A method and system for calculating a herringbone micro anti-slide pile structure

Abstract

The application provides a kind of herringbone micro anti-slide pile structure calculation method and system, herringbone micro pile structure is dispersed, and the interaction of micro pile and stratum is simplified as the lateral and axial nonlinear spring acting on node;Determine the nonlinear spring parameter;According to the motion characteristics of landslide, the soil displacement and direction received by each micro pile structure are calculated;Establish the overall stiffness matrix of the structure;Establish the overall incremental balance equation set including spring stiffness;The landslide displacement is divided into several displacement increments for solving respectively, and the spring stiffness and pile bending stiffness are updated after each incremental step, the internal force and deformation of herringbone micro pile structure under the corresponding landslide displacement are obtained by accumulation, a kind of herringbone micro anti-slide pile structure calculation method and system are proposed, which does not need to set the size and distribution form of landslide thrust in advance, can consider the material and geometric nonlinearity of pile and the nonlinearity of pile and stratum interaction, and has high calculation precision and efficiency.

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 a single row, multiple rows, a herringbone shape, etc. 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, low cost, etc., and has been increasingly applied in landslide treatment projects. It 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 that pile body reinforcement and corrosion prevention are done. At present, many calculation methods have been proposed for the design of micro anti-slide piles, such as the plane steel frame calculation method based on the ground coefficient method, the equivalent method of the “Design Code for Landslide Prevention”, etc. Similar calculation methods have also been applied to herringbone micro pile structures, but these methods are mainly based on transverse stress analysis and do not consider the axial deformation and development of axial force of the micro pile, nor do they perform 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] 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 a herringbone micro anti-slide pile structure are achieved by the following specific technical means:

[0004] A calculation method for a herringbone micro anti-slide pile structure, comprising the following steps:

[0005] 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;

[0006] 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 mass;

[0007] Calculate the soil displacement and direction received by each micro pile structure according to the movement characteristics of the landslide body;

[0008] Based on the updated Lagrange format, a two-node Euler-Bernoulli beam element is used to establish the overall stiffness matrix of the structure;

[0009] The landslide body displacement increment is used as the loading input parameter to establish the overall incremental balance equation set including the spring stiffness;

[0010] The displacement of the landslide body is divided into several displacement increments, and 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 body displacement are obtained by accumulation.

[0011] 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 transverse and axial nonlinear spring acting on the node, comprising:

[0012] Adopting 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 .

[0013] Among them, the herringbone micro pile structure includes + +1 nodes;

[0014] The action of the stratum on the herringbone micro pile structure at each node is simplified as a transverse and axial nonlinear spring along the herringbone micro pile structure.

[0015] As a further scheme of the present application, the method further comprises:

[0016] The transverse nonlinear spring constitutive relation is:

[0017] ;

[0018] Among them, represents the transverse displacement of the herringbone micro anti-slide pile structure, and the unit is m; represents the transverse displacement of the landslide body along the herringbone micro anti-slide pile structure, and the unit is m, and the displacement of the stratum below the sliding surface =0; is the transverse foundation coefficient, and the unit is kN / m 2 ; is the transverse pile-soil interaction force, and the unit is kN / m; is the limit transverse pile-soil interaction force, and the unit is kN / m;

[0019] The axial nonlinear spring constitutive relation is:

[0020] ;

[0021] Among them, represents the axial displacement of the herringbone micro anti-slide pile structure, and the unit is m; S is the displacement of the landslide along the micro anti-slide pile structure, in units of m, and is the displacement of the landslide below the sliding surface =0. is the axial pile-soil interface friction stiffness, in units of kN / m 2 ; is the axial pile-soil interface friction, in units of kN / m is the limit axial pile-soil interface friction, in units of kN / m.

[0022] As a further scheme of the present application, the nonlinear spring parameters are determined according to the physical and mechanical properties of the landslide and the stratum of the slide bed and the interface properties of the herringbone micro pile structure and the rock-soil mass, and include:

[0023] The nonlinear spring parameters include a lateral foundation coefficient, a limit lateral pile-soil interaction force, an axial pile-soil interface friction stiffness, and a limit axial pile-soil interface friction.

