A method for optimizing the thickness of inverted asphalt pavement structures

Abstract

This invention relates to the fields of road engineering and civil engineering, and particularly to a method for optimizing the thickness design of inverted asphalt pavement structures. The method includes selecting the thickness and modulus of the asphalt surface layer, aggregate transition layer, and semi-rigid layer as control variables; using the stress level of the aggregate layer and the fatigue performance of the surface layer as preliminary design objectives; employing the D-optimal solution response surface design method to formulate an experimental scheme; simulating the stress dependence characteristics of the aggregate transition layer through finite element analysis combined with a nonlinear constitutive model; evaluating the impact of variable combinations on the preliminary design objectives; comparing the performance verification indicators of the asphalt pavement structure; and finally determining the optimized design scheme. This invention effectively reduces material usage, lowers construction costs, and significantly improves the pavement's resistance to fatigue cracking and deformation, thus extending its service life.

Description

Technical Field

[0001] This invention relates to the fields of road engineering and civil engineering, and in particular to a method for optimizing the thickness design of inverted asphalt pavement structures. Background Technology

[0002] The thickness design of asphalt pavement structures is typically based on empirical formulas and linear elastic models, but these methods fail to fully consider the comprehensive impact of the thickness, modulus, and nonlinear stress dependence of different layers on the overall pavement performance. Traditional linear elastic asphalt pavement thickness design methods are difficult to apply to inverted pavement structures. Most existing technologies employ fixed-thickness design methods, resulting in generally excessively thick layers in inverted pavement structures, leading to material waste or insufficient performance. Furthermore, traditional techniques lack precise analysis of different loads, environmental conditions, and the stress dependence characteristics of aggregate materials, making inverted asphalt surface layers prone to fatigue cracking, aggregate transition layers susceptible to permanent deformation, and semi-rigid layers facing the risk of long-term fatigue failure. These techniques, failing to comprehensively optimize the thickness and modulus of each layer, result in insufficient pavement durability and stability, increasing maintenance costs. Summary of the Invention

[0003] To address the numerous problems existing in the prior art, this invention provides a method for optimizing the thickness of inverted asphalt pavement structures. Based on finite element analysis and a nonlinear stress-dependent characteristic model, combined with the D-optimal solution response surface design method, this invention optimizes the thickness and modulus of each layer in the inverted asphalt pavement structure. By maximizing the volumetric stress of the aggregate transition layer and minimizing the tensile strain at the bottom of the asphalt surface layer, the overall durability and load-bearing capacity of the pavement are improved, and cost optimization is achieved by reducing material usage.

[0004] like Figure 1 As shown, a method for optimizing the thickness of an inverted asphalt pavement structure includes the following steps:

[0005] The thickness and modulus of each layer of the inverted asphalt pavement structure were selected as control variables. The D-optimal solution response surface design method was used to formulate an experimental scheme containing multiple combinations of different thicknesses and moduli, and the significance of each control variable to the target response value was evaluated.

[0006] like Figure 2 As shown, by using the thickness and modulus of each layer in an inverted asphalt pavement structure as control variables, personalized designs can be implemented for different layers. For example, the thickness and modulus of the asphalt surface layer primarily affect the pavement's fatigue resistance, while the thickness and modulus of the aggregate transition layer affect its stress dependence characteristics, thus influencing the overall structural stability of the pavement. Meanwhile, the thickness and modulus of the semi-rigid layer, as the load-bearing layer in the pavement structure, determine the overall compressive strength of the pavement. Therefore, optimizing the thickness and modulus of each layer in the design can achieve optimal pavement performance under different traffic loads and environmental conditions.

[0007] To more efficiently find the optimal combination of thickness and modulus, this invention employs the D-optimal response surface methodology. The D-optimal response surface methodology is an experimental design method commonly used in multivariate optimization. By maximizing the acquisition of experimental information, it can achieve more accurate optimization results while reducing the number of experiments. In this invention, this method is used to formulate experimental schemes containing multiple combinations of different thicknesses and moduli. The control variables corresponding to each combination (i.e., the thickness and modulus of each layer) are input into the experimental design. Through experimental verification under different conditions, the significance of each control variable to the target response value can be evaluated. For example, by evaluating the tensile strain at the bottom of the asphalt pavement and the volumetric stress of the aggregate transition layer, it is possible to determine how these variable combinations affect the fatigue performance and stress dependence characteristics of the pavement.

[0008] This invention utilizes the D-optimal response surface methodology to develop an experimental scheme that effectively evaluates the significance of various combinations of control variables, thereby identifying the optimal combination of thickness and modulus. This method not only reduces the consumption of experimental resources but also ensures that the experimental scheme has sufficient representativeness and accuracy. Finally, through comprehensive analysis of the experimental results, an optimized design scheme that achieves the best balance between material usage and structural performance can be determined, recommending the optimal combination of thickness and modulus for inverted asphalt pavement structures.

[0009] Based on the stress-dependent nonlinear characteristics of the granular transition layer, the mechanical response of the inverted asphalt pavement structure is calculated to obtain the tensile strain at the bottom of the asphalt surface layer and the volumetric stress of the granular transition layer, so as to evaluate the fatigue performance of the asphalt surface layer and the stress-dependent characteristics of the granular transition layer.

[0010] The aggregate transition layer in inverted asphalt pavement structures exhibits significant stress dependence, meaning that its mechanical properties (such as resilient modulus) change nonlinearly with varying stress levels under different traffic loads. Therefore, this invention first quantifies the stress dependence of the aggregate transition layer by simulating its mechanical behavior under different stress conditions using finite element analysis and a nonlinear constitutive model. Through this nonlinear mechanical response calculation, the invention accurately obtains the volumetric stress of the aggregate transition layer. This stress index reflects the load-bearing and deformation capacity of the aggregate transition layer within the entire structure, directly affecting the overall stability and resistance to permanent deformation of the pavement.

