High-speed railway roadbed structure design method based on dynamic stability

Abstract

The invention discloses a high-speed railway roadbed structure design method based on dynamic stability. The method comprises the following steps: starting a design process: clearly designing load and control conditions; constructing a lumped parameter dynamic coupling model of the high-speed railway vehicle-track-roadbed layered structure; setting parameter input and verification are carried out on the model based on the design parameter system; solving a roadbed layered dynamic response result through the dynamic coupling model; judging critical conditions of the first design threshold and the second design threshold; various design parameters meeting the first design control threshold value and the second design control threshold value are substituted into the dynamic coupling model for recalculation, it is verified that various dynamic response rules meet design requirements, and finally the design target is completed. According to a typical high-speed railway subgrade structure subgrade bed surface layer graded broken stone and subgrade bed bottom layer coarse-grained soil filler type, a high-speed railway subgrade filler dynamic stability critical state judgment standard is established in combination with a long-term deformation development rule and hysteresis energy characteristics of different fillers under the action of train power; and the support is provided for the stability design of the high-speed railway roadbed structure.

Description

Technical Field

[0001] The invention belongs to the technical field related to railway roadbed engineering, and specifically relates to a high-speed railway roadbed structure design method based on dynamic stability. Background Art

[0002] The subgrade structure of high-speed railway is an important foundation for the safe and smooth operation of high-speed trains. The scientific design of the subgrade structure is the fundamental guarantee for its durable service and technical economy. By the end of 2023, the operating mileage of high-speed railways in China will reach 45,000 kilometers, ranking first in the world. The subgrade structure of high-speed railways is subjected to cyclic dynamic loads during its formation and service process. The dynamic effect runs through the entire life cycle of the subgrade structure of high-speed railways. The dynamic performance and deformation control of the subgrade structure of high-speed railways are key technologies to ensure the safety, high speed and smooth operation of trains. Its dynamic deformation state is closely related to the post-construction settlement control of the foundation, the matching of the vertical stiffness of the structure, and the coordination of the longitudinal stiffness. The influencing factors are complex. The precise control of the dynamic deformation of the subgrade structure and the long-term maintenance of the state are global technical problems. At present, the cumulative length of my country's high-speed railway subgrade is about 13,300 kilometers, and high-speed railway lines account for nearly 30%. A number of representative high-speed railway subgrade projects have been built in different regions and climate environments. Through high-standard structural design and filler selection and control, the high-quality construction of large-scale high-speed railway subgrades in my country is guaranteed. However, with the further increase in high-speed rail speeds and the emergence of more complex and diverse construction and service environments, the dynamic performance and deformation control of high-speed rail subgrade structures face huge challenges.

[0003] Strictly controlling the accumulation of long-term deformation of the roadbed and providing a solid and stable foundation for the upper track structure is a prerequisite for achieving high-speed, safe and smooth operation of trains for a long time. Establishing a scientific and effective high-speed railway roadbed structure design method is a basic theoretical problem that must be overcome to achieve high-precision deformation control and long-term service of high-speed railway roadbeds. In design practice, my country's high-speed railway roadbed design has achieved a transition from strength control such as bearing capacity to refined structural deformation control. In order to ensure the long-term stability of roadbed subgrade deformation, the existing design method determines the design criteria for total deformation control of the roadbed surface and critical strain control of the subgrade. The simplified equivalent load analysis method is used, the roadbed is assumed to be a semi-infinite elastic space body, and the Boussinesq formula is used to calculate the stress and strain of the roadbed. Then, the dynamic strain of the subgrade bottom layer and the deformation of the roadbed surface are compared with the design value to achieve the control of the long-term deformation stability of the roadbed. This method has laid an important foundation for my country's large-scale high-speed railway construction and played an important role in the application of roadbed structure design. However, this design method simplifies the dynamic process of the roadbed structure during its service period, and transforms it into a quasi-static problem through theoretical assumptions. It is insufficient in characterizing the dynamic service status of each layer of filler in the roadbed structure, and lacks scientific and effective consideration of the long-term dynamic performance of the high-speed railway roadbed structure. The design parameter selection involves the use of both dynamic and static parameters, and the calculated structural load distribution law and filler stress and deformation characteristics are somewhat different from the service status of the roadbed structure under dynamic excitation. Establishing a new method for high-speed railway roadbed structure design that meets the above-mentioned refined functional requirements will help to further improve and develop the high-speed railway roadbed structure design theory, optimize the high-speed railway roadbed structure, and thus ensure the design goal of durable and stable roadbed service for a hundred years under higher speeds and complex environments.

