Parameter calculation method and system for bored double-row anti-slide pile for rapid support

Abstract

The application provides a drilling and pouring double-row anti-slide pile parameter calculation method and system for rapid support, and relates to the railway slope retaining technology field. In view of the problems of low calculation efficiency, insufficient consideration of the vertical resistance contribution of the pile bottom, spatial collaborative stress characteristics and failure to effectively cover the prestressed anchor combined support situation in the prior art, the application establishes a load analysis model containing a front pile, a rear pile, a connecting beam and a prestressed anchor, constructs a control equation based on the finite difference theory, calculates the stiffness coefficient and the rigidity coefficient of the pile top, and respectively solves the internal force of the pile body under the action of the lateral load and the connecting beam, finally synthesizes the complete internal force and deformation distribution of the pile body, so that the spatial collaborative stress mechanism and the vertical resistance of the pile bottom are considered, and the working condition of the anchor combined support is covered, and an efficient unified analysis method is provided for the rapid and scientific design of the structure in the complex slope engineering.

Description

Technical Field

[0001] This invention relates to the field of railway slope support technology, and in particular to a method and system for calculating parameters of bored cast-in-place double-row anti-slide piles for rapid support. Background Technology

[0002] In railway and other infrastructure construction, slope protection engineering is crucial for ensuring the safety and stability of the railway line. Traditional anti-slide pile retaining structures are mostly constructed using manual excavation, which suffers from significant problems such as low construction efficiency, long construction periods, and high safety risks. In particular, with the release of the "Catalogue of Construction Techniques, Equipment, and Materials Endangering Production Safety in Housing Construction and Municipal Infrastructure Projects (First Batch)," manual excavation technology has been strictly restricted, requiring its replacement in situations where mechanical drilling is feasible. Furthermore, in some overseas railway projects, concerns about the safety of underground operations among local construction workers often force a change from manually excavated piles to mechanically drilled piles. Therefore, the use of bored piles has become an inevitable trend in the development of railway slope protection engineering.

[0003] For manually excavated bored piles, drilled cast-in-place piles offer a high degree of mechanization and construction safety, especially in complex geological conditions. However, with the same amount of concrete, single-row circular drilled piles have weaker bending and sliding resistance, making them unsuitable for large landslides. Therefore, double-row drilled cast-in-place anti-slide piles, capable of forming a portal frame structure, have emerged. This structure boasts high lateral stiffness and good spatial integrity, enabling rapid construction and demonstrating significant advantages in emergency rescue projects.

[0004] However, due to its unique structural form and complex interaction mechanism between the piles and the soil, the deformation characteristics and stress mechanisms of bored cast-in-place double-row anti-slide piles are currently poorly studied, and a unified and mature analytical method is lacking in engineering design. Existing methods mostly rely on the traditional subgrade coefficient method and table lookup calculations, which are inefficient and fail to fully consider the beneficial contribution of the vertical resistance at the pile bottom to the lateral bearing capacity of the double-row piles, thus failing to truly reflect their spatial synergistic stress characteristics. Furthermore, current analytical methods do not effectively cover the situation of combined support of double-row anti-slide piles and prestressed anchor cables, limiting the optimized design and widespread application of this structure in complex slope engineering.

[0005] Therefore, developing a parameter calculation method for bored cast-in-place double-row anti-slide piles for rapid support is of great theoretical and engineering value for promoting the scientific design, safe application and performance optimization of this structure in complex slope engineering. Summary of the Invention

[0006] To address the problems of low efficiency in stress analysis and calculation of bored cast-in-place double-row anti-slide piles in existing technologies, insufficient consideration of the contribution of vertical resistance at the pile bottom, spatial collaborative stress characteristics, and failure to effectively cover the situation of combined support with prestressed anchor cables, this invention proposes a parameter calculation method for bored cast-in-place double-row anti-slide piles for rapid support, including: Obtain the parameters to be calculated and the load analysis model of the bored cast-in-place double-row anti-slide pile. The load analysis model includes the front pile, the rear pile, the connecting beam and the prestressed anchor cable. The front pile and the rear pile are divided into an upper load section and a lower anchorage section by the sliding surface. The parameters to be calculated include the pile body dimensions, foundation coefficient, load parameters and anchor cable parameters of the front pile and the rear pile. Based on the load analysis model and the parameters to be calculated, the finite difference control equations for the front pile and the rear pile are constructed. The pile top compliance coefficients of the front pile and the rear pile are calculated based on the finite difference governing equations and boundary constraints. The boundary constraints include the pile bottom free boundary conditions and the pile top load boundary conditions. The pile top compliance coefficients are used to characterize the deformation response of the pile body under a given load. The pile top stiffness coefficients of the front pile and the rear pile are calculated based on the pile top flexibility coefficient and the foundation coefficient. The pile top stiffness coefficient is used to characterize the pile top's ability to resist deformation. Based on the pile top flexibility coefficient and load parameters, calculate the first shear force and first bending moment of the front pile under lateral load, and the second shear force and second bending moment of the rear pile under lateral load. Based on the pile top stiffness coefficient and the stress state of the coupling beam, calculate the first axial force, third shear force and third bending moment of the front pile under the action of the coupling beam, and the second axial force, fourth shear force and fourth bending moment of the rear pile under the action of the coupling beam. The internal forces and pile deformation distribution of the front pile and the rear pile are determined based on the first shear force, the first bending moment, the second shear force, the second bending moment, the third shear force, the third bending moment, the fourth shear force, the fourth bending moment, the first axial force, and the second axial force.

[0007] Furthermore, the construction of the finite difference governing equations for the front pile and the rear pile based on the load analysis model and the parameters to be calculated includes: The pile bodies of the front pile and the rear pile are divided into units and discretized at nodes; Based on the load analysis model and the parameters to be calculated, the deflection differential control equations at each unit node of the front pile and the rear pile are established using the Euler-Bernoulli beam theory. The flexural differential control equations are transformed into finite difference schemes based on the central difference scheme, thus obtaining the finite difference control equations.

[0008] Furthermore, the pile top compliance coefficient includes the pile top horizontal compliance coefficient, the pile top rotational compliance coefficient, and the pile top coupling compliance coefficient. The calculation of the pile top compliance coefficients of the front pile and the rear pile based on the finite difference governing equations and boundary constraints includes: Based on the finite difference control equations, the free boundary conditions at the pile bottom, and the load boundary conditions at the pile top, a set of linear calculation equations for pile displacement in matrix form is constructed to solve for the horizontal displacement of each node of the front and rear piles. The solution is obtained by applying a unit horizontal force or a unit bending moment at the pile top as load boundary conditions to the linear calculation equations of the pile displacement. The solution results include the horizontal displacement at the pile top corresponding to the unit horizontal force at the pile top and the horizontal displacement at the pile top and adjacent nodes corresponding to the unit bending moment at the pile top. Based on the solution results, calculate the pile top horizontal compliance coefficient, pile top rotational compliance coefficient, and pile top coupling compliance coefficient; Wherein, the pile top horizontal flexibility coefficient is the pile top horizontal displacement caused by only a unit horizontal force acting on the pile top, the pile top rotational flexibility coefficient is the pile top rotation angle caused by only a unit bending moment acting on the pile top, and the pile top coupling flexibility coefficient is the pile top horizontal displacement caused by only a unit bending moment acting on the pile top or the pile top rotation angle caused by only a unit horizontal force acting on the pile top.

