Karst region pile-slab structure subgrade deformation correction L / 3 method calculation method

Abstract

The application discloses a kind of karst area pile-slab structure subgrade deformation correction L / 3 method calculation methods, belong to high-speed railway subgrade engineering technical field.The method includes: obtaining the design parameter of pile-slab structure subgrade, load diffusion starting surface is determined based on pile length;With stress ratio not more than 0.2 as the termination condition to determine the depth of underlying layer compression layer, the total compression of underlying layer is calculated using layer summation method, the elastic compression of pile body is calculated;According to the sum of total compression of underlying layer and elastic compression of pile body, determine post-construction settlement estimate, calculate the equivalent value of underlying layer compression modulus;Finally, the correction value is compared with threshold value and iterative optimization design parameter.The application introduces the settlement empirical correction coefficient based on compression modulus equivalent value to modify the traditional L / 3 method, solves the problem that traditional method has large deviation in karst area settlement prediction, and can control subgrade settlement in millimeter level.

Description

Technical Field

[0001] This invention belongs to the technical field of high-speed railway subgrade engineering, specifically relating to a method for calculating deformation correction using the L / 3 method for subgrades with pile-slab structures in karst areas. Background Technology

[0002] In parts of southwest and southeast my country, the covered, moderately to strongly developed karst geology is a major source of disaster for engineering construction. This type of geological condition not only makes the construction of high-speed railways extremely difficult, but also makes it difficult to effectively control the deformation of the roadbed.

[0003] As high-speed railway construction extends to karst-developed areas in the southwest and southeast, controlling subgrade deformation under covered karst geological conditions has become a key technical challenge in high-speed railway construction. The bedrock surface in covered karst areas is highly undulating, with highly random distribution of karst caves and fissures, and significant differences in the physical and mechanical properties of the foundation soil over short distances, posing a severe challenge to controlling millimeter-level post-construction settlement in high-speed railways.

[0004] Pile-slab structures, due to their high stiffness, high bearing capacity, and good overall stability, have become an effective technical approach for controlling differential settlement of roadbeds under adverse karst geological conditions. This structure consists of reinforced concrete pile foundations, a reinforced concrete bearing slab, and roadbed fill rigidly connected to form a composite bearing system, effectively leveraging the combined bearing capacity of the piles and the soil between them. Based on the connection method between the piles and the bearing slab, pile-slab structures can be divided into three main forms: independent pier type, beam type, and embedded type. Among these, the independent pier type offers advantages such as clear force distribution, a clear force transmission path, high settlement control accuracy, convenient construction, and strong adaptability.

[0005] Currently, the L / 3 method is mainly used for settlement calculation of pile-slab subgrade structures. This method is a composite calculation method that integrates the equivalent pier foundation method and the stress diffusion angle method. For different pile types, this method sets differentiated calculation starting surfaces. However, the traditional L / 3 method, based on the "solid pier diffusion" assumption, ignores the collaborative working mechanism of the pile-soil-slab system, and has the following drawbacks: First, there are limitations to using a fixed correction factor. This method mechanically defines the penetration correction depth as L / 3 of the pile length. However, the actual pile tip penetration and stress diffusion range are affected by various factors such as the distribution of pile side friction, the nature of the bearing layer at the pile tip, the pile length-to-diameter ratio, and the load level. Using a fixed empirical factor leads to significant deviations in the calculation results. In deep soft soil or hard rock layers, a fixed empirical factor may result in a deviation of more than 30% in the calculation results.

[0006] Second, the stress distribution is overly idealized. A simple trapezoidal diffusion model is used ( Assuming the distribution of additional stress, without considering the synergistic effect of pile-soil-slab working, the calculated deep additional stress differs significantly from the actual data.

[0007] Third, its applicability to complex working conditions is limited. This method is not suitable for scenarios with negative skin friction or heterogeneous strata. In karst areas with beaded caves, the traditional L / 3 method severely overestimates settlement, with errors exceeding 300%.

[0008] Therefore, there is an urgent need for a design method for deformation control of pile-slab roadbed that can fully consider the collaborative working mechanism of pile-soil-slab and is applicable to complex karst geological conditions. Summary of the Invention

[0009] (a) Technical problems to be solved To address the shortcomings of existing technologies, this invention, targeting the characteristics of beaded karst cave development and strong stratigraphic heterogeneity in covered karst areas, comprehensively characterizes the underlying strata through the equivalent value of compression modulus, effectively solving the problem of poor adaptability of traditional methods in karst cave strata.