[0011] Meanwhile, the fatigue performance of asphalt pavement is a key indicator of pavement service life. In this mechanical response calculation model, by obtaining the tensile strain at the bottom of the asphalt pavement layer, the fatigue performance of the pavement under long-term loads can be accurately assessed. The tensile strain at the bottom of the asphalt pavement layer is a critical parameter; excessive tensile strain will lead to cracking in the asphalt pavement, affecting the pavement's service life. This invention, by accurately calculating this strain value and combining it with other parameters in pavement design, can optimize the thickness and material selection of the asphalt pavement, thereby improving its fatigue resistance and extending pavement life.

[0012] Based on this, the entire mechanical response calculation model comprehensively evaluates the pavement structure performance by combining the tensile strain at the bottom of the asphalt pavement layer and the volumetric stress of the aggregate transition layer. The fatigue performance of the asphalt pavement layer determines the pavement's crack resistance, while the stress-dependent characteristics of the aggregate transition layer determine the structure's stability and deformation resistance. This evaluation method enables the present invention to design the optimal pavement structure thickness combination according to different traffic loads, climatic conditions, and other actual working conditions, ensuring the overall performance of the pavement structure while minimizing material costs.

[0013] Based on the fatigue performance of the asphalt surface layer and the stress dependence characteristics of the aggregate transition layer, the optimal design range of the inverted asphalt pavement structure is determined. The optimal solution is determined based on the satisfaction theory, and the mechanical verification indicators of other pavement structures are compared. The optimal combination scheme of thickness and modulus of the inverted asphalt pavement structure is recommended.

[0014] In the optimization design process, the fatigue performance of the asphalt pavement is measured by the tensile strain at its base, which reflects the deformation of the asphalt pavement under external loads. If the tensile strain exceeds a certain critical value, the asphalt pavement is prone to fatigue cracks, thus affecting the overall service life of the pavement. Therefore, this invention uses mechanical response calculations in the design to accurately obtain the tensile strain data of the asphalt pavement, ensuring that the thickness and modulus of the pavement meet fatigue performance requirements while minimizing material waste.

[0015] On the other hand, the stress-dependent characteristics of the granular transition layer have a significant impact on its compressive and deformation resistance. The modulus of the granular transition layer exhibits nonlinear characteristics with stress level changes, making it impossible for traditional linear mechanical models to accurately describe its performance. Therefore, this invention uses a nonlinear mechanical model to accurately calculate the volumetric stress of the granular transition layer, ensuring that it maintains good mechanical properties under different load conditions.

[0016] After determining the fatigue performance of the asphalt pavement and the stress dependence characteristics of the aggregate transition layer, this invention employs the satisfaction theory to further optimize the design scheme. The satisfaction theory is a method for selecting the optimal solution by maximizing the consistency between the design result and the target expectation. This method has significant advantages in multivariate optimization, balancing multiple design objectives and ensuring that the final design scheme meets structural performance requirements while minimizing material costs. In this invention, the application of the satisfaction theory aims to find the optimal combination of thickness and modulus that simultaneously satisfies the fatigue performance of the asphalt pavement and the stress dependence characteristics of the aggregate transition layer through multiple iterative calculations.

[0017] Preferred, such as Figure 3 As shown, the D-optimal solution response surface design method is implemented using Design-expert software to determine the optimal combination of asphalt pavement thickness, asphalt pavement modulus, aggregate transition layer thickness, aggregate transition layer modulus, semi-rigid layer thickness, semi-rigid layer modulus, and subgrade modulus.

[0018] In this invention, the D-optimal solution response surface methodology is implemented using Design-expert software to determine the optimal combination of asphalt pavement thickness, asphalt pavement modulus, aggregate transition layer thickness, aggregate transition layer modulus, semi-rigid layer thickness, semi-rigid layer modulus, and subgrade modulus. The core of this method lies in designing an optimal experimental scheme to maximize the acquisition of experimental information while minimizing the number of experiments, thereby effectively improving design efficiency and accuracy.

[0019] D-optimal response surface methodology is an experimental design method for handling multi-factor optimization problems. It is particularly suitable for systems with numerous and complex interactions, such as optimizing the thickness and modulus of each layer in an inverted asphalt pavement structure. In this invention, the thickness and modulus of the asphalt surface layer, aggregate transition layer, and semi-rigid layer are key design variables. The thickness and modulus of the asphalt surface layer determine the fatigue resistance of the pavement structure, while the thickness and modulus of the aggregate transition layer and semi-rigid layer have a crucial impact on the compressive strength and long-term stability of the pavement. Therefore, by rationally selecting and optimizing these variable combinations, the durability and structural stability of the pavement can be significantly improved.

[0020] In practice, Design-expert software was used to implement the D-optimal response surface methodology. This software provides powerful experimental design and analysis capabilities, enabling the selection of optimal experimental schemes in a multi-dimensional space. During optimization, the thickness and modulus of the asphalt surface layer, aggregate transition layer, semi-rigid layer, and subgrade were first used as input variables. Through experimental scheme design, multiple sets of experimental points with different variable combinations were generated. Each experimental point represents a different combination of thickness and modulus. Then, based on these experimental points, the impact of different combinations on pavement performance was evaluated through finite element simulation or actual measurement.

[0021] The Design-expert software's D-optimization function ensures the acquisition of maximum information with the fewest experiments. This feature is particularly suitable for the design of inverted asphalt pavement structures, as conducting numerous experiments in practical engineering is both time-consuming and labor-intensive. By reducing unnecessary experimental steps, this invention can obtain sufficient data with limited experimental resources to comprehensively analyze the effects of different thickness and modulus combinations.

[0022] After summarizing all experimental results, the Design-expert software was used to perform regression analysis on the response values ​​at each experimental point, calculating the significance of the impact of each design variable on pavement performance. Finally, the optimal combination of thickness and modulus was selected using the D-optimal solution algorithm to minimize material usage while ensuring pavement structural durability. This combination not only improves pavement fatigue resistance and long-term stability but also significantly reduces construction and material costs.

[0023] Preferably, the response surface methodology is generated based on multiple sets of experimental data and evaluates the effects of different thickness and modulus combinations on the fatigue performance of asphalt pavement and the stress dependence characteristics of aggregate transition layer.

