Method for determining the control standard of permanent deformation of highway subgrade based on the service performance of pavement structure

Abstract

The present invention discloses a method for determining a control standard for permanent deformation of a highway subgrade based on the service performance of a pavement structure, comprising the following steps: step S1, selecting a pavement structure long-term service performance evaluation index associated with permanent deformation of the subgrade; step S2, establishing a tensile stress estimation formula for the bottom of an inorganic binder stabilized layer according to the long-term service performance evaluation index; step S3, determining a control standard for permanent deformation of the subgrade based on the long-term service performance of the pavement structure; the step S2 includes an estimation formula for tensile stress at the bottom of an inorganic binder stabilized sub-base layer and an estimation formula for tensile stress at the bottom of an inorganic binder stabilized sub-base layer. The present invention solves the problems that the existing control indicators and standards for permanent deformation of highway subgrades are difficult to match the actual situation, lack consideration of the correlation between permanent deformation of the subgrade and the service performance of the pavement structure and the variability of influencing factors, and cannot effectively avoid early damage to the pavement structure and fatigue failure of the pavement structure within the target service life.

Description

Technical Field

[0001] The invention belongs to the technical field of road engineering and relates to a method for determining a permanent deformation control standard of a highway subgrade based on the service performance of a pavement structure. Background Art

[0002] Subgrade soils subjected to tens of millions of high-cycle loads can experience cumulative plastic deformation, leading to permanent deformation. As the foundation of the pavement, excessive permanent deformation can lead to premature failure of the pavement structure, such as fatigue cracking, and fail to meet its design target service life. Conversely, if the pavement structure is to function properly within its target service life, requirements for permanent deformation of the subgrade, based on performance, must be established—in other words, clear control standards must be established to effectively control this deformation.

[0003] Existing research mainly controls the permanent deformation of the roadbed from three aspects: (1) critical dynamic stress of the roadbed soil, (2) improvement of the roadbed soil performance, and (3) roadbed structural measures. For (1), by controlling the actual stress of the roadbed soil to be less than the critical dynamic stress, its permanent deformation is within the plastic stability limit, thereby ensuring that the roadbed has excellent elastic properties. For (2), by adding lime, cement, fiber and other modified materials to the roadbed soil to improve the strength of the roadbed soil and thus improve the deformation resistance of the roadbed. For (3), by replacing the plain soil within a certain thickness range on the top surface of the roadbed with a higher strength granular material or laying geotechnical reinforcement in the roadbed to improve the overall strength of the roadbed structure, the purpose of reducing the permanent deformation of the roadbed is achieved. However, whether (1), (2) or (3), the permanent deformation of the subgrade is controlled from the perspective of the subgrade itself, which is independent of the long-term service performance requirements of the pavement structure. There is a lack of a standard for controlling the permanent deformation of the subgrade under the coordinated integrated design of the subgrade and the pavement. As a result, there is no clear basis for evaluating whether the control effect of the permanent deformation of the subgrade is insufficient or excessive in the existing technology. If the effect is insufficient, the expected requirements cannot be met. If the control is excessive, it will lead to material waste and increased construction costs. In addition, although the current 17th edition of the "Asphalt Pavement Design Code" proposes to use the elastic index of the subgrade top surface compressive strain to control the permanent deformation of the subgrade, this index is still proposed for the subgrade itself and is based on foreign road data. It is not applicable to my country's road structure. Therefore, it is urgent to propose a standard for controlling the permanent deformation of highway subgrade based on the service performance of the pavement structure.

[0004] On the other hand, existing research on subgrade permanent deformation control relies solely on permanent deformation data from reshaped subgrade specimens obtained through indoor dynamic triaxial testing. Although the test data for subgrade permanent deformation under given physical and stress conditions obtained through indoor dynamic triaxial testing are the most reliable and direct, these test results are fixed values ​​and the data volume is limited. This means that the numerical calculations based on these fixed values, along with their control standards, are unable to mitigate the application risks arising from the uncertainty of the subgrade's actual environmental conditions. In actual engineering, factors such as subgrade moisture and the speed, axle load, and number of vehicle loads are not constants but rather discrete data with variability. This results in fixed-value design results that cannot truly guide actual engineering practice. Although the current 17th edition of the "Asphalt Pavement Design Code" specifies target reliability and target reliability indicators for pavement structures at different road grades, subgrade-related specifications, including design specifications, fail to address the issues of probability and reliability. Consequently, research on the reliability and probability of permanent deformation in highway subgrades is scarce. Therefore, for the proposed control standard for permanent deformation of highway subgrade based on the service performance of pavement structure, it is also urgent to consider the probabilistic limit state, that is, it is necessary to control both the threshold of permanent deformation of highway subgrade and the degree of variation of the factors affecting permanent deformation of highway subgrade. Summary of the Invention

[0005] To achieve the above objectives, the present invention provides a method for determining the control standard for permanent deformation of highway subgrade based on the service performance of the pavement structure, so as to address the problems that the existing highway subgrade permanent deformation control indicators and standards are difficult to match with the actual domestic situation, lack of consideration of the correlation between the permanent deformation of the subgrade and the service performance of the pavement structure and the variability of the influencing factors, and are unable to effectively avoid the early damage of the pavement structure and the fatigue failure of the pavement structure within the target service life.

[0006] The technical solution adopted by the present invention is a method for determining the control standard of permanent deformation of highway subgrade based on the service performance of the pavement structure, comprising the following steps:

[0007] Step S1, selecting a pavement structure long-term service performance evaluation index associated with roadbed permanent deformation;

[0008] Step S2: establishing a tensile stress estimation formula for the bottom of the inorganic binder stabilized layer based on the long-term service performance evaluation index;

[0009] Step S3: Determine the control standard for permanent deformation of the roadbed based on the long-term service performance of the pavement structure.

[0010] Furthermore, the step S2 includes establishing a tensile stress estimation formula for the bottom layer of the inorganic binder stabilized base layer and a tensile stress estimation formula for the bottom layer of the inorganic binder stabilized base layer.

[0011] Furthermore, the tensile stress estimation formula of the inorganic binder stabilized base layer in step S2 is:

[0012] σ subb,max =f(ε pmax )·f(E i )·f(H i ) (1)

[0013] Where σ subb,max is the maximum tensile stress at the bottom of the subgrade layer; f(ε pmax ) is the influence function of the maximum permanent deformation of the subgrade on the tensile stress at the bottom of the subgrade layer; f(E i ) is the influence function of the material modulus of each structural layer of the pavement on the tensile stress of the subbase layer; f(H i ) is the influence function of the thickness of each pavement structure layer on the tensile stress of the subbase layer; i represents the pavement structure layer, including the surface layer, base layer, and subbase layer. When i refers to the surface layer, E i is the modulus of the surface material, H i is the thickness of the surface layer; when i refers to the base layer, E i is the base material modulus, H i is the thickness of the base layer; when i refers to the base layer, E i is the modulus of the base material, H i is the thickness of the base layer.

[0014] Furthermore, the intermediate parameters in the base layer bottom tensile stress estimation formula are taken as follows:

[0015]

[0016]

[0017] Where, ε pmax is the maximum permanent deformation of the roadbed; E pave 、E base 、E subb are the material moduli of the surface layer, base layer, and subbase layer respectively; H pave 、H base 、H subb are the thicknesses of the surface layer, base layer, and subbase layer, respectively; exp represents an exponential function with the natural constant e as the base.