[0004] In recent years, shakedown design has become one of the important concepts in the design of structures such as transportation infrastructure. Different from the conventional elastoplastic incremental analysis and critical state design methods, it not only requires the structure to meet the requirements of bearing capacity and instantaneous deformation under cyclic dynamic loads, but also provides new control conditions from the perspective of controlling the development trend, rate of change, and convergence of long-term deformation of materials and structures. Key parameters such as shakedown load have gradually become an important theoretical basis for the plastic failure criterion in the engineering strength design specification, providing a powerful analysis tool for the selection of critical dynamic stress, structural safety assessment, and long-term deformation control. In recent years, shakedown design has been increasingly widely used in geotechnical engineering, such as in the relevant analysis of pavement rutting deformation, offshore platform foundation, slope stability, and ballastless track structure. For high-speed railway subgrade structures subjected to high-frequency dynamic cyclic traffic loads, this method can effectively determine whether the deformation under different stress-strain states can reach a stable state, and give the critical envelope that meets the structural dynamic stability, thereby giving a reasonable design threshold for the high-speed railway subgrade to meet the long-term service durability requirements.

[0005] The existing technical solution of the Railway Construction Institute of China Academy of Railway Sciences Group Co., Ltd., namely the high-speed railway subgrade structure design method (CN 202010329656.3), is to realize the high-speed railway subgrade structure design. This method is mainly based on the multi-layer system design theory. By determining the load distribution structure of the subgrade surface, constructing the analytical formula of the stress and strain of a single-layer soil body, and proposing the stress and displacement expressions of each layer of the subgrade, it is then iterated and solved by comparing with the dynamic deformation of the subgrade surface and the dynamic strain control criteria of the subgrade bottom layer to achieve the optimization adjustment of the parameters of each layer of the subgrade structure. The main deficiencies of this technical solution are as follows: ① The load action form of the roadbed surface and the distribution and transfer law inside the roadbed are mainly based on the vertical concentrated force assumption. The static method is used to analyze the dynamic strain of the single-layer soil, the stress and displacement expressions of each layer, and the dynamic effects of different train speeds, dynamic action frequency, damping, etc. cannot be considered; ② The core design control indicators - the dynamic deformation of the roadbed surface, the dynamic strain of the subgrade bottom layer and the maximum strain constraint criterion. The method for determining the critical value is mainly derived from the critical strain value described in foreign literature where no deformation accumulation occurs, that is, the critical volume effect strain threshold value summarized by Vucetic et al. based on fine-grained soil test data. Whether this critical value is applicable to typical coarse-grained soil filling materials of high-speed railway subgrade structures remains to be studied; ③ The idea of ​​judging the design threshold is limited to comparing the average and maximum values ​​of the dynamic strain of the subgrade bottom layer and the size of the dynamic deformation of the roadbed surface to see if they meet the requirements. The three are representative, but there is still room for improvement in reflecting the stable state of service deformation at different points along the roadbed depth, and this method does not reasonably consider the critical strain of the subgrade surface.

[0006] Tongji University's existing technical solution is a method for optimizing the parameters of high-speed railway roadbed filling (CN202310356164.7). This method mainly considers the typical layered interface of the roadbed structure and the differences in the physical and mechanical properties of materials between different layers from the perspective of wave dynamics and micromechanics, as well as the propagation behaviors of stress wave signal waveform distortion, transflection, etc., and establishes a stress wave interface transflection model. The effective frequency response range of the roadbed is determined by calculating the circular frequency of the stress wave, and the key parameters of each layer of filling are adjusted to reduce the vibration deformation of the upper layer and suppress the vibration deformation amplification effect of the roadbed layered interface. From the perspective of filling design parameter optimization, relevant technologies for roadbed structure deformation control are proposed. The main deficiencies of this technical solution are: ① Its core model is mainly based on a one-dimensional layered viscoelastic granular material interface contact model. The calculation is based on the assumption of an ideal viscoelastic interface. Although it can reflect the dynamic characteristics and fluctuation characteristics of filler particles and the influence of parameters to a certain extent, it is difficult to consider the three-dimensional spatial fluctuation characteristics and stress wave diffusion characteristics of the roadbed structure, and has limitations when applied to actual roadbed structure design; ② The optimization objects of this method for filler parameters mainly include effective density, normal contact stiffness, damping coefficient, etc., which are mainly aimed at the contact characteristics and frequency response range between particles. It is unable to consider the influence on the dynamic stress-strain and cumulative deformation of the bed filler, and is difficult to apply to the design needs of high-speed railway roadbed structures for long-term durable service.

[0007] Zhejiang University's existing technical solution is a high-speed railway subgrade mechanical-empirical design method for long-term service performance (CN 202310119573.5). This method mainly takes controlling the total deformation of the high-speed railway subgrade as the design goal, calculates the dynamic load of the train on the top of the subgrade through the track-subgrade dynamic analytical model, and calculates the dynamic stress distribution in the subgrade based on the 2.5-dimensional or 3-dimensional finite element analysis model, and then obtains the cumulative deformation of the subgrade based on the soil cyclic cumulative deformation mechanical-empirical model. The main deficiencies of this technical solution are: ① This method is mainly aimed at the design goal of cumulative settlement deformation of high-speed railway subgrade, and takes into account the static deformation requirements, but it is impossible to verify and compare the dynamic deformation requirements at different speeds; ② The source of the cumulative deformation value of the subgrade obtained by this model is mainly based on the layered summation method. The cumulative deformation of different layers in the subgrade at each automatic stress level is calculated by the cumulative strain empirical formula. It does not stipulate the influence of the key parameter of the number of cycles N, that is, it still needs to be optimized in terms of the number or time of load action; ③ The design idea of ​​not exceeding the limit of the total deformation of the subgrade structure is of reference value for short-term post-construction settlement calculation, but for the high-speed railway subgrade structure with a service life of 100 years, the size of its total settlement value is difficult to accurately estimate and is not solely derived from the deformation of the subgrade structure itself. Therefore, it is more critical to clarify whether the long-term deformation of the subgrade structure can converge quickly rather than continuously accumulate. The total deformation judgment idea proposed by this method is difficult to consider the impact of long-term stability in this regard. Summary of the invention

