Method for determining equivalent permeability coefficient of pile-soil composite based on improved KC equation

Abstract

The application provides a pile-soil composite equivalent permeability coefficient determination method based on an improved KC equation, comprising: obtaining geometric configuration parameters and hydrogeological parameters of a pile-soil composite under an actual working condition; obtaining a general formula for calculating the equivalent permeability coefficient of the pile-soil composite based on the KC equation improved by using a velocity correction factor and a tortuosity correction factor; determining the corresponding horizontal correction factor and vertical correction factor of the pile-soil composite based on the geometric configuration parameters and the hydrogeological parameters; substituting the horizontal correction factor into the general formula to obtain the horizontal equivalent permeability coefficient of the pile-soil composite; and substituting the vertical correction factor into the general formula to obtain the vertical equivalent permeability coefficient of the pile-soil composite. The correction factors of the application consider the influence of the geometric configuration parameters and the hydrogeological parameters of the pile-soil composite under different working conditions, and the equivalent permeability coefficients of the pile-soil composite with different geometric configurations can be accurately matched.

Description

Technical Field

[0001] This application relates to the field of seepage in geotechnical engineering, and more specifically, to a method for determining the equivalent permeability coefficient of pile-soil composites based on an improved KC equation. Background Technology

[0002] Pile-soil composites (such as gravel piles, sand piles, and cement-soil pile composite foundations) are widely used in soft soil foundation reinforcement, seepage prevention and drainage design of dams and hydraulic structures. Their equivalent permeability coefficient is a core parameter for seepage analysis, consolidation settlement calculation, anti-buoyancy safety evaluation, and seepage prevention safety evaluation. In large-scale projects, it is difficult to accurately simulate each pile individually. Therefore, the pile-soil composite is usually simulated as an equivalent homogeneous material. Thus, how to accurately and easily obtain the equivalent permeability coefficient of this hypothetical equivalent homogeneous material directly determines the accuracy of seepage analysis and the reliability of engineering safety.

[0003] The equivalent permeability coefficient of the composite material can be calculated using analytical methods such as the replacement rate correction method, the equivalent particle medium method, and the effective medium theory correction method. A literature search of existing technologies revealed that Chinese patent CN121118519A proposes a method for calculating the equivalent permeability coefficient of vibratory compacted stone pile composite foundations. Through finite element numerical simulation and theoretical analysis, a power function analytical formula is established based on the pile-soil permeability coefficient and replacement rate. However, the calculation results lack an explicit quantitative mechanism for the flow around the pile and the tortuous seepage path, making it difficult to directly generalize to different geometric configurations. Chinese patent CN118586069A proposes a method for calculating the soil permeability coefficient based on equivalent soil particles and a model construction method. This method discretizes the soil into an equivalent particle aggregate and constructs a microscopic seepage model to obtain the permeability coefficient. However, constructing the equivalent particle model requires extensive micro-parameter calibration, making the calculation process cumbersome, and the model cannot directly reflect the geometric configuration characteristics of the pile-soil composite, such as pile diameter and pile arrangement. In 2014, Ma et al. published "Evaluation of the hydraulic conductivity of aquifers with piles" in the Journal of Hydrogeology. Based on the modified effective medium theory, they derived the equivalent permeability coefficient of pile-soil composites. The study considered the changes in seepage path caused by the pile arrangement, but did not consider the head loss caused by the change in seepage velocity when seepage bypasses the pile body.

[0004] The Kozeny-Carman (KC) equation is a semi-empirical formula widely used in the field of seepage for predicting the permeability coefficient of porous media. In 2021, Zhang et al. published "A New Modified Model of the StreamingPotential Coupling Coefficient Depends on Structural" in Geofluids, introducing a modified KC equation based on density and rock content, and establishing a coupled flow potential model for soil-rock mixtures. However, its research object is a randomly dispersed soil-rock mixture, which has an essential difference in geometry from pile-soil composites.

[0005] Therefore, there is an urgent need for a method to determine the equivalent permeability coefficient of pile-soil composites that can take into account the geometry of the pile-soil composite. Summary of the Invention

[0006] In view of the deficiencies in the prior art, the purpose of this application is to provide a method for determining the equivalent permeability coefficient of pile-soil composites based on the improved KC equation.

[0007] According to the first aspect of this application, a method for determining the equivalent permeability coefficient of a pile-soil composite based on an improved KC equation is provided, comprising: Obtain the geometric configuration parameters and hydrogeological parameters of the pile-soil composite under actual working conditions; The KC equation is improved by introducing velocity correction factors and tortuosity correction factors. Based on the improved KC equation, a general formula for calculating the equivalent permeability coefficient of pile-soil composite is obtained. The equivalent permeability coefficient of pile-soil composite includes the horizontal equivalent permeability coefficient and the vertical equivalent permeability coefficient of pile-soil composite. Based on the geometric configuration parameters and hydrogeological parameters, the horizontal correction factor and vertical correction factor corresponding to the pile-soil composite are determined. The horizontal correction factor and vertical correction factor are determined based on the improved KC equation to reflect the head loss caused by groundwater seepage through the pile-soil composite. Substituting the horizontal correction factor into the general formula yields the horizontal equivalent permeability coefficient of the pile-soil composite; substituting the vertical correction factor into the general formula yields the vertical equivalent permeability coefficient of the pile-soil composite.

[0008] Optionally, the geometric configuration parameters include the length, width, number of piles, number of pile rows, shape of the pile, pile diameter, pile center-to-center spacing, and pile arrangement of the pile-soil composite material. The pile arrangement method includes at least one of the following: multiple rows of rectangular piles, multiple rows of staggered piles, and single row of piles. The hydrogeological parameters include the horizontal permeability coefficient and the vertical permeability coefficient of the soil around the pile, wherein the horizontal permeability coefficient is the permeability coefficient in the horizontal seepage direction, and the vertical permeability coefficient is the permeability coefficient in the seepage direction perpendicular to the horizontal plane where the horizontal seepage direction is located.

