overall resultant force through integral summation. The expression for the resultant force consists of two integral terms, representing the cumulative lateral stress values ​​in different depth intervals. To further clarify the actual location of the resultant force on the structure, i.e., the point of application of the resultant force, the method establishes a corresponding static moment calculation model. By using the weighted integral of the stress distribution with respect to depth, the static moment of the resultant force about the bottom point is determined, and the depth position of the point of application of the resultant force is obtained by the ratio of the resultant force to the static moment. Finally, based on the obtained earth pressure coefficient and the height of the point of application of the resultant force, the calculation of the non-ultimate earth pressure is completed. This calculation process can accurately reflect the nonlinear and non-uniform variation characteristics of the stress on finite soil under the drum-shaped displacement mode, avoid the errors caused by the simplified assumptions, improve the ability to judge the stress state of structures under complex foundation conditions, and thus provide a more accurate and reliable theoretical basis for the design of foundation pit support.

[0034] In step S1, the angle between the slip surface of the linear slip surface model and the horizontal plane is determined by the friction angle within the soil and the friction angle at the wall-soil interface, and the heights of the rectangular main pressure arch zone and the triangular passive wedge zone are determined by combining geometric relationships.

[0035] This implementation utilizes the internal friction angle of the soil and the friction angle at the wall-soil interface as key physical parameters to determine the angle β between the linear slip surface and the horizontal plane, thereby reflecting the inclination of the potential failure surface. This method introduces geometric relationships as a mathematical tool for zoning description. In this relationship, the height H1 of the rectangular main arch zone and the height H2 of the triangular passive wedge zone are jointly determined by the slip surface angle β and the soil width l. Specifically, the slip surface angle β is jointly determined by the internal friction angle φ of the soil and the friction angle δ at the wall-soil interface, reflecting the dominant influence of soil shear strength on the sliding tendency. Simultaneously, the heights of the rectangular main arch zone and the triangular passive wedge zone can be accurately located using the angle and distance parameters in the geometric relationship. This method couples soil mechanical properties with a geometric model, enhancing the ability to characterize the sliding mechanism and laying a theoretical foundation for subsequent earth pressure distribution and resultant force calculations, thus contributing to improving the accuracy of stability assessment in foundation pit support structure design.

[0036] A straight slip surface is used to represent the potential slip path of the soil and to divide the spatial range of the rectangular main arch zone and the triangular passive wedge zone by the slip surface.

[0037] This implementation uses a linear slip surface as a potential path model for soil slippage, reflecting the possible deformation trend of the excavation pit soil after disturbance. This slip surface not only has a clear physical meaning, describing the failure trajectory of the soil under extreme conditions, but also possesses clear geometric characteristics, facilitating mathematical processing. By using this slip surface as a boundary, the soil space can be effectively divided into a rectangular main arch zone and a triangular passive wedge zone: the rectangular main arch zone is the area above the slip surface where the soil arching effect is significant, typically exhibiting strong stress redistribution; while the triangular passive wedge zone is the soil pressure transmission area below the slip surface, primarily bearing the source of the reaction force required by the support structure. This spatial division method not only clearly defines the differences in the effects of soil on the support structure in different areas but also provides clear boundary conditions for subsequent earth pressure integral calculation and distribution analysis, contributing to improving the scientific rigor and applicability of the overall support system calculation model.

[0038] The linear relationship model between the soil internal friction angle and the wall-soil interface friction angle in step S2, which varies with the displacement and depth of the support structure, is used to reflect the degree to which the soil shear strength is utilized under non-limit conditions.

[0039] This implementation method establishes the internal friction angle φ of the soil. m Friction angle δ at the wall-soil interface m Linear relationship models relating to the displacement and depth of the supporting structure are used to simulate the shear strength utilization mechanism of actual soil under non-limit states. These models, based on local displacement and depth, reflect the differences in the equivalent value of the soil friction angle caused by drum-shaped displacement, resulting in a non-uniform distribution of shear strength. This model can accurately describe the degree of shear strength utilization of the soil at different depths, thus revealing the specific impact of earth pressure distribution under non-limit states. This method not only improves the accuracy of earth pressure calculations but also makes the model more adaptable and provides greater engineering guidance when simulating the mechanical response under complex foundation pit conditions.

