A method and system for roadbed state evolution under intermittent load

Abstract

The application discloses a method and system for roadbed state evolution under intermittent load. The method comprises: obtaining roadbed filling information corresponding to a roadbed, wherein the roadbed filling information comprises a particle system corresponding to a plurality of different filling materials; determining stress and strain corresponding to the structure of the particle system under intermittent load, and establishing a state evolution model of the roadbed based on the stress and the strain; obtaining a historical strain parameter of the roadbed, and determining a characteristic strain of the particle system based on the historical strain parameter; and correcting the state evolution model based on the characteristic strain, so as to determine a state evolution variable of the roadbed under intermittent load by using the corrected state evolution model. The application can accurately determine the state evolution variable of the roadbed under intermittent load, guarantee the safe and smooth operation of road traffic, prolong the service life of the roadbed, and reduce the road maintenance cost.

Description

Technical Field

[0001] This application relates to the field of roadbed design technology, specifically to a method and system for the evolution of roadbed state under intermittent loads. Background Technology

[0002] In the field of road engineering, subgrade settlement prediction is crucial for ensuring the long-term stability and driving safety of roads. Currently, although numerous research findings exist on subgrade settlement prediction and corresponding state evolution models have been constructed, most existing subgrade settlement state evolution models are based on continuous loading conditions. While models under continuous loading conditions can reflect the settlement patterns of the subgrade under sustained stress to a certain extent, in actual engineering applications, the loads borne by the subgrade are not always continuous.

[0003] Therefore, existing subgrade settlement state evolution models based on continuous loading conditions have significant limitations in predicting subgrade settlement under intermittent loading, and are difficult to accurately reflect the actual settlement of the subgrade under intermittent loading. This urgently requires the development of a new state evolution model that can accurately consider the characteristics of intermittent loading and its impact on subgrade settlement. Summary of the Invention

[0004] To address the aforementioned technical problems, embodiments of this application provide a method and system for the evolution of roadbed state under intermittent loading.

[0005] According to one aspect of the embodiments of this application, a method for the state evolution of a roadbed under intermittent loading is provided, comprising: acquiring roadbed filler information corresponding to the roadbed, the roadbed filler information including a particle system corresponding to multiple layers of different filler materials; determining the stress and strain corresponding to the structure of the particle system under intermittent loading, and establishing a state evolution model of the roadbed based on the stress and strain; acquiring historical strain parameters of the roadbed, and determining the characteristic strain of the particle system based on the historical strain parameters; and correcting the state evolution model based on the characteristic strain, so as to determine the state evolution variables of the roadbed under intermittent loading through the corrected state evolution model.

[0006] According to one aspect of the embodiments of this application, the method further includes: under intermittent loading, acquiring the phase transition characteristics of the particle system when subjected to force, and determining the state evolution variables of the particle system based on the phase transition characteristics; determining the steady-state conditions and the non-equilibrium potential functions of the non-equilibrium states corresponding to the state evolution variables, and determining the dynamic equilibrium relationship corresponding to the particle system based on the steady-state conditions and the non-equilibrium potential functions; constructing a state evolution model corresponding to the state evolution variables based on the dynamic equilibrium relationship, wherein the state evolution model includes explicit expressions for the state evolution variables.

[0007] According to one aspect of the embodiments of this application, the method further includes: performing a stress analysis on the particle system, and determining the phase transition characteristics of the particle system under stress based on the analysis results, wherein the phase transition characteristics include a solid phase, a liquid phase, and a critical state; determining a quantitative index of the non-equilibrium thermodynamics of the particle system based on the phase transition characteristics, and using the quantitative index as a state evolution variable of the particle system.

[0008] According to one aspect of the embodiments of this application, determining the steady-state conditions and the non-equilibrium potential function of the non-equilibrium state corresponding to the state evolution variable, and determining the dynamic equilibrium relationship of the particle system based on the steady-state conditions and the non-equilibrium potential function, includes: establishing a state evolution equation for the state evolution variable by combining the steady-state conditions and the non-equilibrium potential function; solving the state evolution equation to obtain the steady-state solution corresponding to the state evolution equation and the recovery condition corresponding to the steady-state solution; and determining the dynamic equilibrium relationship of the particle system based on the steady-state solution and the recovery condition corresponding to the steady-state solution.

[0009] According to one aspect of the embodiments of this application, after constructing the state evolution model corresponding to the state evolution variables based on the dynamic equilibrium relationship, wherein the state evolution model includes explicit expressions for the state evolution variables, the method further includes: determining the real-time stress and real-time load change rate corresponding to the structure of the particle system under intermittent loading, and incorporating the real-time stress and the real-time load change rate into the explicit expression to obtain an updated explicit expression; and determining the state evolution model of the roadbed under intermittent loading based on the updated explicit expression.

[0010] According to one aspect of the embodiments of this application, the method further includes: under intermittent loading, using a sinusoidal load as the input form of the load in the loading phase; determining the real-time stress of the particle system in the intermittent phase and the real-time stress of the particle system in the loading phase based on the sinusoidal load and the explicit expression; and determining the real-time stress under the intermittent load based on the real-time stress in the intermittent phase and the real-time stress in the loading phase.

[0011] According to one aspect of the embodiments of this application, the method further includes: after the roadbed enters the intermittent stage, determining a first stage load based on the static load of the superstructure of the roadbed; connecting the first stage load with the second stage load to obtain a connecting load, wherein the second stage load is the load corresponding to the loading stage; and determining the real-time load change rate corresponding to the structure of the particle system based on the connecting load.

[0012] According to one aspect of the embodiments of this application, the step of modifying the state evolution model based on the characteristic strain includes: obtaining historical strain parameters of the subgrade under intermittent loading, the historical strain parameters including the strain state of the state evolution variables in the transition state between the loaded state and the intermittent state; determining the characteristic strain of the subgrade based on the strain state, the characteristic strain including the relevant historical strain range of the state evolution variables in the transition state; and introducing an expression for the state evolution variables based on the characteristic strain to obtain the modified state evolution model.

