A pile foundation bearing capacity evaluation method and application

Abstract

This invention relates to the field of building engineering technology, specifically to a method and application for assessing the bearing capacity of pile foundations. The method includes: collecting parameters of the variable cross-section pile; calculating the total vertical load G2 at the top of the pile based on the parameters; determining the total lateral stress F2 at the top of the pile, assuming the top of the pile is free and the bottom is fixed to the top of the pile cap; determining the total bending moment M2 at the top of the pile, assuming the pile cap only undergoes rigid rotation and horizontal displacement; and calculating the vertical bearing capacity N by combining G2, F2, and M2. i and horizontal bearing capacity R i ; N i R i Compare with the design value; if satisfied, proceed to the next step; otherwise, return to the first step. Change the load direction and repeat steps one through six. Take the maximum value N. max R max The analysis was completed using the predicted value of the most unfavorable working condition. This invention considers the influence of the backfill soil above the pile cap on the stress of the pile body, thus solving the problem in the prior art that the influence of the backfill soil above the pile cap was not calculated, resulting in inaccurate analysis of the stress state of the pile body.

Description

Technical Field

[0001] This invention relates to the field of building engineering technology, and in particular to a method and application for evaluating the bearing capacity of pile foundations. Background Technology

[0002] In building construction, pile foundations, as core components that bear the loads of the superstructure and transmit horizontal forces, are widely used in the foundation design of high-rise buildings and large structures. In actual engineering projects, pile foundations need to withstand vertical and horizontal loads from the superstructure, while also being constrained by the surrounding soil. Furthermore, the horizontal displacement of the columns and the pile cap directly affects the stress state of the pile foundation. Accurate calculation of the internal forces of the pile foundation is a key prerequisite for ensuring the safety and stability of the building structure and an indispensable core link in engineering design.

[0003] Currently, the stress analysis of pile foundations in building engineering mainly adopts traditional calculation methods: calculating the axial force and bending moment of the pile foundation by simply distributing vertical loads and estimating lateral earth pressure. Specifically, workers usually separate the horizontal displacement of the pile cap and the horizontal displacement of the column from the earth pressure calculation, using a unified earth pressure calculation model that only considers the influence of the backfill soil below the pile cap.

[0004] In existing technologies, only the impact of backfill soil below the pile cap is considered, without considering the impact of backfill soil at the pile cap and column. This results in inaccurate analysis of the stress state of the piles, leading to discrepancies between the final analysis of pile size and quantity and the actual situation. Summary of the Invention

[0005] The technical problem to be solved by the embodiments of the present invention is to provide a method and application for evaluating the bearing capacity of pile foundations, so as to solve the problem that the influence of the backfill soil above the pile cap is not calculated in the prior art, resulting in inaccurate analysis of the stress state of the pile body.

[0006] In a first aspect, the present invention discloses a method for evaluating the bearing capacity of pile foundations, comprising the following steps: Step S1: Collect the design parameters of the variable cross-section pile; Step S2: Calculate the total vertical load G2 at the top of the pile based on the design parameters of the variable cross-section pile. Step S3: Assuming the top of the column is free and the bottom of the column is fixed to the top of the pile cap, determine the total lateral stress F2 at the top of the pile based on the static equilibrium condition and the lateral stress calculation method of the elastic lateral displacement of the cantilever column. Step S4: Assuming that the pile cap only undergoes rigid body rotation and horizontal displacement, determine the total bending moment M2 at the top of the pile body based on the bending moment equilibrium condition and the side stress calculation method for the elastic lateral displacement of the cantilever column. Step S5: Using the total vertical load G2 at the top of the pile, the total lateral stress F2 at the top of the pile, and the total bending moment M2 at the top of the pile from steps S2 to S4, determine the vertical bearing capacity N under the action of eccentric vertical force and horizontal force. i and horizontal bearing capacity R i ; Step S6: The vertical bearing capacity N from step S5 i and horizontal bearing capacity R i Compare the vertical and horizontal bearing capacities at the pile top with the design values ​​in the design standard. If the vertical bearing capacity N i The horizontal bearing capacity R is less than the design value of the vertical bearing capacity at the pile top. i If the value is less than the design value of the horizontal bearing capacity, proceed to step S7; otherwise, return to step S1. Step S7: Change the direction of the eccentric vertical and horizontal forces in the actual working condition, and repeat steps S1 to S6 to calculate all vertical bearing capacities N and all horizontal bearing capacities R corresponding to each direction, where N = {N1, N2, ..., N...} i , ..., N n}, R = {R1, R2, ..., R} i , ..., R n}, where n is the total number of calculations for vertical and horizontal bearing capacity; Step S8: Take the maximum value among all vertical bearing capacities N as the vertical bearing capacity N corresponding to the most unfavorable working condition. max The maximum value among all horizontal bearing capacities R is taken as the horizontal bearing capacity R corresponding to the most unfavorable working condition. max As a predicted value of the bearing capacity of the variable cross-section pile, the stress analysis of the variable cross-section pile is completed.

[0007] 2. Optionally, in step S1, the design parameters of the variable cross-section pile include the design parameters of the column and the design parameters of the backfill soil at the top of the pile cap; the design parameters of the column include the design horizontal force F1 at the top of the column, the design vertical force G1 at the top of the column, and the design bending moment M1 at the bottom of the column; the design parameters of the backfill soil at the top of the pile cap include the thickness z of the backfill soil and the unit weight p of the backfill soil.

[0008] Optionally, in step S2, the total vertical load G2 at the top of the pile is the sum of the design vertical force G1 of the column and the vertical gravity G3 generated by the backfill soil at the top of the pile cap.

[0009] Optionally, the vertical gravity G3 generated by the backfill soil at the top of the pier cap is: G3 = B × H × z × p; Where B is the calculated length of the foundation, in meters; H is the calculated width of the foundation, in meters; z is the thickness of the backfill soil, in meters; and p is the unit weight of the backfill soil, in kN / m³.

