A modified "m" method of karst foundation considering the constraint degree of pile end

Abstract

The application discloses a karst foundation modified'm' method considering the constraint degree of a pile end, and solves the technical problems that the traditional'm' method cannot accurately quantify the constraint degree of the pile end and lacks scientific basis for m value selection in karst foundation pile foundation design. sim The method builds a finite element model of different combinations of the pile end rock entering depth h and the rock plate thickness t through parameterized numerical modeling, obtains an equivalent foundation proportionality coefficient m sim by numerical simulation and inversion analysis, establishes a quantitative relationship between the constraint coefficient beta and h and t, finally obtains the beta value according to the actual geological parameters and calculates the modified m* = beta x m, which is used for checking the horizontal bearing capacity and deformation of the pile foundation. The application has high precision, clear mechanism, high economic efficiency and wide applicability, fills the gap in the current specification in the karst geological pile foundation design, and realizes the unity of the economy and reliability of the karst area pile foundation design.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering, specifically relating to a method for calculating the horizontal bearing capacity of pile foundations in karst soil, and more particularly to a modified "m" method that considers the degree of pile end constraint and dynamically corrects the traditional "m" method foundation proportional coefficient m. Background Technology

[0002] When designing pile foundations in karst areas, the geological conditions of the bearing stratum at the pile tip are complex and varied, with significant differences in the depth of pile penetration into the rock and the thickness of the underlying rock slab. The constraint effect of the rock stratum at the pile tip has a significant impact on the horizontal bearing characteristics of the pile foundation. The traditional "m" method is a commonly used method in engineering to calculate the internal forces and deformations of horizontally loaded piles. Its core parameter, the foundation proportion coefficient m, is usually selected based on the assumption of uniform soil layers or linear variation, which cannot truly reflect the dynamic changes in the constraint effect at the pile tip in karst areas.

[0003] In current engineering practice, for karst foundations where pile tips are embedded in rock strata, the value of m is often roughly selected based on engineering experience, or an overly conservative design strategy is adopted. If the m value is too small, the pile foundation design will be too risky, leading to structural safety hazards; if the m value is excessively increased for a conservative design, it will result in waste of pile foundation materials and a significant increase in project costs. Existing technology cannot scientifically quantify the comprehensive impact of pile tip embedment depth and rock slab thickness on the degree of pile tip restraint, nor has it established a quantitative correction relationship between the degree of pile tip restraint and the m value. Current standards also lack supplementary methods for pile foundation design that address the variable pile tip restraint conditions in karst geological conditions, making it difficult to balance the accuracy, economy, and reliability of pile foundation design in karst areas.

[0004] Therefore, there is an urgent need to develop a calculation method that can accurately quantify the degree of pile end constraint and scientifically correct the m value accordingly, so as to make up for the shortcomings of existing technologies and provide reliable technical support for the design of pile foundations in karst soil. Summary of the Invention

[0005] The purpose of this invention is to provide a modified "m" method for karst foundations that considers the degree of pile end constraint, solving the technical problems of unscientific selection of m value, inability to quantify the impact of pile end constraint, and difficulty in balancing design economy and reliability in the traditional "m" method for karst foundation pile design, and achieving accurate calculation of the horizontal bearing capacity of pile foundations in karst areas.

[0006] To achieve the above objectives, this invention provides a modified "m" method for karst foundations considering the degree of pile end restraint, comprising the following steps: Step S1: Based on the geological background of the target engineering area, establish a series of three-dimensional pile-soil-rock refined finite element models covering different combinations of pile tip rock penetration depth h and stable rock plate thickness t below the pile tip; Step S2: Perform numerical simulations of each 3D pile-soil-rock refined finite element model under horizontal loads. Through inversion analysis, obtain the equivalent foundation scale factor m that best matches the simulation results. sim ; Step S3: Based on the equivalent foundation ratio coefficient m sim Calculate the constraint coefficient β=m based on the standard reference value m. sim / m, and establish a quantitative relationship between the pile tip rock penetration depth h, the rock plate thickness t and the constraint coefficient β; Step S4: In actual engineering design, based on the actual pile tip rock penetration depth h and rock slab thickness t at the actual pile location, obtain the corresponding constraint coefficient β based on the quantitative relationship, calculate the corrected foundation proportion coefficient design value m* = β × m, and use the corrected foundation proportion coefficient design value m* to verify the horizontal bearing capacity and deformation of the pile foundation.