[0010] (II) Technical Solution To achieve the above objectives, the present invention provides the following technical solution: a method for calculating the deformation correction L / 3 method of roadbed in karst areas using pile-slab structures, comprising the following steps: Obtain the design parameters of the pile-slab structure subgrade, including pile length, pile diameter, pile spacing, bearing plate thickness, and compressibility modulus of each soil layer; The load diffusion initiation surface is determined based on the pile length, and the load diffusion initiation surface is located at a depth of one-third of the pile length below the pile tip; Starting from the load diffusion initiation surface, the additional stress and self-weight stress of each soil layer are calculated layer by layer downwards at a preset diffusion angle until the ratio of additional stress to self-weight stress at the current depth is no greater than 0.2. This depth is then determined as the calculation depth of the underlying compressible layer. Based on the compression modulus and additional stress of each soil layer, the total compression of the underlying layer is calculated using the layer summation method. The elastic compression of the pile body is calculated based on the single pile's shared load, pile length, elastic modulus of the pile concrete, and cross-sectional area. The estimated post-construction settlement is determined based on the sum of the total compression of the underlying layer and the elastic compression of the pile body. Calculate the equivalent value of the compression modulus of the underlying layer, determine the value of the settlement empirical correction coefficient based on the equivalent value of the compression modulus, and use the settlement empirical correction coefficient to correct the estimated post-construction settlement value to obtain the corrected post-construction settlement value. The corrected post-construction settlement value is compared with the preset settlement control threshold. If the corrected post-construction settlement value exceeds the preset settlement control threshold, the design parameters are adjusted and recalculated until the settlement control requirements are met.

[0011] As a preferred embodiment, the method for determining the empirical settlement correction coefficient includes: Calculate the equivalent value of the compressive modulus of the underlying layer using the following formula: ; In the formula, Let be the area of ​​the stress pattern of the i-th soil layer. Let be the compression modulus of the i-th soil layer; When the equivalent value of the compression modulus is greater than or equal to 20 MPa, the empirical correction factor for settlement is 0.2; when the equivalent value of the compression modulus is less than or equal to 4 MPa, the empirical correction factor for settlement is 1.0; when the equivalent value of the compression modulus is between 4 MPa and 20 MPa, the value of the empirical correction factor for settlement is determined by linear interpolation.

[0012] As a preferred embodiment, the additional stress is calculated using the following formula: In the formula, Uniformly distributed additional stress on the roadbed base These represent the length and width of the load distribution, respectively. The depth is relative to the load diffusion initiation surface. The preset diffusion angle is [value].

[0013] As a preferred embodiment, the preset diffusion angle is: The preset settlement control threshold is 15mm.

[0014] As a preferred embodiment, the elastic compression of the pile body is calculated using the following formula: ; In the formula, Single pile load sharing For the pile length, The elastic modulus of the pile concrete. The cross-sectional area of ​​the pile is given; the load shared by a single pile is the total load divided by the total number of piles, and the average axial force is half of the load at the top of the pile.

[0015] As a preferred embodiment, the method further includes an orthogonal experiment optimization step: Four factors were selected: pile diameter, pile length, pile spacing, and bearing plate thickness. Each factor was taken at three levels, using L9 ( Orthogonal arrays are used for experimental design. For each test scheme, the corrected post-construction settlement value was calculated. The post-construction settlement was used as the evaluation index to conduct range analysis and determine the ranking of the influence of each factor on the settlement. Based on the ranking of the degree of impact, the design parameters with the greatest impact are adjusted first for iterative optimization.

[0016] As a preferred embodiment, the method further includes an effective pile length threshold determination step: When the pile length is less than the effective pile length threshold, the pile length is increased so that the corrected post-construction settlement value meets the preset settlement control threshold. Once the pile length reaches the effective pile length threshold, fine optimization is performed by adjusting the pile diameter, pile spacing, or bearing plate thickness. The effective pile length threshold value is the minimum pile length required to make the post-construction settlement value meet the preset settlement control threshold.

[0017] As a preferred embodiment, the method further includes a step of verifying the softening conditions of the karst cave filling soil: The compression modulus of the soil filling the karst caves in the underlying layer was reduced to 50% of its original value. The corrected post-construction settlement value is recalculated based on the reduced compression modulus. If the recalculated post-construction settlement value exceeds the preset settlement control threshold, the pile length is increased to enhance the structural safety reserve.