[0013] According to one aspect of the present application, determining the characteristic strain of the roadbed based on the strain state includes: defining the state evolution variables under the connection state as a weighted average of historical strain paths; establishing an exponential decay weight function between the length of the historical strain path and the weighted average, so as to determine the characteristic strain of the roadbed based on the exponential decay weight function.

[0014] According to one aspect of the embodiments of this application, a roadbed state evolution system under intermittent loading is provided. The system includes a processor, an input device, an output device, and a memory, which are interconnected. The memory is used to store a computer program, which includes program instructions. The processor is configured to call the program instructions to execute the above-described roadbed state evolution method under intermittent loading.

[0015] In the technical solution provided by the embodiments of this application, by obtaining the subgrade filling information corresponding to the subgrade containing a multi-layered particle system of different filling materials, and determining the stress and strain corresponding to the particle system structure under intermittent load, a state evolution model of the subgrade is established. This allows the dynamic change process of the subgrade under specific load conditions to be quantitatively presented, which helps to clearly understand the state evolution law of the subgrade at different intermittent load stages. Furthermore, by obtaining the historical strain parameters of the subgrade and determining the characteristic strain of the particle system, the influence of the mechanical actions experienced by the subgrade in the past on its current performance is fully considered. It can capture the potential change characteristics of the subgrade due to long-term use or complex environmental factors. Finally, the state evolution model is corrected based on the characteristic strain, which greatly improves the accuracy and reliability of the model. The corrected state evolution model can more realistically reflect the actual state of the subgrade under intermittent load, accurately determine the subgrade state evolution variables, ensure the safe and smooth operation of road traffic, extend the service life of the subgrade, and reduce road maintenance costs.

[0016] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0017] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0018] Figure 1 This is a flowchart illustrating a method for the evolution of roadbed state under intermittent loading, as shown in an exemplary embodiment of this application.

[0019] Figure 2 yes Figure 1 The flowchart of step S120 in the illustrated embodiment is shown in an exemplary embodiment.

[0020] Figure 3 Figure 2 The flowchart of step S210 in the illustrated embodiment is shown in an exemplary embodiment.

[0021] Figure 4 yes Figure 2 Step S220 in the illustrated embodiment is a flowchart of an exemplary embodiment.

[0022] Figure 5 yes Figure 1 The flowchart of step S120 in the illustrated embodiment is shown in another exemplary embodiment.

[0023] Figure 6 yes Figure 5 The flowchart of step S510 in the illustrated embodiment is shown in an exemplary embodiment.

[0024] Figure 7 This is another exemplary embodiment of the present application, illustrating the state evolution of the roadbed from dynamic load to static load.

[0025] Figure 8 Figure 5 The flowchart of step S510 in the illustrated embodiment is shown in another exemplary embodiment.

[0026] Figure 9 This is another exemplary embodiment of the present application illustrating the state evolution of a roadbed under static load to dynamic load.

[0027] Figure 10 This is a block diagram illustrating a roadbed state evolution system under intermittent loading, as shown in an exemplary embodiment of this application. Detailed Implementation

[0028] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of systems and methods consistent with some aspects of this application as detailed in the appended claims.

[0029] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0030] The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all content and operations / steps, nor do they necessarily have to be performed in the described order. For example, some operations / steps can be broken down, while others can be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0031] In this application, "multiple" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. The character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0032] First, it should be noted that the most significant characteristic of intermittent loads on high-speed railways is their discontinuity. During the intervals between trains, the roadbed bears almost no direct load from the trains. Therefore, predicting the cumulative strain of the roadbed under intermittent loads on high-speed railways usually requires more complex dynamic analysis and simulation to clarify the difference between intermittent and continuous loads in order to accurately capture the dynamic characteristics of the load and its impact on the roadbed.

[0033] Currently, although numerous research findings exist on subgrade settlement prediction and corresponding state evolution models have been constructed, most existing subgrade settlement state evolution models are based on continuous loading conditions. While models under continuous loading conditions can reflect the settlement law of subgrades under sustained stress to a certain extent, in actual engineering applications, the loads borne by the subgrade are not always continuous. Especially for railway subgrades, the loads generated by train operation are typical intermittent loads; that is, the load is not continuously applied but occurs when a train passes, followed by a load gap. Extensive practice and research show that the cumulative settlement of subgrades under intermittent loading differs significantly from that under continuous loading. The cumulative deformation process of subgrades caused by intermittent loading is more complex, including the partial recovery effect of subgrade fill material during the load gap. Moreover, the intermittent loads generated by passing trains do not simply damage the subgrade; in fact, they have a positive effect on reducing the cumulative plastic strain of the subgrade fill material. Therefore, existing subgrade settlement state evolution models based on continuous loading conditions have significant limitations in predicting subgrade settlement under intermittent loading, and are difficult to accurately reflect the actual settlement of the subgrade under intermittent loading.

[0034] To address the aforementioned issues, this application proposes a method and system for roadbed state evolution under intermittent loading, an electronic device, a computer-readable storage medium, and a computer program product. These embodiments will be described in detail below.

[0035] Please see Figure 1 , Figure 1 The method for roadbed state evolution under intermittent loading, as illustrated in an exemplary embodiment of this application, includes at least steps S110 to S140, which are described in detail below.

[0036] Step S110: Obtain the subgrade filler information corresponding to the subgrade. The subgrade filler information includes the particle system corresponding to multiple layers of different filler materials.

