Method for calculating bearing capacity of inclined pile and vertical pile of bridge

Abstract

The invention relates to the technical field of railway bridge foundation engineering, and particularly discloses a method for calculating bearing capacity of inclined piles and vertical piles of a bridge. According to the method, the calculation and analysis method of the bridge skewback under the action of various loads is established through an elastic theory method, the method is convenient to use, the displacement and load sharing conditions of the bridge skewback under the action of various loads can be directly obtained, and powerful support is provided for optimizing a design scheme and saving the construction cost; according to the established calculation model, calculation parameters are easy to obtain, most parameters are obtained only by looking up industry specifications and geological exploration reports, complex theoretical calculation is not needed, related employees can easily use the calculation model, the engineering application value is high, the employees can further optimize a basic design scheme, the basic bearing performance is improved, and the method is suitable for popularization and application. The engineering cost is saved.

Description

Technical Field

[0001] This invention relates to the field of railway bridge foundation engineering technology, and in particular to a method for calculating the bearing capacity of inclined piles and vertical piles of bridges. Background Technology

[0002] Currently, bridge foundation design standards lack specific provisions for the design of arch bridge foundations. Designers often overlook the impact of bending moment on the arch foundation, which contradicts the actual load conditions of the foundation. In actual engineering projects, arch bridges are affected by environmental loads and foundation displacement, making it impossible to guarantee that the arch section is only subjected to axial pressure without bending moment. In other words, the actual load transmitted from the arch to the arch foundation can be decomposed into three different types of loads: axial force, shear force, and bending moment. For composite foundations with even more complex stress conditions, the load distribution among different parts of the foundation under multiple loads is difficult to obtain directly through theoretical calculations.

[0003] Therefore, a simple and scientific calculation method is urgently needed to solve the bearing mechanism and deformation problem of arch foundations under the combined action of three different types of loads: axial force, shear force, and bending moment. Summary of the Invention

[0004] To overcome the problem that the load distribution of different parts of the foundation in existing bridge foundation designs is difficult to obtain directly through theoretical calculations, this invention provides a method for calculating the bearing capacity of inclined piles and vertical piles in bridges.

[0005] This invention provides a method for calculating the bearing capacity of inclined and vertical piles in bridges, for use in bridge arch abutments. The bridge arch abutment is composed of a block foundation and inclined and vertical piles connecting the block foundation. The method includes: Obtain the external load and uniaxial compressive strength of the rock strata at the location of the bridge arch abutment, and determine the foundation parameters based on the uniaxial compressive strength of the rock strata; Based on the block foundation and the foundation parameters, a block spring model is established, and the inclined piles and vertical piles are assembled into the block spring model; By solving the static equilibrium equations simultaneously for the vertical force, horizontal force, and bending moment in the assembled block spring model, the displacements of the side and bottom surfaces of the block foundation are obtained, thus completing the foundation bearing capacity calculation. Specifically, the vertical force, horizontal force, and bending moment in the block spring model assembled by simultaneously solving the static equilibrium equations include: Select any rotation point on the block foundation to generate degrees of freedom, and construct the displacement of the side and bottom surfaces of the block foundation, as well as the pile top displacement of the inclined piles and vertical piles based on the degrees of freedom. A coordinate system is constructed based on the block spring model. Points representing the block foundation are selected in the coordinate system. The vertical force, horizontal force and bending moment of the block foundation are constructed by integrating the displacement of the side and bottom surfaces of the block foundation and the foundation parameters. Based on the pile top displacement of inclined piles and vertical piles and the internal forces of inclined piles and vertical piles, construct the vertical force, horizontal force and bending moment at the pile top of the inclined pile, as well as the vertical force, horizontal force and bending moment at the pile top of the vertical pile; Based on the vertical force balance, horizontal force balance, and bending moment balance of the block foundation, the vertical force, horizontal force, and bending moment of the inclined pile, the vertical force, horizontal force, and bending moment of the vertical pile, and the external load, the degrees of freedom are obtained by solving. The displacements of the side and bottom surfaces of the block foundation are calculated based on the degrees of freedom obtained from the solution, thus completing the solution.

[0006] According to a specific implementation, in the above calculation method, the foundation parameters include the foundation vertical resistance coefficient, the foundation horizontal resistance coefficient, the vertical foundation friction stiffness, and the horizontal foundation friction stiffness; the vertical force of the block foundation includes the vertical soil resistance at the bottom of the block foundation and the vertical frictional resistance on the sides of the block foundation; the horizontal force of the block foundation includes the horizontal frictional resistance at the bottom of the block foundation and the horizontal soil resistance on the sides of the block foundation; the bending moment of the block foundation includes the bending moment of the normal soil resistance and tangential frictional resistance on the sides and bottom of the block foundation about the point of rotation.

