Differential settlement control method for widening of road reconstruction and expansion roadbed

Abstract

The invention belongs to the technical field of road design, and relates to a road reconstruction and expansion roadbed broadening differential settlement control method, which specifically comprises the following steps: firstly, selecting a pavement modulus parameter, secondly, designing a multi-factor orthogonal test working condition, and carrying out differential settlement control standard calculation. A road surface maximum tensile stress estimation model is established by adopting a multi-population gene expression algorithm, model index contribution is explained through an SHAP method, finally, a differential settlement control standard suitable for different road surface structures is provided, the old road differential settlement standard in the highway semi-rigid base road surface construction period is 0.30%, and the differential settlement control standard in the highway semi-rigid base road surface construction period is 0.30%. The allowed differential settlement standard after new and old road construction is 0.20%; the differential settlement standard of the old road in the construction period of the semi-rigid base pavement of the first-grade highway is 0.40%, the allowable differential settlement standard of the new and old roads after construction is 0.25%, and the technical problems that in the prior art, pavement modulus parameters are not accurate, and highway grades and pavement structures are not comprehensively selected are solved.

Description

Technical Field

[0001] This invention relates to the field of road design technology, and in particular to a method for controlling differential settlement during roadbed widening in highway reconstruction and expansion. Background Technology

[0002] With the rapid development of my country's comprehensive three-dimensional transportation network, the total mileage exceeded 6 million kilometers by the end of 2024, including approximately 190,000 kilometers of expressways. Some of the earlier constructed highways, burdened by long-term heavy traffic, have reached capacity saturation and suffer from inadequate service levels and poor communication, necessitating reconstruction and expansion to improve network efficiency. Unlike new construction projects, the widening load of the roadbed in reconstruction and expansion projects causes stress redistribution, particularly at the junction of old and new roadbeds, where significant settlement differences are likely to occur. Roadbed settlement is gradual, and its harmful effects are difficult to detect immediately, increasing the complexity of control. Although existing research has focused on embankment stability and settlement treatment technologies, such as drainage boards and bored piles, these measures have not fundamentally solved the settlement problem at the junction of old and new roadbeds. Therefore, the design of reconstruction and expansion projects needs to be based on the requirements for differential settlement control between old and new roadbeds, urgently requiring the establishment of effective differential settlement control standards. In-depth research on these standards is of great significance for improving the long-term stability of roadbeds and ensuring project quality.

[0003] Chinese invention patent CN117094060A discloses a method for determining the settlement control standard of steep slope roadbed in mountainous areas. The method involves determining the design parameters of the proposed roadbed and pavement, calculating the settlement at different locations to obtain uneven settlement curves, establishing a differential settlement fitting formula, calculating the maximum additional tensile stress at the bottom of the inorganic binder stabilized layer corresponding to different differential deformation rates on the top surface of the roadbed, calculating the maximum additional tensile stress at the bottom of the inorganic binder stabilized layer under traffic loads, superimposing the additional tensile stress at the bottom of the inorganic binder stabilized layer under combined action, establishing the relationship curve between the tensile stress at the bottom of the inorganic binder stabilized layer and the differential settlement deformation rate, and obtaining a fitting formula; calculating the allowable tensile stress of the inorganic binder stabilized layer; and substituting the values ​​into the fitting formula to obtain the differential settlement control standard for steep slope roadbeds.

[0004] In summary, the existing technology has the following drawbacks:

[0005] (1) Inaccurate selection of pavement modulus parameters: In the current "Specification for Design of Highway Asphalt Pavement" (JTGD50-2017), the modulus selection system stipulates that the modulus of asphalt surface layer is based on the dynamic compression modulus at a standard temperature of 20℃ and a loading frequency of 10Hz, while the modulus of inorganic binder stabilized layer is characterized by the elastic modulus after humidity correction and freeze-thaw cycle adjustment. However, there are significant differences between the stress state under indoor test loading conditions and the stress state under actual operation conditions, and the modulus value has significant stress-dependent characteristics. The current specification ignores the essential difference between material modulus and structural modulus. In addition, the current specification fails to fully consider the performance evolution of roads during actual operation, ignoring the time-varying and degradation laws of pavement material performance under different operating conditions, thus limiting the accuracy and practicality of modulus parameters in long-term performance prediction.

[0006] (2) Incomplete selection of highway grade and pavement structure: Existing studies are usually based on a single highway grade or pavement structure, lacking a systematic study on differential settlement control standards under different highway grades and pavement forms, and the conclusions obtained have low applicability to differential settlement control standards. Summary of the Invention

[0007] To overcome the problems and shortcomings of existing technologies, this invention addresses the issues of inaccurate pavement modulus parameters and incomplete selection of highway grade and pavement structure in existing methods for controlling differential settlement of roadbed widening during reconstruction and expansion. It provides a method for controlling differential settlement of roadbed widening during highway reconstruction and expansion.

[0008] The technical solution adopted in this invention is a method for controlling differential settlement of roadbed widening during highway reconstruction and expansion, comprising the following steps:

[0009] S1: Establish the overall finite element model of the roadbed and pavement structure;

[0010] S2: Calculate the settlement at different locations on the top surface of the roadbed in the model established in S1, and establish a fitting formula for the differential settlement curves of the old roadbed during construction and the new roadbed after construction.

[0011] S3: Based on the fitting formula for the differential settlement curves of the old roadbed during the construction period and the new roadbed after construction established in S2, establish a separate analysis model for the pavement under various working conditions;

[0012] S4: Apply displacement boundary conditions corresponding to different differential settlement amounts 'a' to the pavement individual analysis models under various working conditions established in S3 to obtain the maximum tensile stress S11 of the pavement structural layer corresponding to different differential settlement amounts 'a'. max ;

[0013] S5: Establish the relationship curves and fitting formulas between the tensile stress S11 of the pavement structure layer and different differential settlements a for the pavement individual analysis models established in S4 under various working conditions.

[0014] S6: The maximum allowable differential settlement and differential settlement slope ratio corresponding to the tensile stress S11 of the pavement structure layer are obtained by interpolation, and the differential settlement control standard of the semi-rigid base of the highway is calculated.