[0018] As a preferred embodiment, the calculation range of the total compression of the underlying layer is from the load diffusion initiation surface to the calculation depth of the underlying layer compression layer.

[0019] As a preferred embodiment, the method further includes a numerical simulation verification step: A two-dimensional finite element model was established based on the design parameters, and the constitutive relationship of the soil was simulated using the HSS small strain soil hardening model. The construction process was simulated with phased loading, and the post-construction settlement simulation values ​​were extracted. The corrected post-construction settlement value is compared with the simulated post-construction settlement value. If the error between the two exceeds a preset range, the value of the settlement empirical correction coefficient is adjusted.

[0020] (III) Beneficial Effects Compared with existing technologies, this invention provides a method for calculating the deformation correction L / 3 method of roadbed in karst areas using pile-slab structures, which has the following advantages: I. This invention modifies the traditional L / 3 method by introducing an empirical settlement correction coefficient based on the equivalent value of the compressive modulus, establishing a quantitative mapping relationship between the correction coefficient and the equivalent value of the compressive modulus of the underlying layer. Verification through PLAXIS 2D finite element numerical simulation shows that the calculation error of the modified L / 3 method can be further controlled. Second, this invention addresses the characteristics of beaded karst cave development and strong stratigraphic heterogeneity in covered karst areas. It comprehensively characterizes the underlying strata using the equivalent value of the compression modulus, effectively solving the problem of poor adaptability of traditional methods in karst cave strata. Simultaneously, this invention also provides a specific verification method for the softening conditions of karst cave filling soil. By recalculating and determining settlement under the most unfavorable geological conditions, it ensures that the design scheme has sufficient risk redundancy. Third, this invention provides a complete design process from parameter selection and deformation calculation to optimization and adjustment. Through orthogonal experimental design, it achieves a three-level system sensitivity analysis of four factors: pile diameter, pile length, pile spacing, and slab thickness, providing a quantitative basis for the rational selection and parameter optimization of pile-slab structures in karst areas. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the traditional L / 3 method calculation model upon which this invention is based, wherein... Figure 1 'a' represents the load diffusion calculation model for friction piles. Figure 1 b represents the load diffusion calculation model for end-bearing piles; Figure 2 These are schematic diagrams illustrating three structural forms of the pile-slab structure involved in this invention, wherein... Figure 2 a is an independent pier type. Figure 2 b is a beam-supported type. Figure 2 c indicates embedded type; Figure 3 This is a diagram showing the geometric model construction for PLAXIS 2D numerical simulation in the method of this invention, wherein... Figure 3 'a' represents the soil model's extent and boundary conditions. Figure 3 b represents the soil layering and the upper roadbed fill structure; Figure 4 This is a schematic diagram of the reconstruction of the beaded cavern layer in the method of the present invention; Figure 5 This is a schematic diagram of the pile-slab structure implantation and contact surface setting in the method of the present invention; Figure 6 This is a schematic diagram of mesh generation and mesh quality in the method of the present invention, wherein... Figure 6 'a' represents the grid division effect. Figure 6 b represents grid quality assessment; Figure 7 This is a schematic diagram of the monitoring point layout and deformation control point locations in the method of the present invention; Figure 8 This is a schematic diagram showing the construction stage setup in the method of the present invention; Figure 9 A comparison of vertical displacement cloud diagrams for various orthogonal experimental schemes of this invention; Figure 10 Comparison of vertical displacement cloud maps under softening conditions for filling soil in karst caves; Figure 11 This is a diagram showing the internal force distribution of the bearing plate and pile body in the method of the present invention. Figure 11 a is the bending moment diagram of the load-bearing plate. Figure 11 b is the bending moment diagram of the side piles; Figure 12 This is a flowchart of the method of the present invention. Detailed Implementation

[0022] To better understand the purpose, structure, and function of this invention, the following will further explain the L / 3 method for calculating the deformation correction of roadbed in karst areas using pile-slab structures, in conjunction with specific embodiments and accompanying drawings.

