A method for determining an ultra-wide embankment and a differential settlement control index

Abstract

This invention discloses a method for determining ultra-wide embankments and establishing differential settlement control indices, belonging to the field of highway subgrade engineering. This method equates the embankment widening load to a trapezoidal strip load acting on the ground surface; combining the Boussinesq solution and the layered summation method, it considers the non-uniform reinforcement effect of the foundation compression modulus after long-term loading of the old embankment, calculating the additional settlement distribution caused by widening; establishing a functional relationship between the relative position of the maximum additional settlement and the width-to-height ratio of the widened embankment, obtaining the critical width-to-height ratio; using the critical width-to-height ratio to determine whether the widened embankment belongs to an ultra-wide embankment, and providing calculation methods for the maximum cross slope variation rate under different working conditions, thereby forming differential settlement control indices. This invention solves the problems of existing methods relying on experience, vague judgment criteria, and unreasonable control indices, providing a quantitative and reliable theoretical basis for engineering design.

Description

Technical Field

[0001] This invention relates to a method for determining ultra-wide embankments and identifying differential settlement control indicators, belonging to the field of highway subgrade engineering. Background Technology

[0002] With the rapid development of my country's expressway network, the reconstruction, expansion and widening of existing expressways has become one of the main ways to improve the traffic capacity of the road network. Under soft soil foundation conditions, the differential settlement control between the newly widened embankment and the existing old embankment is the core technical challenge that determines the success or failure of the project and the safety of long-term operation.

[0003] Currently, engineering practices and relevant standards mainly rely on empirical judgments and simplified differential settlement estimation methods to guide design and construction, which has the following main shortcomings:

[0004] First, there is a lack of criteria for judging ultra-wide embankments: Currently, there is no unified and quantitative standard for judging "ultra-wide" embankments with multiple lanes and significant width expansion. In engineering projects, the judgment is often based on empirical values ​​of the number of lanes or the total road width, which lacks objective basis based on mechanical mechanisms. This leads to a lack of understanding of the embankment deformation mode in the early stages of design, making it impossible to carry out targeted design.

[0005] Second, the rationality of differential settlement control indicators is insufficient: Existing standards provide differential settlement control indicators (such as cross slope variation rate) that are mostly based on simplified models or empirical statistics for specific working conditions. These indicators fail to fully consider the fundamental impact of widened embankment geometry (especially the width-to-height ratio) on the lateral distribution pattern of additional foundation settlement. In practice, the location of maximum differential settlement is often simply assumed to be at the shoulder, leading to overly conservative (increasing engineering costs) or unsafe (leaving potential engineering hazards) selection of control indicators.

[0006] Third, the settlement analysis model does not reflect the true state of the foundation: Existing analysis methods usually treat the foundation soil as a homogeneous body, failing to fully consider the objective fact that the old embankment has been consolidated under long-term operational loads, and the stiffness of its underlying foundation soil has significantly increased. This simplification leads to the calculation results of the additional stress and settlement of the foundation caused by the new embankment load deviating from reality, thus reducing the reliability of the settlement control indicators determined accordingly.

[0007] Fourth, there is a disconnect between design and control: existing methods have failed to establish a coherent, closed-loop technical process, from rapidly determining deformation modes based on embankment geometric parameters to accurately locating the most unfavorable control section, and then calculating reasonable control indicators. Design and settlement control are relatively isolated, which is not conducive to comparing and optimizing multiple options.

[0008] Therefore, it is necessary to establish a unified discrimination method based on the width-to-height ratio of widened embankments, starting from the geometric conditions of widened embankments and the mechanism of foundation settlement and deformation. This method should clarify the location of the maximum additional settlement within the top surface of the widened embankment, propose a calculation method for the maximum cross slope change rate, and form a generalizable method for judging ultra-wide embankments and a differential settlement control index for new and old roadbeds. This has significant engineering application value for guiding the design, construction, operation, and maintenance of multi-lane ultra-wide highway reconstruction and expansion projects. Summary of the Invention

[0009] To address the aforementioned technical problems, this invention proposes a method for determining ultra-wide embankments and establishing differential settlement control indicators. This method, through theoretical derivation and semi-analytical analysis, establishes a functional relationship between the width-to-height ratio of widened embankments and the relative position of the maximum additional surface settlement. It provides a method for calculating and calibrating the critical width-to-height ratio, uses this ratio to determine whether the widened embankment qualifies as an ultra-wide embankment, and proposes a method for calculating and determining the overall maximum cross slope change rate of the old and new roadbeds. This provides a unified, quantitative, and highly universal technical basis for determining differential settlement control standards in highway reconstruction and expansion projects.

[0010] To achieve the above-mentioned technical objectives, the present invention adopts the following technical solution:

[0011] A method for determining the criteria for ultra-wide embankments and identifying differential settlement control indicators includes the following steps:

[0012] S1. Obtain the geometric parameters and foundation layering parameters of the old embankment and the widened embankment, and establish a two-dimensional plane strain calculation model;

[0013] S2. In the two-dimensional plane strain calculation model, the self-weight of the embankment fill is equivalent to a trapezoidal strip load acting on the ground surface, and the additional stress distribution generated in the foundation is calculated based on the elastic theory.

[0014] S3. Based on step S2, considering the consolidation effect of the foundation soil caused by the long-term load of the old embankment, construct a non-uniform distribution field of the foundation compression modulus that varies laterally.

[0015] S4. Based on the additional stress distribution in step S2 and the non-uniform distribution field of the foundation compression modulus in step S3, the lateral distribution curve of the additional surface settlement caused by the embankment widening load is calculated using the layered summation method, and the distance of the location of the maximum additional settlement in the curve from the origin is determined. The origin of the coordinate system is set at the center of the bottom of the old embankment, with the horizontal axis pointing to the right and the vertical axis pointing downwards.