[0007] According to a specific implementation, in the above calculation method, the degrees of freedom include the vertical displacement, horizontal displacement, and rotation angle of any rotation point, and the static equilibrium equations include: Based on the simultaneous equilibrium equations for all vertical forces, the formula is as follows: , Based on the simultaneous equilibrium equations of all horizontal forces, the formula is as follows: , Based on the simultaneous equilibrium equations for all bending moments, the formula is as follows: , Among them, the vertical force, horizontal force, and bending moment at the top of the inclined pile are respectively , , The vertical force, horizontal force, and bending moment at the top of the vertical pile are respectively , , The vertical force, horizontal force, and bending moment of the external load are respectively , , , For the vertical soil resistance at the bottom of the block foundation, The vertical frictional resistance on the side of the block foundation. The horizontal frictional resistance at the bottom surface of the block foundation. For the horizontal soil resistance on the side of the block foundation, , and , These are the bending moments of the normal soil resistance and tangential skin friction at the bottom and sides of the block foundation, respectively, about the point of rotation. in: , , , , , , , , in, , , , , , , , These are the coordinates of the points representing the foundation of the block. Any point on the bottom surface of the block foundation i x-axis coordinate value; Any point on the side of the block foundation j of z Axis coordinate values.

[0008] According to one specific implementation method, in the above calculation method, the ratio of the interface friction stiffness to the normal stiffness of the block foundation is obtained through a direct on-site shear test. k According to the ratio k The horizontal foundation friction stiffness is obtained by multiplying the vertical resistance coefficient of the foundation with the horizontal foundation friction stiffness, based on the ratio. k The vertical foundation friction stiffness is obtained by multiplying the coefficient of horizontal resistance of the foundation with the coefficient of horizontal resistance of the foundation.

[0009] According to a specific implementation method, in the above calculation method, the displacements of the sides and bottom of the block foundation include the vertical displacement, horizontal displacement, and rotation of the sides, as well as the vertical displacement, horizontal displacement, and rotation of the bottom; the calculation of the foundation bearing capacity includes: The lateral vertical stress is obtained by multiplying the lateral vertical displacement by the vertical foundation friction stiffness. The lateral horizontal stress is obtained by multiplying the lateral horizontal displacement by the foundation horizontal resistance coefficient. The vertical stress at the bottom surface is obtained by multiplying the vertical displacement of the bottom surface by the vertical resistance coefficient of the foundation. The horizontal stress on the bottom surface is obtained by multiplying the horizontal displacement of the bottom surface with the frictional stiffness of the horizontal foundation.

[0010] According to a specific implementation method, the calculation method above, which constructs the vertical force, horizontal force, and bending moment at the top of the inclined pile and the vertical force, horizontal force, and bending moment at the top of the vertical pile, specifically includes: The stiffness of the pile tops of inclined and vertical piles is calculated by using the internal forces generated at the pile top when a unit displacement occurs. This includes the axial force generated at the pile top when a unit displacement occurs along the axis, the horizontal force generated at the pile top when a unit displacement occurs perpendicular to the pile axis, the bending moment generated at the pile top when a unit displacement occurs perpendicular to the pile axis, the horizontal force generated at the pile top when a unit rotation occurs, and the bending moment generated at the pile top when a unit rotation occurs. The vertical force, horizontal force, and bending moment at the pile top of the inclined pile are determined based on the stiffness of the pile top, and the vertical force, horizontal force, and bending moment at the pile top of the vertical pile are determined based on the stiffness of the pile top.

[0011] According to a specific implementation method, in the above calculation method, the vertical force, horizontal force, and bending moment at the top of the inclined pile are determined based on the stiffness of the inclined pile top, and the vertical force, horizontal force, and bending moment at the top of the vertical pile are determined based on the stiffness of the vertical pile top, specifically including: The reaction force of a single pile top on the block foundation is determined based on the stiffness of the pile tops of the inclined and vertical piles. The vertical force, horizontal force, and bending moment at the top of the vertical pile, as well as the vertical force, horizontal force, and bending moment at the top of the inclined pile, are determined based on the reaction force from the combined displacement of the inclined pile and the vertical pile.

[0012] According to a specific implementation method, the above calculation method determines whether the bridge arch abutment meets the design requirements based on the obtained composite foundation bearing capacity. If it does not meet the requirements, the pile position and stiffness of the inclined pile or vertical pile are adjusted, and the static equilibrium equation is reconstructed for calculation.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention establishes a calculation and analysis method for bridge arch abutments under various loads using elasticity theory. This method is easy to use and can directly determine the displacement and load distribution of bridge arch abutments under various loads, providing strong support for optimizing design schemes and saving engineering costs. The calculation model established by this invention has easily obtainable calculation parameters. Most parameters can be obtained by consulting industry standards and geological survey reports without the need for complex theoretical calculations. Relevant practitioners can easily use it, and it has high engineering application value. It is beneficial for practitioners to further optimize foundation design schemes, improve foundation bearing capacity, and save engineering costs. Attached Figure Description

[0014] Figure 1 A flowchart illustrating a method for calculating the bearing capacity of inclined and vertical piles in bridges, provided in an embodiment of the present invention; Figure 2 A schematic diagram of a block spring model provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the assembly block spring model provided in an embodiment of the present invention; Figure 4 This is a structural schematic diagram of the dimensions of the composite foundation for bridge arch abutments provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of the pile top stiffness direction provided in an embodiment of the present invention; Figure 6 The calculation model and positive direction of the external load are provided in the embodiments of the present invention. Detailed Implementation

