Calculation method and device for active earth pressure of retaining wall based on inclined strip method

Abstract

The present application relates to the technical field of geotechnical mechanics analysis and calculation, in particular to a retaining wall active earth pressure calculation method and device based on inclined strip method. It comprises: S1. obtaining engineering information and constructing a calculation model containing wall back, filling body and rupture surface; S2. dividing the filling body into multiple inclined strip units between the wall back and the rupture surface; S3. establishing a static force balance relationship based on the action of the strip units; S4. introducing strength conditions for limiting the interface force and the force range between the units in the balance relationship; S5. solving the force of the strip units and obtaining the interface force distribution along the wall back under the given rupture surface inclination; S6. calculating the active earth pressure corresponding to the rupture surface inclination and determining the active limit state, and outputting the calculation results. By comprehensively considering the force of the strip units, the interface strength conditions and the rupture surface inclination optimization in a unified calculation framework, accurate calculation of the active earth pressure and the action distribution under complex working conditions is realized.

Description

Technical Field

[0001] This invention relates to the field of geotechnical mechanics analysis and calculation technology, and in particular to a method and apparatus for calculating active earth pressure on retaining walls based on the oblique strip method. Background Technology

[0002] Gravity retaining walls, as a commonly used slope support structure, are widely used in engineering construction due to their simple structural form and convenient construction. In the design of this type of structure, the active earth pressure acting on the back of the wall is a key parameter determining the structural safety and stability. Current design practices often use classical earth pressure theory for calculations, but these theories are usually based on ideal conditions and have strict applicable premises on the fill slope surface, wall back shape, and wall-soil interface conditions. They often only obtain the magnitude of the resultant force of the active earth pressure, making it difficult to accurately describe the pressure distribution along the height direction of the wall back, and also unable to determine the actual location of the point of application of the resultant force, relying only on empirical assumptions.

[0003] With increasing engineering demands, field measurements and model tests have shown that the earth pressure behind walls typically exhibits a nonlinear variation with depth, and traditional theories, based on simplification assumptions, are insufficient to effectively explain this phenomenon. To address this issue, existing technologies have attempted to analyze the stress behind walls by layering or segmenting the soil. However, current layering methods have limitations in applicability when dealing with non-horizontal backfill, inclined walls, and complex interface conditions.

[0004] Furthermore, existing technologies indicate that the shear transfer capacity between different layers within the soil varies with location. If the shear relationship between the sliced ​​elements is not properly considered, the resulting earth pressure distribution often deviates from the actual situation. Meanwhile, the cohesion and frictional effects at the wall-soil interface are significant in many engineering projects, but traditional models often fail to adequately consider these factors or handle them in a coarse manner, leading to discrepancies between calculated results and engineering observations.

[0005] In summary, existing methods for calculating active earth pressure generally face problems such as limited applicability, difficulty in reflecting nonlinear pressure distribution, incomplete handling of shear transfer between slice elements, and insufficient consideration of wall-soil interface effects. There is still a lack of a calculation method and device that can integrate the above factors under a unified calculation framework and accurately solve for the magnitude and distribution of active earth pressure. Summary of the Invention

[0006] This application aims to at least address the technical problems existing in the prior art. This application provides a method and apparatus for calculating active earth pressure on retaining walls based on the oblique slice method. This method can perform slice analysis on the stress state of the backfill soil under complex working conditions, obtaining the magnitude of the active earth pressure and its distribution along the height direction of the back wall, thereby improving the completeness and applicability of the active earth pressure calculation.

[0007] In this application, a calculation model is constructed by obtaining engineering information on the retaining wall and the backfill behind it. Multiple oblique slice elements are divided between the back of the wall and the rupture surface. Static equilibrium relationships can be established based on the self-weight of the slice elements, external loads, inter-element forces, and interfacial forces. By applying wall-soil interface strength conditions and inter-slice strength conditions to the equilibrium relationship, unified constraints on interfacial friction, interfacial cohesion, and the shear transmission capacity within the soil are achieved. Given the inclination angle of the rupture surface, the stress state is solved and the distribution of interfacial forces along the back of the wall is obtained.

[0008] By accumulating and vectorizing the components of the interfacial forces, the active earth pressure at the corresponding rupture surface inclination angle can be obtained. Furthermore, by taking multiple values ​​of the rupture surface inclination angle and comparing the active earth pressure obtained at different inclination angles, the active limit state can be automatically determined, thereby obtaining the active earth pressure under the most unfavorable working condition. This achieves the technical effect of reflecting complex working conditions and accurately calculating the active earth pressure and its distribution.

[0009] In a first aspect, embodiments of this application provide a method for calculating active earth pressure on retaining walls based on the oblique strip method, which may include:

[0010] S1. Obtain engineering information to characterize the retaining wall, the back of the wall, the backfill behind the wall, and the state of the wall-soil interface, and construct a calculation model including the back of the wall, the backfill, and the fracture surface based on the engineering information;

[0011] S2. Divide the backfill between the wall back and the fracture surface into multiple oblique strip units to form an oblique strip structure for unit-by-unit mechanical analysis;

[0012] S3. For each oblique slice unit, establish a static equilibrium relationship based on the forces acting on the slice unit;

[0013] S4. Introduce strength conditions in the static equilibrium relationship to limit the range of values ​​of interface forces and inter-unit forces;

[0014] S5. Given the inclination angle of the fracture surface, solve the inter-element force and interface force of each inclined strip element based on the static equilibrium relationship and the strength condition to obtain the interface force distribution along the wall back height direction;

[0015] S6. Calculate the active earth pressure corresponding to the rupture surface inclination angle based on the interface force distribution, and determine the active earth pressure under the active limit state by changing the rupture surface inclination angle as the calculation result.

[0016] According to some embodiments of this application, the engineering information obtained in S1 includes at least: the height of the retaining wall, the inclination angle of the wall back relative to the vertical direction, the inclination angle of the backfill surface, the unit weight of the backfill, the internal friction angle of the backfill, the cohesive strength of the backfill, the friction angle of the wall-soil interface, the cohesive strength of the wall-soil interface, and the surface load intensity acting on the backfill surface; wherein, the calculation model assumes that the rupture surface of the soil behind the wall is a plane passing through the bottom of the wall back, and uses the inclination angle of the plane relative to the horizontal plane as the rupture surface inclination angle to be determined;

[0017] The forces described in S3 include: the self-weight of the slice unit, the external load applied to the slice unit, the inter-slice forces between adjacent slice units, and the interface forces between the slice unit and the wall back.

[0018] The strength conditions in S4 include: the wall-soil interface strength condition for limiting the range of the interface force values, and the inter-unit strength condition for limiting the range of the inter-unit force values; wherein, the inter-unit strength condition for the oblique slice is used to determine the maximum available shear capacity between adjacent oblique slices, and the maximum available shear capacity is weighted by a shear coefficient related to the position of the slice in the fill to obtain the actual shear force between slices at different positions.

[0019] According to some embodiments of this application, in S2, dividing the fill into multiple oblique strip units includes:

[0020] Using the height of the retaining wall and the preset number of segments as input, the backfill between the wall back and the fracture surface is divided into several segments of the same thickness along the same direction as the fracture surface.

[0021] The upper and lower boundaries of each stripe unit are parallel to the fracture surface, and each stripe unit has a unique height identifier along the height direction of the wall back to distinguish stripe units of different depths.

[0022] In S6, the calculation of active earth pressure based on the interface force distribution includes: summing up the components of the interface force in different directions along the wall back height direction, and combining the summed components in different directions to obtain the active earth pressure corresponding to the rupture surface dip angle.

[0023] The step of determining the active limit state by changing the inclination angle of the rupture surface includes: taking multiple values ​​of the inclination angle of the rupture surface within a preset angle range, and repeating S5 for each value, comparing the active earth pressure corresponding to different rupture surface inclination angles, and selecting the active earth pressure with the largest value as the final calculation result.