[0016] S5. Establish the functional relationship between the relative position parameter of the maximum additional settlement and the width-to-height ratio of the widened embankment, and calculate the distance from the origin of the coordinate system when the position of the maximum additional settlement is... The critical width-to-height ratio that is located exactly at the outer edge of the embankment top surface when it is widened ;

[0017] S6. Compare the width-to-height ratio of the widened embankment in the actual project with the critical width-to-height ratio determined in step S5 to determine whether it belongs to an ultra-wide embankment:

[0018] When the actual width-to-height ratio is greater than or equal to the critical width-to-height ratio, it is determined to be an ultra-wide embankment. At this time, the maximum additional settlement is located within the width range of the top surface of the widened embankment.

[0019] When the actual width-to-height ratio is less than the critical width-to-height ratio, it is determined to be a normal widening embankment. At this time, the maximum additional settlement is located at or outside the top edge of the widening embankment.

[0020] S7. Based on the determination result of step S6, determine the most unfavorable control section for the overall lateral differential settlement of the old and new embankments, and calculate the maximum cross slope change rate of this section. , as an indicator for differential settlement control.

[0021] Beneficial effects: This invention defines and calculates the critical width-to-height ratio, and uses "whether the maximum additional settlement location is located inside the top surface of the widened embankment" as the criterion for judgment, thereby realizing the quantitative determination of ultra-wide embankments. It overcomes the limitations of existing engineering practices that rely solely on empirical judgment based on road width or number of lanes, and has good versatility and physical rationality.

[0022] This invention establishes a method for calculating the lateral distribution of additional settlement of widened embankments based on equivalent trapezoidal loads, Boussinesq elastic solutions, and the layered summation method of non-uniform modulus fields. It can reasonably reflect the spatial variation of foundation stiffness caused by the long-term consolidation of old embankments, accurately determine the location of the maximum additional settlement within the top surface of the widened embankment and its relative location, and provide a theoretical basis for differential settlement control.

[0023] Furthermore, in step S2, simplifying the embankment widening load into a trapezoidal strip load acting on the ground surface specifically includes:

[0024] Based on the geometric parameters of the widened embankment, calculate the upper base, lower base, and height of the equivalent trapezoidal load;

[0025] The trapezoidal load is decomposed into a superposition of a rectangular load and two triangular loads, and the vertical additional stress at any point in the foundation is calculated using the Boussinesq elastic solution.

[0026] Furthermore, in step S3, the construction of a non-uniform distribution field of the foundation compression modulus that varies laterally specifically includes:

[0027] The growth rate of the compressive modulus of the subgrade soil layers below the center line of the old embankment was obtained by in-situ testing. It was assumed that the growth rate of the modulus at any lateral position in each soil layer was proportional to the magnitude of the additional vertical stress caused by the load of the old embankment at that position, thus establishing the distribution function of the compressive modulus as a function of depth and lateral position.

[0028] Furthermore, in step S5, the maximum additional settlement relative position parameter ,in The width of the top surface of the original half of the old embankment, in meters; To widen the top surface of the embankment, the unit is meters;

[0029] The width-to-height ratio of the widened embankment is obtained by the following formula:

[0030] ,

[0031] in Embankment height, in meters (m);

[0032] The functional relationship between the relative position parameter of the maximum additional settlement and the width-to-height ratio of the widened embankment is fitted using the following hyperbolic form:

[0033] ,

[0034] in, , , The fitting parameters are determined through numerical simulation or regression of engineering measured data, and their values ​​are related to the embankment height, foundation compression modulus, and modulus growth rate.

[0035] Furthermore, in step S7, determining the maximum cross slope gradient specifically includes:

[0036] When it is determined to be an ultra-wide embankment, the maximum cross slope change rate is the ratio of the differential settlement between the old road shoulder position and the maximum additional settlement position to the horizontal distance;

[0037] When it is determined to be a normal embankment widening project, the maximum cross slope change rate is the maximum of the following three: the maximum cross slope change rate within the top surface of the old embankment, the maximum cross slope change rate within the top surface of the widened embankment, and the overall maximum cross slope change rate across the old and new embankments.

[0038] Beneficial Effects: Based on the relationship between the width-to-height ratio of widened embankments and the critical width-to-height ratio, this invention establishes explicit calculation methods for the maximum cross slope variation rate under both ordinary embankments and ultra-wide embankments. Compared to the conservative estimation method of directly using the settlement difference between the shoulder and the center of the old road, the method of this invention can more realistically reflect the control section and control zone, avoiding both overly conservative and unsafe extremes, and providing a reliable basis for the reasonable determination of settlement control standards in highway reconstruction and expansion projects.

[0039] Furthermore, in step S2, the distribution of additional stress is calculated, and / or in step S4, the lateral distribution curve of additional surface settlement is calculated. The finite element numerical analysis method is used as a supplement or verification to the elastic theoretical solution and the semi-analytical method of layered summation.

[0040] Furthermore, the critical width-to-height ratio determined in step S5 is further calibrated and corrected by combining the measured settlement data of the target soft soil area.

[0041] Furthermore, the process includes optimization steps: inputting the maximum cross slope variation rate calculated in step S7 into a mechanical analysis model containing the pavement structure layer to calculate key mechanical response indicators; under the premise that the mechanical response indicators meet the specifications, iteratively adjusting the widening geometric parameters or the foundation reinforcement treatment scheme to jointly optimize the control value of the maximum cross slope variation rate.

[0042] Furthermore, the key mechanical response indicators include at least one of the following: tensile strain at the bottom of the asphalt surface layer, tensile strain at the bottom of the base course, and compressive strain at the top of the subgrade.