[0009] Furthermore, the pile top stiffness coefficient includes the pile top vertical stiffness coefficient, the pile top horizontal stiffness coefficient, the pile top coupling stiffness coefficient, and the pile top rotational stiffness coefficient. The pile top stiffness coefficients of the front pile and the rear pile are calculated based on the pile top flexibility coefficient and the foundation coefficient, including: Based on formula Calculate the vertical stiffness coefficient at the pile top; Based on formula Calculate the horizontal stiffness coefficient at the pile top; Based on formula Calculate the coupling stiffness coefficient at the pile top; Based on formula Calculate the rotational stiffness coefficient at the pile top; Where H1 is the length of the loaded section of the front or rear pile; H2 is the length of the anchorage section of the front or rear pile; E is the elastic modulus of the front or rear pile; d is the diameter of the circular pile of the front or rear pile; k v δ1 is the vertical reaction force coefficient of the foundation; δ2 is the horizontal flexibility coefficient of the pile top of the front or rear pile; δ3 is the rotational flexibility coefficient of the pile top of the front or rear pile; δ4 is the coupling flexibility coefficient of the pile top of the front or rear pile.

[0010] Furthermore, the calculation of the first shear force and first bending moment of the front pile under lateral load and the second shear force and second bending moment of the rear pile under lateral load based on the pile top flexibility coefficient and load parameters includes: Based on the cantilever beam method, the relationship function between the first bending moment and the first shear force at the pile top and the sliding surface of the front pile loading segment under the combined action of trapezoidal distributed inter-pile earth pressure and anchor cable horizontal tension is determined. The front pile loading segment is subjected to the combined action of inter-pile earth pressure and anchor cable horizontal tension, and the load of the inter-pile earth pressure is trapezoidal. Based on the pile deformation coordination condition of the front pile at the sliding surface, the flexibility coefficient of the top of the anchorage section of the front pile, and the relationship function between the first bending moment and the first shear force, a linear equation system is established and solved to obtain the first shear force and the first bending moment at the pile top and the first shear force and the first bending moment at the sliding surface under lateral load. Based on the cantilever beam method, the relationship function between the second bending moment and the second shear force at the pile top and the sliding surface of the pile loading segment under the action of trapezoidal earth pressure is determined. The pile loading segment is subjected to the combined action of the earth pressure behind the pile and the inter-pile earth pressure in front of the pile. The resultant load of the earth pressure behind the pile and the inter-pile earth pressure in front of the pile is trapezoidal. Based on the pile deformation coordination condition of the rear pile at the sliding surface, the flexibility coefficient of the top of the rear pile anchorage section, and the relationship function between the second bending moment and the second shear force, a linear equation system is established and solved to obtain the second shear force and the second bending moment at the pile top and the second shear force and the second bending moment at the sliding surface under lateral load.

[0011] Furthermore, based on the pile top stiffness coefficient and the stress state of the coupling beam, the first axial force, third shear force, and third bending moment of the front pile under the action of the coupling beam, and the second axial force, fourth shear force, and fourth bending moment of the rear pile under the action of the coupling beam are calculated, including: The calculation of the first axial force, third shear force, and third bending moment of the front pile under the action of the coupling beam, and the second axial force, fourth shear force, and fourth bending moment of the rear pile under the action of the coupling beam, based on the pile top stiffness coefficient and the stress state of the coupling beam, includes: The horizontal displacement and rotation angle around the center point of the coupling beam under the action of external horizontal force and moment are calculated based on the stiffness coefficients of the front and rear pile tops. Based on the horizontal displacement, rotation angle, and stiffness coefficient of the front pile top, calculate the first axial force, third shear force, and third bending moment of the front pile top under the action of the coupling beam; Based on the horizontal displacement, rotation angle, and pile top stiffness coefficient of the rear pile, calculate the second axial force, fourth shear force, and fourth bending moment at the top of the rear pile under the action of the coupling beam.

[0012] Furthermore, determining the internal force and pile deformation distribution of the front pile and the rear pile based on the first shear force, first bending moment, second shear force, second bending moment, third shear force, third bending moment, fourth shear force, fourth bending moment, first axial force, and second axial force includes: The first shear force and first bending moment at the top of the front pile under lateral load are superimposed with the corresponding parts of the first axial force, third shear force and third bending moment at the top of the front pile under the action of the connecting beam to obtain the first final shear force, first final axial force and first final bending moment at the top of the loaded section of the front pile. The second final shear force and the second final bending moment at the sliding surface of the front pile are calculated based on the first final shear force, the first final bending moment, the distributed load on the front pile body and the anchor cable tension. The second shear force and second bending moment at the top of the rear pile under lateral load are superimposed with the corresponding parts of the second axial force, fourth shear force and fourth bending moment at the top of the rear pile under the action of the connecting beam to obtain the third final shear force, third final axial force and third final bending moment at the top of the loaded section of the rear pile. The fourth final shear force and the fourth final bending moment at the sliding surface of the rear pile are calculated based on the third final shear force, the third final bending moment, and the distributed load on the rear pile body.

[0013] Furthermore, the method for calculating the horizontal tension of the anchor cable includes: Obtain the initial value of the horizontal tension of each row of anchor cables; Calculate the first shear force and the first bending moment based on the initial values; Based on the principle of displacement and deformation coordination between the pile body and the anchor cable at each anchoring point, as well as the first shear force and the first bending moment, a matrix equation [D][R]=[C] with the horizontal tension of the anchor cable as the unknown quantity is established and solved to update the horizontal tension of the anchor cable, where [D] is the coefficient stiffness matrix, [R] is the column vector of the horizontal tension of the anchor cable, and [C] is the column vector of constants; Use the solved horizontal tension of the anchor cable as a new initial value, and repeat the steps of calculating the first shear force and the first bending moment based on the initial value until the difference between the two adjacent calculations of the horizontal tension of the anchor cable is less than the preset value. The final anchor cable horizontal tension is determined based on the difference between the anchor cable horizontal tension and the preset value. The relationship between the first bending moment and the first shear force at the pile top and the sliding surface is determined based on the cantilever beam method using the final anchor cable horizontal tension. This relationship is achieved by using the horizontal tension of the anchor cable to execute the final anchor cable horizontal tension.

[0014] Furthermore, the establishment of the matrix equation specifically includes: Calculate the horizontal displacement components of the first pile body caused at each anchorage point under the combined action of trapezoidal distributed load and connecting beam in the loaded section of the front pile; Calculate the horizontal displacement component of the second pile body caused by the tension of each row of anchor cables at each anchor point; Based on the horizontal displacement components of the first pile body, the horizontal displacement components of the second pile body, and the principle of pile-anchor displacement deformation coordination, a displacement balance equation is established for each anchor point, and the displacement balance equation is transformed to obtain the matrix equation [D][R]=[C].