[0018] Furthermore, the tensile stress estimation formula of the inorganic binder stabilized base layer in step S2 is:

[0019] σ base,max =g(ε pmax )·g(E i )·g(H i ) (3)

[0020] Where, σ base,max is the maximum tensile stress at the bottom of the base layer; g(ε pmax ) is the influence function of the maximum permanent deformation of the roadbed on the tensile stress at the bottom of the base layer; g(E i ) is the influence function of the material modulus of each structural layer of the pavement on the tensile stress at the bottom of the base layer; g(H i ) is the influence function of the thickness of each pavement structure layer on the tensile stress at the bottom of the base layer; i represents the pavement structure layer, including the surface layer, base layer, and subbase layer. When i refers to the surface layer, E i is the modulus of the surface material, H i is the thickness of the surface layer; when i refers to the base layer, E i is the base material modulus, H i is the thickness of the base layer; when i refers to the base layer, E i is the modulus of the base material, H i is the thickness of the base layer.

[0021] Furthermore, the parameters in the base layer bottom tensile stress estimation formula are taken as follows to obtain formula (4):

[0022]

[0023]

[0024] Where: ε pmax is the maximum permanent deformation of the roadbed; E pave 、E base 、E subb Respectively, they are the material modulus of the surface layer, base layer, and subbase layer; H pave 、H base 、H subb They are the thickness of the surface layer, base layer and subbase layer respectively.

[0025] Furthermore, the control standard for permanent deformation of the roadbed in step S3 is: the maximum tensile stress at the bottom of the subbase layer and the base layer is always less than or equal to the upper limit of the tensile stress allowed at the bottom of each layer.

[0026] Furthermore, the step S3 is specifically as follows:

[0027] Determine the maximum allowable upper limit of permanent deformation of the roadbed to ensure that fatigue cracking of the subbase does not occur

[0028] In the formula, [σ subb,max ] is the upper limit of the allowable tensile stress at the bottom of the subbase layer, E pave 、E base 、E subb are the material moduli of the surface layer, base layer, and subbase layer respectively; H pave 、Hbase 、H subb are the thickness of the surface layer, base layer, and subbase layer respectively;

[0029] Determine the maximum allowable upper limit of permanent deformation of the roadbed to ensure that fatigue cracking does not occur in the base layer

[0030]

[0031] Where, The maximum permissible upper limit of tensile stress at the bottom of the base layer is used to determine the control standard for permanent deformation of the roadbed based on the long-term service performance of the pavement structure: the maximum value of permanent deformation of the roadbed shall not exceed In the formula, min means taking the smaller value of the two.

[0032] Furthermore, the method further includes step S4, determining the degree of variation of factors affecting the reliability of the permanent deformation target of the roadbed under the pavement structure, specifically:

[0033] Step S41: Calculate the reliability index β:

[0034] β=1-φ -1 (P f ) (14)

[0035] Where: φ(.) is the standard normal cumulative distribution function; P f is the failure probability:

[0036]

[0037] Where P represents the calculation probability, w is the actual moisture content of the roadbed, v is the driving speed, and M is the tire pressure of a single tire; Z represents the limit state equation of permanent deformation of the highway roadbed:

[0038]

[0039] Where, ε pmax is the maximum permanent deformation of the roadbed structure, N is the number of cyclic loading, OMC is the optimal moisture content, w / OMC is the degree of wetting of the roadbed, H pave 、H base 、H subb are the thickness of the surface layer, base layer, and subbase layer respectively;

[0040] Step S42: setting the degree of variation of factors influencing target reliability;

[0041] Step S43, calculating the reliability index β according to each variation degree set in step S42;

[0042] Step S44: Setting the target reliability index β of the permanent deformation of the highway subgrade target, select the reliability index β>β in S43 target The degree of variation when

[0043] Step S45: Select the reliability index closest to β from the reliability index of each variation degree selected in step S44. target the degree of variation;

[0044] Step S46: Control the variation degree of the influencing factors not to exceed the variation degree selected in step S45, so as to achieve the long-term service reliability of the pavement structure.

[0045] Furthermore, the influencing factors in step S42 include the number of cyclic loading times N, the actual water content of the roadbed w, the driving speed v, and the tire pressure M. The degree of variation of each influencing factor is shown in the following table:

[0046] Degree of variation N w v M <![CDATA[δ( 1 )]]> 0.30 0.10 0.10 0.4 <![CDATA[δ( 2 )]]> 0.35 0.15 0.15 0.5 <![CDATA[δ( 3 )]]> 0.40 0.20 0.20 0.6 <![CDATA[δ( 4 )]]> 0.45 0.25 0.25 0.7 <![CDATA[δ( 5 )]]> 0.50 0.30 0.30 0.8 .

[0047] The beneficial effects of the present invention are:

[0048] 1. For widely used semi-rigid base pavement structures, a multivariate prediction formula was established to correlate the tensile stress at the bottom of the inorganic binder-stabilized base / subbase layer with the pavement structure thickness, pavement material properties, and permanent deformation of the subgrade. Furthermore, an explicit expression model for the maximum allowable upper limit of subgrade permanent deformation, which ensures that inorganic binder-stabilized base / subbase does not experience fatigue cracking within the design target service life, was established. For typical pavement structure combinations, a subgrade permanent deformation control standard based on the long-term service performance of the pavement structure was determined. This control standard, for the first time, directly links the allowable upper limit of subgrade permanent deformation with the long-term service performance of the pavement structure. This control standard, designed to meet the long-term service performance of the pavement structure, achieves integrated dynamic design of the subgrade and pavement structure, effectively avoiding premature failure of the pavement structure due to fatigue failure and ensuring the normal and stable service of the pavement structure within the target service life.

[0049] 2. For typical pavement structures, a limit state equation for permanent deformation of the roadbed was constructed. Based on survey results of the number of vehicle loads applied, the degree of roadbed wetting, vehicle speed, and overload in actual projects, the Monte Carlo random sampling method was used to calculate the probabilistic distribution characteristics of permanent deformation of highway roadbeds in actual projects. This confirmed the fact that there is a probabilistic difference between the results obtained using a deterministic model and the actual project results that consider the variability of influencing factors. The calculation revealed the evolution of the reliability of roadbed permanent deformation as a function of the variability of each influencing factor and determined the maximum variability of each influencing factor that can meet the target reliability. The application of probabilistic methods and reliability theory provides a clear understanding of the discretization and variability of permanent deformation of highway roadbeds under complex soil conditions and arbitrary boundary conditions. This method can reasonably control the upper limit of the allowable permanent deformation of highway roadbeds and the uniformity of the factors affecting permanent deformation of highway roadbeds, making the theoretical design closer to engineering practice and effectively avoiding the application risks of fixed-value design results caused by the variability of the actual environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0051] Figure 1 : This is the influence of the maximum permanent deformation of the roadbed in the embodiment of the present invention on the tensile stress at the bottom of the inorganic binder stabilized subbase layer; wherein, (a) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the subbase layer under different roadbed wetting degrees, (b) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the subbase layer under different driving speeds, (c) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the subbase layer under different overload degrees, (d) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the subbase layer under different surface layer material moduli, (e) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the subbase layer under different base material moduli, (f) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the subbase layer under different subbase material moduli, (g) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the subbase layer under different surface layer thicknesses, (h) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the subbase layer under different base layer thicknesses, and (i) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the subbase layer under different subbase thicknesses.