[0015] S7: Using a multi-population gene expression algorithm, establish the prediction function of the maximum tensile stress of the old road base layer and the prediction function of the maximum tensile stress of the new road bottom base layer of the semi-rigid base pavement of highway.

[0016] S8: Perform SHAP sensitivity analysis on the prediction functions of the maximum tensile stress of the old road base and the maximum tensile stress of the new road subbase of the semi-rigid base pavement of the highway obtained in S7;

[0017] S9: Substitute the pavement structure parameters of Class I highway into the prediction function of the maximum tensile stress of the old road base and the maximum tensile stress of the new road subbase of the semi-rigid base pavement of expressway obtained by S7, and obtain the differential settlement control standard of Class I highway semi-rigid base.

[0018] Furthermore, the specific steps of S2 are as follows:

[0019] The settlement at different locations on the top surface of the roadbed was calculated using ABAQUS software. Based on the differential settlement curves of the old and new roadbeds under widening, a fitting formula for the differential settlement curves of the old roadbed during construction and the new roadbed after construction was established.

[0020] The fitting formula for the differential settlement curve of the old roadbed during the construction period is:

[0021]

[0022] Where: u1 represents the differential settlement of the old road during the widening construction phase, a max The maximum differential settlement of the old roadbed is given by l1, which is half the width of the old roadbed, and x. a Here are the x-coordinates of each calculated point on the surface of the old roadbed along the x-direction.

[0023] The fitting formula for the differential settlement curve of the new roadbed after construction is:

[0024]

[0025] Where u2 is the differential settlement of the new road after construction, b is the maximum differential settlement of the new roadbed, l2 is the distance between the new shoulder and the point of maximum settlement, and x b This is to calculate the distance from the point of maximum settlement.

[0026] Furthermore, the pavement individual analysis models under various working conditions in S3 are specifically: the pavement individual analysis model for old pavement with semi-rigid base on highways, and the pavement individual analysis model for new pavement with semi-rigid base on highways.

[0027] Furthermore, S4 includes the following steps:

[0028] S41: Select a pavement structure, which includes a semi-rigid base old pavement structure for highways and a semi-rigid base new pavement structure for highways; determine the structural parameters and material flexural strength of the pavement structure.

[0029] The road surface structure parameters include the surface layer material modulus E. pave Base material modulus E base Subbase material modulus E subb Surface layer thickness H pave Base layer thickness H base Subbase thickness H subb Road width L, flexural strength, Poisson's ratio v;

[0030] S42: Apply displacement boundary conditions corresponding to different differential settlement amounts 'a' to the individual pavement analysis model under various working conditions through the displacement subroutine;

[0031] S43: Repeat S42 to obtain the maximum tensile stress S11 of the pavement structure corresponding to different differential settlement a. max .

[0032] Furthermore, S6 includes the following steps:

[0033] S61: Maximum tensile stress of pavement structure corresponding to different differential settlement amounts 'a' obtained from S4. max Analyze the overall stress on the new and old road surface structures;

[0034] S62: Based on the overall stress of the new and old pavement structures obtained in S61, compare the stress of each layer in the new and old pavement structures to determine the structural layer with the greatest stress in the new and old pavement structures;

[0035] S63: Determine the critical differential settlement range for failure by utilizing the flexural strength of the materials in the new and old pavement structural layers that bear the greatest stress.

[0036] S64: Calculate the maximum allowable differential settlement corresponding to the tensile stress S11 of the pavement structure layer by interpolation within the critical differential settlement range;

[0037] S65: Calculate the maximum allowable differential settlement slope ratio of the old road during the widening construction period and the maximum allowable differential settlement slope ratio of the old and new roads after construction using the maximum allowable differential settlement obtained from S64.

[0038] The expression for the maximum allowable differential settlement slope ratio of the old road during the widening construction period is:

[0039] Δ=a r / 2 / L (3)

[0040] The expression for the maximum allowable differential settlement between the new and old roads after construction is:

[0041] Δ=a r / L (4)

[0042] Where Δ is the differential settlement slope rate, a r L represents the allowable differential settlement value, and L is the road width.

[0043] S66: Determine the standards for differential settlement control of semi-rigid base courses for highways;

[0044] The allowable differential settlement standard for the old road during the construction period of the semi-rigid base course of the expressway is 0.30%, and the allowable differential settlement standard for the old road and the new road after construction is 0.20%.

[0045] Furthermore, the method for determining the differential settlement control standard for semi-rigid base courses of highways described in S6 is as follows:

[0046] By comparing the differential settlement rates of multiple sets of test data, the maximum value or additional safety redundancy is taken to determine the differential settlement control standard of the old road during the construction period and the allowable differential settlement standard of the new and old roads after construction.

[0047] The security redundancy is calculated by rounding the calculated value up to an integer multiple of 0.05%.

[0048] Furthermore, the prediction model for the maximum tensile stress of the semi-rigid pavement of the highway under multiple factors in S7 is as follows: the prediction model for the maximum tensile stress of the old road base of the semi-rigid base pavement of the highway is as shown in Equation (5), and the prediction model for the maximum tensile stress of the new road bottom base of the semi-rigid base pavement of the highway is as shown in Equation (6).

[0049]

[0050] in: For the prediction model of the maximum tensile stress of the old road base of the semi-rigid base pavement of the highway, H subb H represents the thickness of the base layer. base For the thickness of the base layer, H pave E represents the surface layer thickness. subb E represents the modulus of the base material. pave denoted as the modulus of the surface layer material, 'a' as the maximum differential settlement of the old subgrade, and 'L' as the width of the road surface.

[0051]

[0052] in: A model for predicting the maximum tensile stress in the new subbase of a semi-rigid base roadway for highways.

[0053] Furthermore, the maximum tensile stress prediction models for the old road base layer and the new road subbase layer of the semi-rigid base course of highways established in S7 are used as analysis objects. The maximum tensile stress of the pavement structure is decomposed into the sum of the attribution values ​​of each input feature. The SHAP value is calculated to quantify the contribution of each input feature to the model prediction results, key influencing factors are identified, and the direction and intensity of the influence of each feature parameter on the maximum tensile stress of the pavement structure are analyzed based on the sign and magnitude of the SHAP value.