[0024] According to some embodiments of this application, establishing the oblique slice element static equilibrium relationship in S3 includes:

[0025] For any given sub-unit, the self-weight and external load acting on that sub-unit are decomposed into components along the fracture surface direction and perpendicular to the fracture surface direction;

[0026] The inter-unit force between the segment and adjacent segments is decomposed into a shear component along the fracture surface and a normal component perpendicular to the fracture surface. The interfacial force between the segment and the wall back is decomposed into a tangential component along the wall back surface and a normal component perpendicular to the wall back surface.

[0027] Then, by adding all components in each direction and setting the resultant force in each direction to zero, the balance relationship between the inter-unit forces and the interface forces of each sub-unit is obtained.

[0028] According to some embodiments of this application, establishing the oblique slice element static equilibrium relationship in S3 includes:

[0029] For any given sub-unit, the self-weight and external load acting on that sub-unit are decomposed into components along the fracture surface direction and perpendicular to the fracture surface direction;

[0030] The inter-unit force between the segment and adjacent segments is decomposed into a shear component along the fracture surface and a normal component perpendicular to the fracture surface. The interfacial force between the segment and the wall back is decomposed into a tangential component along the wall back surface and a normal component perpendicular to the wall back surface.

[0031] Then, by adding all components in each direction and setting the resultant force in each direction to zero, the balance relationship between the inter-unit forces and the interface forces of each sub-unit is obtained.

[0032] In the above implementation process, the wall-soil interface strength conditions in S4 include:

[0033] The inputs are the normal pressure at the interface between a certain sub-unit and the back of the wall, the friction angle at the wall-soil interface, and the cohesion strength.

[0034] The tangential bearing capacity provided by friction is obtained by multiplying the interface normal pressure with the friction coefficient determined based on the friction angle.

[0035] The cohesion strength of the wall-soil interface is then multiplied by the contact height of the sub-unit on the back of the wall, and converted in combination with the inclination angle of the back of the wall to obtain the tangential bearing capacity provided by cohesion.

[0036] The tangential bearing capacity of friction and cohesion is added together, and the interfacial tangential force between the sub-unit and the back of the wall is limited to a range not exceeding the sum of the values.

[0037] According to some embodiments of this application, the inter-strip strength conditions in S4 include:

[0038] Using the inter-unit normal pressure between a certain sub-unit and adjacent sub-units, the internal friction angle of the soil, the cohesive strength of the soil, and the contact length between sub-units as inputs, the shear bearing capacity provided by the internal friction of the soil is obtained by multiplying the inter-unit normal pressure with the friction coefficient determined based on the internal friction angle of the soil; then, the shear bearing capacity provided by the cohesive action of the soil is obtained by multiplying the cohesive strength of the soil with the contact length.

[0039] The shear capacity of friction and cohesion is added together to obtain the maximum available shear capacity between units. The maximum available shear capacity is then weighted by a shear force utilization coefficient related to the position of the strip unit in the height direction of the wall back to obtain the actual shear force between the strip unit and adjacent strip units at each depth. The shear force utilization coefficient gradually increases from top to bottom with the position of the strip unit in the height direction of the wall back.

[0040] According to some embodiments of this application, in S5 and S6, solving for the inter-element forces and interface forces of the oblique slice elements and determining the active earth pressure includes:

[0041] The equilibrium relationship of each sub-unit, the strength condition of the wall-soil interface, and the strength condition between sub-units are combined to form a set of algebraic equations. The unknown inter-unit forces and interface forces in the set of equations are solved by numerical solution to obtain the distribution of the interface normal component and interface tangential component along the height direction of the wall back.

[0042] The interface normal components at each height position are added together to obtain the total normal component along the wall back direction. The interface tangential components at each height position are added together to obtain the total tangential component along the wall back direction. The total normal component and the total tangential component are considered as mutually perpendicular force components and vectored together to obtain the active earth pressure at the corresponding rupture surface dip angle.

[0043] The dip angle of the rupture surface is taken multiple times within a preset angle range, and the solution and vector synthesis process is repeated for each value to obtain a set of active earth pressure values ​​corresponding to different dip angles of the rupture surface. The one with the largest value is selected from the active earth pressure values, and the corresponding dip angle of the rupture surface is determined as the dip angle of the rupture surface under the active limit state. The maximum active earth pressure is taken as the final output active earth pressure.

[0044] Secondly, embodiments of this application provide a device for calculating active earth pressure on retaining walls based on the oblique strip method, the device including:

[0045] The engineering information acquisition module is used to take engineering information as input, which is used to characterize the state of the retaining wall, the back of the wall, the backfill and the wall-soil interface. The engineering information acquisition module is configured to construct a calculation model including the back of the wall, the backfill and the fracture surface represented by the inclination angle to be determined based on the engineering information, and output the calculation model to the subsequent modules.

[0046] The oblique strip module, connected to the engineering information acquisition module, is used to divide the backfill into multiple oblique strip units between the wall back and the fracture surface along the direction corresponding to the fracture surface, taking the calculation model as input. The oblique strip units form an oblique strip structure for unit-by-unit mechanical analysis, and the module determines the position identifier of each oblique strip unit along the height direction of the wall back. The oblique strip module is configured to output the oblique strip units and their position identifiers to subsequent modules.

[0047] The equilibrium relationship establishment module, connected to the diagonal strip module, is used to decompose and combine the above forces under a preset reference direction system, taking the self-weight of each diagonal strip unit, the external load acting on each diagonal strip unit, the inter-unit force between each diagonal strip unit and the adjacent diagonal strip unit, and the interface force between each diagonal strip unit and the wall back as inputs, so that each diagonal strip unit satisfies the static equilibrium condition in multiple directions, thereby forming an equilibrium relationship for associating the inter-unit force and the interface force, and outputting the static equilibrium relationship to the subsequent module;

[0048] The strength condition application module, connected to the equilibrium relationship establishment module, is used to introduce, with the static equilibrium relationship as input, a wall-soil interface strength condition to limit the range of interface force values, and a strip unit strength condition to limit the range of inter-unit force values. The inclined strip unit strength condition is used to determine the maximum available shear capacity between adjacent inclined strip units. This maximum available shear capacity is weighted by a shear coefficient related to the position of the strip unit in the fill, thereby obtaining the actual shear force between strip units at different locations. The strength condition application module is configured to output the equilibrium constraints, including the wall-soil interface strength condition and the strip unit strength condition, to subsequent modules.

[0049] The force solution module, connected to the strength condition application module, is used to solve for the inter-element forces and interface forces of all oblique slice elements, taking the equilibrium constraints and the given fracture surface dip angle as input, to obtain the interface force distribution along the height direction of the wall back. The interface force distribution includes a component along the normal direction of the wall back and a component along the tangential direction of the wall back. The force solution module is configured to output the interface force distribution to subsequent modules.

[0050] An active earth pressure determination module, connected to a force solution module, is used to accumulate and synthesize the components of the interface force along the height direction of the wall back in different directions, taking the interface force distribution as input, to obtain the active earth pressure corresponding to the given rupture surface inclination angle. The active earth pressure determination module is also configured to call the force solution module to obtain the interface force distribution under different rupture surface inclination angles by changing the rupture surface inclination angle, and to repeatedly perform the accumulation and synthesis process for each interface force distribution, compare the active earth pressures corresponding to different rupture surface inclination angles, determine the rupture surface inclination angle that makes the active earth pressure reach its extreme value, and output the active earth pressure corresponding to the rupture surface inclination angle as the calculation result of the device.