[0015] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0016] Unless otherwise specified, the terms "horizontal," "vertical," "suspended," and "parallel" appearing in the description of specific embodiments of the present invention do not imply that the corresponding device / component / element must be absolutely horizontal, vertical, suspended, or parallel, but rather that it may be slightly tilted or have deviations. For example, "horizontal" merely means that its direction is more horizontal relative to "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted. Alternatively, it can be simplified to mean that the corresponding device / component / element, when set in a "horizontal," "vertical," "suspended," or "parallel" direction, can have an error / deviation of ±10% relative to the corresponding direction, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, and more preferably within ±4%. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its function in the solution of the present invention.

[0017] Furthermore, the use of terms such as "first," "second," and "third" in terminology is merely for distinguishing descriptions of identical or similar components and should not be interpreted as emphasizing or implying the relative importance of a particular component.

[0018] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to common connection methods in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.

[0019] To address the problems in existing technologies, this invention overcomes the shortcomings of existing calculation methods and provides a method for calculating the bearing capacity of inclined and vertical piles in bridges. Taking rock foundations as an example, by establishing a multi-spring model of the bridge arch abutment, and based on the "C" method in the elastic foundation reaction method, it achieves efficient and accurate calculation of the displacement and load sharing of the bridge arch abutment under multiple loads, clarifies the foundation bearing mechanism, and optimizes the design scheme.

[0020] It should be noted that: 1. This calculation method only considers the longitudinal force balance of the bridge and ignores the transverse force; 2. The calculation steps are only described using rock foundation as an example, so the "C" method is more reasonable; for soil foundation, this calculation system is still applicable, only the "m" method needs to be used when taking the value of the foundation reaction coefficient; 3. The bridge arch abutment mega-inclined-vertical pile composite foundation in this calculation method consists of three parts: block foundation, inclined pile and vertical pile. This calculation method is still applicable to the arch bottom foundation with only block foundation, and the influence of the pile foundation can be ignored during the calculation.

[0021] For details, please refer to Figure 1 It shows a flowchart illustrating a method for calculating the bearing capacity of inclined and vertical piles of bridges provided by the present invention, including: Step 1: Obtain the external load and uniaxial compressive strength of the rock strata at the location of the bridge arch abutment, and determine the foundation parameters based on the uniaxial compressive strength of the rock strata.

[0022] The foundation parameters include the vertical resistance coefficient, the horizontal resistance coefficient, the vertical friction stiffness, and the horizontal friction stiffness; the external loads include self-weight and the vertical force, horizontal force, and bending moment of the transmitted load.

[0023] Taking rock foundations as an example, the uniaxial compressive strength of each rock layer around the bridge arch abutment is obtained based on geological survey data. The vertical resistance coefficient of the corresponding rock strata can be obtained by referring to the tables in the "Code for Design of Railway Bridge and Culvert Foundations" (TB 10093-2017). .

[0024] Table 1 Vertical subgrade coefficient of rock value

[0025] If interbedded rock strata are present, first determine the uniaxial compressive strength of the actual contact rock strata at the base of the block foundation. Calculate the uniaxial compressive strength value by weighting the content of each rock stratum. Then, refer to Table 1 for linear interpolation to obtain the actual vertical resistance coefficient of the foundation. .

[0026] In the same rock stratum, the horizontal resistance coefficient of the foundation can be assumed. The relationship between the two can also be determined based on field tests or geological survey reports.

[0027] The ratio of the interfacial frictional stiffness to the normal stiffness of the block foundation k This can be obtained through direct shear tests in the field. Based on the stated ratio... k The horizontal foundation friction stiffness is obtained by multiplying the vertical resistance coefficient of the foundation with the horizontal foundation friction stiffness, based on the ratio. k The vertical foundation friction stiffness is obtained by multiplying the coefficient of horizontal resistance of the foundation with the coefficient of horizontal resistance of the foundation. Specifically, the vertical foundation friction stiffness of the block foundation... Friction stiffness of horizontal foundation They are respectively: , .

[0028] Step 2: Based on the block foundation and the foundation parameters, establish a block spring model, and assemble the inclined piles and vertical piles into the block spring model.

[0029] Specifically, assuming the block foundation is a rigid foundation, a block spring model is established considering the normal soil resistance and tangential skin friction at the bottom and sides of the block foundation. The normal soil resistance includes the vertical soil resistance at the bottom of the block foundation and the horizontal soil resistance on the sides of the block foundation. The tangential skin friction includes the horizontal skin friction at the bottom of the block foundation and the vertical skin friction on the sides of the block foundation. The established block spring model is as follows: Figure 2 As shown.

[0030] Furthermore, the inclined and vertical piles connected to the block foundation are simplified into shear springs, normal springs, and bending springs, and assembled into the block spring model. The assembled block spring model is as follows: Figure 3 As shown.

[0031] Step 3: Solve the vertical force, horizontal force and bending moment in the assembled block spring model by combining the static equilibrium equations to obtain the displacement of the side and bottom surfaces of the block foundation, and complete the foundation bearing capacity calculation.

