A method for calculating ultimate flexural bearing capacity of FRP bar concrete pile

Abstract

The application discloses a method for calculating ultimate flexural bearing capacity of FRP reinforced concrete pile, and belongs to the technical field of concrete pile bearing capacity analysis. The method comprises the following steps: obtaining the geometric parameters of the pile section and constructing a layered discrete grid model; tracking the actual compressive stress transmission path of the concrete compression zone, and decomposing the actual compressive stress transmission path into a plurality of nonlinear compressive stress transmission sub-paths; calculating the local stiffness attenuation coefficient of each sub-path, and superimposing to generate the global stiffness degradation distribution atlas of the concrete compression zone; determining the actual stress peak point position of the compression zone based on the atlas, updating the initial position of the neutral axis, and iteratively solving the balanced position of the neutral axis; and calculating the ultimate flexural bearing capacity of the FRP reinforced concrete pile according to the balanced position of the neutral axis. The method can more accurately reflect the bending failure mechanism of the pile body by simulating the nonlinear compressive stress transmission and stiffness degradation distribution of the concrete in the compression zone and dynamically determining the neutral axis according to the actual stress peak.

Description

Technical Field

[0001] This invention relates to the field of concrete pile bearing capacity analysis technology, specifically a method for calculating the ultimate flexural bearing capacity of FRP reinforced concrete piles. Background Technology

[0002] Due to the linear elastic constitutive characteristics of FRP (fiberglass reinforced concrete) reinforcement, the flexural failure mode of FRP-reinforced concrete piles differs significantly from that of reinforced concrete piles. The stress state and stiffness variations of the concrete in the compression zone control the position of the neutral axis and the bearing capacity of the cross-section. Existing methods for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles generally employ an equivalent rectangular stress diagram, simplifying the actual stress distribution of the concrete in the compression zone into a uniformly distributed stress block. The position of the neutral axis is directly calculated using fixed stress diagram parameters and the assumption of ultimate compressive strain. This approach ignores the actual behavior of the concrete in the compression zone undergoing layer-by-layer degradation and nonlinear stress transfer along the cross-sectional height in a non-uniform compressive strain field. Therefore, the determined neutral axis position deviates from the actual stress state of the pile. During the bending process of the pile, the compressive strain levels at different heights in the concrete compression zone vary significantly. The stiffness attenuation of each layer of concrete does not occur synchronously but rather forms a continuous degradation distribution based on the strain gradient. Existing equivalent rectangular stress diagram methods can only reflect the total resultant pressure force and its point of application under ultimate conditions, failing to reveal the stiffness degradation path and changes in the direction of compressive stress transmission within the compression zone, moving from the compression edge towards the neutral axis. When concrete enters the plastic stage, the stress peak point shifts inward within the compression zone. The actual stress distribution curve depends not only on the strain distribution but also on the local stiffness attenuation caused by accumulated material damage. Because existing techniques lack a non-uniform description of the spatial distribution of stiffness degradation, the iterative solution for the neutral axis lacks a physical basis to reflect the actual stress redistribution, and the calculation results often deviate from the true ultimate bending capacity of the pile.

[0003] The present invention aims to solve the problem that existing methods cannot accurately describe the nonlinear compressive stress transmission path and stiffness degradation distribution of concrete in the compression zone, and the resulting problem of inaccurate determination of the neutral axis equilibrium position. Summary of the Invention

[0004] This invention provides a method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles. The purpose is to overcome the shortcomings of existing calculation methods that ignore the actual compressive stress transmission path and non-uniform stiffness degradation in the compression zone of the concrete. By tracking the pressure transmission and constructing a global stiffness degradation spectrum, and dynamically determining the position of the neutral axis based on the actual stress peak, the method can accurately solve the ultimate flexural bearing capacity of FRP-reinforced concrete piles.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] This invention provides a method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles. Addressing the significant nonlinear degradation of stiffness in the concrete compression zone and the complex compressive stress transmission path during the flexural failure process of FRP-reinforced concrete piles, this method achieves efficient and accurate calculation of the ultimate flexural bearing capacity by accurately tracing the compressive stress transmission path and constructing a global stiffness degradation distribution map, followed by iteratively solving for the neutral axis equilibrium position. The method includes the following steps:

[0007] Obtain the geometric parameters of the target FRP-reinforced concrete pile's cross-section, and construct a layered discrete mesh model of the pile cross-section based on these parameters. According to the layered discrete mesh model, trace the actual compressive stress transmission path in the concrete compression zone, decomposing the actual compressive stress transmission path into multiple nonlinear compressive stress transmission sub-paths. Calculate the local stiffness attenuation coefficient of each nonlinear compressive stress transmission sub-path, and generate a global stiffness degradation distribution map of the concrete compression zone by superimposing all local stiffness attenuation coefficients. Based on the global stiffness degradation distribution map, determine the actual stress peak point location in the FRP-reinforced concrete pile's compression zone, update the initial position of the neutral axis with the actual stress peak point location, and iteratively solve for the neutral axis equilibrium position. Calculate the ultimate flexural bearing capacity of the FRP-reinforced concrete pile based on the neutral axis equilibrium position.

[0008] As a technical solution of this invention, the process of obtaining the geometric parameters of the pile cross-section and constructing a layered discrete mesh model includes: extracting the outer contour shape parameters of the target FRP-reinforced concrete pile cross-section, the arrangement coordinate parameters of the FRP reinforcement, and the diameter parameters of the FRP reinforcement; using the centroid of the pile cross-section as the origin, dividing the pile cross-section into several continuous horizontal strip layers along the height direction according to a preset initial layer thickness, with each horizontal strip layer containing concrete elements and FRP reinforcement elements; recording the actual distance from the geometric center of each horizontal strip layer to the edge of the compression zone of the pile cross-section, thus obtaining the inter-layer distance sequence of the layered discrete mesh model. Through this layered discretization process, the material distribution and geometric characteristics of the cross-section can be finely characterized, providing a high-resolution computational basis for subsequent nonlinear analysis.

