Calculation method and system for herringbone miniature anti-slide pile structure

Abstract

The invention provides a calculation method and system for a herringbone micro anti-slide pile structure, the herringbone micro anti-slide pile structure is dispersed, and the interaction between a micro pile and a stratum is simplified into transverse and axial non-linear springs acting on nodes; determining nonlinear spring parameters; calculating the soil displacement and direction of each micro pile structure according to the landslide mass motion characteristics; establishing a structural overall stiffness matrix; establishing an overall increment balance equation set including the spring stiffness; the landslide mass displacement is divided into a plurality of displacement increments to be solved respectively, the spring stiffness and the pile bending stiffness are updated after each increment step, and the internal force and deformation of the herringbone micro pile structure under the corresponding landslide mass displacement effect are obtained through accumulation. According to the calculation method and system for the herringbone miniature anti-slide pile structure, material and geometric nonlinearity of the pile and interaction nonlinearity of the pile and the stratum can be considered at the same time, and calculation precision and efficiency are high.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of landslide prevention and slope reinforcement, and more particularly relates to a calculation method and system for a herringbone micro anti-slide pile structure. BACKGROUND

[0002] The micro anti-slide pile (pile diameter 90-300 mm) can be arranged in single row, multiple rows, herringbone and other forms according to the size of the landslide and the demand for anti-slide force, and has the advantages of flexible pile site arrangement, fast construction and low cost, and has been more and more applied in landslide treatment projects, and is often used for emergency treatment of medium and shallow landslides, and can also be used for permanent treatment of landslides instead of large-section ordinary anti-slide piles under the condition of good pile body reinforcement and corrosion prevention. At present, many calculation methods for the design of micro anti-slide piles have been proposed, such as the plane steel frame calculation method based on the ground coefficient method and the equivalent method of the Code for Design of Landslide Prevention, and similar calculation methods have also been applied to herringbone micro piles, but such methods are mainly based on transverse stress analysis, without considering the axial deformation and development of axial force of the micro pile, and without coupling analysis of the transverse and axial stress deformation of the pile, so the internal force calculation of the micro pile structure is not accurate. SUMMARY

[0003] In order to solve the above technical problems, the application provides a calculation method and system for a herringbone micro anti-slide pile structure, and the purpose and effect of the calculation method and system for the herringbone micro anti-slide pile structure are achieved by the following specific technical means: A calculation method for a herringbone micro anti-slide pile structure, comprising the following steps: Discretize the herringbone micro pile structure, and simplify the interaction between the herringbone micro pile structure and the stratum into transverse and axial nonlinear springs acting on the nodes; Determine the nonlinear spring parameters according to the physical and mechanical properties of the stratum of the landslide body and the sliding bed and the interface properties of the herringbone micro pile structure and the rock-soil body; Calculate the soil displacement and direction received by each micro pile structure according to the movement characteristics of the landslide body; Based on the updated Lagrange format, a two-node Euler-Bernoulli beam element is used to establish the overall stiffness matrix of the structure; The displacement increment of the landslide body is used as the loading input parameter to establish the overall incremental balance equation set including the spring stiffness; The landslide body displacement is divided into several displacement increments for solving, and the spring stiffness and pile bending stiffness are updated after each incremental step, and the internal force and deformation of the herringbone micro pile structure under the action of the corresponding landslide body displacement are obtained by accumulation.

[0004] As a further scheme of the present application, the herringbone micro-pile structure is discretized, and the interaction of the herringbone micro-pile structure with the stratum is simplified as a lateral and axial nonlinear spring acting on the node, comprising: By using and nodes, the uphill pile and the downhill pile in the herringbone micro-pile structure are discretized into and units, respectively, and the uphill pile and the downhill pile are fixedly connected at the node . Among them, the herringbone micro-pile structure includes a total of nodes; The action of the stratum on the herringbone micro-pile structure at each node is simplified as a lateral nonlinear spring along the herringbone micro-pile structure and an axial nonlinear spring along the herringbone micro-pile structure.