[0015] A parameter calculation system for bored cast-in-place double-row anti-slide piles for rapid support, the system employing the parameter calculation method for bored cast-in-place double-row anti-slide piles for rapid support as described in any of the preceding claims, specifically including the following modules: The acquisition module is used to acquire the parameters to be calculated and the load analysis model of the bored cast-in-place double-row anti-slide pile. The load analysis model includes a front pile, a rear pile, a connecting beam, and prestressed anchor cables. The front pile and the rear pile are divided into an upper load-bearing section and a lower anchoring section by the sliding surface. The parameters to be calculated include the pile body dimensions, foundation coefficient, load parameters, and anchor cable parameters of the front pile and the rear pile. A construction module, connected to the acquisition module, is used to construct the finite difference control equations for the front pile and the rear pile based on the load analysis model and the parameters to be calculated; The first calculation module, connected to the construction module, is used to calculate the pile top compliance coefficients of the front pile and the rear pile based on the finite difference control equation and boundary constraints. The boundary constraints include the pile bottom free boundary conditions and the pile top load boundary conditions. The pile top compliance coefficient is used to characterize the deformation response of the pile body under a given load. The second calculation module, connected to the first calculation module and the acquisition module, is used to calculate the pile top stiffness coefficient of the front pile and the rear pile based on the pile top flexibility coefficient and the foundation coefficient. The pile top stiffness coefficient is used to characterize the ability of the pile top to resist deformation. The third calculation module, connected to the first calculation module and the acquisition module, is used to calculate the first shear force and the first bending moment of the front pile under lateral load and the second shear force and the second bending moment of the rear pile under lateral load based on the pile top flexibility coefficient and load parameters. The fourth calculation module, connected to the second calculation module, is used to calculate the first axial force, third shear force, and third bending moment of the front pile under the action of the coupling beam, and the second axial force, fourth shear force, and fourth bending moment of the rear pile under the action of the coupling beam, based on the pile top stiffness coefficient and the stress state of the coupling beam. The determination module, connected to the third calculation module and the fourth calculation module, is used to determine the internal forces and pile deformation distribution of the front pile and the rear pile based on the first shear force, the first bending moment, the second shear force, the second bending moment, the third shear force, the third bending moment, the fourth shear force, the fourth bending moment, the first axial force, and the second axial force.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention establishes a load analysis model including front piles, rear piles, connecting beams, and prestressed anchor cables. Based on finite difference theory, it constructs governing equations, calculates the pile top flexibility coefficient and stiffness coefficient, and solves the pile internal forces under lateral loads and connecting beam action. Finally, it synthesizes the complete pile internal force and deformation distribution, thereby realizing the spatial collaborative force mechanism of double-row piles and the vertical resistance of pile bottom, and fully covering the working condition of anchor cable joint support. It provides an efficient and unified analysis method for the rapid and scientific design of this structure in complex slope engineering. Attached Figure Description

[0017] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating a method for calculating parameters of bored cast-in-place double-row anti-slide piles for rapid support, as shown in Example 1. Figure 2 This is a schematic diagram illustrating the load analysis model of the bored cast-in-place double-row anti-slide pile in Example 1; Figure 3 This is a schematic diagram illustrating the unit division and node discretization of the front and rear piles of the double-row anti-slide piles in Example 1; Figure 4 Example 1 illustrates the horizontal displacement y of the front and rear piles of the double-row anti-slide piles. i A diagram illustrating the calculation results; Figure 5 Example 1 illustrates the rotation angle θ between the front and rear piles of the double-row anti-slide piles. i A diagram illustrating the calculation results; Figure 6 In Example 1, the bending moment M of the front and rear piles of the double-row anti-slide piles is shown. i A diagram illustrating the calculation results; Figure 7 This is to illustrate the shear force Q of the front and rear piles of the double-row anti-slide piles in Example 1. i Calculation results diagram; Figure 8 This is a structural block diagram illustrating a parameter calculation system for bored cast-in-place double-row anti-slide piles used for rapid support, as shown in Example 2. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0020] The specific embodiments of the present invention will be described below.

[0021] To address the lack of unified and mature design and analysis methods for existing bored cast-in-place double-row anti-slide piles due to their unique structural form and complex pile-soil interaction, the traditional subgrade coefficient method is commonly used, but it suffers from low computational efficiency and fails to fully consider the contribution of vertical resistance at the pile bottom and the spatial collaborative stress characteristics. Furthermore, it does not effectively cover the situation of combined support with prestressed anchor cables. This invention constructs a load analysis model including the front pile, rear pile, connecting beam, and prestressed anchor cables. Based on finite difference governing equations and boundary constraints, it calculates the pile top flexibility coefficient, stiffness coefficient, and the distribution of internal forces and deformations within the pile body. This improves computational efficiency and accuracy, fully reflects the spatial collaborative working mechanism of double-row piles and the beneficial influence of pile bottom resistance, and is applicable to situations requiring combined anchor cable support. This provides a scientific and unified analysis method for the optimized design and safe application of this structure in complex slope engineering.

[0022] Example 1 like Figure 1 As shown, this invention proposes a method for calculating the parameters of bored cast-in-place double-row anti-slide piles for rapid support, specifically including the following steps: Step S1: Obtain the parameters to be calculated and the load analysis model of the bored cast-in-place double-row anti-slide piles. The load analysis model includes the front pile, the rear pile, the connecting beam, and the prestressed anchor cable. The front pile and the rear pile are divided into an upper load-bearing section and a lower anchoring section by the sliding surface. The parameters to be calculated include the pile body dimensions, foundation coefficient, load parameters, and anchor cable parameters of the front pile and the rear pile. The following describes the load analysis model for bored cast-in-place double-row anti-slide piles: like Figure 2 As shown, the load analysis model consists of a front pile, a rear pile, a connecting beam, and prestressed anchor cables. The connecting beam is rigid, and the tops of both the front and rear piles are rigidly connected to it. The front and rear piles are divided into an upper load-bearing section and a lower anchoring section by the sliding surface. Below the sliding surface, the anchoring sections of the front and rear piles are acted upon by horizontal ground springs on their sides and by vertical ground springs at their bottoms. Above the sliding surface, the load-bearing section of the rear pile bears the soil pressure behind the pile and the inter-pile soil pressure in front of the pile, while the load-bearing section of the front pile bears the inter-pile soil pressure behind the pile and the horizontal tension of the anchor cables. Horizontal force and moment act at the center of the connecting beam.

[0023] In this embodiment, the parameters to be calculated are obtained from the design documents and geological survey report of the bored cast-in-place double-row anti-slide piles. The parameters obtained from the design documents include the total length H of the front and rear piles, the length H1 of the loaded section of the front and rear piles, the length H2 of the anchorage section of the front and rear piles, the net spacing s between the front and rear piles, the horizontal force Q0 acting at the center of the connecting beam, the moment M0 acting at the center of the connecting beam, the diameter d of the circular piles of the front and rear piles, the concrete strength of the pile body of the front and rear piles, the elastic modulus E of the front or rear pile, the flexural stiffness EI of the section of the front and rear piles, the number of anchor cables J acting on the loaded section of the front pile, and the initial horizontal prestress R of each row of anchor cables from top to bottom. 10 R 20 R 30 , ...R J0 Anchor cable stiffness η1, η2, η3, ..., η J The distances from the anchor points to the sliding surface are L1, L2, L3, ..., L J .

[0024] The parameters to be calculated, obtained from the geological survey report, include the subgrade coefficients of the strata below the sliding surface, where the subgrade coefficients include the subgrade horizontal reaction coefficient k. h and foundation vertical reaction coefficient k v Based on the geological survey report, the foundation horizontal reaction coefficient k of the strata below the sliding surface was determined using the standard table lookup method. h Vertical reaction coefficient of foundation k v Take k as the horizontal reaction coefficient h 1 to 3 times.

[0025] In this embodiment, the front pile and the rear pile have the same total length, the same load-bearing section length, and the same anchorage section length.

[0026] In this embodiment, H=20m, H1=8m, H2=12m, d=1.25m; s=3.0m; Q0=200kN, M0=600kN·m; pile concrete strength C30, E=30GPa; EI=3595.27MN·m2, J=3, R 10 R 20 R 30 All values ​​are 100 kN, η1, η2, and η3 are all 10 MN / m, L1=7 m, L2=6 m, and L3=5 m. Based on the geological survey report, the stratum type is determined to be relatively hard limestone. The horizontal reaction coefficient k of the foundation below the sliding surface is determined by referring to tables in the "Code for Design of Railway Subgrade Retaining Structures". h =100MN / m 3 In this embodiment, the vertical reaction coefficient of the foundation is taken as 1 times the horizontal reaction coefficient, and the vertical reaction coefficient k is... v =100MN / m3 .