[0052] Figure 2It is the influence of the modulus of the pavement structure layer material on the tensile stress at the bottom of the inorganic binder stabilized subbase layer in the embodiment of the present invention; wherein, (a) is the relationship between the modulus of the surface layer material and the tensile stress at the bottom of the subbase layer, (b) is the relationship between the modulus of the base layer material and the tensile stress at the bottom of the subbase layer, and (c) is the relationship between the modulus of the subbase layer material and the tensile stress at the bottom of the subbase layer.

[0053] Figure 3 It is the influence of the thickness of the pavement structure layer on the tensile stress at the bottom of the inorganic binder stabilized subbase layer in the embodiment of the present invention; wherein, (a) is the relationship between the surface layer thickness and the tensile stress at the bottom of the subbase layer, (b) is the relationship between the base layer thickness and the tensile stress at the bottom of the subbase layer, and (c) is the relationship between the subbase layer thickness and the tensile stress at the bottom of the subbase layer.

[0054] Figure 4 It is the calculation result of the bottom tensile stress of the inorganic binder stabilized subbase layer corresponding to the supplementary working conditions in the embodiment of the present invention; among them, (a) is the calculation result of the bottom tensile stress of the subbase layer of the supplementary working conditions BC-1 to BC-5, (b) is the calculation result of the bottom tensile stress of the subbase layer of the supplementary working conditions BC-6 to BC-10, (c) is the calculation result of the bottom tensile stress of the subbase layer of the supplementary working conditions BC-11 to BC-15, (d) is the calculation result of the bottom tensile stress of the subbase layer of the supplementary working conditions BC-16 to BC-20, (e) is the calculation result of the bottom tensile stress of the subbase layer of the supplementary working conditions BC-21 to BC-25, and (f) is the calculation result of the bottom tensile stress of the subbase layer of the supplementary working conditions BC-26 to BC-28.

[0055] Figure 5 This is the prediction effect of the bottom tensile stress estimation formula of the subbase layer in the embodiment of the present invention.

[0056] Figure 6 It is the verification result of the bottom tensile stress estimation formula of the subbase layer proposed in the embodiment of the present invention; wherein, (a) is the verification result of the bottom tensile stress estimation formula of the subbase layer for verification conditions YZ-1 to YZ-3, (b) is the verification result of the bottom tensile stress estimation formula of the subbase layer for verification conditions YZ-4 to YZ-6, (c) is the verification result of the bottom tensile stress estimation formula of the subbase layer for verification conditions YZ-7 to YZ-9, and (d) is the verification result of the bottom tensile stress estimation formula of the subbase layer for verification conditions YZ-10 to YZ-12.

[0057] Figure 7: This is the influence of the maximum permanent deformation of the roadbed in the embodiment of the present invention on the tensile stress at the bottom of the inorganic binder stabilized base layer; wherein, (a) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the base layer under different wetting degrees, (b) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the base layer under different driving speeds, (c) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the base layer under different overload degrees, (d) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the base layer under different surface layer material moduli, (e) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the base layer under different base material moduli, (f) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the base layer under different sub-base material moduli, (g) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the base layer under different surface layer thicknesses, (h) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the base layer under different base thicknesses, and (i) is the relationship between the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the base layer under different sub-base thicknesses.

[0058] Figure 8 It is the influence of the modulus of the pavement structure layer material on the tensile stress at the bottom of the inorganic binder stabilized base layer in the embodiment of the present invention; wherein, (a) is the relationship between the modulus of the surface layer material and the tensile stress at the bottom of the base layer, (b) is the relationship between the modulus of the base layer material and the tensile stress at the bottom of the base layer, and (c) is the relationship between the modulus of the sub-base layer material and the tensile stress at the bottom of the base layer.

[0059] Figure 9 It is the influence of the thickness of the pavement structure layer on the tensile stress at the bottom of the inorganic binder stabilized base layer in the embodiment of the present invention; among them, (a) is the relationship between the surface layer thickness and the tensile stress at the bottom of the base layer, (b) is the relationship between the base layer thickness and the tensile stress at the bottom of the base layer, and (c) is the relationship between the sub-base layer thickness and the tensile stress at the bottom of the base layer.

[0060] Figure 10 It is the calculation result of the tensile stress at the bottom of the inorganic binder stabilized base layer corresponding to the supplementary working conditions in the embodiment of the present invention; wherein, (a) is the calculation result of the tensile stress at the bottom of the base layer of the supplementary working conditions BC-1 to BC-5, (b) is the calculation result of the tensile stress at the bottom of the base layer of the supplementary working conditions BC-6 to BC-10, (c) is the calculation result of the tensile stress at the bottom of the base layer of the supplementary working conditions BC-11 to BC-15, (d) is the calculation result of the tensile stress at the bottom of the base layer of the supplementary working conditions BC-16 to BC-20, (e) is the calculation result of the tensile stress at the bottom of the base layer of the supplementary working conditions BC-21 to BC-25, and (f) is the calculation result of the tensile stress at the bottom of the base layer of the supplementary working conditions BC-26 to BC-28.

[0061] Figure 11 This is the prediction effect of the tensile stress prediction formula of the base layer in the embodiment of the present invention.

[0062] Figure 12It is the verification result of the tensile stress estimation formula of the base layer bottom proposed in the embodiment of the present invention; among them, (a) is the verification result of the tensile stress estimation formula of the base layer bottom for verification conditions YZ-1 to YZ-3, (b) is the verification result of the tensile stress estimation formula of the base layer bottom for verification conditions YZ-4 to YZ-6, (c) is the verification result of the tensile stress estimation formula of the base layer bottom for verification conditions YZ-7 to YZ-9, and (d) is the verification result of the tensile stress estimation formula of the base layer bottom for verification conditions YZ-10 to YZ-12.

[0063] Figure 13 This is a diagram of the operating interface of the MEPDG road design software in an embodiment of the present invention.

[0064] Figure 14 is the relationship between the failure probability and the number of sampling points in the embodiment of the present invention; where (a) is the degree of variation of the influencing factor δ (1) The relationship between the failure probability and the number of sampling points in Monte Carlo simulation; (b) the degree of variation of the influencing factors is δ (5) The relationship between the failure probability and the number of sampling points in Monte Carlo simulation.

[0065] Figure 15 is the relationship between the reliability index and the number of sampling points in the embodiment of the present invention; where (a) is the degree of variation of the influencing factor δ (1) The relationship between the reliability index of Monte Carlo simulation and the number of sampling points; (b) the degree of variation of the influencing factors is δ (5) The relationship between the reliability index of Monte Carlo simulation and the number of sampling points.

[0066] Figure 16 is the probability of the maximum permanent deformation of the highway subgrade in the embodiment of the present invention.

[0067] Figure 17 is the cumulative probability of the maximum permanent deformation of the highway subgrade in the embodiment of the present invention.