[0009] Preferably, the process of tracing the actual compressive stress transmission path in the concrete compression zone and decomposing it into multiple nonlinear compressive stress transmission sub-paths includes: starting from the edge of the compression zone in the layered discrete mesh model, sequentially extracting the concrete compressive strain value of each horizontal strip layer along the cross-sectional height direction; using the concrete compressive strain value of the current horizontal strip layer as input, calculating the actual compressive stress value of the horizontal strip layer through a preset concrete constitutive model; using the difference between the actual compressive stress values ​​of two adjacent horizontal strip layers as the stress gradient, and using the positive and negative change points of the stress gradient as the dividing points, dividing the entire compression zone into multiple continuous compressive stress transmission sub-regions, each corresponding to a nonlinear compressive stress transmission sub-path. This scheme adaptively divides the transmission sub-paths based on the actual stress gradient changes, effectively capturing the stress redistribution characteristics of the concrete compression zone caused by damage evolution, and avoiding the fundamental errors caused by the assumption of uniform stress distribution in traditional methods.

[0010] Further, the process of calculating the local stiffness attenuation coefficient of each nonlinear compressive stress transfer sub-path and generating a global stiffness degradation distribution map includes: obtaining the set of horizontal strip layers corresponding to each nonlinear compressive stress transfer sub-path; extracting the initial elastic modulus and current compressive strain value of each horizontal strip layer from the set of horizontal strip layers; comparing the current compressive strain value with the preset peak compressive strain of concrete to calculate the single-layer stiffness reduction factor of each horizontal strip layer; performing a weighted average of all single-layer stiffness reduction factors within the same nonlinear compressive stress transfer sub-path, and using the weighted average as the local stiffness attenuation coefficient of the nonlinear compressive stress transfer sub-path; and sequentially filling the local stiffness attenuation coefficients into the position vector corresponding to the layered discrete mesh model according to the height position order of each nonlinear compressive stress transfer sub-path in the compression zone to generate a global stiffness degradation distribution map. The single-layer stiffness reduction factor is preferably the ratio of the secant modulus corresponding to the current compressive strain value to the initial elastic modulus, i.e.:

[0011]

[0012] in: For the first The single-layer stiffness reduction factor of a horizontal strip layer For the first Secant modulus of a horizontal strip of concrete under current compressive strain This represents the initial elastic modulus of concrete. This reduction factor directly reflects the degree of stiffness degradation corresponding to the level of compressive strain in the concrete.

[0013] When performing a weighted average of all single-layer stiffness reduction factors within the same nonlinear compressive stress transfer sub-path, a preferred approach includes: obtaining the total number of horizontal strip layers corresponding to the current nonlinear compressive stress transfer sub-path, and assigning an initial weight coefficient to each horizontal strip layer, wherein the initial weight coefficient is proportional to the distance from the geometric center of the horizontal strip layer to the edge of the compression zone; extracting the single-layer stiffness reduction factor from each horizontal strip layer, and multiplying the single-layer stiffness reduction factor by the corresponding initial weight coefficient to obtain the weighted stiffness reduction value of each horizontal strip layer; summing the weighted stiffness reduction values ​​of all horizontal strip layers to obtain the total weighted reduction value; summing the initial weight coefficients of all horizontal strip layers to obtain the total weight coefficient; and dividing the total weighted reduction value by the total weight coefficient to obtain the local stiffness attenuation coefficient of the nonlinear compressive stress transfer sub-path, the expression of which is:

[0014]

[0015] in: For the first The local stiffness attenuation coefficient of a nonlinear compressive stress transfer sub-path. This represents the number of horizontal stripe layers contained within this subpath. For the first The weighting coefficients for each horizontal strip layer are such that the closer the horizontal strip layer is to the edge of the compression zone, the greater its contribution to the local stiffness attenuation coefficient. This weighting method allows the stiffness degradation assessment to more closely reflect the true mechanical state of the damage-concentrated area at the edge of the compression zone.

[0016] As a preferred embodiment, the local stiffness attenuation coefficient of the nonlinear compressive stress transfer sub-path can be corrected using an exponential attenuation model associated with concrete damage variables to reflect the stiffness abrupt change effect under high stress levels, thereby further improving the fidelity of the description of the behavior of the softening segment after the peak.

[0017] After generating the global stiffness degradation distribution map, this invention normalizes the data according to the height direction of the pile section and uses cubic spline interpolation to extend the discrete local stiffness attenuation coefficients into a continuous stiffness degradation curve, thereby obtaining a continuous and smooth global stiffness degradation distribution map, which facilitates the accurate determination of the actual stress peak point location.

[0018] Based on the global stiffness degradation distribution map, the process of determining the actual stress peak point location in the compression zone and iteratively solving for the neutral axis equilibrium position includes: finding the horizontal strip layer corresponding to the minimum local stiffness attenuation coefficient in the global stiffness degradation distribution map, and taking the distance from the geometric center of this horizontal strip layer to the edge of the compression zone as the actual stress peak point location; obtaining a preset initial neutral axis position, calculating the resultant force of concrete compressive stress in all horizontal strip layers above the initial neutral axis position and the resultant force of tensile stress in all FRP reinforcements; if the absolute value of the difference between the resultant force of concrete compressive stress and the resultant force of tensile stress in FRP reinforcement is greater than a preset equilibrium threshold, then the midpoint between the actual stress peak point location and the current neutral axis position is taken as the updated neutral axis position, and the resultant force difference is recalculated until the absolute value of the resultant force difference is less than or equal to the preset equilibrium threshold, thus obtaining the neutral axis equilibrium position. This iterative strategy uses the location with the most significant stiffness degradation as the stress peak point to guide the neutral axis update, significantly accelerating the convergence speed of axial force equilibrium and ensuring the consistency between the equilibrium position and the actual damage state of the structure.

[0019] The process of calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles based on the neutral axis equilibrium position includes: dividing the pile cross-section into a compression zone and a tension zone with the neutral axis equilibrium position as the boundary; extracting the compressive stress values ​​and corresponding lever arm lengths of all horizontal strip layers in the compression zone from the layered discrete mesh model; calculating the product of the compressive stress value of each horizontal strip layer and the area of ​​that horizontal strip layer to obtain the pressure contribution value of that horizontal strip layer; summing the pressure contribution values ​​of all horizontal strip layers and the product with respect to the stress arm length to obtain the bending moment component contributed by the concrete compression zone; extracting the tensile stress values ​​of all FRP bars in the tension zone, the cross-sectional area of ​​a single FRP bar, and the lever arm length of each FRP bar to the neutral axis equilibrium position from the layered discrete mesh model; calculating the tensile force contribution value of each FRP bar and the product with respect to the stress arm length and summing the products to obtain the bending moment component contributed by the FRP bars; adding the bending moment component contributed by the concrete compression zone to the bending moment component contributed by the FRP bars to obtain the ultimate flexural bearing capacity of the FRP-reinforced concrete pile. This calculation method integrates the true distribution of stiffness degradation in the compression zone concrete with the linear elastic tensile characteristics of FRP reinforcement, overcoming the problem of overestimating bearing capacity due to neglecting the non-uniformity of stiffness degradation in traditional section analysis methods, and significantly improving the calculation accuracy and engineering applicability of ultimate flexural bearing capacity.