[0024] The present invention discloses a thickness optimization design method for inverted asphalt pavement structures. This method utilizes response surface methodology to generate specific optimization models based on multiple sets of experimental data. It comprehensively evaluates the impact of different thickness and modulus combinations on the fatigue performance of the asphalt surface layer and the stress dependence characteristics of the aggregate transition layer. In this process, the role of response surface methodology is to identify the optimal solution for different thickness and modulus combinations on pavement performance through experimental design and data analysis, ensuring the stability and durability of the pavement structure under various working conditions.

[0025] This invention collected extensive performance data on different thickness and modulus combinations through experiments and finite element simulations, including the fatigue performance of asphalt pavement and the stress-dependent characteristics of aggregate transition layers. The fatigue performance of asphalt pavement is primarily measured by its bottom tensile strain. A larger bottom tensile strain indicates a greater susceptibility to cracking and a shorter fatigue life under long-term traffic loads. Therefore, adjusting the thickness and modulus combination of the asphalt pavement can reduce the tensile strain value, thereby improving the fatigue performance and service life of the pavement. The stress-dependent characteristics of the aggregate transition layer refer to the nonlinear characteristics of its modulus as a function of stress. This characteristic is crucial to the load-bearing capacity and deformation resistance of the pavement structure. The behavior of the aggregate transition layer under different stress states determines its ability to effectively distribute traffic loads and prevent excessive pavement deformation or failure.

[0026] This invention utilizes response surface methodology to generate a multidimensional optimization model based on multiple sets of experimental data. In this model, the thickness and modulus of the asphalt surface layer and the aggregate transition layer are used as input variables, while fatigue performance and stress dependence characteristics are used as output responses. Through experimental design, the software automatically generates different combinations of variables and performs data analysis on the results of each set of experiments. The advantage of response surface methodology lies in its ability to generate a wide range of experimental schemes containing different thickness and modulus combinations with a small number of experiments, and to accurately assess the significance of each combination's impact on pavement performance.

[0027] Through calculation and analysis using this model, the optimal thickness and modulus configurations for different combinations can be determined. Specifically, when the thickness and modulus of the asphalt surface layer are adjusted to a suitable range, the tensile strain at the bottom of the layer is minimized, and fatigue performance is maximized. Furthermore, when the combination of thickness and modulus of the granular transition layer is optimal, its stress-dependent characteristics are fully utilized, maintaining stability and compressive strength under traffic loads. Thus, the design method of this invention not only ensures the durability and fatigue resistance of the overall pavement structure but also reduces engineering costs by decreasing thickness and material usage.

[0028] Preferred, such as Figure 4 As shown, the mechanical response calculation is based on the finite element analysis method. The compiled UMAT subroutine is used to give the stress-dependent nonlinear characteristics of the granular transition layer, and the stress response of the granular transition layer is accurately simulated through the constitutive model.

[0029] In this invention, the mechanical response calculation employs the finite element method, combined with a compiled UMAT subroutine, to impart stress-dependent nonlinear characteristics to the granular transition layer. A nonlinear constitutive model is then used to accurately simulate the stress response of the granular transition layer. The core of this process lies in the fact that the mechanical properties of the granular transition layer do not change linearly, but rather exhibit complex nonlinear behavior with varying stress levels. To accurately describe this stress dependence, traditional linear elastic models cannot meet the accuracy requirements; therefore, this invention introduces a more complex nonlinear constitutive model.

[0030] In practical applications, the aggregate transition layer in inverted asphalt pavement structures serves as the load transfer layer between the upper asphalt surface layer and the lower semi-rigid layer. Due to the repeated action of traffic loads, the aggregate transition layer needs to possess certain compressive and deformation resistance capabilities, and these mechanical properties are significantly affected by stress levels. Under different load conditions, the modulus of the aggregate layer undergoes nonlinear changes, which significantly affect the structural stability of the entire pavement. Therefore, mechanical response calculations must not only consider the geometric and material properties of each layer but also accurately simulate the stress response characteristics of the aggregate transition layer.

[0031] The finite element method (FEM) is an effective tool for simulating the mechanical behavior of complex structures. It solves for mechanical responses such as stress, strain, and displacement by discretizing complex structures into finite elements. In this invention, FEM can not only accurately simulate the stress distribution in asphalt pavement structures, but also simulate the nonlinear stress response of the aggregate transition layer through the UMAT subroutine. UMAT (User Material Subroutine) is a user material subroutine in finite element software that allows researchers to define custom constitutive models of materials. In this invention, the UMAT subroutine is compiled into a nonlinear constitutive model specifically for the stress-dependent characteristics of the aggregate transition layer, enabling the finite element model to accurately reflect the stress-strain relationship of the aggregate layer under different loading conditions.

[0032] The constitutive model is a core component in mechanical response calculations, used to describe the stress-strain relationship of a material under external forces. In this invention, the constitutive model of the granular transition layer incorporates stress-dependent nonlinear characteristics, meaning its modulus varies with the stress level. This model is implemented in finite element analysis using the UMAT subroutine, enabling the simulation results to more accurately reflect real-world mechanical behavior. In this way, the simulated volumetric stress of the granular transition layer not only reflects the pavement's performance under static conditions but also reveals its long-term mechanical behavior under dynamic loads.

[0033] Preferably, the fatigue performance of the asphalt pavement is determined by evaluating the maximum principal strain at the bottom of the asphalt pavement, and the upper limit of the maximum principal strain at the bottom of the asphalt pavement is 120 με.

[0034] In this invention, the fatigue performance of the asphalt pavement is determined by evaluating the maximum principal strain at the bottom of the asphalt pavement layer. The fatigue performance of the asphalt pavement is a key factor affecting the long-term service life of the pavement, especially under repeated traffic loads, where cracks gradually appear, eventually leading to structural failure. To accurately evaluate and optimize the fatigue resistance of the asphalt pavement, this invention quantifies fatigue performance by calculating the maximum principal strain at the bottom of the asphalt pavement layer, where the upper limit of the maximum principal strain is set at 120 με.