[0023] Example 1: Basic Design Process and Determination of Load Diffusion Initiation Surface I. Obtaining Design Parameters The design parameters of the pile-slab subgrade structure are obtained. This example uses a pile-slab subgrade cross-section in a karst area covered by a high-speed railway station as an example. The subgrade width is 27m, the embankment height is 5.5m, the slope is 1:1.75, and the subgrade base has uniformly distributed additional stress. =250kPa. The pile-slab structure uses reinforced concrete bored piles, with a total of 15 piles. The initial design parameters are: pile length 50m, pile diameter 1.5m, pile spacing 4m, and bearing plate thickness 0.7m. The concrete strength grade of the pile body is C35, and the elastic modulus is 250kPa. =3.15× kPa.

[0024] The stratigraphic information was determined based on geological survey data. From the surface downwards, the stratigraphic layers are: Quaternary silty clay layer, coarse gravelly soil layer, strongly weathered limestone layer, and weakly weathered limestone layer, with multiple layers of beaded karst caves developed in between.

[0025] II. Determining the Load Diffusion Initiation Surface This step determines the load diffusion initiation surface based on the L / 3 method. For example... Figure 1 As shown in diagram a, for friction piles, the calculated top surface of the underlying layer is raised to a depth of L / 3 below the pile tip, and the corrected depth of pile tip penetration is taken as one-third of the pile length. The load is transferred downwards from this starting surface at a diffusion angle of 30°. Figure 1 As shown in b, for end-bearing piles, since the pile tip penetration effect is ignored, the top surface of the bearing stratum at the pile tip is directly used as the starting point for calculation. In this embodiment, the pile tip is embedded in the weakly weathered limestone bearing stratum and is calculated as an end-bearing pile. However, in order to fully consider the compression deformation of the underlying strata in the karst area, the L / 3 point below the pile tip is still taken as the load diffusion starting surface.

[0026] The depth of the load diffusion initiation surface is calculated using the following formula: ; In the formula, L For the pile length, This represents the depth of the load diffusion initiation surface. In this embodiment, L =50m, then That is, the load diffusion initiation surface is located 33.33m below the ground surface.

[0027] III. Determining the Calculation Depth of the Underlying Compressed Layer Starting from the load diffusion initiation surface, the additional stress and self-weight stress of each soil layer are calculated layer by layer downwards at a diffusion angle of 30°. The additional stress is calculated using the following formula: In the formula, Uniformly distributed additional stress on the roadbed base These represent the length and width of the load distribution, respectively. The depth is relative to the load diffusion initiation surface. The preset diffusion angle is [value]. In this embodiment, =27m, =19m, Take 30°, tanθ=0.577.

[0028] Self-weight stress is calculated using the following formula: ; In the formula, The unit weight of the i-th soil layer The thickness of the i-th soil layer. Calculate layer by layer until the termination condition is met: The stress ratio is ≤0.2, and the corresponding depth is the calculated depth of the underlying compression layer. In this embodiment, after layer-by-layer determination, the stress ratio first drops to 0.135≤0.2 at a depth of -39.9m. Therefore, the calculated depth of the underlying layer is -39.9m, and the total thickness of the compression layer is 6.57m.

[0029] IV. Calculate the total compression of the underlying layer. Using the layered summation method, the compression of each soil layer is calculated according to the following formula: ; In the formula, Let be the average additional stress at the midpoint of the i-th soil layer. Let be the thickness of the i-th soil layer. Let be the compression modulus of the i-th soil layer. Summing the compression values ​​of all soil layers within the compression zone yields the total compression value of the underlying layer. The hierarchical calculation summary in this embodiment yields... =34.4mm.

[0030] V. Calculate the elastic compression of the pile body The elastic compression of the pile body is calculated using the following formula: ; In the formula, To distribute the load across a single pile, divide the total load by the total number of piles. The length of the pile; The elastic modulus of the pile concrete; Let be the cross-sectional area of ​​the pile. The average axial force is taken as half of the load at the pile top.

[0031] VI. Determine the estimated post-construction settlement and introduce a correction factor. Post-construction settlement estimate S = + =34.4+3.84=38.24mm.

[0032] Calculate the equivalent value of the compressive modulus of the underlying layer using the following formula: ; That is, 40MPa > 20MPa. Take 0.2; Corrected settlement results: . The preset settlement control threshold is 15mm. In this embodiment, the post-construction settlement value is less than 15mm, which meets the settlement control requirements.

[0033] Example 2: Selection of Pile-Slab Structure Form and Characteristics of Internal Force Distribution This embodiment illustrates the three main structural forms of pile-slab structures to which this invention applies and their internal force distribution characteristics.