[0051] The method and apparatus for calculating active earth pressure on retaining walls based on the oblique strip method according to the present invention have at least the following beneficial effects:

[0052] This application presents a method for calculating active earth pressure on retaining walls based on the oblique slice method. First, it acquires engineering information characterizing the retaining wall, its back wall, the backfill, and the wall-soil interface. A computational model is then constructed, including the back wall, the backfill, and the rupture surface. An oblique slice structure is established between the back wall and the rupture surface, and the backfill is discretized element by element for stress analysis, allowing the soil stress state to be expressed within a unified computational framework. By establishing a static equilibrium relationship for each oblique slice element and introducing strength conditions to limit the range of interface forces and inter-element forces, the stress transfer between slice elements and the wall-soil interface effect can be incorporated into the overall solution process in a constrained manner. This avoids the problem of traditional methods that only calculate the resultant earth pressure while ignoring the internal stress distribution. Solving for the stress state of each slice element under a given rupture surface inclination angle yields the interface force distribution along the wall back height, enabling the active earth pressure to not only have a resultant force value but also reflect its distribution characteristics along the wall back. Furthermore, by changing the inclination angle of the rupture surface and repeating the solution process, the active earth pressure corresponding to different inclination angles is compared and the extreme values ​​are determined. This automatically determines the rupture surface and corresponding active earth pressure under the active limit state, making the calculation results more consistent with actual stress conditions. This method comprehensively considers the stress balance and strength constraints of the sliced ​​elements under a unified calculation framework, making the solution process for active earth pressure more systematic and complete, which helps improve the accuracy and engineering applicability of retaining wall design and stability analysis.

[0053] The active earth pressure calculation device for retaining walls based on the oblique slice method of this application firstly achieves unified collection and modeling of structural and soil parameters through an engineering information acquisition module, enabling the calculation process to have a standardized and scalable input mechanism. Then, the oblique slice module generates multiple oblique slice elements according to preset rules, so that the number, range, and position of the slice elements can be automatically adapted to different engineering scenarios. Next, the equilibrium relationship establishment module transforms the force relationship of the oblique slice elements into a unified mathematical form, and the strength condition application module applies constraints to each force channel, so that interface effects and interactions between slice elements can be consistently incorporated into the solution process. Finally, the force solution module and the active earth pressure determination module operate collaboratively with a unified data flow to achieve the solution of the stress state of the slice elements, the formation of active earth pressure, and the automatic determination of the rupture surface inclination angle under the active limit state. This application utilizes a modular device structure to enable the active earth pressure calculation, from parameter input, model construction, constraint application, solution to result output, to be executed sequentially within the same system, achieving a complete, clear, and reusable calculation architecture. Through the orderly data flow between modules, the stress analysis and optimization process under complex working conditions can be automated, improving calculation efficiency and maintainability, and facilitating rapid integration and expansion in engineering applications.

[0054] Other features and advantages of this application will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing this application. Attached Figure Description

[0055] Figure 1 This is a schematic diagram illustrating the steps of the active earth pressure calculation method for retaining walls based on the oblique strip method in Embodiment 1 of this application;

[0056] Figure 2 This is a schematic diagram of the inclined strip calculation model for active earth pressure in Embodiment 2 of this application;

[0057] Figure 3 This is a schematic diagram of the soil strip stress analysis in Embodiment 2 of this application;

[0058] Figure 4 This is a schematic diagram of the horizontal earth pressure distribution values ​​in Example 3 of Embodiment 2 of this application;

[0059] Figure 5 This is a schematic diagram comparing the calculated and measured values ​​of earth pressure intensity in Example 4 of Embodiment 2 of this application;

[0060] Figure 6 This is a structural block diagram of the active earth pressure calculation device for retaining walls based on the oblique strip method in Embodiment 3 of this application. Detailed Implementation

[0061] The present application will now be described in further detail with reference to experimental examples and specific embodiments. However, this should not be construed as limiting the scope of the subject matter of the present application to the following embodiments. All technologies implemented based on the content of the present application fall within the scope of protection of the present application.

[0062] Unless otherwise specified, the use of terms such as "upper," "lower," "left," "right," "center," "inner," "outer," and "side" to indicate orientation or positional relationships in the description of specific embodiments of this application is based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is usually placed during use. These terms are merely for the purpose of facilitating the description of the solution in this application or simplifying the description in specific embodiments, and for enabling those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship, and therefore should not be construed as a limitation of this application.

[0063] In the description of the embodiments of this application, technical terms such as "first" and "second" only distinguish one entity or operation from another, and should not be construed as indicating or implying relative importance or implicitly specifying the number, specific order, or primary or secondary relationship of the indicated technical features. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly defined.

[0064] In this method, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this method can be combined with other embodiments.

[0065] Example 1

[0066] During the research process, the applicant found that when using the traditional active earth pressure theory based on simplified assumptions to analyze the stress of retaining walls, if it is necessary to obtain the magnitude of the resultant force of the active earth pressure and its actual distribution along the height direction of the wall back at the same time in order to accurately assess the safety and stability of the retaining wall, the existing technology can usually only perform a holistic analysis of the soil as a whole or make distribution estimations through local empirical assumptions. It is difficult to obtain reliable calculation results under complex working conditions, and can only give a relatively idealized pressure model. Moreover, it cannot take into account multiple factors such as the inclination of the wall back, the slope of the fill, the cohesion of the soil, and the wall-soil interface conditions.

[0067] In solving practical engineering problems, in order to achieve the technical goal of being able to handle complex boundary conditions, reflect the nonlinear distribution of earth pressure behind the wall, and determine the location of the rupture surface under the active limit state in a unified calculation process, existing technologies cannot meet the need for coordinated expression of force transmission path, interface strength conditions, and shear capacity between slice elements.

[0068] Therefore, after studying this problem, the applicant proposed a method for calculating active earth pressure on retaining walls based on the oblique slice method. By constructing an analysis system with oblique slice units as the main body, and performing model construction, slice division, static equilibrium relationship establishment, application of wall-soil interface strength conditions, application of strength conditions between slice units, force solution and extreme value search in a unified calculation framework, the method realizes the overall solution of the magnitude of active earth pressure and its nonlinear distribution along the back of the wall.

[0069] To address the aforementioned technical issues, this paper proposes a method that uses a strip structure to represent the stress element, multi-directional equilibrium to represent the force transmission, and the strength conditions between the interface and the element to represent the constraint relationship. The method also involves repeatedly solving the problem under different values ​​of the rupture surface dip angle to search for the active limit state. This method achieves a calculation process for active earth pressure that can reflect complex working conditions, provides complete and stable calculation results, and achieves the technical effect of simultaneously obtaining the resultant force and distribution of active earth pressure, being applicable to various engineering scenarios, and having high computational applicability and accuracy.

[0070] Please refer to Figure 1 , Figure 1 A schematic diagram illustrating the steps of the active earth pressure calculation method for retaining walls based on the oblique strip method provided in this application embodiment. This method may include:

[0071] S1. Obtain engineering information to characterize the retaining wall, the back of the wall, the backfill behind the wall, and the state of the wall-soil interface, and construct a calculation model including the back of the wall, the backfill, and the fracture surface based on the engineering information;

[0072] S2. Divide the backfill between the wall back and the fracture surface into multiple oblique strip units to form an oblique strip structure for unit-by-unit mechanical analysis;

[0073] S3. For each oblique slice unit, establish a static equilibrium relationship based on the forces acting on the slice unit;

[0074] S4. Introduce strength conditions in the static equilibrium relationship to limit the range of values ​​of interface forces and inter-unit forces;

[0075] S5. Given the inclination angle of the fracture surface, solve the inter-element force and interface force of each inclined strip element based on the static equilibrium relationship and the strength condition to obtain the interface force distribution along the wall back height direction;

[0076] S6. Calculate the active earth pressure corresponding to the rupture surface inclination angle based on the interface force distribution, and determine the active earth pressure under the active limit state by changing the rupture surface inclination angle as the calculation result.