[0068] Figure 18 : is the relationship between the reliability index of permanent deformation of highway subgrade and the coefficient of variation of each influencing factor in the embodiment of the present invention; wherein, (a) is the relationship between the coefficient of variation of the number of cyclic loading and the reliability index of permanent deformation of highway subgrade; (b) is the relationship between the coefficient of variation of the actual moisture content of the subgrade and the reliability index of permanent deformation of highway subgrade; (c) is the relationship between the coefficient of variation of the driving speed and the reliability index of permanent deformation of highway subgrade; (d) is the relationship between the coefficient of variation of the single tire pressure and the reliability index of permanent deformation of highway subgrade. DETAILED DESCRIPTION

[0069] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0070] The present invention provides a method for determining a control standard for permanent deformation of a highway subgrade based on the service performance of a pavement structure, comprising the following steps:

[0071] Step 1: Select the long-term service performance evaluation index of the pavement structure related to the permanent deformation of the roadbed.

[0072] To develop a control standard for permanent deformation of the subgrade based on the service performance of the pavement structure, it is necessary to determine long-term service performance evaluation indicators related to the permanent deformation of the subgrade. Based on the design indicators for different structural combinations of pavements provided in the "Highway Asphalt Pavement Design Code" (JTG D50-2017), the widely used design indicators for inorganic binder-stabilized base / subbase pavement structures are the tensile stress at the bottom of the inorganic binder-stabilized layer and the permanent deformation of the asphalt mixture layer. The permanent deformation of the asphalt mixture layer is primarily determined by the material strength of the asphalt mixture itself and the environmental load conditions, and has no significant correlation with the permanent deformation of the subgrade. This is demonstrated on page 28 of Appendix GG-2 of the Mechanical Empirical Design Guide (MEPDG): "First of all, for all levels of AC thickness, it can be clearly observed that the magnitude of rutting in the AC layer does not change significantly as the subgrade support changes. Thus, AC rutting is primarily influenced by the external load properties (gear type, load pressure) and the quality of the AC layer itself." Therefore, the tensile stress at the bottom of the inorganic binder stabilized subbase / base layer is used as an evaluation index of the long-term service performance of the semi-rigid base pavement structure affected by the permanent deformation of the roadbed.

[0073] Step 2: Establish a formula for estimating the tensile stress of the base layer stabilized with inorganic binders.

[0074] When designing a road, along with the determination of the pavement structure and pavement materials, the thickness and material modulus values ​​of the corresponding pavement structure layers, namely the surface layer, base layer, and sub-base layer, are also determined. That is, without considering the lateral uneven deformation of the roadbed, the tensile stress value at the bottom of the sub-base layer is determined. Therefore, the pavement structure and pavement materials should be considered as factors affecting the tensile stress at the bottom of the sub-base layer. At the same time, the present invention makes requirements on the permanent deformation of the roadbed based on the use target that the tensile stress at the bottom of the inorganic binder stabilized sub-base / base layer meets the design life. Therefore, step two needs to consider the influence characteristics of the seven influencing factors, namely, the permanent deformation of the roadbed, the thickness of the surface layer, the thickness of the base layer, the thickness of the sub-base layer, the modulus of the surface layer material, the modulus of the base material, and the modulus of the sub-base material, on the tensile stress at the bottom of the sub-base layer. Since the maximum permanent deformation of the roadbed corresponds to the maximum tensile stress of the subbase layer (hereinafter referred to as the subbase layer tensile stress refers to the maximum value unless otherwise specified), the calculated data of the subbase layer tensile stress corresponding to the maximum permanent deformation point of the roadbed after 50 million cycles of cyclic loading under different working conditions in the invention patent application number 2024106265298 of the inventor are derived and the results are plotted on Figures 1 to 3 It should be noted that this patent calculates the permanent deformation of the roadbed including the pavement structure. Therefore, in addition to the permanent deformation of the roadbed, the calculation results also include the dynamic response results of the pavement structure. It is only necessary to read the data at the corresponding position of the pavement structure.

[0075] Depend on Figure 1 It can be seen from (a) to (i) that as the maximum permanent deformation of the roadbed increases, the tensile stress at the bottom of the subbase layer shows an approximately linear increasing trend. At the same time, the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the subbase layer caused by different roadbed wetting levels, driving speeds, and overload levels are basically distributed on a straight line, and the difference in their rate of change is small. In addition, the calculation results corresponding to the material modulus and thickness of different pavement structural layers are in the form of a cluster of straight lines, and the slopes of the straight lines corresponding to different levels of each variable are significantly different. Therefore, the influence of the material modulus and thickness of each structural layer of the pavement on the tensile stress at the bottom of the subbase layer needs to be analyzed in detail. Figure 2 As can be seen from (a) to (c) in the figure, the tensile stress at the bottom of the subbase decreases with the increase of the modulus of the surface layer and base layer materials, and increases with the increase of the modulus of the subbase layer material. This means that in actual road design, the surface layer and base layer should be made of materials with a higher dynamic rebound modulus, while the dynamic rebound modulus of the subbase layer material should not be too high to avoid excessive tensile stress at the bottom of the subbase layer. Figure 3As can be seen from (a) to (c) in the figure, the tensile stress at the bottom of the subbase decreases with the increase of the surface layer thickness, base layer thickness, and subbase layer thickness, and the rate of decrease gradually decreases with the increase of the thickness of each layer. In order to ensure the comprehensiveness of the working conditions, 28 supplementary working conditions were designed in the invention patent with application number 2024106265298, as shown in Table 1. The calculation results of the tensile stress at the bottom of the subbase corresponding to the 28 supplementary working conditions are shown in Table 1. Figure 4 As shown in (a) to (f).

[0076] Table 1 Random operating conditions used to supplement the calculation results

[0077]

[0078] The above analysis shows that the permanent deformation of the roadbed, the thickness of each pavement structure layer, and the material modulus of each pavement structure layer all affect the magnitude of the subbase layer's bottom tensile stress. Assuming these variables are independent and only affect the subbase layer's bottom tensile stress, the formula for estimating the subbase layer's bottom tensile stress, taking all these factors into account, can be written as the following general formula:

[0079] σ subb,max =f(ε pmax )·f(E i )·f(H i ) (1)

[0080] Where: σ subb,max is the tensile stress at the bottom of the subbase layer (maximum value); f(ε pmax ) is the influence function of the maximum permanent deformation of the subgrade on the tensile stress at the bottom of the subgrade layer; f(E i ) is the influence function of the material modulus of each structural layer of the pavement on the tensile stress of the subbase layer; f(H i ) is the influence function of the thickness of each pavement structure layer on the tensile stress of the subbase layer; i represents the pavement structure layer, including the surface layer, base layer, and subbase layer. When i refers to the surface layer, E i is the modulus of the surface material, H i is the thickness of the surface layer; when i refers to the base layer, E i is the base material modulus, H i is the thickness of the base layer; when i refers to the base layer, E i is the modulus of the base material, H i is the thickness of the base layer.

[0081] according to Figures 1 to 3 Based on the analysis results, a linear function is used to describe the evolution of the tensile stress at the bottom of the subbase layer with the maximum permanent deformation of the roadbed and the material modulus of each structural layer of the pavement, and an exponential function is used to describe the evolution of the tensile stress at the bottom of the subbase layer with the thickness of each structural layer of the pavement. Figure 1 60 design conditions and Figure 4The parameter values ​​of the influence functions of different factors were obtained by fitting 8000 data points of 88 working conditions in 28 random working conditions, as shown in Table 2.