[0043] Furthermore, the foundation reinforcement treatment scheme includes adjusting at least one of the following: drainage consolidation parameters, composite foundation design parameters, or pile foundation layout parameters.

[0044] In summary, the present invention provides a method for determining ultra-wide embankments and identifying differential settlement control indicators. This method is based on a relatively complete theoretical derivation. In engineering applications, it only requires obtaining the geometric parameters of the widened embankment and the conventional survey parameters of the foundation soil layer. Combined with the width-to-height ratio and the relative positional relationship curve or empirical function of the maximum additional settlement given in this invention, it is possible to quickly determine whether it belongs to an ultra-wide embankment and calculate the maximum cross slope change rate. This avoids the high cost problem of needing to perform complex numerical simulations for each working condition. It has the advantages of simple operation, high calculation efficiency, and strong applicability. Attached Figure Description

[0045] Figure 1 This is a flowchart illustrating the overall process of determining ultra-wide embankments and differentiating settlement control indicators according to the present invention.

[0046] Figure 2 A simplified schematic diagram for expanding the embankment calculation model;

[0047] Wherein: 1-Old embankment; 2-Wideened embankment; 3-Ground surface line; 4-Coordinate origin; 5-First layer of foundation soil; 6-Second layer of foundation soil; 7-Nth layer of foundation soil; It is a Cartesian coordinate system; The width of the top surface of the original half of the old embankment, in meters; Embankment height, in meters (m); The slope of the embankment; To widen the top surface of the embankment, the unit is meters; The depth of the top surface of the second layer of foundation soil, in meters; The depth of the bottom surface of the second layer of foundation soil, in meters; The depth of the top surface of the nth layer of foundation soil, in meters; The depth of the bottom surface of the nth layer of foundation soil, in meters; This represents the thickness of the first layer of foundation soil, in meters (m). The thickness of the nth layer of foundation soil, in meters (m). The thickness of the nth layer of foundation soil, in meters (m). The thickness of the foundation compression layer is expressed in meters (m).

[0048] Figure 3 A schematic diagram of equivalent trapezoidal loads for widening the embankment;

[0049] Wherein: 8 - equivalent trapezoidal strip load; 9 - upper base of equivalent trapezoidal load; 10 - lower base of equivalent trapezoidal load; 11 - height of equivalent trapezoidal load; For local coordinate systems; Unit weight of embankment fill, in kN / m³ 3 ; For the upper base of the equivalent trapezoidal load, For the lower base of the equivalent trapezoidal load, The height of the equivalent trapezoidal load; The distance from the center of the bottom of the equivalent trapezoidal load to the center of the bottom of the old road;

[0050] Figure 4 This is a schematic diagram of equivalent trapezoidal loads under different embankment width-to-height ratios, where (a) corresponds to Case (b) corresponds to Case (c) corresponds to situation;

[0051] Figure 5 A schematic diagram for calculating the additional stress of an equivalent trapezoidal load in a local coordinate system;

[0052] Where: 12 - any point P in the foundation soil; The width of the top half of the equivalent trapezoidal load is in meters; A, D, E, and F are the four vertices of the equivalent trapezoid; B and C are the projection positions of vertices F and E on the ground line, respectively.

[0053] Figure 6 A theoretical diagram showing the relationship between the embankment's width-to-height ratio and the relative positional parameters of the maximum additional settlement;

[0054] in: This represents the distance from the origin of the coordinate system to the location of maximum additional settlement.

[0055] Figure 7 A schematic diagram showing the relative positional relationship between the embankment's width-to-height ratio and the maximum additional settlement;

[0056] Wherein: 13 - Fitted curve; 14 - Point corresponding to critical aspect ratio; The relative position parameter for the maximum additional settlement; To widen the width-to-height ratio of the embankment; The critical aspect ratio; , , These are the fitting parameters;

[0057] Figure 8 This is a schematic diagram for calculating the maximum cross slope ratio based on the width-to-height ratio of a widened embankment, where (a) corresponds to the case of an ultra-wide embankment and (b) corresponds to the case of a normal widened embankment.

[0058] Among them: 15-Old road shoulder; 16-New road shoulder; 17-Location of maximum additional settlement; 18-Surface additional settlement distribution curve; 19-Calculation section of maximum cross slope ratio; 20-Calculation section of cross slope ratio of the top surface of the old embankment; 21-Calculation section of cross slope ratio of the top surface of the widened embankment; 22-Calculation section of cross slope ratio of the top surface of the overall embankment. The maximum cross slope ratio; The slope variation rate of the cross slope of the top surface of the old embankment; To increase the slope ratio of the embankment top surface; The overall cross slope variation rate of the old and new embankments. Detailed Implementation

[0059] The present invention will now be described with reference to the embodiments shown in the accompanying drawings. The embodiments disclosed herein are illustrative in all respects and are not intended to be limiting. The scope of the present invention is not limited to the following description of the embodiments.