[0007] Furthermore, in step S1, the three-dimensional pile-soil-rock refined finite element model includes pile body elements, pile surrounding soil elements, and pile end rock layer elements. A pile-rock contact surface element is provided between the pile body elements and the pile end rock layer elements. The pile-rock contact surface element is configured to simulate slippage and separation behavior.

[0008] Furthermore, in step S2, the inversion analysis specifically includes: using the pile horizontal displacement curve obtained from numerical simulation as the target, iterative fitting is performed using the traditional "m" method theory until the error between the theoretically calculated curve and the numerically simulated curve is less than a preset threshold. The m value used at this time is the equivalent foundation scaling factor m. sim .

[0009] Furthermore, in step S1, the rock mass and soil mass in the three-dimensional pile-soil-rock refined finite element model are simulated using a Mohr-Coulomb constitutive model or a hardened soil constitutive model, and the material parameters are assigned values ​​according to the geological survey report.

[0010] Furthermore, in step S3, the quantitative relationship is an empirical formula, which is established by multiple regression analysis and has the form β = a + b·ln(h) + c·ln(t), where a, b, and c are regression coefficients, h is the depth of the pile tip into the rock, and t is the thickness of the rock slab, in meters. The formula is determined by fitting the numerical simulation results of the series of three-dimensional pile-soil-rock refined finite element models.

[0011] Furthermore, in step S3, the quantitative relationship is a lookup table, which contains the constraint coefficient β values ​​corresponding to different combinations of pile tip rock penetration depth h and rock slab thickness t.

[0012] Furthermore, in step S1, in the series of three-dimensional pile-soil-rock refined finite element models covering different combinations of pile tip rock penetration depth h and rock slab thickness t, the value range of pile tip rock penetration depth h is 0.5m to 2.0m, and the value range of rock slab thickness t is 2m to 5m.

[0013] Furthermore, the method also includes step S5: integrating the quantitative relationship between the constraint coefficient β, the pile tip rock penetration depth h and the rock slab thickness t into the pile foundation design software or calculation table, for direct querying or automatic calculation of the corrected foundation proportion coefficient design value m*.

[0014] Furthermore, the method is applicable to pile foundation projects in karst-developed areas where the pile tip is embedded in rock strata and there is a stable rock slab below the pile tip, wherein the stable rock slab is a complete or substantially complete limestone, dolomite, or sandstone slab.

[0015] Furthermore, in step S2, the numerical simulation under horizontal load includes applying multiple levels of horizontal loads to the top of the model pile, obtaining the horizontal displacement curves and internal force distributions of the pile body under each level of horizontal load, which are used as the equivalent foundation scaling factor m under different load levels. sim Inversion analysis.

[0016] The beneficial effects of this invention are: This invention utilizes a refined three-dimensional pile-soil-rock finite element model to realistically reproduce the complex pile-soil-rock interaction mechanism in karst areas. It accurately captures changes in pile end constraint caused by variations in pile tip penetration depth and rock slab thickness, providing a solid mechanical basis for the correction of the m-value. The calculation results better reflect the actual engineering conditions of karst foundations, effectively improving the accuracy of pile foundation design. It eliminates the need for time-consuming, labor-intensive, and costly on-site pile foundation horizontal load tests; the required parameters for correction can be obtained through numerical simulation, significantly reducing data acquisition costs and design cycles. This method is suitable for the early design stages of projects and for karst area projects lacking detailed experimental data. It is effectively adaptable to the simulation analysis of complex karst geological conditions such as inclined rock surfaces, caves, and uneven rock slab thickness. The numerical simulation process exhibits good repeatability and controllability, facilitating parameter sensitivity analysis of pile tip penetration depth and rock slab thickness, as well as comparative optimization of different pile foundation design schemes, providing a reliable and transparent scientific basis for design decisions. This paper addresses the design problems of pile foundations in karst geology, where pile end constraints are highly variable and not adequately considered in current geotechnical engineering codes. It provides a systematic and scientific method and design tool for correcting the m-value, filling a gap in the codes and offering significant technical support for pile foundation design in karst areas. By scientifically quantifying the degree of pile end constraint, the method achieves dynamic correction of the m-value, avoiding design risks or overly conservative approaches caused by empirical values. While ensuring the safety and reliability of the pile foundation structure, it effectively reduces material waste and lowers project costs, achieving a balance between economy and reliability in pile foundation design in karst areas. Attached Figure Description