[0082] Table 2 Estimation formula of tensile stress at the bottom of subbase layer and its parameter values

[0083]

[0084] From the positive and negative values ​​of the parameters in Table 2, it can be seen that the proposed influence functions well capture the increase and decrease rules of the tensile stress at the bottom of the subgrade layer with different factors. Substituting the influence functions and their parameters into formula (1) and sorting them out, the tensile stress prediction formula at the bottom of the subgrade layer shown in formula (2) is obtained. The prediction effect is as follows Figure 5 As shown by R 2 =95.11%, which means its accuracy is relatively high.

[0085]

[0086] Where: σ subb,max (MPa) is the tensile stress at the bottom of the subbase layer (maximum value); ε pmax (mm) is the maximum permanent deformation of the roadbed; E pave (MPa), E base (MPa), E subb (MPa) are the material moduli of the surface layer, base layer and sub-base layer respectively; H pave (cm), H base (cm), H subb (cm) are the thicknesses of the surface layer, base layer and subbase layer respectively; exp represents the exponential function with the natural constant e as the base.

[0087] In order to verify the rationality and accuracy of the proposed formula for estimating the tensile stress of the subbase layer, the calculation results of the tensile stress of the subbase layer under 12 working conditions randomly generated in the invention patent with application number 2024106265298 are used for verification. The 12 verification working conditions are shown in Table 3. First, the calculation data of the tensile stress of the subbase layer under each working condition are extracted in COMSOL, and then each group of working conditions is substituted into the above formula (2) to estimate the tensile stress of the subbase layer, and the calculated value and the estimated value under the same working condition are compared. The verification results are shown in Table 3. Figure 6 From (a) to (d) in the figure, it can be seen that the estimated value obtained by formula (2) is very close to the calculated result, that is, the proposed estimation formula can reasonably estimate the bottom tensile stress of the subbase layer.

[0088] Table 3 Working conditions for verifying the tensile stress estimation formula of subbase / base layer

[0089]

[0090]

[0091] Step 3: Establish a formula for estimating the tensile stress at the bottom of the base layer stabilized with inorganic binders.

[0092] Similar to the analysis of the bottom tensile stress of the subbase layer in step 2, the calculation data of the bottom tensile stress of the subbase layer corresponding to the maximum point of permanent deformation of the roadbed after 50 million cycles of cyclic loading under different working conditions in the inventor's previous invention patent application number 2024106265298 (hereinafter referred to as the bottom tensile stress of the subbase layer refers to the maximum value unless otherwise specified) are derived and the results are plotted on Figures 7 to 9 .Depend on Figure 7 As can be seen from (a) to (i) in the figure, as the maximum permanent deformation of the roadbed increases, the tensile stress at the bottom of the base layer shows an approximately linear increasing trend. At the same time, the maximum permanent deformation of the roadbed and the tensile stress at the bottom of the base layer caused by different roadbed wetting levels, driving speeds, and overload levels are basically distributed on a straight line. In addition, the calculation results corresponding to the modulus and thickness of the material of different pavement structure layers are in the form of a cluster of straight lines, and the slopes of the straight lines corresponding to different levels of each variable are significantly different. Figure 8 From (a) to (c) in the figure, it can be seen that the tensile stress at the bottom of the base layer decreases with the increase of the modulus of the surface layer and base layer materials, and increases with the increase of the modulus of the sub-base layer materials. Figure 9 As can be seen from (a) to (c) in the figure, the tensile stress at the bottom of the base layer decreases with the increase of the thickness of the surface layer, the thickness of the base layer, and the thickness of the sub-base layer, and the reduction rate gradually decreases with the increase of the thickness of each layer. In order to ensure the comprehensiveness of the working conditions, the calculation results of the tensile stress at the bottom of the base layer corresponding to the 28 supplementary working conditions shown in Table 1 are derived, as shown in Figure 1. Figure 10 As shown in (a) to (f).

[0093] Based on the above analysis results, the formula for estimating the tensile stress at the bottom of the base layer, which comprehensively considers the permanent deformation of the roadbed, the thickness of each structural layer of the pavement, and the material modulus of each structural layer of the pavement, can be written as the following general formula:

[0094] σ base,max =g(ε pmax )·g(E i )·g(H i ) (3)

[0095] Where: σ base,max is the tensile stress at the bottom of the base layer (maximum value); g(ε pmax ) is the influence function of the maximum permanent deformation of the roadbed on the tensile stress at the bottom of the base layer; g(E i ) is the influence function of the material modulus of each structural layer of the pavement on the tensile stress at the bottom of the base layer; g(H i ) is the influence function of the thickness of each pavement structure layer on the tensile stress at the bottom of the base layer; i represents the pavement structure layer, including the surface layer, base layer, and subbase layer. When i refers to the surface layer, E iis the modulus of the surface material, H i is the thickness of the surface layer; when i refers to the base layer, E i is the base material modulus, H i is the thickness of the base layer; when i refers to the base layer, E i is the modulus of the base material, H i is the thickness of the base layer.

[0096] according to Figures 7 to 9 Based on the analysis results, a linear function is used to describe the evolution of the tensile stress at the bottom of the base layer with the maximum permanent deformation of the roadbed and the material modulus of each structural layer of the pavement, and a power function is used to describe the evolution of the tensile stress at the bottom of the base layer with the thickness of each structural layer of the pavement. Figure 7 60 design conditions and Figure 10 The parameter values ​​of the influence functions of different factors were obtained by fitting 8000 data points of 88 working conditions in 28 random working conditions, as shown in Table 4.

[0097] Table 4 The tensile stress prediction formula and parameter values ​​of the base layer

[0098]

[0099] Substitute each influence function and its parameters into formula (3) and sort it out to obtain the tensile stress prediction formula of the base layer shown in formula (4). The prediction effect is as follows: Figure 11 As shown by R 2 =94.72%, which shows that its accuracy is relatively high.

[0100]

[0101] Where: σ base,max (MPa) is the tensile stress at the bottom of the base layer (maximum value); ε pmax (mm) is the maximum permanent deformation of the roadbed; E pave (MPa), E base (MPa), E subb (MPa) are the material moduli of the surface layer, base layer and sub-base layer respectively; H pave (cm), H base (cm), H subb (cm) are the thickness of the surface layer, base layer and subbase layer respectively.

[0102] In order to verify the rationality and accuracy of the proposed tensile stress estimation formula for the base layer bottom, the calculation results of the tensile stress of the base layer bottom under 12 randomly generated working conditions shown in Table 3 were used as the basis for verification. First, the calculation data of the tensile stress of the base layer bottom under each working condition were extracted in COMSOL, and then each group of working conditions was substituted into the above formula (4) to estimate the tensile stress of the base layer bottom, and the calculated values ​​and estimated values ​​under the same working conditions were compared. The verification results are shown in Figure 3. Figure 12As shown in (a) to (d) in the figure, it can be seen that the estimated value obtained by formula (4) is very close to the calculated result, that is, the proposed estimation formula can reasonably estimate the tensile stress at the bottom of the base layer.

[0103] Step 4: Determine the control standard for permanent deformation of roadbed based on the long-term service performance of the pavement structure.