[0009] Optionally, the general formula for calculating the equivalent permeability coefficient of the pile-soil composite is as follows: in, Indicates the equivalent permeability coefficient of the pile-soil composite. Indicates the correction factor. This represents the permeability coefficient of the soil surrounding the pile. Indicates the speed correction factor. Indicates the tortuosity correction factor; The correction factors include horizontal and vertical correction factors; the permeability coefficient of the soil surrounding the pile includes the horizontal and vertical permeability coefficients of the soil surrounding the pile; the velocity correction factor includes horizontal and vertical velocity correction factors; the tortuosity correction factor includes horizontal and vertical tortuosity correction factors; when obtaining the horizontal equivalent permeability coefficient of the pile-soil composite, the horizontal correction factors, the horizontal permeability coefficient of the soil surrounding the pile, the horizontal velocity correction factor, and the horizontal tortuosity correction factor are substituted into the general formula; when obtaining the vertical equivalent permeability coefficient of the pile-soil composite, the vertical correction factors, the vertical permeability coefficient of the soil surrounding the pile, the vertical velocity correction factor, and the vertical tortuosity correction factor are substituted into the general formula.

[0010] Optionally, for the multi-row rectangular pile arrangement, a horizontal correction factor corresponding to the pile-soil composite is obtained based on the geometric configuration parameters and hydrogeological parameters. The horizontal correction factor is determined based on the velocity correction factor and tortuosity correction factor in the improved KC equation, and its expression is as follows: in, This is a horizontal correction factor; This is a horizontal velocity correction factor; This is a horizontal tortuosity correction factor; The width of the pile-soil composite; The length of the pile-soil composite, For pile-soil composite pile cross-section shape factor; This represents the total number of piles in the pile-soil composite structure. Pile diameter; This is the pile perimeter coefficient; , , , , All are given regression coefficients.

[0011] Optionally, for the multi-row staggered pile arrangement, a horizontal correction factor corresponding to the pile-soil composite is obtained based on the geometric configuration parameters and hydrogeological parameters. The horizontal correction factor is determined based on the velocity correction factor and tortuosity correction factor in the improved KC equation, and its expression is as follows: in, This is a horizontal correction factor; To account for the additional head loss caused by the multi-row staggered pile arrangement ( V R,h T R,h ) -1 distributed,( V R,h T R,h ) -1 Dimensionless flow velocity correction factor V R,h T R,h The reciprocal of the dimensionless velocity correction factor V R,h T R,h In For horizontal velocity correction factor, This is a horizontal tortuosity correction factor. The width of the pile-soil composite. This refers to the total number of piles in the single-row pile with the fewest piles in the pile-soil composite structure. L p This represents the center-to-center spacing of the piles.

[0012] Optionally, for the single-row pile arrangement, a horizontal correction factor corresponding to the pile-soil composite is obtained based on the geometric configuration parameters and hydrogeological parameters. The horizontal correction factor is determined based on the velocity correction factor and tortuosity correction factor in the improved KC equation, and its expression is as follows: like > If the value is 0.800, then the expression for the level correction factor is as follows: In the formula, This is a horizontal correction factor; This is a horizontal velocity correction factor; This is a horizontal tortuosity correction factor; The width of the pile-soil composite; The length of the pile-soil composite, For pile-soil composite pile cross-section shape factor; This represents the total number of piles in the pile-soil composite structure. Pile diameter; This is the pile perimeter coefficient; , , , , All are given regression coefficients; like ≤ If the value is 0.800, then the expression for the level correction factor is as follows: In the formula, VT For local simplification ( V R,h T R,h ) -1 distributed, L p The center-to-center spacing of the piles r The distance from the target point to a certain pile is along the width of the pile-soil composite.

[0013] Optionally, a vertical correction factor corresponding to the pile-soil composite is obtained based on the geometric configuration parameters and hydrogeological parameters. The vertical correction factor is determined based on the velocity correction factor and tortuosity correction factor in the improved KC equation, and its expression is as follows: in, This is the vertical correction factor; This is the vertical velocity correction factor; This is the vertical tortuosity correction factor; The width of the pile-soil composite; The length of the pile-soil composite, For pile-soil composite pile cross-section shape factor; This represents the total number of piles in the pile-soil composite structure. This refers to the pile diameter.

[0014] Optionally, the expression for the horizontal equivalent permeability coefficient of the pile-soil composite is as follows: in, The horizontal equivalent permeability coefficient of the pile-soil composite is given. As a level correction factor, It is the horizontal equivalent permeability coefficient of the soil around the pile.

[0015] Optionally, the expression for the vertical equivalent permeability coefficient of the pile-soil composite is as follows: in, Let be the vertical equivalent permeability coefficient of the pile-soil composite. This is the vertical correction factor. is the vertical equivalent permeability coefficient of the soil around the pile.

[0016] According to a second aspect of this application, a system for determining the equivalent permeability coefficient of pile-soil composites based on an improved KC equation is provided, comprising: The data acquisition module is used to obtain the geometric configuration parameters and hydrogeological parameters of the pile-soil composite under actual working conditions. A general standard setting module is used to improve the KC equation by introducing velocity correction factors and tortuosity correction factors. Based on the improved KC equation, a general formula for calculating the equivalent permeability coefficient of pile-soil composite is obtained. The equivalent permeability coefficient of pile-soil composite includes the horizontal equivalent permeability coefficient and the vertical equivalent permeability coefficient of pile-soil composite. The correction module is used to determine the horizontal correction factor and vertical correction factor corresponding to the pile-soil composite based on the geometric configuration parameters and hydrogeological parameters. The horizontal correction factor and vertical correction factor are determined based on the improved KC equation to reflect the head loss caused by groundwater seepage through the pile-soil composite. The coefficient determination module is used to substitute the horizontal correction factor into the general formula to obtain the horizontal equivalent permeability coefficient of the pile-soil composite; and to substitute the vertical correction factor into the general formula to obtain the vertical equivalent permeability coefficient of the pile-soil composite.

[0017] According to the third aspect of this application, the method for determining the equivalent permeability coefficient of pile-soil composite based on the improved KC equation provided in the first aspect of this application is applied to seepage analysis, consolidation settlement calculation, anti-buoyancy safety evaluation, and seepage prevention safety evaluation under actual engineering conditions.

[0018] This application provides a method for determining the equivalent permeability coefficient of pile-soil composites based on an improved KC equation. The method improves the KC equation by using a correction factor to obtain the equivalent permeability coefficient of pile-soil composites. This correction factor can comprehensively reflect the additional head loss caused by groundwater seepage through the pile-soil composite. It takes into account the influence of the geometric configuration parameters and hydrogeological parameters of the pile-soil composite under different working conditions. Therefore, it can obtain the equivalent permeability coefficient of pile-soil composites that accurately matches different geometric configurations.