[0005] As a further scheme of the present application, the method further comprises: The lateral nonlinear spring constitutive relation is: ; Among them, represents the lateral displacement of the herringbone micro-pile structure, with the unit of m; represents the displacement of the landslide along the lateral direction of the herringbone micro-pile structure, with the unit of m, below the sliding surface ; is the lateral foundation coefficient, with the unit of kN / m 2 ; is the lateral pile-soil interaction force, with the unit of kN / m; is the limit lateral pile-soil interaction force, with the unit of kN / m; The axial nonlinear spring constitutive relation is: ; Among them, represents the axial displacement of the herringbone micro-pile structure, with the unit of m; represents the displacement of the landslide along the axial direction of the herringbone micro-pile structure, with the unit of m, below the sliding surface ; is the axial pile-soil interface friction resistance stiffness, with the unit of kN / m 2 ; is the axial pile-soil interface friction resistance, with the unit of kN / m; is the limit axial pile-soil interface friction resistance, with the unit of kN / m.

[0006] As a further solution of the present invention, the nonlinear spring parameters are determined based on the physical and mechanical properties of the landslide body and the slide bed and the interface properties between the herringbone micropile structure and the rock and soil, including: The nonlinear spring parameters include lateral foundation coefficient, ultimate lateral pile-soil interaction force, axial pile-soil interface friction stiffness and ultimate axial pile-soil interface friction; Among them, the lateral foundation coefficient and the ultimate lateral pile-soil interaction force are used to describe the lateral pile-soil interaction, and the axial pile-soil interface friction stiffness and the ultimate axial pile-soil interface friction are used to describe the axial pile-soil interaction force.

[0007] As a further solution of the present invention, the calculation of the soil displacement and direction of each micropile structure according to the movement characteristics of the landslide body includes: When the landslide moves as a whole along the sliding plane, the part of the herringbone micropile structure above the sliding surface is uniformly affected by the landslide displacement S, which can be expressed in the global coordinate system as follows: ; in, It is expressed as the angle between the sliding surface and the horizontal plane, in degrees; The displacement of the landslide body needs to be converted into the displacement of the unit local coordinate system according to the following expression relationship: ; in, and are the lateral and axial landslide displacements of the nodes in the local coordinate system of the unit, in m; The angle between the unit z-axis and the x-axis, in degrees.

[0008] As a further solution of the present invention, based on the updated Lagrangian format, a two-node Euler-Bernoulli beam element is used to establish the overall stiffness matrix of the structure, including: The updated Lagrangian scheme is used to describe the geometric nonlinearity of the system. That is, in each incremental step analysis, the equilibrium deformation system obtained in the previous step analysis is used as the benchmark to establish the incremental equilibrium equations: ; in, is the node load increment vector; is the node displacement increment vector; is the tangent stiffness matrix, which is calculated as follows: ; in, is the elastic stiffness matrix, which is mainly related to the material properties; For the geometric stiffness matrix, the system stiffness change caused by large deformation is described; The two-node Euler-Bernoulli beam element and Hermitian shape function are adopted to obtain the element elastic stiffness matrix, the element geometric stiffness matrix is obtained based on the simplified internal energy expression, and the element stiffness matrix considering the geometric nonlinearity of the pile is obtained based on the element elastic stiffness matrix and the element geometric stiffness matrix; The element stiffness matrix considering the geometric nonlinearity of the pile is converted from the element local coordinate system to the global coordinate system, and is assembled according to the node order to obtain the global stiffness matrix, that is, the overall stiffness matrix of the structure.

[0009] As a further scheme of the present application, the method further comprises: The element elastic stiffness matrix is represented as: ; Wherein, l is the element length; EI is the bending stiffness; EA is the tensile / compressive stiffness; The element geometric stiffness matrix is represented as: ; Wherein, N is the element axial force; The element stiffness matrix considering the geometric nonlinearity of the pile is represented as: ; Wherein, The element stiffness matrix considering the geometric nonlinearity of the pile is represented as: The element elastic stiffness matrix is represented as: The element geometric stiffness matrix is represented as.

[0010] As a further scheme of the present application, the method further comprises: Under the action of the landslide displacement increment: ; Wherein, The node soil displacement increment vector is: The tangent stiffness matrix of the spring is: In the element local coordinate system, it is represented as: ; Wherein, And The tangent stiffness of the transverse and axial springs is respectively represented as: And The tangent stiffness of the transverse and axial springs is respectively represented as: ; The element-level stiffness matrix Convert the local coordinate system of the unit to the global coordinate system and assemble it into a global stiffness matrix according to the node order to obtain the overall incremental equilibrium equations of the micropile structure under the action of the landslide displacement increment: .