[0010] Optionally, the unit weight p of the backfill soil ranges from 16 kN / m³ to 20 kN / m³.

[0011] Optionally, in step S3, the total lateral stress F2 at the top of the pile is: ; Where F1 is the design horizontal force at the top of the column, in kN; m is the proportional coefficient of the horizontal resistance coefficient of the backfill soil, in kN / m³; Z1 and Z2 are different pile depths, in m; y1 is the horizontal displacement distance of the column, in m; y2 is the horizontal displacement distance of the pile cap, in m; b0 is the calculated width of the column, in m; H is the calculated width of the pile cap, in m; dz1 and dz2 are the heights of the pile segments, in m.

[0012] Optionally, in step S4, the total bending moment M2 at the top of the pile is: ; Where M1 is the design bending moment at the bottom of the column, in kN·m; m is the backfill soil pressure coefficient, in kN / m³; Z1 and Z2 are different pile depths, in m; y1 is the horizontal displacement distance of the column, in m; y2 is the horizontal displacement distance of the pile cap, in m; b0 is the calculated width of the column, in m; H is the calculated width of the pile cap, in m; dz1 and dz2 are the heights of the pile segments, in m; and h is the height of the pile cap, in m.

[0013] Optionally, in step S5, the vertical bearing capacity N i for: ; Where M2 is the total bending moment at the top of the pile, in kN·m; G2 is the total vertical load at the top of the pile, in kN; n is the total number of piles, Y i The distance from the i-th pile to the center of the pile cap is in meters.

[0014] Optionally, in step S5, the horizontal bearing capacity R i for: ; Where F2 is the total lateral stress at the top of the pile, in kN; n is the total number of piles.

[0015] Secondly, the present invention also discloses an application of a pile foundation bearing capacity assessment method, including the pile foundation bearing capacity assessment method described in any of the above claims, wherein the pile foundation bearing capacity assessment method is applied to the stress analysis of variable cross-section piles in old building renovation and new building construction.

[0016] Compared with existing technologies, the beneficial effects of the pile foundation bearing capacity assessment method provided in this embodiment of the invention are as follows: Step S1 collects the design parameters of the variable cross-section pile, providing accurate basic data for all subsequent stress calculations and avoiding analysis deviations caused by missing parameters; Step S2 accurately calculates the total vertical load G2 at the top of the pile based on the collected parameters, providing core load basis for bearing capacity analysis; Step S3 accurately obtains the total lateral stress F2 at the top of the pile through reasonable mechanical assumptions and combined with the elastic lateral displacement calculation method for cantilever columns, truly reflecting the stress state of the pile under horizontal loads; Step S4 continues the reasonable mechanical assumptions and, combined with the bending moment balance principle, accurately calculates the total bending moment M2 at the top of the pile, making up for the deficiency of traditional calculations that ignore the influence of pile cap displacement; Step S5 integrates the preceding parameters to comprehensively calculate the vertical bearing capacity N of a single pile. i and horizontal bearing capacity R i This achieves unified analysis of vertical and horizontal forces; step S6 compares the load with the design standard value to complete the force verification, forming a closed loop of data acquisition, calculation, and verification, thus avoiding calculation errors; step S7 changes the load direction to comprehensively cover various stress conditions, avoiding the one-sidedness of analysis caused by a single condition; step S8 selects the maximum value N. max and R max The analysis of vertical and horizontal bearing capacities under the most unfavorable working conditions ensures that the results closely match the actual engineering situation. The entire process considers the influence of the backfill soil above the pile cap on the stress of the pile body, effectively solving the problem of inaccurate stress state analysis of the pile body caused by neglecting the effect of the backfill soil above the pile cap in the existing technology. This provides a precise and reliable stress analysis basis for the design and construction of variable cross-section piles. Attached Figure Description

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a schematic flowchart of the pile foundation bearing capacity assessment method provided in an embodiment of the present invention; Figure 2 A plan view of the variable cross-section pile provided in this embodiment of the invention; Figure 3 for Figure 2 The top view of the variable cross-section pile shown. Detailed Implementation

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0019] This invention provides a method for evaluating the bearing capacity of pile foundations, such as... Figure 1 As shown, the method includes the following steps: Step S1: Collect the design parameters of the variable cross-section pile; Step S2: Calculate the total vertical load G2 at the top of the pile based on the design parameters of the variable cross-section pile. Step S3: Assuming the top of the column is free and the bottom of the column is fixed to the top of the pile cap, determine the total lateral stress F2 at the top of the pile based on the static equilibrium condition and the lateral stress calculation method of the elastic lateral displacement of the cantilever column. Step S4: Assuming that the pile cap only undergoes rigid body rotation and horizontal displacement, determine the total bending moment M2 at the top of the pile body based on the bending moment equilibrium condition and the side stress calculation method for the elastic lateral displacement of the cantilever column. Step S5: Using the total vertical load G2 at the top of the pile, the total lateral stress F2 at the top of the pile, and the total bending moment M2 at the top of the pile from steps S2 to S4, determine the vertical bearing capacity N under the action of eccentric vertical force and horizontal force. i and horizontal bearing capacity R i ; Step S6: The vertical bearing capacity N from step S5 i and horizontal bearing capacity R i Compare the vertical and horizontal bearing capacities at the pile top with the design values ​​in the design standard. If the vertical bearing capacity N i The horizontal bearing capacity R is less than the design value of the vertical bearing capacity at the pile top. i If the value is less than the design value of the horizontal bearing capacity, proceed to step S7; otherwise, return to step S1. Step S7: Change the direction of the eccentric vertical and horizontal forces, and repeat steps S1 to S6 to calculate all vertical bearing capacities N and all horizontal bearing capacities R corresponding to each direction, where N = {N1, N2, ..., N...} i , ..., N n}, R = {R1, R2, ..., R} i , ..., R n}, where n is the total number of calculations for vertical and horizontal bearing capacity; Step S8: Take the maximum value among all vertical bearing capacities N as the vertical bearing capacity N corresponding to the most unfavorable working condition. max The maximum value among all horizontal bearing capacities R is taken as the horizontal bearing capacity R corresponding to the most unfavorable working condition. max As a predicted value of the bearing capacity of the variable cross-section pile, the stress analysis of the variable cross-section pile is completed.