[0019] Other technical effects resulting from the additional features will be further illustrated in the corresponding embodiments. Attached Figure Description

[0020] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart of a method for determining the equivalent permeability coefficient of a pile-soil composite in one embodiment of this application; Figure 2 This is a flowchart of a method for calculating the equivalent permeability coefficient of a pile-soil composite in one embodiment of this application; Figure 3 This is a schematic diagram of a pile-soil composite material according to an embodiment of this application; Figure 4 This is a schematic diagram of a pile arrangement according to an embodiment of the present application, wherein (a) is a schematic diagram of multiple rows of rectangular piles, (b) is a schematic diagram of multiple rows of staggered piles, and (c) is a schematic diagram of a single row of piles. Figure 5 This is a schematic diagram of seepage in a pile-soil composite material according to an embodiment of this application.

[0021] Figure 6 This is a schematic diagram of a system for determining the equivalent permeability coefficient of a pile-soil composite in one embodiment of this application. Detailed Implementation

[0022] The present application will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present application, and these all fall within the protection scope of the present application. Parts not described in detail in the following embodiments can be implemented using existing technology.

[0023] It should be noted that all information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of related data must comply with relevant regulations.

[0024] Pile-soil composites are widely used in soft soil foundation reinforcement, seepage prevention and drainage design of dams and hydraulic structures. Their equivalent permeability coefficient is a core parameter for seepage analysis, consolidation settlement calculation, anti-buoyancy safety evaluation, and seepage prevention safety evaluation. In large-scale projects, it is difficult to accurately simulate each pile individually. Therefore, the pile-soil composite is usually simulated as an equivalent homogeneous material. Thus, how to accurately and easily obtain the equivalent permeability coefficient of this hypothetical equivalent homogeneous material directly determines the accuracy of seepage analysis and the reliability of engineering safety. Existing methods for calculating the equivalent permeability coefficient of pile-soil composites lack explicit quantification mechanisms for flow bypass effects and seepage path tortuosity. They do not consider head loss caused by changes in seepage velocity when seepage bypasses the pile, making it difficult to directly extend to different geometric configurations and accurately obtain the equivalent permeability coefficient of the pile-soil composite. Based on the above problems, this application provides a method for determining the equivalent permeability coefficient of pile-soil composites based on an improved KC equation to solve the aforementioned problems.

[0025] Reference Figure 1 As shown in the embodiments of this application, a method for determining the equivalent permeability coefficient of a pile-soil composite based on an improved KC equation is provided, including: M1. Obtain the geometric configuration parameters and hydrogeological parameters of the pile-soil composite under actual working conditions; M2. The KC equation is improved by introducing velocity correction factor and tortuosity correction factor. Based on the improved KC equation, a general formula for calculating the equivalent permeability coefficient of pile-soil composite is obtained. The equivalent permeability coefficient of pile-soil composite includes the horizontal equivalent permeability coefficient and the vertical equivalent permeability coefficient of pile-soil composite. M3. Based on geometric configuration parameters and hydrogeological parameters, determine the horizontal and vertical correction factors corresponding to the pile-soil composite. The horizontal and vertical correction factors are determined based on the velocity correction factor and tortuosity correction factor in the improved KC equation to reflect the head loss caused by groundwater seepage through the pile-soil composite. M4. Substitute the horizontal correction factor into the general formula to obtain the horizontal equivalent permeability coefficient of the pile-soil composite; substitute the vertical correction factor into the general formula to obtain the vertical equivalent permeability coefficient of the pile-soil composite.

[0026] It should be noted that the equivalent permeability coefficient of the pile-soil composite can provide a quantitative basis for seepage analysis, consolidation settlement calculation, anti-buoyancy safety evaluation, and seepage prevention safety evaluation under actual working conditions.

[0027] In the above embodiments of this application, the KC equation is improved by a correction factor to obtain the equivalent permeability coefficient of the pile-soil composite. This correction factor can comprehensively reflect the additional head loss caused by groundwater seepage through the pile-soil composite. It takes into account the influence of the geometric configuration parameters and hydrogeological parameters of the pile-soil composite under different working conditions. Therefore, the equivalent permeability coefficient of the pile-soil composite that accurately matches different geometric configurations can be obtained.

[0028] In some specific embodiments of this application, the geometric configuration parameters include the length, width, number of piles, number of pile rows, shape of piles, pile diameter, center-to-center spacing of piles, and pile arrangement; the pile arrangement includes at least one of multiple rows of rectangular piles, multiple rows of staggered piles, and single row of piles; the hydrogeological parameters include the horizontal permeability coefficient and vertical permeability coefficient of the soil around the piles, wherein the horizontal permeability coefficient is the permeability coefficient in the horizontal seepage direction, and the vertical permeability coefficient is the permeability coefficient in the seepage direction perpendicular to the horizontal plane where the horizontal seepage direction is located.

[0029] For example, the length of the pile-soil composite L D The length of the pile-soil composite along the horizontal seepage direction (i.e., the X-axis direction); the width of the pile-soil composite. W This refers to the width of the pile-soil composite material on a horizontal plane along the direction perpendicular to the horizontal seepage direction (i.e., the Y-axis direction). Number of pile rows. m This refers to the number of rows of piles arranged along the horizontal seepage direction on a horizontal plane. Pile shapes include circular and square. Based on their cross-sectional shape, piles can be classified as round piles and square piles; round piles have a circular cross-section, and square piles have a square cross-section. Pile diameter. D For round piles, the value is the pile diameter; for square piles, it is the pile side length. Pile center-to-center spacing. L p This represents the center-to-center distance between adjacent piles in each pile row. The pile arrangement is based on the center-to-center distance between piles. L p A constant and regularly arranged pile layout, specifically determined by the number of pile rows and the planar arrangement of the piles; pile layout methods include multi-row rectangular pile layout, multi-row staggered pile layout, and single-row pile layout. Among these, multi-row rectangular pile layout refers to the number of pile rows... m A pile arrangement with a value greater than 1 and the piles arranged in a rectangular pattern on the horizontal plane; multi-row staggered pile arrangement refers to the number of pile rows. m A pile arrangement with a value greater than 1 and staggered piles on the horizontal plane; a single-row pile arrangement refers to the number of pile rows. m A pile arrangement with a value of 1.