[0054] Furthermore, in S8, a SHAP sensitivity analysis is performed on the prediction model obtained in S7. The SHAP sensitivity analysis formula is shown in equation (7):

[0055]

[0056] Where: i is the feature, φ i Let be the SHAP value of feature i, M be the set of all features, S be a feature subset, |S| be the number of features in feature subset S, and f(S) be the prediction value of the current sample by the model trained using the features in feature subset S. Let S be the predicted value of the current sample by the model trained using features from the feature subset S∪{i}, where |S|!(M-|S|-1)! is the weight factor, {i} is the set of features i, and ∪ is the union of the features. For the model being explained, ! represents the factorial.

[0057] Furthermore, the specific differential settlement control indicators for the semi-rigid base course of Class I highway S9 are as follows:

[0058] The allowable differential settlement standard for the old road during the construction period of semi-rigid base pavement for Class I highways is 0.40%, and the allowable differential settlement standard for the old road and the new road after construction is 0.25%.

[0059] The beneficial effects of this invention are:

[0060] 1) Traditional methods for determining roadbed settlement control standards all refer to the current "Specifications for Design of Asphalt Pavement on Highways" (JTGD50-2017) for selecting pavement parameter moduli. This specification explicitly states that the material modulus used in the design of new asphalt pavements is a dynamic modulus obtained in the laboratory, essentially representing the material modulus of the pavement structure. This modulus differs significantly from the actual pavement equivalent structural modulus. Directly referencing existing specification modulus values ​​for numerical calculations is unreasonable, ignoring the fundamental difference between material modulus and structural modulus. This invention first refers to current specifications and related literature, selecting pavement modulus parameters from the perspective of in-situ testing (Falling Weight Deflectometer, FWD). This significantly improves the fit with actual conditions and effectively solves the problem of inaccurate parameter selection. Furthermore, current specifications fail to fully consider the performance evolution of roads during actual operation, neglecting the time-varying and degradation patterns of pavement material properties under different operating conditions, thus limiting the accuracy and practicality of modulus parameters in long-term performance prediction.

[0061] 2) Traditional methods for determining roadbed settlement control standards employ various settlement curve forms, which deviate from actual conditions. The selection of settlement curves requires further adjustment. Furthermore, existing specifications stipulate that the increase in cross slope after construction should not exceed 0.5%. The aim is to reduce differential settlement and minimize cracking and damage to the pavement structure. However, these regulations do not consider the construction period; in fact, excessive differential settlement during construction leading to pavement cracking is unacceptable. Therefore, this invention redefines the control standards for differential settlement, establishing two sets of differential settlement curve fitting formulas for the old embankment and new roadbed during the widening period. Based on these formulas, two standards are established for the old road during the widening construction period and the new road after construction.

[0062] 3) Traditional methods for determining roadbed settlement control standards are all based on a single highway grade or pavement structure, lacking a systematic study on differential settlement control standards under different highway grades and pavement forms. The applicability of the conclusions obtained to differential settlement control standards is questionable. This invention considers different highway grades and pavement structure forms of semi-rigid base courses for expressways and semi-rigid base courses for Class I highways, and proposes differential settlement control standards for semi-rigid base courses for expressways and semi-rigid base courses for Class I highways respectively, forming a systematic study on differential settlement control standards. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 This is a settlement curve diagram of the roadbed widening according to an embodiment of the present invention;

[0065] Figure 2 This is a tensile stress distribution diagram of the old highway base course of Eg1-Eg3 in the embodiments of the present invention (E represents modulus change, g represents highway).

[0066] Figure 3 This is a diagram showing the calculation results of the maximum tensile stress of the old road base layer of the semi-rigid base pavement of the expressway in the embodiment of the present invention, wherein: (a) Base layer S11 of Eg1-Eg9 max (b)Eg10-Eg18 Basic S11 max (c)Eg19-Eg27 Basic S11 max (d)Hg1 (H indicates thickness change) -Hg6 base layer S11 max (e)Hg7-Hg12 base layer S11 max (f)Hg13-Hg18 base layer S11 max ;

[0067] Figure 4 This is a tensile stress distribution diagram of the new roadbed base layer of expressways En (E represents modulus change, n represents first-class highway) 1-En3 in the embodiments of the present invention;

[0068] Figure 5 This is a diagram showing the calculation results of the maximum tensile stress in the new subbase of a semi-rigid base roadway for highways according to an embodiment of the present invention, wherein: (a) En1-En9 subbase S11 max (b)En10-En18 subbase S11 max (c)En19-En27 subbase S11 max (d)Hn1 (H thickness change)-Hn6 subbase S11 max ;

[0069] Figure 6 These are fitting results of the maximum tensile stress for different road structures in embodiments of the present invention, wherein: (a) fitting results of the old road base layer of semi-rigid base pavement, and (b) fitting results of the new road subbase layer of semi-rigid base pavement;

[0070] Figure 7These are hive diagrams showing the distribution of the maximum tensile stress (SHAP) value of the pavement structure under different factors in embodiments of the present invention, as well as the absolute average SHAP (Shapley Additive Explanation) value, where: (a) hive diagram of SHAP value distribution of the old semi-rigid base course of the highway, (b) hive diagram of SHAP value distribution of the new semi-rigid base course of the highway, (c) absolute average SHAP of each factor in the old semi-rigid base course of the highway, and (d) new semi-rigid base course of the highway. The absolute average of all factors at the grassroots level (SHAP). Detailed Implementation

[0071] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0072] The concept of this invention is as follows: First, referring to current standards and relevant literature, pavement modulus parameters were selected from the perspective of field-worn dynamics (FWD). Second, considering the actual stress state of the pavement under traffic loads, multi-factor orthogonal test conditions were designed, and differential settlement control standards were calculated based on the limit state. Furthermore, a prediction model for the maximum tensile stress of the pavement under multi-factor conditions was established using a multi-population gene expression algorithm, and the contribution of the maximum tensile stress prediction model index was explained using the SHAP method. Finally, differential settlement control standards for semi-rigid base pavements of expressways and first-class highways were proposed for different pavement structures.