[0020] The beneficial effects of this invention are:

[0021] Starting from the edge of the compression zone in the layered discrete mesh model, the concrete compressive strain values ​​of each horizontal strip layer are extracted sequentially along the cross-sectional height. Using the points of positive and negative stress gradient changes formed by the actual compressive stress difference between adjacent strip layers as boundaries, the entire compression zone is divided into multiple continuous compressive stress transfer sub-regions, each corresponding to a nonlinear compressive stress transfer sub-path. Based on this, the current compressive strain value of the horizontal strip layers contained in each sub-path is obtained using the concrete constitutive relation. The current compressive strain value is compared with the peak compressive strain of the concrete to calculate the single-layer stiffness reduction factor for each layer. The reduction factors of each layer within the same sub-path are weighted and averaged according to their distance from the edge of the compression zone to obtain the local stiffness attenuation coefficient for each sub-path. The local stiffness attenuation coefficients of all sub-paths are filled in order of height to generate a global stiffness degradation distribution map of the concrete compression zone. This approach no longer treats the concrete in the compression zone as a uniformly degraded body. Instead, it captures the differences in stiffness attenuation paths caused by strain gradient changes along the actual compressive stress transmission direction. The resulting degradation map can realistically reflect the nonlinear degradation characteristics of the compression zone, where edge damage is severe while internal damage gradually weakens. This overcomes the shortcomings of traditional methods that use a single degradation coefficient to describe the entire compression zone, providing distribution information reflecting the physical process of concrete softening layer by layer for subsequent neutral axis position determination. After obtaining the global stiffness degradation distribution map, the horizontal strip layer corresponding to the minimum local stiffness attenuation coefficient is located in the map, and this location is taken as the actual stress peak point of the concrete in the compression zone. The preset initial neutral axis position is updated using this actual stress peak point position. Guided by the balance condition of the resultant force of concrete compressive stress and the resultant force of FRP reinforcement tension, the midpoint between the actual stress peak point position and the current neutral axis position is taken as the updated neutral axis position in each iteration. The resultant force is recalculated until the resultant force difference meets the preset balance threshold, thus obtaining the neutral axis equilibrium position. Based on the neutral axis equilibrium position, the contributions of each horizontal strip layer of concrete in the compression zone and each FRP bar in the tension zone to the section bending moment are calculated and summed to obtain the ultimate flexural bearing capacity. Since the neutral axis iteration process directly incorporates the actual stress peak point position obtained from the global stiffness degradation spectrum, the neutral axis adjustment direction always follows the change in the stress distribution pattern in the compression zone. This reflects the phenomenon of stress peak shifting inward due to further attenuation of local stiffness after the concrete reaches peak stress, overcoming the problem of the neutral axis position deviating from the actual stress state in conventional methods that ignore stress peak shift. Therefore, the calculated ultimate flexural bearing capacity is closer to the actual flexural capacity of the FRP-reinforced concrete pile at failure. Attached Figure Description

[0022] The invention will now be further described with reference to the accompanying drawings.

[0023] Figure 1 This is a flowchart of the calculation method for the ultimate flexural bearing capacity of FRP reinforced concrete piles;

[0024] Figure 2 This is a flowchart of the iterative solution for the neutral axis equilibrium position;

[0025] Figure 3 This is a flowchart for calculating the ultimate flexural bearing capacity of FRP reinforced concrete piles. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] See Figure 1 This invention provides a method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles, comprising the following steps:

[0028] Obtain the geometric parameters of the pile body section of the target FRP reinforced concrete pile, and construct a layered discrete mesh model of the pile body section based on the geometric parameters of the pile body section;

[0029] Based on the hierarchical discrete mesh model, the actual compressive stress transmission path in the concrete compression zone is traced and decomposed into multiple nonlinear compressive stress transmission sub-paths.

[0030] Calculate the local stiffness attenuation coefficient for each nonlinear compressive stress transfer sub-path, and generate a global stiffness degradation distribution map of the concrete compression zone by superimposing all local stiffness attenuation coefficients.

[0031] Based on the global stiffness degradation distribution map, the actual stress peak point location in the compression zone of the FRP reinforced concrete pile is determined, the initial position of the neutral axis is updated with the actual stress peak point location, and the equilibrium position of the neutral axis is iteratively solved.

[0032] Calculate the ultimate flexural bearing capacity of FRP reinforced concrete piles based on the neutral axis equilibrium position.

[0033] This application provides a method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles, wherein the specific implementation process of constructing a layered discrete mesh model is as follows.

[0034] Extract the geometric parameters of the target FRP-reinforced concrete pile's cross-section. These parameters include the pile's outer contour shape, the coordinate parameters of the FRP reinforcement arrangement, and the diameter of the FRP reinforcement. The outer contour shape describes the dimensions of the cross-section's outer boundary. When the pile cross-section is circular, the outer contour shape includes the pile diameter; when the cross-section is rectangular, it includes the width and height. The coordinate parameters describe the position of each FRP reinforcement within the pile cross-section. A Cartesian coordinate system is established with the centroid of the pile cross-section as the origin. These parameters include the x-coordinate and y-coordinate of the center point of each FRP reinforcement. The diameter parameter is the nominal diameter of each FRP reinforcement.

[0035] After extracting the geometric parameters of the pile section, the pile section is divided into several continuous horizontal strip layers along the height direction, with the centroid of the pile section as the origin of the coordinate system and a preset initial layer thickness. The preset initial layer thickness is set to one-fiftieth of the pile section height. This value ensures that the total number of horizontal strip layers along the height direction is no less than fifty, meeting the requirements for the discretization accuracy of the section stress integral. During the division, starting from the edge of the compression zone of the pile section, the section is sequentially divided along the height direction towards the edge of the tension zone, resulting in multiple horizontal strip layers. Each horizontal strip layer contains concrete elements and FRP reinforcement elements. The area of ​​the concrete elements is calculated based on the height and width of the horizontal strip layer, while the FRP reinforcement elements are included in the horizontal strip layer by including the cross-sectional area of ​​the FRP reinforcement within the height range of the horizontal strip layer. When the center ordinate of an FRP reinforcement lies between the upper and lower boundary ordinates of a horizontal strip layer, the entire cross-sectional area of ​​this FRP reinforcement belongs to that horizontal strip layer.