[0017] Figure 1 Schematic diagram of pile tip embedded in rock strata.

[0018] Figure 2 A typical schematic diagram of a three-dimensional finite element numerical model. Detailed Implementation

[0019] The technical solution of the present invention will be further described in detail below with reference to specific embodiments. These embodiments are only used to explain the present invention and are not intended to limit the scope of protection of the present invention.

[0020] The specific implementation steps of this invention are as follows: (1) Determination of geological parameters and selection of benchmark m value: A detailed geological survey was conducted at the pile location to accurately determine the pile tip penetration depth h and the thickness t of the stable rock slab below the pile tip. Simultaneously, based on the lithology of the surrounding soil and rock, the benchmark foundation ratio m was determined according to current specifications.

[0021] (2) Establish a three-dimensional finite element numerical model: Using general-purpose finite element software, such as ABAQUS, MIDAS GTS NX, or PLAXIS 3D, a three-dimensional numerical model including piles, soil, and rock strata is established. Figure 1 and Figure 2 As shown. The model should appropriately set the pile-rock contact surface to simulate possible slippage and separation. Appropriate constitutive models are used to simulate the rock and soil masses, and material parameters are assigned based on the geological survey report.

[0022] (3) Parametric analysis and numerical simulation: Different rock penetration depths h (e.g., 0.5m, 1.0m, 1.5m, 2.0m) and rock slab thicknesses t (e.g., 2m, 3m, 4m, 5m) are systematically set to form a series of analysis conditions. For each (h,t) combination condition, a horizontal load is applied to the top of the model pile, and static calculations are performed to accurately obtain the horizontal displacement curve and internal force distribution of the pile body.

[0023] (4) Inversion calculation of constraint coefficient β: Inverse analysis is performed on the simulation results for each working condition in step (3). Taking the horizontal displacement curve of the pile body obtained from the numerical simulation as the target, the traditional "m" method theory is used for iterative fitting until the theoretical calculation curve and the numerical simulation curve are most consistent. The m value used at this time is the equivalent foundation ratio coefficient m under this working condition. sim Subsequently, using the formula β=m sim / m, the pile end constraint coefficient β under this geological condition is calculated.

[0024] (5) Construct a β database or empirical formula: The calculated β values ​​for all working conditions are compiled into a lookup table of pile end constraint coefficient β based on their corresponding h and t. To further facilitate engineering applications, multiple regression analysis can be used to express β as a continuous function of h and t. For example, through multiple regression analysis, an empirical formula of the form β = a + b * ln(h) + c * ln(t) can be established, where a, b, and c are regression coefficients that need to be determined based on numerical simulation results. This formula can be directly integrated into design software or calculation tables.

[0025] (6) Engineering design and verification: In actual engineering design, based on the h and t values ​​of the specific pile location, the β value is calculated by referring to the β table generated in step (5) or by substituting it into the empirical formula. Then, the corrected foundation proportion coefficient design value m*=β×m is calculated. Finally, the m* value is used to verify the horizontal bearing capacity and deformation of the pile foundation, and the pile reinforcement and size design are completed.