[0077] In some specific implementations, this method may include:

[0078] First, the necessary parameter information for the retaining wall project is obtained, including various types of engineering information characterizing the retaining wall, the back wall, the backfill, and the wall-soil interface. Based on this information, a model is established that includes the back wall, the backfill, and the fracture surface with the fracture surface dip angle as a variable, providing an overall geometric and stress basis for subsequent calculations.

[0079] After forming the overall model, the backfill soil behind the wall is divided into several oblique slice elements along the same direction as the rupture surface, between the wall back and the rupture surface. Each slice element has a corresponding height position to reflect its depth in the direction of the wall back, so that subsequent stress analysis can be performed element by element.

[0080] Subsequently, for each oblique slice element, its self-weight, external loads, inter-element forces with adjacent slice elements, and interface forces with the wall back are considered. These forces are decomposed into the direction of the fracture surface, the direction perpendicular to the fracture surface, and the normal and tangential directions of the wall back. By balancing the resultant forces in each direction, each slice element satisfies the static equilibrium requirements, and equilibrium equations reflecting the relationship between inter-element forces and interface forces are obtained.

[0081] After establishing the equilibrium relationship, a wall-soil interface strength condition is applied to the interfacial forces, limiting the tangential interfacial forces to be determined by the interface normal force, friction angle, and cohesion strength. Simultaneously, an inter-unit strength condition is applied to the inter-unit forces between the slice elements, causing the available shear capacity between units to vary depending on the height of the slice element in the wall-back direction, thus allowing deeper slice elements to have a higher degree of shear capacity utilization. In this embodiment, the degree of shear capacity utilization refers to the ratio of the actual shear force between slice elements to their maximum available shear capacity, which is adjusted by a shear coefficient related to the slice element's position in the wall-back height direction. By setting the shear coefficient to gradually increase from top to bottom with the slice element's position, the actual shear force between deeper slice elements is made closer to their maximum available shear capacity, thereby reflecting the stress characteristics of the soil as shear stress gradually develops along the potential slip surface.

[0082] Given the dip angle of the fracture surface, the inter-element forces and inter-element forces between each slice element are solved by combining the equilibrium relationship, the interface strength condition, and the inter-element strength condition, so as to obtain the distribution of the interface normal component and the interface tangential component along the height direction of the wall back.

[0083] Next, by accumulating the interface normal and tangential components along the wall back direction in the height direction, and then vector-combining them as mutually perpendicular components, the active earth pressure at the corresponding rupture surface dip angle is obtained. To determine the active limit state, the above solution and synthesis process is repeated for each dip angle by changing the rupture surface dip angle, obtaining a set of active earth pressure values ​​corresponding to different dip angles. The active earth pressure with the largest value is selected as the final active earth pressure, and the corresponding rupture surface dip angle is taken as the rupture surface under the active limit state.

[0084] Through the above steps, this embodiment realizes the solution of the active earth pressure of the retaining wall and its distribution along the height direction of the wall back in a unified slice calculation framework. It can adapt to a variety of complex boundary conditions, and the calculation results have good engineering applicability.

[0085] Unlike some existing active earth pressure calculation methods that do not consider slope loads during modeling and simplify the shear force between slice elements to a position-independent constant or directly take it as the ultimate shear strength of the soil, the calculation model established in steps S1 and S2 of this application obtains engineering information such as the inclination angle of the backfill surface and the surface load acting on the slope, and constructs an overall model that reflects the slope working conditions accordingly. In steps S2 and S3, by dividing the backfill into inclined slice elements and decomposing and combining the self-weight, external load, inter-element forces, and interface forces of each element, the stress differences of slice elements at different depths are accurately reflected. In step S4 and related constraints, by setting a shear force utilization coefficient that gradually increases with the height of the wall back, the actual shear force between the slice elements gradually approaches the shear strength of the soil near the rupture surface. This is more in line with the actual law of the gradual development of shear stress in the soil along the potential slip surface, and avoids the shortcomings of directly applying the tension depth or stress assumptions under flat conditions to the slope conditions. In steps S5 and S6, by repeatedly solving the stress of the slice elements under multiple rupture surface inclination angles and selecting the extreme values ​​of the active earth pressure, a unified judgment of the active limit state under slope conditions is achieved, thereby obtaining the magnitude of the active earth pressure and its nonlinear distribution along the wall back that is closer to the actual working conditions.

[0086] The active earth pressure calculation method for retaining walls based on the oblique slice method provided in this application can be applied to many technical fields, such as geotechnical engineering investigation, slope retaining structure design, retaining wall safety and stability analysis, and auxiliary stress analysis of foundation pit engineering. This includes gravity retaining walls, cantilever retaining walls, sheet pile structures, and other engineering structures requiring earth pressure distribution analysis. In the above implementation, when performing slice analysis on the backfill behind the wall, the number of slice units can be set according to engineering requirements. The slice direction can be automatically adjusted based on the backfill geometry. Interface conditions and inter-unit strength conditions can also be introduced within a unified stress framework. A comprehensive analysis of the active earth pressure can be achieved through multi-directional equilibrium solutions, thus achieving the effect of accurately obtaining the magnitude of the active earth pressure and its nonlinear distribution along the back of the wall even under complex working conditions. Specific implementation methods of this method can be found in the descriptions in the following embodiments, which will not be elaborated here.

[0087] Example 2

[0088] Within the overall framework of the active earth pressure calculation method and device for retaining walls based on the oblique strip method described in Example 1, this example further provides a specific implementation of the method. To facilitate understanding of the application process of the above calculation architecture in actual engineering, this example provides a more detailed explanation of the calculation process of active earth pressure by clarifying the geometric relationships, force relationships, and related mechanical constraints of each strip unit, combined with specific parameter symbols and mechanical expressions.

[0089] In this embodiment, firstly, based on the geometric conditions of the retaining wall and the distribution of the backfill, the geometric relationship of the slice elements is established, and the static equilibrium equation is constructed based on the self-weight of each element, external load, inter-element forces, and interface forces. Subsequently, by introducing the wall-soil interface strength condition and the inter-slice element strength condition, necessary strength constraints are applied to the unknowns in the static equilibrium equation. Finally, by solving the obtained equation set and searching for the rupture surface inclination angle, the active earth pressure under the active limit state and its distribution along the back of the wall are obtained.

[0090] The following section will elaborate on the mathematical expression of the above slice analysis process using specific symbol systems and formulas, so as to clearly demonstrate the complete derivation process and calculation steps of the method.

[0091] I. Earth Pressure Calculation Model and Formula Derivation

[0092] like Figure 2 This is a slice-based calculation and analysis model for the active earth pressure of a retaining wall, with a wall height of... H The angle between the back wall AB and the vertical direction is α The inclination angle of the backfill behind the wall is β The top of the backfill has a size of q The uniformly distributed load, the internal friction angle of the backfill soil is φ The cohesion is c At the wall-soil interface AB, the external friction angle between the wall and the soil is... δ The cohesion between the wall and the soil is c w BC is the fracture surface of the soil behind the wall, and its dip angle is... θ The soil wedge ABC, which has reached its limit state behind the wall, is divided into strips. The top and bottom surfaces of the trapezoidal soil strips are parallel to the rupture surface BC. ABC is divided into sections of equal thickness. n A piece of earthenware, Figure 2 The first one is shown in the middle. i A strip of earth DEFG.