[0020] In this embodiment, step S1 collects the design parameters of the variable cross-section pile to provide accurate basic data for all subsequent stress calculations and avoid analysis deviations caused by missing parameters; step S2 accurately calculates the total vertical load G2 at the top of the pile based on the collected parameters, providing core load basis for bearing capacity analysis; step S3 accurately obtains the total lateral stress F2 at the top of the pile by using reasonable mechanical assumptions and combining the elastic lateral displacement calculation method for cantilever columns, truly reflecting the stress state of the pile under horizontal loads; step S4 continues the reasonable mechanical assumptions and, combined with the bending moment balance principle, accurately calculates the total bending moment M2 at the top of the pile, making up for the deficiency of traditional calculations that ignore the influence of pile cap displacement; step S5 integrates the preceding parameters to comprehensively calculate the vertical bearing capacity N of a single pile. i and horizontal bearing capacity R i This achieves unified analysis of vertical and horizontal forces; step S6 compares the load with the design standard value to complete the force verification, forming a closed loop of data acquisition, calculation, and verification, thus avoiding calculation errors; step S7 changes the load direction to comprehensively cover various stress conditions, avoiding the one-sidedness of analysis caused by a single condition; step S8 selects the maximum value N. max and R max The analysis of vertical and horizontal bearing capacities under the most unfavorable working conditions ensures that the results closely match the actual engineering situation. The entire process considers the influence of the backfill soil above the pile cap on the stress of the pile body, effectively solving the problem of inaccurate stress state analysis of the pile body caused by neglecting the effect of the backfill soil above the pile cap in the existing technology. This provides a precise and reliable stress analysis basis for the design and construction of variable cross-section piles.

[0021] In this embodiment, reference Figure 2 and Figure 3 The variable cross-section pile body includes a column, a pile cap at the bottom of the column, and several piles at the bottom of the pile cap. The design standard referenced and compared is the "Code for Design of Building Pile Foundations" JGJ94-2008.

[0022] In step S1, all design parameters related to the variable cross-section pile are collected comprehensively and accurately, including the parameters of the backfill soil above the pile cap. By collecting the above parameters completely, accurate and comprehensive data support is provided for all subsequent load calculations and bearing capacity analyses.

[0023] Furthermore, in step S1, the design parameters of the variable cross-section pile include the design parameters of the column and the design parameters of the backfill soil at the top of the pile cap; the design parameters of the column include the design horizontal force F1 at the top of the column, the design vertical force G1 at the top of the column, and the design bending moment M1 at the bottom of the column; the design parameters of the backfill soil at the top of the pile cap include the thickness z of the backfill soil and the unit weight p of the backfill soil.

[0024] In this embodiment, the design parameters of the column include the design horizontal force F1 at the top of the column, the design vertical force G1, and the design bending moment M1 at the bottom of the column. These parameters directly correspond to the core stress sources of the pile. The design horizontal force F1 at the top of the column reflects the lateral stress of the structure. The design vertical force G1 reflects the vertical stress of the structure. The design bending moment M1 at the bottom of the column reflects the stress state at the end of the structure. These parameters can fully reflect the various loads and bending moments that the pile itself needs to bear, providing a basis for subsequent calculations of the pile's stress and bearing capacity, and avoiding analytical deviations caused by the absence of the design horizontal force F1 at the top of the column, the design vertical force G1, and the design bending moment M1 at the bottom of the column.

[0025] Secondly, the thickness *z* of the backfill soil at the top of the pile cap and the unit weight *p* of the backfill soil reflect the external constraint and additional vertical effect of the backfill soil on the pile. The thickness *z* of the backfill soil affects the range of lateral constraint. The unit weight *p* of the backfill soil affects the value of vertical load transfer. Including these parameters in the data collection range allows subsequent stress analysis to include the effect of the backfill soil on the pile, making the analysis conditions consistent with the actual engineering situation.

[0026] It should be noted that the unit weight ρ of the backfill soil is determined by the soil composition and the soil density of the backfill soil.

[0027] In step S2, based on the design parameters collected in step S1, and combined with the vertical effects such as the column's self-weight and live load, the total vertical load G2 at the top of the pile is calculated. During the calculation, the parameters of the backfill soil are taken into account, considering its influence on the vertical load at the top of the pile.

[0028] The force of the backfill soil is transferred to the pile body through the pile cap, indirectly increasing the vertical force on the pile top. This allows for the accurate calculation of the total vertical load G2 at the top of the pile, avoiding any impact on the accuracy of subsequent vertical bearing capacity analysis. Simultaneously, the above calculation steps clarify the total vertical load G2 borne by the pile body, which is the basis for the subsequent single pile vertical bearing capacity N. i The calculation provides the load input, ensuring that the vertical stress analysis of the pile body is consistent with the actual stress state of the project.