[0073] Considering the complex deformation patterns of highway reconstruction and expansion projects, treating the foundation as a semi-infinite space foundation would greatly increase the computational complexity. Related numerical analyses also show that the maximum tensile stress of the pavement structure calculated without considering the foundation's influence is almost the same as that calculated with the foundation's influence. Therefore, this invention simplifies the calculation of additional stress on the pavement structure caused by differential settlement to solving for additional stress on the pavement structure under the corresponding displacement boundary conditions. This method greatly simplifies the numerical analysis process and has been widely used in solving for additional stress on the pavement structure caused by differential settlement. The calculation assumptions in this study are as follows: (1) Each layer of the pavement is considered homogeneous, continuous, and transversely isotropic, and the mechanical material properties are characterized by the elastic modulus E and Poisson's ratio μ; (2) The contact conditions between the pavement structure layers are assumed to be completely continuous in the vertical direction and without friction. As the highway reconstruction and expansion project proceeds, the pavement structure layers will slowly deform with the settlement of the subgrade, and there will be no voiding between the layers during operation; (3) The pavement structure is a strip structure and is considered as a plane strain problem; (4) Only the additional stress on the pavement structure caused by differential settlement is analyzed.

[0074] An example of a method for controlling differential settlement during roadbed widening in highway reconstruction and expansion includes the following steps:

[0075] S1: Establish the overall finite element model of the roadbed and pavement structure;

[0076] Step S1 is as follows: After determining the calculation parameters of the roadbed and foundation based on the climate conditions, geological survey data and construction design drawings of the field test section, the ABAQUS software is used to establish an overall finite element model of the roadbed and pavement structure. In the model, the slope ratio of the new and old roadbeds is set to 1:1.5, and a semi-symmetric structure is adopted to study the influence of boundary effects. The boundary conditions of the model are set as follows: horizontal displacement is constrained on the left and right sides, fixed constraints are adopted at the bottom, the groundwater level is set as a permeable boundary, and the rest is an impermeable boundary. Finally, numerical calculations are carried out based on the above settings.

[0077] S2: Calculate the settlement at different locations on the top surface of the roadbed in the model established in S1, and establish a fitting formula for the differential settlement curves of the old roadbed during construction and the new roadbed after construction.

[0078] Step S2 specifically involves inputting the soil parameters of the subgrade and foundation into the finite element model of the subgrade and pavement structure established in ABAQUS software. The specific soil parameters input for the subgrade and foundation are: dry density γ. d Elastic modulus E, Poisson's ratio v, shear strength c, angle of internal friction The settlement at different locations on the top surface of the roadbed in the model built in S1 can be calculated using the permeability coefficient k and the void ratio.

[0079] Then, establish a fitting formula for the differential settlement curves of the old roadbed during construction and the new roadbed after construction, referring to... Figure 1After obtaining the settlement curve of the roadbed, it can be decomposed into the old road part and the new road part. Then, by fitting the formula, the differential settlement curve formulas of the old road and the new road can be obtained respectively.

[0080] The basis for this is that under the action of widening load, the settlement of the old roadbed is distributed in the shape of "inverted bending basin" and the settlement of the new roadbed is distributed in the shape of "saddle". The differential settlement curves of the old and new roadbeds during the construction period are obtained by translating the original differential settlement curves.

[0081] The fitting formula for the differential settlement curve of the old roadbed during the construction period is:

[0082]

[0083] Where: u1 represents the differential settlement of the old road during the widening construction phase, in cm; a max The maximum differential settlement of the old roadbed is expressed in cm, l1 is half the width of the old roadbed in meters, and x is the value of x. a The x-coordinates of each calculated point on the surface of the old roadbed are given in meters.

[0084] The fitting formula for the differential settlement curve of the new and old roadbeds after construction is:

[0085]

[0086] Where u2 represents the differential settlement of the new road during the widening construction phase, in cm; b represents the maximum differential settlement of the new roadbed, in cm; l2 represents the distance between the new road shoulder and the point of maximum settlement, in meters; and x... b The distance from the calculation point to the maximum settlement point is expressed in meters.

[0087] Interpret the dimensions of the variables in equation (2), and interpret the right side of the equation (2). Simplifying, we can consider it as dimensionless, so the dimensions of both sides of equation (2) are cm.

[0088] It needs to be explained that: with Figure 1 Taking the differential settlement curve of the China-Laos road as an example, the abscissa of each data point on the differential settlement curve of the old road is the abscissa of each point on the surface of the old roadbed.

[0089] S3: Based on the fitting formula for the differential settlement curves of the old roadbed during the construction period and the new roadbed after construction established in S2, establish a separate analysis model for the pavement under various working conditions;

[0090] The specific pavement individual analysis models under various working conditions in S3 are: highway semi-rigid base old pavement individual analysis model, and highway semi-rigid base new pavement individual analysis model.

[0091] S4: Write a subroutine to apply displacement boundary conditions corresponding to different differential settlement amounts 'a' to the pavement individual analysis models under various working conditions established in S3, and obtain the maximum tensile stress S11 of the pavement structure corresponding to different differential settlement amounts 'a'. max ;

[0092] Step S4 is as follows:

[0093] S41: Select the pavement structure, which includes the pavement structure of the old semi-rigid base pavement of the expressway and the pavement structure of the new semi-rigid base pavement of the expressway. Determine the structural parameters and material flexural strength of the pavement structure.

[0094] Road surface structural parameters include the surface layer material modulus E pave Base material modulus E base Subbase material modulus E subb Surface layer thickness H pave Base layer thickness H base Subbase thickness H subb Road width L, flexural strength, Poisson's ratio v;

[0095] S42: Apply displacement boundary conditions corresponding to different differential settlement amounts 'a' to the individual pavement analysis model under various working conditions through the displacement subroutine;

[0096] In this embodiment, the displacement subroutine in finite element analysis (using ABAQUS software) is a user-defined subroutine specifically designed to define complex, non-standard displacement boundary conditions.

[0097] S43: Repeat S42 to obtain the maximum tensile stress S11 of the pavement structure corresponding to different differential settlement a. max The operating conditions selected for the calculation are shown in Tables 2 and 3.