[0036] After dividing the pile into all horizontal strip layers, the actual distance from the geometric center of each horizontal strip layer to the edge of the compression zone of the pile section is recorded. The actual distances corresponding to all horizontal strip layers are then arranged to obtain the inter-layer distance sequence of the layered discrete mesh model. The edge of the compression zone of the pile section is the outermost boundary of the side of the section subjected to compressive stress. For a horizontal strip layer with index i, i is counted starting from the edge of the compression zone and i is a positive integer, i≥1. The actual distance from the geometric center of the horizontal strip layer to the edge of the compression zone is... express, Calculate according to the following formula:

[0037]

[0038] in: The distance between the geometric center of the i-th horizontal strip layer and the edge of the compression zone of the pile section is the actual distance. This refers to the sequence number of the horizontal strip layer. The value ranges from 1 to N, where N is the total number of horizontal strip layers. N is equal to the quotient of the pile section height divided by the initial layer thickness t, rounded down. The initial layer thickness, The value is taken as one-fiftieth of the pile section height. The calculated values ​​are then processed according to the horizontal strip layer number i in ascending order. The resulting sequence is the inter-layer distance sequence of the hierarchical discrete grid model.

[0039] In practice, starting from the edge of the compression zone in the layered discrete mesh model, the concrete compressive strain values ​​of each horizontal strip layer are extracted sequentially along the cross-sectional height. The extraction of concrete compressive strain values ​​is based on the plane section assumption. The ultimate compressive strain value of the concrete at the edge of the compression zone under the current calculation state is set, and the currently assumed neutral axis position is obtained. The ultimate compressive strain value of the concrete at the edge of the compression zone is taken as 0.0033 according to the concrete structure design code for non-uniform compression. According to the plane section assumption, the concrete compressive strain value at each point on the cross-section is proportional to the distance from that point to the neutral axis. For the horizontal strip layer with sequence number k, the inter-layer distance sequence of the layered discrete mesh model provides the actual distance from the geometric center of the horizontal strip layer to the edge of the compression zone. Combined with the currently assumed neutral axis position, the distance from the geometric center of the horizontal strip layer to the neutral axis can be calculated, and thus the concrete compressive strain value of the horizontal strip layer can be calculated. Following the order from the edge of the compression zone towards the tension zone, the extraction of concrete compressive strain values ​​for all horizontal strip layers within the compression zone is completed sequentially.

[0040] In practical implementation, the concrete compressive strain value of the currently extracted horizontal strip layer is used as input, and the actual compressive stress value of the current horizontal strip layer is calculated through a preset concrete constitutive model. The preset concrete constitutive model adopts the uniaxial compressive stress-strain full curve equation proposed by Guo Zhenhai. The uniaxial compressive stress-strain full curve equation proposed by Guo Zhenhai consists of an ascending segment and a descending segment. The ascending segment adopts a polynomial form, and the descending segment adopts a rational fractional form. The model parameters include the peak compressive stress of the concrete, the peak compressive strain corresponding to the peak compressive stress of the concrete, and the shape control parameters of the descending segment. All model parameters are determined according to the concrete strength grade, and the specific values ​​can be obtained from the standard tables of the current concrete structure design code. Substituting the concrete compressive strain value of each horizontal strip layer into the uniaxial compressive stress-strain full curve equation proposed by Guo Zhenhai, the actual compressive stress value corresponding to that horizontal strip layer is output.

[0041] In practical implementation, after calculating the actual compressive stress values ​​of all horizontal strip layers in the compression zone, the actual compressive stress values ​​of two adjacent horizontal strip layers are differentially calculated to obtain the stress gradient between adjacent layers. For two adjacent horizontal strip layers with serial numbers k and k+1, the stress gradient is obtained by subtracting the actual compressive stress value of the horizontal strip layer with serial number k+1 from the actual compressive stress value of the horizontal strip layer with serial number k. Using the points where the stress gradient changes sign as boundary points, the entire compression zone is divided into multiple continuous compressive stress transfer sub-regions. The points where the stress gradient changes sign refer to the transition layers where the stress gradient changes from positive to negative or vice versa. If the sign of the stress gradient changes between adjacent horizontal strip layers, this point is used as the boundary. Each compressive stress transfer sub-region corresponds to an independent nonlinear compressive stress transfer sub-path. The actual compressive stress value within the nonlinear compressive stress transfer sub-path exhibits a unidirectional increasing or decreasing nonlinear variation characteristic along the cross-sectional height direction. All nonlinear compressive stress transfer sub-paths are connected end to end, together forming a complete decomposition of the actual compressive stress transfer path in the concrete compression zone.

[0042] In practical implementation, the set of horizontal strip layers corresponding to each nonlinear compressive stress transfer sub-path is obtained. The nonlinear compressive stress transfer sub-path consists of continuous horizontal strip layers between two adjacent points of positive and negative stress gradient change. All horizontal strip layers belonging to the current nonlinear compressive stress transfer sub-path are extracted from the inter-layer distance sequence of the layered discrete mesh model, forming a set of horizontal strip layers. The initial elastic modulus and current compressive strain value of each horizontal strip layer are extracted from the set of horizontal strip layers. The initial elastic modulus is the tangential elastic modulus when the concrete is undamaged, directly retrieved from the standard table of the concrete structure design code based on the concrete strength grade used in the current FRP reinforced concrete pile. The concrete strength grade is determined by the pile design documents. The current compressive strain value is the concrete compressive strain value at the geometric center of the horizontal strip layer, calculated using the plane section assumption under the preset load conditions.

[0043] In practice, the current compressive strain value of each horizontal strip layer is compared with the preset peak compressive strain of the concrete to calculate the single-layer stiffness reduction factor for each horizontal strip layer. The preset peak compressive strain of the concrete is the compressive strain value corresponding to the peak compressive stress of the concrete, determined from the concrete structure design code based on the concrete strength grade. The single-layer stiffness reduction factor is defined as the ratio of the secant modulus corresponding to the current compressive strain value to the initial elastic modulus. For the horizontal strip layer with serial number p, the single-layer stiffness reduction factor is calculated as follows: first, the actual compressive stress value corresponding to the current compressive strain value is obtained through the preset concrete constitutive model; then, the actual compressive stress value is divided by the current compressive strain value to obtain the secant modulus; finally, the secant modulus is divided by the initial elastic modulus to obtain the single-layer stiffness reduction factor. The single-layer stiffness reduction factor ranges from 0 to 1. When the current compressive strain value is zero, the single-layer stiffness reduction factor is 1; when the current compressive strain value exceeds the ultimate compressive strain of the concrete, the single-layer stiffness reduction factor approaches 0.