[0011] As a further solution of the present invention, the landslide displacement is divided into several displacement increments and solved separately, and the spring stiffness and pile bending stiffness are updated after each incremental step, and the internal force and deformation of the herringbone micropile structure under the corresponding landslide displacement are accumulated, including: The standard Newton-Raphson method is used to calculate the error and incremental step control, and the incremental step for each bit is obtained. Displacement increment of the node under action Based on this, the internal force increment of the herringbone micropile structure is calculated, and the total displacement of the herringbone micropile structure under the current increment step is obtained by accumulation. and internal force; Among them, the internal force increment includes the shear force increment , bending moment increment and axial force increment , the total internal force includes shear force , bending moment and axial force ; The pile bending stiffness EI considering the material nonlinearity of the pile is updated according to the following formula: ; in, is the bending stiffness of the pile section in the elastic stage, in units of ; is the residual bending stiffness of the pile section after yielding, in units of ; is the cross-sectional bending moment of the herringbone micropile structure, the unit is ; is the yield moment of the herringbone micropile structure, the unit is ; In the calculation of each incremental step, 、 as well as All remain unchanged and are updated after the calculation of the incremental step is completed in order to solve the next incremental step. The calculation results of each incremental step are saved and accumulated to obtain the response of the micro anti-slide pile under different landslide displacements.

[0012] A calculation system for a herringbone micro anti-slide pile structure, comprising: A parameter input module, wherein the parameter input module is used to input basic parameters required for calculation; A model building module, wherein the model building module is used to discretize the herringbone micropile structure and simplify the interaction between the herringbone micropile structure and the stratum into lateral and axial nonlinear springs acting on the nodes; A calculation module is used to calculate the soil displacement and direction of each micropile structure, establish the overall stiffness matrix of the structure and the overall incremental equilibrium equation group and solve them; An analysis module is used to obtain the internal force and deformation of the herringbone micropile structure under the displacement of the corresponding landslide body.

[0013] Compared with the prior art, the present invention has the following beneficial effects: Firstly, the herringbone micropile structure is discretized, and the interaction between the herringbone micropile structure and the stratum is simplified into lateral and axial nonlinear springs acting on the nodes. Then, the nonlinear spring parameters are determined according to the physical and mechanical properties of the stratum between the landslide body and the sliding bed, as well as the interface properties between the herringbone micropile structure and the rock and soil. Secondly, the soil displacement and direction of each micropile structure are calculated according to the motion characteristics of the landslide body. Then, based on the updated Lagrangian scheme, the two-node Euler-Bernoulli beam element is used to establish the overall stiffness matrix of the structure. Subsequently, the The landslide displacement increment is used as the loading input parameter, and an overall incremental equilibrium equation group including the spring stiffness is established. Finally, the landslide displacement is divided into several displacement increments and solved separately. After each incremental step, the spring stiffness and pile bending stiffness are updated. The internal forces and deformations of the herringbone micropile structure under the corresponding landslide displacement are accumulated to obtain the internal forces and deformations. A calculation method and system for herringbone micro anti-slide pile structures with high calculation accuracy and efficiency is proposed, which does not require the size and distribution of the landslide thrust to be set in advance, can simultaneously consider the material and geometric nonlinearity of the pile, as well as the nonlinearity of the interaction between the pile and the stratum. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a flow chart of the steps of a calculation method for a herringbone micro anti-slide pile structure of the present invention; Figure 2 Schematic diagram of the herringbone micro anti-slide pile structure for landslide prevention and control in the present invention; Figure 3 Schematic diagram of pile body dispersion and landslide displacement decomposition of the herringbone micro anti-slide pile structure of the present invention; Figure 4 Schematic diagram of the deformation of the herringbone micro anti-slide pile structure of the present invention; Figure 5 is a schematic diagram of the lateral displacement, axial displacement and cross-sectional rotation of an uphill pile in the present invention; Figure 6is a schematic diagram of the lateral displacement, axial displacement and cross-sectional rotation of a downhill pile in the present invention; Figure 7 is a schematic diagram of the axial force, bending moment and shear force of the uphill pile in the present invention; Figure 8 is a schematic diagram of the axial force, bending moment and shear force of the downhill pile in the present invention; Figure 9 It is a schematic diagram of a calculation system of a herringbone micro anti-slide pile structure of the present invention. DETAILED DESCRIPTION

[0015] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the technical solutions of the present invention, but are not intended to limit the scope of protection of the present invention.