[0024] The lateral foundation coefficient and the limit lateral pile-soil interaction force are used to describe the lateral pile-soil interaction, and the axial pile-soil interface friction stiffness and the limit axial pile-soil interface friction are used to describe the axial pile-soil interaction force.

[0025] As a further scheme of the present application, the soil displacement and direction received by each micro pile structure are calculated according to the movement characteristics of the landslide, and include:

[0026] For the case where the landslide moves as a whole along the sliding plane, the part of the herringbone micro pile structure above the sliding surface is uniformly subjected to the displacement S of the landslide, which is expressed in the global coordinate system as:

[0027] ;

[0028] ;

[0029] wherein is the angle between the sliding surface and the horizontal plane, in units of degrees;

[0030] The landslide displacement needs to be converted into the unit local coordinate system displacement, and the conversion is performed according to the following expression relationship:

[0031] ;

[0032] wherein and are the lateral and axial landslide displacements of the node in the unit local coordinate system, is the angle between the z-axis and the X-axis of the unit, in units of degrees.

[0033] As a further scheme of the present application, the global stiffness matrix of the structure is established based on the updated Lagrange formulation, using two-node Euler-Bernoulli beam elements, including:

[0034] The updated Lagrange formulation is used to describe the geometric nonlinearity of the system, that is, the equilibrium deformation system obtained in the last step of analysis is used as the basis to establish the incremental equilibrium equation set in each incremental step analysis:

[0035] ;

[0036] 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:

[0037] ;

[0038] 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;

[0039] The two-node Euler-Bernoulli beam element and Hermitian shape function are used to obtain the elastic stiffness matrix of the element, the geometric stiffness matrix of the element 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 elastic stiffness matrix of the element and the geometric stiffness matrix of the element.

[0040] 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 global stiffness matrix of the structure.

[0041] As a further scheme of the present application, the method further comprises:

[0042] The elastic stiffness matrix of the element is represented as:

[0043] ;

[0044] Wherein, l is the length of the element; EI is the bending stiffness; EA is the tensile / compressive stiffness;

[0045] The geometric stiffness matrix of the element is represented as:

[0046] ;

[0047] Wherein, N is the axial force of the element;

[0048] The element stiffness matrix considering the geometric nonlinearity of the pile is represented as:

[0049] ;

[0050] wherein, is the element stiffness matrix considering the nonlinear of pile geometry, is the element elastic stiffness matrix, is the element geometric stiffness matrix.

[0051] As a further scheme of the present application, the whole incremental equilibrium equation set including spring stiffness is established by using the landslide displacement increment as the loading input parameter, including:

[0052] Under the action of the landslide displacement increment:

[0053] ;

[0054] wherein, is the node soil displacement increment vector, is the spring tangent stiffness matrix;

[0055] In the element local coordinate system, it is expressed as:

[0056] ;

[0057] ;

[0058] ;

[0059] wherein, and are the tangent stiffness of the transverse and axial springs respectively, and the subscript number 1 and the subscript number 2 are the local node numbers in the element;

[0060] and are respectively expressed as:

[0061] ;

[0062] ;

[0063] The element level stiffness matrix is converted from the element local coordinate system to the global coordinate system, and is assembled into the global stiffness matrix according to the node order to obtain the whole incremental equilibrium equation set of the micro pile structure under the action of the landslide displacement increment:

[0064] .

[0065] As a further scheme of the present application, the landslide displacement is divided into several displacement increments for solving respectively, the spring stiffness and the pile bending stiffness are updated after each increment step, the internal force and deformation of the herringbone micro-pile structure under the corresponding landslide displacement are obtained by accumulation, including:

[0066] The standard Newton-Raphson method is used for calculation error and increment step control, and the displacement increment of the node under the action of each displacement increment step is obtained. According to the internal force increment of the herringbone micro-pile structure, the total displacement and internal force of the herringbone micro-pile structure under the current increment step are obtained by accumulation.

[0067] Among them, the internal force increment includes shear force increment , bending moment increment and axial force increment , and the total internal force includes shear force , bending moment and axial force .