[0032] Step 3 specifically includes: Step 301: Select any rotation point on the block foundation to generate degrees of freedom, and construct the displacement of the side and bottom surfaces of the block foundation, as well as the pile top displacement of the inclined piles and vertical piles based on the degrees of freedom.

[0033] Specifically, taking the center of the arch rib as the assumed rotation point P, let the horizontal displacement of the assumed rotation point P be... y The vertical displacement is The corner is Its positive direction is the same as the positive direction of the load. Based on the assumption of rigid body motion, and neglecting the coupling effect of vertical and horizontal loads, the displacement of the rigid body (i.e., the block foundation) under load is decomposed into: rigid body translational displacement (including horizontal and vertical translational displacement) + rigid body rotational deformation. Then, the displacement of any point on the block foundation is: Horizontal displacement

[0034] Vertical displacement

[0035] corner

[0036] in This represents the horizontal translational displacement of a rigid body. This represents the vertical translational displacement of the rigid body. Rigid body caused by rigid body rotation n Horizontal displacement at point, Rigid body caused by rigid body rotation n Vertical displacement at point.

[0037] Furthermore, the displacement of the top A of the vertical pile is as follows: Horizontal displacement

[0038] Vertical displacement

[0039] corner .

[0040] The displacement of the top B of the inclined pile is: Horizontal displacement

[0041] Vertical displacement

[0042] corner .

[0043] Furthermore, any point on the bottom surface of the block foundation i The displacement is: Horizontal displacement

[0044] Vertical displacement

[0045] corner

[0046] Furthermore, any point on the side of the block foundation j The displacement is: Horizontal displacement

[0047] Vertical displacement

[0048] corner .

[0049] Step 302: Construct a coordinate system based on the block spring model, select points in the coordinate system that represent the block foundation, and integrate the displacements of the side and bottom surfaces of the block foundation and the foundation parameters to construct the vertical force, horizontal force and bending moment of the side and bottom surfaces of the block foundation.

[0050] Specifically, in such Figure 3 In the coordinate system shown, the following can be listed:

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] In the formula: , , , for Figure 3 Points O, D, P, and E shown x Coordinate values Any point on the bottom surface of the block foundation i of x Coordinate values; , , , for Figure 3 Points O, F, E, and P shown z Coordinate values Any point on the side of the block foundation j of z Coordinate values; For the vertical soil resistance at the bottom of the block foundation, The vertical frictional resistance on the side of the block foundation. The horizontal frictional resistance at the bottom surface of the block foundation. For the horizontal soil resistance on the side of the block foundation, , and , These represent the bending moments at the rotation points caused by the normal soil resistance and tangential skin friction at the bottom and sides of the block foundation, respectively. It is understood that points O, D, P, E, and F are used to characterize the block foundation and are intended to construct the aforementioned integral formula. To obtain the various forces or bending moments of the block foundation using the integral formula, points characterizing the block foundation can be selected in the spring model provided in this embodiment of the invention in a reasonable manner for construction and solution.

[0059] Furthermore, it is understood that tangential and normal directions are defined for ease of description regarding the directions of various forces on the bottom and side surfaces. Those skilled in the art know that the normal direction for the bottom surface is its vertical direction, the tangential direction for the bottom surface is its horizontal direction, the normal direction for the side surface is its horizontal direction, and the tangential direction for the side surface is its vertical direction. Specifically, the vertical forces of the block foundation include the vertical soil resistance at the bottom surface of the block foundation and the vertical skin friction of the side surfaces of the block foundation; the horizontal forces of the block foundation include the horizontal skin friction of the bottom surface of the block foundation and the horizontal soil resistance of the side surfaces of the block foundation; the bending moment of the block foundation includes the bending moment about the point of rotation caused by the normal soil resistance and tangential skin friction of the side and bottom surfaces of the block foundation.

[0060] Step 303: Based on the pile top displacement of the inclined pile and the vertical pile, and combined with the internal forces of the inclined pile and the vertical pile, construct the vertical force, horizontal force and bending moment at the pile top of the inclined pile, as well as the vertical force, horizontal force and bending moment at the pile top of the vertical pile.

[0061] Specifically, the stiffness of the pile tops of inclined and vertical piles is calculated by the internal forces generated at the pile top when a unit displacement occurs. This includes the axial force generated at the pile top when a unit displacement occurs along the axis, the horizontal force generated at the pile top when a unit displacement occurs perpendicular to the pile axis, the bending moment generated at the pile top when a unit displacement occurs perpendicular to the pile axis, the horizontal force generated at the pile top when a unit rotation occurs, and the bending moment generated at the pile top when a unit rotation occurs. The vertical force, horizontal force, and bending moment at the pile top of the inclined pile are determined based on the stiffness of the pile top, and the vertical force, horizontal force, and bending moment at the pile top of the vertical pile are determined based on the stiffness of the pile top.