[0008] In order to solve the defects existing in the prior art, the present invention discloses a high-speed railway subgrade structure design method based on dynamic stability, and its technical solution is as follows:

[0009] The high-speed railway subgrade structure design method based on dynamic stability is characterized by:

[0010] Step 1: Start of the design process: clarify the design objectives, including determining the line grade, operating speed, basic line geometry requirements and design-related standards, which provide prerequisites for clarifying the design load and basic parameters;

[0011] Step 2: Define the design load and control conditions, define the design load under the corresponding vehicle type, vehicle speed and other conditions, and assign the modulus dynamic parameters and initial value of layer thickness to each layer;

[0012] Step 3: Construct a lumped parameter dynamic coupling model of the high-speed railway vehicle-track-roadbed hierarchical structure;

[0013] Step 4: Based on the design parameter system, set the parameters for the coupling model and perform calculation verification;

[0014] Step 5: Solve the subgrade layered dynamic response results through the dynamic coupling model;

[0015] Step 6: Verify the stability characteristics of the filler using the dynamic response of the roadbed layer as the first design threshold critical condition. If it is satisfied, proceed to step 7. If it is not satisfied, readjust the design parameters of the layer and return to step 4 to reassign the design parameters of the dynamic coupling model.

[0016] Step 7: Use the total dynamic displacement of the roadbed surface as the second design threshold critical condition to verify the vehicle-track-road overall coupled dynamic response. If it is satisfied, proceed to step 7. If not, re-adjust the design parameters and return to step 4 to re-assign the design parameters of the dynamic coupling model.

[0017] Step 8: Substitute the design parameters that meet the first and second design control thresholds into the dynamic coupling model for recalculation, verify that the dynamic response laws meet the design requirements, conduct scheme comparison and optimization analysis, and finally achieve the design goal.

[0018] Beneficial Effects

[0019] 1. Based on the concept of shakedown theory, the critical design thresholds of typical fillers for high-speed railway subgrades of different groups and layers are clarified

[0020] Different from the traditional strength / deformation design approach, from the perspective of structural stability design, the changing law of the dynamic characteristics of fillers under long-term service conditions is considered, and a filler stability state judgment standard based on equivalent volume dissipated energy is proposed in combination with the deformation convergence law and energy dissipation law. Based on the stability theory, a method for determining the critical thresholds of dynamic stress and dynamic strain stability of roadbed fillers in different groups and layers is given, which solves the problem of determining the design parameter values ​​and control standards of various coarse-grained soil fillers and graded crushed stone in the bottom and surface layers of the subgrade in the refined design of high-speed railway subgrades.

[0021] 2. Taking into account the coupling characteristics of the vehicle-track-road system, the design control requirements are clarified from the perspective of the static smoothness of the high-speed railway subgrade and the smoothness and comfort of the train ride.

[0022] It breaks through the limitations of quasi-static assumptions and empirical design control standards of traditional design methods. Starting from the dynamic equation, the layered structure of high-speed railway trains, tracks, and roadbed is regarded as the design elements that jointly affect the dynamic response of the system. A lumped parameter dynamic generalization model of the layered structure of high-speed railway vehicles, tracks, and roadbed is constructed, and the calculation and analysis of the dynamic response of vehicle-track-layered roadbed under different train running speeds, smoothness, layer stiffness, damping and other parameter conditions are realized. The static smoothness of the roadbed based on indicators such as wheel-rail force and dynamic displacement of the roadbed surface and the design control thresholds that affect the dynamic driving smoothness and comfort of the train are proposed.

[0023] 3. It breaks through the limitations of traditional design methods in terms of parameter system and design threshold, and realizes the refined design of high-speed railway subgrade layered composite structure considering dynamic response and long-term stability.

[0024] A more complete design parameter system including vehicle type, suspension properties of each system, vehicle speed, roughness, geometric parameters of the surface layer, bottom layer and main body layer of the subgrade, and static and dynamic parameters was proposed from three aspects: upper train, track structure parameters, design load input end parameters, and layered subgrade structure parameters. A critical strain design threshold based on the stability characteristics of the subgrade filler and a vibration response design threshold based on the comfort level of train operation were proposed, and a design process of initial assignment of design indicators - construction of coupling model - calculation of dynamic response - comparison of discriminant indicators - iterative optimization parameters - updating of design solutions was constructed, which supported the refined design of high-speed railway subgrade layered composite structures suitable for different filler types, different static and dynamic smoothness control levels, and long-term stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 The high-speed railway subgrade structure design process based on dynamic stability of the present invention;