[0026] Taking a bridge pile foundation project in a karst-developed area as an example, the modified "m" method of this invention is used to design the horizontal bearing capacity of the pile foundation. The pile foundation is designed with a diameter of 1.5m and a length of 25m, with the pile tip embedded in a limestone layer. The specific implementation steps are as follows: Geological parameter determination and selection of benchmark m value Drilling was conducted at the pile location, and the pile tip penetration depth into the rock was measured to be h = 1.0 m, with a stable limestone slab thickness t = 3 m below the pile tip. Based on the lithology of the surrounding soil (silty clay) and the rock mass (slightly weathered limestone), the benchmark foundation ratio coefficient was determined to be m = 8000 kN / m according to the "Technical Code for Building Pile Foundations". 4 .

[0027] Establish a three-dimensional finite element numerical model A three-dimensional pile-soil-rock finite element model was constructed using MIDAS GTS NX finite element software. The model range was 10 times the pile diameter (horizontal) and 1.5 times the pile length (vertical). The pile body was simulated using solid elements, the soil body was simulated using the Mohr-Coulomb constitutive model, and the rock body was simulated using the elastoplastic constitutive model. The pile-rock contact surface was set as surface-to-surface contact, the normal direction was set as hard contact, and the tangential direction was set as the Coulomb friction model with a friction coefficient of 0.35. All material parameters were assigned according to the geological survey report.

[0028] Parametric Analysis and Numerical Simulation In addition to the h=1.0m and t=3m working conditions in this embodiment, additional combined working conditions of h=0.5m, 1.5m, 2.0m and t=2m, 4m, 5m are set, forming a total of 12 sets of analysis working conditions. For each working condition, a horizontal graded load (0~500kN) is applied to the pile top, and static calculations are performed to obtain the horizontal displacement curve of the pile body under each working condition. In this embodiment, the horizontal displacement of the pile top is 6.2mm (when the load is 500kN).

[0029] Inversion calculation of constraint coefficient β Taking the horizontal displacement curve of the pile body under the working condition of this embodiment as the target, the traditional "m" method is used for iterative fitting. When m sim =8920kN / m 4 At that time, the theoretical displacement curve and the simulated displacement curve showed a consistency of over 98%; the calculated constraint coefficient β=m sim / m=8920 / 8000=1.115.

[0030] Constructing a quantitative relationship system for β The β, h, and t values ​​for 12 working conditions were compiled into a β lookup table. Simultaneously, a multivariate regression analysis was used to fit an empirical function: β = 1.06 + 0.11 × ln(h) + 0.05 × ln(t). Substituting h = 1.0m and t = 3m into this example, β = 1.06 + 0.11 × 0 + 0.05 × 1.0986 = 1.115 was calculated, consistent with the inversion calculation result, thus verifying the accuracy of the empirical function.

[0031] Engineering Design Applications Based on β=1.115 in this embodiment, the corrected foundation proportion coefficient m*=β×m=1.115×8000=8920kN / m 4 Substituting m* into the traditional "m" method formula, the characteristic value of the horizontal bearing capacity of the pile foundation is calculated to be 280kN, and the maximum bending moment of the pile body is 1250kN·m. Based on this, the pile body reinforcement design is carried out (HRB400 steel bars are selected, and the reinforcement ratio is 0.8%), and the pile foundation size is checked. The check results meet the requirements of the specifications.

[0032] The results of this embodiment show that the m value obtained by the modified "m" method of the present invention is more in line with the actual situation of karst foundation. The designed pile foundation not only meets the structural safety requirements, but also avoids overly conservative design. Compared with the conservative scheme based on empirical values, the amount of pile foundation reinforcement is reduced by about 12%, which effectively reduces the project cost.