[0068] The bending stiffness EI of the pile considering the material nonlinearity of the pile is updated according to the following formula:

[0069] ;

[0070] Among them, is the bending stiffness of the pile section in the elastic stage, with the unit of ; is the residual bending stiffness of the pile section after yielding, with the unit of ; is the bending moment of the herringbone micro-pile structure, with the unit of ; is the yield bending moment of the herringbone micro-pile structure, with the unit of ;

[0071] In the calculation of each increment step, , and remain unchanged, and are updated after the end of the calculation of the increment step for the solution of the next increment step. The calculation results of each increment step are saved and accumulated, so that the response of the micro anti-slide pile under different landslide displacements can be obtained.

[0072] A calculation system of a herringbone micro anti-slide pile structure, comprising:

[0073] A parameter input module, the parameter input module is used for inputting the basic parameters required for calculation;

[0074] A model establishing module is configured to discretize the herringbone micro-pile structure and simplify the interaction between the herringbone micro-pile structure and the stratum into lateral and axial nonlinear springs acting on nodes;

[0075] A calculation module is configured to calculate the soil displacement and direction of each micro-pile structure, establish a global stiffness matrix and a global incremental balance equation set of the structure and solve the equation set;

[0076] An analysis module is configured to obtain the internal force and deformation of the herringbone micro-pile structure under the displacement of the corresponding landslide.

[0077] Compared with the prior art, the present application has the following beneficial effects:

[0078] First, the herringbone micro-pile structure is discretized, and the interaction between the herringbone micro-pile structure and the stratum is simplified into lateral and axial nonlinear springs acting on nodes; then, the nonlinear spring parameters are determined according to the physical and mechanical properties of the stratum of the landslide and the sliding bed and the interface properties of the herringbone micro-pile structure and the rock-soil body; secondly, the soil displacement and direction of each micro-pile structure are calculated according to the movement characteristics of the landslide; then, the global stiffness matrix of the structure is established based on the updated Lagrange format and using two-node Euler-Bernoulli beam elements; subsequently, the global incremental balance equation set including the spring stiffness is established by taking the displacement increment of the landslide as the loading input parameter; finally, the displacement of the landslide is divided into several displacement increments for solving, and the spring stiffness and the bending stiffness of the pile are updated after each incremental step, and the internal force and deformation of the herringbone micro-pile structure under the displacement of the corresponding landslide are obtained by accumulation, thereby providing a calculation method and system for the herringbone micro-pile structure, which does not need to set the landslide thrust size and distribution form in advance, can simultaneously consider the material and geometric nonlinearity of the pile and the nonlinearity of the interaction between the pile and the stratum, and has high calculation precision and efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0079] Figure 1 is a step flow chart of the calculation method for the herringbone micro-pile structure according to the present application;

[0080] Figure 2 is a schematic diagram of the herringbone micro-pile structure for landslide prevention according to the present application;

[0081] Figure 3 is a schematic diagram of the discretization of the pile body of the herringbone micro-pile structure and the decomposition of the displacement of the landslide according to the present application;

[0082] Figure 4 is a schematic diagram of the deformation of the herringbone micro-pile structure according to the present application;

[0083] Figure 5This is a schematic diagram of the lateral displacement, axial displacement, and cross-sectional rotation of the uphill pile in this invention;

[0084] Figure 6 This is a schematic diagram of the lateral displacement, axial displacement, and cross-sectional rotation of the downslope pile in this invention;

[0085] Figure 7 This is a schematic diagram of the axial force, bending moment, and shear force of the uphill pile in this invention;

[0086] Figure 8 This is a schematic diagram of the axial force, bending moment, and shear force of the downslope pile in this invention;

[0087] Figure 9 This is a schematic diagram of the calculation system for a herringbone-shaped micro anti-slide pile structure according to the present invention. Detailed Implementation

[0088] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are used to illustrate the technical solutions of the present invention, but should not be used to limit the scope of protection of the present invention.

[0089] Example:

[0090] As attached Figure 1 To be continued Figure 9 As shown:

[0091] This invention provides a calculation method for a herringbone-shaped micro anti-slide pile structure, comprising the following steps:

[0092] Step S1: Discretize the herringbone micropile structure and simplify the interaction between the herringbone micropile structure and the stratum into a transverse and axial nonlinear spring acting on the node.