[0104] Based on the above analysis, the requirement for permanent deformation of the roadbed should be based on the tensile stress at the bottom of the inorganic binder stabilized subbase / base layer meeting the design service life. In actual roads, the tensile stress at the bottom of the subbase / base layer has an upper limit or critical threshold. If the tensile stress at the bottom of the subbase / base layer can always be less than or equal to the upper limit during operation, that is, σ subb,max ≤[σ subb,max ]、σ base,max ≤[σ base,max ], it can avoid the road structure being unable to complete normal service within the target service life due to fatigue cracking of the inorganic binder stabilized subbase / base.

[0105] The current "Highway Asphalt Pavement Design Code" (JTG D50-2017) provides a calculation formula for fatigue cracking of the inorganic binder stabilized layer within the target service life, as shown in formula (5) and the symbols are explained as follows:

[0106]

[0107] N f2 : Fatigue cracking life of the inorganic binder stabilization layer (axle times);

[0108] k a : Adjustment coefficient for seasonal frozen areas, determined according to Table 5;

[0109] k T2 : Temperature adjustment coefficient, determined according to Appendix G of the "Highway Asphalt Pavement Design Code";

[0110] R s : flexural tensile strength of inorganic binder stabilized materials (MPa);

[0111] a, b: Fatigue test regression parameters, determined according to Table 6;

[0112] k c : On-site comprehensive correction coefficient, determined according to formula (6);

[0113]

[0114] c1, c2, c3: parameters, values ​​are as shown in Table 7;

[0115] h a , h b: are the thickness of the asphalt mixture layer and the inorganic binder stabilization layer above the calculation point respectively;

[0116] β: target reliability index, which is determined according to Table 8 based on the highway grade;

[0117] σ t : Tensile stress at the bottom of the inorganic binder stabilized layer (MPa).

[0118] Table 5 Adjustment coefficient k for seasonally frozen regions a

[0119] Frozen area Heavy frozen area mid-frozen area Lightly frozen area Other regions <![CDATA[k a ]]> 0.60～0.70 0.70～0.80 0.80～1.00 1.00

[0120] Table 6 Fatigue failure model parameters of inorganic binder stabilized layer

[0121] Material Type a b Inorganic binder stabilized pellets 13.24 12.52 Inorganic binder stabilized soil 12.18 12.79

[0122] Table 7 On-site comprehensive correction coefficient k c Related parameters

[0123]

[0124] Table 8 Target reliability and target reliability index

[0125] Highway grade highway First-class highway Secondary highway Class III highway Class IV highway Target reliability (%) 95 90 85 80 70 Target reliability index β 1.65 1.28 1.04 0.84 0.52

[0126] From the analysis of formula (5), we can know that if the fatigue cracking life of the inorganic binder stabilized layer N f2 Take as the total number of traffic load cycles within the target service life, then the tensile stress σ at the bottom of the inorganic binder stabilized layer in the formula t That is its allowable upper limit [σ t,max Combining equations (5) and (6), the upper limit of the allowable tensile stress at the bottom of the inorganic binder stabilized layer is:

[0127]

[0128] In the formula: All symbols have the same meaning as above; when [σ t,max ] is [σ subb,max ], formula (7) is the upper limit of the allowable tensile stress at the bottom of the subbase layer; when [σ t,max ] is [σ base,max ], formula (7) is the upper limit of the allowable tensile stress at the bottom of the base layer.

[0129] Without considering the lateral uneven deformation of the roadbed, when the road structure and road materials are selected, according to the above analysis, it can be seen that the tensile stress at the bottom of the subbase / base layer is only related to the maximum permanent deformation of the roadbed. Therefore, if the tensile stress at the bottom of the subbase / base layer is used as the evaluation basis to control the maximum permanent deformation of the roadbed, the following should be satisfied: subb,max ≤[σsubb,max ]、σ base,max ≤[σ base,max ] conditions.

[0130] According to the formula (2) for estimating the tensile stress at the bottom of the subbase layer, it can be obtained that the following conditions must be met to ensure that the subbase does not suffer from fatigue cracking:

[0131]

[0132] Therefore, the maximum allowable upper limit of permanent deformation of the roadbed to ensure that fatigue cracking does not occur in the subbase is:

[0133]

[0134] According to the formula (4) for estimating the tensile stress at the bottom of the base layer, it can be obtained that the following conditions must be met to ensure that the base layer does not suffer from fatigue cracking:

[0135]

[0136] Therefore, the maximum allowable upper limit of permanent deformation of the roadbed to ensure that fatigue cracking does not occur in the base layer is:

[0137]

[0138] To clearly understand the process of determining the control standard for permanent deformation of roadbed, a specific example of a typical pavement structure is given here:

[0139] For a newly built expressway, the design speed is 100 km / h. The vehicle load is set at 1.12 MPa per axle and two wheels, taking into account a 60% overload degree. The equilibrium humidity of the roadbed is 1.4 OMC. The number of times the vehicle load acts within the target service life is 5×10 7 The thickness of the asphalt mixture surface layer is 18 cm, the thickness of the cement-stabilized crushed stone base layer is 38 cm, and the thickness of the low-dose cement-stabilized crushed stone subbase layer is 20 cm. The moduli of the surface layer, base layer, and subbase layer materials are 11,000, 9,000, and 7,000 MPa, respectively.

[0140] Step (a): Determine the upper limit of the allowable tensile stress at the bottom of the subbase / base layer.

[0141] For R s The "Highway Asphalt Pavement Design Specification" (JTG D50-2017) specifies the flexural tensile strength range for inorganic binder-stabilized materials: 0.9-1.5 MPa for subbase materials and 1.5-2.0 MPa for base materials. Here, the flexural tensile strength is 1.5 MPa for subbase materials and 2.0 MPa for base materials.

[0142] For a and b, take a=13.24 and b=12.52 respectively according to Table 6.

[0143] For c1, c2, and c3, according to Table 7, take c1 = 14.0, c2 = -0.0076, and c3 = -1.47 respectively.

[0144] For h a , take h a =180mm.

[0145] For h b , the base layer is h b =580mm, base layer takes h b =380mm.

[0146] For β, take β=1.65 according to Table 8.

[0147] For N f2 , take N f2 =5×10 7 Second-rate.

[0148] For k a Hunan Province is a light freezing area, and k is taken according to Table 5. a =0.9.

[0149] For k T2 Appendix G of the specification gives the values ​​of Changsha, Changning and Xiangxi, and takes the average value k T2 =1.42.

[0150] Substituting the above parameters into formula (7), we can get [σ subb,max ]、[σ base,max ] are 0.3565MPa and 0.5002MPa respectively.

[0151] Step (b): Determine the maximum allowable upper limit of the permanent deformation of the roadbed to ensure that fatigue cracking of the subbase does not occur.

[0152] [σ subb,max ]=0.3565MPa,E pave =11000MPa, E base =9000MPa, E subb =7000MPa, H pave =18cm, H base =38cm, H subb = 20cm, and the maximum permissible upper limit of the permanent deformation of the roadbed to ensure that the subbase does not suffer from fatigue cracking is obtained as [ε p1,max ]=26.55mm.

[0153] Step (c): Determine the maximum allowable upper limit of the permanent deformation of the roadbed to ensure that fatigue cracking does not occur in the base layer.