[0034] like Figure 2 As shown in Figure a, the independent pier-type pile-slab structure consists of an upper continuous reinforced concrete bearing plate and a lower reinforced concrete cast-in-place pile. The pile body is directly and rigidly connected to the bearing plate. It has advantages such as clear force distribution, clear force transmission path, high settlement control accuracy, convenient construction, and strong adaptability, and is the preferred structural form of this invention.

[0035] like Figure 2 As shown in b, the beam-supported pile-slab structure adds a beam structure to the top of each row of piles in the transverse direction. Both the pile cap and the beam are cast-in-place reinforced concrete structures, which are suitable for working conditions with large loads.

[0036] like Figure 2 As shown in c, the embedded pile-slab structure completely embeds the bearing plate under the roadbed fill. Its core components include the bearing plate, pile foundation, pile cap and roadbed fill. Its advantages are strong load diffusion capacity and good overall stability.

[0037] The selection principles for the three structural forms are as follows: Independent pier-type pile-slab structures are preferred for road sections with complex geological conditions and high risk of differential settlement; in areas with thick soft soil, the side friction resistance is increased by increasing the pile length; in karst areas, the pile ends are ensured to be firmly embedded in the intact bedrock; the thickness and reinforcement of the bearing plate are determined based on the bending moment, shear force, and temperature stress under train load; the pile spacing is designed in conjunction with the plate thickness to balance differential settlement and project cost.

[0038] like Figure 11As shown in Figure a, the load-bearing plate exhibits distinct zoning characteristics. The pile top connection is controlled by negative bending moment, with a maximum negative bending moment of 118.9 kN·m, while the mid-span region between piles is subjected to positive bending moment, with a maximum positive bending moment of 237.8 kN·m. Figure 11 As shown in b, the bending moment of the side pile is nonlinearly distributed along the pile body.

[0039] Example 3: Orthogonal Experiment and Parameter Sensitivity Analysis This embodiment illustrates the specific implementation method of parameter sensitivity analysis through orthogonal experiments.

[0040] I. Orthogonal Experimental Design Four factors were selected: pile diameter, pile length, pile spacing, and bearing plate thickness. Three levels were used for each factor. ( An orthogonal array was used for the experimental design. The factor levels are shown in Table 1 below: Table 1

[0041] This embodiment uses post-construction settlement as the core standard. To verify the accuracy of the modified L / 3 method, the following three models are used for calculation: Traditional L / 3 method: uses the standard recommended fixed diffusion angle tan θ =0.577 (approximately) ).

[0042] Modified L / 3 method: This method uses the empirical settlement coefficient proposed in this paper, which is determined by determining the equivalent value of the compression modulus. .

[0043] PLAXIS 2D Finite Element Model: Establish a two-dimensional plane strain model and input the actual soil layer parameters as reference values.

[0044] II. Numerical Simulation and Result Comparison Numerical simulations of each scheme were performed using PLAXIS 2D software. For example... Figure 3 As shown in Figure a, a soil model is established with a width of 150m (X-axis) and a depth of 140m (Y-axis). The boundary conditions are set as follows: the soil is constrained by normal displacement on both sides, the bottom is completely fixed, and the top surface is free. Figure 3 As shown in b, the upper artificially filled roadbed is divided into three layers from bottom to top: ABC group filler, AB group filler, and graded crushed stone.

[0045] like Figure 9As shown, the vertical displacement cloud maps of the nine orthogonal test schemes exhibit different settlement characteristics: Scheme 1 (pile length 50m, pile diameter 1.5m, spacing 4m, plate thickness 0.7m) has a maximum vertical displacement of 7.047mm; Scheme 2 has 14.76mm; Scheme 3 has 59.85mm; Scheme 4 has 36.79mm; Scheme 5 has 8.94mm; Scheme 6 has 6.44mm; Scheme 7 has 6.375mm; Scheme 8 has 12.19mm; and Scheme 9 has 142.3mm.

[0046] III. Sensitivity Analysis Through range analysis, the influence of each factor on settlement was ranked as follows: pile length (L) > slab thickness (H) > pile diameter (D) > pile spacing (S).

[0047] The pile length exhibits the highest sensitivity. When the pile length increases from 35m to 50m, the settlement decreases by approximately 0.56mm for every 1m increase in pile length. When the pile length is 20m, the settlement increases dramatically and non-linearly, indicating the existence of an "effective pile length threshold." Even if the minimum pile length required to meet the 15mm control requirement for post-construction settlement is corrected, the effective pile length threshold is 35m under the geological conditions of this embodiment.