[0016] Example: As attached Figure 1 To the attached Figure 9 As shown: The present invention provides a calculation method for a herringbone micro anti-slide pile structure, comprising the following steps: Step S1: discretize the herringbone micropile structure and simplify the interaction between the herringbone micropile structure and the stratum into transverse and axial nonlinear springs acting on the nodes.

[0017] Understandable, as Figure 2 As shown, attached Figure 2 The number 1 in the bid is a herringbone micro pile structure, the number 2 is a landslide body, and the number 3 is a sliding surface. The landslide body slides down along the sliding surface. The herringbone micro anti-slide pile structure is generally in two rows, one row is inclined toward the top of the slope, which is the uphill pile, and the other row is inclined toward the foot of the slope, which is the downhill pile. The two rows of piles are connected at the top of the piles, and the bottom of the piles passes through the sliding surface and is embedded in the sliding bed to a certain depth.

[0018] Specifically, as attached Figure 3 As shown, respectively, and The uphill pile and downhill pile (lengths Lup and Ldn respectively) in the herringbone micro anti-slide pile structure are discretized as and Unit, two piles at the node The structural system under analysis has The action of the stratum on the pile at each node is simplified to a nonlinear spring along the lateral direction of the pile and along the axial direction of the pile.

[0019] Furthermore, the constitutive relation of the lateral nonlinear spring is: ; in, It is expressed as the lateral displacement of the herringbone micro anti-slide pile structure, in m; It is expressed as the lateral displacement of the landslide body along the herringbone micro anti-slide pile structure, in meters, below the sliding surface. ; is the lateral foundation coefficient, in kN / m 2 ; is the lateral pile-soil interaction force, in kN / m; is the ultimate lateral pile-soil interaction force, in kN / m; Furthermore, the constitutive relation of the axial nonlinear spring is: ; in, It is expressed as the axial displacement of the herringbone micro anti-slide pile structure, in m; It is expressed as the displacement of the landslide body along the axial direction of the herringbone micro anti-slide pile structure, in m, below the sliding surface ; is the axial pile-soil interface friction stiffness, in kN / m 2 ; is the axial pile-soil interface friction resistance, in kN / m; is the ultimate axial pile-soil interface friction resistance, unit is kN / m.

[0020] Step S2: determining nonlinear spring parameters according to the physical and mechanical properties of the landslide body and the sliding bed and the interface properties between the herringbone micropile structure and the rock and soil.

[0021] Specifically, the nonlinear spring parameters include the lateral foundation coefficient , Ultimate lateral pile-soil interaction force , axial pile-soil interface friction stiffness and ultimate axial pile-soil interface friction ; Among them, the lateral foundation coefficient and the ultimate lateral pile-soil interaction force It is used to describe the lateral pile-soil interaction and can be determined based on field tests of conventional anti-slide piles and horizontally loaded piles, regional experience, and code lookup tables. The axial pile-soil interface friction stiffness The ultimate axial pile-soil interface friction It is used to describe the axial pile-soil interaction force and can be determined based on field tests of tension and compression piles, regional experience, and code lookup tables.

[0022] Step S3: Calculate the soil displacement and direction of each micropile structure according to the movement characteristics of the landslide.

[0023] Specifically, for the case of the landslide body moving as a whole along the sliding plane, as shown in FIG. 1, the part of the micro-pile above the sliding plane is uniformly subjected to the displacement S of the landslide body, which is expressed in the global coordinate system as follows: Figure 3 wherein, is the angle between the sliding surface and the horizontal plane, in degrees °.

[0024] Further, the displacement of the landslide body needs to be converted into the local coordinate system of the unit, according to the following relationship: wherein, and are the lateral and axial displacements of the nodes in the local coordinate system of the unit, in meters m; and is the angle between the z-axis and the x-axis of the unit, in degrees.

[0025] It should be noted that for the nodes below the sliding surface, and are both 0; for the nodes above the sliding surface, if the survey data shows that the movement characteristics of the landslide body are non-uniform displacement distribution along the depth, the values of and can be calculated according to the and of each node. The purpose of calculating and is to calculate the relative displacement of the pile-soil in the local coordinate system, and then to calculate the values of p and t of the nodes and update the spring stiffness.

[0026] Step S4, based on the updated Lagrange format, a two-node Euler-Bernoulli beam element is used to establish the global stiffness matrix of the structure.