[0062] In one possible implementation, referring to the calculation formula for the internal force generated at the pile top when a unit displacement occurs at the pile top in the "Code for Design of Railway Bridge and Culvert Foundations" (TB 10093-2017), the axial force generated at the pile top when only a unit displacement occurs along the axis is calculated for inclined piles and vertical piles respectively. The horizontal force generated at the top of the pile when the displacement is perpendicular to the pile axis. The bending moment generated at the top of the pile when a unit displacement occurs perpendicular to the pile axis. The horizontal force generated at the top of the pile when the pile rotates by a unit angle The bending moment generated at the pile top when the pile top rotates by a unit angle There are a total of five stiffness values, and the specific calculation steps are as follows:

[0063]

[0064]

[0065]

[0066]

[0067] In the formula: This is the distance from the bottom of the foundation to the ground. This is the distribution coefficient of pile side friction. h This is the distance from the ground surface to the rock-embedded surface. E The compressive elastic modulus of the pile concrete. A This represents the cross-sectional area of ​​the pile foundation. A 0 represents the compressive area of ​​the foundation at the pile bottom plane; , The unit horizontal force acting on the pile top H The horizontal displacement and rotation angle generated at the pile top when =1 , Unit bending moment acting at the pile top M When =1, the horizontal displacement and rotation angle generated at the top of the pile can all be directly solved by the formulas in the specification, which will not be elaborated here.

[0068] Furthermore, the reaction force of a single pile top on the block foundation is determined based on the stiffness of the inclined and vertical pile tops. The vertical force, horizontal force, and bending moment at the top of the vertical pile, as well as the vertical force, horizontal force, and bending moment at the top of the inclined pile, are determined based on the combined reaction force of the displacement of the inclined and vertical piles. Specifically, when the block foundation undergoes a unit displacement, the reaction force of a single pile top on the block foundation is simplified as follows:

[0069]

[0070]

[0071]

[0072] In the formula: The vertical reaction force at the pile top when a unit vertical displacement occurs in the block foundation. The horizontal reaction force at the pile top when a unit horizontal displacement occurs in the block foundation. The horizontal reaction force at the pile top when a unit rotation angle is generated in the block foundation. The pile top inflection moment when a unit horizontal displacement occurs in the block foundation. The pile top inflection moment when a unit rotation angle is generated for the block foundation.

[0073] Based on this, and considering the displacement at the pile top, the vertical force, horizontal force, and bending moment at the top of a single vertical pile are respectively... , , They are respectively:

[0074]

[0075] .

[0076] Furthermore, the vertical force at the top of the pile along the axial direction of a single inclined pile Horizontal force perpendicular to the axis of the inclined pile They are respectively:

[0077]

[0078] .

[0079] The vertical force, horizontal force, and bending moment at the top of a single inclined pile are respectively... , , They are respectively:

[0080]

[0081] .

[0082] Step 304: Based on the vertical force balance, horizontal force balance, and bending moment balance of the block foundation, the vertical force, horizontal force, and bending moment of the inclined pile, the vertical force, horizontal force, and bending moment of the vertical pile, and the external load, solve for the degrees of freedom.

[0083] Furthermore, based on the simultaneous equilibrium equations of all vertical forces, the formula is as follows: , Based on the simultaneous equilibrium equations of all horizontal forces, the formula is as follows: , Based on the simultaneous equilibrium equations for all bending moments, the formula is as follows: .

[0084] Among them, the vertical force, horizontal force, and bending moment of the external load are respectively , , .

[0085] Specifically, the horizontal displacement of the assumed point of rotation is obtained by solving three static equilibrium equations. y Vertical displacement and corners The horizontal and vertical displacements of the sides and bottom of the block foundation are determined by geometric relationships. Multiplying these displacements by the corresponding soil resistance coefficient yields the stress on the block foundation. Furthermore, the calculation of the foundation bearing capacity includes: The lateral vertical stress is obtained by multiplying the vertical displacement of the side surface by the vertical friction stiffness of the foundation; the lateral horizontal stress is obtained by multiplying the horizontal displacement of the side surface by the horizontal resistance coefficient of the foundation; the bottom vertical stress is obtained by multiplying the vertical displacement of the bottom surface by the vertical resistance coefficient of the foundation; and the bottom horizontal stress is obtained by multiplying the horizontal displacement of the bottom surface by the horizontal friction stiffness of the foundation.

[0086] Furthermore, the load on the top of the vertical pile can be solved by multiplying the displacement at the top of the vertical pile by the corresponding stiffness. When calculating the inclined pile, the horizontal and vertical displacements at the top of the inclined pile are first decomposed along the axis of the inclined pile and perpendicular to the axis. The load on the top of the inclined pile can be solved by multiplying the decomposed displacements by the corresponding stiffness.

[0087] Furthermore, when the basic design scheme is adjusted, the foundation displacement and load sharing of each part also change, requiring remodeling and analysis, which involves a large workload. In one possible implementation, this embodiment of the invention also includes determining whether the bridge arch abutment meets the design requirements based on the obtained composite foundation bearing capacity. If it does not meet the requirements, the pile position and stiffness of the inclined piles or vertical piles are adjusted, and the static equilibrium equations are reconstructed for calculation.