[0154] [σ base,max ]=0.5002MPa,Epave =11000MPa, E base =9000MPa, E subb =7000MPa, H pave =18cm, H base =38cm, H subb = 20cm, and the maximum permissible upper limit of the permanent deformation of the roadbed to ensure that the base does not suffer from fatigue cracking is obtained as [ε p2,max ]=9.32mm.

[0155] Step (d): Determine the control standard for permanent deformation of the roadbed based on the long-term service performance of the pavement structure.

[0156] Take the smaller of the two maximum allowable upper limits of roadbed permanent deformation in steps (b) and (c) to obtain the roadbed permanent deformation control standard based on the service performance of the pavement structure: ε pmax-standard =min{26.55mm, 9.32mm}=9.32mm.

[0157] Figure 13 This is the operating interface for the US MEPDG road design software. Assuming minimal permanent deformation of the flexible base layer, the maximum subgrade permanent deformation control standard is 13 mm, which is higher than the control standard proposed in this invention for Chinese road conditions. This is because the flexible base layers commonly used abroad have a greater ability to withstand tensile stress at the bottom of the layer, while the semi-rigid base layers commonly used in my country can withstand relatively low tensile stress at the bottom of the layer. Therefore, the subgrade permanent deformation control standard for Chinese road structures is also more stringent, further demonstrating the rationality of the highway subgrade permanent deformation control standard proposed in this invention.

[0158] Step 5: Determine the degree of variation of factors affecting the reliability of the permanent deformation target of the roadbed under the typical pavement structure of the semi-rigid base.

[0159] According to the proposed control standard, the maximum permanent deformation of the highway subgrade corresponding to a typical pavement structure with a semi-rigid base cannot exceed 9.32 mm. Combined with the maximum permanent deformation prediction formula of the subgrade established in the applicant's previous invention patent application number 2024106265298, the limit state equation for the permanent deformation of the highway subgrade is expressed as:

[0160]

[0161] According to reliability theory, the failure probability P f And the reliability index β is:

[0162]

[0163] β=1-φ -1 (P f) (14)

[0164] Where: φ(.) is the standard normal cumulative distribution function, and P represents the calculated probability.

[0165] Before conducting reliability analysis, the coefficient of variation of the influencing factors needs to be determined. From formula (12), we can see that the factors that theoretically affect the reliability analysis results are the number of cyclic loading N, the actual water content of the roadbed w, the driving speed v, the tire pressure M, the surface layer thickness H pave , base thickness H base , base layer thickness H subb In actual construction, the thickness of each pavement structure typically changes very little during operation, so their variability is not considered here. Specifically, in the reliability analysis, the surface layer thickness of this typical pavement structure is fixed at 18 cm, the base layer thickness is fixed at 38 cm, and the subbase layer thickness is fixed at 20 cm. Based on axle load surveys on the Guangdong section of the Beijing-Zhuhai Expressway, the coefficient of variation of the number of cyclic loading cycles N ranges from 0.3 to 0.448, and is hereby taken as 0.3 to 0.5. Based on surveys of the equilibrium moisture content of the subgrade on the Heliu, Lianzhu, and Changzhang Expressways, the coefficient of variation of the actual subgrade moisture content w is taken as 0.1 to 0.3. Based on speed surveys on the Huxian section of the G5 Expressway in Shaanxi Province, the coefficient of variation of the driving speed v is 0.128 to 0.279, and is hereby taken as 0.1 to 0.3. Based on surveys of vehicle masses on different lanes, the coefficient of variation of single tire pressure M is hereby taken as 0.4 to 0.8. In summary, in this embodiment, the coefficient of variation of each influencing factor is analyzed at five levels of variation, and the analysis levels are set as shown in Table 9.

[0166] Table 9 Coefficient of variation of influencing factors

[0167] Degree of variation N w v M <![CDATA[δ (1) ]]> 0.30 0.10 0.10 0.4 <![CDATA[δ (2) ]]> 0.35 0.15 0.15 0.5 <![CDATA[δ (3) ]]> 0.40 0.20 0.20 0.6 <![CDATA[δ (4) ]]> 0.45 0.25 0.25 0.7 <![CDATA[δ (5) ]]> 0.50 0.30 0.30 0.8

[0168] The Monte Carlo method is used to calculate the probability distribution of permanent deformation and failure probability P of highway subgrade. f and reliability index β. First, the number of sampling points must be determined, and then random sampling is performed according to the normal distribution function of each influencing factor. Then, the sample is substituted into formula (12) to obtain the failure sample with the maximum permanent deformation of the highway subgrade. Finally, the corresponding probability distribution and failure probability P are determined. f and the reliability index β. It should be noted that the stability of the results when using the Monte Carlo method to calculate probability depends on the number of sampling points. The more sufficient the sampling points, the more reliable the corresponding probability results. Therefore, it is necessary to first determine the number of sampling points when the probability reaches a stable state. In this embodiment, the number of sampling points in the trial calculation is first taken as 100×2 17 , and the minimum (δ (1) ) and the maximum (δ (5)) are calculated. If the probability of both has not reached a stable state, the number of sampling points will be increased and recalculated until the results are stable. Figure 14 (a) to (b) and Figure 15 As shown in (a) to (b), it can be seen that when the number of sampling points reaches 10 6 When the minimum and maximum variation degrees correspond to the failure probability and reliability index, they reach a stable state. Therefore, the number of sampling points is 10. 6 .

[0169] Considering the variability of different influencing factors, the probability distribution curve and cumulative probability distribution curve of the permanent deformation of the highway subgrade under the five degrees of variation shown in Table 9 are calculated, as shown in Figure 9. Figures 16 and 17 As shown in the figure, after accounting for the variability of the number of vehicle loads, the degree of subgrade wetting, vehicle speed, and the degree of overloading, the calculated maximum permanent deformation of the highway subgrade under long-term cyclic loading approximately follows a normal distribution. This provides a probabilistic prediction of the possible permanent deformation of the highway subgrade in actual situations. Furthermore, as the variability of the influencing factors increases, the distribution of the permanent deformation of the highway subgrade becomes more discrete, meaning that the probability of approaching the results calculated by the deterministic model decreases.

[0170] In order to analyze the impact of the variability of each influencing factor on the reliability index of permanent deformation of highway subgrade, when conducting sensitivity analysis on the coefficient of variation of one factor, the coefficients of variation of the other three factors are fixed. Figure 18 δ in (a) to (d) (1) ~δ (5) The coefficient of variation combinations represented by correspond to those shown in Table 9. Figure 18 It can be seen that the variability of the number of cyclic loading times N and the single tire pressure M has the most significant impact on the reliability index, while the variability of the actual water content w of the roadbed has a slightly lower impact on the reliability index. Although the variability of the driving speed v has the smallest impact, it cannot be ignored. This analysis result shows that during the design stage of the highway roadbed, it is necessary to pay attention to the impact of the variability of various factors on the permanent deformation of the structure. During the operation stage, it is necessary to control not only the number of vehicles on the road, driving speed, vehicle overload and the degree of roadbed wetting, but also its uniformity. Assuming that the target reliability index of the permanent deformation of the highway roadbed is β target =2.0, by Figure 18 The calculation results of the reliability index show that when the degree of variation is in δ (1) , δ (2) or δ (3) When β>β target , that is, the variability of each influencing factor should be controlled within the variability degree δ (3)As the variability of influencing factors continues to increase, the reliability index β of the permanent deformation of the highway subgrade will continue to be lower than the target reliability index β. target , resulting in failure to meet the reliability design requirements. Based on this, highway subgrade design should combine the fixed value design method with reliability analysis, that is, to guide highway subgrade design with reliability as the goal. Therefore, if the target reliability index of the permanent deformation of the subgrade under this typical pavement structure is 2.0, if conditions permit, the subbase and base materials with excellent flexural tensile performance can be selected, and δ (3) As the upper limit of the control of the variability of the influencing factors. That is to say, for this typical pavement structure, if the long-term service performance and reliability of the pavement structure are to meet the target requirements, it is necessary to control the maximum value of the permanent deformation of the roadbed not to exceed the certain value standard of 9.32mm, and also to control the variability of the influencing factors not to exceed δ (3) , that is, the variability of the number of cyclic loading times N, the actual moisture content of the roadbed w, the driving speed v, and the single tire pressure M cannot exceed 0.4, 0.2, 0.2, and 0.6 respectively.