[0027] Step S2: Construct the finite difference control equations for the front pile and the rear pile based on the load analysis model and the parameters to be calculated; Specifically, the pile bodies of the front pile and the rear pile are divided into elements and discretized at nodes; based on the load analysis model and the parameters to be calculated, the deflection differential control equations at each element node of the front pile and the rear pile are established using Euler-Bernoulli beam theory; the deflection differential control equations are transformed into finite difference schemes based on the central difference scheme to obtain the finite difference control equations.

[0028] like Figure 3 As shown, the front and rear piles of the double-row anti-slide piles are divided into elements and discretized into nodes. First, the front and rear piles are divided into n elements, each with a length of h and containing n+1 nodes. The nodes from the pile top to the pile bottom are numbered 3, 4, 5, ..., n+3. Two virtual nodes are added to both the pile top and the pile bottom, for a total of n+5 nodes.

[0029] In this embodiment, the length h of each unit of the front pile and the rear pile is 0.1m. The pile body is divided into 200 units, containing 201 nodes. The node numbers from the pile top to the pile bottom are 3, 4, 5, ..., n+3. Two virtual nodes are added to the pile top and the pile bottom, for a total of 205 nodes.

[0030] According to the Euler-Bernoulli beam theory, the differential governing equations for deflection at each node of the front and rear piles are: ; Where EI is the flexural stiffness of the front or rear pile section, y i The horizontal displacement of a node i in the pile body of the front or rear pile; z i k is the vertical distance from a node i on the pile body of the front or rear pile to the pile top; hi q is the horizontal ground reaction coefficient at a node i of the front or rear pile; b0 is the calculated width of the front or rear pile, b0 = 0.9(d+1); i For a certain node i of the front or rear pile body, in this embodiment, b0 = 0.9(d+1) = 2.025m.

[0031] Based on the central difference scheme, the deflection differential control equations at the nodes of the front and rear pile elements are expressed in finite difference form as follows: Among them, y i-2 Let y be the horizontal displacement at node i-2. i-1 Let y be the horizontal displacement at node i-1. i+1 Let y be the horizontal displacement at node i+1.i+2 Let be the horizontal displacement at node i+2, and h be the length of the element.

[0032] Step S3: Calculate the pile top compliance coefficients of the front pile and the rear pile based on the finite difference control equation and boundary constraints. The boundary constraints include the pile bottom free boundary conditions and the pile top load boundary conditions. The pile top compliance coefficient is used to characterize the deformation response of the pile body under a given load. Specifically, based on the finite difference governing equations, the free boundary conditions at the pile bottom, and the load boundary conditions at the pile top, a matrix-form linear calculation equation set for pile displacement is constructed to solve for the horizontal displacements of each node of the front and rear piles. The solution is obtained by applying a unit horizontal force or a unit bending moment at the pile top as load boundary conditions to the linear calculation equation set for pile displacement. The solution results include the horizontal displacement at the pile top corresponding to the unit horizontal force and the horizontal displacements at the pile top and adjacent nodes corresponding to the unit bending moment at the pile top. Based on the solution results, the pile top horizontal compliance coefficient, pile top rotational compliance coefficient, and pile top coupling compliance coefficient are calculated. The pile top horizontal compliance coefficient is the horizontal displacement at the pile top caused by only a unit horizontal force acting on the pile top; the pile top rotational compliance coefficient is the pile top rotation angle caused by only a unit bending moment acting on the pile top; and the pile top coupling compliance coefficient is the horizontal displacement at the pile top caused by only a unit bending moment acting on the pile top or the pile top rotation angle caused by only a unit horizontal force acting on the pile top.

[0033] In this embodiment, the free boundary conditions at the pile bottom include zero bending moment and shear force at the pile bottom, and the load boundary conditions at the pile top include horizontal force Q1 and bending moment M2. The matrix form of the linear calculation equations for the horizontal displacement of each node of the front and rear piles is as follows: Among them, [Y i [K] represents the pile displacement matrix. i [H] is the stiffness coefficient matrix. i ] represents the load matrix.

[0034] a i For matrix [K i The coefficients on the main diagonal of the i-th row in the equation.

[0035] Given the horizontal displacement y at node i of the front and rear pile elements. i The rotation angle θ at the node i Bending moment M i and shear force Qi Calculate using the following formula: When the load on the top of the current and subsequent piles is a unit horizontal force, i.e., Q1 = 1N, according to the formula... The horizontal displacement at the top of the pile was calculated. The horizontal flexibility coefficient δ1 of the pile tops of the front and rear piles of the double-row anti-slide piles is: .

[0036] When the load on the top of the current and subsequent piles is a unit bending moment, M2 = 1 N·m, according to the formula... The horizontal displacement y of the pile top and adjacent nodes was calculated. 2，M2 y 3，M2 y 4，M2 According to the rotation angle calculation method, the rotational flexibility coefficient δ2 of the pile tops of the front and rear piles of the double-row anti-slide piles is: .

[0037] The coupling flexibility coefficient δ3 of the pile tops of the front and rear piles of the double-row anti-slide piles is: .

[0038] In this embodiment, the pile top flexibility coefficients of the front and rear piles of the double-row anti-slide piles are calculated based on the parameters to be calculated, as shown in Table 1.

[0039] Table 1

[0040] In this embodiment, the finite difference method and structural mechanics method are combined to propose a method for calculating the pile top flexibility coefficient of the front and rear piles of double-row anti-slide piles. This avoids the tedious table lookup process of the previous single-row anti-slide pile method using the foundation coefficient method and improves the calculation efficiency.

[0041] Step S4: Calculate the pile top stiffness coefficients of the front pile and the rear pile based on the pile top flexibility coefficient and the foundation coefficient. The pile top stiffness coefficient is used to characterize the pile top's ability to resist deformation. Specifically, based on the formula Calculate the vertical stiffness coefficient at the pile top; based on the formula Calculate the horizontal stiffness coefficient at the pile top; based on the formula Calculate the coupling stiffness coefficient at the pile top; based on the formula Calculate the rotational stiffness coefficient at the pile top; where H1 is the length of the loaded section of the front or rear pile; H2 is the length of the anchorage section of the front or rear pile; E is the elastic modulus of the front or rear pile; d is the diameter of the circular pile of the front or rear pile; k v δ1 is the vertical reaction force coefficient of the foundation; δ2 is the horizontal flexibility coefficient of the pile top of the front or rear pile; δ3 is the rotational flexibility coefficient of the pile top of the front or rear pile; δ4 is the coupling flexibility coefficient of the pile top of the front or rear pile.

[0042] Among them, the vertical stiffness coefficient p1 at the pile top is the axial force at the top of the front or rear pile caused by a unit displacement of the connecting beam along the pile axis; the horizontal stiffness coefficient p2 at the pile top is the horizontal force at the pile top caused by a unit horizontal displacement of the connecting beam along the direction perpendicular to the pile axis; the coupling stiffness coefficient p3 at the pile top is the bending moment at the pile top caused by a unit horizontal displacement of the connecting beam along the direction perpendicular to the pile axis; and the rotational stiffness coefficient p4 at the pile top is the bending moment at the pile top caused by a unit rotation of the connecting beam along the direction of the bending moment at the pile top.

[0043] It should be noted that the stiffness coefficient of the front pile is calculated using its flexibility coefficient, the length of its loaded section, and the length of its anchorage section; similarly, the stiffness coefficient of the rear pile is calculated using its flexibility coefficient, the length of its loaded section, and the length of its anchorage section. For example, when calculating the horizontal stiffness coefficient of the front pile top... Calculate the horizontal stiffness coefficient at the top of the pile. .

[0044] In this embodiment, the stiffness coefficients of the front and rear piles of the double-row anti-slide piles are calculated based on the parameters to be calculated, as shown in Table 2.