[0029] Further, refer to Figure 2 and Figure 3 In step S2, the total vertical load G2 at the top of the pile is the sum of the design vertical force G1 of the column and the vertical gravity G3 generated by the backfill soil at the top of the pile cap. The vertical gravity G3 generated by the backfill soil at the top of the pile cap is: G3 = B × H × z × p; Where B is the calculated length of the foundation cap (m); H is the calculated width of the foundation cap (m); z is the thickness of the backfill soil (m); and p is the unit weight of the backfill soil (kN / m³). The unit weight p of the backfill soil ranges from 16 kN / m³ to 20 kN / m³. Specifically, the vertical force G1 of the column design directly reflects the vertical force transmitted from the superstructure to the pile. The vertical gravity G3 generated by the backfill soil at the top of the pile cap reflects the vertical force transmitted from the weight of the backfill soil itself to the pile through the pile cap. Determining the total vertical load G2 at the top of the pile using a superposition method conforms to the principle of static load superposition. This method can fully encompass the vertical force generated by the superposition of the superposition of the superstructure and the backfill soil.

[0030] On the other hand, the vertical gravity G3 generated by the backfill soil at the top of the pile cap can be quantified by calculating the contribution of the backfill soil to the vertical stress of the pile using the formula G3=B×H×z×p. The pile cap length B and width H determine the distribution area of ​​the backfill soil. The backfill soil thickness z determines the vertical extent of the backfill soil. The unit weight p of the backfill soil determines the weight per unit volume of soil. The combination of these parameters allows for an accurate calculation of the vertical gravity G3 generated by the backfill soil at the top of the pile cap.

[0031] The unit weight (p) of the backfill soil is limited to the range of 16 kN / m³ to 20 kN / m³, which conforms to the conventional physical properties of soil. This value ensures that the calculation results are consistent with engineering realities.

[0032] In step S3, a mechanical assumption that fits the actual engineering is adopted, namely, "the top of the column is free and the bottom of the column is fixed to the top of the foundation". This assumption is consistent with the connection state between the column and the foundation and the stress characteristics of the column in the actual project, and can simulate the deformation law of the column under horizontal load.

[0033] In the calculation process, combining static equilibrium conditions and utilizing the lateral stress calculation method for the elastic lateral displacement of cantilever columns, the lateral displacement and lateral stress of the column are correlated, while also considering the lateral constraint effect of the backfill soil on the pile. The backfill soil generates passive earth pressure on the pile, and the direction of this passive earth pressure is opposite to the direction of the horizontal displacement of the column, which can offset part of the horizontal force. Through the above method, the total lateral stress F2 at the top of the pile is obtained. The total lateral stress F2 at the top of the pile reflects the actual stress state of the pile under horizontal load, and is used as the basis for the subsequent single pile horizontal bearing capacity H. i The calculations provide a reliable basis.

[0034] Furthermore, in step S3, it can be seen from the static equilibrium condition that: ; in, ; This indicates that within the depth range of 0 to z, the horizontal resistance F1 generated by the lateral earth pressure on the pile top is the design horizontal force at the top of the column; ; F1 represents the horizontal resistance of the lower section of the pile to the pile top caused by the lateral earth pressure within the depth range of z to z+h; F1 is the design horizontal force of the upper part of the column, in kN; m is the proportional coefficient of the horizontal resistance coefficient of the backfill soil, in kN / m³; Z1 and Z2 are different pile depths, in m; y1 is the horizontal displacement distance of the column, in m; y2 is the horizontal displacement distance of the pile cap, in m; b0 is the calculated width of the column, in m; H is the calculated width of the pile cap, in m; dz1 and dz2 are the heights of the pile segments, in m; the backfill soil pressure is the passive pressure of the backfill soil on the pile, in the opposite direction to F1, used to counteract the horizontal force transmitted from the column, therefore F2 is: .

[0035] In the formula, the backfill soil pressure coefficient *m* characterizes the lateral restraint capacity of the backfill soil, and its value is related to the type and compaction degree of the backfill soil. The column calculation width *b0* converts the actual cross-sectional dimensions of the column into an equivalent calculation width, applicable to piles with different cross-sectional forms. *H* is the pile cap calculation width, ensuring the accuracy of passive earth pressure calculations in the pile cap area.

[0036] It should be noted that the principle of static load superposition is the fundamental principle for calculating the forces on a structure in engineering mechanics. Its core is that when multiple loads (such as vertical forces, horizontal forces, etc.) act on a structure together, the total force (or displacement, internal force) at a certain point of the structure is equal to the algebraic sum of the forces (or displacements, internal forces) generated at that point when each load acts alone.

[0037] The method for calculating the lateral stress of the elastic lateral displacement of a cantilever column is a structural mechanics analysis method based on the theory of elastic foundation beams. This method simulates the pile as a bottom-fixed cantilever elastic beam, designating the bottom of the pile as the fixed end, which can withstand bending moment and shear force with zero horizontal displacement, while the top of the pile is designated as the free end, allowing free horizontal displacement without bending moment constraints. Under horizontal load, the pile enters the elastic deformation stage, and its horizontal displacement has a clear elastic correspondence with the internal forces. This method obtains the horizontal displacement distribution along the depth of the pile by solving the deflection curve equation of the beam, and then calculates the lateral stress distribution by combining the earth pressure characteristics, ultimately achieving a two-way correlation between internal forces and displacements.

[0038] Because it is in the elastic stage, the deformation and internal forces of the pile satisfy the linear elastic relationship: the bending moment M is proportional to the curvature, the shear force V is proportional to the first derivative of the bending moment M, and the distribution of the lateral stress is proportional to the lateral displacement y(z) and the soil pressure coefficient m of the pile, that is, p(z) = m·z·y(z).

[0039] In step S3, the horizontal displacements y1(z1) and y2(z2) at various depths of the pile are first obtained through elastic lateral displacement analysis of the cantilever column; then, the elastic constraint relationship of the soil, p(z) = m, is used. z y(z) is used to calculate the passive earth pressure intensity at each depth; the total passive earth pressure resultant is obtained by integrating along the pile body; based on static equilibrium, the passive earth pressure resultant is obtained by subtracting the passive earth pressure resultant from the design horizontal force F1 at the top of the pile body.