[0060] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0061] like Figure 1As shown, this invention provides a method for determining ultra-wide embankments and establishing differential settlement control indices. The method equates the embankment widening load to a trapezoidal strip load acting on the ground surface. Combining the Boussinesq solution and the layered summation method, it considers the non-uniform reinforcement effect of the foundation compression modulus after long-term loading of the old embankment, calculating the additional settlement distribution caused by widening. It establishes a functional relationship between the relative position of the maximum additional settlement and the width-to-height ratio of the widened embankment, obtaining the critical width-to-height ratio. The critical width-to-height ratio is used to determine whether the widened embankment belongs to an ultra-wide embankment, and calculation methods for the maximum cross slope change rate under different working conditions are given, thereby forming differential settlement control indices. Specifically, the method includes the following steps:

[0062] (1) Under the assumption of two-dimensional plane strain, a simplified calculation model for widening embankments of highways is established, as shown in the attached figure. Figure 2 As shown, obtain the relevant calculation parameters: The width of the top surface of the original half of the old embankment, in meters; Embankment height, in meters (m); The slope of the embankment; To widen the top surface of the embankment, the unit is meters; Unit weight of embankment fill, in kN / m³ 3 ; The effective unit weight of the i-th layer of foundation soil is expressed in kN / m³. 3 ; The depth of the top surface of the i-th layer of foundation soil, in meters; The thickness of the i-th layer of foundation soil, in meters; denoted as the initial compression modulus of the i-th foundation soil layer, in MPa.

[0063] (2) The embankment widening load is simplified into an equivalent trapezoidal strip load acting on the ground surface, as shown in the attached figure. Figure 3 and 4 As shown, where For the upper base of the equivalent trapezoidal load, For the lower base of the equivalent trapezoidal load, Define the height of the equivalent trapezoidal load. Let P be the center of the bottom of the equivalent trapezoidal load. Based on the Boussinesq elastic solution of the strip load, the equivalent trapezoidal load for widening the embankment is decomposed into a superposition of a rectangular load and two triangular loads. The vertical additional stress generated at any point P in the foundation soil is then calculated. As attached Figure 5 As shown. In the center of the old road. Based on, adopt The criterion solution yields the thickness of the foundation compressible layer as follows: The thickness of the compressible layer of the foundation can be obtained based on the soil layer division. There are n layers of soil within the area, among which This indicates the depth below the center line of the old embankment is... The effective self-weight stress of the foundation soil at that location, This indicates that the depth of the old embankment below its center line is... The vertical additional stress generated at the location.

[0064] (3) Considering the enhancing effect of foundation soil consolidation on the compression modulus under long-term load of the old embankment: Assuming that the compression modulus of the i-th soil layer below the center line of the old embankment is increased by... Growth ,in The modulus growth rate can be measured using the static cone penetration test method. It is assumed that the modulus growth rate within the i-th soil layer is related to the depth of the top surface of that layer. The relative magnitude of the additional stress on the old road is proportional to the relative magnitude of the stress. Therefore, at any lateral position within the i-th soil layer... The modulus growth rate at the point satisfies ,in For the load of the old embankment at depth Additional vertical stress at the location. Construct a non-uniform distribution field of the foundation's compressibility modulus. .

[0065] (4) Based on the elastic assumption of small strain line, the i-th soil layer is located at... At this point, the one-dimensional vertical strain caused by the equivalent trapezoidal load of the widened embankment is: By measuring vertical strain From the surface ( Down to the bottom of the foundation compression layer Integral calculation of the lateral distribution curve of additional surface settlement caused by embankment widening Using the hierarchical summation method, it can be rewritten as:

[0066] ;

[0067] (5) A first-order Taylor expansion of the formula for calculating the compression modulus of the foundation soil in step (4) yields the following results: Substitute the lateral distribution curve of surface subsidence into step (4). We can obtain:

[0068] ;

[0069] make This represents the additional surface settlement caused by the equivalent trapezoidal load of widening the embankment under a uniform modulus field without considering the consolidation and strengthening effect of the old embankment. This represents the first-order correction term caused by the non-uniform modulus field effect. It defines the distance of the location of maximum additional settlement from the origin. satisfy Substituting, we can get .

[0070] If the consolidation effect of the old road is not considered, then ,Right now At this point, the distance from the origin of the coordinate system to the location of the maximum additional settlement. satisfy Based on the symmetry of the equivalent trapezoidal load of the embankment widening, If we consider the consolidation effect of the old road, let's assume... , This represents the distance offset from the location of the maximum additional surface settlement towards the direction away from the old road. Substituting this into the above formula, and then... and exist Performing a first-order Taylor expansion, we get:

[0071] ;

[0072] neglect Item, substitute We can obtain:

[0073] ;

[0074] In actual calculations, , It can be obtained by numerical integration. , It can be done in The finite difference approximation at the location is used to obtain the distance from the origin of the coordinate system to the location of the maximum additional settlement. A semi-analytical estimation method.

[0075] (6) Define the relative position of the maximum additional settlement Widen the embankment's width-to-height ratio Theoretical analysis and numerical simulation results under multiple working conditions show that, given the embankment height and soil conditions, the width-to-height ratio of the widened embankment is... Relative positional parameters of maximum additional settlement It exhibits a clear nonlinear negative correlation, and can be fitted using an empirical function in hyperbolic form, as shown in the attached figure. Figure 7 As shown, that is ,in, , , Fitting parameters related to the geometric parameters of the embankment load and the soil parameters can be calibrated through numerical analysis or field measurements. The location of the maximum additional settlement should be precisely at the outer edge of the widened embankment top surface. Substitute into the hyperbolic function relation Solving for the critical width-to-height ratio for widening the embankment. .

[0076] (7) Based on the actual width-to-height ratio of the widening project With critical aspect ratio Based on the size relationship, determine the area where the maximum additional settlement of the widened embankment is located, and thus distinguish between ordinary widened embankments and extra-widened embankments, as shown in the attached figure. Figure 8 As shown:

[0077] ①When hour, This indicates the location of maximum additional settlement. If the settlement falls within the area of ​​the top surface of the widened embankment, then the location of the maximum additional settlement within the area of ​​the top surface of the widened embankment is: At that location, its value is At this point, it can be considered an ultra-wide embankment;

[0078] ②When hour, This indicates the location of maximum additional settlement. Located outside the outer edge of the widened top surface, the widened embankment exhibits a monotonically increasing settlement distribution within its top surface area. Therefore, the location of the maximum additional settlement within the top surface area of ​​the widened embankment is at the shoulder of the widened embankment. The maximum additional settlement value is At this point, it can be considered as a normal embankment widening.