[0035] Asphalt pavement undergoes repeated stretching and compression under long-term traffic loads. If the strain at the base of the layer is too large, cracks in the pavement will propagate more rapidly, leading to premature pavement failure. Therefore, controlling the tensile strain at the base of the layer within a reasonable range is crucial for extending the service life of the pavement. In this invention, the maximum principal strain is calculated using finite element analysis, reflecting the maximum tensile strain state of the asphalt pavement under external loads. Setting 120 με as the upper limit is based on extensive engineering experience and experimental results to ensure that the pavement does not fail rapidly due to excessive tensile strain.

[0036] In the design process, the thickness and modulus of the asphalt surface layer are two key variables that directly affect the maximum principal strain. A larger thickness can effectively reduce the tensile strain of the surface layer because a thicker asphalt surface layer can more evenly distribute external loads, thereby reducing strain concentration. The modulus, on the other hand, affects the rigidity of the material; a higher modulus makes the material less prone to large deformations, thus reducing the tensile strain at the bottom of the layer. In this invention, by optimizing the thickness and modulus of the asphalt surface layer, the maximum principal strain can be controlled within 120 με, thereby improving the fatigue resistance of the surface layer.

[0037] By evaluating the maximum principal strain, this invention enables precise control of the fatigue performance of asphalt pavement, allowing it to maintain good crack resistance under long-term loading. This optimization not only improves pavement durability but also extends its service life, reducing subsequent maintenance and repair costs. Simultaneously, by setting an upper limit of 120 με, this invention ensures design safety, avoiding fatigue failure caused by excessive strain. By combining the control of the maximum principal strain at the bottom of the layer with material optimization, this invention provides a more scientific and rational design method for asphalt pavement structures, achieving material cost optimization while ensuring structural performance.

[0038] Preferably, the volumetric stress of the granular transition layer is used to characterize the stress dependence of the granular transition layer, and the lower limit of its volumetric stress level is 150 kPa.

[0039] In the thickness optimization design of the inverted asphalt pavement structure of this invention, the volumetric stress of the aggregate transition layer is used to characterize its stress dependence characteristics. Specifically, volumetric stress is a key indicator reflecting the comprehensive stress state borne by the aggregate transition layer. Located between the asphalt surface layer and the semi-rigid layer, the aggregate transition layer plays a role in load transfer and stress dispersion. Under traffic loads, the stress characteristics of the aggregate transition layer are not linear but exhibit a significant stress dependence. Therefore, accurate calculation and evaluation of the volumetric stress level can help to better understand the mechanical behavior of the aggregate transition layer under different loads, thereby optimizing its thickness and modulus design. In this invention, the lower limit of the volumetric stress level of the aggregate transition layer is set at 150 kPa. This critical value is used to ensure that its stress characteristics maintain a reasonable response capability under load.

[0040] Volumetric stress is represented by the sum of principal stresses, and stress dependence refers to the change in modulus of the aggregate transition layer as it is subjected to varying stresses. Specifically, as volumetric stress increases, the modulus of the aggregate transition layer exhibits a non-linear change. This characteristic is crucial for the long-term stability of the pavement, as it determines the load-bearing capacity and deformation behavior of the aggregate layer under different stress levels. If the volumetric stress is below the set lower limit of 150 kPa, the stress response of the aggregate transition layer may be insufficient, leading to premature material failure or significant deformation, thereby affecting the overall mechanical properties and durability of the pavement.

[0041] To accurately capture this stress-dependent characteristic, this invention employs finite element analysis and a stress-dependent nonlinear constitutive model to precisely simulate the volumetric stress of the granular transition layer. In this model, the mechanical properties of the granular transition layer under different stress conditions are quantified, enabling the assessment of its performance under long-term loading. The lower limit of 150 kPa for volumetric stress was determined through extensive experimental and simulation results; it represents a critical value for the granular transition layer in terms of load-bearing capacity and deformation capacity. Below this value, the granular layer may fail to effectively withstand external loads, thereby increasing the risk of pavement structure failure.

[0042] By setting the lower limit of the volumetric stress of the granular transition layer to 150 kPa, this invention ensures that this layer in the pavement structure maintains sufficient strength and stability under load. Reasonable control of the volumetric stress level not only improves the compressive strength of the granular layer but also prevents excessive deformation, making the pavement structure more durable and stable. This setting also provides a scientific basis for optimizing the thickness and modulus of the granular transition layer, enabling rational material use and cost optimization in practical applications. Ultimately, this invention, through the control of volumetric stress, ensures the long-term performance and safety of inverted asphalt pavement structures, reduces maintenance frequency and material waste, and improves the overall efficiency of the pavement system.

[0043] Preferably, the goal of the optimized design is to reduce the thickness of the asphalt surface layer and improve the durability of the asphalt pavement by minimizing the tensile strain at the bottom of the asphalt surface layer and maximizing the volumetric stress of the aggregate transition layer.

[0044] The core objective of the thickness optimization design of the inverted asphalt pavement structure of this invention is to reduce the thickness of the asphalt surface layer and improve the overall durability of the asphalt pavement by minimizing the tensile strain at the bottom of the asphalt surface layer and maximizing the volumetric stress of the aggregate transition layer. In the optimization design process, the tensile strain of the asphalt surface layer and the volumetric stress of the aggregate transition layer are two key mechanical parameters that directly determine the fatigue resistance and stability of the pavement structure.

[0045] Tensile strain at the base of the asphalt pavement is one of the main causes of fatigue damage to the pavement under long-term traffic loads. Excessive tensile strain leads to rapid crack propagation in the pavement, thus affecting pavement life. Therefore, controlling the tensile strain at the base of the pavement within a reasonable range can effectively improve its crack resistance and extend its service life. In the optimization design, by accurately calculating and analyzing the thickness and modulus of the asphalt pavement, a combination that minimizes the tensile strain at the base can be found, thereby achieving better fatigue resistance. At the same time, reducing the thickness of the pavement is also one of the important objectives of this invention. Through optimized design, while ensuring the fatigue resistance of the pavement, the amount of asphalt material used can be significantly reduced, thereby reducing construction costs.

[0046] On the other hand, the volumetric stress of the aggregate transition layer is a key indicator for evaluating the structural stability of this layer. Located between the asphalt surface layer and the underlying structure, the aggregate transition layer plays a role in dispersing and transferring stress. When the volumetric stress is high, the aggregate layer can better distribute traffic loads, prevent stress concentration, and maintain pavement stability. Therefore, in optimized design, maximizing the volumetric stress of the aggregate transition layer can enhance its load-bearing capacity and deformation resistance, ensuring the stability and durability of the entire pavement structure under long-term loads.