[0037] For example, in the complex scenarios of road construction and maintenance, accurately understanding the subgrade condition is a crucial prerequisite for ensuring road safety and durability. When conducting research or maintenance work on the subgrade, the first step is to carry out a comprehensive and detailed on-site survey and sample collection. Professional technicians will drill and sample at different depths based on the layered structure of the subgrade to ensure that original samples of each layer of subgrade fill material can be obtained. These samples cover multiple layers of different fill materials because subgrades are often constructed in layers according to geological conditions and design requirements, and different layers may use various fill materials such as gravel, cohesive soil, and crushed stone. After collecting samples, particle system analysis is performed on each layer of filler samples. Through sieving tests, the distribution ratio of particles of different sizes can be determined, and the composition of coarse and fine particles in the filler can be understood. With the help of microscopic observation and image analysis technology, the microscopic characteristics such as particle shape and surface texture are further studied. At the same time, the physical properties of the filler, such as density and moisture content, as well as the mechanical properties, such as compression modulus and shear strength, are measured. By combining these analysis results, the complete information of the subgrade filler corresponding to the subgrade can be obtained, and the particle system characteristics of each layer of different filler materials can be clarified, including particle size, shape, gradation, and physical and mechanical properties of the filler. This provides a solid data foundation for subsequent performance analysis and evaluation of the subgrade under various loads.

[0038] Step S120: Determine the stress and strain corresponding to the structure of the particle system under intermittent loading, and establish a state evolution model of the roadbed based on the stress and strain.

[0039] For example, intermittent loading scenarios are simulated in the laboratory. Using advanced geotechnical testing equipment, such as a dynamic triaxial testing machine, intermittent loads are applied to roadbed samples containing different filler particle systems, precisely controlling parameters such as load magnitude, frequency, and interval time, according to the intermittent load characteristics generated by train travel and vehicle traffic in actual engineering. During the test, high-precision sensors and data acquisition systems are used to monitor and record the stress and strain data of the particle system structure at different times in real time. Stress data reflects the magnitude of the internal forces borne by the particle system under intermittent loading, while strain data reflects the deformation of the particle system. The two are interrelated and jointly describe the mechanical response of the particle system under intermittent loading. Subsequently, the large amount of stress and strain data collected is analyzed in depth. Mathematical modeling and statistical analysis methods are used to uncover the patterns behind the data and explore the intrinsic relationship between stress and strain. Considering the special characteristics of intermittent loading, the analysis process must fully consider the influence of the intermittent effect of the load on the stress and strain of the particle system, such as the stress relaxation and strain recovery phenomena of the particle system during the load pause. Based on these analytical results, a model was constructed that can accurately describe the state evolution of the roadbed under intermittent loading. This model takes stress and strain as key variables, comprehensively considers the characteristics of the filler particle system, the parameters of the intermittent loading, and the time factor, and can dynamically simulate the changes in internal stress and strain of the roadbed over time from its initial state under repeated intermittent loading, thereby predicting the state evolution trend of the roadbed.

[0040] Step S130: Obtain the historical strain parameters of the roadbed, and determine the characteristic strain of the particle system based on the historical strain parameters.

[0041] For example, in the long-term operation and maintenance of road engineering projects, accurately grasping the deformation of the roadbed during past use plays a crucial role in assessing the current condition of the roadbed and predicting future development trends. To obtain historical strain parameters of the roadbed, it is first necessary to collect roadbed inspection and monitoring data from different time periods since the road was built and opened to traffic. These data sources are extensive. On the one hand, past regular professional roadbed inspection reports are important evidence. Inspectors use professional measuring instruments, such as high-precision levels and total stations, to conduct on-site measurements of roadbed settlement, horizontal displacement, and other deformation indicators. After processing and analysis, this measurement data can directly or indirectly reflect the roadbed's strain. On the other hand, if the road is equipped with a long-term monitoring system, such as strain sensors and settlement plates deployed inside the roadbed, these devices continuously record the roadbed's strain data under different working conditions. This real-time data is stored in a dedicated database, providing a rich and continuous source of information for obtaining historical strain parameters. After collecting sufficiently comprehensive historical strain data, it is systematically organized and preprocessed to remove abnormal data caused by instrument malfunctions, human error, etc., ensuring the accuracy and reliability of the data. Then, statistical analysis methods are used to analyze the processed data. By plotting strain versus time curves, the growth trend and fluctuation characteristics of strain at different stages are observed. Simultaneously, considering actual road operation conditions, such as traffic flow changes, heavy vehicle traffic, and surrounding environmental influences (such as rainfall and earthquakes), the causes and patterns of historical strain data are analyzed in depth. Based on the detailed analysis of historical strain parameters, the characteristic strain of the granular system is determined. Considering that the roadbed is a granular system composed of multiple layers of different filler materials, and that the mechanical properties and deformation characteristics of different fillers vary, characteristic parameters that can represent the typical deformation behavior of the granular system under actual working conditions such as intermittent loading are selected as characteristic strains based on the strain conditions at different depths and locations reflected in the historical strain data, combined with the type and distribution of fillers.

[0042] Step S140: Based on the characteristic strain modified state evolution model, the state evolution variables of the subgrade under intermittent load are determined by the modified state evolution model.

[0043] For example, the initially established subgrade state evolution model, while based on certain theoretical assumptions and preliminary data, inevitably has limitations when facing the complex and variable intermittent load conditions in actual engineering. This is because actual subgrades are affected by a complex interplay of factors such as traffic flow fluctuations, vehicle load variations, and changes in environmental temperature and humidity. These factors cause the magnitude, frequency, and duration of intermittent loads to constantly change, resulting in the stress-strain relationship of the subgrade not entirely conforming to the initial model settings. Therefore, the state evolution model is modified using a defined characteristic strain as a "benchmark." Specifically, the deformation law of the subgrade particle system reflected by the characteristic strain is incorporated into the adjustment of key model parameters. For instance, if the characteristic strain shows that the plastic deformation of the subgrade develops faster than initially predicted by the model under a specific intermittent load frequency, the parameters related to plastic deformation in the model are adjusted accordingly, allowing the model to more accurately reflect this actual deformation trend. Simultaneously, considering the differences in characteristic strain at different depths of the subgrade base, the model is modified layer by layer to ensure that the stress-strain relationship of each layer closely matches the actual situation. After such meticulous corrections, the state evolution model is as if it has been given a more acute "sensory ability", enabling it to more realistically simulate the dynamic changes of the roadbed under intermittent loads.