[0098] In this embodiment, for old pavements, the input differential settlement displacement 'a' can be 1cm, 2cm, 3cm, ..., 14cm, 15cm. This set of values ​​covers a large settlement range and aims to simulate the significant differential settlement that old pavements may experience. For new pavements, the input differential settlement displacement 'a' can be 0.2cm, 0.4cm, 0.6cm, ..., 1.4cm. This set of values ​​is smaller and more refined, reflecting the characteristics of new pavements in the early stages of service or more sensitive to smaller deformations.

[0099] In this application, the flexural tensile strength of typical pavement structures and pavement structures are determined according to the "Specifications for Design of Asphalt Pavement of Highways" (JTGD50-2017). The pavement structure parameters are based on the results of typical FWD modulus inversion research, as shown in Table 1. The repeated action of vehicle loads and the influence of environmental factors such as ultraviolet radiation, temperature, and water cause continuous changes in the material properties of the pavement structure layer, ultimately leading to a significant reduction in pavement performance. Furthermore, the degree of pavement attenuation varies with the increase in service life. In my country's expressways and first-class highways, the use of semi-rigid base pavements accounts for over 90%. This application focuses on this structural type, specifically including semi-rigid base pavements for expressways and first-class highways. This application implements the displacement application of the pavement structure by writing a displacement subroutine and adopts a widening method on both sides, taking half of the symmetrical subgrade for research.

[0100] Table 1. Results of modulus inversion study using FWD (Falling Weight Deflectometer).

[0101]

[0102] In this embodiment, the tensile stress of the pavement structure of an old road with different differential settlements under seven factors (Eg1-Eg3) was calculated, and the results are as follows: Figure 2 As shown in the analysis, the cement-stabilized crushed stone base course of the old highway is under tension, and the maximum tensile stress is concentrated at a distance of about 1-1.5m from the shoulder of the old road. This phenomenon reveals the reason why cracks in the spliced ​​sections of the pavement are located 1-2m inward from the joint in actual engineering. In addition, the differential settlement of the subgrade has a significant impact on the tensile stress of the pavement structure. Under the same pavement structure parameters, the cement-stabilized crushed stone base course shows a significant increase with the increase of differential settlement.

[0103] Table 2 shows the orthogonal factor conditions for semi-rigid base old road pavement of expressways.

[0104] Group number <![CDATA[E pave ]]> <![CDATA[E base ]]> <![CDATA[E subb ]]> <![CDATA[H pave ]]> <![CDATA[H base ]]> <![CDATA[H subb ]]> L Group number <![CDATA[E pave ]]> <![CDATA[E base ]]> <![CDATA[E subb ]]> <![CDATA[H pave ]]> <![CDATA[H base ]]> <![CDATA[H subb ]]> L Eg1 3000 4000 1500 15 30 20 14 Eg24 4000 5000 2500 15 30 20 14 Eg2 3000 4000 2000 15 30 20 14 Eg25 4000 6000 1500 15 30 20 14 Eg3 3000 4000 2500 15 30 20 14 Eg26 4000 6000 2000 15 30 20 14 Eg4 3000 5000 1500 15 30 20 14 Eg27 4000 6000 2500 15 30 20 14 Eg5 3000 5000 2000 15 30 20 14 Hg1 3000 6000 2500 12 30 16 14 Eg6 3000 5000 2500 15 30 20 14 Hg2 3000 6000 2500 12 30 20 14 Eg7 3000 6000 1500 15 30 20 14 Hg3 3000 6000 2500 12 32 16 14 Eg8 3000 6000 2000 15 30 20 14 Hg4 3000 6000 2500 12 32 20 14 Eg9 3000 6000 2500 15 30 20 14 Hg5 3000 6000 2500 12 36 16 14 Eg10 3500 4000 1500 15 30 20 14 Hg6 3000 6000 2500 12 36 20 14 Eg11 3500 4000 2000 15 30 20 14 Hg7 3000 6000 2500 15 30 16 14 Eg12 3500 4000 2500 15 30 20 14 Hg8 3000 6000 2500 15 30 20 14 Eg13 3500 5000 1500 15 30 20 14 Hg9 3000 6000 2500 15 32 16 14 Eg14 3500 5000 2000 15 30 20 14 Hg10 3000 6000 2500 15 32 20 14 Eg15 3500 5000 2500 15 30 20 14 Hg11 3000 6000 2500 15 36 16 14 Eg16 3500 6000 1500 15 30 20 14 Hg12 3000 6000 2500 15 36 20 14 Eg17 3500 6000 2000 15 30 20 14 Hg13 3000 6000 2500 18 30 16 14 Eg18 3500 6000 2500 15 30 20 14 Hg14 3000 6000 2500 18 30 20 14 Eg19 4000 4000 1500 15 30 20 14 Hg15 3000 6000 2500 18 32 16 14 Eg20 4000 4000 2000 15 30 20 14 Hg16 3000 6000 2500 18 32 20 14 Eg21 4000 4000 2500 15 30 20 14 Hg17 3000 6000 2500 18 36 16 14 Eg22 4000 5000 1500 15 30 20 14 Hg18 3000 6000 2500 18 36 20 14 Eg23 4000 5000 2000 15 30 20 14 Lg1 3000 6000 2500 12 36 20 13

[0105] Table 3. Orthogonal factors of semi-rigid base road surface in highway construction conditions

[0106]

[0107]

[0108] Figure 3 (a)-(f) are the calculated results of the maximum tensile stress of cement-stabilized crushed stone base course under different differential settlement for groups Eg1-Eg27 and Hg1-Hg18 (including Lg1).