[0093] like Figure 3 The diagram illustrates the force analysis of soil strip DEFG. This soil strip maintains force equilibrium under the influence of adjacent soil strips, the retaining wall, gravity, and the load from above. The force equilibrium equations for the soil strip in the horizontal and vertical directions are:

[0094] (1)

[0095] (2)

[0096] in W i For the first i The weight of a soil strip, where γ represents the unit weight of the soil strip, is:

[0097] (3)

[0098] According to geometric relationships, we can obtain:

[0099] (4)

[0100] Similarly, based on geometric relationships, we can obtain:

[0101] (5)

[0102] Force analysis is performed on the soil strip DEFG. The unknown forces are: N i , T i , p i and s i Four, of which N i Let be the resultant normal support force on the bottom surface of the i-th soil strip in the direction parallel to the slip surface. T i Let be the resultant tangential friction force on the bottom surface of the i-th soil strip in the direction parallel to the sliding surface. p i Let be the normal pressure exerted by the i-th soil strip on the wall surface. s i Let be the tangential friction force between the i-th soil strip and the wall surface. Divide the soil wedge behind the wall into... n If there are 4 such earthen strips, then a total of 4 are needed. n Only one equation can be completely solved. For each soil strip, equations (1) and (2) can be derived through force equilibrium, thus yielding 2 n There are several equations. For the wall-back interface, when the soil behind the wall reaches its active limit state, the shear strength of the wall-soil interface can be fully utilized, hence:

[0103] (6)

[0104] The wall-soil interface of each soil strip satisfies the above equation, totaling... n There are several constraint equations. To obtain the solution to the entire problem, we also need... nGiven these constraint equations, we can only find supplementary equations relating the tangential and normal forces between soil strips. Note that at the interfaces between soil strips, the shear stress at each point cannot exceed its shear strength; therefore, there is an inequality relationship between the tangential and normal forces at each interface. Taking the DG interface as an example, it is:

[0105] (7)

[0106] The length of DG is determined by geometric relationships:

[0107] (8)

[0108] The analytical approach of dividing a soil wedge into several independent slice elements and solving the static equilibrium equations for each element is widely used in layered or discretized soil stress analysis methods, and is employed in slope stability analysis and related geotechnical engineering calculation methods. In existing research, to more accurately describe the mechanical transmission relationship between slice elements, some methods have proposed expressing the relationship between inter-slice shear force and inter-slice normal force as a function that varies with the position of the slice interface, reflecting the mechanical characteristics of the gradual development of inter-slice shear along the potential slip surface. Therefore, it is assumed that the shear force utilization coefficient between each soil slice is... k i Taking the interface DG as an example, that is:

[0109] (9)

[0110] According to equation (7), it can be found that 0≤ k i ≤1, and when i = n At that time, the DG interface is a smooth surface BC. k i =1.

[0111] It is not difficult to see that the closer the soil strip is to the bottom layer, the higher the shear force utilization coefficient between the soil strips. k i The closer the coefficient is to 1, and the closer it is to the top layer, the weaker the shear force utilization becomes, potentially even reaching 0. Based on this, we assume the shear force utilization coefficient between soil layers is... k i The depth of the soil strip interface increases linearly, that is:

[0112] (10)

[0113] in, λ These are undetermined coefficients. Because when i = n hour, k i =1, therefore λ =1 / H.

[0114] Finally, the resultant force of the active earth pressure on the retaining wall is:

[0115] (11)

[0116] Therefore, the magnitude of the active earth pressure is only related to the dip angle of the rupture surface of the soil behind the wall. θ It is related to, it is about θ For a univariate function that reaches its active limit state, we have:

[0117] (12)

[0118] At this time, the result is θ It refers to the fracture surface dip angle corresponding to the active limit state. E a This is the value of the active earth pressure we are looking for.

[0119] II. Calculation Example Verification

[0120] In the process of verifying the numerical examples, in order to facilitate the comparison of the active earth pressure calculation results under different technical approaches, this application selected several representative existing research results as references, including the "Technical Specification for Building Slope Engineering" and several academic studies on active earth pressure models for cohesive soil, analysis methods considering wall back adhesion, improved methods of Coulomb theory for cohesive soil, limit analysis methods for active earth pressure, studies on earth pressure distribution under different wall displacement conditions, and experimental studies on soil arching effect and shear transmission law of sliced ​​units. The aforementioned literature includes: GB50330—2013 Technical Specification for Building Slope Engineering; Gu Weici, Research on Calculation of Active Earth Pressure in Cohesive Soil; Lu Tinghao, Analysis of Active Earth Pressure Considering Cohesion and Back-of-Wall Adhesion; Hu Xiaojun, Improved Research on Coulomb Theory of Active Earth Pressure in Cohesive Soil; Ou Mingxi et al., Analysis of the Upper Limit of Active Earth Pressure; Fang and Ishibashi's Research on Earth Pressure Distribution Law under Different Wall Displacement Conditions; Ying Hongwei et al., Research on Active Earth Pressure Distribution under Soil Arching Effect; Xia Tangdai et al., Research on the Influence of Interlayer Shear on Active Earth Pressure; Zhou Yingying et al., Model Test Research on Earth Pressure of Rigid Retaining Walls.

[0121] By comparing and analyzing the calculation results of this invention with typical results in the aforementioned literature, the applicability and rationality of the method of this invention under different working conditions can be verified. Specific calculation examples are as follows:

[0122] (1) Calculation example 1

[0123] The unit weight of the backfill soil behind a retaining wall with a height of 10 m is 18.6 kN / m³. 3The internal friction angle is 24°, and the backfill indicates no overload. In this example, parameters such as the retaining wall back slope angle and the backfill slope angle vary. A comparison of the results from this method and existing methods is shown in Table 1, where "-" indicates that this method is not applicable to this situation. First, for the case of a smooth, vertical retaining wall and horizontal backfill of pure sand, the results obtained by this method are completely consistent with all existing methods. Furthermore, the results of this method are consistent with the recommended method in the "Technical Specification for Building Slope Engineering" and the results of Coulomb earth pressure, indicating that this method is an extension of the aforementioned two methods. Compared with other methods, when the backfill cohesion is not zero, this method differs somewhat from some existing methods, but the difference is within 5%, which is also quite consistent.

[0124] Table 1 Calculated values ​​of active earth pressure in Example 1

[0125]

[0126] (2) Calculation example 2

[0127] Ou Mingxi et al. did not choose the same approach as the traditional Rankine and Coulomb earth pressure methods, but instead used the upper limit method of limit analysis to give the calculated value of the active earth pressure on the retaining wall. A comparison of their results is shown in Table 2. It can be seen that the results of this method are in good agreement with those based on the upper limit method of limit analysis.

[0128] Table 2 Calculated values ​​of active earth pressure in Example 2

[0129]

[0130] (3) Calculation example 3

[0131] This method can not only determine the magnitude of the resultant earth pressure on the retaining wall, but more importantly, it can obtain the distribution pattern of the thrust behind the wall. Fang et al. conducted a model test on the active earth pressure of the retaining wall and obtained the horizontal earth pressure behind the wall. In this test, the backfill soil behind the wall was sand with a unit weight of 15.4 kN / m³. 3 The internal friction angle is 34°, the wall height is 1.015m, and the back friction angle is 23.75°. The horizontal earth pressure distribution results obtained by this method are as follows: Figure 4 Ying Hongwei et al. and Tang Daixia et al. used this as a calculation example to give the calculation results of earth pressure distribution, and their results are plotted together in Figure 4 In terms of trends, the results of this method are consistent with existing methods, and the numerical results of this method are closer to the experimental results.