[0044] In some embodiments of this application, by obtaining information on roadbed filler material containing multiple layers of different filler particles, the stress and strain of the particle system under intermittent load are determined to establish a state evolution model. Then, by combining historical strain parameters to determine characteristic strains to correct the model, the roadbed state evolution variables under intermittent load can be accurately determined, providing a reliable basis for accurately evaluating the performance and stability of the roadbed.

[0045] Furthermore, based on the above embodiments, please refer to... Figure 2 In one exemplary embodiment provided in this application, the specific implementation process of the above-mentioned subgrade state evolution method under intermittent loading may further include steps S210 to S230, which are described in detail below:

[0046] Step S210: Under intermittent load, obtain the phase transition characteristics of the particle system when it is subjected to force, and determine the state evolution variables of the particle system based on the phase transition characteristics.

[0047] Step S220: Determine the steady-state conditions corresponding to the state evolution variables and the non-equilibrium potential function of the non-equilibrium state, and determine the dynamic equilibrium relationship of the particle system based on the steady-state conditions and the non-equilibrium potential function.

[0048] Step S230: Construct a state evolution model corresponding to the state evolution variables based on the dynamic equilibrium relationship. The state evolution model includes explicit expressions for the state evolution variables.

[0049] For example, in practical scenarios involving the study of roadbeds and soil granular systems, such as road engineering and geotechnical mechanics, accurately grasping the behavior of granular systems under stress is crucial for the safety and stability of engineering structures. To obtain the phase transition characteristics of granular systems under stress, a professional experimental platform needs to be built in the laboratory to simulate the complex stress conditions experienced by the roadbed in reality, such as applying intermittent or cyclic loads using a dynamic triaxial testing machine. During the experiment, high-precision sensors and data acquisition systems are used to monitor the changes in parameters such as stress, strain, and pore water pressure of the granular system in real time. By analyzing the curves of these parameters changing with the stress process, the critical points at which the granular system transitions from one stable state to another can be identified, such as the transition from a loose state to a dense state, or from an elastic deformation stage to a plastic deformation stage. This clarifies its phase transition characteristics, including the conditions for phase transition and the energy changes during the phase transition. Based on the obtained phase transition characteristics, the state evolution variables of the granular system are further determined. These variables can comprehensively describe the state changes of the granular system during stress, such as the particle arrangement structure, porosity, and effective stress. The determination of state evolution variables provides key indicators for a deeper understanding of the dynamic behavior of particulate systems. Subsequently, for the determined state evolution variables, their corresponding steady-state conditions are analyzed. Steady-state conditions refer to the physical constraints satisfied by the particulate system when it reaches a stable state under specific stress conditions. For example, under a constant load, the strain of the particulate system no longer changes with time; the combination of parameters such as stress and porosity at this point constitutes the steady-state condition. Simultaneously, for non-equilibrium states, the concept of a non-equilibrium potential function is introduced. The non-equilibrium potential function is a measure of the degree to which the particulate system deviates from its steady state. By establishing a suitable non-equilibrium potential function, the evolutionary trend of the particulate system under non-equilibrium states can be quantified.

[0050] Finally, based on the steady-state conditions and the non-equilibrium potential function, and using relevant theories such as thermodynamics and statistical mechanics, the dynamic equilibrium relationship corresponding to the particle system is derived. This dynamic equilibrium relationship reflects the balance and transformation between various forces acting on the particle system during the force application process. It comprehensively considers factors such as inter-particle interactions, external forces, and energy dissipation within the system, and is the core equation describing the dynamic behavior of the particle system. Finally, based on the determined dynamic equilibrium relationship, through mathematical derivation and simplification, a state evolution model corresponding to the state evolution variables is constructed, and explicit expressions for the state evolution variables are obtained.

[0051] In some embodiments provided in this application, the state evolution variables are determined by obtaining the phase transition characteristics of the particle system under stress, and the dynamic equilibrium relationship is clarified based on its steady-state conditions and non-equilibrium potential functions. In this way, a state evolution model containing explicit expressions of state evolution variables is constructed, which can accurately predict and describe the state change law of the particle system under stress.

[0052] Furthermore, based on the above embodiments, please refer to... Figure 3 In one exemplary embodiment provided in this application, the specific implementation process of obtaining the phase transition characteristics of the particle system under stress and determining the state evolution variables of the particle system based on the phase transition characteristics may further include steps S310 and S320, which are described in detail below:

[0053] Step S310: Perform stress analysis on the particle system and determine the phase transition characteristics of the particle system under stress based on the analysis results. The phase transition characteristics include solid phase, liquid phase and critical state.

[0054] Step S320: Determine the quantitative index of the non-equilibrium thermodynamics of the particle system based on the phase transition characteristics, and use the quantitative index as the state evolution variable of the particle system.

[0055] For example, detailed stress analysis can be conducted on specific granular systems, such as soil-rock mixtures in roadbeds or loose soil and rock masses on slopes. In a laboratory environment, advanced geotechnical testing equipment, such as dynamic triaxial apparatus and direct shear apparatus, can be used to simulate the complex stress conditions experienced by granular systems in actual engineering projects, such as intermittent cyclic stress generated by road traffic loads and random dynamic stress under seismic action. During the experiment, high-precision sensors are used to monitor key parameters of the granular system in real time, such as stress-strain relationships and pore water pressure changes. Simultaneously, numerical simulation methods, such as the discrete element method (DEM), can be used to further analyze the microscopic stress conditions of the granular system, observe the distribution of contact forces between particles, and the trajectory of particle motion. Furthermore, by combining experiments and simulations, comprehensive and in-depth information on the mechanical response of the granular system under stress can be obtained.