[0088] The calculation method provided by the present invention will be further introduced and explained below with reference to specific implementation methods.

[0089] Taking a major railway bridge in Southwest China as an example, to simplify calculations, the transverse forces are not considered; instead, the problem is treated as a plane strain problem. Please refer to [reference needed]. Figure 4 This illustrates a structural schematic diagram of the dimensions of the bridge arch abutment composite foundation provided in an embodiment of the present invention. For example... Figure 4 As shown, two vertical piles and two inclined piles are installed on the bottom and side surfaces of the block foundation, respectively. To simplify the calculation, the top stiffness of the two vertical piles is superimposed at the center point of this surface. Based on the plane strain assumption, the top stiffness of the two vertical piles is applied to point A; similarly, the top stiffness of the inclined piles is superimposed and applied to point B. The constructed spring model is roughly as follows. Figure 3 Same. Furthermore, Figure 5 This is a schematic diagram showing the direction of pile top stiffness. Figure 6 This represents the calculation model and the positive direction of the external load in this calculation method.

[0090] The horizontal distance from the center of gravity W of the block foundation to the front toe is 13.196 m, and the vertical distance is 6.743 m. The horizontal distance from the abutment node C to the front toe of the foundation is 18.916 m, and the vertical distance is 15.053 m.

[0091] External load under a certain working condition F 支竖 145477 kN F 支水平 0 kN, M 支 41664 kN m, F 拱竖 771446 kN F 拱水平 803955 kN, M 拱 161679 kN m. The site has interbedded rock strata; the vertical resistance coefficient of the foundation in the geological survey report is... 3540 MPa / m, foundation horizontal resistance coefficient 2124 MPa / m; Based on field direct shear tests, the friction stiffness is taken as 0.35, calculated using the formula... , Calculated 743.4 MPa / m 1239 MPa / m. The block foundation is completely embedded in the rock strata, and its volume is approximately 7936 m³. 3 Material density 25 kN / m 3 The average unit weight of the rock strata is approximately 23.35 kN / m³. 3 .

[0092] In the composite foundation, the vertical piles have a rectangular cross-section of 5×7 m, with an enlarged head of 5×9 m at the pile bottom and an enlarged section length of 5 m; the inclined piles have an arched cross-section of 6.8×7.4 m, with an enlarged head of 6.8×8.9 m at the pile bottom and an enlarged section length of 7.5 m. The horizontal inclination angle of the inclined piles is... 25°; To simplify the calculation, the pile foundation enlargement section is not considered when calculating the pile top stiffness, and it is calculated as a uniform cross section.

[0093] Referring to the formula for calculating the internal force generated at the pile top when a unit displacement occurs at the pile top in the "Code for Design of Railway Bridge and Culvert Foundations" (TB 10093-2017), the pile top stiffness was calculated as shown in Table 2.

[0094] Table 2. Schematic diagram of pile top stiffness data

[0095] Furthermore, based on the unit displacement of the block foundation, the reaction force of the single pile top on the block foundation is simplified to determine the vertical force, horizontal force and bending moment of the vertical pile top, as well as the vertical force, horizontal force and bending moment of the inclined pile top.

[0096] Assuming the block foundation is a rigid body, and setting the center point P of the arch rib as the assumed rotation point, a four-spring model of the block foundation is established, considering the normal and tangential soil resistances at the bottom and sides of the foundation. Taking into account the stiffness of the inclined and vertical pile tops, the pile foundation top springs are assembled to the block foundation. The static equilibrium equations of the assumed rotation point P of the composite foundation are established, and the horizontal displacement, vertical displacement, and rotation angle at point P are solved. The composite foundation calculation model is as follows: Figure 6 As shown; Assume the horizontal displacement of the rotation point P is y The vertical displacement is The corner is Its positive direction is the same as the positive direction of the load. Based on the assumption of rigid body motion, without considering the coupling effect of vertical and horizontal loads, the displacement of the rigid body (i.e., block foundation) under load is decomposed into: rigid body translational displacement (including horizontal and vertical translational displacement) + rigid body rotational deformation. The vertical force, horizontal force, and bending moment at the top of the vertical pile, as well as the vertical force, horizontal force, and bending moment at the top of the inclined pile, are determined based on the combined reaction force of the displacements of the inclined piles and vertical piles.

[0097] Solve the static equilibrium equations of the combined foundation to determine the horizontal displacement, vertical displacement, and rotation angle of the assumed rotation point of the block foundation. The specific equations are as follows:

[0098]

[0099]

[0100] The displacement of the assumed rotation point P is: Horizontal displacement mm (vertically downwards) Vertical displacement mm (horizontal to the left) corner rad (rotate counterclockwise) The load distribution of the pile foundation is as follows: The vertical force, horizontal force, and bending moment at the top of the vertical pile are respectively , , They are respectively: kN kN kN m The vertical force, horizontal force, and bending moment at the top of the inclined pile are respectively... , , They are respectively: kN kN kN m The load conditions of the composite foundation are as follows: The maximum horizontal translation is 0.337 mm (i.e., the maximum horizontal displacement value at any point on the bottom surface of the block foundation), the maximum vertical settlement is 0.224 mm (i.e., the maximum vertical displacement value at any point on the side of the block foundation), the maximum vertical stress is 792 kPa, the average vertical stress of the base is 701 kPa, the average horizontal stress on the side of the foundation is 688 kPa, and the proportion of horizontal soil resistance on the back of the foundation is 0.413.