[0109] from Figure 3As can be seen, there is a clear linear relationship between the maximum tensile stress of the pavement structure and the differential settlement. Compared with pavement structure parameters, thickness and width have a more significant impact on the corresponding results. Figure 3 As shown in (d), when the differential settlement of Hg6 group is 8cm, the maximum tensile stress of the cement-stabilized crushed stone base course is 0.904MPa, which has reached its tensile strength. Linear interpolation yields an allowable differential settlement of 7.96cm. The existing standard, "Design Specifications for Highway Reconstruction and Expansion" (JTG-TL11-2014), stipulates that the increase in cross slope after construction should not exceed 0.5%. The purpose is to reduce differential settlement and minimize cracking and damage to the pavement structure. However, the above regulations do not consider the construction period. In fact, excessive differential settlement during construction leading to cracking of the old pavement is also unacceptable. Since the settlement during construction has reached 50%–75% of the total settlement, considering the most unfavorable situation, the maximum allowable differential settlement is 7.96*50% = 3.98cm. Therefore, the maximum allowable differential settlement slope ratio during the widening construction period is 3.98cm / 14cm = 0.28%. Figure 3 As shown in (d), when the differential settlement of Lg1 group is 7cm, the maximum tensile stress of the cement-stabilized crushed stone base course is 0.916MPa, the allowable differential settlement is 6.88cm, and the allowable slope difference is 6.88 / 2 / 13=0.26%. Since the extreme state is considered, the differential settlement control standard of the old road during the construction period can be taken as 0.30%.

[0110] Drawing as Figure 4 The diagram shows the tensile stress distribution in the new subbase of a semi-rigid base course for a highway. From... Figure 4 It can be seen that as the differential settlement of the subgrade increases, the tensile stress of each structural layer of the new road surface changes in the same way as that of the old road surface. The difference is that the bottom surface of the new road surface is under tension, and the maximum tensile stress occurs in the cement-stabilized crushed stone subbase, and the maximum tensile stress occurs at about 1m on the new shoulder.

[0111] Figure 5 (a)-(d) show the calculated maximum tensile stress of cement-stabilized crushed stone subbase under different differential settlement for groups En1-En27 and Hn1-Hn6 (including Ln1). Compared to older roads, newer roads are more sensitive to changes in differential settlement, such as... Figure 5 (d) It can be seen that for group Hg6, when the differential settlement is 0.8cm, the maximum tensile stress of the cement-stabilized crushed stone subbase is 1.029MPa, which has reached its flexural strength. Linear interpolation shows that its allowable differential settlement is 0.7cm and the allowable slope difference is 0.18%. For group Ln1, when the differential settlement is 0.6cm, the maximum tensile stress of the cement-stabilized crushed stone subbase is 1.031MPa, the allowable differential settlement is 0.52cm, and the allowable slope difference is 0.15%, which can be taken as 0.20%.

[0112] S5: Establish the relationship curve and fitting formula between the tensile stress S11 of the pavement structure layer and the differential settlement a for the pavement individual analysis model under each working condition established in S4.

[0113] S6: The maximum allowable differential settlement and differential settlement slope ratio corresponding to the tensile stress S11 of the pavement structure layer are obtained by interpolation, and the differential settlement control standard of the semi-rigid base of the highway is calculated.

[0114] S6 includes the following steps:

[0115] S61: Maximum tensile stress of pavement structure corresponding to different differential settlement amounts 'a' obtained based on S44. max Analyze the overall stress on the new and old road surface structures;

[0116] S62: Based on the overall stress of the new and old pavement structures obtained in S61, compare the stress of each layer in the new and old pavement structures to determine the structural layer with the greatest stress in the new and old pavement structures;

[0117] S63: Determine the critical differential settlement range for failure by utilizing the flexural strength of the materials in the new and old pavement structural layers that bear the greatest stress.

[0118] S64: Calculate the maximum allowable differential settlement corresponding to the tensile stress S11 of the pavement structure layer by interpolation within the critical differential settlement range;

[0119] S65: Calculate the maximum allowable differential settlement slope ratio of the old road during the widening construction period and the maximum allowable differential settlement slope ratio of the old and new roads after construction using the maximum allowable differential settlement obtained from S64.

[0120] The expression for the maximum allowable differential settlement slope ratio of the old road during the widening construction period is:

[0121] Δ=a r / 2 / L (3)

[0122] The expression for the maximum allowable differential settlement between the new and old roads after construction is:

[0123] Δ=a r / L (4)

[0124] Where Δ is the differential settlement slope rate, a r The value represents the allowable differential settlement in cm, and L represents the road width.

[0125] S66: Determine the standards for differential settlement control of semi-rigid base courses for highways;

[0126] The method for determining the differential settlement control standard for semi-rigid base courses of highways is as follows: compare the differential settlement variability of multiple sets of test data, take the maximum value or add safety redundancy, and then determine the differential settlement control standard for the old road during the construction period and the allowable differential settlement standard for the new and old roads after construction.

[0127] The allowable differential settlement standard for the old road during the construction period of the semi-rigid base pavement of the expressway is 0.30%, and the allowable differential settlement standard for the old road and the new road after construction is 0.20%.

[0128] S7: Using a multi-population gene expression algorithm, establish the prediction function of the maximum tensile stress of the old road base layer and the prediction function of the maximum tensile stress of the new road bottom base layer of the semi-rigid base pavement of highway.

[0129] The specific prediction models for the maximum tensile stress of semi-rigid pavement on highways under multiple factors in S7 are as follows: the prediction model for the maximum tensile stress of the old road base layer of semi-rigid base pavement on highways is as shown in equation (5), and the prediction model for the maximum tensile stress of the new road base layer of semi-rigid base pavement on highways is as shown in equation (6).

[0130]

[0131] in: For the prediction model of the maximum tensile stress of the old road base of the semi-rigid base pavement of the highway, H subb H represents the thickness of the base layer. base For the thickness of the base layer, H pave E represents the surface layer thickness. subb E represents the modulus of the base material. pave denoted as the modulus of the surface layer material, 'a' as the maximum differential settlement of the old subgrade, and 'L' as the width of the road surface.

[0132]

[0133] in: A model for predicting the maximum tensile stress in the new subbase of a semi-rigid base course for highways;

[0134] Equations (5) and (6) were fitted respectively, and the fitting results are as follows: Figure 6 (a) and Figure 6 As shown in (b), from Figure 6 (a) and Figure 6 (b) It can be seen that the R values ​​of the maximum tensile stress predicted by the model are all above 0.98, and the fitting effect is good. The proposed prediction model can obtain the maximum tensile stress of various pavement structures by using only equations (5) and (6) when the pavement structure parameters are uncertain.