[0056] Based on the above stress analysis results, the phase transition characteristics of the particle system under stress are determined. When the stress on the particle system is small, the relative positions between particles are relatively fixed, and stress is mainly transferred through contact forces between particles. At this time, the particle system exhibits solid-like characteristics, with high stiffness and strength, and can withstand certain external forces without significant deformation. As the stress gradually increases, when a certain critical value is reached, the contact between particles begins to loosen, some particles begin to slide relative to each other, and the fluidity of the particle system gradually increases, entering a critical state. In this state, the particle system has both certain solid-state characteristics and some liquid characteristics, and its mechanical properties become extremely complex. When the stress further increases, exceeding the stress level corresponding to the critical state, the relative motion between particles becomes free, and the particle system exhibits obvious liquid-phase characteristics, with significantly enhanced fluidity, making it difficult to withstand large shear stresses. After determining the phase transition characteristics of the particle system, the quantitative indicators of the non-equilibrium thermodynamics of the particle system can be determined accordingly. By using these quantitative indicators as state evolution variables of particulate systems, they can comprehensively and dynamically describe the evolution process of particulate systems from solid phase to critical state and then to liquid phase under stress, providing important quantitative basis for a deeper understanding of the mechanical behavior and thermodynamic properties of particulate systems.

[0057] In some embodiments of this application, by performing stress analysis on the particle system, the phase transition characteristics including the solid phase, liquid phase and critical state are clarified, and the quantitative index of non-equilibrium thermodynamics is determined as the state evolution variable. This can accurately quantify the dynamic changes of the particle system during the stress process, providing a key basis for a deeper understanding of its mechanical behavior and state evolution laws.

[0058] Furthermore, based on the above embodiments, please refer to... Figure 4 In one exemplary embodiment provided in this application, the specific implementation process of determining the steady-state conditions corresponding to the state evolution variables and the non-equilibrium potential function of the non-equilibrium state, and determining the dynamic equilibrium relationship of the particle system based on the steady-state conditions and the non-equilibrium potential function, may further include steps S410 to S430, which are described in detail below:

[0059] Step S410: Establish the state evolution equation of the state evolution variables by combining steady-state conditions and non-equilibrium potential functions.

[0060] Step S420: Solve the state evolution equation to obtain the steady-state solution and the recovery condition corresponding to the steady-state solution.

[0061] Step S430: Determine the dynamic equilibrium relationship of the particle system based on the steady-state solution and the recovery conditions corresponding to the steady-state solution.

[0062] For example, following the steady-state conditions and non-equilibrium potential functions in the above embodiments, a state evolution equation for the state evolution variables can be established. These state evolution variables are key parameters that comprehensively describe the state of the particle system, such as particle arrangement, effective stress, and pore water pressure. Then, by applying relevant theories such as thermodynamics and statistical mechanics, combined with the system equilibrium characteristics reflected by the steady-state conditions and the dynamic process of the system deviating from equilibrium described by the non-equilibrium potential function, a differential equation that accurately reflects the changes of the state evolution variables over time can be constructed. However, state evolution equations are usually quite complex, making it difficult to obtain their analytical solutions directly. Therefore, numerical solution methods, such as the finite difference method and the finite element method, can be used to solve the state evolution equations. During the solution process, by setting appropriate initial and boundary conditions, the initial state and external constraints of the particle system in actual engineering are simulated, and further computer simulation calculations are used to obtain the steady-state solution corresponding to the state evolution equation. The steady-state solution represents the stable state that the particle system finally reaches after long-term evolution, reflecting the equilibrium characteristics of the system under specific conditions. Simultaneously, the solution process is analyzed to determine the recovery conditions corresponding to the steady-state solution, that is, under what conditions the particle system can recover to steady state after being disturbed by external forces and deviating from steady state. The recovery conditions may involve factors such as the magnitude of the disturbance, the duration of its action, and the inherent characteristics of the system. Finally, based on the obtained steady-state solution and the corresponding recovery conditions, the dynamic equilibrium relationship of the particle system is further determined.

[0063] In some embodiments of this application, by combining steady-state conditions and non-equilibrium potential functions to construct and solve the state evolution equations of the state evolution variables, the steady-state solutions and recovery conditions are obtained, thereby accurately determining the dynamic equilibrium relationship of the particle system, providing strong theoretical support for in-depth research on the dynamic behavior and stability mechanism of particle systems under complex forces.

[0064] Furthermore, based on the above embodiments, please refer to... Figure 5 In one exemplary embodiment provided in this application, after constructing a state evolution model corresponding to the state evolution variables based on the dynamic equilibrium relationship, and the state evolution model including explicit expressions of the state evolution variables, the specific implementation process of the above-mentioned subgrade state evolution method under intermittent load may further include steps S510 and S520, which are detailed below:

[0065] Step S510: Determine the real-time stress and real-time load change rate corresponding to the structure of the particle system under intermittent loading, and introduce the real-time stress and real-time load change rate into the explicit expression to obtain the updated explicit expression.

[0066] Step S520: Determine the state evolution model of the roadbed under intermittent loads based on the updated explicit expression.

[0067] For example, the most significant characteristic of intermittent loads on high-speed railways is their discontinuity; during the intervals between trains, the roadbed bears almost no direct load from the trains. Therefore, predicting the cumulative strain of the roadbed under intermittent loads on high-speed railways typically requires more complex dynamic analysis and model simulations to clearly distinguish between intermittent and continuous loads, in order to accurately capture the dynamic characteristics of the load and its impact on the roadbed. Based on a state evolution model, a state evolution model for the cumulative settlement of the roadbed under long-term cyclic loads was successfully constructed. This state evolution model fully considers the input of cyclic dynamic loads, that is, it considers the magnitude and rate of change of the real-time load.

[0068] Therefore, if accurate simulation of intermittent load input can be achieved in this model, the cumulative strain of the subgrade under intermittent load can be predicted. In some feasible embodiments, the updated explicit expression of the state evolution model can be expressed as:

[0069]

[0070] In the formula, and They are respectively Stress and strain at any given moment; for The rate of change of stress at time t; The elastic modulus of the roadbed; for i The state variables of the roadbed at any given time; Δ t To calculate the step size; Here, are the characteristic coefficients, where , These are undetermined coefficients, which are affected by the soil condition. It is a reference strain rate introduced for dimensional consistency. This refers to characteristic strain. To achieve accurate simulation of intermittent load input, the real-time stress and real-time load change rate corresponding to the structure of the granular system under intermittent load can be introduced into the above explicit expression to obtain an updated explicit expression. Then, the state evolution model of the roadbed under intermittent load can be determined based on the updated explicit expression.