[0079] (8) Based on the semi-analytical derivation method of the distance l from the origin of the maximum additional settlement position in step (5) and the determination method of ultra-wide embankment based on the width-to-height ratio of the widened embankment in step (7), the maximum cross slope ratio based on the width-to-height ratio of the widened embankment is proposed. Calculation and judgment methods:

[0080] ①When This is an ultra-wide embankment, and there are extreme values ​​for additional settlement within the top surface area of ​​the embankment. The location of the maximum additional settlement is... At that location, its value is At this point, the maximum cross slope change rate is... The old road shoulder should be used. At the location of maximum additional settlement Differential settlement calculation at the location, i.e. ;

[0081] ②When This is a typical road widening project. The additional settlement within the top surface area of ​​the widened embankment increases monotonically from the old road shoulder to the new road shoulder, with the maximum additional settlement occurring at the outer shoulder of the widened embankment. Its value is At this point, the maximum cross slope change rate is... The maximum value among the transverse slope ratios of the old embankment top surface, the widened embankment top surface, and the overall embankment (old and new) should be taken, i.e. ,in: , , .

[0082] The calculated maximum cross slope ratio of the widened embankment By comparing with relevant standards or engineering control indicators, it can be determined whether the current widening scheme meets the requirements for differential settlement control; if it does not, the widening width, embankment height, soft soil treatment scheme and post-construction preloading time can be synergistically optimized by combining the method of this invention.

[0083] In this invention, step (2) involves widening the top surface width of the embankment. Embankment height and embankment slope Calculate the upper base of the equivalent trapezoidal load. Bottom and high The embankment will be widened and the soil filling will be dense. With the height of the equivalent trapezoidal load The product of these is used as the equivalent uniformly distributed load intensity.

[0084] In this invention, the critical aspect ratio In order to be in Time The back calculation yields the results, which are verified through numerical analysis or on-site observation of a specific project, given the existing embankment structure and foundation soil conditions.

[0085] In this invention, the additional stress on the foundation under the equivalent load of widening the embankment in steps (2) and (4) is... Lateral distribution curve of additional surface subsidence The solution can be obtained by using the finite element numerical analysis method instead of the analytical solution. Specifically, this involves: establishing the geometric and foundation layered structures of the old embankment and the widened embankment in a two-dimensional or three-dimensional finite element numerical model; assigning corresponding elastoplastic constitutive parameters to each soil layer; correcting the spatial non-uniform distribution of the compression modulus of the foundation soil beneath the old embankment based on the consolidation results of the old embankment under long-term loads; solving for the additional stress and additional settlement distribution at each calculation point in the foundation; and extracting the additional settlement curve at the ground surface. and the location of maximum additional settlement The results obtained by the alternative semi-analytical method are used in subsequent steps.

[0086] In this invention, the critical aspect ratio In addition to semi-analytical methods and numerical analysis based on theoretical derivation, the determination of the value is also corrected by combining engineering experience or field observation results in soft soil areas. Specifically, this includes: obtaining measured settlement data during the construction and operation periods of widened embankments in typical highway reconstruction and expansion projects in soft soil areas; inverting the location of the maximum additional settlement and its relative position parameters based on the measured settlement data, and matching them with the width-to-height ratio of the widened embankment; and matching the data results of multiple engineering examples with the theoretical or numerical fitting results obtained in step (6). A comparative analysis of the relationships is conducted, and the function parameters are evaluated based on the least squares method or other error criteria. , , To perform a second-order fitting correction; in the corrected... In the relationship Re-determine the critical aspect ratio. This value will be used as the criterion for ultra-wide embankments under specific soft soil conditions.

[0087] In this invention, the maximum cross slope variation rate of the new and old embankments is determined. Based on comparison with control indicators, further... The mechanical response of the pavement structure layer is analyzed and optimized in conjunction with the mechanical response of the pavement structure layer, specifically including: establishing a mechanical analysis model that includes the pavement structure layer and the subgrade, and applying the differential settlement distribution or maximum cross slope ratio calculated according to the method of this invention. The model analysis was applied; key indicators such as tensile strain at the bottom of the asphalt surface layer, tensile strain at the bottom of the base course, and compressive strain on the top surface of the subgrade were calculated and compared with corresponding fatigue or deformation control standards; under the premise of ensuring that the calculation results of the mechanical response model of the key pavement structural layers do not exceed the allowable values, the maximum allowable cross slope variation rate was adjusted. Expand the geometric parameters of the embankment and the foundation treatment measures, and conduct joint optimization to determine a more reasonable differential settlement control index for the old and new embankments; and use the maximum cross slope ratio obtained through the above joint optimization. The corresponding allowable settlement difference serves as the control standard for engineering design, operation, and maintenance.

[0088] Example:

[0089] Taking a typical cross-section of a highway reconstruction and expansion project in the soft soil region of the Yangtze River Delta as the analysis object, the project adopts a widening method on both sides. By constructing a non-uniform foundation modulus field and calculating the distribution of additional surface settlement caused by the equivalent trapezoidal load of the widened embankment, the relative position of the maximum additional settlement and the critical width-to-height ratio are obtained. This determines whether it is an ultra-wide embankment and calculates the maximum cross slope variation rate.