[0040] In step S4, this step continues the reasonable mechanical assumption of step S3 (the bottom of the column is fixed to the top of the foundation), while also taking into account the actual stress and deformation characteristics of the foundation. Under the action of horizontal force and vertical eccentric load, the foundation will only undergo rigid body rotation and horizontal displacement. This assumption is more in line with engineering reality.

[0041] In the calculation process, combining the moment equilibrium condition and utilizing the lateral stress calculation method for the elastic lateral displacement of cantilever columns, the distribution of lateral stress along the column height is correlated with the moment calculation. Simultaneously, the constraint effect of backfill on the pile cap displacement is considered; the lateral support force of the backfill can suppress the horizontal displacement and rigid body rotation of the pile cap, thus affecting the magnitude of the total bending moment at the top of the pile. This step, by calculating the total bending moment M2 at the top of the pile, compensates for the shortcomings of traditional calculations that neglect the pile cap displacement and the constraint effect of backfill, laying the foundation for the subsequent calculation of the single pile vertical bearing capacity N. i The eccentricity distribution calculation provides accurate bending moment parameters.

[0042] Furthermore, in step S4, the distance from the bottom embedded end of the pile can be obtained as follows: ; Where M1 is the design bending moment at the bottom of the column, and M2 is the total bending moment at the top of the pile, which is assumed to be positive, while the lateral earth pressure reverse bending moment is negative; If we stipulate that the total bending moment M2 at the top of the pile is positive in the direction of offsetting M1, the passive reverse bending moment of the lateral earth pressure is taken as positive, and the design bending moment M1 at the bottom of the column is taken as positive, then M2 is: ; Where M1 is the design bending moment at the bottom of the column, in kN·m; m is the backfill soil pressure coefficient, in kN / m³; Z1 and Z2 are different pile depths, in m; y1 is the horizontal displacement distance of the column, in m; y2 is the horizontal displacement distance of the pile cap, in m; b0 is the calculated width of the column, in m; H is the calculated width of the pile cap, in m; dz1 and dz2 are the heights of the pile segments, in m; and h is the height of the pile cap, in m.

[0043] It should be noted that the moment equilibrium condition is that, under the combined action of horizontal force and lateral earth pressure, when moments are taken about a specified section, the bending moments generated by the external forces and the bending moments generated by the internal resistance are in balance. This condition requires that the clockwise and counterclockwise bending moments generated by all external forces acting on the structure about a given section are equal in magnitude. Under this condition, the structure does not undergo additional rotation and remains in a stable state.

[0044] In step S4, the moment equilibrium condition is calculated based on the top section of the pile. The design horizontal force F1 at the top of the column generates an external bending moment on the top section of the pile. The passive earth pressure from the backfill and the pile cap area is distributed along the pile depth, generating a reverse constraint bending moment on the top section of the pile. The design bending moment M1 at the bottom of the column, which is borne by the pile, also participates in the moment equilibrium. The combined effect of these moments keeps the pile in force equilibrium.

[0045] The total bending moment M2 at the top of the pile is determined according to the bending moment equilibrium condition. M2 is obtained by combining the moment generated by the design horizontal force F1 at the top of the column, the constraint moment generated by the passive earth pressure in the backfill area, the constraint moment generated by the passive earth pressure in the pile cap area, and the design bending moment M1 at the bottom of the column.

[0046] The moment equilibrium condition integrates the moments generated by horizontal forces, earth pressure constraint moments, and bottom bending moments into the calculation. This condition ensures that the pile satisfies moment equilibrium under horizontal loads and soil constraints. This condition provides the basis for calculating the total bending moment M2 at the top of the pile. This condition makes the bending moment calculation conform to the static stress law of the structure. This condition is also the basis for calculating the subsequent vertical bearing capacity N of the single pile. i With horizontal bearing capacity R i Provides accurate bending moment input.

[0047] In step S5, G2, F2, and M2 obtained from steps S2 to S4 are integrated to construct a complete force calculation system, avoiding the limitation of calculating vertical and horizontal forces separately. During the calculation, based on the vertical distribution principle of G2 (average distribution combined with the effect of bending moment eccentricity), and combined with the eccentric effect of M2 on the vertical bearing capacity, the vertical bearing capacity N of each pile is calculated. i Simultaneously, based on the horizontal distribution principle of F2 and combined with the lateral restraint effect of the backfill soil on the pile body, the horizontal bearing capacity R of each pile was calculated. i This step considers both the indirect effects of backfill on vertical and horizontal loads and the eccentric effect of bending moment, ensuring that the bearing capacity calculation of each pile can truly reflect its actual bearing capacity under the combined action of eccentric vertical and horizontal forces.

[0048] Further, in step S5, N i The sum of the total weight evenly distributed to each pile and the additional (or less) vertical force borne by each pile due to the total bending moment M2 at the top of the pile, therefore: ; Where M2 is the total bending moment at the top of the pile, in kN·m; G2 is the total vertical load at the top of the pile, in kN; n is the total number of piles; and Yi is the horizontal distance from the i-th pile to the center of the pile cap, in m.

[0049] In step S6, the rationality and safety of the current calculation results are verified to ensure that the pile stress analysis meets the engineering design requirements. In specific operation, the vertical bearing capacity N of the single pile calculated in step S5 is used... i The horizontal bearing capacity Ri is compared with the design values ​​of the vertical bearing capacity and horizontal bearing capacity of the pile top specified in the design standard to determine whether the design parameters and stress calculations of the current variable cross-section pile meet the standards.

[0050] If N i Greater than the design value of the vertical bearing capacity at the pile top, and / or R i If the load exceeds the design value of the pile top horizontal bearing capacity, it fails to meet the standard and requires returning to step S1 to re-collect and adjust the design parameters, and to redo the subsequent calculations; if N i Less than the design value of the vertical bearing capacity at the pile top, and R i If the load is less than the design value of the horizontal bearing capacity at the pile top, the standard is met, and subsequent working condition verification will proceed. This step can identify deviations in parameter acquisition and stress calculation, avoiding unsafe or substandard pile designs caused by calculation errors.