[0071] In some embodiments of this application, an updated version is obtained by introducing the real-time stress and real-time load change rate of the granular system structure under intermittent load into an explicit expression, thereby accurately constructing a state evolution model that reflects the dynamic change law of the subgrade under the actual action of intermittent load, providing a reliable basis for subgrade performance evaluation and prediction.

[0072] Furthermore, based on the above embodiments, please refer to... Figure 6In one exemplary embodiment provided in this application, the specific implementation process of the above-mentioned subgrade state evolution method under intermittent loading may further include steps S610 to S630, which are described in detail below:

[0073] Step S610: Under intermittent load, sinusoidal load is used as the input form of load during the loading stage.

[0074] Step S620: Determine the real-time stress of the particle system during the intermittent phase and the real-time stress of the particle system during the loading phase based on the sinusoidal load and the explicit expression.

[0075] Step S630: Determine the real-time stress under intermittent load based on the real-time stress during the intermittent phase and the real-time stress during the loading phase.

[0076] For example, to achieve accurate simulation of intermittent load input, the intermittent load input is divided into a loading stage and an intermittent stage in the state evolution model. In the loading stage, the load input form (taking a sinusoidal load as an example) is as follows:

[0077]

[0078] In the formula, For the load during the loading phase, This represents the rate of change of load during the loading phase. For the load period, This refers to the time step for calculation; The number of computation steps in the loading phase, where, , The duration of the loading phase, and when hour, .

[0079] After entering the intermittent phase, the roadbed no longer bears the load generated by the train, but only the static load of the roadbed superstructure. Therefore, the load in this phase is a constant value. To connect with the load in the loading phase, let the load in the intermittent phase be:

[0080]

[0081] in, Load during intermittent phases, The load at the initial moment of the intermittent phase. The load at the final moment of the loading phase. The static stress generated by the superstructure of the roadbed. The number of calculation steps in the intermittent phase, where, , Given the duration of the intermittent phase, the load change rate during the intermittent phase can be further expressed as follows:

[0082]

[0083] Since the load on the roadbed during the intermittent phase is significantly less than that during the loading phase, and experimental analysis shows that the roadbed state variables will be at a minimum during the intermittent phase, to simplify the model's complexity, we can assume that the roadbed state variables at the initial moment of entering the intermittent phase are... Therefore, subsequent values ​​can be calculated using explicit expressions. The cumulative strain of the subgrade at the moment the subgrade enters the intermittent stage is equal to the cumulative strain of the subgrade at the last moment of the loading stage, that is, Its subsequent values ​​can also be calculated using explicit expressions.

[0084] Furthermore, in some feasible embodiments, calculation code is written using Matlab according to the above approach. The calculated load, its rate of change, strain, and state variables are as follows: Figure 7 As shown. From Figure 7 As can be seen in (a), the state evolution model accurately reproduces the characteristics of intermittent loading, that is, the load changes from dynamic load in the loading phase to static load in the intermittent phase. Furthermore, Figure 7 The cumulative strain curve of the subgrade calculated using this model, shown in (b) in the figure, clearly shows the rebound effect of strain in the intermittent stage, which is consistent with the subgrade settlement data observed under intermittent loading in the model test. Figure 7 The results shown in (c) indicate that during the intermittent phase, the subgrade state variables remain at extremely low levels, which is consistent with the assumptions made during model establishment and reflects the flow characteristics of the actual subgrade system. In summary, this state evolution model demonstrates good accuracy in simulating the subgrade response during the transition from the loading phase to the intermittent phase.

[0085] In some embodiments of this application, under intermittent load scenarios, sinusoidal load is used as the input for the loading stage, and the real-time stress of the particle system in the intermittent and loading stages is determined by combining explicit expressions, thereby accurately determining the real-time stress under the entire intermittent load, providing key data support for in-depth analysis of the mechanical response of the particle system and the evolution of the subgrade state.

[0086] Furthermore, based on the above embodiments, please refer to... Figure 8 In one exemplary embodiment provided in this application, the specific implementation process of the above-mentioned subgrade state evolution method under intermittent loading may further include steps S710 to S730, which are described in detail below:

[0087] Step S710: After the roadbed enters the intermittent stage, the first stage load is determined based on the static load of the superstructure of the roadbed.

[0088] Step S720: Connect the first stage load with the second stage load to obtain the connected load. The second stage load is the load corresponding to the loading stage.

[0089] Step S730: Determine the real-time load change rate corresponding to the structure of the particle system based on the connecting load.

[0090] For example, following the above embodiments, which simulated the transition of intermittent load from the loading phase to the intermittent phase and illustrated the feasibility of the model through simple calculation examples, this embodiment will further describe the transition of intermittent load from the intermittent phase to the loading phase. Specifically, after re-entering the loading phase, the roadbed will again bear the load generated by the train. Again, taking a sinusoidal load as an example, to connect with the load of the intermittent phase, the load re-entering the loading phase is:

[0091]

[0092] In the formula, For the load during the reloading phase, This is the load at the initial moment of this loading phase. This refers to the load at the last moment of the previous interval phase; Static stress generated in the superstructure of the roadbed; This represents the dynamic stress amplitude. This represents the number of calculation steps during the intermittent phase. , Given the duration of the intermittent phase, the load change rate during the reloading phase can be further derived:

[0093]

[0094] Similarly, the accumulated strain of the subgrade at the initial moment of re-entering the loading stage is equal to the accumulated strain of the subgrade at the last moment of the previous intermittent stage: The subsequent values ​​are still calculated using the explicit expression described above. The difference from the above embodiment is that the roadbed state variable at the initial moment of re-entering the loading stage is equal to the roadbed state variable at the last moment of the previous loading stage: Its subsequent values ​​can still be calculated using the explicit expression mentioned above.