[0048] Thickness sensitivity is the second most important factor. For every 0.1m increase in slab thickness, the average settlement decreases by about 3-4mm. This is the most effective structural means to adjust uneven settlement and compensate for geological defects.

[0049] The pile diameter sensitivity is moderate; for every 0.1m increase in pile diameter, the average settlement decreases by about 2-3mm.

[0050] The pile spacing has the lowest sensitivity. Within a reasonable range of 4m to 6m, changes in pile spacing have little effect on settlement. For every 1m increase in spacing, the settlement fluctuation is only about 1.5mm.

[0051] Example 4: Determination and Verification of the Optimal Solution I. Determining the Optimal Solution Based on the results of the orthogonal experiment and the engineering cost analysis, three preliminary alternative schemes were proposed for comparison. The technical indicators of the alternative schemes are compared as shown in Table 2 below: Table 2

[0052] Option 5 has the lowest total cost due to its short pile length, but it carries a higher risk under soft karst conditions. Option 6 has the highest cost due to the increased slab thickness. Option 7 has a settlement of 6.375mm under normal working conditions, which meets the 15mm limit requirement, and its cost is moderate, so it is determined to be the optimal option.

[0053] II. Detailed Calculation of Scheme 7 A detailed verification of Scheme 7 was performed. For example... Figure 6As shown in Figure a, the model employs an "ultra-fine" mesh generation level, combined with an adaptive refinement method to locally refine the pile-soil contact zone, plate-soil contact zone, and stress concentration areas, ultimately generating 30,643 elements and 248,971 nodes. Figure 6 As shown in b, the grid quality assessment is mainly green, indicating that the overall quality is good.

[0054] like Figure 7 As shown, 13 vertical displacement monitoring points (JCD2-1 to JCD2-14) are set up along the centerline at half pile spacing. The bottom of the bearing plate and the soil settlement between piles are the main monitoring points. Horizontal displacement points are set up at the slope toe (JCD15) and the middle of the pile body (JCD7). Stress monitoring points are set up at the pile top, pile middle, pile bottom and the middle of the slab span.

[0055] like Figure 8 As shown, the construction phase is divided into five steps: the first stage is initial equilibrium, which activates all soil to complete the initial ground stress equilibrium; the second stage is to simulate the grouting reinforcement of the beaded karst caves at the pile bottom; the third stage is to activate the pile unit, plate unit and contact surface in sequence; the fourth stage is to clear the displacement to eliminate the displacement caused by self-weight; the fifth stage is to apply train load and extract the post-construction settlement results.

[0056] Scheme 7 calculates the compression amount of the underlying layer. =28.5mm, elastic compression of the pile body 13.5mm, estimated post-construction settlement S =42mm. Equivalent value of compression modulus. =14.69MPa, obtained by linear interpolation =0.212.

[0057] III. Numerical Simulation Verification like Figure 7 The vertical displacement data of each monitoring point was extracted during the final load application stage, as shown. Figure 11 As shown in a-11b, the bending moment distributions of the bearing plate and the side piles are extracted and compared with the settlement distribution calculated by the modified L / 3 method for verification. The PLAXIS 2D numerical simulation verification result is 6.375 mm, with a relative error of 31.7% compared with the calculated value of 8.4 mm by the method of this invention. The calculated value is on the safe side.

[0058] Example 5: Verification of softening conditions for filling karst caves with soil I. Softening Condition Settings like Figure 4 As shown, considering the beaded development characteristics of karst caves in the karst area, the caves within the site are distributed in multiple layers in a "candied hawthorn" pattern, with the main cave layers located in multiple depth ranges. The softening condition is set as follows: the compression modulus of the soil filling the caves below the pile bottom is... EThe pressure _s is reduced to 50% of the original value (i.e., from 20MPa to 10MPa) to simulate the most unfavorable working condition of soil mechanical property deterioration under groundwater erosion or long-term dynamic load of train.

[0059] II. Comparison of different pile length schemes Select Option 1 ( L =50m), Scheme 2 ( L =35m), Scheme 3 ( L A comparative analysis was conducted on three representative working conditions (e.g., 20m). Figure 10 As shown, the vertical displacement contour maps of the various schemes under softened working conditions exhibit significant differences. The calculation results are shown in Table 3 below: Table 3

[0060] The traditional L / 3 method relies too heavily on the underlying soil properties, resulting in significant data fluctuations after the karst cave softens. In contrast, the modified L / 3 method is minimally affected by fluctuations in soil modulus and maintains high computational stability and engineering safety even under the most unfavorable geological deterioration conditions.