[0093] Understandable, as shown in the attached document. Figure 2 As shown, attached Figure 2 Number 1 is the herringbone-shaped micropile structure, number 2 is the landslide body, and number 3 is the sliding surface. The landslide body slides down the sliding surface. The herringbone-shaped micropile structure is generally in two rows. One row is inclined towards the top of the slope and is called the uphill pile, and the other row is inclined towards the bottom of the slope and is called 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 into the sliding bed to a certain depth.

[0094] For details, see attached. Figure 3 As shown, respectively using and Each node discretizes the upslope and downslope piles (lengths Lup and Ldn, respectively) in the herringbone micro anti-slide pile structure as follows: and One unit, two piles at the node The structural system analyzed has a total of fixed connections at various points. + +1 node, numbered in the order of the figure. The stratum's action on the pile at each node is simplified as one nonlinear spring along the lateral direction of the pile and one nonlinear spring along the axial direction of the pile.

[0095] Further, the lateral nonlinear spring constitutive relation is:

[0096] ;

[0097] wherein, denotes the lateral displacement of the herringbone micro-pile structure, in units of m; denotes the displacement of the landslide along the lateral direction of the herringbone micro-pile structure, in units of m, below the sliding surface =0; is the lateral foundation coefficient, in units of kN / m 2 ; is the lateral pile-soil interaction force, in units of kN / m; is the limit lateral pile-soil interaction force, in units of kN / m;

[0098] Further, the axial nonlinear spring constitutive relation is:

[0099] ;

[0100] wherein, denotes the axial displacement of the herringbone micro-pile structure, in units of m; denotes the displacement of the landslide along the axial direction of the herringbone micro-pile structure, in units of m, below the sliding surface =0; is the axial pile-soil interface frictional resistance stiffness, in units of kN / m 2 ; is the axial pile-soil interface frictional resistance, in units of kN / m; is the limit axial pile-soil interface frictional resistance, in units of kN / m.

[0101] Step S2, determining the nonlinear spring parameters according to the physical and mechanical properties of the stratum of the landslide and the sliding bed and the interface properties of the herringbone micro-pile structure and the rock-soil mass.

[0102] Specifically, the nonlinear spring parameters include the lateral foundation coefficient , the limit lateral pile-soil interaction force , the axial pile-soil interface frictional resistance stiffness , and the limit axial pile-soil interface frictional resistance ;

[0103] wherein, the lateral foundation coefficient and the limit lateral pile-soil interaction force For describing lateral pile-soil interaction, it can be determined based on conventional anti-slide pile, field test related to horizontally loaded pile, regional experience and specification table lookup, etc. and ultimate axial pile-soil interface frictional resistance For describing axial pile-soil interaction force, it can be determined based on field test of anti-uplift and anti-compression pile, regional experience and specification table lookup.

[0104] Step S3, according to the movement characteristics of the landslide mass, the soil displacement and direction received by each micro pile structure are calculated.

[0105] Specifically, for the case that the landslide mass moves 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 mass, which is expressed in the global coordinate system as follows: Figure 3

[0106] ;

[0107] ;

[0108] wherein, is the angle between the sliding plane and the horizontal plane, in degrees °.

[0109] Further, the displacement of the landslide mass needs to be converted into the local coordinate system displacement of the unit, according to the following relationship:

[0110] ;

[0111] wherein, and are the lateral and axial displacements of the nodes in the local coordinate system of the unit, in meters; is the angle between the z-axis and the x-axis of the unit, in degrees.

[0112] It should be noted that for the nodes below the sliding plane, and are both 0; for the nodes above the sliding plane, if the survey data shows that the movement characteristics of the landslide mass is a non-uniform displacement distribution along the depth, the corresponding and values can be calculated according to the and values of each node. The calculation of and is to calculate the relative displacement of the pile-soil in the local coordinate system, and then to calculate the p and t values received by the nodes and update the spring stiffness.