[0030] The horizontal permeability coefficient is the permeability coefficient in the horizontal seepage direction; the vertical permeability coefficient is the permeability coefficient in the seepage direction perpendicular to the horizontal plane (i.e., the vertical seepage direction, along the Z-axis). A pile-soil composite refers to an artificial foundation in which piles of a certain stiffness and strength are installed in the natural ground, and the piles and the surrounding soil jointly bear the load from the superstructure and coordinate deformation. In a pile-soil composite, all piles have the same shape and diameter.

[0031] In some specific embodiments of this application, the general formula for calculating the equivalent permeability coefficient of the pile-soil composite is as follows: in, Indicates the equivalent permeability coefficient of the pile-soil composite. Indicates the correction factor. This represents the permeability coefficient of the soil surrounding the pile. Indicates the speed correction factor. Indicates the tortuosity correction factor; The correction factors include horizontal and vertical correction factors. The permeability coefficient of the pile-soil mixture includes both horizontal and vertical permeability coefficients. The velocity correction factors include both horizontal and vertical velocity correction factors. The tortuosity correction factors include both horizontal and vertical tortuosity correction factors. When obtaining the horizontal equivalent permeability coefficient of the pile-soil composite, the horizontal correction factors, the horizontal permeability coefficient of the pile-soil mixture, the horizontal velocity correction factor, and the horizontal tortuosity correction factor are substituted into the general formula. When obtaining the vertical equivalent permeability coefficient of the pile-soil composite, the vertical correction factors, the vertical permeability coefficient of the pile-soil mixture, the vertical velocity correction factor, and the vertical tortuosity correction factor are substituted into the general formula.

[0032] For example, in step M2, the general formula for calculating the equivalent permeability coefficient of the pile-soil composite is determined based on the improved KC equation. The improved KC equation is derived by introducing a velocity correction factor and a tortuosity correction factor. The expression of the improved KC equation is as follows: In the formula, Indicates head loss, v 0 represents the seepage velocity at the endpoint of the calculation range; K The permeability coefficient of the soil surrounding the pile; v The seepage velocity at a certain calculation point on the seepage path; L The length of the seepage straight path (i.e., the line connecting the endpoint to the calculation point); L R This is the length of the seepage path from the endpoint to the calculation point; L mThe length of the pile-soil composite along the straight path of seepage; V R This is a speed correction factor; T R This is a tortuosity correction factor; K' is the equivalent permeability coefficient of the pile-soil composite.

[0033] Specifically, speed correction factor V R In the improved KC equation, it is defined as v / v The average value of the integral over the straight seepage path. Tortuosity correction factor. T R The improved KC equation is defined as L R / L The average value of the integral along the straight path of seepage. Permeability coefficient of the soil surrounding the pile. K Including the horizontal permeability coefficient of the soil around the pile K h Vertical permeability coefficient of the soil around the pile K v Velocity correction factor V R This reflects the additional head loss caused by changes in seepage velocity when groundwater flows through the pile-soil composite structure. Velocity correction factor. V R Including horizontal velocity correction factor V R,h and vertical velocity correction factor V R,v The horizontal velocity correction factor and vertical velocity correction factor represent the velocity correction factors for horizontal and vertical seepage, respectively. Tortuosity correction factor. T R This reflects the additional head loss caused by changes in the seepage path when groundwater seeps through the pile-soil composite. Tortuousness correction factor. T R Including horizontal tortuosity correction factor T R,h and vertical tortuosity correction factor T R,v The horizontal tortuosity correction factor and the vertical tortuosity correction factor represent the tortuosity correction factors for horizontal and vertical seepage, respectively. The equivalent permeability coefficient of the pile-soil composite is... K' Including the horizontal equivalent permeability coefficient of pile-soil composite K' h Vertical equivalent permeability coefficient of pile-soil compositeK' v The general formula for the equivalent permeability coefficient of pile-soil composites is obtained based on the head loss of groundwater seeping through the pile-soil composite.

[0034] Specifically, the horizontal velocity correction factor and the horizontal tortuosity correction factor correspond to the horizontal correction factor and the horizontal permeability coefficient of the soil around the pile, and are used to calculate the horizontal equivalent permeability coefficient of the pile-soil composite. The vertical velocity correction factor and the vertical tortuosity correction factor correspond to the vertical correction factor and the vertical permeability coefficient of the soil around the pile, and are used to calculate the vertical equivalent permeability coefficient of the pile-soil composite.

[0035] In some specific embodiments of this application, for multi-row rectangular pile layouts, a horizontal correction factor corresponding to the pile-soil composite is obtained based on geometric configuration parameters and hydrogeological parameters. The horizontal correction factor is derived based on the definitions of the velocity correction factor and tortuosity correction factor in the improved KC equation, and its expression is as follows: in, This is a horizontal correction factor; This is a horizontal velocity correction factor; This is a horizontal tortuosity correction factor; The width of the pile-soil composite; The length of the pile-soil composite, For pile-soil composite pile cross-section shape factor; This represents the total number of piles in the pile-soil composite structure. Pile diameter; This is the pile perimeter coefficient; , , , , All are given regression coefficients.

[0036] For example, in step M3, the horizontal correction factor R H Determined based on the pile arrangement method.

[0037] For multi-row rectangular pile layout, the horizontal correction factor R H Based on correction factor R The general formula, based on the horizontal velocity correction factor V R,h and horizontal tortuosity correction factor T R,h Sure.

[0038] Horizontal velocity correction factorV R,h The expression is: In the formula, W The width of the pile-soil composite; B From the perspective of pile cross-section shape factor, pile cross-section shape factor B Determined based on the shape of the pile: For round piles B Pick For square piles, B Take 1. N This represents the total number of piles in the pile-soil composite structure. D Pile diameter; s 1. a 1 is the regression coefficient, taken as... s 1 = 1.0, a 1 = 1.0.

[0039] Horizontal tortuosity correction factor T R,h The expression is: In the formula, A This refers to the pile perimeter coefficient. A Determined based on the shape of the pile: For round piles A Pick For square piles, A Choose 4. s 2. a 2. b Let be the regression coefficient, and take . s 2 = 0.9988 a 2 = 0.8221, b= -0.0265.