[0045] Table 2

[0046] In this embodiment, in addition to the horizontal reaction coefficient of the foundation, the contribution of the vertical foundation coefficient to the lateral bearing capacity of the double-row anti-slide piles is also considered. A method for calculating the pile top stiffness coefficient of the front and rear piles of the double-row anti-slide piles is proposed, which can better reflect the spatial stress characteristics of the double-row anti-slide piles.

[0047] Step S5: Calculate the first shear force and first bending moment of the front pile under lateral load and the second shear force and second bending moment of the rear pile under lateral load based on the pile top flexibility coefficient and load parameters. Specifically, based on the cantilever beam method, the relationship between the first bending moment and the first shear force at the pile top and the sliding surface is determined under the combined action of trapezoidal distributed inter-pile earth pressure and anchor cable horizontal tension in the loaded section of the front pile. The front pile is subjected to the combined action of inter-pile earth pressure and anchor cable horizontal tension, with the inter-pile earth pressure load being trapezoidal. Based on the pile deformation compatibility conditions at the sliding surface, the flexibility coefficient at the top of the front pile anchorage section, and the relationship between the first bending moment and the first shear force, a system of linear equations is established and solved to obtain the first shear force and the first bending moment at the pile top and the first shear force and the first bending moment at the sliding surface under lateral load. The relationship between the second bending moment and the second shear force at the pile top and the sliding surface under trapezoidal earth pressure is determined based on the cantilever beam method. The loaded segment of the pile is subjected to the combined action of the earth pressure behind the pile and the inter-pile earth pressure in front of the pile, and the resultant load of the earth pressure behind the pile and the inter-pile earth pressure in front of the pile is trapezoidally distributed. Based on the pile deformation coordination condition at the sliding surface, the flexibility coefficient at the top of the pile anchorage segment, and the relationship between the second bending moment and the second shear force, a system of linear equations is established and solved to obtain the second shear force and the second bending moment at the pile top and the second shear force and the second bending moment at the sliding surface under lateral load.

[0048] For the front pile, for example, the top load q 1，前 =0kN / m, bottom load q 2，前 =50kN / m; The rigid connection between the pile top and the connecting beam can be considered as a fixed end. The relationship between the first bending moment and the first shear force at the pile top and the sliding surface of the front pile, obtained by the cantilever beam method, is: Among them, M tq，前 and Q tq，前 M represents the first bending moment and the first shear force at the top of the loaded section of the front pile. mq，前 Q mq，前 R represents the first bending moment and the first shear force at the sliding surface of the loaded section of the front pile. j Let L be the horizontal tension of a certain row of anchor cables. i H1 is the distance from a certain anchor point i to the sliding surface, and H1 is the length of the loaded section of the front pile.

[0049] Based on the pile deformation compatibility conditions at the sliding surface of the front pile, a system of four linear equations for the front pile is established, and M is solved. tq，前 Q tq，前 M mq，前 Q mq，前 : ; in, These are the horizontal compliance coefficient, rotational compliance coefficient, and coupling compliance coefficient at the top of the front pile anchorage section, respectively.

[0050] In this embodiment, for the rear pile, for example, the top load q 1，前 =50kN / m, bottom load q2，前 =300kN / m; The rigid connection between the pile top and the connecting beam can be considered as a fixed end. Using the cantilever beam method, the relationship between the second bending moment and the second shear force at the pile top and sliding surface of the rear pile can be obtained as follows: Among them, M tq，后 and Q tq，后 These are the second bending moment and the second shear force at the top of the rear-loaded section, respectively. mq，后 and Q mq，后 These are the second bending moment and the second shear force at the sliding surface of the loaded section of the rear pile, respectively, and H1 is the length of the loaded section of the rear pile.

[0051] Based on the pile deformation compatibility conditions at the sliding surface, a system of four linear equations for the pile is established, and M is solved. tq，后 Q tq，后 M mq，后 Q mq，后 : ; in, , , These are the horizontal compliance coefficient, rotational compliance coefficient, and coupling compliance coefficient at the top of the rear pile anchorage section, respectively.

[0052] The flexibility coefficients at the top of the anchorage section are obtained according to the calculation method of the pile top flexibility coefficient in step S3, as shown in Table 3.

[0053] Table 3

[0054] The method for calculating the horizontal tension of the anchor cables includes: obtaining the initial value of the horizontal tension of each row of anchor cables; calculating the first shear force and the first bending moment based on the initial value; establishing and solving the matrix equation [D][R]=[C] with the horizontal tension of the anchor cables as the unknown quantity based on the principle of displacement and deformation coordination between the front pile body and the anchor cables at each anchoring point, as well as the first shear force and the first bending moment, to update the horizontal tension of the anchor cables, where [D] is the coefficient stiffness matrix, [R] is the column vector of the horizontal tension of the anchor cables, and [C] is the column vector of constants; using the solved horizontal tension of the anchor cables as the new initial value, repeating the steps of calculating the first shear force and the first bending moment based on the initial value until the difference between the horizontal tension of the anchor cables calculated in two adjacent calculations is less than a preset value; determining the final horizontal tension of the anchor cables based on the difference of the horizontal tension of the anchor cables less than the preset value; and using the final horizontal tension of the anchor cables to perform the function of determining the relationship between the first bending moment and the first shear force at the pile top and the sliding surface under the combined action of the trapezoidal distributed soil pressure between the piles and the horizontal tension of the anchor cables in the front pile loading section based on the cantilever beam method.

[0055] Specifically, the establishment of the matrix equation includes: calculating the first pile horizontal displacement component caused by the combined action of the trapezoidal distributed load and the connecting beam at each anchor point of the front pile loading section; calculating the second pile horizontal displacement component caused by the tension of each row of anchor cables at each anchor point; based on the first pile horizontal displacement component, the second pile horizontal displacement component and the pile-anchor displacement deformation coordination principle, establishing a displacement balance equation for each anchor point, and transforming the displacement balance equation to obtain the matrix equation [D][R]=[C].

[0056] In this embodiment, the initial value of the horizontal tension of each row of anchor cables is 0, and it is assumed that the horizontal tension R of each row of anchor cables in step S5 is 0. j Initial values ​​are all 0. Calculate the first shear force Q at the top of the front pile without the horizontal tension of the anchor cables. t，前 and the first bending moment Mt, 前 ; According to structural mechanics, the horizontal displacement Δ at a certain anchoring point i (the node where the anchor cable is located) caused by the combined action of the trapezoidal load and the coupling beam on the loaded section of the front pile is... iq That is, the horizontal displacement component of the first pile is: ; in, ζ is a dimensionless position parameter.

[0057] The horizontal tension R of the j-th row of anchor cables j (1≤j≤J) The horizontal displacement Δ caused at anchor point i ij That is, the horizontal displacement component of the second pile is: ; Where, λ ij R is the horizontal tension of the j-th row of anchor cables. j The displacement coefficient acting on anchor point i is calculated using the structural mechanics diagram multiplication method: Among them, L i L is the distance from anchor point i to the sliding surface. j γ is the distance from the anchor point of the j-th row of anchor cables to the sliding surface. i This is the relative position coefficient of the anchor cable.

[0058] Based on the principle of pile-anchor displacement-deformation coordination, the horizontal displacement of the pile at anchor point i is equal to the horizontal component of the anchor cable elongation at that point. The following displacement equilibrium equation is established: ; Organize, get in, ; .

[0059] Where, ξ ij This is the comprehensive influence coefficient of the horizontal tension of the anchor cable on the displacement. Let R be the stiffness of the i-th anchor cable. i R is the horizontal tension of the anchor cable at anchor point i. i0 C represents the initial horizontal prestress at anchor point i. i is a constant coefficient.

[0060] Based on the linear equations obtained above, the solution for the horizontal tension of the anchor cable can be transformed into the following matrix equations: [D][R]=[C]; Where [D] is the coefficient stiffness matrix; [R] is the column vector composed of the horizontal tension of the anchor cable; and [C] is the constant column vector.