[0113] 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.​

[0114] Specifically, the updating Lagrange formulation is adopted to describe the geometric nonlinearity of the system, i.e. in each increment step analysis, the equilibrium deformation system obtained in the last step analysis is taken as the reference to establish the increment equilibrium equation set:

[0115]

[0116] 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:

[0117]

[0118] 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.

[0119] Further, the two-node Euler-Bernoulli beam element and the Hermitian shape function are adopted, and the element elastic stiffness matrix is:

[0120]

[0121] wherein, l is the element length; EI is the bending stiffness; EA is the tensile / compressive stiffness.

[0122] Further, based on the simplified internal energy expression, the element geometric stiffness matrix is:

[0123]

[0124] wherein, N is the element axial force.

[0125] Further, the element stiffness matrix considering the geometric nonlinearity of the pile is:

[0126]

[0127] Finally, the element level stiffness matrix 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 .

[0128] Step S5, the landslide displacement increment is taken as the loading input parameter to establish the overall increment equilibrium equation set including the spring stiffness.

[0129] Specifically, under the action of the landslide displacement increment : ​​​​​

[0130] ;

[0131] wherein, is the node soil displacement increment vector; is the spring tangent stiffness matrix.

[0132] Further, the unit local coordinate system level can be expressed as:

[0133] ;

[0134] ;

[0135] ;

[0136] wherein, the numbers 1 and 2 in the subscript are the local node numbers in the unit; and are the tangent stiffness of the transverse and axial springs respectively, expressed as:

[0137] ;

[0138] ;

[0139] The above unit level stiffness matrix is converted from the unit local coordinate system to the global coordinate system, and is assembled into the global stiffness matrix according to the node order to obtain the overall incremental balance equation of the micro pile structure under the action of the landslide displacement increment

[0140] .

[0141] Step S6, the landslide 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 displacement are obtained by accumulation.

[0142] Specifically, the standard Newton-Raphson method is used for calculation error and incremental step control to obtain the node displacement increment under the action of each displacement increment step , according to which the internal force increment (shear force increment , bending moment increment , and axial force increment ) of the micro pile is calculated, and the total displacement (total displacement ) and internal force (total shear force , and total axial force ) of the micro pile under the current incremental step are obtained by accumulation.

[0143] ​Further, the bending stiffness EI of the pile considering the material nonlinearity of the pile is updated according to the following formula:

[0144] ;

[0145] wherein, is the bending stiffness of the pile section in the elastic stage, and the unit is kN·m2; ; is the residual bending stiffness of the pile section after yielding, and the unit is kN·m2; ; is the bending moment of the micro pile section, and the unit is kN·m; . is the yield bending moment of the micro pile, and the unit is kN·m; .

[0146] It can be understood that in the calculation of each increment step, , and remain unchanged, and are updated after the end of the increment step calculation in order to solve the next increment step. The calculation results of each increment step are saved and accumulated, that is, the response of the micro anti-slide pile under different landslide displacements can be obtained.

[0147] It should be noted that in order to facilitate the understanding and application of the industry technical personnel, the following example calculation is carried out on the determination of the discrete, nonlinear spring parameters of the herringbone micro anti-slide pile structure, the calculation of the lateral and axial soil displacement of each pile, and the solving process of the displacement increment method. Finally, the internal force and deformation of the herringbone micro pile structure under the action of different landslide displacements are obtained. It is particularly pointed out that the ground spring parameters can be determined by referring to the field test, regional experience or specification table method. The embodiment case is based on the experience and specification to assign the values of , , and .

[0148] It should be noted that the units of various process parameters or calculation parameters involved in the following calculation method are standard units, unless otherwise specified.

[0149] 1. Micro anti-slide pile parameters:

[0150] A herringbone micro pile is used as an anti-slide support measure for a certain landslide, and the basic parameters of the micro pile are as follows:

[0151] The diameter of the micro pile D: D = 0.168 m; the initial bending stiffness of the micro pile : EA of the micro pile: 2096.77 kN·m2; the axial tensile / compressive stiffness of the micro pile : the yield bending moment of the micro pile: = 77.0 kN-m; residual stiffness of micro-pile after yielding : = 7.7 kN-m; total length of uphill pile : = 17 m; total length of downhill pile : = 19°; angle between the axis of uphill pile and X-axis : ; angle between the axis of downhill pile and X-axis : ; length of discrete element: l = 0.1 m; number of elements of uphill pile : ; number of elements of downhill pile : .