[0047] This invention, by comprehensively considering these two key parameters and employing experimental data and finite element simulation analysis, determines the optimal combination of thickness and modulus. In its implementation, multiple iterative calculations are performed on the asphalt surface layer and the aggregate transition layer to progressively optimize the design scheme, identifying the optimal solution that minimizes the tensile strain at the bottom of the layer while maximizing the volumetric stress. Utilizing the D-optimal solution response surface design method, the effects of various thickness and modulus combinations can be rapidly evaluated without significantly increasing experimental resources, thereby obtaining an optimal solution that balances pavement performance and economy.

[0048] Through this optimized design method, this invention not only significantly reduces the thickness of the asphalt surface layer, lowering material costs, but also ensures high durability and stability of the pavement structure during long-term use. Specifically, minimizing the tensile strain at the bottom of the asphalt surface layer reduces fatigue cracking and improves the pavement's fatigue resistance; maximizing the volumetric stress of the aggregate transition layer enhances the pavement's load-bearing capacity and deformation resistance, ensuring that the pavement does not deform or fail prematurely under long-term loads. Furthermore, maintaining structural performance while thinning the surface layer makes pavement design more economical and feasible, meeting the cost and performance requirements of engineering practice. Ultimately, this invention, by optimizing the combination of thickness and modulus, provides an efficient, reliable, and economical pavement structure optimization design scheme, extending pavement service life, reducing later maintenance costs, and improving the overall structural performance.

[0049] Preferably, the thickness of the asphalt surface layer ranges from 8cm to 18cm, the thickness of the granular transition layer ranges from 10cm to 30cm, and the thickness of the semi-rigid layer ranges from 15cm to 40cm.

[0050] In this invention, the thickness ranges of the asphalt surface layer, the granular transition layer, and the semi-rigid layer are set to 8cm to 18cm, 10cm to 30cm, and 15cm to 40cm, respectively. These thickness ranges are based on extensive experimental data, engineering experience, and comprehensive analysis of the mechanical properties of pavement structures. The aim is to achieve economical material usage while meeting the requirements of durability and stability by adjusting the thickness of each layer.

[0051] In inverted asphalt pavement structures, the asphalt surface layer, aggregate transition layer, and semi-rigid layer each serve different functions. The asphalt surface layer is primarily responsible for bearing the fatigue stress caused by traffic loads and providing sufficient wear resistance. The aggregate transition layer acts as a stress transfer layer, reducing stress concentration on the underlying semi-rigid layer by alleviating the load on the upper surface layer. The semi-rigid layer, on the other hand, provides overall pavement support, ensuring that the pavement maintains sufficient structural strength and deformation resistance under long-term heavy traffic.

[0052] In the design, the thickness of the asphalt pavement directly affects its fatigue resistance. A thicker pavement can better distribute traffic loads, thereby reducing tensile strain and extending pavement life. However, excessively thick pavements lead to material waste. Therefore, within a thickness range of 8cm to 18cm, optimized design can achieve efficient material utilization while meeting fatigue resistance requirements. 8cm is the lower limit to ensure basic fatigue resistance, while the upper limit of 18cm takes into account the enhanced durability required under special traffic conditions.

[0053] The thickness of the granular transition layer is set between 10cm and 30cm, primarily based on its stress buffering function within the structure. By adjusting the thickness of the granular layer, its volumetric stress can be regulated, ensuring sufficient stress dispersion under load. A thinner granular layer (e.g., 10cm) is suitable for lighter traffic loads, while increasing the thickness of the granular transition layer (e.g., 30cm) under conditions of high traffic volume or heavy loads can effectively prevent excessive deformation of the pavement structure.

[0054] The thickness of the semi-rigid layer ranges from 15cm to 40cm, primarily to provide overall load-bearing capacity for the pavement. A thicker semi-rigid layer can better bear the loads transferred from the superstructure, prevent deformation of the subgrade, and increase the overall stiffness of the pavement structure. 15cm is the minimum thickness for a semi-rigid layer, ensuring basic load-bearing capacity, while a thickness of 40cm can significantly enhance the overall load-bearing capacity of the pavement under conditions of heavy traffic or poor foundation.

[0055] By setting the thickness ranges of the asphalt surface layer, aggregate transition layer, and semi-rigid layer, this invention enables flexible pavement structure design under various traffic conditions and environments. Combinations of different thicknesses not only ensure the durability and stability of the pavement structure but also optimize material usage and reduce construction costs based on specific engineering requirements. Optimized design within the asphalt surface layer range improves its fatigue resistance and reduces the probability of cracking; optimized aggregate transition layer thickness ensures reasonable stress distribution and reduces pavement structure deformation; and optimized semi-rigid layer thickness enhances the overall pavement's load-bearing capacity and long-term stability. Through these reasonable thickness settings, this invention provides a scientific and efficient optimization scheme for the design of inverted asphalt pavements.

[0056] Preferred, such as Figure 5 As shown, the dynamic modulus of the asphalt surface layer is determined by actual traffic parameters, temperature conditions and subgrade soil properties, and the dynamic modulus under different environmental conditions is calculated based on the design formula.

[0057] In this invention, the dynamic modulus of the asphalt pavement is a crucial parameter affecting pavement performance, directly influencing its fatigue resistance, crack resistance, and load-bearing capacity. The dynamic modulus represents the material's ability to deform under repeated loading, and it is influenced by various factors, including actual traffic parameters, temperature conditions, and the properties of the subgrade soil. By comprehensively considering these variables, this invention can accurately calculate the dynamic modulus under different environmental conditions, thereby optimizing pavement structure design.