[0027] Specifically, the updated Lagrange format is used to describe the geometric nonlinearity of the system, that is, in each incremental step analysis, the equilibrium deformation system obtained in the last step analysis is used as the basis to establish the incremental equilibrium equation set: wherein, is the node load increment vector; is the node displacement increment vector; is the tangent stiffness matrix, which is calculated by the following formula: wherein, is the elastic stiffness matrix, which is mainly related to the material properties; is the geometric stiffness matrix, which is used to describe the change of the system stiffness caused by large deformation.​​​​​

[0028] Furthermore, a two-node Euler-Bernoulli beam element and Hermitian shape function are used, and the element elastic stiffness matrix is: ; Where l is the unit length; EI is the bending stiffness; EA is the tensile / compressive stiffness.

[0029] Furthermore, based on the simplified internal energy expression, the unit geometric stiffness matrix is: ; Where N is the unit axial force.

[0030] Furthermore, the element stiffness matrix considering the geometric nonlinearity of the pile is: ; Finally, the element-level stiffness matrix Convert the local coordinate system of the element to the global coordinate system and assemble it in the order of the nodes to obtain the global stiffness matrix .

[0031] Step S5: Using the landslide displacement increment as a loading input parameter, an overall incremental equilibrium equation group including spring stiffness is established.

[0032] Specifically, the landslide displacement increment Under the effect of: ; in, is the incremental displacement vector of the node soil; is the spring tangent stiffness matrix.

[0033] Furthermore, at the unit local coordinate system level, it can be expressed as: ; The numbers 1 and 2 in the subscripts are the local node numbers in the element; and are the tangential stiffness of the transverse and axial springs, respectively, expressed as: ; The stiffness matrix of the above element level Convert the local coordinate system of the unit to the global coordinate system and assemble it into a global stiffness matrix according to the node order to obtain the displacement increment of the micropile structure in the landslide. The overall incremental balance equations under the action of: .

[0034] In step S6, the displacement of the landslide body is divided into several displacement increments and solved separately. After each incremental step, the spring stiffness and pile bending stiffness are updated, and the internal force and deformation of the herringbone micropile structure under the corresponding landslide body displacement are accumulated to obtain.

[0035] Specifically, the standard Newton-Raphson method is used to calculate the error and incremental step control, and each bit shift incremental step is obtained. Displacement increment of the node under action , based on which the internal force increment of the micropile (shear increment , bending moment increment , and axial force increment ), the total displacement of the micropile in the current incremental step is obtained by accumulation ( ) and internal force ( 、 and ).

[0036] Furthermore, the pile bending stiffness EI considering the material nonlinearity of the pile is updated according to the following formula: ; in, is the bending stiffness of the pile section in the elastic stage, in units of ; is the residual bending stiffness of the pile section after yielding, in units of ; is the cross-sectional bending moment of the micropile, in units of . is the yield moment of the micropile, in units of .

[0037] It is understandable that in the calculation of each incremental step, 、 as well as The results of each incremental step are saved and accumulated to obtain the response of the micro anti-slide pile under different landslide displacements.

[0038] It should be noted that, in order to facilitate the understanding and application of technical personnel in this industry, the following example calculation is carried out on the determination of discrete and nonlinear spring parameters of the herringbone micro anti-slide pile structure, the calculation of the transverse and axial soil displacements of each pile, and the solution process of the displacement increment method. Finally, the internal force and deformation of the herringbone micro pile structure under different landslide displacements are obtained. It is particularly pointed out that the formation spring parameters can be determined by referring to field tests, regional experience or standard lookup table method. This implementation case is based on experience and standards. 、 、 and Assignment.

[0039] It should be noted that the measurement units of various process parameters or calculation parameters involved in the following calculation methods, unless otherwise specified, all adopt the standard unit system.

[0040] 1. Micro anti-slide pile parameters: A landslide uses herringbone micropiles as an anti-slide support measure. The basic parameters of the micropiles are: Micropile diameter D: D = 0.168 m; Micropile initial bending stiffness : = 2096.77 kN·m2; micropile axial tensile / compressive stiffness Micropile yield moment ; Residual stiffness of micropile after yield ;Total length of uphill pile Total length of downhill pile ; Angle between the uphill pile axis and the X axis ; Angle between the downhill pile axis and the X axis ; Discrete unit length l: l = 0.1 m; Number of uphill pile units ; Number of downhill pile units .