[0101] When the design scheme is adjusted, taking the adjustment of the pile position as an example: the vertical pile is moved 2m to the front toe position of the foundation (that is, point A is moved 2m to the right), and the displacement of the composite foundation and the load sharing are calculated again.

[0102] After adjusting the pile position, the displacement of the assumed rotation point P is obtained as follows: Horizontal displacement mm (vertically downwards) Vertical displacement mm (horizontal to the left) corner rad (rotate counterclockwise) The load distribution of the pile foundation is as follows: The vertical force, horizontal force, and bending moment at the top of the vertical pile are respectively , , They are respectively: kN kN kN m The vertical force, horizontal force, and bending moment at the top of the inclined pile are respectively... , , They are respectively: kN kN kN m The load conditions of the composite foundation are as follows: The maximum horizontal translation is 0.356 mm, the maximum vertical settlement is 0.226 mm, the maximum vertical stress is 801 kPa, the average vertical stress of the foundation base is 646 kPa, the average horizontal stress on the side of the foundation is 709 kPa, and the proportion of horizontal soil resistance on the back of the foundation is 0.421.

[0103] This example, based on the assumption of rigid body motion, calculates the displacement of the block foundation and pile tops by solving for the horizontal displacement, vertical displacement, and rotation angle of the assumed rotation point, and then determines the displacement of the composite foundation and the load distribution. When the design scheme is adjusted, there is no need to change the calculation model; only the calculation parameters need to be changed to conveniently calculate the displacement of the composite foundation and the load distribution after the pile position adjustment. This can help designers further optimize the design scheme until it meets the design requirements.

[0104] Based on the above technical solutions, this invention proposes a method for calculating the bearing capacity of inclined and vertical piles in bridges. This method has high engineering application value, helping professionals to further optimize foundation design schemes, improve foundation bearing performance, and save engineering costs. Addressing the lack of calculation methods for bridge arch abutments under various loads in current relevant standards, this invention establishes a calculation and analysis method for bridge arch abutments under various loads based on elastic theory. This method is convenient to use, directly determining the displacement and load distribution of bridge arch abutments under various loads, providing strong support for optimizing design schemes and saving engineering costs. The calculation model established in this invention has easily obtainable calculation parameters; most parameters can be obtained simply by consulting industry standards and geological survey reports, without the need for complex theoretical calculations, allowing relevant professionals to easily use it.

[0105] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the bearing capacity of inclined and vertical piles of a bridge, used for bridge arch abutments, wherein the bridge arch abutment is composed of a block foundation and inclined and vertical piles connecting the block foundation, characterized in that... The method includes: Obtain the external load and uniaxial compressive strength of the rock strata at the location of the bridge arch abutment, and determine the foundation parameters based on the uniaxial compressive strength of the rock strata; Based on the block foundation and the foundation parameters, a block spring model is established, and the inclined piles and vertical piles are assembled into the block spring model; By solving the static equilibrium equations simultaneously for the vertical force, horizontal force, and bending moment in the assembled block spring model, the displacements of the side and bottom surfaces of the block foundation are obtained, thus completing the foundation bearing capacity calculation. Specifically, the vertical force, horizontal force, and bending moment in the block spring model assembled by simultaneously solving the static equilibrium equations include: Select any rotation point on the block foundation to generate degrees of freedom, and construct the displacement of the side and bottom surfaces of the block foundation, as well as the pile top displacement of the inclined piles and vertical piles based on the degrees of freedom. A coordinate system is constructed based on the block spring model. Points representing the block foundation are selected in the coordinate system. The vertical force, horizontal force and bending moment of the block foundation are constructed by integrating the displacement of the side and bottom surfaces of the block foundation and the foundation parameters. Based on the pile top displacement of inclined piles and vertical piles and the internal forces of inclined piles and vertical piles, construct the vertical force, horizontal force and bending moment at the pile top of the inclined pile, as well as the vertical force, horizontal force and bending moment at the pile top of the vertical pile; Based on the vertical force balance, horizontal force balance, and bending moment balance of the block foundation, the vertical force, horizontal force, and bending moment of the inclined pile, the vertical force, horizontal force, and bending moment of the vertical pile, and the external load, the degrees of freedom are obtained by solving. The displacements of the side and bottom surfaces of the block foundation are calculated based on the degrees of freedom obtained from the solution, thus completing the solution.

2. The method for calculating the bearing capacity of inclined piles and vertical piles of bridges according to claim 1, characterized in that, The foundation parameters include the vertical resistance coefficient, horizontal resistance coefficient, vertical ground friction stiffness, and horizontal ground friction stiffness; the vertical force of the block foundation includes the vertical soil resistance at the bottom of the block foundation and the vertical frictional resistance on the sides of the block foundation; the horizontal force of the block foundation includes the horizontal frictional resistance at the bottom of the block foundation and the horizontal soil resistance on the sides of the block foundation; the bending moment of the block foundation includes the bending moment of the normal soil resistance and tangential frictional resistance on the sides and bottom of the block foundation about the point of rotation.