[0058] The dynamic modulus of asphalt pavement varies with the frequency of traffic load and temperature. At higher load frequencies, asphalt materials exhibit a higher modulus, meaning the material becomes more rigid, while at lower frequencies, the modulus decreases, and the material's deformation capacity increases. Temperature also has a significant impact on the dynamic modulus. Higher temperatures reduce the rigidity of asphalt, leading to a smaller modulus and greater deformation; conversely, lower temperatures increase the rigidity and thus the dynamic modulus. The properties of the subgrade soil also affect the dynamic modulus of the pavement; the rigidity and stability of different soil types exert force feedback on the mechanical behavior of the asphalt pavement. Therefore, when designing pavement structures, these variables must be comprehensively considered to ensure that the dynamic modulus of the asphalt pavement meets the requirements under actual service conditions.

[0059] This invention incorporates factors such as traffic load, temperature, and subgrade soil into the calculation formula for dynamic modulus through a specific design formula. This formula is fitted using multiple sets of experimental data and simulation analysis, and can be adjusted according to specific traffic conditions, temperature environments, and subgrade conditions. During the calculation process, the frequency of actual traffic loads, vehicle types, and travel speeds are included in the calculation model, thus reflecting the performance of the asphalt pavement under various dynamic loads. Simultaneously, the impact of environmental temperature changes on the rigidity of asphalt materials is quantified, and combined with different subgrade soil types, a dynamic modulus calculation model adaptable to various conditions is formed.

[0060] This design formula allows for flexible adjustment of the thickness and modulus of the asphalt pavement to adapt to different environmental conditions. For example, in higher-temperature regions, the dynamic modulus may be lower, necessitating an increase in the asphalt pavement thickness or the selection of materials with higher modulus to resist excessive deformation due to softening. In colder regions, the asphalt pavement may become too rigid, increasing the risk of cracking; therefore, adjusting the dynamic modulus helps optimize the pavement thickness and material properties, preventing brittle fracture.

[0061] By combining traffic parameters, temperature conditions, and subgrade soil properties, this invention achieves accurate calculation of the dynamic modulus of asphalt pavement. This design method, which comprehensively considers multiple variables, effectively improves the structural performance of the pavement, enabling it to maintain good mechanical behavior under different environmental and traffic conditions. Simultaneously, the combination of dynamic modulus calculation and thickness optimization effectively reduces material waste and lowers construction costs. Ultimately, through optimized dynamic modulus calculation, this invention not only improves pavement durability and fatigue resistance but also maintains stability in various complex environments, extending pavement service life and reducing the frequency and cost of subsequent maintenance.

[0062] Preferably, the optimized design simultaneously considers the fatigue cracking resistance of the asphalt surface layer, the fatigue performance of the semi-rigid layer, and the resistance to permanent deformation of the granular transition layer, so as to ensure the overall structural performance and economic benefits of the inverted asphalt pavement.

[0063] In this invention, the optimized design not only considers the fatigue cracking resistance of the asphalt pavement, but also comprehensively considers the fatigue performance of the semi-rigid layer and the resistance to permanent deformation of the granular transition layer, to ensure the performance and economic benefits of the entire pavement structure. This comprehensive design method, through fine adjustment of the thickness and modulus of each layer, enables the pavement structure to maintain high durability and stability during long-term use, while controlling material usage and reducing construction costs.

[0064] The fatigue crack resistance of asphalt pavement is one of the key indicators for the long-term bearing capacity of road surfaces under traffic loads. Over time, asphalt pavement is prone to fatigue cracks under repeated loading, and the gradual propagation of these cracks will affect the integrity of the overall pavement structure. To improve the fatigue crack resistance of asphalt pavement, this invention optimizes the thickness and modulus of the pavement to reduce tensile strain at the bottom of the layer, thereby slowing down the formation and propagation of cracks. This optimization process, combined with finite element analysis and experimental data, can precisely control stress concentration points and improve the durability of the asphalt pavement.

[0065] Meanwhile, the fatigue performance of the semi-rigid layer plays a crucial role in the entire pavement structure. As the load-bearing core of the pavement structure, the semi-rigid layer needs to maintain good fatigue resistance under long-term loads. Since the semi-rigid layer mainly bears compressive and shear stresses, optimizing its thickness and material modulus can effectively disperse the load from the upper layer and prevent the accumulation of fatigue damage within the layer. This invention, through reasonable thickness adjustment of the semi-rigid layer, ensures that the layer is not prone to fatigue failure under long-term traffic conditions, thereby extending the service life of the pavement.

[0066] The granular transition layer is a crucial transition layer connecting the asphalt surface layer and the semi-rigid layer, and its resistance to permanent deformation determines the stability of the entire pavement. Due to the nonlinear stress-dependent characteristics of the granular layer, its deformation capacity under traffic loads is closely related to the stress level. To ensure that the granular transition layer does not undergo permanent deformation during long-term use, this invention employs a stress-dependent nonlinear constitutive model and, combined with experimental data, optimizes the thickness and modulus of the granular layer, enabling it to maintain good load-bearing capacity and deformation stability even under high stress.

[0067] By simultaneously optimizing the fatigue cracking resistance of the asphalt pavement, the fatigue performance of the semi-rigid layer, and the resistance to permanent deformation of the granular transition layer, this invention provides a comprehensive pavement thickness design scheme. This optimized design ensures that the pavement structure maintains high durability and stability under different traffic conditions and environments, effectively reducing the risks of pavement cracking, fatigue failure, and permanent deformation. At the same time, a reasonable thickness design can reduce material usage, decrease construction costs, and improve economic efficiency. Furthermore, the improved long-term stability and fatigue resistance of the pavement also reduce the frequency and cost of subsequent maintenance, further enhancing the overall project benefits. Therefore, this invention maximizes structural economy and long-term benefits while optimizing pavement performance.

[0068] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows:

[0069] By combining finite element analysis with nonlinear constitutive modeling techniques, the thickness and modulus of the asphalt surface layer, aggregate transition layer, and semi-rigid layer were precisely optimized, effectively controlling fatigue cracking of the asphalt surface layer and permanent deformation of the aggregate transition layer, thereby improving the overall stability of the pavement structure.

[0070] By using the D-optimal solution response surface design method, a reasonable allocation of the thickness and modulus of each layer was achieved, which not only reduced the use of materials, but also ensured the long-term durability of the pavement under different load and environmental conditions.