[0051] Furthermore, the horizontal bearing capacity R i Given that F2 is evenly distributed among each pile, therefore: ; Where F2 is the total lateral stress at the top of the pile, in kN; n is the total number of piles.

[0052] In step S7, the purpose is to comprehensively cover all types of stress conditions in actual engineering, avoiding the one-sidedness of analysis caused by a single condition. In actual engineering, the direction of action of eccentric vertical force and horizontal bearing capacity is uncertain. Different directions of action will lead to differences in the stress state and bearing capacity distribution of the pile, and the constraint effect of backfill soil on the pile will also change with the load direction, so as to avoid incomplete stress analysis.

[0053] In this step, by changing the direction of the eccentric vertical force and the horizontal bearing capacity, the complete process of steps S1 to S6 is repeated to calculate the vertical bearing capacity N and the horizontal bearing capacity R of each pile under different load directions. This comprehensively captures the stress situation of the pile under various possible working conditions, while fully considering the different effects of backfill soil on the pile under different load directions, providing comprehensive and accurate data support for the subsequent identification of the most unfavorable working conditions.

[0054] In step S8, the purpose of this step is to identify the most unfavorable stress condition and use the stress condition of the most unfavorable stress condition as the predicted value of the bearing capacity of the variable cross-section pile, so as to ensure the accuracy and safety of construction, thereby ensuring the safety and reliability of the pile design.

[0055] In this step, the vertical bearing capacity N and horizontal bearing capacity R calculated in step S7 under all load directions are summarized, and the maximum value N is selected. max and R max As the predicted bearing capacity under the most unfavorable working conditions, this predicted value reflects the maximum bearing capacity of the pile under extreme stress. Ultimately, it is expressed as N... max and R max As a predicted value of the bearing capacity of the variable cross-section pile, the entire stress analysis is completed, providing an accurate and reliable stress analysis basis for the design and construction of the variable cross-section pile, and ensuring the safety and rationality of subsequent engineering design.

[0056] An application of a pile foundation bearing capacity assessment method is also disclosed in the embodiments of the present invention. This application includes the pile foundation bearing capacity assessment method in any of the foregoing embodiments. The pile foundation bearing capacity assessment method is applied to the stress analysis of variable cross-section piles in old building renovation and new building construction.

[0057] In old building renovation projects, variable cross-section piles are often used as the core load-bearing components for foundation reinforcement or building expansion. The pile foundation bearing capacity assessment method of this invention can accurately solve special stress problems under renovation conditions. In the renovation of old buildings, the piles must simultaneously bear the vertical load of the existing building, the eccentric load of the new structure, and the additional horizontal force caused by uneven settlement of the foundation. This method, through multi-condition cyclic calculation, can simulate the stress state of the piles under different load directions, accurately identify the most unfavorable stress direction, avoid the bearing capacity prediction deviation caused by traditional single-condition calculation, and provide a basis for the safety redundancy design of renovation projects.

[0058] The soil in the foundation of old buildings has undergone long-term consolidation, resulting in significant spatial variability in its physical and mechanical parameters. Furthermore, renovation work easily disturbs the soil surrounding the piles, leading to complex lateral stress distribution. This method, based on the elastic lateral displacement theory of cantilever columns and combined with the Winkler foundation model, can accurately calculate the lateral stress distribution at different depths of the pile. By integrating the soil reaction force, the actual stress response of the pile is determined, effectively evaluating the collaborative performance of the pile and soil after renovation, and providing data support for optimizing reinforcement schemes.

[0059] During the renovation and construction process, the piles may be subjected to additional effects such as temporary construction loads and mechanical vibrations. This method can simulate the temporary load conditions during the construction phase by adjusting the input parameters, quickly calculate the short-term bearing capacity of the piles, predict the risk of pile deformation during construction, and ensure the structural safety of the renovation and construction process.

[0060] In new construction projects, variable cross-section piles are widely used in the foundation engineering of high-rise buildings and large-span structures due to their advantages of high bearing capacity and good economy. The pile foundation bearing capacity assessment method of this invention can realize accurate stress analysis in the design stage: The design of piles for new buildings must consider vertical bearing capacity, horizontal bearing capacity, and bending moment bearing capacity. Traditional design methods often use empirical formulas to simplify calculations, making it difficult to fully utilize the mechanical advantages of variable cross-section piles. This method, through the joint calculation of coupled vertical loads, horizontal forces, and bending moments, can quickly assess the impact of different pile parameters (such as the location of the variable cross-section, the stiffness of the upper and lower sections, and the width) on the pile bearing capacity. This assists designers in optimizing pile cross-sectional dimensions and reinforcement schemes, reducing project costs while meeting design requirements.

[0061] New buildings often face dynamic horizontal loads such as wind and seismic loads, requiring piles to withstand horizontal forces and bending moments of multiple directions and amplitudes. This method changes the direction of load application, iteratively calculates the bearing capacity under various working conditions, and extracts the maximum bearing capacity under the most unfavorable condition. This ensures that the piles can still meet design requirements under extreme loads, thereby improving the overall risk resistance of new buildings.

[0062] After the construction of a new building is completed, this method is used for reverse verification to confirm whether the actual stress performance of the piles is consistent with the design expectations. Simultaneously, this method can serve as an auxiliary analytical tool for pile integrity testing and static load testing of bearing capacity, providing a scientific basis for project acceptance and ensuring the construction quality of the foundation engineering of new buildings.

[0063] The application of this pile foundation bearing capacity assessment method includes the same structure and beneficial effects as the pile foundation bearing capacity assessment method in the foregoing embodiments. The structure and beneficial effects of the pile foundation bearing capacity assessment method have been described in detail in the foregoing embodiments and will not be repeated here.