[0026] Figure 2 Schematic diagram of the design load time history curve of high-speed railway subgrade based on track irregularity excitation;

[0027] Figure 3 Schematic diagram of the lumped parameter dynamic coupling model of the vehicle-track-roadbed layered structure;

[0028] Figure 4 Schematic diagram of hysteresis curve of dynamic triaxial test of coarse-grained soil filling of typical high-speed railway subgrade;

[0029] Figure 5 Schematic diagram of the particle gradation curve of typical fillers for high-speed railway subgrade, including (a) coarse-grained soil filler at the bottom layer of the subgrade; (b) graded crushed stone at the surface layer of the subgrade;

[0030] Figure 6 Schematic diagram of the relationship curve of 1 / Ed-εd of a typical filler;

[0031] Figure 7 Schematic diagram of the normalized curve of dynamic modulus of typical fillers;

[0032] Figure 8 Schematic diagram of stable state partition based on unit volume dissipated energy;

[0033] Fig. 9 Critical threshold curve of dynamic stress stability of fillers, including (a) Group A fillers; (b) Group B fillers; c) Group C fillers; (d) Group D fillers; (e) Type I graded crushed stone on the surface of the subgrade; (f) Type II graded crushed stone on the surface of the subgrade;

[0034] Fig.10 Critical threshold curve of dynamic strain stability of fillers, including (a) Group A fillers; (b) Group B fillers; c) Group C fillers; (d) Group D fillers; (e) Type I graded crushed stone on the surface of the subgrade; (f) Type II graded crushed stone on the surface of the subgrade;

[0035] Fig.11 Schematic diagram of wheel-rail forces under different roadbed settlement unevenness conditions;

[0036] Fig.12 Schematic diagram of vehicle acceleration under different roadbed settlement unevenness conditions;

[0037] Fig.13 Schematic diagram of the control threshold zoning for roadbed settlement irregularity;

[0038] Fig.14 Schematic diagram of the relationship between vehicle acceleration and roadbed surface dynamic deformation and control threshold under uneven settlement conditions;

[0039] Fig.15 Schematic diagram of wheel-rail forces under different conditions of uneven roadbed camber;

[0040] Fig.16 Schematic diagram of vehicle acceleration under different roadbed camber and unevenness conditions;

[0041] Fig.17Schematic diagram of the control threshold zoning for roadbed buckling irregularity;

[0042] Fig.18 Schematic diagram of the relationship between vehicle acceleration and roadbed surface dynamic deformation and control threshold under the camber unevenness condition. DETAILED DESCRIPTION

[0043] The high-speed railway subgrade structure design method based on dynamic stability mainly includes the following steps: initial assignment of design indexes - construction of coupling model - calculation of dynamic response - comparison of discriminant indexes - iterative optimization of parameters - updating of design schemes, etc. Figure 1 As shown:

[0044] The main steps of the design process of the present invention include:

[0045] ①The design process begins;

[0046] ② Clarify the design load and control conditions, clarify the design load under the corresponding vehicle model, vehicle speed and other conditions, and assign the dynamic modulus parameters of each layer and the initial value of the layer thickness (the dynamic modulus of each layer is related to the strain level and is assigned through the critical threshold strain);

[0047] ③Construct a lumped parameter dynamic coupling model of high-speed railway vehicle-track-roadbed layered structure;

[0048] ④ Based on the design parameter system, set the model and input parameters;

[0049] ⑤ Solve the dynamic response results of the roadbed layering through the dynamic coupling model;

[0050] ⑥ Determination of critical conditions of the first design threshold (verification of filler stability characteristics) - Based on the dynamic stability analysis of high-speed railway subgrade fillers, clarify the critical dynamic stress and dynamic strain design thresholds of different layers, and substitute the obtained dynamic stress and dynamic strain into the dynamic stability threshold of each layer of fillers for determination. If they meet the requirements, proceed to the next step. If not, readjust the design parameters of the layer, including increasing the modulus to reduce the strain, changing the design thickness, etc., and return to step ④ to reassign the model design parameters.

[0051] ⑦ Second design threshold critical condition judgment (verification of vehicle-track-road overall coupled dynamic response) - Substitute the obtained wheel-rail force, roadbed surface dynamic displacement and other indicators into the thresholds under different comfort control conditions for judgment. If they meet the requirements, proceed to the next stage. If not, readjust the design parameters, including increasing the modulus to reduce the strain, changing the design thickness, etc., and return to step ④ to re-assign the model design parameters;

[0052] ⑧Verify the design results and complete the design if all design threshold conditions are met.

[0053] The key steps mentioned above are introduced as follows:

[0054] 1. Design process begins

[0055] Clarify the design objectives, including determining the line grade, operating speed, basic line geometry and other requirements and design-related standards, to provide a prerequisite for clarifying the design load and basic parameters.