[0071] This invention also addresses the neglect of the stress-dependent characteristics of granular materials in traditional methods, significantly improving the structural performance and economic benefits of road surfaces. Attached Figure Description

[0072] Figure 1 This is a schematic flowchart of the method of the present invention;

[0073] Figure 2 This is a schematic diagram of the structure of the asphalt surface layer, the granular transition layer, and the semi-rigid layer in this invention;

[0074] Figure 3 This is a schematic diagram of the experimental scheme for the D-optimal solution response surface design method in this invention;

[0075] Figure 4 This is a flowchart of the analysis of the inverted asphalt pavement structure based on the nonlinear characteristics of the granular layer in this invention;

[0076] Figure 5 This is a schematic diagram of the preliminary design of the target response range in this invention. Detailed Implementation

[0077] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0078] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0079] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0080] Step one: Using the D-optimal response surface methodology, the thickness and modulus of each structural layer of the inverted asphalt pavement are selected as control variables to design an experimental scheme with good spatial distribution, such as... Figure 5 As shown, the significance of the influence of each control variable on the target response value is evaluated.

[0081] Based on domestic and international research on the application of inverted asphalt pavement structural layers, and considering actual traffic parameters (medium load level), temperature conditions (minimum temperature can reach -15.2℃, maximum temperature can reach 31.0℃), and subgrade soil properties, the thickness and modulus ranges of inverted asphalt pavement structural layers were determined as discrete variables. The asphalt surface layer (AC layer) thickness was 8cm, 10cm, 12cm, 15cm, and 18cm; the aggregate transition layer (UAB layer) thickness was 10cm, 15cm, 20cm, 25cm, and 30cm; and the semi-rigid subbase layer (CTB layer) thickness was 15cm, 20cm, 32cm, 36cm, and 40cm. The modulus values ​​for the AC layer under summer conditions were 3000MPa, 5000MPa, and 7000MPa. The nonlinear modulus parameters are taken as Eu1 (k1=5.43,k2=0.32,k3=0.11), Eu2 (k1=4.09,k2=0.41,k3=0.17) and Eu3 (k1=2.64,k2=0.45,k3=0.15), the CTB layer modulus is taken as 10000MPa, 12000MPa and 14000MPa, and the subgrade (SUB) modulus is taken as 40MPa, 60MPa and 80MPa.

[0082] Based on the D-optimal design principle, five repeated test points and five missing fit points are allowed, and five blocks are used to estimate the experimental design error. Among them, setting repeated points helps to reduce experimental error and improve the reliability of experimental design. The test points with good spatial distribution are designed, and a total of 50 experimental scheme combinations are designed.

[0083] Step 2: Perform mechanical response calculations for inverted asphalt pavement structures based on the nonlinear characteristics of aggregates, and evaluate the fatigue performance of the asphalt surface layer and the stress-force dependence nonlinearity of the aggregate transition layer under different test schemes.

[0084] The calculation of the mechanical response of inverted asphalt pavement structure needs to be based on the theory of layered elastic system and adopt the finite element analysis method of inverted asphalt pavement structure based on the nonlinear characteristics of aggregate. It is achieved by compiling the UMAT subroutine and giving the aggregate transition layer a stress-dependent nonlinear constitutive model.

[0085] A standard axle load of 100KN is applied to a single axle double wheel assembly in an elastic layered system, with a converted load of 0.7MPa; a double rectangular uniformly distributed load is converted from a double circular uniformly distributed load with equal area, the load length is 22.5cm, the width is 15.5cm, and the distance between the inner sides of the double rectangular loads is 16.4cm.

[0086] When determining the material parameters, the dynamic modulus of the asphalt surface layer is predicted using the constitutive models shown in formulas (1) and (2), the resilient modulus of the granular transition layer is predicted using formula (3), and the modulus of the semi-rigid layer and the subgrade is selected empirically.

[0087] Formula (1) is as follows:

[0088]

[0089] The formula (2) is:

[0090]

[0091] The formula (3) is:

[0092]

[0093] In the formula, E * Represents the dynamic modulus; max represents the maximum value of the dynamic modulus; f is the load frequency at the test temperature; α(T) is the shift factor at temperature T; β and γ are the fitting parameters; ΔE a This represents the activation energy, which is also a regression coefficient; T is the experimental temperature, T r For reference temperature; M r Represents the spring modulus; k1, k2, and k3 are regression parameters; confining pressure P a =100kPa.

[0094] The finite element method is used to calculate the structural mechanical response, and the calculated stress, strain and vertical displacement response results are output. According to the selected structural design control index, the structural design index value is output. The calculation point is selected as the maximum mechanical response at the bottom of the structural layer.

[0095] Fatigue performance evaluation of asphalt surface layer of inverted asphalt pavement structure: The highest temperature reached 31.0℃, at which time the dynamic modulus of the asphalt surface layer was 3000MPa; and the modulus of the aggregate transition layer was low, which was much different from that of the surface layer. The tensile strain at the bottom of the inverted asphalt surface layer was large in summer. The maximum principal strain (MPS) at the bottom of the asphalt mixture layer was selected as the response variable to evaluate its fatigue resistance.

[0096] Evaluation of the stress-dependent nonlinear characteristics of the aggregate transition layer in inverted asphalt pavement structures: The increase in volumetric stress can lead to an increase in the stress-dependent resilient modulus of the aggregate transition layer. By fully utilizing the stress-dependent role of the aggregate transition layer, its own stress-dependent resilient modulus can be improved. The average volumetric stress (BS) of the aggregate transition layer is selected as the response variable.

[0097] Furthermore, the mechanical response variables of the inverted asphalt pavement structure were calculated, and the significance of the influence of each control variable on the response value was independently evaluated. The F-value and P-value were used to determine whether a significant relationship existed between the response variable and each control variable: a P-value less than 0.05 indicated a significant relationship, while a P-value greater than 0.05 indicated no significant relationship; the F-value was the ratio of the average effect term to the error term, and could not be negative; the higher the value, the greater the influence. The significance analysis results of the stress dependence nonlinearity of the aggregate transition layer are shown in Table 1, and the significance analysis results of the fatigue performance of the asphalt pavement are shown in Table 2.

[0098]

[0099] Table 2. Results of the significance analysis of maximum principal strain.