[0041] 2. Landslide parameters: There are two layers of strata where the herringbone micropiles are set, the upper part is hard clay, the lower part is bedrock, and the sliding surface is the soil-rock interface.

[0042] Angle between the sliding surface and the horizontal plane ; Landslide displacement S: S = 0.1 m; Based on the relationship between the position of the sliding surface and the pile, the pile length and embedded length of each micropile above the sliding surface can be calculated: Length above the sliding surface of uphill pile ; Uphill pile embedded length ; Length above the sliding surface of the downhill pile ; Downhill pile embedded length .

[0043] 3. Formation nonlinear spring parameters: Lateral foundation coefficient of landslide body ; Transverse foundation coefficient of the slider bed ;Lateral ultimate resistance of landslide body ; Transverse foundation coefficient of the slider bed ; Axial pile-soil interface stiffness of landslide body ; Axial pile-soil interface stiffness of the slider bed ; Axial pile-soil interface friction strength of landslide ; Axial pile-soil interface friction strength of the slider bed .

[0044] 4. Solution of internal forces and deformations of herringbone micro anti-slide pile structures The top of the herringbone micropile structure is fixed and set as a free boundary, and the bottom of the pile is also set as an automatic boundary. The landslide displacement increment of the first step is set to 0.001S, and the standard Newton-Raphson method is used to calculate the error and increment step control. The displacement of the herringbone micropile under different landslide displacements is obtained ( ) and internal force ( 、 and ).

[0045] A calculation system for a herringbone micro anti-slide pile structure, comprising: The parameter input module is used to input basic parameters required for calculation.

[0046] Furthermore, the basic parameters include micropile parameters, landslide parameters, nonlinear spring parameters of the formation, etc., wherein the micropile parameters include diameter, initial bending stiffness, yield bending moment, residual bending stiffness after yield, axial tensile / compressive stiffness, pile length, angle with the X-axis, etc., the landslide parameters include the angle between the sliding surface and the horizontal plane, landslide body displacement, sliding surface depth, etc., and the nonlinear spring parameters of the formation include lateral foundation coefficient, lateral ultimate resistance, axial pile-soil interface stiffness, axial pile-soil interface friction strength, etc.

[0047] The model building module is used to discretize the herringbone micropile structure and simplify the interaction between the herringbone micropile structure and the stratum into lateral and axial nonlinear springs acting on the nodes, that is, to assign the input parameters to the discretized units and nodes.

[0048] The calculation module is used to calculate the soil displacement and direction of each micropile structure, establish the overall stiffness matrix of the structure and the overall incremental equilibrium equation group and solve them.

[0049] Furthermore, the calculation module is used to implement incremental step solution calculations, establish the overall stiffness matrix of the structure and the overall incremental equilibrium equation group in each incremental step, accumulate and obtain the internal force and deformation of the herringbone micro anti-slip pile structure under the current incremental step after the solution calculation of each incremental step is completed, update the bending stiffness and spring stiffness of the pile, and then perform the calculation of the next incremental step until the end.

[0050] An analysis module is used to obtain the internal force and deformation of the herringbone micropile structure under the displacement of the corresponding landslide body.

[0051] Furthermore, the analysis module is used to extract and display data results, including the internal force and deformation of the herringbone micro anti-slide pile structure under different landslide displacements, the anti-slide force of the herringbone micro anti-slide pile on the landslide, etc.

[0052] The above embodiments can be implemented in whole or in part via software, hardware (e.g., circuits), firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product comprises one or more computer instructions or computer programs. When loaded or executed on a computer, the processes or functions described in accordance with the embodiments of the present invention are fully or partially performed. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another. For example, the computer instructions can be transferred from one website, computer, server, or data center to another website, computer, server, or data center via wireless communication (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium accessible by a computer, or a data storage device such as a server or data center that contains a collection of one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media. The semiconductor media can be a solid-state drive.

[0053] It should be understood that the term "and / or" as used herein simply describes an association between related objects, indicating that three possible relationships exist. For example, "A and / or B" can represent the existence of A alone, the existence of both A and B, or the existence of B alone. A and B can be singular or plural. Furthermore, the character " / " as used herein generally indicates an "or" relationship between the related objects, but it may also indicate an "and / or" relationship. For specific understanding, please refer to the context.

[0054] It should be understood that in the embodiments of the present invention, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0055] The embodiments described above are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention, and should all be included in the scope of protection of the present invention.