[0040] For multi-row rectangular pile layout, the horizontal correction factor R H Calculate using the following formula: In the formula, s , a t Let be the regression coefficient, and have s=s 1 s 2; a t =a 1+ a 2.

[0041] In some specific embodiments of this application, for multi-row staggered pile arrangement, the horizontal correction factor corresponding to the pile-soil composite is obtained based on geometric configuration parameters and hydrogeological parameters; the expression of the horizontal correction factor is derived according to the definitions of velocity correction factor and tortuosity correction factor in the improved KC equation as follows: in, This is a horizontal correction factor; To account for the additional head loss caused by the multi-row staggered pile arrangement ( V R,h T R,h ) -1 distributed,( V R,h T R,h ) -1 Dimensionless flow velocity correction factor V R,h T R,h The reciprocal of the dimensionless velocity correction factor V R,h T R,h In For horizontal velocity correction factor, This is a horizontal tortuosity correction factor. The width of the pile-soil composite. This refers to the number of piles in the row with the fewest piles in the pile-soil composite structure. L p This represents the center-to-center spacing of the piles.

[0042] For example, for multi-row staggered pile layout, the horizontal correction factor R H Calculate using the following formula: In the formula, VT E,c To account for the additional head loss due to staggered pile placement ( V R,h T R,h ) -1 Distribution, represented as: In the formula, L p This represents the center-to-center spacing of the piles.

[0043] In some specific embodiments of this application, for single-row pile arrangement, the horizontal correction factor corresponding to the pile-soil composite is obtained based on geometric configuration parameters and hydrogeological parameters; the expression of the horizontal correction factor is derived according to the definitions of velocity correction factor and tortuosity correction factor in the improved KC equation, wherein: like > If the value is 0.800, then the expression for the level correction factor is as follows: In the formula, This is a horizontal correction factor; This is a horizontal velocity correction factor; This is a horizontal tortuosity correction factor; The width of the pile-soil composite; The length of the pile-soil composite, For pile-soil composite pile cross-section shape factor; This represents the total number of piles in the pile-soil composite structure. Pile diameter; This is the pile perimeter coefficient; , , , , All are given regression coefficients; like ≤ If the value is 0.800, then the expression for the level correction factor is as follows: In the formula, VT For local simplification ( V R,h T R,h ) -1 distributed, L p The center-to-center spacing of the piles r The distance from the target point to a certain pile is along the width of the pile-soil composite.

[0044] For example, for a single row of piles, when ( V R,h T R,h ) -1 > At 0.800, the horizontal correction factor RH The calculation method is the same as for multi-row rectangular pile layout. For single-row pile layout, when ( V R,h T R,h ) -1 ≤ At 0.800, the horizontal correction factor R H Calculate using the following formula: in, VT For local simplification ( V R,h T R,h ) -1 The distribution is expressed as follows: In the formula, r The distance from the target point to a certain pile is along the width of the pile-soil composite.

[0045] In some specific embodiments of this application, the vertical correction factor is obtained based on geometric configuration parameters and hydrogeological parameters. The expression for the vertical correction factor is derived based on the definitions of the velocity correction factor and tortuosity correction factor in the improved KC equation as follows: in, This is the vertical correction factor; This is the vertical velocity correction factor; This is the vertical tortuosity correction factor; The width of the pile-soil composite; The length of the pile-soil composite, For pile-soil composite pile cross-section shape factor; This represents the total number of piles in the pile-soil composite structure. This refers to the pile diameter.

[0046] For example, in step M3, the vertical correction factor R V Based on correction factor R The general formula, based on the vertical velocity correction factor V R,v and vertical tortuosity correction factor T R,v Sure.

[0047] Vertical velocity correction factor V R,v The velocity correction factor for vertical seepage is expressed as follows: Vertical curvature correction factor T R,v This is the tortuosity correction factor for vertical seepage, and its value is approximately 1.0.

[0048] Therefore, the vertical correction factor R V The expression is as follows: In some specific embodiments of this application, the expression for the horizontal equivalent permeability coefficient of the pile-soil composite is as follows: in, The horizontal equivalent permeability coefficient of the pile-soil composite is given. As a level correction factor, It is the horizontal equivalent permeability coefficient of the soil around the pile.

[0049] For example, in step M4, the horizontal equivalent permeability coefficient of the pile-soil composite is... K' h Based on the general formula for the equivalent permeability coefficient of pile-soil composites, and according to the horizontal correction factor... R H and the horizontal permeability coefficient of the soil around the pile K h The calculation is expressed as: In the formula, the level correction factor R H The arrangement of the piles is determined according to step M3.

[0050] In some specific embodiments of this application, the expression for the vertical equivalent permeability coefficient of the pile-soil composite is as follows: in, Let be the vertical equivalent permeability coefficient of the pile-soil composite. This is the vertical correction factor. is the vertical equivalent permeability coefficient of the soil around the pile.

[0051] For example, in step M4, the vertical equivalent permeability coefficient of the pile-soil composite is... K' v Based on the general formula for the equivalent permeability coefficient of pile-soil composites, and according to the vertical correction factor... R V Vertical permeability coefficient of the soil around the pile K v The calculation is expressed as: In the formula, the vertical correction factor R V Determine according to step M3.

[0052] Due to the presence of piles in the soil, there are differences in seepage velocity and tortuous seepage paths. This application improves the KC equation by comprehensively considering the influence of seepage velocity and seepage path by using a correction factor. This quantifies the influence of seepage velocity and seepage path changes on the permeability coefficient, thereby obtaining a method for calculating the equivalent permeability coefficient of pile-soil composites that can take into account the geometric configuration of the pile-soil composite.

[0053] The embodiments described above in this application improve the KC equation to obtain the equivalent permeability coefficient of the pile-soil composite by using a correction factor. This correction factor comprehensively reflects the additional head loss caused by changes in seepage velocity and seepage path when groundwater seeps through the pile-soil composite, thereby quantifying the impact of seepage velocity and seepage path changes on the permeability coefficient. The equivalent permeability coefficient of the pile-soil composite based on the improved KC equation takes into account the geometric configuration of the pile-soil composite, making the obtained equivalent permeability coefficient of the pile-soil composite more accurate and consistent with actual working conditions.