[0056] 2. Determine the design load and control conditions

[0057] The dynamic load on the roadbed is the dynamic stress that is transmitted to the roadbed surface through the absorption and attenuation of the track after the dynamic load acting on the rail during train operation. Its characteristics are related to the train axle weight, wheelbase and dynamic characteristics, running speed, line smoothness and track structure, and are the basic parameters for roadbed subgrade design. The main reason for the generation of vertical wheel-rail force is various unevenness and local flat scars around the wheel. Existing studies have shown that vertical wheel-rail force mainly occurs in three frequency ranges: (1) low frequency range (0.5-10 Hz), which is almost entirely generated by the relative movement of the vehicle body to the suspension part; (2) medium frequency range (30-60 Hz), which is generated by the rebound effect of the unsprung wheelset mass on the rail; (3) high frequency range (100-400 Hz), which is generated by the movement of the rail being resisted by the wheel-rail contact surface. Actual measurements show that the wheel-rail force is more intense in the medium and low frequency ranges, and the high frequency range mainly affects the dynamic response of the vehicle body. When considering the use of seamless lines, the main reasons affecting the wheel-rail force are track unevenness and the wear effect of the rail surface waveform. In addition, the foundation under the track of high-speed lines is more solid, so this unevenness is mainly random unevenness.

[0058] Based on the above theoretical research results and measured laws, the present invention adopts the train load expressed in the form of Fourier series of multiple wheelsets, which is applicable to the wave conduction unit. It is manifested as an excitation force that can reflect the periodic characteristics. It includes static load and dynamic load formed by superposition of a series of sine functions. The sub-items of the excitation force correspond to high, medium and low frequencies, and are used to reflect the influence of unevenness, additional dynamic load and rail surface corrugation effect respectively. The expression is

[0059] F(t)=P0+P1sinω1t+P2sinω2t+P3sinω3t (1)

[0060] P0 is the static load of the wheel; P1, P2, and P3 correspond to the vibration load of a typical value in the control conditions Ⅰ, Ⅱ, and Ⅲ in Table 1 respectively.

[0061] Let the unsprung mass of the train be M0, then the corresponding vibration load amplitude is:

[0062] P i =M0a i ω i2 (2)

[0063] Among them, a i Corresponding to a typical sagittal height in the three cases of Ⅰ, Ⅱ and Ⅲ in Table 1; ω i It is the circular frequency at the wavelength of the uneven vibration under the corresponding vehicle speed conditions Ⅰ, Ⅱ and Ⅲ.

[0064] The calculation formula of circular frequency is:

[0065]

[0066] Among them, υ is the running speed of the train; L i These are the typical wavelengths corresponding to the three cases Ⅰ, Ⅱ and Ⅲ.

[0067] Table 1 Track irregularity management standards

[0068]

[0069] According to different line smoothness and control level requirements, the parameter values ​​under the corresponding three types of control conditions in formulas (1), (2) and (3) should be adjusted.

[0070] According to the typical axle weight and track conditions of my country's high-speed railways, taking a 17t axle weight train as an example, the single-side wheel weight P0 = 85kN. The unsprung mass is M0 = 750kg = 750N·s 2 / m. The corresponding three control conditions Ⅰ, Ⅱ and Ⅲ take the typical uneven vibration wavelength and the corresponding vector height as follows: L1=10m, a1=3.5mm; L2=2m, a2=0.4mm; L3=0.5m, a3=0.08mm. Corresponding to the vehicle speed of υ=180~324km / h, the low frequency, medium frequency and high frequency ranges are 5~9Hz, 25~45Hz and 100~200Hz respectively, which conforms to the aforementioned experimental rules. The exciting force is an irregular waveform. Take υ=324km / h and the 0.1s time history waveform of the uneven excitation load at different speed levels as shown in the following figure Figure 2 shown.

[0071]

[0072] 3. Construction of lumped parameter dynamic coupling model for high-speed railway vehicle-track-roadbed layered structure

[0073] The present invention constructs the coupled dynamic relationship control equations of the vehicle, rail and lower track structure, layered roadbed structure, etc. under the train load, defines the basic model units of each layer based on the concept of lumped parameters, and obtains the dynamic response solutions of each structural layer of the vehicle-track-roadbed through iterative solution. The model schematic diagram under the action of a single train wheel set is shown in Figure 3 shown.

[0074] The model mainly considers the vibration coupling relationship between vehicle, track and filler in the vertical direction, and combines the filler deformation mechanical model with the dynamic equation of the layered structure under the action of train load. The upper part of the model is composed of the car body, bogie, wheelset and primary and secondary suspension, and the lower part of the model is the elastic-plastic deformation mechanical model of each layer of filler in the roadbed. The vibration coupling and response transmission between the two are realized by the wheel-rail contact relationship and wheel-rail force.

[0075] The basic model unit of the lumped parameter of the layered roadbed structure is the filler compaction deformation mechanics model, which is composed of two parts in series: viscoelasticity and viscoplasticity. e is the elastic stiffness, c e is the elastic damping coefficient, f(x) is the load-plastic deformation relationship, c p is the plastic damping coefficient. The viscoelastic part adopts the Kelvin model, that is, the elastic spring and the viscoelastic pot are connected in parallel. This structure can better describe the hysteresis of the elastic deformation of the filler and is often used to analyze the dynamic characteristics of the filler. The hyperbola in the form of formula (5) is selected as the load-deformation relationship of the plastic spring.