Claims

1. A calculation method for a herringbone micro anti-slide pile structure, characterized in that: The following steps are included: The herringbone micropile structure is discretized, and the interaction between the herringbone micropile structure and the stratum is simplified into lateral and axial nonlinear springs acting on the nodes. The nonlinear spring parameters are determined based on the physical and mechanical properties of the landslide body and the sliding bed, as well as the interface properties between the herringbone micropile structure and the rock and soil. Calculate the soil displacement and direction of each micropile structure according to the movement characteristics of the landslide; Based on the updated Lagrangian scheme, the two-node Euler-Bernoulli beam element is used to establish the overall stiffness matrix of the structure; The landslide displacement increment is used as the loading input parameter to establish the overall incremental equilibrium equations including the spring stiffness. The landslide displacement is divided into several displacement increments and solved separately. The spring stiffness and pile bending stiffness are updated after each incremental step, and the internal force and deformation of the herringbone micropile structure under the action of the corresponding landslide displacement are accumulated to obtain.

2. The calculation method of a herringbone micro anti-slide pile structure according to claim 1 is characterized in that: The method of discretizing the herringbone micropile structure and simplifying the interaction between the herringbone micropile structure and the stratum into transverse and axial nonlinear springs acting on the nodes includes: use and The nodes are used to discretize the uphill piles and downhill piles in the herringbone micropile structure into and Units, uphill piles and downhill piles at nodes Fixed connection; Among them, the herringbone micropile structure includes nodes; The effect of the stratum on the herringbone micropile structure at each node is simplified to a nonlinear spring along the lateral direction of the herringbone micropile structure and along the axial direction of the herringbone micropile structure.

3. The calculation method of a herringbone micro anti-slide pile structure according to claim 2 is characterized in that: The method further comprises: The constitutive relation of the lateral nonlinear spring is: ； in, It is expressed as the lateral displacement of the herringbone micro anti-slide pile structure, in m; It is expressed as the lateral displacement of the landslide body along the herringbone micro anti-slide pile structure, in meters, below the sliding surface. ; is the lateral foundation coefficient, in kN / m 2 ; is the lateral pile-soil interaction force, in kN / m; is the ultimate lateral pile-soil interaction force, in kN / m; The constitutive relationship of the axial nonlinear spring is: ； in, It is expressed as the axial displacement of the herringbone micro anti-slide pile structure, in m; It is expressed as the displacement of the landslide body along the axial direction of the herringbone micro anti-slide pile structure, in m, below the sliding surface ; is the axial pile-soil interface friction stiffness, in kN / m 2 ; is the axial pile-soil interface friction resistance, in kN / m; is the ultimate axial pile-soil interface friction resistance, unit is kN / m.

4. The calculation method of a herringbone micro anti-slide pile structure according to claim 1 is characterized in that: The nonlinear spring parameters are determined according to the physical and mechanical properties of the landslide body and the sliding bed and the interface properties between the herringbone micropile structure and the rock and soil body, including: The nonlinear spring parameters include lateral foundation coefficient, ultimate lateral pile-soil interaction force, axial pile-soil interface friction stiffness and ultimate axial pile-soil interface friction; Among them, the lateral foundation coefficient and the ultimate lateral pile-soil interaction force are used to describe the lateral pile-soil interaction, and the axial pile-soil interface friction stiffness and the ultimate axial pile-soil interface friction are used to describe the axial pile-soil interaction force.

5. The calculation method of a herringbone micro anti-slide pile structure according to claim 1 is characterized in that: The calculation of the soil displacement and direction of each micropile structure according to the movement characteristics of the landslide body includes: When the landslide moves as a whole along the sliding plane, the part of the herringbone micropile structure above the sliding surface is uniformly affected by the landslide displacement S, which can be expressed in the global coordinate system as follows: ； in, It is expressed as the angle between the sliding surface and the horizontal plane, in degrees; The displacement of the landslide body needs to be converted into the displacement of the unit local coordinate system according to the following expression relationship: ； in, and are the lateral and axial landslide displacements of the nodes in the local coordinate system of the unit, in m; The angle between the unit z-axis and the x-axis, in degrees.