[0054] The present application will be further described below with reference to specific embodiments in order to better understand the above technical solutions of the present application. It should be understood that the following are only some examples and are not intended to limit the present application.

[0055] Example 1: A method for calculating the equivalent permeability coefficient of pile-soil composites based on an improved KC equation is proposed. The implementation steps are as follows: Figure 2 As shown, it specifically includes: Step S1: Obtain the geometric configuration parameters and hydrogeological parameters of the pile-soil composite material based on the actual working conditions.

[0056] like Figure 3 As shown, the geometric configuration parameters of the pile-soil composite include the length of the pile-soil composite. L D = 2000cm, width W= 1200cm, number of pile rows m =6. Total number of piles N =30. The number of piles in a single row is 5. N′ =5. The length of the pile-soil composite is along the horizontal seepage direction. x The length of the direction; the width of the pile-soil composite is perpendicular to the horizontal seepage direction on the horizontal plane. y Width in the direction. The pile is round, with a diameter of... D= 50cm. Pile arrangement methods include, for example... Figure 4 The multiple rows of rectangular piles shown in (a) are as follows: Figure 4 The multi-row staggered pile arrangement shown in (b) and Figure 4 The single-row pile arrangement shown in (c) of this embodiment. m A pile spacing greater than 1, with piles staggered in the plane, constitutes a multi-row staggered pile arrangement. (Pile center-to-center spacing) L p It is 100cm.

[0057] Hydrogeological parameters include the soil around the pile. x Horizontal permeability coefficient in the direction K h = 1×10 -3 cm / s and z Vertical permeability coefficient in the direction K v = 1×10 -3 cm / s.

[0058] Step S2: Determine the general formula for the equivalent permeability coefficient of the pile-soil composite.

[0059] In step S2, the equivalent permeability coefficient of the pile-soil composite is... K' Based on the permeability coefficient of the soil around the pile K and correction factor R Confirmed. Figure 5 As shown, the permeability coefficient of the soil around the pile K include x Horizontal permeability coefficient of soil around pile in the direction K h and z Vertical permeability coefficient of the soil around the pile in the direction of the pile K v Equivalent permeability coefficient of pile-soil composite K' include x Horizontal equivalent permeability coefficient of pile-soil composite in the direction K' h and z Vertical equivalent permeability coefficient of pile-soil composite in the direction of the direction K' v .

[0060] Step S3: Determine the level correction factor R H .

[0061] Specifically, in step S3, the horizontal correction factor R H Determined based on the pile arrangement. For Figure 4 The multi-row staggered pile arrangement shown in (b) has a horizontal correction factor. R H Based on horizontal velocity correction factor V R,h and horizontal tortuosity correction factorT R,h Determined, and taking into account the additional head loss due to staggered pile placement ( V R,h T R,h ) -1 Distribution. Pile perimeter coefficient A and pile cross-section shape factor B Determined based on the shape of the pile. For circular piles, the pile perimeter coefficient... A= Pile cross-section shape factor B= .

[0062] Horizontal velocity correction factor V R,h for: Horizontal tortuosity correction factor T R,h for: Considering the additional head loss due to staggered pile placement ( V R,h T R,h ) -1 distributed VT E,c for: Horizontal correction factor R H for: Step S4: Calculate the horizontal equivalent permeability coefficient of the pile-soil composite.

[0063] Specifically, in step S4, the horizontal equivalent permeability coefficient of the pile-soil composite is... K' h for: Step S5: Determine the vertical correction factor R V .

[0064] Specifically, in step S5, the vertical correction factor... R V Based on the vertical velocity correction factor V R,v and vertical tortuosity correction factor T R,v Sure.

[0065] Vertical velocity correction factor VR,v for: Vertical curvature correction factor T R,v We approximate it to 1.0.

[0066] Vertical correction factor R V for: Step S6: Calculate the vertical equivalent permeability coefficient of the pile-soil composite.

[0067] Specifically, in step S6, the vertical equivalent permeability coefficient of the pile-soil composite is... K' v for In this embodiment, the horizontal equivalent permeability coefficient of the pile-soil composite is... K' h and vertical equivalent permeability coefficient K' v The horizontal equivalent permeability coefficients of the soil surrounding the piles are respectively less than those of the soil surrounding the piles. K h and vertical equivalent permeability coefficient K v This indicates that the presence of the piles has a certain water-blocking effect on both horizontal and vertical seepage. K' h Comparison K h A decrease of approximately 10.26%. K' v Comparison K v The permeability decreased by approximately 2.46%, with a more significant water-blocking effect in the horizontal seepage direction. The measured horizontal equivalent permeability coefficient for this condition was 0.91 × 10⁻⁶. -3 cm / s, the horizontal equivalent permeability coefficient obtained through this application K' h The error between the measured result and the actual result is 1.385%; the measured vertical equivalent permeability coefficient for this working condition is 0.96 × 10⁻⁶. -3 cm / s, the vertical equivalent permeability coefficient obtained through this application K' v The error between the measured results and the actual results was 1.604%, which verifies the feasibility of this application.

[0068] The equivalent permeability coefficient of the pile-soil composite obtained by the method of this application can be applied to seepage analysis, consolidation settlement calculation, anti-buoyancy safety evaluation, and seepage prevention safety evaluation in actual engineering conditions.

[0069] The following examples will be used to further illustrate this application in order to better understand the above-mentioned technical solutions. It should be understood that the following are only some examples and are not intended to limit this application.

[0070] I. Application in seepage analysis: When conducting seepage analysis and calculations at construction sites such as foundation pits, it is not necessary to model each pile in the soil individually. Instead, the distribution area of ​​the pile group can be directly regarded as a pile-soil composite. The horizontal equivalent permeability coefficient and the vertical equivalent permeability coefficient are assigned according to the seepage direction. By combining the site boundary water level and other conditions, the steady-state or transient seepage field can be solved, and key results in seepage analysis such as the head distribution, seepage velocity, and hydraulic gradient of the entire site can be obtained.