[0061] Equation for solving the horizontal tension matrix of 3 rows of prestressed anchor cables: Based on the solution to the equation, update the horizontal tension R of each row of anchor cables. j Then repeat the above steps iteratively until the tolerance of the horizontal tension of the anchor cable in the two calculations is less than 0.001kN.

[0062] The horizontal tension of each row of anchor cables was calculated using the parameters to be calculated as follows: R1 = 255.436 kN, R2 = 234.667 kN, R3 = 213.626 kN. The specific iterative calculation results are shown in Table 4. Substituting the calculated horizontal tension of the anchor cables into step S5 to calculate the first shear force Q at the top of the pile. tq，前 and the first bending moment M tq，前 .

[0063] Table 4

[0064] In this embodiment, considering the presence of prestressed anchor cables in the bored cast-in-place double-row anti-slide piles, an equation for solving the anchor cable horizontal tension matrix is ​​proposed. The iterative calculation of the anchor cable horizontal tension can be achieved through a programming language, resulting in higher calculation efficiency and more accurate results.

[0065] Step S6: Based on the pile top stiffness coefficient and the stress state of the connecting beam, calculate the first axial force, third shear force and third bending moment of the front pile under the action of the connecting beam, and the second axial force, fourth shear force and fourth bending moment of the rear pile under the action of the connecting beam. Specifically, based on the stiffness coefficients of the front and rear pile tops, the horizontal displacement and rotation angle of the coupling beam under the action of external horizontal force and moment are calculated; based on the horizontal displacement, rotation angle, and stiffness coefficient of the front pile top, the first axial force, third shear force, and third bending moment of the front pile top under the action of the coupling beam are calculated; based on the horizontal displacement, rotation angle, and stiffness coefficient of the rear pile top, the second axial force, fourth shear force, and fourth bending moment of the rear pile top under the action of the coupling beam are calculated.

[0066] In this embodiment, the formulas for calculating the horizontal displacement 'a' and the rotation angle 'θ' around the center point of the connecting beam are as follows: ; Where, γ aa γ βa γ aβ γ ββ To adjust the coefficients, Q0 is the horizontal force acting at the center of the coupling beam, M0 is the moment acting at the center of the coupling beam, and p 1，前 p is the vertical stiffness coefficient of the front pile top. 1，后 p is the vertical stiffness coefficient at the top of the pile. 2，前 p is the horizontal stiffness coefficient of the pile top. 2，后 p is the horizontal stiffness coefficient of the pile top. 3，前 p is the coupling stiffness coefficient at the top of the front pile. 3，后 p is the coupling stiffness coefficient at the top of the pile. 4，前 p is the rotational stiffness coefficient of the pile top. 4，后 Q is the rotational stiffness coefficient at the top of the rear pile. tq，前 For the first shear force, M tq，前 Let Q be the first bending moment. tq，后 For the second shear force, M tq，后 This is the second bending moment.

[0067] The first axial force V at the top of the loaded section of the front and rear piles caused by the coupling beam is calculated using the following formula. tb，前 Second axial force V tb，后 The third shear force Q tb，前 Fourth shear force Q tb，后 The third bending moment M tb，前 Fourth bending moment M tb，后 : ; Step S7: Determine the internal forces and pile deformation distribution of the front pile and the rear pile based on the first shear force, the first bending moment, the second shear force, the second bending moment, the third shear force, the third bending moment, the fourth shear force, the fourth bending moment, the first axial force, and the second axial force.

[0068] Specifically, the first shear force and first bending moment at the top of the front pile under lateral load are superimposed with the corresponding portions of the first axial force, third shear force, and third bending moment at the top of the front pile under the action of the connecting beam to obtain the first final shear force, first final axial force, and first final bending moment at the top of the loaded section of the front pile. Based on the first final shear force, first final bending moment, distributed load on the front pile body, and anchor cable tension, the second final shear force and second final bending moment at the sliding surface of the front pile are calculated. The second shear force and second bending moment at the top of the rear pile under lateral load are superimposed with the corresponding portions of the second axial force, fourth shear force, and fourth bending moment at the top of the rear pile under the action of the connecting beam to obtain the third final shear force, third final axial force, and third final bending moment at the top of the loaded section of the rear pile. Based on the third final shear force, third final bending moment, and distributed load on the rear pile body, the fourth final shear force and fourth final bending moment at the sliding surface of the rear pile are calculated.

[0069] In this embodiment, the first final axial force V at the top of the front pile is calculated under the combined action of lateral load and coupling beam. t，前 First final shear force Q t，前 and the first final bending moment M t，前 : Calculate the second final shear force Q at the sliding surface caused by the pile under lateral load and the final first axial force. m，前 Second final bending moment M m，前 : .

[0070] Calculate the second final axial force V at the top of the pile caused by the combined action of lateral load and coupling beam. t，后 The third final shear force Q t and the third final bending moment M t，后 : Calculate the fourth final shear force Q at the sliding surface caused by the pile under lateral load and final axial force. m，后 and the fourth final bending moment M m，后 :

[0071] In this embodiment, the first final axial force V is calculated based on the parameters to be calculated mentioned above. t，前 =305.485kN, second final axial force V t，后 = -305.485kN, first final shear force Q t，前 =743.651kN, third final shear force Q t，后 =-543.651kN, first bending moment M t，前 = -1303.415 kN·m, first bending moment M t，后 =986.959kN·m.

[0072] In this embodiment, the second final shear force Q at the sliding surface of the front and rear piles is calculated based on the parameters to be calculated. m，前 The fourth final shear force Q m，后 The second final bending moment M m，前 Fourth final bending moment M m，后 As shown in Table 5.

[0073] Table 5

[0074] Finally, based on the first final axial force V t，前 First final shear force Q t，前 First final bending moment M t，前 Second final shear force Q m，前 Second final bending moment M m，前 Second final axial force V t，后 The third final shear force Q t The third final bending moment M t，后 The fourth final shear force Q m，后和 Fourth final bending moment M m，后 The internal forces and deformations of the loaded sections of the front and rear piles were calculated using the structural statics method, and the internal forces and deformations of the anchorage sections of the front and rear piles were calculated using the finite difference method.

[0075] In this embodiment, the horizontal displacement y of the front and rear piles of the bored cast-in-place double-row anti-slide pile is obtained based on the parameters to be calculated above. i Angle θ i Bending moment M i and shear force Q i The calculation results are as follows Figures 4-7 As shown.

[0076] Example 2 like Figure 8 As shown, the present invention also proposes a parameter calculation system for bored cast-in-place double-row anti-slide piles for rapid support, using a parameter calculation method for bored cast-in-place double-row anti-slide piles for rapid support as described in any one of Embodiment 1, comprising the following modules: The acquisition module is used to acquire the parameters to be calculated and the load analysis model of the bored cast-in-place double-row anti-slide pile. The load analysis model includes a front pile, a rear pile, a connecting beam, and prestressed anchor cables. The front pile and the rear pile are divided into an upper load-bearing section and a lower anchoring section by the sliding surface. The parameters to be calculated include the pile body dimensions, foundation coefficient, load parameters, and anchor cable parameters of the front pile and the rear pile. A construction module, connected to the acquisition module, is used to construct the finite difference control equations for the front pile and the rear pile based on the load analysis model and the parameters to be calculated; The first calculation module, connected to the construction module, is used to calculate the pile top compliance coefficients of the front pile and the rear pile based on the finite difference control equation and boundary constraints. The boundary constraints include the pile bottom free boundary conditions and the pile top load boundary conditions. The pile top compliance coefficient is used to characterize the deformation response of the pile body under a given load. The second calculation module, connected to the first calculation module and the acquisition module, is used to calculate the pile top stiffness coefficient of the front pile and the rear pile based on the pile top flexibility coefficient and the foundation coefficient. The pile top stiffness coefficient is used to characterize the ability of the pile top to resist deformation. The third calculation module, connected to the first calculation module and the acquisition module, is used to calculate the first shear force and the first bending moment of the front pile under lateral load and the second shear force and the second bending moment of the rear pile under lateral load based on the pile top flexibility coefficient and load parameters. The fourth calculation module, connected to the second calculation module, is used to calculate the first axial force, third shear force, and third bending moment of the front pile under the action of the coupling beam, and the second axial force, fourth shear force, and fourth bending moment of the rear pile under the action of the coupling beam, based on the pile top stiffness coefficient and the stress state of the coupling beam. The determination module, connected to the third calculation module and the fourth calculation module, is used to determine the internal forces and pile deformation distribution of the front pile and the rear pile based on the first shear force, the first bending moment, the second shear force, the second bending moment, the third shear force, the third bending moment, the fourth shear force, the fourth bending moment, the first axial force, and the second axial force.