[0044] In practice, a weighted average is performed on all single-layer stiffness reduction factors within the same nonlinear compressive stress transfer sub-path, and this weighted average is used as the local stiffness attenuation coefficient for that nonlinear compressive stress transfer sub-path. The weighted averaging operation is implemented as follows: First, the total number of horizontal strip layers corresponding to the current nonlinear compressive stress transfer sub-path is obtained, and an initial weight coefficient is assigned to each horizontal strip layer. The initial weight coefficient is proportional to the distance from the geometric center of the horizontal strip layer to the edge of the compression zone. The closer the distance to the edge of the compression zone, the more significant the contribution of the horizontal strip layer to compressive stress transfer, and the larger its assigned initial weight coefficient. Second, the single-layer stiffness reduction factor is extracted from each horizontal strip layer, and the single-layer stiffness reduction factor is multiplied by the corresponding initial weight coefficient to obtain the weighted stiffness reduction value for each horizontal strip layer. Third, the weighted stiffness reduction values ​​of all horizontal strip layers are summed to obtain the total weighted reduction value. Finally, the initial weight coefficients of all horizontal strip layers are summed to obtain the total weight coefficient. Dividing the weighted reduction total by the sum of the weighting coefficients yields the local stiffness attenuation coefficient of the current nonlinear compressive stress transfer subpath.

[0045] In practice, according to the height position of each nonlinear compressive stress transfer sub-path in the compression zone, the calculated local stiffness attenuation coefficients are sequentially filled into the position vectors corresponding to the layered discrete mesh model, generating a global stiffness degradation distribution map. The position vectors corresponding to the layered discrete mesh model are one-dimensional arrays, the length of which is equal to the total number of horizontal strip layers, and each element in the array corresponds to a horizontal strip layer. The filling method is as follows: for all horizontal strip layers belonging to the same nonlinear compressive stress transfer sub-path, the same local stiffness attenuation coefficient value is filled into the element positions corresponding to these horizontal strip layers in the position vector. When the local stiffness attenuation coefficients of all nonlinear compressive stress transfer sub-paths are filled, all elements in the position vector are assigned values, and this fully assigned position vector is the global stiffness degradation distribution map of the concrete compression zone. The value of each element in the global stiffness degradation distribution map reflects the degree of stiffness attenuation at the corresponding horizontal strip layer position; the lower the value, the more severe the stiffness degradation.

[0046] In practical implementation, the local stiffness attenuation coefficient of the nonlinear compressive stress transfer sub-path is corrected using an exponential attenuation model associated with the concrete damage variable. The concrete damage variable is defined as the reduction ratio of the bearing area caused by the development of microcracks within the material, ranging from 0 to 1. A concrete damage variable of 0 indicates no damage, while a value of 1 indicates complete damage. The exponential attenuation model expresses the local stiffness attenuation coefficient as an exponential function of the concrete damage variable, expressed as the corrected local stiffness attenuation coefficient equal to the initial local stiffness attenuation coefficient multiplied by the natural constant e raised to the power of the negative concrete damage variable. The value of the concrete damage variable is calculated based on the ratio of the average compressive strain value of each horizontal strip layer within the current nonlinear compressive stress transfer sub-path to the ultimate compressive strain of the concrete. When the average compressive strain value is less than 0.3 times the ultimate compressive strain of the concrete, the concrete damage variable is 0; when the average compressive strain value exceeds the ultimate compressive strain of the concrete, the concrete damage variable is 1. The intermediate interval is determined by linear interpolation. Through the correction of the exponential attenuation model, the local stiffness attenuation coefficient exhibits a nonlinear accelerated decreasing trend under high stress levels, reflecting the abrupt stiffness change effect when the concrete is near failure. The corrected local stiffness attenuation coefficient is used to replace the original calculated value and fill in the global stiffness degradation distribution map.

[0047] In practice, the global stiffness degradation distribution map is normalized along the pile section height, and cubic spline interpolation is used to extend the discrete local stiffness attenuation coefficients into a continuous stiffness degradation curve. Normalization maps the height of the compression zone of the pile section to a range of 0 to 1, where 0 corresponds to the edge of the compression zone and 1 corresponds to the neutral axis. When using cubic spline interpolation, the normalized height position is used as the independent variable, and the local stiffness attenuation coefficient at the corresponding height position is used as the dependent variable. A cubic polynomial is constructed between every two adjacent data points, ensuring that adjacent cubic polynomials have equal function values, first derivative values, and second derivative values ​​at the connection point. This results in a second-order continuously differentiable stiffness degradation curve within the domain. The normalized continuous stiffness degradation curve is independent of the absolute size of the pile section and can be applied to describe the stiffness degradation of FRP-reinforced concrete piles with different section heights.

[0048] In specific implementation, please refer to Figure 2 The method involves locating the horizontal strip layer corresponding to the minimum local stiffness attenuation coefficient from the global stiffness degradation distribution map. The actual distance from the geometric center of the found horizontal strip layer to the edge of the compression zone is taken as the location of the actual stress peak point. The global stiffness degradation distribution map is a one-dimensional array, where each element corresponds to a horizontal strip layer, and the element's value is the local stiffness attenuation coefficient. The method iterates through all elements in the global stiffness degradation distribution map, finding the element with the minimum local stiffness attenuation coefficient and recording its index number in the map. The horizontal strip layer corresponding to the minimum local stiffness attenuation coefficient indicates the location of the most severe stiffness degradation within the concrete compression zone. At this location, the development of microcracks in the concrete is most severe, the reduction ratio of the bearing area reaches its maximum, and the actual compressive stress reaches its peak. The actual distance from the geometric center of the horizontal strip layer to the edge of the pressure zone is obtained by calling the interlayer distance sequence of the layered discrete mesh model. The interlayer distance sequence stores the actual distance value from the geometric center of each horizontal strip layer to the edge of the pressure zone. The corresponding actual distance value is extracted from the interlayer distance sequence according to the recorded index number. The extracted actual distance value is the actual stress peak point position.