[0135] S8: Perform SHAP sensitivity analysis on the prediction functions of the maximum tensile stress of the old road base and the maximum tensile stress of the new road subbase of the semi-rigid base pavement of the highway obtained in S7;

[0136] S8 is detailed below:

[0137] The maximum tensile stress prediction models for the old road base and the new road subbase of the semi-rigid base pavement established in S7 are used as the analysis objects. The maximum tensile stress of the pavement structure is decomposed into the sum of the attribution values ​​of each input feature. The SHAP value is calculated to quantify the contribution of each input feature to the model prediction results, key influencing factors are identified, and the direction and intensity of the influence of each feature parameter on the maximum tensile stress of the pavement structure are analyzed based on the sign and magnitude of the SHAP value.

[0138] In S8, a SHAP sensitivity analysis is performed on the prediction model obtained in S7. The SHAP sensitivity analysis formula is shown in equation (7):

[0139]

[0140] Where: i is the feature, φ i Let be the SHAP value of feature i, M be the set of all features, S be a feature subset, |S| be the number of features in feature subset S, and f(S) be the prediction value of the current sample by the model trained using the features in feature subset S. Let S be the predicted value of the current sample by the model trained using features from the feature subset S∪{i}, where |S|!(M-|S|-1)! is the weight factor, {i} is the set of features i, and ∪ is the union of the features. For the model being explained, ! represents the factorial.

[0141] Figure 7 This is a peak distribution diagram of the maximum tensile stress (SHAP) of the pavement structure under different factors in this embodiment of the invention, along with the absolute average SHAP value. Figure 7 (a) and (b) present the beehive plots showing the distribution of SHAP values ​​for each factor. A positive SHAP value indicates that the influencing factor has a positive effect on the model, while a negative SHAP value indicates a negative effect. A more dispersed distribution of sample points indicates a greater overall influence of the factor on the model; if most points are around zero, the factor has a smaller influence. Figure 7 As can be seen from (a) and (b), the distribution of a is relatively wide, exhibiting the most significant impact on the tensile stress of the pavement structure. Taking an old highway with a semi-rigid base as an example, the base S11... max The SHAP value varies with a, E base H base The value of L increases with the increase of L, and the eigenvalues ​​of most samples are relatively large, indicating that the above factors have a positive effect on the maximum tensile stress of the base layer. In addition, L has a negative effect on the maximum tensile stress of the base layer. Figure 7(c) and (d) show the ranking of the average SHAP values ​​of different factors, with the importance of the factors decreasing from top to bottom. Taking the semi-rigid base pavement of a high-speed road as an example, the ranking of the average SHAP values ​​of different factors on the tensile stress of the old road base is a > E. base >L>H base >E subb >H pave >H subb >E pave Their importance percentages were 41%, 25.77%, 9.986%, 8.565%, 5.914%, 5.117%, 2.884%, and 1.795%, respectively. Except for a, E... base The core factor affecting the maximum tensile stress in the base layer is L, followed by H. base The impact is secondary, E pave The impact is minimal.

[0142] S9: Substitute the estimated functions of maximum tensile stress of old road base and maximum tensile stress of new road base obtained from S7 into the pavement structure parameters of Class I highway to obtain the differential settlement control standard of semi-rigid base of Class I highway.

[0143] The specific differential settlement control indicators for the semi-rigid base course of Class I highway S9 are as follows:

[0144] The allowable differential settlement standard for the old road during the construction period of semi-rigid base pavement of Class I highway is 0.40%, and the allowable differential settlement standard for the old road after construction is 0.25%.

[0145] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0146] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for controlling differential settlement during roadbed widening in highway reconstruction and expansion, characterized in that, Includes the following steps: S1: Establish the overall finite element model of the roadbed and pavement structure; S2: Calculate the settlement at different locations on the top surface of the roadbed in the model established in S1, and establish a fitting formula for the differential settlement curves of the old roadbed during construction and the new roadbed after construction. S3: Based on the fitting formula for the differential settlement curves of the old roadbed during the construction period and the new roadbed after construction established in S2, establish a separate analysis model for the pavement under various working conditions; S4: Apply displacement boundary conditions corresponding to different differential settlement amounts 'a' to the pavement individual analysis models under various working conditions established in S3 to obtain the maximum tensile stress S11 of the pavement structural layer corresponding to different differential settlement amounts 'a'. max ; S5: Establish the relationship curves and fitting formulas between the tensile stress S11 of the pavement structure layer and different differential settlements a for the pavement individual analysis models established in S4 under various working conditions. S6: The maximum allowable differential settlement and differential settlement slope ratio corresponding to the tensile stress S11 of the pavement structure layer are obtained by interpolation, and the differential settlement control standard of the semi-rigid base of the highway is calculated. S7: Using a multi-population gene expression algorithm, establish the prediction function of the maximum tensile stress of the old road base layer and the prediction function of the maximum tensile stress of the new road bottom base layer of the semi-rigid base pavement of highway. S8: Perform SHAP sensitivity analysis on the prediction functions of the maximum tensile stress of the old road base and the maximum tensile stress of the new road subbase of the semi-rigid base pavement of the highway obtained in S7; S9: Substitute the pavement structure parameters of Class I highway into the prediction function of the maximum tensile stress of the old road base and the maximum tensile stress of the new road subbase of the semi-rigid base pavement of expressway obtained by S7, and obtain the differential settlement control standard of Class I highway semi-rigid base.

2. The method for controlling differential settlement of roadbed widening during highway reconstruction and expansion according to claim 1, characterized in that, The specific steps for S2 are as follows: The settlement at different locations on the top surface of the roadbed was calculated using ABAQUS software. Based on the differential settlement curves of the old and new roadbeds under widening, a fitting formula for the differential settlement curves of the old roadbed during construction and the new roadbed after construction was established. The fitting formula for the differential settlement curve of the old roadbed during the construction period is: Where: u1 represents the differential settlement of the old road during the widening construction phase, a max The maximum differential settlement of the old roadbed is given by l1, which is half the width of the old roadbed, and x. a Here are the x-coordinates of each calculated point on the surface of the old roadbed along the x-direction. The fitting formula for the differential settlement curve of the new roadbed after construction is: Where u2 is the differential settlement of the new road after construction, b is the maximum differential settlement of the new roadbed, l2 is the distance between the new shoulder and the point of maximum settlement, and x b This is to calculate the distance from the point of maximum settlement.