[0076]

[0077] In the formula, F is the load, x is the plastic spring deformation, and A and B are two plastic parameters in the hyperbola. Parameter A reflects the speed of the development trend of plastic deformation, and plastic parameter B mainly controls the approach limit of the hyperbola, which is determined by the loosest and densest states of the filler and is only related to the composition of the filler particles. When F→∞, it is easy to get x→1 / B, that is, the limit compaction deformation S lim =1 / B.

[0078] In order to describe the characteristics of plastic deformation developing over time, the model connects the plastic spring and the viscosity pot in parallel. The viscosity pot describes the time correlation of plastic deformation and the energy consumption when plastic deformation occurs. The larger the plastic damping coefficient, the slower the development speed of plastic deformation and the more energy is consumed to produce plastic deformation.

[0079] According to the form of the filler deformation mechanics model, its load-deformation relationship is as shown in formula (6).

[0080]

[0081] in:

[0082]

[0083] Where: σ(t) is the load at time t; ε(t) is the total strain at time t; k e is the elastic stiffness; ε ve (t) is the elastic deformation at time t; c eis the elastic damping coefficient; ε vp (t) is the plastic deformation at time t; is the elastic deformation rate at time t; c p is the plastic damping coefficient; is the plastic deformation rate at time t.

[0084] The plastic deformation rate is calculated according to formula (8):

[0085]

[0086] During the operation of the train, the track plate can only produce pressure on the filler, not tension, and the plastic deformation of the filler can only develop in one direction. can only be positive when σ(t)-f(ε vp When (t))≤0, no plastic deformation occurs, that is,

[0087] Taking the free state of each basic unit as the reference zero point, the dynamic equation of the "vehicle-track-roadbed" coupling system is:

[0088]

[0089]

[0090] Where m c 、m z 、m l 、m g 、m d are the masses of the car body, bogie, wheelset, rail, track plate and supporting structure, g is the acceleration of gravity, k c , k z are the stiffness of the primary suspension and the secondary suspension, k g is the stiffness between the rail and the supporting structure, c c 、c z are the damping coefficients of the primary suspension and the secondary suspension, c g is the damping coefficient between the rail and the supporting structure, λ1, λ2, λ3, λ soil-i are the deformation of the primary and secondary suspension, rails and supporting structures, and the ith (i=1,2,3,…,n) layer of roadbed, are the deformation rates of the primary and secondary suspension, rails, supporting structures, and the i-th roadbed, respectively, soil-ie , is the elastic deformation and elastic deformation rate of the i-th layer of roadbed, λ soil-ip is the plastic deformation of the ith layer of roadbed, x c 、x z 、x l 、x g 、xd are the displacements of the car body, bogie, wheelset, rail, track plate and supporting structure, are the accelerations of the car body, bogie, wheelset, rail, track plate and supporting structure, respectively, N is the reaction force of the rail on the wheelset, and F(t) is the unevenness excitation load in the design load and control conditions determined in step ②.

[0091] The interaction force F between wheel and rail s The depth is transferred downward from rails-support structure-layered roadbed in sequence, expressed as:

[0092]

[0093] During the operation of the train, the wheelset and the rail are not always in contact. When the wheel-rail interaction force is large, the wheelset will separate from the rail. Since only pressure but no tension can be generated between the wheelset and the rail, the interaction force is 0 when the rail and wheelset separate from each other.

[0094]

[0095] Considering the diffusion effect of load as the depth increases, the bearing area and system parametric mass of each layer of the layered roadbed change accordingly, and the stiffness and damping coefficient of each layer also change; considering the layer width d i , layer thickness h i , diffusion angle θ i The influence of parameters such as the stiffness k of the lumped parameter unit corresponding to the i-th layer of roadbed ei and the damping coefficient c ei The first layer parameter unit stiffness k located on the surface of the subgrade e1 , damping coefficient c e1 The relationship between the layer width d1 is:

[0096]

[0097] 4. Design parameter input and calculation verification

[0098] In the design method, the following three aspects of the design parameter index system should be considered:

[0099] (1) Upper train and track structure parameters: basic train parameters such as car body mass m0, bogie mass m1, wheelset mass m2, and related structural dimension parameters, primary suspension and secondary suspension stiffness, damping coefficients k0, k1, c0, c1, etc.; track mass, track plate and support layer mass m3, m4, and related structural dimensions; rail-support layer fastener connection stiffness and damping coefficients k2, c2;

[0100] (2) Design load input parameters: train speed v, track irregularity spectrum related parameters including irregularity wavelengths L1 to L3 and irregularity amplitudes η1 to η3 within three typical frequency response ranges; track irregularity related parameters including irregularity wavelength L4 and irregularity amplitude η4 caused by the roadbed;

[0101] (3) Layered roadbed parameters: including the dynamic modulus E of each layer d , damping ratio ζ, density ρ, diffusion angle θ, design thickness h, etc. are defined for the subgrade surface layer, subgrade bottom layer and roadbed body layer respectively.

[0102] The key design parameters are mainly shown in Table 3-7.