[0064] The technical solution of this application will be further described below with reference to specific embodiments. Example This embodiment discloses a computer implementation of a pile foundation bearing capacity assessment method. This embodiment is based on the elastic lateral displacement theory of cantilever columns and the Winkler elastic foundation model, and uses a numerical discretization method to complete the calculation of the entire process of pile stress, thus fully implementing steps S1 to S8 described in this application.

[0065] 1. Example Hardware and Software Environment This embodiment uses a computer device as the running platform. The computer device is equipped with a processor, memory, and input / output components. The running environment supports the Python programming language and is equipped with a numerical computing library to realize matrix operations, solving linear equations, and mesh generation functions.

[0066] 2. Specific Implementation Steps of the Example Step S1: Collect design parameters of the variable cross-section pile. In this embodiment, the design parameters of the variable cross-section pile are input through a graphical interactive interface. These parameters include column length z=5m, pile cap height h=10m, column width b0=0.6m, pile cap width H=0.8m, and column bending stiffness EI1=4.5e. 6 kN·m 2 The bending stiffness of the foundation is EI2 = 9.0e. 6 kN·m 2 Subgrade coefficient m=10e 3 kN·m 4 The horizontal force at the top of the column is F1 = 120 kN, the design bending moment at the bottom of the column is M1 = -80 kN·m, the number of upper segment elements is n1 = 100, and the number of lower segment elements is n2 = 100. The computer program receives the above parameters and completes data storage and verification, providing basic data for subsequent calculations.

[0067] Step S2: Calculate the total vertical load G2 at the top of the pile. Based on the collected geometric and soil parameters, the program calculates the vertical gravity generated by the backfill soil at the top of the pile cap, and superimposes the vertical design gravity of the column to obtain the total vertical load G2 at the top of the pile. This total vertical load G2 at the top of the pile, as a core component of the eccentric vertical force, participates in subsequent bearing capacity coupling calculations.

[0068] Step S3: Determine the total lateral stress F2 at the top of the pile. The program assumes the top of the column is free and the bottom is fixed to the top of the pile cap, constructing a discrete computational mesh for the pile and dividing the pile into several computational units. The program assembles the bending stiffness matrix of the beam unit and the Winkler foundation stiffness matrix separately, superimposing them to form a global stiffness matrix. The program applies a bottom consolidation boundary condition and a top load condition, solving a system of linear equations to obtain the horizontal displacement and rotation distribution of the pile along its depth. Based on static equilibrium conditions and the method for calculating the lateral stress of the elastic lateral displacement of a cantilever column, the program integrates to calculate the total lateral reaction force of the soil, ultimately determining the total lateral stress at the top of the pile as F2 = 33.5768209 kN.

[0069] Step S4: Determine the total bending moment M2 at the top of the pile. The program assumes that the bottom of the column is fixed to the top of the pile cap, and that the pile cap only undergoes rigid body rotation and horizontal displacement. Based on the displacement distribution results obtained in step S3, the program calculates the constraint moment generated by the soil on the pile. According to the moment equilibrium condition, the program couples the moment generated by the horizontal force at the top, the bending moment at the top, and the soil moment to complete the moment equilibrium equation solution, determining the total bending moment at the top of the pile to be M2 = 24.4602036 kN·m.

[0070] Step S5: Calculate the vertical bearing capacity N i and horizontal bearing capacity H i The program calls upon the total vertical load G2 at the top of the pile, the total lateral stress F2 at the top of the pile, and the total bending moment M2 at the top of the pile to establish a mechanical calculation model under the combined action of eccentric vertical and horizontal forces. Combining the cross-sectional characteristics of the variable cross-section pile with the soil resistance parameters, the program calculates the vertical bearing capacity N of the pile under the current working condition. i With horizontal bearing capacity H i .

[0071] Step S6: Bearing capacity verification and judgment The program will determine the vertical bearing capacity N. i Horizontal bearing capacity H i Compare with the preset design standard value. If the vertical bearing capacity N i Less than the design standard value, and the horizontal bearing capacity H i If the value is less than the design standard, the program proceeds to the next step; if the requirements are not met, the program automatically returns to step S1, prompting the user to readjust the design parameters.

[0072] Step S7: Multi-directional working condition cycle calculation The program automatically cycles through steps S1 to S6, changing the directions of the eccentric vertical and horizontal forces according to preset rules. The program sequentially calculates the vertical bearing capacity N corresponding to different load directions. i With horizontal bearing capacity H i And store all calculation results completely.

[0073] Step S8: Determine the predicted bearing capacity value under the most unfavorable working condition. The program iterates through the calculation results for all working conditions and extracts the maximum value N from the vertical bearing capacity Ni. max Extract the maximum value H from the horizontal bearing capacity Hi. max The program will N max With H max As the predicted values ​​of vertical and horizontal bearing capacity under the most unfavorable working conditions, a complete calculation report is output to complete the stress analysis of the variable cross-section pile.

[0074] 3. Output results of the example This embodiment displays the calculation process log through a graphical interactive interface, and finally outputs the total lateral stress F2 at the top of the pile, the total bending moment M2 at the top of the pile, and the total soil reaction (negative to the right) = -1.535762e 2 Soil moment = -1.744462e 3 The program provides core results, including the predicted bearing capacity under the most unfavorable conditions, presented in a visually intuitive numerical format. This provides accurate data support for the engineering design and safety assessment of variable cross-section piles.

[0075] 4. Technical Effects of the Embodiments This embodiment uses a computer program to automatically implement the stress analysis method described in this application. It can accurately perform coupled calculations of vertical loads, lateral stresses, and bending moments, strictly adhering to static equilibrium conditions and bending moment equilibrium conditions, and realistically simulating the rigid body displacement characteristics of the foundation. This embodiment supports multi-condition cyclic calculations and extraction of the most unfavorable value, significantly improving the efficiency and accuracy of stress analysis, and making the calculation results more closely match the actual stress state of the project.