[0071] II. Application in consolidation settlement calculation: When calculating the consolidation deformation of pile-reinforced foundations, the reinforced section of the pile is treated as an independent pile-soil composite. The vertical equivalent permeability coefficient is used as the vertical seepage control parameter of the pile-soil composite, and the horizontal equivalent permeability coefficient is used as the horizontal seepage control parameter of the pile-soil composite. Combined with the upper load conditions of the pile-soil composite, the pore water pressure and effective stress of the pile-soil composite at different time points are calculated, and then the settlement during construction, settlement after construction, and settlement stabilization time are estimated.

[0072] III. Application in anti-buoyancy safety evaluation: In the calculation of the anti-buoyancy of underground structures, the distribution area of ​​the anti-buoyancy piles at the base is equivalent to a pile-soil composite. After substituting the equivalent horizontal and vertical permeability coefficients, the seepage field is solved with the highest historical groundwater level of the site as the boundary condition. The total anti-buoyancy force is calculated by combining the self-weight of the structure, the overburden load, and the pull-out bearing capacity of the anti-buoyancy components. Finally, the anti-buoyancy safety factor is verified.

[0073] IV. Application in seepage prevention safety evaluation: For a pile-based seepage prevention system formed by mixing piles, it can be regarded as a pile-soil composite material. The horizontal equivalent permeability coefficient and the vertical equivalent permeability coefficient are assigned according to the seepage direction. By combining the thickness of the seepage prevention body and the most unfavorable head difference of the project, the total seepage flow through the pile-based seepage prevention system, the maximum hydraulic gradient at the inside and the outlet can be obtained. The seepage stability and seepage flow control requirements can then be verified.

[0074] Reference Figure 6 As shown, based on the same inventive concept, another embodiment of this application provides a system for determining the equivalent permeability coefficient of pile-soil composites based on the improved KC equation. The system 100 includes: The acquisition module 110 is used to acquire the geometric configuration parameters and hydrogeological parameters of the pile-soil composite under actual working conditions. The general standard setting module 120 is used to introduce velocity correction factors and tortuosity correction factors to improve the KC equation. Based on the improved KC equation, a general formula for calculating the equivalent permeability coefficient of pile-soil composite is obtained. The equivalent permeability coefficient of pile-soil composite includes the horizontal equivalent permeability coefficient and the vertical equivalent permeability coefficient of pile-soil composite. The correction module 130 is used to determine the horizontal correction factor and vertical correction factor corresponding to the pile-soil composite based on the geometric configuration parameters and hydrogeological parameters. The horizontal correction factor and vertical correction factor are determined based on the improved KC equation to reflect the head loss caused by groundwater seepage through the pile-soil composite. The coefficient determination module 140 is used to substitute the horizontal correction factor into the general formula to obtain the horizontal equivalent permeability coefficient of the pile-soil composite; and to substitute the vertical correction factor into the general formula to obtain the vertical equivalent permeability coefficient of the pile-soil composite. Based on the horizontal and vertical equivalent permeability coefficients, quantitative basis is provided for seepage analysis, consolidation settlement calculation, anti-buoyancy safety evaluation, and seepage prevention safety evaluation under actual working conditions.

[0075] It should be noted that the modules in the pile-soil composite equivalent permeability coefficient determination system based on the improved KC equation provided in the above embodiments of this application correspond to the steps of the pile-soil composite equivalent permeability coefficient determination method based on the improved KC equation in any of the above embodiments. Those skilled in the art can refer to the step features of the pile-soil composite equivalent permeability coefficient determination method based on the improved KC equation to implement the corresponding modules in the pile-soil composite equivalent permeability coefficient determination system based on the improved KC equation, which will not be elaborated here.

[0076] The preferred features in the above embodiments can be used individually in any embodiment, or in any combination thereof, provided they do not conflict with each other. Furthermore, parts not described in detail in the embodiments can be implemented using existing technologies.

[0077] The foregoing has described some specific embodiments of this application. It should be understood that this application is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the substantive content of this application. The above-described preferred features can be used in any combination without conflict.

Claims

1. A method for determining the equivalent permeability coefficient of a pile-soil composite based on an improved KC equation, characterized in that, include: Obtain the geometric configuration parameters and hydrogeological parameters of the pile-soil composite under actual working conditions; The KC equation is improved by introducing velocity correction factors and tortuosity correction factors. Based on the improved KC equation, a general formula for calculating the equivalent permeability coefficient of pile-soil composite is obtained. The equivalent permeability coefficient of pile-soil composite includes the horizontal equivalent permeability coefficient and the vertical equivalent permeability coefficient of pile-soil composite. Based on the geometric configuration parameters and hydrogeological parameters, the horizontal correction factor and vertical correction factor corresponding to the pile-soil composite are determined. The horizontal correction factor and vertical correction factor are determined based on the improved KC equation to reflect the head loss caused by groundwater seepage through the pile-soil composite. Substituting the horizontal correction factor into the general formula yields the horizontal equivalent permeability coefficient of the pile-soil composite; substituting the vertical correction factor into the general formula yields the vertical equivalent permeability coefficient of the pile-soil composite.

2. The method for determining the equivalent permeability coefficient of pile-soil composites based on the improved KC equation according to claim 1, characterized in that, The geometric configuration parameters include the length, width, number of piles, number of pile rows, shape, diameter, center-to-center spacing, and arrangement of the pile-soil composite. The pile arrangement method includes at least one of the following: multiple rows of rectangular piles, multiple rows of staggered piles, and single row of piles. The hydrogeological parameters include the horizontal permeability coefficient and the vertical permeability coefficient of the soil around the pile, wherein the horizontal permeability coefficient is the permeability coefficient in the horizontal seepage direction, and the vertical permeability coefficient is the permeability coefficient in the seepage direction perpendicular to the horizontal plane where the horizontal seepage direction is located.

3. The method for determining the equivalent permeability coefficient of pile-soil composites based on the improved KC equation according to claim 2, characterized in that, The general formula for calculating the equivalent permeability coefficient of the pile-soil composite is as follows: ； ； in, This represents the equivalent permeability coefficient of the pile-soil composite. Indicates the correction factor. This represents the permeability coefficient of the soil surrounding the pile. Indicates the speed correction factor. Indicates the tortuosity correction factor; The correction factors include horizontal and vertical correction factors; the permeability coefficient of the soil surrounding the pile includes the horizontal and vertical permeability coefficients of the soil surrounding the pile; the velocity correction factor includes horizontal and vertical velocity correction factors; the tortuosity correction factor includes horizontal and vertical tortuosity correction factors; when obtaining the horizontal equivalent permeability coefficient of the pile-soil composite, the horizontal correction factors, the horizontal permeability coefficient of the soil surrounding the pile, the horizontal velocity correction factor, and the horizontal tortuosity correction factor are substituted into the general formula; when obtaining the vertical equivalent permeability coefficient of the pile-soil composite, the vertical correction factors, the vertical permeability coefficient of the soil surrounding the pile, the vertical velocity correction factor, and the vertical tortuosity correction factor are substituted into the general formula.