[0095] Optionally, in some feasible embodiments, calculation code can be written using Matlab based on the ideas of the above embodiments. The calculated load, its rate of change, strain, and state variables are as follows: Figure 9 As shown, from Figure 9 As can be seen from (a) in the figure, the load input of the state evolution model accurately reproduces the situation where the intermittent load changes from the static load in the intermittent stage to the dynamic load in the loading stage. Figure 9The cumulative strain curve of the subgrade shown in (b) in the figure shows that when the loading stage is re-entered, the cumulative strain returns to the state of the previous loading stage, which is consistent with the subgrade settlement data observed in the model test. Figure 9 The results shown in (c) indicate that the subgrade state variables, after re-entering the loading stage, revert to the state under dynamic load. In summary, the state evolution model provided in the above embodiments can effectively simulate the subgrade response under intermittent loads.

[0096] In some embodiments of this application, when the roadbed enters the intermittent stage, the first stage load is determined based on the static load of the superstructure, and then it is connected with the second stage load of the loading stage to obtain the connecting load. Based on the connecting load, the real-time load change rate of the particle system structure is accurately determined, providing key parameters for accurately analyzing the mechanical properties of the particle system during the intermittent and loading transition process.

[0097] Furthermore, based on the above embodiments, in one exemplary embodiment provided in this application, the specific implementation process of the above-mentioned characteristic strain-based modified state evolution model may further include steps S810 to S830, which are described in detail below:

[0098] Step S810: Under intermittent loading, obtain the historical strain parameters of the roadbed. The historical strain parameters include the strain state of the state evolution variables in the transition state between the loaded state and the intermittent state.

[0099] Step S820: Determine the characteristic strain of the roadbed based on the strain state. The characteristic strain includes the relevant historical strain range of the state evolution variables under the connection state.

[0100] Step S830: Based on the characteristic strain, introduce the expression of the state evolution variables to obtain the modified state evolution model.

[0101] For example, in practical engineering applications for subgrade performance evaluation and prediction, when the subgrade is under intermittent loading, high-precision strain monitoring equipment can be used to continuously collect strain data of the subgrade at different times, thereby obtaining its historical strain parameters. The focus is on the instant of transition between the loaded and intermittent states, accurately recording the strain state corresponding to the state evolution variables in the transition state. This strain state accurately reflects the mechanical response characteristics of the subgrade during the transition between these two states. Subsequently, based on the acquired strain state data, professional data analysis algorithms and engineering experience are used to deeply analyze and determine the characteristic strain of the subgrade. The characteristic strain covers the historical strain range related to the state evolution variables in the transition state. This range effectively summarizes the strain change law of the subgrade under different intermittent loading, providing a key basis for subsequent model correction. Finally, based on the determined characteristic strain, combined with the mechanical properties of the subgrade material and the actual stress conditions, an expression for the state evolution variables is introduced through a combination of theoretical derivation and numerical simulation. This expression is then integrated into the original state evolution model, resulting in a modified state evolution model. This model can more accurately and comprehensively reflect the actual mechanical behavior and state changes of the subgrade under intermittent loading, providing more reliable technical support for subgrade maintenance, reinforcement, and service life prediction.

[0102] In some embodiments of this application, under intermittent loading, the characteristic strain is determined by obtaining historical strain parameters such as the strain state of the state evolution variables of the roadbed when the loading and intermittent states are connected. Based on this, the state evolution variable expression is introduced to obtain a modified state evolution model, which can more accurately simulate and predict the mechanical behavior and state evolution of the roadbed under complex intermittent loading.

[0103] Furthermore, based on the above embodiments, in one exemplary embodiment provided in this application, the specific implementation process of determining the characteristic strain of the roadbed based on the strain state may further include steps S910 and S920, which are described in detail below:

[0104] Step S910: Define the state evolution variables in the transition state as the weighted average of the historical strain paths.

[0105] Step S920: Establish an exponential decay weight function between the length of the historical strain path and the weighted average value, so as to determine the characteristic strain of the roadbed based on the exponential decay weight function.

[0106] For example, in actual engineering scenarios for evaluating the long-term performance and stability of roadbeds under complex intermittent load environments, in order to accurately characterize the changes in the mechanical state of the roadbed, the state evolution variables under the transition state can be scientifically defined and set as the weighted average of historical strain paths. This setting fully considers the comprehensive impact of the strain history experienced by the roadbed at different times on its current state, so that the state evolution variables can more comprehensively and accurately reflect the mechanical memory characteristics of the roadbed.

[0107] Next, considering the varying degrees of influence of strain information at different stages of the historical strain path on the current state, and the gradual weakening of the influence of earlier strain information on the current state over time, an exponentially decaying weighting function is established between the length of the historical strain path and the state evolution variables in the transition state. This function, by introducing an exponential decay factor, can reasonably allocate the weights of historical strains at different times when calculating the state evolution variables in the transition state, giving greater weight to historical strains closer to the current time and gradually decreasing weight to earlier historical strains, thus better reflecting the actual laws governing the evolution of the roadbed's mechanical state.

[0108] Finally, based on the established exponential decay weighting function, the strain at each point on the historical strain path is weighted and calculated to determine the characteristic strain corresponding to the state evolution variables in the transition state. This characteristic strain can highlight the key mechanical characteristics of the subgrade under the influence of the state evolution variables in the transition state, providing important data support and theoretical basis for subsequent in-depth analysis of the mechanical behavior of the subgrade, prediction of its performance changes, and formulation of scientific and reasonable maintenance strategies.

[0109] In some embodiments of this application, by defining the state evolution variables in the transition state as the weighted average of historical strain paths, and establishing an exponential decay weight function of the historical strain path length and the state evolution variables in the transition state to determine the characteristic strain, the influence of historical strain on the current state can be considered more scientifically and reasonably, thereby providing a reliable basis for accurately describing the state evolution of the roadbed particle system under intermittent load.

[0110] Please see Figure 10In another exemplary embodiment of this application, a roadbed state evolution system under intermittent loading is provided. In this system, input devices, a processor, an output device, and a memory are interconnected. The memory stores a computer program, which includes program instructions. The processor is configured to call the program instructions and execute specific steps as described in the relevant embodiments of the roadbed state evolution method under intermittent loading provided by this invention. The roadbed state evolution system under intermittent loading of this invention has a complete and stable structure, and can efficiently execute the roadbed state evolution method under intermittent loading of this invention, thereby improving the overall applicability and practical application capability of this invention.