[0100]

[0101] Based on the results of the single-factor significance analysis, four variables were selected: AC layer thickness and modulus, UAB layer thickness and modulus, to carry out the combined optimization design of the inverted asphalt pavement structure.

[0102] Step 3: Based on the fatigue performance of asphalt pavement and the stress dependence characteristics of aggregate transition layer as the balance design principle, determine the optimal design range of pavement structure combination, determine the optimal solution based on the satisfaction theory, conduct comparative verification of other pavement structure mechanical indicators, and finally recommend the optimal pavement structure combination scheme.

[0103] The smaller the maximum principal strain (MPS) value at the bottom of the asphalt pavement layer, the better the fatigue cracking resistance of the asphalt pavement layer (AC layer); the larger the volumetric stress (BS), the stronger the stress dependence of the aggregate transition layer (UAB), which helps to improve the resilience modulus of the UAB layer. 120 με was adopted as the MPS limit design value, and 150 kPa was selected as the lower limit value for the volumetric stress level optimization design.

[0104] Furthermore, the structural mechanical response variables were calculated according to the 50 test combination schemes designed in step one, and the results are shown in Table 3.

[0105] Table 3 Design Schemes for Response Surface Methodology

[0106]

[0107]

[0108] Furthermore, the optimization design calculations included two cases: one considering the stress-dependent nonlinear characteristics of the aggregate transition layer and the other not. Case 1, considering the stress-dependent characteristics of the aggregate transition layer: the design objective was the MPS value of the asphalt surface layer (objective: minimize, upper limit: 120 με), and the volumetric stress level of the aggregate transition layer (objective: maximize, lower limit: 150 kPa). Case 2, not considering the stress-dependent characteristics of the aggregate transition layer: the design objective was the MPS value (objective: minimize, upper limit: 120 με), and the volumetric stress level (objective: none). In the `optimal` function, the mathematical index "desirability" was used to evaluate the accuracy of the solution; a higher "desirability" value indicates that the calculated solution is closer to the target value.

[0109] As shown in Table 4, in Design Case 2, NS1, NS2, and NS3 are the three solutions with the highest "desirability" values, and the designed structural combination has thicker AC and UAB layers. In contrast, in Design Case 1, YS1, YS2, and YS3 are the three solutions with the highest "desirability" values. The MPS value obtained is only 1.8% different from the MPS value obtained from solutions NS1, NS2, and NS3, while the volumetric stress value of the aggregate layer is 30% higher. This indicates that the inverted asphalt pavement designed according to the structural thickness and modulus parameters in the optimized solutions YS1, YS2, and YS3 has both better fatigue performance and stronger stress dependence characteristics.

[0110] Table 4 Optimization Design Solution

[0111]

[0112] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects.

[0113] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for optimizing the thickness of an inverted asphalt pavement structure, characterized in that, Includes the following steps: The thickness and modulus of each layer of the inverted asphalt pavement structure were selected as control variables. The D-optimal solution response surface design method was used to formulate an experimental scheme containing multiple combinations of different thicknesses and moduli, and the significance of each control variable to the target response value was evaluated. The D-optimal solution response surface design method is implemented using Design-expert software to determine the optimal combination of asphalt surface layer thickness, asphalt surface layer modulus, aggregate transition layer thickness, aggregate transition layer modulus, semi-rigid layer thickness, semi-rigid layer modulus, and subgrade modulus. Based on the stress-dependent nonlinear characteristics of the granular transition layer, the mechanical response of the inverted asphalt pavement structure is calculated to obtain the tensile strain at the bottom of the asphalt surface layer and the volumetric stress of the granular transition layer, so as to evaluate the fatigue performance of the asphalt surface layer and the stress-dependent characteristics of the granular transition layer. The mechanical response calculation is based on the finite element analysis method. Using the compiled UMAT subroutine, the stress-dependent nonlinear characteristics of the granular transition layer are given, and the stress response of the granular transition layer is accurately simulated through the constitutive model. Based on the fatigue performance of the asphalt surface layer and the stress dependence characteristics of the aggregate transition layer, the optimal design range of the inverted asphalt pavement structure is determined. The optimal solution is determined based on the satisfaction theory, and the mechanical verification indexes of other pavement structures are compared. The optimal combination scheme of thickness and modulus of the inverted asphalt pavement structure is recommended. The goal of the optimized design is to reduce the thickness of the asphalt surface layer and improve the durability of the asphalt pavement by minimizing the tensile strain at the bottom of the asphalt surface layer and maximizing the volumetric stress of the aggregate transition layer. The thickness of the asphalt surface layer ranges from 8cm to 18cm, the thickness of the granular transition layer ranges from 10cm to 30cm, and the thickness of the semi-rigid layer ranges from 15cm to 40cm. The dynamic modulus of asphalt pavement is determined by actual traffic parameters, temperature conditions and subgrade soil properties, and the dynamic modulus under different environmental conditions can be calculated based on the design formula.

2. The method for optimizing the thickness of inverted asphalt pavement structures according to claim 1, characterized in that, The response surface methodology is generated based on multiple sets of experimental data and evaluates the effects of different thickness and modulus combinations on the fatigue performance of asphalt pavement and the stress dependence characteristics of aggregate transition layer.

3. The method for optimizing the thickness of inverted asphalt pavement structures according to claim 1, characterized in that, The fatigue performance of the asphalt pavement is determined by evaluating the maximum principal strain at the bottom of the asphalt pavement, with an upper limit of 120 με for the maximum principal strain at the bottom of the asphalt pavement.

4. The method for optimizing the thickness of inverted asphalt pavement structures according to claim 1, characterized in that, The volumetric stress of the granular transition layer is used to characterize the stress dependence of the granular transition layer, and the lower limit of its volumetric stress level is 150 kPa.

5. The method for optimizing the thickness of inverted asphalt pavement structures according to claim 1, characterized in that, The optimized design takes into account the fatigue cracking resistance of the asphalt surface layer, the fatigue performance of the semi-rigid layer, and the resistance to permanent deformation of the granular transition layer to ensure the overall structural performance and economic benefits of the inverted asphalt pavement.

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