[0076] It should be understood that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Those skilled in the art can modify the technical solutions described in the above embodiments, or make equivalent substitutions for some of the technical features; and all such modifications and substitutions should fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for evaluating the bearing capacity of pile foundations, characterized in that, Includes the following steps: Step S1: Collect the design parameters of the variable cross-section pile; Step S2: Calculate the total vertical load G2 at the top of the pile based on the design parameters of the variable cross-section pile. Step S3: Assuming the top of the column is free and the bottom of the column is fixed to the top of the pile cap, determine the total lateral stress F2 at the top of the pile based on the static equilibrium condition and the lateral stress calculation method of the elastic lateral displacement of the cantilever column. Step S4: Assuming that the pile cap only undergoes rigid body rotation and horizontal displacement, determine the total bending moment M2 at the top of the pile body based on the bending moment equilibrium condition and the side stress calculation method for the elastic lateral displacement of the cantilever column. Step S5: Using the total vertical load G2 at the top of the pile, the total lateral stress F2 at the top of the pile, and the total bending moment M2 at the top of the pile from steps S2 to S4, determine the vertical bearing capacity N under the action of eccentric vertical force and horizontal force. i and horizontal bearing capacity R i ; Step S6: The vertical bearing capacity N from step S5 i and horizontal bearing capacity R i Compare the vertical and horizontal bearing capacities at the pile top with the design values ​​in the design standard. If the vertical bearing capacity N i The horizontal bearing capacity R is less than the design value of the vertical bearing capacity at the pile top. i If the value is less than the design value of the horizontal bearing capacity, proceed to step S7; otherwise, return to step S1. Step S7: Change the direction of the eccentric vertical and horizontal forces in the actual working condition, and repeat steps S1 to S6 to calculate all vertical bearing capacities N and all horizontal bearing capacities R corresponding to each direction, where N = {N1, N2, ..., N...} i , ..., N n }, R = {R1, R2, ..., R} i , ..., R n }, where n is the total number of calculations for vertical and horizontal bearing capacity; Step S8: Take the maximum value among all vertical bearing capacities N as the vertical bearing capacity N corresponding to the most unfavorable working condition. max The maximum value among all horizontal bearing capacities R is taken as the horizontal bearing capacity R corresponding to the most unfavorable working condition. max As a predicted value of the bearing capacity of the variable cross-section pile, the stress analysis of the variable cross-section pile is completed.

2. The method for evaluating the bearing capacity of pile foundations according to claim 1, characterized in that, In step S1, the design parameters of the variable cross-section pile include the design parameters of the column and the design parameters of the backfill soil at the top of the pile cap; the design parameters of the column include the design horizontal force F1 at the top of the column, the design vertical force G1 at the top of the column, and the design bending moment M1 at the bottom of the column; the design parameters of the backfill soil at the top of the pile cap include the thickness z of the backfill soil and the unit weight p of the backfill soil.

3. The method for evaluating the bearing capacity of pile foundations according to claim 2, characterized in that, In step S2, the total vertical load G2 at the top of the pile is the sum of the designed vertical force G1 of the column and the vertical gravity G3 generated by the backfill soil at the top of the pile cap.

4. The method for evaluating the bearing capacity of pile foundations according to claim 3, characterized in that, The vertical gravity G3 generated by the backfill soil at the top of the foundation is: G3 = B × H × z × p; Where B is the calculated length of the foundation, in meters; H is the calculated width of the foundation, in meters; z is the thickness of the backfill soil, in meters; and p is the unit weight of the backfill soil, in kN / m³.

5. The method for evaluating the bearing capacity of pile foundations according to claim 4, characterized in that, The unit weight p of the backfill soil ranges from 16 kN / m³ to 20 kN / m³.

6. The method for evaluating the bearing capacity of pile foundations according to claim 2, characterized in that, In step S3, the total lateral stress F2 at the top of the pile is: ； Where F1 is the design horizontal force at the top of the column, in kN; m is the proportional coefficient of the horizontal resistance coefficient of the backfill soil, in kN / m³; Z1 and Z2 are different pile depths, in m; y1 is the horizontal displacement distance of the column, in m; y2 is the horizontal displacement distance of the pile cap, in m; b0 is the calculated width of the column, in m; H is the calculated width of the pile cap, in m; dz1 and dz2 are the heights of the pile segments, in m.

7. The method for evaluating the bearing capacity of pile foundations according to claim 6, characterized in that, In step S4, the total bending moment M2 at the top of the pile is: ； Where M1 is the design bending moment at the bottom of the column, in kN·m; m is the backfill soil pressure coefficient, in kN / m³; Z1 and Z2 are different pile depths, in m; y1 is the horizontal displacement distance of the column, in m; y2 is the horizontal displacement distance of the pile cap, in m; b0 is the calculated width of the column, in m; H is the calculated width of the pile cap, in m; dz1 and dz2 are the heights of the pile segments, in m; and h is the height of the pile cap, in m.

8. The method for evaluating the bearing capacity of pile foundations according to claim 7, characterized in that, In step S5, the vertical bearing capacity N i for: ； Where M2 is the total bending moment at the top of the pile, in kN·m; G2 is the total vertical load at the top of the pile, in kN; n is the total number of piles, Y i The distance from the i-th pile to the center of the pile cap is in meters.

9. The method for evaluating the bearing capacity of pile foundations according to claim 7, characterized in that, In step S5, the horizontal bearing capacity R i for: ； Where F2 is the total lateral stress at the top of the pile, in kN; n is the total number of piles.

10. An application of a method for evaluating the bearing capacity of pile foundations, characterized in that, The method for assessing the bearing capacity of pile foundations, as described in any one of claims 1-9, is applied to the stress analysis of variable cross-section piles in old building renovations and new constructions.

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