[0040] In step S3, the mechanical equilibrium equations are established for the rectangular main pressure arch area and the triangular passive wedge area respectively, and different boundary conditions are set according to the transverse stress micro-element method.

[0041] In this implementation method, during the modeling process, independent stress deflection analysis systems are established for the soil in the rectangular main arch zone and the triangular passive wedge zone, which are divided by a straight slip surface. This method fully considers the uneven stress distribution and soil structure differences caused by the drum-shaped displacement mode. For the rectangular main arch zone, corresponding mechanical boundary conditions are set based on the potential soil arch structure, self-weight influence, and stress deflection behavior. For the triangular passive wedge zone, the boundary stress conditions are determined based on the contact state between the soil and the slip surface, the reaction characteristics of the passive zone, and the sliding trend. This regional and condition-specific modeling approach makes the overall earth pressure analysis more targeted and accurate, truly reflecting the stress characteristics and interactions of each section under the drum-shaped displacement mode, which helps optimize support design and improve the safety of foundation pit engineering.

[0042] In step S4, the resultant force calculation is based on the integration of the lateral earth pressure over the entire depth range of the support structure to obtain the total earth pressure on the support structure and the location of the resultant force application point.

[0043] This implementation method integrates the lateral earth pressure across the entire depth range of the support structure, systematically accumulating the earth pressure values ​​at each depth to obtain the total resultant force borne by the support structure. Based on the earth pressure distribution results previously obtained through numerical integration, this method uses continuously varying pressure data as the integration function, performing integration along the depth direction of the excavation pit. Since earth pressure may exhibit nonlinear variations at different depths, especially under the influence of the drum-shaped displacement mode, this integration process can comprehensively capture the cumulative effect of lateral earth pressure, avoiding errors caused by using average values ​​or simplified distributions, thus providing a more accurate stress assessment result for the support structure. This integration-based resultant force calculation method not only enhances the theoretical depth of earth pressure analysis but also provides reliable boundary load conditions for structural design, ensuring that the support system possesses good stability and safety margin under actual working conditions.

[0044] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for calculating earth pressure in a foundation pit with drum-shaped displacement and stress zoning in a confined space, characterized in that, Includes the following steps: S1. Establish a potential slip surface model described by a straight line, divide the soil in the limited space behind the support structure into a rectangular main arch zone and a triangular passive wedge zone, and solve the soil height in the rectangular main arch zone and the soil height in the triangular passive wedge zone based on the force equilibrium condition of the slip wedge. S2. Considering the drum-shaped displacement mode of the support structure and the difference in the equivalent value of the soil friction angle at different depths, establish a model for the variation of the soil internal friction angle and the wall-soil interface friction angle with the displacement and depth of the support structure under non-limit conditions. S3. Perform stress deflection analysis on the rectangular main pressure arch area and the triangular passive wedge area respectively, and establish the expression for the distribution of non-limit earth pressure based on the transverse stress micro-element method. S4. Solve for the earth pressure coefficient and the height of the resultant force application point to complete the calculation of non-ultimate earth pressure under the drum-shaped displacement mode in finite space.

2. The method for calculating earth pressure in a foundation pit with drum-shaped displacement and stress zoning in a confined space according to claim 1, characterized in that: Step S1 includes: As shown in Figure 2, the potential slip surface is set as a plane with an angle of β with the horizontal plane. The slip surface divides the soil into a rectangular main arch region 1 and a triangular passive wedge region 2. Earth pressure is obtained from the overall force equilibrium condition of the sliding wedge. E a : ； Where n is the width-to-height ratio of the finite soil mass, H is the height of the flexible support structure, q is the soil surface load, γ is the soil weight, δ is the friction angle of the wall-soil interface, β is the angle between the sliding surface and the horizontal plane, and φ is the internal friction angle of the soil mass. Different β values ​​result in different failure surfaces and different Ea values. The maximum value of Ea is the ultimate earth pressure of the support structure. Solve for the β corresponding to the extreme value: ； Solve for the soil height H1 in the rectangular main arch zone and the soil height H2 in the triangular passive wedge zone: .