[0033] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A modified "m" method for karst foundations considering the degree of pile end restraint, characterized in that, Includes the following steps: Step S1: Based on the geological background of the target engineering area, establish a series of three-dimensional pile-soil-rock refined finite element models covering different combinations of pile tip rock penetration depth h and stable rock plate thickness t below the pile tip; Step S2: Perform numerical simulations of each 3D pile-soil-rock refined finite element model under horizontal loads. Through inversion analysis, obtain the equivalent foundation scale factor m that best matches the simulation results. sim ; Step S3: Based on the equivalent foundation ratio coefficient m sim Calculate the constraint coefficient β=m based on the standard reference value m. sim / m, and establish a quantitative relationship between the pile tip rock penetration depth h, the rock plate thickness t and the constraint coefficient β; Step S4: In actual engineering design, based on the actual pile tip rock penetration depth h and rock slab thickness t at the actual pile location, obtain the corresponding constraint coefficient β based on the quantitative relationship, calculate the corrected foundation proportion coefficient design value m* = β × m, and use the corrected foundation proportion coefficient design value m* to verify the horizontal bearing capacity and deformation of the pile foundation.

2. The modified "m" method for considering pile end restraint in karst foundations according to claim 1, characterized in that, In step S1, the three-dimensional pile-soil-rock refined finite element model includes pile body elements, pile surrounding soil elements, and pile end rock layer elements. A pile-rock contact surface element is provided between the pile body element and the pile end rock layer element. The pile-rock contact surface element is configured to simulate slippage and separation behavior.

3. The modified "m" method for considering the degree of pile end restraint in karst foundations according to claim 1, characterized in that, In step S2, the inversion analysis specifically includes: using the pile horizontal displacement curve obtained from numerical simulation as the target, iterative fitting is performed using the traditional "m" method theory until the error between the theoretically calculated curve and the numerically simulated curve is less than a preset threshold. The m value used at this time is the equivalent foundation scaling factor m. sim .

4. The modified "m" method for considering the degree of pile end restraint in karst foundations according to claim 1, characterized in that, In step S1, the rock mass and soil mass in the three-dimensional pile-soil-rock refined finite element model are simulated using the Mohr-Coulomb constitutive model or the hardened soil constitutive model, and the material parameters are assigned according to the geological survey report.

5. The modified "m" method for considering the degree of pile end restraint in karst foundations according to claim 1, characterized in that, In step S3, the quantitative relationship is an empirical formula, which is established by multiple regression analysis. Its form is β = a + b·ln(h) + c·ln(t), where a, b, and c are regression coefficients, which are determined by fitting the numerical simulation results of the series of three-dimensional pile-soil-rock refined finite element models.

6. The modified "m" method for considering the degree of pile end restraint in karst foundations according to claim 1, characterized in that, In step S3, the quantitative relationship is a lookup table, which contains the constraint coefficient β values ​​corresponding to different combinations of pile tip rock penetration depth h and rock slab thickness t.

7. The modified "m" method for considering the degree of pile end restraint in karst foundations according to claim 1, characterized in that, In step S1, in the series of three-dimensional pile-soil-rock refined finite element models covering different combinations of pile tip rock penetration depth h and rock slab thickness t, the value range of pile tip rock penetration depth h is 0.5m to 2.0m, and the value range of rock slab thickness t is 2m to 5m.

8. The modified "m" method for considering the degree of pile end restraint in karst foundations according to claim 1, characterized in that, The method further includes step S5: integrating the quantitative relationship between the constraint coefficient β, the pile tip rock penetration depth h and the rock slab thickness t into the pile foundation design software or calculation table, for direct querying or automatic calculation of the corrected foundation proportion coefficient design value m*.

9. The modified "m" method for considering the degree of pile end restraint in karst foundations according to claim 1, characterized in that, The method is applicable to pile foundation projects in karst-developed areas where the pile tip is embedded in rock strata and there is a stable rock slab below the pile tip. The stable rock slab is a complete or substantially complete limestone, dolomite, or sandstone slab.

10. The modified "m" method for considering the degree of pile end restraint in karst foundations according to claim 1, characterized in that, In step S2, the numerical simulation under horizontal load includes applying multiple levels of horizontal loads to the top of the model pile, obtaining the horizontal displacement curves and internal force distributions of the pile body under each level of horizontal load, and using the equivalent foundation scaling factor m under different load levels. sim Inversion analysis.

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