[0049] In practice, a preset initial position of the neutral axis is obtained. This preset initial position is set at half the height of the pile section. The pile section height is the total dimension of the section from the edge of the compression zone to the edge of the tension zone. Using the edge of the compression zone as the zero reference point, the distance between the initial position of the neutral axis and the edge of the compression zone is half the height of the pile section.

[0050] In practical implementation, the resultant force of concrete compressive stress in all horizontal strip layers above the initial position of the neutral axis and the resultant force of tensile stress in all FRP bars are calculated. The area above the initial position of the neutral axis is the concrete compression zone, which includes all horizontal strip layers from the edge of the compression zone to the initial position of the neutral axis. The resultant force of concrete compressive stress is calculated as follows: traverse each horizontal strip layer above the initial position of the neutral axis, obtain the actual compressive stress value and area of ​​the current horizontal strip layer, multiply the actual compressive stress value by the area of ​​the horizontal strip layer to obtain the compressive stress contribution value of the current horizontal strip layer, and sum the compressive stress contribution values ​​of all horizontal strip layers above the initial position of the neutral axis to obtain the resultant force of concrete compressive stress. The resultant force of tensile stress in FRP bars is calculated as follows: traverse all FRP bars in the pile section, and for each FRP bar, determine whether the ordinate of the center point of the FRP bar is below the initial position of the neutral axis. If the ordinate of the center point of the FRP bar is below the initial position of the neutral axis, then the FRP bar is in the tension zone. The tensile stress value of the FRP reinforcement in the tension zone is determined by multiplying the tensile modulus of elasticity of the FRP reinforcement by its tensile strain. The tensile strain of the FRP reinforcement is calculated based on the plane section assumption from the initial position of the neutral axis and the ultimate compressive strain value of the concrete at the edge of the compression zone. The tensile stress value of each FRP reinforcement in the tension zone is multiplied by its cross-sectional area to obtain the tensile force contribution value of a single FRP reinforcement. The resultant tensile force of the FRP reinforcement is obtained by summing the tensile force contributions of all FRP reinforcements in the tension zone.

[0051] In practical implementation, the absolute value of the difference between the resultant force of concrete compressive stress and the resultant force of FRP reinforcement tensile stress is compared with a preset equilibrium threshold. The absolute value of the difference between the resultant force of concrete compressive stress and the resultant force of FRP reinforcement tensile stress reflects the degree of deviation from the axial force balance of the section. The preset equilibrium threshold is a convergence tolerance value, set at one-thousandth of the total compressive bearing capacity of the entire section. The total compressive bearing capacity of the entire section is estimated by multiplying the peak compressive stress of the concrete by the area of ​​the compression zone of the pile section.

[0052] If the absolute value of the difference between the resultant compressive stress of the concrete and the resultant tensile force of the FRP reinforcement is greater than the preset equilibrium threshold, it indicates that the current neutral axis position does not meet the section equilibrium condition, and the neutral axis position needs to be updated and the resultant force equilibrium verification needs to be performed again. The updated neutral axis position is determined by the midpoint between the actual stress peak point position and the current neutral axis position. The updated neutral axis position is obtained by adding the coordinates of the actual stress peak point position and the current neutral axis position and dividing by two. The updated neutral axis position replaces the current neutral axis position, the concrete compression zone is redefined, the resultant compressive stress of the concrete in all horizontal strip layers above the updated neutral axis position is recalculated, the resultant tensile force of all FRP reinforcements below the updated neutral axis position is recalculated, the absolute value of the difference between the resultant compressive stress of the concrete and the resultant tensile force of the FRP reinforcement is recalculated, and compared with the preset equilibrium threshold again.

[0053] If the absolute value of the difference between the resultant compressive stress of concrete and the resultant tensile stress of FRP reinforcement is less than or equal to the preset equilibrium threshold, it indicates that the current neutral axis position meets the section equilibrium condition, the iteration process stops, and the current neutral axis position is determined as the neutral axis equilibrium position.

[0054] The convergence determination of the difference between the resultant force of concrete compressive stress and the resultant force of FRP reinforcement tensile force during the iterative adjustment of the neutral axis position is based on the following formula:

[0055]

[0056] in: This refers to the resultant compressive stress of concrete in all horizontal strip layers above the neutral axis. The unit is kilonewtons. It is obtained by multiplying the actual compressive stress value of the horizontal strip layer in each compression zone with the area of ​​the horizontal strip layer. This is the resultant tensile force of all FRP bars below the neutral axis position. The unit is kilonewtons. It is obtained by multiplying the tensile stress value of each tensile FRP bar by the cross-sectional area of ​​the FRP bar. This is the absolute value of the difference between the resultant compressive stress in the concrete and the resultant tensile stress in the FRP reinforcement. The preset balance threshold, The unit is kilonewtons. The value is taken as one-thousandth of the total compressive bearing capacity of the FRP reinforced concrete pile section. The total compressive bearing capacity of the section is equal to the peak compressive stress of the concrete multiplied by the area of ​​the compression zone of the pile section.

[0057] See Figure 3 In practical implementation, the pile cross-section is divided into a compression zone and a tension zone, with the neutral axis equilibrium position as the boundary. The neutral axis equilibrium position is the final position of the neutral axis that satisfies the axial force equilibrium condition of the cross-section after iterative solution. The compression zone is defined as the area from the neutral axis equilibrium position to the edge of the compression zone of the pile cross-section, and the tension zone is defined as the area from the neutral axis equilibrium position to the edge of the tension zone of the pile cross-section. The compressive stress values ​​and corresponding lever arm lengths of all horizontal strip layers in the compression zone are extracted from the layered discrete mesh model. Every horizontal strip layer within the compression zone in the layered discrete mesh model participates in the extraction, and the compressive stress value of each horizontal strip layer is the actual compressive stress value calculated by the preset concrete constitutive model under the current neutral axis equilibrium position. The lever arm length of each horizontal strip layer is defined as the vertical distance from the geometric center of the horizontal strip layer to the neutral axis equilibrium position. The lever arm length is obtained by subtracting the distance from the neutral axis equilibrium position to the edge of the pressure zone from the actual distance from the geometric center of the horizontal strip layer to the edge of the pressure zone. If the difference is positive, it means that the horizontal strip layer is located in the pressure zone, and the absolute value of the difference is the lever arm length.