[0132] (4) Calculation example 4

[0133] Zhou Yingying et al. measured the active earth pressure strength of a rigid retaining wall through model experiments. In this model experiment, the wall height was 4.45m and the unit weight of the backfill soil was 14.27kN / m³. 3The internal friction angle is 24.26°, the wall-back friction angle is 21.4°, the backfill cohesion is 1.472 kPa, and the cohesion at the contact surface between the wall back and the backfill is 0.98 kPa. The wall back is vertical, and the backfill is horizontal and without overload. The measured results are compared with the results calculated using this method as follows: Figure 5 It is not difficult to find that the earth pressure distribution pattern obtained by this method is consistent with the measured results. In particular, the part with the greatest earth pressure intensity is located between 1 / 3 and 1 / 2 of the wall height. This indicates that when using this method for design, the calculated overturning moment of the retaining wall is greater than the result obtained by the earth pressure distribution pattern according to the triangle distribution, making the design more realistic and safer.

[0134] III. Conclusion

[0135] This embodiment, based on the limit equilibrium theory in geotechnical engineering, discretizes the soil behind the wall into oblique slice elements and applies mechanical equilibrium constraints to each element, thereby realizing the engineering calculation and stress distribution analysis of the active earth pressure on a gravity retaining wall. It achieves the following technical effects:

[0136] (1) Based on the traditional planar slip surface model, an analysis structure of oblique strips is introduced. By characterizing the degree of shear force between strip units in a positional manner, the calculation of active earth pressure can simultaneously output the resultant force of the back wall pressure and the distribution pattern along the height direction of the back wall. This allows the key stress information required for the structural design of retaining walls, such as overturning and sliding resistance, to be directly obtained from the calculation model, thus enhancing the technical correlation between earth pressure analysis and engineering design.

[0137] (2) The case studies based on actual engineering conditions show that the results obtained by this method are in good agreement with existing engineering experience, improved theories and experimental observations, both in predicting the magnitude of the resultant active earth pressure and in assessing the nonlinear distribution characteristics of the active earth pressure along the back of the wall. By incorporating engineering factors such as slope load, wall-soil interface conditions and shear transfer capacity between slice units into the calculation framework, the stability and accuracy of active earth pressure calculation under complex working conditions are improved, and it can be directly used for engineering design and safety verification.

[0138] (3) This method is applicable to various types of fill materials such as sand and cohesive soil. It explicitly considers the cohesive effect at the back interface of the wall during the calculation process, so that the interface friction and interface cohesion can participate in the stress solution in the form of engineering quantities. It can reflect the common interface action characteristics in actual retaining wall structures. It is an engineering improvement of the traditional earth pressure calculation model in terms of material applicability and interface treatment.

[0139] Example 3

[0140] Please refer to Figure 6 , Figure 6A schematic diagram of an active earth pressure calculation device for retaining walls based on the oblique strip method provided in an embodiment of this application.

[0141] The engineering information acquisition module is used to take engineering information as input, which is used to characterize the state of the retaining wall, the back of the wall, the backfill behind the wall, and the wall-soil interface. The engineering information acquisition module is configured to construct a calculation model including the back of the wall, the backfill, and the fracture surface represented by the inclination angle to be determined based on the engineering information, and output the calculation model to the subsequent modules.

[0142] The oblique strip module, connected to the engineering information acquisition module, is used to divide the backfill into multiple oblique strip units between the wall back and the fracture surface along the direction corresponding to the fracture surface, using the calculation model as input. The oblique strip units form an oblique strip structure for unit-by-unit mechanical analysis, and the module determines the position identifier of each oblique strip unit along the height direction of the wall back. The oblique strip module is configured to output the oblique strip units and their position identifiers to subsequent modules.

[0143] The equilibrium relationship establishment module, connected to the diagonal strip module, is used to decompose and combine the above forces under a preset reference direction system, taking the self-weight of each diagonal strip unit, the external load acting on each diagonal strip unit, the inter-unit forces between each diagonal strip unit and adjacent diagonal strip units, and the interface forces between each diagonal strip unit and the wall back as inputs. This makes each diagonal strip unit satisfy the static equilibrium conditions in multiple directions, thereby forming an equilibrium relationship for associating the inter-unit forces and the interface forces, and outputting the static equilibrium relationship to subsequent modules.

[0144] The strength condition application module, connected to the equilibrium relationship establishment module, is used to introduce a wall-soil interface strength condition that limits the range of interface force values, and a strip unit strength condition that limits the range of inter-unit force values, taking the static equilibrium relationship as input. The inclined strip unit strength condition is used to make the shear capacity between adjacent inclined strip units have different degrees of exertion depending on the different positions of the inclined strip units in the fill. The strength condition application module is configured to output the equilibrium constraints with the wall-soil interface strength condition and the strip unit strength condition to the subsequent modules. The strength condition application module is specifically configured as follows: taking the interface normal force between each inclined slice unit and the wall back as input, and combining the friction angle and cohesion strength of the wall-soil interface, the interface tangential bearing capacity provided by friction is obtained by multiplying the interface normal force by the friction coefficient determined based on the friction angle; then, the cohesion strength of the wall-soil interface is multiplied by the contact height of the corresponding inclined slice unit on the wall back, and converted by combining the inclination angle of the wall back, to obtain the interface tangential bearing capacity provided by cohesion; and the normal force between each inclined slice unit and the adjacent inclined slice unit is used as input. The maximum available shear capacity between the slice elements is obtained by inputting the normal action, the internal friction angle of the soil, the cohesive strength of the soil, and the contact length between the slice elements. This is achieved by multiplying the normal action by the friction coefficient determined based on the internal friction angle and adding this product to the product of the soil cohesive strength and the contact length. The maximum available shear capacity is then weighted according to the position of the oblique slice elements in the height direction of the wall back, yielding the actual shear capacity between the slice elements at each depth. The interface tangential action and the actual shear action between the slice elements are each limited to a range within which their corresponding bearing capacities are not exceeded. This limitation means that, during the solution process, the bearing capacity determined by the strength condition is incorporated as a constraint into the equation system, ensuring that the solution results remain within the feasible region and do not exceed this bearing capacity.

[0145] The force solution module, connected to the strength condition application module, is used to solve for the inter-element forces and interface forces of all oblique slice elements, taking the equilibrium constraints and the given fracture surface dip angle as input. This yields the interface force distribution along the height direction of the wall back, which includes components along the wall back normal direction and components along the wall back tangential direction. The force solution module is configured to output the interface force distribution to subsequent modules. Specifically, the force solution module is configured to: construct a system of algebraic equations by combining the equilibrium relationship output by the equilibrium relationship establishment module with the wall-soil interface strength conditions and inter-element strength conditions output by the strength condition application module; and solve for the inter-element forces and interface forces in the system of equations using numerical methods to obtain the distribution of the interface normal and tangential components along the height direction of the wall back.

[0146] An active earth pressure determination module, connected to a force solution module, is used to accumulate and synthesize the components of the interface force along the height direction of the wall back in different directions, taking the interface force distribution as input, to obtain the active earth pressure corresponding to the given rupture surface inclination angle. The active earth pressure determination module is also configured to call the force solution module to obtain the interface force distribution under different rupture surface inclination angles by changing the rupture surface inclination angle, and to repeatedly perform the accumulation and synthesis process for each interface force distribution, compare the active earth pressures corresponding to different rupture surface inclination angles, determine the rupture surface inclination angle that makes the active earth pressure reach its extreme value, and output the active earth pressure corresponding to the rupture surface inclination angle as the calculation result of the device. The active earth pressure determination module is specifically configured to: sum the interface normal components at each height position to obtain the total normal component along the wall back direction; sum the interface tangential components at each height position to obtain the total tangential component along the wall back direction; and consider the total normal component and the total tangential component as mutually perpendicular force components for vector synthesis to obtain the active earth pressure at the corresponding rupture surface inclination angle; further, using preset angle start value, end value and angle step as input, the rupture surface inclination angle is discretely obtained within a preset range; for each discrete value, the force solution module and vector synthesis process are called to obtain a set of active earth pressure values ​​corresponding to different rupture surface inclination angles; the active earth pressure with the largest value is selected from these values, and the corresponding rupture surface inclination angle is determined as the rupture surface inclination angle under the active limit state.