4. The method for determining the equivalent permeability coefficient of pile-soil composites based on the improved KC equation according to claim 3, characterized in that, For the aforementioned multi-row rectangular pile arrangement, a horizontal correction factor corresponding to the pile-soil composite is obtained based on the geometric configuration parameters and hydrogeological parameters. This horizontal correction factor is determined based on the velocity correction factor and tortuosity correction factor in the improved KC equation, and its expression is as follows: ； ； ； in, This is a horizontal correction factor; This is a horizontal velocity correction factor; This is a horizontal tortuosity correction factor; The width of the pile-soil composite; The length of the pile-soil composite, For pile-soil composite pile cross-section shape factor; This represents the total number of piles in the pile-soil composite structure. Pile diameter; This is the pile perimeter coefficient; , , , , All are given regression coefficients.

5. The method for determining the equivalent permeability coefficient of pile-soil composites based on the improved KC equation according to claim 3, characterized in that, For the aforementioned multi-row staggered pile arrangement, a horizontal correction factor corresponding to the pile-soil composite is obtained based on the geometric configuration parameters and hydrogeological parameters. This horizontal correction factor is determined based on the velocity correction factor and tortuosity correction factor in the improved KC equation, and its expression is as follows: ； ； in, This is a horizontal correction factor; To account for the additional head loss caused by the multi-row staggered pile arrangement ( V R, h T R,h ) -1 distributed,( V R,h T R,h ) -1 Dimensionless flow velocity correction factor V R,h T R,h The reciprocal of the dimensionless velocity correction factor V R,h T R,h In This is a horizontal velocity correction factor. This is a horizontal tortuosity correction factor. The width of the pile-soil composite. This refers to the total number of piles in the single-row pile with the fewest piles in the pile-soil composite structure. L p This represents the center-to-center spacing of the piles.

6. The method for determining the equivalent permeability coefficient of pile-soil composites based on the improved KC equation according to claim 3, characterized in that, For the single-row pile arrangement, a horizontal correction factor corresponding to the pile-soil composite is obtained based on the geometric configuration parameters and hydrogeological parameters. The horizontal correction factor is determined based on the velocity correction factor and tortuosity correction factor in the improved KC equation, and its expression is as follows: like > If the value is 0.800, then the expression for the level correction factor is as follows: ； ； ； In the formula, This is a horizontal correction factor; This is a horizontal velocity correction factor; This is a horizontal tortuosity correction factor; The width of the pile-soil composite; The length of the pile-soil composite, For pile-soil composite pile cross-section shape factor; This represents the total number of piles in the pile-soil composite structure. Pile diameter; This is the pile perimeter coefficient; , , , , All are given regression coefficients; like ≤ If the value is 0.800, then the expression for the level correction factor is as follows: ； ； ； In the formula, VT For local simplification ( V R,h T R,h ) -1 distributed, L p The center-to-center spacing of the piles r The distance from the target point to a certain pile is along the width of the pile-soil composite.

7. The method for determining the equivalent permeability coefficient of pile-soil composites based on the improved KC equation according to claim 3, characterized in that, Based on the geometric configuration parameters and hydrogeological parameters, the vertical correction factor corresponding to the pile-soil composite is obtained. The vertical correction factor is determined based on the velocity correction factor and tortuosity correction factor in the improved KC equation, and its expression is as follows: ； ； in, This is the vertical correction factor; This is the vertical velocity correction factor; This is the vertical tortuosity correction factor; The width of the pile-soil composite; The length of the pile-soil composite, For pile-soil composite pile cross-section shape factor; This represents the total number of piles in the pile-soil composite structure. This refers to the pile diameter.

8. The method for determining the equivalent permeability coefficient of pile-soil composites based on the improved KC equation according to claim 3, characterized in that, The expression for the horizontal equivalent permeability coefficient of the pile-soil composite is as follows: ； in, The horizontal equivalent permeability coefficient of the pile-soil composite is given. As a level correction factor, The horizontal equivalent permeability coefficient of the soil around the pile; The expression for the vertical equivalent permeability coefficient of the pile-soil composite is as follows: ； in, Let be the vertical equivalent permeability coefficient of the pile-soil composite. This is the vertical correction factor. is the vertical equivalent permeability coefficient of the soil around the pile.

9. A system for determining the equivalent permeability coefficient of pile-soil composites based on an improved KC equation, characterized in that, include: The data acquisition module is used to obtain the geometric configuration parameters and hydrogeological parameters of the pile-soil composite under actual working conditions. A general standard setting module is used to improve the KC equation by introducing velocity correction factors and tortuosity correction factors. Based on the improved KC equation, a general formula for calculating the equivalent permeability coefficient of pile-soil composite is obtained. The equivalent permeability coefficient of pile-soil composite includes the horizontal equivalent permeability coefficient and the vertical equivalent permeability coefficient of pile-soil composite. The correction module is used to determine the horizontal correction factor and vertical correction factor corresponding to the pile-soil composite based on the geometric configuration parameters and hydrogeological parameters. The horizontal correction factor and vertical correction factor are determined based on the improved KC equation to reflect the head loss caused by groundwater seepage through the pile-soil composite. The coefficient determination module is used to substitute the horizontal correction factor into the general formula to obtain the horizontal equivalent permeability coefficient of the pile-soil composite; and to substitute the vertical correction factor into the general formula to obtain the vertical equivalent permeability coefficient of the pile-soil composite.

10. The application of the method for determining the equivalent permeability coefficient of pile-soil composite based on the improved KC equation as described in any one of claims 1-8 in seepage analysis, consolidation settlement calculation, anti-buoyancy safety evaluation, and seepage prevention safety evaluation under actual engineering conditions.

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