[0111] It should be noted that the subgrade state evolution system under intermittent loading provided in the above embodiments and the subgrade state evolution method under intermittent loading provided in the above embodiments belong to the same concept. The specific operation methods of each module and unit have been described in detail in the method embodiments and will not be repeated here. In practical applications, the subgrade state evolution system under intermittent loading provided in the above embodiments can be assigned to different functional modules as needed, that is, the internal structure of the system can be divided into different functional modules to complete all or part of the functions described above. This is not a limitation here.

[0112] Embodiments of this application also provide an electronic device, including: one or more processors; and a storage device for storing one or more programs, which, when executed by one or more processors, enable the electronic device to implement the roadbed state evolution method under intermittent load provided in the above embodiments.

[0113] It should be noted that the computer-readable medium shown in the embodiments of this application can be a computer-readable signal medium or a computer-readable storage medium, or any combination of the two. A computer-readable storage medium can be, for example, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), flash memory, optical fiber, portable compact disc read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying a computer-readable computer program. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media can also be any computer-readable medium other than computer-readable storage media, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The computer program contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to wireless, wired, etc., or any suitable combination thereof.

[0114] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. Each block in a flowchart or block diagram may represent a module, segment, or portion of code, which contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0115] The units described in the embodiments of this application can be implemented in software or hardware, and the described units can also be located in a processor. The names of these units do not necessarily limit the specific unit itself.

[0116] Another aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned method for roadbed state evolution under intermittent loading. This computer-readable storage medium may be included in the electronic device described in the above embodiments, or it may exist independently and not incorporated into the electronic device.

[0117] Another aspect of this application provides a computer program product or computer program including computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the subgrade state evolution method under intermittent loading provided in the various embodiments above.

[0118] The above description is merely a preferred exemplary embodiment of this application and is not intended to limit the implementation of this application. Those skilled in the art can easily make corresponding modifications or alterations based on the main concept and spirit of this application. Therefore, the scope of protection of this application should be determined by the scope of protection claimed in the claims.

Claims

1. A method for the evolution of roadbed state under intermittent loading, characterized in that, include: Obtain information on roadbed fill material corresponding to the roadbed, wherein the roadbed fill material information includes a particle system corresponding to multiple layers of different filler materials; Determine the stress and strain corresponding to the structure of the particle system under intermittent loading, and establish a state evolution model of the roadbed based on the stress and strain; The historical strain parameters of the roadbed are obtained, and the characteristic strain of the particle system is determined based on the historical strain parameters. The state evolution model is modified based on the characteristic strain, so as to determine the state evolution variables of the subgrade under intermittent load through the modified state evolution model; The process of modifying the state evolution model based on the characteristic strain includes: Under intermittent loading, the historical strain parameters of the subgrade are obtained, including the strain state of the state evolution variables in the transition state between the loaded state and the intermittent state; The characteristic strain of the roadbed is determined based on the strain state, and the characteristic strain includes the relevant historical strain range of the state evolution variables under the connection state; Determining the characteristic strain of the roadbed based on the strain state includes: The state evolution variables in the aforementioned transition state are defined as the weighted average of historical strain paths; An exponential decay weighting function is established between the length of the historical strain path and the weighted average value, so as to determine the characteristic strain of the roadbed based on the exponential decay weighting function; Based on the aforementioned characteristic strain, expressions for state evolution variables are introduced to obtain the modified state evolution model; The method further includes: Under intermittent loading, the phase transition characteristics of the particle system under stress are obtained, and the state evolution variables of the particle system are determined based on the phase transition characteristics, including: The particle system is subjected to stress analysis, and the phase transition characteristics of the particle system under stress are determined based on the analysis results. The phase transition characteristics include solid phase, liquid phase and critical state. Based on the phase transition characteristics, a quantitative index of the non-equilibrium thermodynamics of the particle system is determined, and the quantitative index is used as a state evolution variable of the particle system. Determine the steady-state conditions and non-equilibrium potential functions corresponding to the state evolution variables, and determine the dynamic equilibrium relationship of the particle system based on the steady-state conditions and the non-equilibrium potential functions, including: The state evolution equations of the state evolution variables are established by combining the steady-state conditions and the non-equilibrium potential function; The state evolution equation is solved to obtain the steady-state solution corresponding to the state evolution equation and the recovery condition corresponding to the steady-state solution; The dynamic equilibrium relationship of the particle system is determined based on the steady-state solution and the recovery condition corresponding to the steady-state solution; Based on the dynamic equilibrium relationship, a state evolution model corresponding to the state evolution variables is constructed, and the state evolution model includes explicit expressions for the state evolution variables; Determine the real-time stress and real-time load change rate corresponding to the structure of the particle system under intermittent loading, and introduce the real-time stress and the real-time load change rate into the explicit expression to obtain the updated explicit expression; The state evolution model of the roadbed under intermittent loads is determined based on the updated explicit expression. Under intermittent loading, sinusoidal load is used as the input form of load during the loading stage; The real-time stress of the particle system during the intermittent phase and the real-time stress of the particle system during the loading phase are determined based on the sinusoidal load and the explicit expression. The real-time stress under the intermittent load is determined based on the real-time stress during the intermittent phase and the real-time stress during the loading phase. After the roadbed enters the intermittent phase, the first stage load is determined based on the static load of the superstructure of the roadbed. The first stage load is connected to the second stage load to obtain the connected load, where the second stage load is the load corresponding to the loading stage. The real-time load change rate corresponding to the structure of the particle system is determined based on the connecting load.

2. A roadbed state evolution system under intermittent loading, characterized in that, The system includes a processor, an input device, an output device, and a memory, which are interconnected. The memory stores a computer program, which includes program instructions. The processor is configured to call the program instructions to execute the roadbed state evolution method under intermittent loading as described in claim 1.

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