[0090] The specific implementation steps are as follows:

[0091] (1) Obtain relevant parameters for the simplified calculation model of widening the embankment: Assuming that the soft soil base is uniformly distributed, from the surface downwards it is ②-1a silty clay, ②-2 silty clay, ②-4b silt, ②-6b silty clay, and the width of the top surface of the old road embankment is set. The slope of the embankment is 18m. The ratio is 1:1.5, and the unit weight of the embankment fill is... 18.0 kN / m 3 The relevant material parameters of the foundation soil, obtained from geological survey data and in-situ testing techniques, are shown in Table 1.

[0092] Table 1. Material parameters of foundation soil layers

[0093]

[0094] (2) Under the assumption of two-dimensional plane strain, with the center of the bottom of the old embankment as the origin of the coordinate system, and the horizontal direction to the right as... The positive direction of the axis, vertically downwards is In the positive direction of the axis, a simplified calculation model for widening the embankment is established, as shown in the attached figure. Figure 2 As shown.

[0095] The load on widening the embankment is simplified into an equivalent trapezoidal strip load acting on the ground surface, as shown in the attached figure. Figure 3 As shown, where For the upper base of the equivalent trapezoidal load, For the lower base of the equivalent trapezoidal load, Define the height of the equivalent trapezoidal load. This is the center of the bottom of the equivalent trapezoidal load. Depending on the geometry of the widened embankment, the equivalent trapezoidal load can be divided into three forms:

[0096] ①When At that time, as attached Figure 4 As shown in (a), the upper base of the equivalent trapezoidal load is The lower base of the equivalent trapezoidal load The height of the equivalent trapezoidal load ;

[0097] ②When At that time, as attached Figure 4 As shown in (b), the equivalent load is triangular in shape, with the base being... The height of the equivalent trapezoidal load ;

[0098] ③When At that time, as attached Figure 4 As shown in (c), the upper base of the equivalent trapezoidal load The lower base of the equivalent trapezoidal load The height of the equivalent trapezoidal load .

[0099] Center of the bottom of the equivalent trapezoidal load Local origin Calculate the additional stress of the equivalent trapezoidal load. .

[0100] As attached Figure 5 As shown, the additional stress generated at point P in the foundation soil by the equivalent trapezoidal load is calculated based on the Boussinesq elastic solution of the strip load. The equivalent trapezoidal load ADEF can be decomposed into a rectangular load BCEF, a triangular load ABF, and a triangular load CDE, that is:

[0101] ;

[0102] ; ;

[0103] ;

[0104] Restore the calculation results to the attached Figure 2 In the original coordinate system, the additional stress caused by the equivalent trapezoidal load of widening the embankment is .

[0105] (3) Assuming the thickness of the foundation compression layer There are n layers of soil within the area, where the top surface of the i-th layer is buried at a depth of . ( For the surface, ), thickness is Effective severe cases are , Indicates depth as The soil layer number at that location, i.e. Then at a depth of The effective self-weight stress at the location is .

[0106] use Criteria for determining the thickness of the foundation compressible layer Based on the equivalent trapezoidal load of the old embankment, at the center of the old road... Depth is The additional stress at the point is calculated using the elastic solution from the previous section. ,according to The thickness of the foundation compression layer can be obtained by numerical methods. .

[0107] (4) Considering the enhancing effect of foundation soil consolidation on the compression modulus under long-term load of the old embankment: Assuming that the compression modulus of the i-th soil layer below the center line of the old embankment is increased by... Growth ,in The modulus growth rate can be obtained through in-situ testing using the cone penetration test (CPT). Specifically, the compression modulus is calculated using the method outlined in the "Specifications for In-situ Testing of Geological Structures in Highway Engineering" (JTG 3223-2021) at both the old and new road subgrades. The compression modulus of different soil layers in the old and new road subgrades is calculated using the intercone resistance. Comparing the two calculations yields the modulus growth rate. Assume that the growth rate of the modulus in the i-th soil layer is related to the depth of the top surface of that layer. The relative magnitude of the additional stress on the old road is proportional to the relative magnitude of the stress. Therefore, at any lateral position within the i-th soil layer... The modulus growth rate at the point satisfies ,in For the load of the old embankment at depth Additional vertical stress at the location. Construct a non-uniform distribution field of the foundation's compressibility modulus. .

[0108] (5) Based on the elastic assumption of small strain line, the i-th soil layer is located at... At this point, the one-dimensional vertical strain caused by the equivalent trapezoidal load of the widened embankment... For a given lateral position From the surface ( Down to the bottom of the foundation compression layer Additional settlement By integrating the vertical strain along the depth, we obtain:

[0109] ;

[0110] The above equation can be rewritten using the layered summation method as follows:

[0111] ;

[0112] (6) The results of on-site in-situ testing indicate the degree of increase in the compressibility modulus of the foundation soil layer. The typical value range is approximately 0% to 10%, with a few weak layers reaching 20% ​​to 30%, i.e. In engineering terms, this can be considered a small quantity. Therefore, a first-order Taylor expansion can be performed on the formula for calculating the compression modulus of the foundation soil in step (4), resulting in:

[0113] ;

[0114] Substitute the lateral distribution curve of surface subsidence in step (5) We can obtain:

[0115] ;

[0116] make This represents the additional surface settlement caused by the equivalent trapezoidal load of widening the embankment under a uniform modulus field without considering the consolidation and strengthening effect of the old embankment. This represents the first-order correction term caused by the non-uniform modulus field effect. Substituting it, we get: Define the distance of the location of maximum additional settlement from the origin of the coordinate system. satisfy Substituting the values, we get: .