[0147] It should be understood that the various modules of the retaining wall active earth pressure calculation device based on the oblique strip method provided in the above embodiments are only illustrated by the division of each functional module in the above description. In practical applications, the above functions can be assigned to different functional modules as needed. That is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above.

[0148] The functional modules in the above embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of the embodiments of this application.

[0149] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects.

[0150] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0151] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for calculating active earth pressure on retaining walls based on the oblique strip method, characterized in that, include: S1. Obtain engineering information characterizing the retaining wall, the back of the wall, the backfill behind the wall, and the wall-soil interface. The engineering information includes at least the height of the retaining wall, the inclination angle of the back of the wall relative to the vertical direction, the inclination angle of the backfill surface, the unit weight of the backfill, the internal friction angle of the backfill, the cohesive strength of the backfill, the friction angle of the wall-soil interface, the cohesive strength of the wall-soil interface, and the surface load intensity acting on the backfill surface. Based on the engineering information, construct a calculation model including the back of the wall, the backfill, and the fracture surface. The fracture surface is a planar fracture surface passing through the bottom of the back of the wall, and the inclination angle of the planar fracture surface relative to the horizontal plane is used as the fracture surface inclination angle to be determined. S2. Divide the backfill between the wall back and the fracture surface into multiple oblique strip units, wherein the strip units are trapezoidal strip units. The division includes: taking the height of the retaining wall and the preset number of strips as input, dividing the backfill between the wall back and the fracture surface into several trapezoidal strip units of the same thickness along the same direction as the fracture surface, and making the upper and lower boundaries of each trapezoidal strip unit parallel to the fracture surface. Each trapezoidal strip unit has a unique height identifier along the height direction of the wall back to distinguish trapezoidal strip units of different depths, forming an oblique strip structure for unit-by-unit mechanical analysis. S3. For each inclined trapezoidal strip unit, establish a static equilibrium relationship based on the forces acting on the trapezoidal strip unit; wherein, the forces include: the self-weight of the trapezoidal strip unit, the external load applied to the trapezoidal strip unit, the inter-unit forces between the trapezoidal strip unit and adjacent trapezoidal strip units, and the interface forces between the trapezoidal strip unit and the wall back; establishing the static equilibrium relationship includes: decomposing the inter-unit forces between the trapezoidal strip unit and adjacent trapezoidal strip units into shear components along the direction of the fracture surface and normal components perpendicular to the fracture surface, decomposing the interface forces between the trapezoidal strip unit and the wall back into tangential components along the surface of the wall back and normal components perpendicular to the surface of the wall back, and establishing force equilibrium relationships in the horizontal and vertical directions respectively; S4. In the static equilibrium relationship, strength conditions are introduced to limit the range of values ​​of the interface force and the inter-unit force; wherein, the strength conditions include the wall-soil interface strength condition for limiting the range of values ​​of the interface force, and the inter-unit strength condition of the oblique strip unit for limiting the range of values ​​of the inter-unit force. The wall-soil interface strength condition includes: taking the interface normal pressure between a trapezoidal strip unit and the wall back, as well as the friction angle and cohesion strength of the wall-soil interface as inputs, multiplying the interface normal pressure by the friction coefficient determined based on the friction angle to obtain the tangential bearing capacity provided by friction; then multiplying the cohesion strength of the wall-soil interface by the contact height of the trapezoidal strip unit on the wall back, and converting it in combination with the inclination angle of the wall back to obtain the tangential bearing capacity provided by cohesion; adding the tangential bearing capacities of friction and cohesion, and limiting the interface tangential force between the trapezoidal strip unit and the wall back to a range not exceeding the sum of the results; The strength conditions between the oblique strip units include: taking the inter-unit normal pressure between a trapezoidal strip unit and adjacent trapezoidal strip units, the internal friction angle of the soil, the cohesive strength of the soil, and the contact length between the trapezoidal strip units as inputs; multiplying the inter-unit normal pressure by the friction coefficient determined based on the internal friction angle of the soil to obtain the shear bearing capacity provided by the internal friction of the soil; then multiplying the cohesive strength of the soil by the contact length to obtain the shear bearing capacity provided by the cohesive action of the soil; adding the shear bearing capacities of friction and cohesion to obtain the maximum available shear capacity between units; and weighting the maximum available shear capacity with a shear force utilization coefficient related to the height direction position of the trapezoidal strip unit on the wall back to obtain the actual shear force between the trapezoidal strip unit and adjacent trapezoidal strip units at each depth; wherein, the shear force utilization coefficient satisfies 0 ≤ ≤1, and when the corresponding segmentation interface is the fracture surface =1, the shear force utilization coefficient increases linearly from top to bottom with the depth of the corresponding strip interface; S5. Given the dip angle of the fracture surface, solve the inter-unit forces and interface forces of each inclined trapezoidal strip unit based on the static equilibrium relationship and the strength condition to obtain the interface force distribution along the height direction of the wall back; wherein, the static equilibrium relationship of each trapezoidal strip unit, the wall-soil interface strength condition and the inter-unit strength condition of the inclined strip unit together form an algebraic equation system, and the inter-unit forces and interface forces in the algebraic equation system are solved numerically to obtain the distribution of the interface normal component and interface tangential component along the height direction of the wall back; S6. Calculate the active earth pressure corresponding to the rupture surface inclination angle based on the interface force distribution, and determine the active earth pressure under the active limit state by changing the rupture surface inclination angle as the calculation result; wherein, the calculation of the active earth pressure corresponding to the rupture surface inclination angle based on the interface force distribution includes: adding the interface normal components at each height position to obtain the total normal component along the wall back direction, adding the interface tangential components at each height position to obtain the total tangential component along the wall back direction, and vector synthesizing the total normal component and the total tangential component as mutually perpendicular components to obtain the active earth pressure under the corresponding rupture surface inclination angle; The step of determining the active earth pressure under the active limit state by changing the rupture surface inclination angle includes: taking multiple values ​​for the rupture surface inclination angle within a preset angle range, and for each rupture surface inclination angle, repeatedly performing the algebraic equation solution and vector synthesis process based on the geometric relationship of the strip element corresponding to the rupture surface inclination angle to obtain a set of active earth pressure values ​​corresponding to different rupture surface inclination angles, selecting the one with the largest value from the active earth pressure values, determining the corresponding rupture surface inclination angle as the rupture surface inclination angle under the active limit state, and taking the maximum active earth pressure as the final output active earth pressure.

2. The method for calculating active earth pressure on retaining walls based on the oblique strip method according to claim 1, characterized in that, The trapezoidal strip unit is a strip unit formed by the back wall, the fracture surface, and two adjacent strip interfaces parallel to the fracture surface. The contact height of the trapezoidal strip unit on the back wall, the contact length between adjacent trapezoidal strip units, and the self-weight of the trapezoidal strip unit are determined based on the height of the retaining wall, the inclination angle of the back wall, the inclination angle of the backfill surface, the inclination angle of the fracture surface, and the number of strips.

3. The method for calculating active earth pressure on retaining walls based on the oblique strip method according to claim 1, characterized in that, The shear force utilization coefficient is determined according to the linear relationship between the depth of the corresponding strip interface and the wall height, and the reciprocal of the wall height is used as the proportionality coefficient in the linear relationship, so that the shear force utilization coefficient is 1 when the corresponding strip interface is the rupture surface.

4. The method for calculating active earth pressure on retaining walls based on the oblique strip method according to claim 1, characterized in that, The interface force distribution along the wall back height direction is used to form the distribution curve of active earth pressure along the wall back height direction, and to determine the resultant force of active earth pressure and the location of its point of application.