[0058] In practical implementation, the compressive stress value of each horizontal strip layer is calculated by multiplying the area of ​​that horizontal strip layer to obtain its pressure contribution value. The area of ​​a single horizontal strip layer is equal to the layer thickness multiplied by the cross-sectional width of the horizontal strip layer. The layer thickness is a preset initial layer thickness, and the cross-sectional width is determined based on the outer contour shape parameters of the pile body. The pressure contribution value of each horizontal strip layer is multiplied by its corresponding lever arm length to obtain its bending moment contribution value. The bending moment contribution values ​​of all horizontal strip layers are summed to obtain the bending moment component contributed by the concrete compression zone. The bending moment component contributed by the concrete compression zone is the algebraic sum of the moments taken by all horizontal strip layers about the neutral axis equilibrium position, reflecting the resistance bending moment provided by the concrete compression zone.

[0059] In practical implementation, the tensile stress values ​​of all FRP bars in the tension zone, the cross-sectional area of ​​a single FRP bar, and the lever arm length of each FRP bar to the neutral axis equilibrium position are extracted from the layered discrete mesh model. The method for determining whether an FRP bar is located in the tension zone is to compare the ordinate of the center point of the FRP bar with the ordinate of the neutral axis equilibrium position. When the ordinate of the center point of the FRP bar is located on the side of the neutral axis equilibrium position away from the edge of the compression zone, the FRP bar belongs to the tension zone. The tensile stress value of the FRP bar in the tension zone is determined by multiplying the tensile modulus of elasticity of the FRP bar by its tensile strain. The tensile strain of the FRP bar is calculated based on the plane section assumption from the ultimate compressive strain value of the concrete at the neutral axis equilibrium position and the edge of the compression zone. The cross-sectional area of ​​a single FRP bar is calculated based on the diameter parameter of the FRP bar, and the cross-sectional area is equal to one-quarter of pi multiplied by the square of the FRP bar diameter. The lever arm length of each FRP bar to the neutral axis equilibrium position is defined as the vertical distance from the center point of the FRP bar to the neutral axis equilibrium position. The lever arm length is obtained by subtracting the distance from the neutral axis equilibrium position to the edge of the pressure zone from the actual distance from the center point of the FRP bar to the edge of the pressure zone and taking the absolute value.

[0060] In practical implementation, the tensile stress value of each FRP bar is calculated by multiplying it by the cross-sectional area of ​​the single FRP bar to obtain the tensile force contribution value of that FRP bar. The tensile force contribution value of each FRP bar is then multiplied by the lever arm length of that FRP bar to the neutral axis equilibrium position to obtain the bending moment contribution value of that FRP bar. The bending moment contribution values ​​of all FRP bars in the tension zone are summed to obtain the bending moment component contributed by the FRP bars. The bending moment component contributed by the FRP bars is the algebraic sum of the moments taken by all tensile FRP bars about the neutral axis equilibrium position, reflecting the resistance to bending moment provided by the FRP bars.

[0061] In practical implementation, the bending moment component contributed by the concrete compression zone is added to the bending moment component contributed by the FRP reinforcement to obtain the ultimate bending capacity of the FRP-reinforced concrete pile. The ultimate bending capacity is the maximum bending moment that the pile section can withstand when it reaches its ultimate bearing capacity state.

[0062] Ultimate flexural capacity is calculated using the following formula:

[0063]

[0064] in: This represents the ultimate flexural bearing capacity of FRP-reinforced concrete piles. The unit is kilonewton-meter; This represents the total number of horizontal stripe layers in the compression zone. The value is obtained by statistically analyzing all horizontal stripe layers contained from the neutral axis equilibrium position to the edge of the pressure zone. This is the index of the horizontal strip layer in the pressure zone. The value range is 1 to ; For the serial number The compressive stress value of the horizontal strip layer under pressure, The unit is megapascal; For the serial number The area of ​​the horizontally compressed strip layer, The unit is square millimeters. It equals the layer thickness of the horizontal strip layer multiplied by the cross-sectional width; For the serial number The lever arm length from the geometric center of the compressed horizontal strip layer to the neutral axis equilibrium position. The unit is millimeters; This refers to the total number of FRP reinforcement bars in the tension zone. The value is obtained by statistically analyzing all FRP bars whose center point ordinates are located at the neutral axis equilibrium position on the tension side; This is the index of the FRP reinforcement bars in the tension zone. The value range is 1 to ; For the serial number The tensile stress value of the FRP reinforcement under tension, The unit is megapascal; For the serial number The cross-sectional area of ​​the tensile FRP reinforcement, The unit is square millimeters. It equals one-quarter of pi multiplied by the square of the FRP bar diameter; For the serial number The lever arm length from the center point of the tensioned FRP reinforcement to the equilibrium position of the neutral axis. The unit is millimeters.

[0065] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles, characterized in that, Includes the following steps: Obtain the geometric parameters of the pile body section of the target FRP reinforced concrete pile, and construct a layered discrete mesh model of the pile body section based on the geometric parameters of the pile body section; Based on the hierarchical discrete mesh model, the actual compressive stress transmission path in the concrete compression zone is traced, and the actual compressive stress transmission path is decomposed into multiple nonlinear compressive stress transmission sub-paths. Calculate the local stiffness attenuation coefficient for each nonlinear compressive stress transfer sub-path, and generate a global stiffness degradation distribution map of the concrete compression zone by superimposing all local stiffness attenuation coefficients. Based on the global stiffness degradation distribution map, the actual stress peak point location in the compression zone of the FRP reinforced concrete pile is determined, the initial position of the neutral axis is updated with the actual stress peak point location, and the equilibrium position of the neutral axis is iteratively solved. The ultimate flexural bearing capacity of the FRP-reinforced concrete pile is calculated based on the neutral axis equilibrium position.

2. The method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles according to claim 1, characterized in that, The process of obtaining the geometric parameters of the target FRP reinforced concrete pile section and constructing a layered discrete mesh model of the pile section based on the geometric parameters includes the following steps: Extract the outer contour shape parameters of the pile body section, the layout coordinate parameters of the FRP reinforcement, and the diameter parameters of the FRP reinforcement of the target FRP reinforced concrete pile; With the centroid of the pile section as the origin of the coordinate system, the pile section is divided into several continuous horizontal strip layers along the height direction according to the preset initial layer thickness. Each horizontal strip layer contains concrete units and FRP reinforcement units. Record the actual distance from the geometric center of each horizontal strip layer to the edge of the compression zone of the pile section to obtain the interlayer distance sequence of the layered discrete grid model.