[0061] Example 6: A Complete Method for Determining Empirical Settlement Correction Coefficients This embodiment details the empirical correction factor for settlement. The complete method for determining this.

[0062] Settlement empirical correction factor The value is based on the equivalent value of the compressive modulus of the underlying layer. The specific mapping relationship is shown in Table 4 below: Table 4

[0063] when When ≥20MPa, =0.2; when When ≤4MPa, =1.0; When 4MPa < When the pressure is <20 MPa, linear interpolation is used to determine the value. The value of .

[0064] Example 7: Complete Design Process In summary, as described in the above embodiments, Figure 12 As shown, the complete process of the deformation control design method for pile-slab structure subgrade in karst areas provided by this invention is as follows: Step 1: Obtain design parameters. Collect engineering geological survey data, determine the physical and mechanical parameters of each soil layer, and preliminarily determine the pile length. L Pile diameter DPile spacing S , plate thickness H Design parameters, etc.

[0065] Step 2: Determine the load diffusion initiation surface and calculate the depth of the load diffusion initiation surface based on the pile length.

[0066] Step 3: Calculate the additional stress and self-weight stress layer by layer. Starting from the load diffusion initiation surface, The additional stress and self-weight stress are calculated layer by layer downwards from the diffusion angle.

[0067] Step 4: Determine the calculated depth of the compression layer and check if the stress ratio meets the requirement of ≤0.2. If it does not meet the requirement, continue to calculate the next layer. If it does meet the requirement, determine the depth as the calculated depth of the compression layer of the next layer.

[0068] Step 5: Calculate the total compression of the underlying layers. The compression of each soil layer is calculated using the layered summation method and then summed to obtain the total compression of the underlying layers, S1 and S2.

[0069] Step 6: Calculate the elastic compression of the pile body.

[0070] Step 7: Calculate the equivalent value of the compression modulus and determine the correction factor.

[0071] Step 8: Calculate the corrected post-construction settlement value.

[0072] Step Nine: Verification and Iteration. S 'Compare with the 15mm threshold. If the requirement is met, proceed to the next step. If not, increase the pile length first and return to step two to recalculate.'

[0073] Step 10: Orthogonal Experiment Optimization and Numerical Simulation Verification. Orthogonal experiments are conducted on multiple schemes that meet the requirements to determine the optimal parameter combination. Calculations are performed under softening conditions with a 50% reduction in the modulus of the karst cave filling soil. A PLAXIS 2D finite element model is then established for verification to ensure the reliability of the design results.

[0074] In summary, this invention improves upon traditional methods by introducing an empirical settlement correction coefficient based on the equivalent value of the compression modulus. L The / 3 method is used for correction, which solves the problem of large deviation in settlement prediction in karst areas by traditional methods, and can control the roadbed settlement within the millimeter range.

[0075] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method for calculating the deformation correction L / 3 method of roadbed in karst areas using pile-slab structures, characterized in that, Includes the following steps: Obtain the design parameters of the pile-slab structure subgrade, including pile length, pile diameter, pile spacing, bearing plate thickness, and compressibility modulus of each soil layer; The load diffusion initiation surface is determined based on the pile length, and the load diffusion initiation surface is located at a depth of one-third of the pile length below the pile tip; Starting from the load diffusion initiation surface, the additional stress and self-weight stress of each soil layer are calculated layer by layer downwards at a preset diffusion angle until the ratio of additional stress to self-weight stress at the current depth is no greater than 0.

2. This depth is then determined as the calculation depth of the underlying compressible layer. Based on the compression modulus and additional stress of each soil layer, the total compression of the underlying layer is calculated using the layer summation method. The elastic compression of the pile body is calculated based on the single pile's shared load, pile length, elastic modulus of the pile concrete, and cross-sectional area. The estimated post-construction settlement is determined based on the sum of the total compression of the underlying layer and the elastic compression of the pile body. Calculate the equivalent value of the compression modulus of the underlying layer, determine the value of the settlement empirical correction coefficient based on the equivalent value of the compression modulus, and use the settlement empirical correction coefficient to correct the estimated post-construction settlement value to obtain the corrected post-construction settlement value. The corrected post-construction settlement value is compared with the preset settlement control threshold. If the corrected post-construction settlement value exceeds the preset settlement control threshold, the design parameters are adjusted and recalculated until the settlement control requirements are met.