[0077] To address the problems of low computational efficiency, insufficient consideration of the contribution of vertical resistance at the pile bottom, spatial collaborative stress characteristics, and failure to effectively cover the situation of combined support with prestressed anchor cables in existing technologies, this invention establishes a load analysis model including front piles, rear piles, connecting beams, and prestressed anchor cables. Based on finite difference theory, it constructs governing equations, calculates the pile top flexibility coefficient and stiffness coefficient, and solves the pile internal forces under lateral loads and connecting beam action, ultimately synthesizing a complete pile internal force and deformation distribution. This allows for the consideration of the spatial collaborative stress mechanism and vertical resistance at the pile bottom of double-row piles, and covers the working condition of combined support with anchor cables. It provides an efficient and unified analysis method for the rapid and scientific design of this structure in complex slope engineering.

[0078] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating parameters of bored cast-in-place double-row anti-slide piles for rapid support, characterized in that, include: Obtain the parameters to be calculated and the load analysis model of the bored cast-in-place double-row anti-slide pile. The load analysis model includes the front pile, the rear pile, the connecting beam and the prestressed anchor cable. The front pile and the rear pile are divided into an upper load section and a lower anchorage section by the sliding surface. The parameters to be calculated include the pile body dimensions, foundation coefficient, load parameters and anchor cable parameters of the front pile and the rear pile. Based on the load analysis model and the parameters to be calculated, the finite difference control equations for the front pile and the rear pile are constructed. The pile top compliance coefficients of the front pile and the rear pile are calculated based on the finite difference governing equations and boundary constraints. The boundary constraints include the pile bottom free boundary conditions and the pile top load boundary conditions. The pile top compliance coefficients are used to characterize the deformation response of the pile body under a given load. The pile top stiffness coefficients of the front pile and the rear pile are calculated based on the pile top flexibility coefficient and the foundation coefficient. The pile top stiffness coefficient is used to characterize the pile top's ability to resist deformation. Based on the pile top flexibility coefficient and load parameters, calculate the first shear force and first bending moment of the front pile under lateral load, and the second shear force and second bending moment of the rear pile under lateral load. Based on the pile top stiffness coefficient and the stress state of the coupling beam, calculate the first axial force, third shear force and third bending moment of the front pile under the action of the coupling beam, and the second axial force, fourth shear force and fourth bending moment of the rear pile under the action of the coupling beam. The internal forces and pile deformation distribution of the front pile and the rear pile are determined based on the first shear force, the first bending moment, the second shear force, the second bending moment, the third shear force, the third bending moment, the fourth shear force, the fourth bending moment, the first axial force, and the second axial force.

2. The method for calculating parameters of bored cast-in-place double-row anti-slide piles for rapid support according to claim 1, characterized in that, The construction of the finite difference governing equations for the front pile and the rear pile based on the load analysis model and the parameters to be calculated includes: The pile bodies of the front pile and the rear pile are divided into units and discretized at nodes; Based on the load analysis model and the parameters to be calculated, the deflection differential control equations at each unit node of the front pile and the rear pile are established using the Euler-Bernoulli beam theory. The flexural differential control equations are transformed into finite difference schemes based on the central difference scheme, thus obtaining the finite difference control equations.

3. The method for calculating parameters of bored cast-in-place double-row anti-slide piles for rapid support according to claim 2, characterized in that, The pile top compliance coefficient includes the pile top horizontal compliance coefficient, the pile top rotational compliance coefficient, and the pile top coupling compliance coefficient. The calculation of the pile top compliance coefficients of the front pile and the rear pile based on the finite difference governing equations and boundary constraints includes: Based on the finite difference control equations, the free boundary conditions at the pile bottom, and the load boundary conditions at the pile top, a set of linear calculation equations for pile displacement in matrix form is constructed to solve for the horizontal displacement of each node of the front and rear piles. The solution is obtained by applying a unit horizontal force or a unit bending moment at the pile top as load boundary conditions to the linear calculation equations of the pile displacement. The solution results include the horizontal displacement at the pile top corresponding to the unit horizontal force at the pile top and the horizontal displacement at the pile top and adjacent nodes corresponding to the unit bending moment at the pile top. Based on the solution results, calculate the pile top horizontal compliance coefficient, pile top rotational compliance coefficient, and pile top coupling compliance coefficient; Wherein, the pile top horizontal flexibility coefficient is the pile top horizontal displacement caused by only a unit horizontal force acting on the pile top, the pile top rotational flexibility coefficient is the pile top rotation angle caused by only a unit bending moment acting on the pile top, and the pile top coupling flexibility coefficient is the pile top horizontal displacement caused by only a unit bending moment acting on the pile top or the pile top rotation angle caused by only a unit horizontal force acting on the pile top.

4. A method for calculating parameters of bored cast-in-place double-row anti-slide piles for rapid support, as described in claim 1 or 3, characterized in that, The pile top stiffness coefficient includes the pile top vertical stiffness coefficient, pile top horizontal stiffness coefficient, pile top coupling stiffness coefficient, and pile top rotational stiffness coefficient. The pile top stiffness coefficients of the front pile and the rear pile are calculated based on the pile top flexibility coefficient and the foundation coefficient, including: Based on formula Calculate the vertical stiffness coefficient at the pile top; Based on formula Calculate the horizontal stiffness coefficient at the pile top; Based on formula Calculate the coupling stiffness coefficient at the pile top; Based on formula Calculate the rotational stiffness coefficient at the pile top; Where H1 is the length of the loaded section of the front or rear pile; H2 is the length of the anchorage section of the front or rear pile; E is the elastic modulus of the front or rear pile; d is the diameter of the circular pile of the front or rear pile; k v δ1 is the vertical reaction force coefficient of the foundation; δ2 is the horizontal flexibility coefficient of the pile top of the front or rear pile; δ3 is the rotational flexibility coefficient of the pile top of the front or rear pile; δ4 is the coupling flexibility coefficient of the pile top of the front or rear pile. This is the vertical stiffness coefficient at the pile top; This is the horizontal stiffness coefficient at the pile top; This is the coupling stiffness coefficient at the pile top; This is the rotational stiffness coefficient at the pile top.