3. The method for controlling differential settlement of roadbed widening during highway reconstruction and expansion according to claim 1, characterized in that, The specific pavement individual analysis models under various working conditions in S3 are: the pavement individual analysis model for old pavement with semi-rigid base on highways, and the pavement individual analysis model for new pavement with semi-rigid base on highways.

4. The method for controlling differential settlement of roadbed widening during highway reconstruction and expansion according to claim 1, characterized in that, S4 includes the following steps: S41: Select a pavement structure, which includes a semi-rigid base old pavement structure for highways and a semi-rigid base new pavement structure for highways; determine the structural parameters and material flexural strength of the pavement structure. The road surface structure parameters include the surface layer material modulus E. pave Base material modulus E base Subbase material modulus E subb Surface layer thickness H pave Base layer thickness H base Subbase thickness H subb Road width L, flexural strength, Poisson's ratio v; S42: Apply displacement boundary conditions corresponding to different differential settlement amounts 'a' to the individual pavement analysis model under various working conditions through the displacement subroutine; S43: Repeat S42 to obtain the maximum tensile stress S11 of the pavement structure corresponding to different differential settlement a. max .

5. The method for controlling differential settlement of roadbed widening during highway reconstruction and expansion according to claim 1, characterized in that, S6 includes the following steps: S61: Maximum tensile stress of pavement structure corresponding to different differential settlement amounts 'a' obtained from S4. max Analyze the overall stress on the new and old road surface structures; S62: Based on the overall stress of the new and old pavement structures obtained in S61, compare the stress of each layer in the new and old pavement structures to determine the structural layer with the greatest stress in the new and old pavement structures; S63: Determine the critical differential settlement range for failure by utilizing the flexural strength of the materials in the new and old pavement structural layers that bear the greatest stress. S64: Calculate the maximum allowable differential settlement corresponding to the tensile stress S11 of the pavement structure layer by interpolation within the critical differential settlement range; S65: Calculate the maximum allowable differential settlement slope ratio of the old road during the widening construction period and the maximum allowable differential settlement slope ratio of the old and new roads after construction using the maximum allowable differential settlement obtained from S64. The expression for the maximum allowable differential settlement slope ratio of the old road during the widening construction period is: Δ=a r / 2 / L (3) The expression for the maximum allowable differential settlement between the new and old roads after construction is: Δ=a r / L (4) Where Δ is the differential settlement slope rate, a r L represents the allowable differential settlement value, and L is the road width. S66: Determine the standards for differential settlement control of semi-rigid base courses for highways; The allowable differential settlement standard for the old road during the construction period of the semi-rigid base course of the expressway is 0.30%, and the allowable differential settlement standard for the old road and the new road after construction is 0.20%.

6. A method for controlling differential settlement of roadbed widening during highway reconstruction and expansion according to claim 1 or 5, characterized in that, The method for determining the differential settlement control standard for semi-rigid base courses of highways as described in S6 is as follows: By comparing the differential settlement rates of multiple sets of test data, the maximum value or additional safety redundancy is taken to determine the differential settlement control standard of the old road during the construction period and the allowable differential settlement standard of the new and old roads after construction. The security redundancy is calculated by rounding the calculated value up to an integer multiple of 0.05%.

7. The method for controlling differential settlement of roadbed widening during highway reconstruction and expansion according to claim 1, characterized in that, The specific prediction models for the maximum tensile stress of semi-rigid pavement on highways under multiple factors in S7 are as follows: the prediction model for the maximum tensile stress of the old road base layer of semi-rigid base pavement on highways is as shown in equation (5), and the prediction model for the maximum tensile stress of the new road base layer of semi-rigid base pavement on highways is as shown in equation (6). in: For the prediction model of the maximum tensile stress of the old road base of the semi-rigid base pavement of the highway, H subb H represents the thickness of the base layer. base For the thickness of the base layer, H pave E represents the surface layer thickness. subb E represents the modulus of the base material. pave denoted as the modulus of the surface layer material, 'a' as the maximum differential settlement of the old subgrade, and 'L' as the width of the road surface. in: A model for predicting the maximum tensile stress in the new subbase of a semi-rigid base roadway for highways.

8. The method for controlling differential settlement of roadbed widening during highway reconstruction and expansion according to claim 1, characterized in that, S8 is detailed below: The maximum tensile stress prediction models for the old road base and the new road subbase of the semi-rigid base pavement established in S7 for highways are used as the analysis objects. The maximum tensile stress of the pavement structure is decomposed into the sum of the attribution values ​​of each input feature. The SHAP value is calculated to quantify the contribution of each input feature to the model prediction results, key influencing factors are identified, and the direction and intensity of the influence of each feature parameter on the maximum tensile stress of the pavement structure are analyzed based on the sign and magnitude of the SHAP value.

9. A method for controlling differential settlement during roadbed widening in highway reconstruction and expansion according to claim 1 or 8, characterized in that, In S8, a SHAP sensitivity analysis is performed on the prediction model obtained in S7. The SHAP sensitivity analysis formula is shown in equation (7): Where: i is the feature, φ i Let be the SHAP value of feature i, M be the set of all features, S be a feature subset, |S| be the number of features in feature subset S, and f(S) be the prediction value of the model trained using the features in feature subset S for the current sample. Let S be the predicted value of the current sample by the model trained using features from the feature subset S∪{i}, where |S|!(M-|S|-1)! is the weight factor, {i} is the set of features i, and ∪ is the union of the features. For the model being explained, ! represents the factorial.

10. A method for controlling differential settlement of roadbed widening during highway reconstruction and expansion according to claim 1, characterized in that, The specific differential settlement control indicators for the semi-rigid base course of Class I highway S9 are as follows: The allowable differential settlement standard for the old road during the construction period of semi-rigid base pavement of Class I highway is 0.40%, and the allowable differential settlement standard for the old road after construction is 0.25%.

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