6. The calculation method of a herringbone micro anti-slide pile structure according to claim 1, characterized in that: The updated Lagrangian scheme is used to establish the overall stiffness matrix of the structure using a two-node Euler-Bernoulli beam element, including: The updated Lagrangian scheme is used to describe the geometric nonlinearity of the system. That is, in each incremental step analysis, the equilibrium deformation system obtained in the previous step analysis is used as the benchmark to establish the incremental equilibrium equations: ； in, is the node load increment vector; is the node displacement increment vector; is the tangent stiffness matrix, which is calculated as follows: ； in, is the elastic stiffness matrix, which is mainly related to the material properties; is the geometric stiffness matrix, which is used to describe the change in system stiffness caused by large deformation; The two-node Euler-Bernoulli beam element and Hermitian shape function are used to obtain the element elastic stiffness matrix. Based on the simplified internal energy expression, the element geometric stiffness matrix is ​​obtained. Based on the element elastic stiffness matrix and the element geometric stiffness matrix, the element stiffness matrix considering the geometric nonlinearity of the pile is obtained. The unit stiffness matrix considering the geometric nonlinearity of the pile is converted from the unit local coordinate system to the global coordinate system, and assembled according to the node order to obtain the global stiffness matrix, that is, the overall stiffness matrix of the structure.

7. The calculation method of a herringbone micro anti-slide pile structure according to claim 6, characterized in that: The method further comprises: The element elastic stiffness matrix is ​​expressed as: ； Where l is the unit length; EI is the bending stiffness; EA is the tensile / compressive stiffness; The element geometric stiffness matrix is ​​expressed as: ； Where N is the unit axial force; The element stiffness matrix considering the geometric nonlinearity of the pile is expressed as: ； in, Expressed as the element stiffness matrix considering the geometric nonlinearity of the pile, Expressed as the element elastic stiffness matrix, Expressed as the element geometric stiffness matrix.

8. The calculation method of a herringbone micro anti-slide pile structure according to claim 1 is characterized in that: The displacement increment of the landslide body is used as the loading input parameter to establish the overall incremental balance equation group including the spring stiffness, including: Under the action of landslide displacement increment: ； in, is the incremental displacement vector of the node soil, is the spring tangent stiffness matrix; At the element local coordinate system level it is expressed as: ； in, and are the tangential stiffness of the transverse and axial springs, respectively. Subscript numbers 1 and 2 are the local node numbers in the element. and Respectively expressed as: ； The element-level stiffness matrix Convert the local coordinate system of the unit to the global coordinate system and assemble it into a global stiffness matrix according to the node order to obtain the overall incremental equilibrium equations of the micropile structure under the action of the landslide displacement increment: 。 9. The calculation method of a herringbone micro anti-slide pile structure according to claim 1, characterized in that: The landslide displacement is divided into several displacement increments and solved separately. After each incremental step, the spring stiffness and pile bending stiffness are updated, and the internal force and deformation of the herringbone micropile structure under the corresponding landslide displacement are accumulated, including: The standard Newton-Raphson method is used to calculate the error and incremental step control, and the incremental step for each bit is obtained. Displacement increment of the node under action Based on this, the internal force increment of the herringbone micropile structure is calculated, and the total displacement of the herringbone micropile structure under the current increment step is obtained by accumulation. and internal force; Among them, the internal force increment includes the shear force increment , bending moment increment and axial force increment , the total internal force includes shear force , bending moment and axial force ; The pile bending stiffness EI considering the material nonlinearity of the pile is updated according to the following formula: ； in, is the bending stiffness of the pile section in the elastic stage, in units of ; is the residual bending stiffness of the pile section after yielding, in units of ; is the cross-sectional bending moment of the herringbone micropile structure, the unit is ; is the yield moment of the herringbone micropile structure, the unit is ; In the calculation of each incremental step, 、 as well as All remain unchanged and are updated after the calculation of the incremental step is completed in order to solve the next incremental step. The calculation results of each incremental step are saved and accumulated to obtain the response of the micro anti-slide pile under different landslide displacements.

10. A calculation system for a herringbone micro anti-slide pile structure, characterized in that: include: A parameter input module, wherein the parameter input module is used to input basic parameters required for calculation; A model building module, wherein the model building module is used to discretize the herringbone micropile structure and simplify the interaction between the herringbone micropile structure and the stratum into lateral and axial nonlinear springs acting on the nodes; A calculation module is used to calculate the soil displacement and direction of each micropile structure, establish the overall stiffness matrix of the structure and the overall incremental equilibrium equation group and solve them; An analysis module is used to obtain the internal force and deformation of the herringbone micropile structure under the displacement of the corresponding landslide body.

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