[0152] 2. Parameters of landslide:

[0153] The stratum at the location of the herringbone micro-pile has two layers, the upper layer being hard clay and the lower layer being bedrock, and the sliding surface is the interface between the soil and the rock.

[0154] Angle between the sliding surface and the horizontal plane : ; displacement of landslide S: S = 0.1 m;

[0155] According to the relationship between the location of the sliding surface and the pile, the length of each micro-pile above the sliding surface and the embedded length can be calculated:

[0156] Length of uphill pile above the sliding surface : = 10.8 m; embedded length of uphill pile : = 6.2 m; length of downhill pile above the sliding surface : = 12.5 m; embedded length of downhill pile : = 6.5 m.

[0157] 3. Parameters of nonlinear spring of stratum:

[0158] Lateral ground coefficient of landslide : ; lateral ground coefficient of slide bed : ; lateral limit resistance of landslide : ; lateral ground coefficient of slide bed : ; axial pile-soil interface stiffness of landslide : ; axial pile-soil interface stiffness of slide bed : ; axial pile-soil interface friction strength of slide body : ; axial pile-soil interface friction strength of slide bed : .

[0159] 4. Internal force and deformation solving of herringbone micro anti-slide pile structure

[0160] The top of the herringbone micro pile structure is fixedly connected and is set as a free boundary, and the bottom is also set as an automatic boundary. The displacement increment of the landslide in the first step is set as 0.001S, the standard Newton-Raphson method is used for calculation error and increment step control, and the displacement ( ) and internal force ( , and ) of the herringbone micro pile under different landslide displacements are obtained.

[0161] A calculation system of a herringbone micro anti-slide pile structure, comprising:

[0162] A parameter input module is configured to input basic parameters required for calculation.

[0163] Further, the basic parameters include micro pile parameters, landslide parameters, stratum nonlinear spring parameters, etc., wherein the micro pile parameters include diameter, initial bending stiffness, yield bending moment, residual bending stiffness after yield, axial tensile / compressive stiffness, pile length, angle with X-axis, etc., the landslide parameters include angle between sliding surface and horizontal plane, landslide displacement, sliding surface depth, etc., and the stratum nonlinear spring parameters include lateral foundation coefficient, lateral limit resistance, axial pile-soil interface stiffness, axial pile-soil interface friction strength, etc.

[0164] A model establishing module is configured to discretize the herringbone micro pile structure, and simplify the interaction between the herringbone micro pile structure and the stratum into lateral and axial nonlinear springs acting on the nodes, i.e., assign the input parameters to the discretized units and nodes.

[0165] A calculation module is configured to calculate the soil displacement and direction received by each micro pile structure, establish a global stiffness matrix and a global incremental balance equation set of the structure, and solve them.

[0166] Furthermore, the calculation module is used to implement incremental step calculations. In each incremental step, the overall stiffness matrix and the overall incremental equilibrium equations of the structure are established. After the calculations of each incremental step are completed, the internal forces and deformations of the herringbone micro anti-slide pile structure under the current incremental step are accumulated. The bending stiffness and spring stiffness of the pile are updated, and then the calculation of the next incremental step is performed until the end.

[0167] The analysis module is used to obtain the internal forces and deformations of the herringbone micropile structure under the displacement of the corresponding landslide body.

[0168] Furthermore, the analysis module is used to extract and display data results, including the internal forces and deformations of the herringbone micro anti-slide pile structure under different landslide displacements, and the anti-slide force of the herringbone micro anti-slide pile on the landslide.

[0169] The above embodiments can be implemented, in whole or in part, by software, hardware (such as circuits), firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. 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 transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via limited means (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. A semiconductor medium can be a solid-state drive.

[0170] It should be understood that the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. A and B can be singular or plural. Additionally, the character " / " in this article generally indicates an "or" relationship between the preceding and following related objects, but it can also represent an "and / or" relationship. Please refer to the context for a more accurate understanding.