3. The method for calculating earth pressure in a foundation pit with drum-shaped displacement and stress zoning in a confined space according to claim 1, characterized in that: Step S2 includes: The displacement at the midpoint of the support structure in the drum-shaped displacement mode is S. a The displacement required to reach the active ultimate failure is S. max Where z is the depth, Δz is the soil element thickness, and φ is the equivalent value of the internal friction angle affected by the depth of the support structure. m Equivalent value of the friction angle at the wall-soil interface δ m As shown in the following formula: When the displacement at the midpoint of the support structure in the drum-shaped displacement mode is greater than the displacement required for active ultimate failure... ； ； When the displacement at the midpoint of the support structure in the drum-shaped displacement mode is less than the displacement required for active ultimate failure: ； 。 4. The method for calculating earth pressure in a foundation pit with drum-shaped displacement and stress zoning in a confined space according to claim 1, characterized in that: Step S3 includes: In the drum-shaped displacement mode, the flexible support structure is considered to rotate around the top of the support structure at the top and around the bottom of the support structure at the bottom. Each soil layer will undergo relative motion with respect to the lower soil layer in the direction of rotation. By introducing the transverse stress infinitesimal element method and comparing the magnitudes of H and H1, the differential equations of earth pressure in the non-limit state are calculated for both cases: When H1 > H / 2, the horizontal earth pressure σ acting on the soil in the finite space behind the support structure can be obtained according to the mechanical equilibrium condition of the differential element. w for: ； Where k is the principal stress ratio, q is the soil surface load, l is the width of the soil in the finite space, γ is the soil weight, and φ is the equivalent value of the internal friction angle. m The equivalent value of the friction angle at the wall-soil interface is δ m Undetermined coefficients , , , , , , ; When H1 < H / 2, the horizontal earth pressure σ acting on the soil in the finite space behind the support structure can be obtained according to the mechanical equilibrium condition of the differential element. w for: ； Where k is the principal stress ratio, q is the soil surface load, l is the width of the soil in the finite space, γ is the soil weight, and φ is the equivalent value of the internal friction angle. m The equivalent value of the friction angle at the wall-soil interface is δ m Undetermined coefficients , , , , , , .

5. The method for calculating earth pressure in a foundation pit based on drum-shaped displacement and stress zoning in a confined space according to claim 1, characterized in that: Step S4 includes: When H1 > H / 2, the resultant horizontal earth pressure is obtained by integrating along the height of the support structure: ； When H1 < H / 2, the resultant horizontal earth pressure is obtained by integrating along the height of the support structure: ； The expression for the resultant force is: ； When H1 > H / 2, the moment of the horizontal earth pressure about the bottom of the support structure is: ； When H1 is less than H / 2, the moment of the horizontal earth pressure about the bottom of the support structure is: ； The relative height of the point of application of the resultant horizontal earth pressure is: 。 6. The method for calculating earth pressure in a foundation pit based on drum-shaped displacement and stress zoning in a confined space according to claim 1, characterized in that: In step S1, the potential slip surface is a plane with an included angle. β Using the extreme value method, the sliding wedge is divided into two regions for force analysis: a rectangular main pressure arch region and a triangular passive wedge region.

7. The method for calculating earth pressure in a foundation pit with drum-shaped displacement and stress zoning in a confined space according to claim 1, characterized in that: In step S2, the equivalent value of the friction angle adopts a piecewise linear model, which comprehensively considers the influence of the displacement and depth of the midpoint of the support structure on the degree of friction angle utilization.

8. The method for calculating earth pressure in a foundation pit with drum-shaped displacement and stress zoning in a confined space according to claim 1, characterized in that: In step S3, the transverse stress infinitesimal method is used to establish differential equations for two cases based on the location of the maximum displacement point, and the earth pressure distribution is solved iteratively through boundary conditions.

9. The method for calculating earth pressure in a foundation pit based on drum-shaped displacement and stress zoning in a confined space according to claim 1, characterized in that: In step S4, the calculation of the resultant force and the point of application is based on the integration of the earth pressure distribution curve, which yields the nonlinear distribution characteristics of earth pressure under the drum-shaped displacement mode.

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