3. The method for calculating the bearing capacity of inclined piles and vertical piles of bridges according to claim 2, characterized in that, The degrees of freedom include the vertical displacement, horizontal displacement, and rotation angle of any rotation point, and the static equilibrium equations include: Based on the simultaneous equilibrium equations for all vertical forces, the formula is as follows: ， Based on the simultaneous equilibrium equations of all horizontal forces, the formula is as follows: ， Based on the simultaneous equilibrium equations for all bending moments, the formula is as follows: ， Among them, the vertical force, horizontal force, and bending moment at the top of the inclined pile are respectively , , The vertical force, horizontal force, and bending moment at the top of the vertical pile are respectively , , The vertical force, horizontal force, and bending moment of the external load are respectively , , , For the vertical soil resistance at the bottom of the block foundation, The vertical frictional resistance on the side of the block foundation. The horizontal frictional resistance at the bottom surface of the block foundation. For the horizontal soil resistance on the side of the block foundation, , and , These are the bending moments of the normal soil resistance and tangential skin friction at the bottom and sides of the block foundation, respectively, about the point of rotation. in: ， ， ， ， ， ， ， ， in, , , , , , , , These are the coordinates of the points representing the foundation of the block. Any point on the bottom surface of the block foundation i x-axis coordinate value; Any point on the side of the block foundation j of z Axis coordinate values.

4. The method for calculating the bearing capacity of inclined piles and vertical piles of bridges according to claim 2, characterized in that, The ratio of interfacial frictional stiffness to normal stiffness of the block foundation was obtained through on-site direct shear tests. k According to the ratio k The horizontal foundation friction stiffness is obtained by multiplying the vertical resistance coefficient of the foundation with the horizontal foundation friction stiffness, based on the ratio. k The vertical foundation friction stiffness is obtained by multiplying the coefficient of horizontal resistance of the foundation with the coefficient of horizontal resistance of the foundation.

5. The method for calculating the bearing capacity of inclined piles and vertical piles of bridges according to claim 2, characterized in that, The displacements of the sides and bottom of the block foundation include vertical displacement, horizontal displacement, and rotation of the sides, as well as vertical displacement, horizontal displacement, and rotation of the bottom; the calculation of the foundation bearing capacity includes: The lateral vertical stress is obtained by multiplying the lateral vertical displacement by the vertical foundation friction stiffness. The lateral horizontal stress is obtained by multiplying the lateral horizontal displacement by the foundation horizontal resistance coefficient. The vertical stress at the bottom surface is obtained by multiplying the vertical displacement of the bottom surface by the vertical resistance coefficient of the foundation. The horizontal stress on the bottom surface is obtained by multiplying the horizontal displacement of the bottom surface with the frictional stiffness of the horizontal foundation.

6. The method for calculating the bearing capacity of inclined piles and vertical piles of bridges according to claim 1, characterized in that, The vertical force, horizontal force, and bending moment at the top of the inclined pile and the vertical force, horizontal force, and bending moment at the top of the vertical pile are constructed, specifically including: The stiffness of the pile tops of inclined and vertical piles is calculated by using the internal forces generated at the pile top when a unit displacement occurs. This includes the axial force generated at the pile top when a unit displacement occurs along the axis, the horizontal force generated at the pile top when a unit displacement occurs perpendicular to the pile axis, the bending moment generated at the pile top when a unit displacement occurs perpendicular to the pile axis, the horizontal force generated at the pile top when a unit rotation occurs, and the bending moment generated at the pile top when a unit rotation occurs. The vertical force, horizontal force, and bending moment at the pile top of the inclined pile are determined based on the stiffness of the pile top, and the vertical force, horizontal force, and bending moment at the pile top of the vertical pile are determined based on the stiffness of the pile top.

7. The method for calculating the bearing capacity of inclined piles and vertical piles of bridges according to claim 6, characterized in that, The vertical force, horizontal force, and bending moment at the top of the inclined pile are determined based on the stiffness of the pile top. Similarly, the vertical force, horizontal force, and bending moment at the top of the vertical pile are determined based on the stiffness of the pile top. Specifically, this includes: The reaction force of a single pile top on the block foundation is determined based on the stiffness of the pile tops of the inclined and vertical piles. The vertical force, horizontal force, and bending moment at the top of the vertical pile, as well as the vertical force, horizontal force, and bending moment at the top of the inclined pile, are determined based on the reaction force from the combined displacement of the inclined pile and the vertical pile.

8. The method for calculating the bearing capacity of inclined piles and vertical piles of bridges according to claim 1, characterized in that, The method further includes: Based on the obtained composite foundation bearing capacity, it is determined whether the bridge arch abutment meets the design requirements. If it does not meet the requirements, the pile position and stiffness of the inclined piles or vertical piles are adjusted, and the static equilibrium equations are reconstructed for calculation.

Images