[0117] If the consolidation effect of the old road is not considered, then ,Right now At this point, the distance from the origin of the coordinate system to the location of the maximum additional settlement. satisfy Based on the symmetry of the equivalent trapezoidal load of the embankment widening, If we consider the consolidation effect of the old road, let's assume... , This represents the distance offset from the location of the maximum additional surface subsidence towards the old road. Substituting this into the above formula, and considering... and exist Performing a first-order Taylor expansion, we get:

[0118] ;

[0119] neglect Item, substitute We can obtain:

[0120] ;

[0121] In actual calculations, , It can be obtained by numerical integration. , It can be done in The finite difference approximation at the location is used to solve for the distance of the maximum additional settlement from the origin. A semi-analytical estimation method.

[0122] (7) Define the relative position of the maximum additional settlement Widen the embankment's width-to-height ratio Substitute the distance from the origin of the maximum additional settlement location in step (6) into the equation. After calculating the formula, we get:

[0123] ;

[0124] Given the geometric parameters of the embankment load and the relevant soil parameters, the terms in the above formula can be regarded as widening the embankment width-to-height ratio. The function is shown in theoretical analysis and numerical simulation results under multiple working conditions. These results indicate that, given the embankment height and soil conditions, the width-to-height ratio of the widened embankment is... Relative positional parameters of maximum additional settlement It exhibits a clear nonlinear negative correlation, and can be fitted using an empirical function in hyperbolic form, i.e.:

[0125] ;

[0126] in, , , The fitting parameters related to the geometric parameters of the embankment load and the soil parameters can be numerically calibrated using the least squares method with multiple working conditions.

[0127] Given embankment heights H of 3.0m, 3.5m, 4.0m, 4.5m, 5.0m, 5.5m, and 6.0m, plot the aspect ratio of the widened embankment. Relative positional parameters of the maximum additional surface settlement Relationship diagram, as attached Figure 6 As shown.

[0128] (8) The location of the maximum additional settlement is located exactly at the outer edge of the top surface of the widened embankment, i.e. Substitute the hyperbolic relationship between the two obtained in step (7) Solving for the critical width-to-height ratio for widening the embankment. As attached Figure 7 As shown.

[0129] The calculation results for different embankment heights H are summarized in Table 2. Given the embankment and soil parameters of the old road, Values ​​and geometric parameters of embankment widening and Irrelevant.

[0130] Table 2 Fitting curve parameters and critical aspect ratio

[0131]

[0132] (9) Based on the actual width-to-height ratio of the widening project With critical aspect ratio Based on the size relationship, determine the area where the maximum additional settlement of the widened embankment is located, and thus distinguish between ordinary widened embankments and extra-widened embankments:

[0133] ①When hour, This indicates the location of maximum additional settlement. If the settlement falls within the area of ​​the top surface of the widened embankment, then the location of the maximum additional settlement within the area of ​​the top surface of the widened embankment is: At that location, its value is At this point, it can be considered an ultra-wide embankment;

[0134] ②When hour, This indicates the location of maximum additional settlement. Located outside the outer edge of the widened top surface, the widened embankment exhibits a monotonically increasing settlement distribution within its top surface area. Therefore, the location of the maximum additional settlement within the top surface area of ​​the widened embankment is at the shoulder of the widened embankment. The maximum additional settlement value is At this point, it can be considered as a normal embankment widening.

[0135] (10) Based on the semi-analytical derivation method of the distance l from the origin of the maximum additional settlement position in step (6) and the determination method of ultra-wide embankment based on the width-to-height ratio of the widened embankment in step (9), the maximum cross slope ratio based on the width-to-height ratio of the widened embankment is proposed. The calculation and judgment methods are as follows: Figure 8 As shown:

[0136] ①When At that time, as attached Figure 8 The image shown in (a) is of an ultra-wide embankment. There are extreme values ​​for additional settlement within the top surface area of ​​the embankment. The location of the maximum additional settlement is... At that location, its value is At this point, the maximum cross slope change rate is... The old road shoulder should be used. At the location of maximum additional settlement Differential settlement calculation at the location, i.e. ;

[0137] ②When At that time, as attached Figure 8 As shown in (b), this is a typical widened embankment. The additional settlement within the top surface of the widened embankment increases monotonically from the old road shoulder to the new road shoulder, with the maximum additional settlement occurring at the outer shoulder of the widened embankment. Its value is At this point, the maximum cross slope change rate is... The maximum value among the transverse slope ratios of the old embankment top surface, the widened embankment top surface, and the overall embankment (old and new) should be taken, i.e. ,in , , .

[0138] Taking typical working conditions with different embankment top widths and embankment heights as examples, the maximum cross slope ratio is calculated, as shown in Table 3.

[0139] Table 3 Maximum cross slope ratio under different working conditions

[0140]

[0141] (11) The calculated maximum cross slope ratio Compare with current specifications or design targets, such as the "Design Specifications for Highway Reconstruction and Expansion" (JTGT L11-2014), which stipulates that "differential settlement control should meet the requirement that the increase in the cross slope of the widened roadbed should not exceed 0.5%." If this requirement is not met, the settlement can be reduced by adjusting the structure of the widened embankment and foundation treatment measures. Until the control standard requirements are met.

[0142] This embodiment demonstrates that the method of the present invention can provide reasonable criteria for judging ultra-wide embankments and a method for calculating the maximum cross slope change rate, based on the consolidation effect of the old road and the widening geometry. Based on this, a universal differential settlement control index for ultra-wide highway reconstruction and expansion projects can be established, providing a reliable basis for engineering design.

[0143] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. For example, finite element numerical analysis can be used instead of analytical solutions to solve for the additional stress and settlement of the equivalent load on the widened embankment; the range of the critical width-to-height ratio of the widened embankment can be modified based on experience in soft soil engineering in different regions; and the control index of the maximum cross slope variation rate can be optimized in conjunction with the stress-deformation response of the pavement structure layer without departing from the basic concept of the invention. All such variations, applications, or adaptations should fall within the scope of protection of this invention. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims. Various modifications and changes can be made to the specific form and details of the invention by those skilled in the art without departing from the concept of the invention. The scope of the invention is limited only by the appended claims.