[0171] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention are included in the scope of protection of the present invention.

Claims

1. A method for determining the control standard of permanent deformation of highway subgrade based on the service performance of pavement structure, characterized in that: The following steps are involved: Step S1, selecting a pavement structure long-term service performance evaluation index associated with permanent deformation of the roadbed; Step S2, establishing a tensile stress estimation formula for the bottom of the inorganic binder stabilized layer according to the long-term service performance evaluation index; Step S3, determining a control standard for permanent deformation of the roadbed based on the long-term service performance of the pavement structure; The step S2 includes establishing a tensile stress estimation formula for the bottom of the base layer stabilized by inorganic binder and a tensile stress estimation formula for the bottom of the base layer stabilized by inorganic binder; The formula for estimating the tensile stress at the bottom of the inorganic binder stabilized base layer is: s subb,max =f(e pmax )·f(E i )·f(H i ) (1) In the formula, σ subb,max is the maximum tensile stress at the bottom of the subgrade layer; f(ε pmax ) is the influence function of the maximum permanent deformation of the subgrade on the tensile stress at the bottom of the subbase layer; f(E i ) is the influence function of the material modulus of each pavement structure layer on the tensile stress of the subbase layer; f(H i ) is the influence function of the thickness of each pavement structure layer on the tensile stress of the subbase layer; i represents the pavement structure layer, including the surface layer, base layer, and subbase layer. When i refers to the surface layer, E i is the modulus of the surface material, H i is the thickness of the surface layer; when i refers to the base layer, E i is the base material modulus, H i is the thickness of the base layer; when i refers to the base layer, E i is the modulus of the base material, H i is the thickness of the base layer; The intermediate parameters in the bottom tensile stress estimation formula of the subbase layer are taken as follows: In the formula, ε pmax is the maximum permanent deformation of the roadbed; E pave 、E base 、E subb are the material moduli of the surface layer, base layer, and subbase layer respectively; H pave , H base , H subb are the thickness of the surface layer, base layer, and subbase layer respectively; exp represents an exponential function with the natural constant e as the base; The formula for estimating the tensile stress at the bottom of the inorganic binder stabilized base layer in step S2 is: s base,max =g(e pmax )·g(E i )·g(H i ) (3) In the formula, σ base,max is the maximum tensile stress at the bottom of the base layer; g(ε pmax ) is the influence function of the maximum permanent deformation of the roadbed on the tensile stress at the bottom of the base layer; g(E i ) is the influence function of the material modulus of each structural layer of the pavement on the tensile stress at the bottom of the base layer; g(H i ) is the influence function of the thickness of each pavement structure layer on the tensile stress at the bottom of the base layer; i represents the pavement structure layer, including the surface layer, base layer, and subbase layer. When i refers to the surface layer, E i is the modulus of the surface material, H i is the thickness of the surface layer; when i refers to the base layer, E i is the base material modulus, H i is the thickness of the base layer; when i refers to the base layer, E i is the modulus of the base material, H i is the thickness of the base layer; The parameters in the base layer bottom tensile stress estimation formula are taken as follows to obtain formula (4): Where: ε pmax is the maximum permanent deformation of the roadbed; E pave 、E base 、E subb They are the material modulus of the surface layer, base layer, and sub-base layer respectively; H pave , H base , H subb are the thickness of the surface layer, base layer, and subbase layer respectively; The control standard of permanent deformation of the roadbed in step S3 is: the maximum tensile stress at the bottom of the subbase and the base layer is always less than or equal to the upper limit of the tensile stress at the bottom of each layer; The step S3 is specifically as follows: Determine the maximum allowable upper limit of permanent deformation of the roadbed to ensure that fatigue cracking of the subbase does not occur [ε p1,max ]: In the formula, [σ subb,max ] is the upper limit of the allowable tensile stress at the bottom of the base layer, E pave 、E base 、E subb are the material moduli of the surface layer, base layer, and subbase layer respectively; H pave , H base , H subb are the thickness of the surface layer, base layer, and subbase layer respectively; Determine the maximum allowable upper limit of permanent deformation of the roadbed to ensure that fatigue cracking does not occur in the base layer [ε p2,max ]: In the formula, [σ base,max ] is the upper limit of the permissible tensile stress at the bottom of the base layer, and the control standard of permanent deformation of the roadbed is determined based on the long-term service performance of the pavement structure: the maximum value of the permanent deformation of the roadbed does not exceed min{[ε p1,max ],[ε p2,max ]}, where min means taking the smaller value of the two.

2. The method for determining the control standard of permanent deformation of highway subgrade based on the service performance of pavement structure according to claim 1 is characterized in that: The method further includes step S4, determining the degree of variation of the factors affecting the reliability of the permanent deformation target of the roadbed under the pavement structure, specifically: Step S41, calculating the reliability index β: β=1-φ -1 (P f ) (14) Where: φ(.) is the standard normal cumulative distribution function; P f is the failure probability: In the formula, P represents the calculation probability, w is the actual moisture content of the roadbed, v is the driving speed, M is the tire pressure of a single tire; Z represents the limit state equation of permanent deformation of the highway roadbed: In the formula, ε pmax is the maximum permanent deformation of the roadbed structure, N is the number of cyclic loading, OMC is the optimal moisture content, w / OMC is the degree of wetting of the roadbed, H pave , H base , H subb are the thickness of the surface layer, base layer, and subbase layer respectively; Step S42, setting the degree of variation of the factors affecting the target reliability; Step S43, calculating the reliability index β according to each variation degree set in step S42; Step S44: Setting the target reliability index β of the permanent deformation of the highway subgrade target , select the reliability index β>β in S43 target The degree of variability when Step S45: Select the reliability index closest to β from the reliability index of each variation degree selected in step S44. target the degree of variation; Step S46, controlling the variation degree of the influencing factors not to exceed the variation degree selected in step S45, so as to achieve the long-term service reliability of the pavement structure.

3. The method for determining the control standard of permanent deformation of highway subgrade based on the service performance of pavement structure according to claim 2 is characterized in that: The influencing factors in step S42 include the number of cyclic loading times N, the actual water content of the roadbed w, the driving speed v, and the tire pressure M of a single tire. The variation degree of each influencing factor is shown in the following table: 。

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