[0171] It should be understood that the size of the sequence number of each process described above in the embodiments of the present application does not mean the order of execution, and the execution order of each process should be determined according to its function and inherent logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0172] The above-described embodiments are only used to illustrate the technical solutions of the present application, but not limit it; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that the technical solutions recorded in the foregoing embodiments can still be modified, or some technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application.

Claims

1. A calculation method of a herringbone micro anti-slide pile structure, characterized in that, The method comprises the following steps: The herringbone micro-pile structure is discretized, and the interaction between the herringbone micro-pile structure and the stratum is simplified as a lateral and axial nonlinear spring acting on a node; Nonlinear spring parameters are determined 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; The soil displacement and direction of each micro-pile structure are calculated 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; A total incremental balance equation set including spring stiffness is established by taking the displacement increment of the landslide body as a loading input parameter; The displacement of the landslide body 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.

2. The method according to claim 1, wherein, The herringbone micro-pile structure is discretized, and the interaction between the herringbone micro-pile structure and the stratum is simplified as a lateral and axial nonlinear spring acting on a node. Adopt With The upper slope pile and the lower slope pile in the herringbone micro pile structure are respectively dispersed into With Units, the upper slope pile and the lower slope pile are fixedly connected at the node ​ In the herringbone micro-pile structure, a total of 1 node​ The method further comprises:

3. The method according to claim 2, wherein, The lateral nonlinear spring constitutive relation is: The axial nonlinear spring constitutive relation is: ； wherein, represents the lateral displacement of the herringbone micro anti-slide pile structure, in m; represents the displacement of the landslide along the lateral direction of the herringbone micro anti-slide pile structure, in m, below the sliding surface = 0; is the lateral ground 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 nonlinear spring parameters are determined 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. ； wherein, denotes the axial displacement of the herringbone micro anti-slide pile structure, in m; denotes the displacement of the landslide along the axial direction of the herringbone micro anti-slide pile structure, in m, below the sliding surface =0; is the axial pile-soil interface frictional resistance stiffness, in kN / m 2 ; is the axial pile-soil interface frictional resistance, in kN / m; is the limit axial pile-soil interface frictional resistance, in kN / m.

4. The method according to claim 1, wherein, The nonlinear spring parameters include a lateral foundation coefficient, a limit lateral pile-soil interaction force, an axial pile-soil interface friction resistance stiffness and a limit axial pile-soil interface friction resistance. The lateral foundation coefficient and the limit lateral pile-soil interaction force are used to describe the lateral pile-soil interaction, and the axial pile-soil interface friction resistance stiffness and the limit axial pile-soil interface friction resistance are used to describe the axial pile-soil interaction force. The soil displacement and direction of each micro-pile structure are calculated according to the movement characteristics of the landslide body.

5. The method according to claim 1, wherein, For the case that the landslide body moves as a whole along the sliding plane, the part of the herringbone micro-pile structure above the sliding plane is uniformly subjected to the displacement S of the landslide body, which is expressed in the global coordinate system as: The landslide body displacement needs to be converted into the local coordinate system displacement of the element, and the conversion is performed according to the following expression relationship: ； ； wherein denotes the angle between the sliding surface and the horizontal plane in degrees; Based on the updated Lagrange format, a two-node Euler-Bernoulli beam element is used to establish the overall stiffness matrix of the structure. ； wherein, and are the lateral and axial displacements of the node in the local coordinate system of the element, respectively, in meters; is the angle between the local z-axis of the element and the global X-axis, in degrees.

6. The method according to claim 1, wherein, The geometric nonlinearity of the system is described by using the updated Lagrange format, that is, the equilibrium deformation system obtained in the last step is used as a reference to establish the incremental balance equation set in each incremental step analysis: The two-node Euler-Bernoulli beam element and the Hermitian shape function are used to obtain the elastic stiffness matrix of the element, the geometric stiffness matrix of the element 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 elastic stiffness matrix of the element and the geometric stiffness matrix of the element. ； wherein, is the node load increment vector; is the node displacement increment vector; is the tangent stiffness matrix, calculated by the following equation: ； wherein K is the elastic stiffness matrix, mainly related to material properties; K is the geometric stiffness matrix, used to describe the change of system stiffness due to large deformation; ​ 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 sequence to obtain the global stiffness matrix, i.e., the overall stiffness matrix of the structure.