[0103] Table 2 Key design parameters

[0104]

[0105] The upper train and track structure parameters can be determined by clarifying the model of the train object in the design target, thereby determining the corresponding car body, bogie, wheelset and various suspension related parameters. The parameters of rails, track plates and fasteners can be determined through relevant specifications and standards.

[0106] The design parameters of the design load input end mainly refer to the relevant methods in step ② to determine the design load and control conditions, and construct the time history curve of the train wheel-rail interaction force under the line irregularity conditions caused by different track irregularity spectra and roadbed foundation structures as the initial excitation for the relevant design model input.

[0107] The design parameters of the layered roadbed structure need to determine the basic physical and mechanical parameters of each layer of filler, such as the subgrade surface layer, subgrade bottom layer, and main body layer, as well as dynamic parameters such as dynamic modulus and damping ratio. They are mainly derived from the relevant dynamic parameters of different groups of fillers in indoor tests such as dynamic triaxial test results. Figure 4 As shown in Figure 1, for a typical high-speed railway subgrade coarse-grained soil filling dynamic triaxial test hysteresis curve, the dynamic elastic modulus and damping ratio of the filling can be calculated using equations (14) and (15) respectively.

[0108]

[0109]

[0110] AB and OB represent the length of the line segment between point A and point B and the length of the line segment between point O and point B in the figure, respectively. s1 , Δ s2 They are the areas of regions S1 and S2 in the figure respectively.

[0111] For the typical filling types of high-speed railway subgrade, here are given the typical coarse-grained soil fillings of groups A, B, C, and D of the subgrade bottom layer, as well as the relevant grading curves of type I and II graded gravel of the subgrade surface layer and the method of determining the dynamic modulus.

[0112] The value of the dynamic modulus of the filler is closely related to the stress-strain level of the filler. Based on the Hardin-Drnevich equivalent linear viscoelastic model widely used in dynamic analysis, it is believed that the relationship between dynamic stress, dynamic strain and modulus obeys the hyperbolic model, which can be expressed as:

[0113]

[0114] where σ d and ε d are the dynamic stress and dynamic strain amplitudes, respectively; a and b are the vertical intercept and slope determined based on the test parameters, respectively; 1 / a is the maximum dynamic elastic modulus E dmax , 1 / b is the maximum dynamic stress σ dmax .

[0115] By plotting 1 / E d -ε d The relationship curve can be used to determine the maximum dynamic elastic modulus E of the filler. dmax ,like Figure 6 The maximum dynamic modulus parameters of six typical filler types are shown in Table 3.

[0116] Table 3 Maximum dynamic modulus parameters of 6 typical high-speed railway subgrade fillers

[0117]

[0118]

[0119] Construct dynamic elastic modulus ratio E d / E dmax and dynamic strain amplitude ε d The relationship is as follows:

[0120]

[0121] Where ε r is the reference dynamic strain value, ε r =σ dmax / E dmax , substituting into the maximum dynamic modulus expression, we can get ε r =σ dmax / (k Ed σ3+E d0 ). where k Ed 、E d0are the slope parameters of the dynamic modulus changing with the confining pressure and the initial dynamic modulus parameters obtained based on the test. The typical relationship curve between the dynamic modulus ratio and the dynamic strain amplitude is shown in Figure 7 As shown, it mainly shows the hyperbolic attenuation model and the relationship between the typical decline segment of the dynamic modulus data and the model predicted value.

[0122] The present invention provides relevant parameter values ​​based on the attenuation model of each group of fillers as shown in Table 4.

[0123] Table 4 Parameter values ​​of the equations for calculating dynamic parameters of six typical high-speed railway subgrade filling materials

[0124]

[0125] According to the above method, the actual working modulus of various types of fillers under different confining pressure depths and different dynamic strain states can be clarified, providing a basis for the design of dynamic parameter values ​​of different groups of high-speed railway subgrade fillers.

[0126] 5. Layered coupled dynamic response solution

[0127] First, according to the dynamic equations described in step ③, the vehicle-track-filler coupling dynamic system is established. Under the excitation of the set track irregularity, the train load is dynamically calculated for the vehicle, track, track support structure and layered roadbed structure, and the vibration state response and deformation law of each layer such as acceleration are obtained. Then, the next time step is entered and the above calculation steps are repeated. In order to facilitate the extraction and analysis of the model output signal, the fixed step size ode4 algorithm is used in the iterative calculation, and the simulation step size is 0.001s.

[0128] Acceleration of each layer of the car body, bogie, wheelset, rail and supporting structure in the model The dynamic displacement x is calculated by the following formula:

[0129]

[0130]

[0131] The dynamic stress of the roadbed layer is determined by the interlayer interaction force F between the layered soils. N The interlayer interaction force between the layered soils is related to the wheel-rail interaction force transmission law, and the interlayer filler load equivalent action area is obtained by dividing by the interlayer filler load equivalent action area, where the interlayer interaction force between the layered soils is related to the wheel-rail interaction force transmission law, and the interlayer filler load equivalent action area is determined by the width W and length L of the upper support structure, the thickness h of the surface layer and the bottom layer of the subgrade i , load diffusion angle α i The simplified formula is:

[0132]

[0133] Dynamic strain of roadbed layer ε i Mainly through the layered filling soil deformation λ i The filler thickness h after the layer is discretized i The ratio of is related, expressed as:

[0134]

[0135] 6. First design threshold

[0136] The design threshold in the design method described in the present invention is mainly discussed for the dynamic response of the roadbed layer (dynamic stress, dynamic strain) and the total dynamic displacement of the roadbed surface, which are respectively defined as the first design threshold critical judgment condition and the second design threshold critical judgment condition.