Claims

1. A method for determining the criteria for ultra-wide embankments and identifying differential settlement control indicators, characterized in that, Includes the following steps: S1. Obtain the geometric parameters and foundation layering parameters of the old embankment and the widened embankment, and establish a two-dimensional plane strain calculation model; S2. In the two-dimensional plane strain calculation model, the self-weight of the embankment fill is equivalent to a trapezoidal strip load acting on the ground surface, and the additional stress distribution generated in the foundation is calculated based on the elastic theory. S3. Based on step S2, considering the consolidation effect of the foundation soil caused by the long-term load of the old embankment, construct a non-uniform distribution field of the foundation compression modulus that varies laterally. S4, based on the additional stress distribution of step S2 and the non-uniform distribution field of the foundation compression modulus of step S3, the layered summation method is used to calculate the transverse distribution curve of the additional settlement of the ground surface caused by the widening embankment load, and the distance of the position of the maximum additional settlement in the curve from the coordinate origin is determined , the coordinate origin is arranged at the center of the bottom of the old embankment, the horizontal right is the positive direction of the coordinate horizontal axis, and the vertical downward is the positive direction of the coordinate vertical axis. S5, establish the function relationship between the maximum additional settlement relative position parameter and the widening embankment width-height ratio, and solve the distance of the maximum additional settlement position from the coordinate origin The critical width-height ratio corresponding to the outer edge of the widening embankment top surface; S6. Compare the width-to-height ratio of the actual widened embankment with the critical width-to-height ratio determined in step S5 to determine whether it is an ultra-wide embankment: when the actual width-to-height ratio is greater than or equal to the critical width-to-height ratio, it is determined to be an ultra-wide embankment, and the maximum additional settlement is located within the width range of the top surface of the widened embankment; when the actual width-to-height ratio is less than the critical width-to-height ratio, it is determined to be a normal widened embankment, and the maximum additional settlement is located at or outside the outer edge of the top surface of the widened embankment. S7、According to the determination result of step S6, determine the most unfavorable control section of the overall transverse differential settlement of the new and old embankment, and calculate the maximum transverse slope change rate of the section , as the differential settlement control index.

2. The method of claim 1, wherein, In step S2, simplifying the embankment widening load into a trapezoidal strip load acting on the ground surface specifically includes: Based on the geometric parameters of the widened embankment, calculate the upper base, lower base, and height of the equivalent trapezoidal load. The trapezoidal load is decomposed into a superposition of a rectangular load and two triangular loads, and the vertical additional stress at any point in the foundation is calculated using the Boussinesq elastic solution.

3. The method of claim 1, wherein the method is characterized by: In step S3, the construction of a non-uniform distribution field of the foundation compression modulus that varies laterally specifically includes: The growth rate of the compressive modulus of the subgrade soil layers below the center line of the old embankment was obtained by in-situ testing. It was assumed that the growth rate of the modulus at any lateral position in each soil layer was proportional to the magnitude of the additional vertical stress caused by the load of the old embankment at that position, thus establishing the distribution function of the compressive modulus as a function of depth and lateral position.

4. The method of claim 1, wherein, In step S5, the maximum additional settlement relative position parameter wherein is the original half-width of the embankment top surface, in meters; is the widened embankment top surface width, in meters; The width-to-height ratio of the widened embankment is obtained by the following formula: ， wherein H is the height of the embankment, in m; The functional relationship between the relative position parameter of the maximum additional settlement and the width-to-height ratio of the widened embankment is fitted using the following hyperbolic form: ， wherein , , are fitting parameters determined by numerical simulation or engineering measured data regression, the values of which are related to the embankment height, the ground compression modulus and the modulus growth rate.

5. The method of claim 1, wherein, In step S7, determining the maximum cross slope variation rate specifically includes: When it is determined to be an ultra-wide embankment, the maximum cross slope change rate is the ratio of the differential settlement between the old road shoulder position and the maximum additional settlement position to the horizontal distance; When it is determined to be a normal embankment widening project, the maximum cross slope change rate is the maximum of the following three: the maximum cross slope change rate within the top surface of the old embankment, the maximum cross slope change rate within the top surface of the widened embankment, and the overall maximum cross slope change rate across the old and new embankments.

6. The method of claim 1, wherein, In step S2, the distribution of additional stress is calculated, and / or in step S4, the lateral distribution curve of additional surface settlement is calculated. The finite element numerical analysis method is used as a supplement or verification to the elastic theoretical solution and the semi-analytical method of layered summation.

7. The method of claim 1, wherein, The critical width-to-height ratio determined in step S5 is further calibrated and corrected by combining the measured settlement data of the target soft soil area.

8. The method of claim 1, wherein, It also includes optimization steps: The maximum cross slope variation rate calculated in step S7 is input into the mechanical analysis model containing the pavement structure layer. Key mechanical response indicators are calculated. Under the premise that the mechanical response indicators meet the specifications, the widening geometric parameters or foundation reinforcement treatment scheme are iteratively adjusted to jointly optimize the control value of the maximum cross slope variation rate.

9. The method of claim 8, wherein, The key mechanical response indicators include at least one of the following: tensile strain at the bottom of the asphalt surface layer, tensile strain at the bottom of the base course, and compressive strain at the top of the subgrade.

10. The method of claim 8, wherein the method is characterized by: The foundation reinforcement treatment scheme includes adjusting at least one of the following: drainage consolidation parameters, composite foundation design parameters, or pile foundation layout parameters.

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