3. The method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles according to claim 2, characterized in that, Based on the aforementioned hierarchical discrete mesh model, the process of tracing the actual compressive stress transmission path in the concrete compression zone and decomposing the actual compressive stress transmission path into multiple nonlinear compressive stress transmission sub-paths includes the following steps: Starting from the edge of the compression zone of the layered discrete mesh model, the concrete compressive strain values ​​of each horizontal strip layer are extracted sequentially along the cross-sectional height direction; Using the current concrete compressive strain value of the horizontal strip layer as input, the actual compressive stress value of the horizontal strip layer is calculated through the preset concrete constitutive model; The difference between the actual compressive stress values ​​of two adjacent horizontal strip layers is taken as the stress gradient. The positive and negative change points of the stress gradient are used as the dividing points to divide the entire compression zone into multiple continuous compressive stress transfer sub-regions. Each compressive stress transfer sub-region corresponds to a nonlinear compressive stress transfer sub-path.

4. The method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles according to claim 3, characterized in that, The process of calculating the local stiffness attenuation coefficient of each nonlinear compressive stress transfer sub-path and generating a global stiffness degradation distribution map of the concrete compression zone by superimposing all local stiffness attenuation coefficients includes the following steps: Obtain the set of horizontal strip layers corresponding to each nonlinear compressive stress transfer sub-path, and extract the initial elastic modulus and current compressive strain value of each horizontal strip layer from the set of horizontal strip layers; Compare the current compressive strain value with the preset peak compressive strain of concrete, and calculate the single-layer stiffness reduction factor for each horizontal strip layer; The weighted average of all single-layer stiffness reduction factors within the same nonlinear compressive stress transfer sub-path is used as the local stiffness attenuation coefficient of that nonlinear compressive stress transfer sub-path. According to the height position order of each nonlinear compressive stress transfer sub-path in the compression zone, the local stiffness attenuation coefficient is sequentially filled into the position vector corresponding to the layered discrete grid model to generate a global stiffness degradation distribution map.

5. The method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles according to claim 4, characterized in that, The process of weighted averaging of all single-layer stiffness reduction factors within the same nonlinear compressive stress transfer sub-path, and using the weighted average as the local stiffness attenuation coefficient of that nonlinear compressive stress transfer sub-path, includes the following steps: Obtain the total number of horizontal strip layers corresponding to the current nonlinear compressive stress transfer sub-path, and assign an initial weight coefficient to each horizontal strip layer. The initial weight coefficient is proportional to the distance from the geometric center of the horizontal strip layer to the edge of the compression zone. Extract the single-layer stiffness reduction factor from each horizontal strip layer, and multiply the single-layer stiffness reduction factor by the corresponding initial weight coefficient to obtain the weighted stiffness reduction value of each horizontal strip layer; Sum the weighted stiffness reduction values ​​of all horizontal strip layers to obtain the total weighted reduction value; Sum the initial weight coefficients of all horizontal stripe layers to obtain the total weight coefficients; Dividing the weighted reduction total by the sum of the weighting coefficients yields the local stiffness attenuation coefficient of this nonlinear compressive stress transfer sub-path. The horizontal strip layer closer to the edge of the compression zone contributes more to the local stiffness attenuation coefficient.

6. The method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles according to claim 4, characterized in that, The single-layer stiffness reduction factor is the ratio of the secant modulus corresponding to the current compressive strain value to the initial elastic modulus.

7. The method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles according to claim 4, characterized in that, Based on the global stiffness degradation distribution map, the actual stress peak point location in the compression zone of the FRP-reinforced concrete pile is determined. The initial position of the neutral axis is updated with the actual stress peak point location, and the equilibrium position of the neutral axis is iteratively solved. The process includes the following steps: Find the horizontal strip layer corresponding to the minimum local stiffness attenuation coefficient from the global stiffness degradation distribution map, and take the distance from the geometric center of the horizontal strip layer to the edge of the compression zone as the actual stress peak point location. Obtain the preset initial position of the neutral axis, and calculate the resultant force of the concrete compressive stress in all horizontal strip layers above the initial position of the neutral axis and the resultant force of the tensile stress in all FRP bars; If the absolute value of the difference between the resultant force of the concrete compressive stress and the resultant force of the FRP reinforcement tensile stress is greater than the preset equilibrium threshold, then the midpoint between the actual stress peak point and the current neutral axis position is taken as the updated neutral axis position, and the resultant force difference is recalculated until the absolute value of the resultant force difference is less than or equal to the preset equilibrium threshold, thus obtaining the neutral axis equilibrium position.

8. The method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles according to claim 7, characterized in that, The process of calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles based on the neutral axis equilibrium position includes the following steps: Using the neutral axis equilibrium position as the boundary, the pile section is divided into a compression zone and a tension zone. The compressive stress values ​​and corresponding lever arm lengths of all horizontal strip layers in the compression zone are extracted from the layered discrete mesh model. Calculate the product of the compressive stress value of each horizontal strip layer and the area of ​​that horizontal strip layer to obtain the pressure contribution value of that horizontal strip layer. Sum the pressure contribution values ​​of all horizontal strip layers and the product of the stress arm length to obtain the bending moment component contributed by the concrete compression zone. The tensile stress values ​​of all FRP bars in the tension zone, the cross-sectional area of ​​a single FRP bar, and the lever arm length of each FRP bar to the neutral axis equilibrium position are extracted from the layered discrete mesh model. The tensile force contribution value of each FRP bar is calculated and the product of the lever arm length is summed to obtain the bending moment component contributed by the FRP bar. The ultimate flexural bearing capacity of the FRP-reinforced concrete pile is obtained by adding the bending moment component contributed by the concrete compression zone to the bending moment component contributed by the FRP reinforcement.

9. The method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles according to claim 1, characterized in that, The local stiffness attenuation coefficient of the nonlinear compressive stress transfer sub-path is corrected using an exponential attenuation model associated with concrete damage variables to reflect the abrupt stiffness change effect under high stress levels.

10. The method for calculating the ultimate flexural bearing capacity of FRP-reinforced concrete piles according to claim 1, characterized in that, The global stiffness degradation distribution map is normalized according to the height direction of the pile section, and the discrete local stiffness attenuation coefficient is extended into a continuous stiffness degradation curve by cubic spline interpolation.

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