7. The method according to claim 6, wherein, The method further comprises: The element elastic stiffness matrix is represented as: ； wherein l is the element length; EI is the bending stiffness; and 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, Kgdenotes the element stiffness matrix accounting for the geometric nonlinearity of the pile, Kgdenotes the element stiffness matrix accounting for the geometric nonlinearity of the pile, Kgdenotes the element stiffness matrix accounting for the geometric nonlinearity of the pile.

8. The method according to claim 1, wherein, The overall incremental equilibrium equation group including the spring stiffness is established by using the displacement increment of the landslide body as the loading input parameter, and comprises: Under the action of the landslide displacement increment: ； wherein, is the node soil displacement increment vector, is the spring tangent stiffness matrix, is the node displacement increment vector, is the node load increment vector; In the element local coordinate system level, it is represented as: ； ； ； wherein with respectively the tangential stiffness of the lateral and axial spring, the subscripted numbers 1 and 2 are the local node numbers in the element; with respectively: ； ； wherein, is the ultimate lateral pile-soil interaction force, in kN / m; is the lateral pile-soil interaction force, in kN / m; is the axial pile-soil interface frictional resistance stiffness, in kN / m 2 ; is the axial pile-soil interface frictional resistance, in kN / m; is the ultimate axial pile-soil interface frictional resistance, in kN / m; is the lateral ground coefficient, in kN / m 2 ; The stiffness matrix of the element level is calculated Convert from the element local coordinate system to the global coordinate system, and assemble into the global stiffness matrix according to the node order to obtain the overall incremental equilibrium equation set of the micropile structure under the action of the landslide displacement increment: ； wherein, denotes the node displacement increment vector, denotes the node soil displacement increment vector, is the tangent stiffness matrix, is the spring tangent stiffness matrix.

9. The method according to claim 8, wherein, The displacement of the landslide body is divided into a plurality of displacement increments for solving, and the spring stiffness and the bending stiffness of the pile 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 accumulated and obtained, and comprise: The standard Newton-Raphson method is used to control computational errors and incremental steps, resulting in the shift increment step for each bit. 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 summing them up. With internal force; Wherein, the internal force increment includes shear force increment , bending moment increment and axial force increment , the total internal force includes shear force , bending moment and axial force ; The bending stiffness EI of the pile considering the material nonlinearity of the pile is updated according to the following formula: ； wherein, is the bending stiffness of the pile section in the elastic phase, with units of ; is the residual bending stiffness of the pile section after yielding, with units of ; is the bending moment of the herringbone micro-pile structure section, with units of ; is the yield bending moment of the herringbone micro-pile structure, with units of ; In the calculation of each increment step, , and are kept constant, updated at the end of the increment step calculation for the solution of the next increment step, and the results of the calculation of each increment step are saved and accumulated, obtaining the response of the micro anti-slide pile under different landslide displacements.

10. A computing system for herringbone micro-pile structure, for implementing any of the methods of claims 1 to 9, characterized in that, Comprise: A parameter input module, which is configured to input basic parameters required for calculation; A model establishment module, which is configured to 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 nodes, and determine nonlinear spring parameters; A calculation module, which is configured to calculate the soil displacement and direction received by each micro pile structure, establish an overall stiffness matrix and an overall incremental equilibrium equation group, and solve, specifically, based on an updated Lagrange format, an overall stiffness matrix of the structure is established by using a two-node Euler-Bernoulli beam element, and an overall incremental equilibrium equation group including spring stiffness is established by using the displacement increment of the landslide body as the loading input parameter; An analysis module, which is configured to obtain the internal force and deformation of the herringbone micro pile structure under the action of the corresponding landslide body displacement, specifically, the displacement of the landslide body is divided into a plurality of displacement increments for solving, and the spring stiffness and the bending stiffness of the pile 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 accumulated and obtained.

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