5. A device for calculating active earth pressure on retaining walls based on the oblique strip method, characterized in that, The device includes: The engineering information acquisition module is used to take engineering information as input, which is used to characterize the retaining wall, the back of the wall, the backfill behind the wall, and the wall-soil interface. The engineering information includes at least: the height of the retaining wall, the inclination angle of the back of the wall relative to the vertical direction, the inclination angle of the backfill surface, the unit weight of the backfill, the internal friction angle of the backfill, the cohesive strength of the backfill, the friction angle of the wall-soil interface, the cohesive strength of the wall-soil interface, and the surface load strength acting on the backfill surface. The engineering information acquisition module is configured to construct a calculation model based on the engineering information, including the back of the wall, the backfill, and a rupture surface represented by an inclination angle to be determined. The rupture surface is a planar rupture surface passing through the bottom of the back of the wall, and the inclination angle of the planar rupture surface relative to the horizontal plane is used as the rupture surface inclination angle to be determined. The calculation model is then output to subsequent modules. The oblique strip module, connected to the engineering information acquisition module, is used to divide the backfill between the wall back and the fracture surface into multiple oblique strip units along the direction corresponding to the fracture surface, using the calculation model as input. The strip units are trapezoidal strip units. The oblique strip module is configured to: use the height of the retaining wall and a preset number of strips as input, divide the backfill between the wall back and the fracture surface into several trapezoidal strip units of the same thickness along the direction consistent with the fracture surface, and make the upper and lower boundaries of each trapezoidal strip unit parallel to the fracture surface. Each trapezoidal strip unit has a unique height identifier along the height direction of the wall back to distinguish trapezoidal strip units of different depths, so that the oblique strip units constitute an oblique strip structure for unit-by-unit mechanical analysis, and determine the position identifier of each oblique strip unit along the height direction of the wall back. The oblique strip module is configured to output the oblique strip units and their position identifiers to subsequent modules. A balance relationship establishment module, connected to the diagonal strip module, is used to decompose and combine the forces mentioned above under a preset reference direction system, taking the self-weight of each diagonal trapezoidal strip unit, the external load acting on each diagonal trapezoidal strip unit, the inter-unit forces between each diagonal trapezoidal strip unit and adjacent diagonal trapezoidal strip units, and the interface forces between each diagonal trapezoidal strip unit and the wall back as inputs. Specifically, the balance relationship establishment module is configured to decompose the inter-unit forces between each trapezoidal strip unit and adjacent trapezoidal strip units into shear components along the fracture surface and normal components perpendicular to the fracture surface; decompose the interface forces between each trapezoidal strip unit and the wall back into tangential components along the wall back surface and normal components perpendicular to the wall back surface; and establish force balance relationships in the horizontal and vertical directions respectively, so that each diagonal trapezoidal strip unit satisfies the static equilibrium condition, thereby forming a balance relationship for associating the inter-unit forces and the interface forces, and outputting the static balance relationship to subsequent modules. The strength condition application module, connected to the equilibrium relationship establishment module, is used to introduce wall-soil interface strength conditions that limit the range of values ​​for the interface forces, and inter-unit strength conditions that limit the range of values ​​for the inter-unit forces, taking the static equilibrium relationship as input. The wall-soil interface strength conditions are used with the interface normal pressure between a trapezoidal segment and the wall back, the friction angle of the wall-soil interface, and the cohesion strength as input. The interface normal pressure is multiplied by the friction coefficient determined based on the friction angle to obtain the tangential bearing capacity provided by friction. Then, the cohesion strength of the wall-soil interface is multiplied by the contact height of the trapezoidal segment on the wall back, and converted using the inclination angle of the wall back to obtain the tangential bearing capacity provided by cohesion. Finally, the tangential bearing capacities of friction and cohesion are added together, limiting the interface tangential force between the trapezoidal segment and the wall back to a range not exceeding the sum of the values. The strength condition between the oblique strip units is used as inputs: the inter-unit normal pressure between a trapezoidal strip unit and its adjacent trapezoidal strip units, the internal friction angle of the soil, the cohesive strength of the soil, and the contact length between the trapezoidal strip units. The shear bearing capacity provided by internal friction is obtained by multiplying the inter-unit normal pressure by the friction coefficient determined based on the internal friction angle of the soil. Then, the shear bearing capacity provided by cohesion is obtained by multiplying the soil cohesive strength by the contact length. The shear bearing capacities from friction and cohesion are added together to obtain the maximum available shear capacity between units. This maximum available shear capacity is then weighted by a shear force utilization coefficient related to the height direction position of the trapezoidal strip unit on the wall back, yielding the actual shear force between the trapezoidal strip unit and its adjacent trapezoidal strip units at each depth. The shear force utilization coefficient satisfies 0 ≤ ≤1, and when the corresponding segmentation interface is the fracture surface =1, the shear force utilization coefficient increases linearly from top to bottom with the depth of the corresponding strip interface; the strength condition application module is configured to output the balance constraint with the wall-soil interface strength condition and the inter-strip unit strength condition to the subsequent module; The force solution module, connected to the strength condition application module, is used to solve for the inter-element forces and interface forces of all inclined trapezoidal strip elements, taking the equilibrium constraints and the given fracture surface inclination angle as input, to obtain the interface force distribution along the height direction of the wall back. The interface force distribution includes components along the normal direction of the wall back and components along the tangential direction of the wall back. The force solution module is configured to form an algebraic equation system by combining the static equilibrium relationship of each trapezoidal strip element, the wall-soil interface strength condition, and the inter-element strength condition of the inclined strip elements, and to solve the inter-element forces and interface forces in the algebraic equation system using a numerical solution method to obtain the distribution of the interface normal component and interface tangential component along the height direction of the wall back. The force solution module is configured to output the interface force distribution to subsequent modules. An active earth pressure determination module, connected to a force solution module, is used to take the interface force distribution as input, accumulate and synthesize the components of the interface force in different directions along the height direction of the wall back, and obtain the active earth pressure corresponding to the given rupture surface inclination angle. Specifically, the active earth pressure determination module is configured to: add the interface normal components at each height position to obtain the total normal component along the wall back direction; add the interface tangential components at each height position to obtain the total tangential component along the wall back direction; and vector synthesize the total normal component and the total tangential component as mutually perpendicular forces to obtain the corresponding rupture surface inclination angle. The active earth pressure determination module is further configured to: take multiple values ​​for the rupture surface inclination angle within a preset angle range, and for each rupture surface inclination angle, based on the geometric relationship of the slice element corresponding to the rupture surface inclination angle, call the force solution module to solve the algebraic equation system, and perform the vector synthesis process to obtain a set of active earth pressure values ​​corresponding to different rupture surface inclination angles. Select the one with the largest value from the active earth pressure values, determine the corresponding rupture surface inclination angle as the rupture surface inclination angle under the active limit state, and output the maximum active earth pressure as the calculation result of the retaining wall active earth pressure calculation device based on the oblique slice method.

6. The active earth pressure calculation device for retaining walls based on the oblique strip method according to claim 5, characterized in that, The trapezoidal strip unit obtained by the oblique striping module is a strip unit surrounded by the wall back, the fracture surface and two adjacent strip interfaces parallel to the fracture surface. The contact height of the trapezoidal strip unit on the wall back, the contact length between adjacent trapezoidal strip units and the self-weight of the trapezoidal strip unit are determined according to the height of the retaining wall, the inclination angle of the wall back, the inclination angle of the backfill surface, the inclination angle of the fracture surface and the number of strips.

7. The active earth pressure calculation device for retaining walls based on the oblique strip method according to claim 5, characterized in that, The shear force utilization coefficient is determined according to the linear relationship between the depth of the corresponding strip interface and the wall height, and the reciprocal of the wall height is used as the proportionality coefficient in the linear relationship, so that the shear force utilization coefficient is 1 when the corresponding strip interface is the rupture surface.

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