5. The method for calculating parameters of bored cast-in-place double-row anti-slide piles for rapid support according to claim 1, characterized in that, The calculation of the first shear force and first bending moment of the front pile under lateral load and the second shear force and second bending moment of the rear pile under lateral load based on the pile top flexibility coefficient and load parameters includes: Based on the cantilever beam method, the relationship function between the first bending moment and the first shear force at the pile top and the sliding surface of the front pile loading segment under the combined action of trapezoidal distributed inter-pile earth pressure and anchor cable horizontal tension is determined. The front pile loading segment is subjected to the combined action of inter-pile earth pressure and anchor cable horizontal tension, and the load of the inter-pile earth pressure is trapezoidal. Based on the pile deformation coordination condition of the front pile at the sliding surface, the flexibility coefficient of the top of the anchorage section of the front pile, and the relationship function between the first bending moment and the first shear force, a linear equation system is established and solved to obtain the first shear force and the first bending moment at the pile top and the first shear force and the first bending moment at the sliding surface under lateral load. Based on the cantilever beam method, the relationship function between the second bending moment and the second shear force at the pile top and the sliding surface of the pile loading segment under the action of trapezoidal earth pressure is determined. The pile loading segment is subjected to the combined action of the earth pressure behind the pile and the inter-pile earth pressure in front of the pile. The resultant load of the earth pressure behind the pile and the inter-pile earth pressure in front of the pile is trapezoidal. Based on the pile deformation coordination condition of the rear pile at the sliding surface, the flexibility coefficient of the top of the rear pile anchorage section, and the relationship function between the second bending moment and the second shear force, a linear equation system is established and solved to obtain the second shear force and the second bending moment at the pile top and the second shear force and the second bending moment at the sliding surface under lateral load.

6. The method for calculating parameters of bored cast-in-place double-row anti-slide piles for rapid support according to claim 5, characterized in that, The calculation of the first axial force, third shear force, and third bending moment of the front pile under the action of the coupling beam, and the second axial force, fourth shear force, and fourth bending moment of the rear pile under the action of the coupling beam, based on the pile top stiffness coefficient and the stress state of the coupling beam, includes: The horizontal displacement and rotation angle around the center point of the coupling beam under the action of external horizontal force and moment are calculated based on the stiffness coefficients of the front and rear pile tops. Based on the horizontal displacement, rotation angle, and stiffness coefficient of the front pile top, calculate the first axial force, third shear force, and third bending moment of the front pile top under the action of the coupling beam; Based on the horizontal displacement, rotation angle, and pile top stiffness coefficient of the rear pile, calculate the second axial force, fourth shear force, and fourth bending moment at the top of the rear pile under the action of the coupling beam.

7. The method for calculating parameters of bored cast-in-place double-row anti-slide piles for rapid support according to claim 1, characterized in that, The determination of the internal force and pile deformation distribution of the front pile and the rear pile based on the first shear force, first bending moment, second shear force, second bending moment, third shear force, third bending moment, fourth shear force, fourth bending moment, first axial force, and second axial force includes: The first shear force and first bending moment at the top of the front pile under lateral load are superimposed with the corresponding parts of the first axial force, third shear force and third bending moment at the top of the front pile under the action of the connecting beam to obtain the first final shear force, first final axial force and first final bending moment at the top of the loaded section of the front pile. The second final shear force and the second final bending moment at the sliding surface of the front pile are calculated based on the first final shear force, the first final bending moment, the distributed load on the front pile body and the anchor cable tension. The second shear force and second bending moment at the top of the rear pile under lateral load are superimposed with the corresponding parts of the second axial force, fourth shear force and fourth bending moment at the top of the rear pile under the action of the connecting beam to obtain the third final shear force, third final axial force and third final bending moment at the top of the loaded section of the rear pile. The fourth final shear force and the fourth final bending moment at the sliding surface of the rear pile are calculated based on the third final shear force, the third final bending moment, and the distributed load on the rear pile body.

8. The method for calculating parameters of bored cast-in-place double-row anti-slide piles for rapid support according to claim 5, characterized in that, The method for calculating the horizontal tension of the anchor cable includes: Obtain the initial value of the horizontal tension of each row of anchor cables; Calculate the first shear force and the first bending moment based on the initial values; Based on the principle of displacement and deformation coordination between the pile body and the anchor cable at each anchoring point, as well as the first shear force and the first bending moment, a matrix equation [D][R]=[C] with the horizontal tension of the anchor cable as the unknown quantity is established and solved to update the horizontal tension of the anchor cable, where [D] is the coefficient stiffness matrix, [R] is the column vector of the horizontal tension of the anchor cable, and [C] is the column vector of constants; Use the solved horizontal tension of the anchor cable as a new initial value, and repeat the steps of calculating the first shear force and the first bending moment based on the initial value until the difference between the two adjacent calculations of the horizontal tension of the anchor cable is less than the preset value. The final anchor cable horizontal tension is determined based on the difference between the anchor cable horizontal tension and the preset value. The relationship between the first bending moment and the first shear force at the pile top and the sliding surface is determined based on the cantilever beam method using the final anchor cable horizontal tension. This relationship is achieved by using the horizontal tension of the anchor cable to execute the final anchor cable horizontal tension.

9. The method for calculating parameters of bored cast-in-place double-row anti-slide piles for rapid support according to claim 8, characterized in that, The establishment of the matrix equation specifically includes: Calculate the horizontal displacement components of the first pile body caused at each anchorage point under the combined action of trapezoidal distributed load and connecting beam in the loaded section of the front pile; Calculate the horizontal displacement component of the second pile body caused by the tension of each row of anchor cables at each anchor point; Based on the horizontal displacement components of the first pile body, the horizontal displacement components of the second pile body, and the principle of pile-anchor displacement deformation coordination, a displacement balance equation is established for each anchor point, and the displacement balance equation is transformed to obtain the matrix equation [D][R]=[C].

10. A parameter calculation system for bored cast-in-place double-row anti-slide piles for rapid support, characterized in that, The system employs a parameter calculation method for bored cast-in-place double-row anti-slide piles for rapid support, as described in any one of claims 1 to 9, and specifically includes the following modules: The acquisition module is used to acquire the parameters to be calculated and the load analysis model of the bored cast-in-place double-row anti-slide pile. The load analysis model includes a front pile, a rear pile, a connecting beam, and prestressed anchor cables. The front pile and the rear pile are divided into an upper load-bearing section and a lower anchoring section by the sliding surface. The parameters to be calculated include the pile body dimensions, foundation coefficient, load parameters, and anchor cable parameters of the front pile and the rear pile. A construction module, connected to the acquisition module, is used to construct the finite difference control equations for the front pile and the rear pile based on the load analysis model and the parameters to be calculated; The first calculation module, connected to the construction module, is used to calculate the pile top compliance coefficients of the front pile and the rear pile based on the finite difference control equation and boundary constraints. The boundary constraints include the pile bottom free boundary conditions and the pile top load boundary conditions. The pile top compliance coefficient is used to characterize the deformation response of the pile body under a given load. The second calculation module, connected to the first calculation module and the acquisition module, is used to calculate the pile top stiffness coefficient of the front pile and the rear pile based on the pile top flexibility coefficient and the foundation coefficient. The pile top stiffness coefficient is used to characterize the ability of the pile top to resist deformation. The third calculation module, connected to the first calculation module and the acquisition module, is used to calculate the first shear force and the first bending moment of the front pile under lateral load and the second shear force and the second bending moment of the rear pile under lateral load based on the pile top flexibility coefficient and load parameters. The fourth calculation module, connected to the second calculation module, is used to calculate the first axial force, third shear force, and third bending moment of the front pile under the action of the coupling beam, and the second axial force, fourth shear force, and fourth bending moment of the rear pile under the action of the coupling beam, based on the pile top stiffness coefficient and the stress state of the coupling beam. The determination module, connected to the third calculation module and the fourth calculation module, is used to determine the internal forces and pile deformation distribution of the front pile and the rear pile based on the first shear force, the first bending moment, the second shear force, the second bending moment, the third shear force, the third bending moment, the fourth shear force, the fourth bending moment, the first axial force, and the second axial force.

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