2. The L / 3 method for calculating the deformation correction of roadbed in karst pile-slab structures according to claim 1, characterized in that, The method for determining the empirical settlement correction factor includes: Calculate the equivalent value of the compressive modulus of the underlying layer using the following formula: ; In the formula, Let be the area of ​​the stress pattern of the i-th soil layer. Let be the compression modulus of the i-th soil layer; When the equivalent value of the compression modulus is greater than or equal to 20 MPa, the empirical correction factor for settlement is 0.2; when the equivalent value of the compression modulus is less than or equal to 4 MPa, the empirical correction factor for settlement is 1.0; when the equivalent value of the compression modulus is between 4 MPa and 20 MPa, the value of the empirical correction factor for settlement is determined by linear interpolation.

3. The L / 3 method for calculating the deformation correction of roadbed in karst pile-slab structures according to claim 1, characterized in that, The additional stress is calculated using the following formula: In the formula, Uniformly distributed additional stress on the roadbed base These represent the length and width of the load distribution, respectively. The depth is relative to the load diffusion initiation surface. The preset diffusion angle is [value].

4. The L / 3 method for calculating the deformation correction of roadbed in karst pile-slab structures according to claim 1, characterized in that, The elastic compression of the pile body is calculated using the following formula: ; In the formula, Single pile load sharing For the pile length, The elastic modulus of the pile concrete. The cross-sectional area of ​​the pile is given; the load shared by a single pile is the total load divided by the total number of piles, and the average axial force is half of the load at the top of the pile.

5. The L / 3 method for calculating the deformation correction of roadbed in karst pile-slab structures according to claim 1, characterized in that, The method also includes an orthogonal experiment optimization step: Four factors were selected: pile diameter, pile length, pile spacing, and bearing plate thickness. Each factor was taken at three levels, using L9 ( Orthogonal arrays are used for experimental design. For each test scheme, the corrected post-construction settlement value was calculated. The post-construction settlement was used as the evaluation index to conduct range analysis and determine the ranking of the influence of each factor on the settlement. Based on the ranking of the degree of impact, the design parameters with the greatest impact are adjusted first for iterative optimization.

6. The L / 3 method for calculating the deformation correction of roadbed in karst pile-slab structures according to claim 5, characterized in that, It also includes the steps for determining the effective pile length threshold: When the pile length is less than the effective pile length threshold, the pile length is increased so that the corrected post-construction settlement value meets the preset settlement control threshold. Once the pile length reaches the effective pile length threshold, fine optimization is performed by adjusting the pile diameter, pile spacing, or bearing plate thickness. The effective pile length threshold value is the minimum pile length required to make the post-construction settlement value meet the preset settlement control threshold.

7. The L / 3 method for calculating the deformation correction of roadbed in karst pile-slab structures according to claim 6, characterized in that, It also includes the steps for calculating the softening conditions of the soil used to fill karst caves: The compression modulus of the soil filling the karst caves in the underlying layer was reduced to 50% of its original value. The corrected post-construction settlement value is recalculated based on the reduced compression modulus. If the recalculated post-construction settlement value exceeds the preset settlement control threshold, the pile length is increased to enhance the structural safety reserve.

8. The L / 3 method for calculating the deformation correction of roadbed in karst pile-slab structures according to claim 1, characterized in that, The preset diffusion angle is: The preset settlement control threshold is 15mm.

9. The L / 3 method for calculating the deformation correction of roadbed in karst pile-slab structures according to claim 1, characterized in that, The calculation range of the total compression of the underlying layer is from the load diffusion initiation surface to the calculation depth of the underlying layer compression layer.

10. The L / 3 method for calculating the deformation correction of roadbed in karst pile-slab structures according to claim 1, characterized in that, It also includes a numerical simulation verification step: A two-dimensional finite element model was established based on the design parameters, and the constitutive relationship of the soil was simulated using the HSS small strain soil hardening model. The construction process was simulated with phased loading, and the post-construction settlement simulation values ​​were extracted. The corrected post-construction settlement value is compared with the simulated post-construction settlement value. If the error between the two exceeds a preset range, the value of the settlement empirical correction coefficient is adjusted.

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