[0137] The first design threshold is mainly based on the long-term deformation stability of each layer of the roadbed filler. It is necessary to make it meet the dynamic stability state and not accumulate deformation during the service life, so as to ensure the durability and stability of the roadbed structure. Based on this, the dynamic stress and dynamic strain of each layer of the roadbed should be less than the critical dynamic stress and dynamic strain threshold of the dynamic stability of the filler at the corresponding layer, which is specifically expressed as follows:

[0138]

[0139]

[0140] Where λ σ基床表层 , σ基床底层 , σ路基本体层 are the critical thresholds of dynamic stress stability of the filler materials of the subgrade surface layer, subgrade layer and subgrade body layer, respectively, ε基床表层 , ε基床底层 , ε路基本体层 They are the critical thresholds of dynamic strain stability of the filler of the surface layer, bottom layer and subgrade layer of the roadbed, respectively. n is the safety factor proposed according to different deformation stability requirements. The larger the value, the stricter the design requirements. It is determined according to different line grades, design speeds and control targets. 3基床表层 , σ 3基床底层 , σ 3路基本体层 They are the confining pressure of the filler material of the subgrade surface layer, subgrade layer and roadbed body layer, i.e. the third principal stress. * is the critical cyclic stress ratio, which is related to the confining pressure of the filler, i.e., the third principal stress σ3, and is expressed as:

[0141] CSR=Aσ3 b (twenty four)

[0142] Where A and b are fitting parameters obtained based on indoor test of different types of fillers.

[0143] The first design threshold proposed by the present invention is mainly based on the relationship between dissipated energy and stable state, which is used as the basis for judging the critical threshold of power stability. As the basic indicator for judging the critical stability of fillers, the calculation formula is:

[0144]

[0145] Where: is the mean value of the dissipated energy per unit volume under the action of the circulation dynamics, is the influencing term reflecting the magnitude of the dissipated energy value, and the superscript d represents the influence of the circulation dynamics; is the final unit volume dissipation energy corresponding to the maximum vibration order m, is the energy dissipated per unit volume corresponding to the characteristic vibration order m / 10, and the term in brackets is a dimensionless influence term reflecting the increasing trend of the dissipated energy.

[0146] Equivalent unit volume dissipation energy under different conditions Calculations are performed and scatter plots are drawn. The threshold line approximation idea for determining the upper and lower limits of the critical stability state is adopted to divide the equivalent unit volume dissipated energy into three types of stability states: A plastic stability, B plastic creep, and C incremental destruction. See Figure 8 .

[0147] The maximum value of the equivalent unit volume dissipated energy in the A plastic stable state The minimum value of the equivalent unit volume dissipation energy of B plastic creep state The shaded area between the envelope lines is the critical value area of ​​the AB state; similarly, and The shaded area between represents the critical value area of ​​the BC state. Taking the average value of the equivalent unit volume dissipation energy in the critical area as the critical line of division, the stable state judgment criterion is given:

[0148]

[0149]

[0150]

[0151] Where: A-B , B-C They correspond to the critical values ​​of equivalent unit volume dissipated energy between the AB state and the BC state, respectively. Different filler types and loading test conditions may affect the value, but the above judgment criteria and threshold calculation method are still applicable. For typical filler types of my country's high-speed railway subgrade, the critical thresholds are shown in Table 5.

[0152] Table 5 Critical threshold values ​​of equivalent unit volume dissipation energy of different groups of fillers

[0153]

[0154]

[0155] According to the critical state judgment criterion based on unit volume dissipated energy, the critical threshold curves between the AB and BC states of different groups of high-speed railway subgrade fillings are determined as follows: Fig. 9 , Fig.10 shown.

[0156] For six types of typical high-speed railway subgrade fillers, the values ​​of the relevant threshold parameters of the cyclic stress ratio CSR* in formula (24) are shown in Table 6.

[0157] Table 6 Parameters of critical cyclic stress ratio threshold curve

[0158]

[0159] The values ​​of parameters related to the dynamic strain threshold can be considered to be independent of the confining pressure / depth changes, and the values ​​are shown in Table 7.

[0160] Table 7 Parameters of critical threshold curve of dynamic strain stability of typical high-speed railway subgrade filling

[0161]

[0162] 7. Second design threshold

[0163] The coupled dynamic response of the high-speed railway subgrade should meet the requirements of safe, smooth and comfortable train operation, that is, the static and dynamic irregularities of the subgrade should be controlled so that the train wheel-rail force F s The roadbed surface dynamic displacement U d The corresponding train acceleration meets the dynamic quality tolerance management values ​​of level I and II. The specific expressions are as follows:

[0164]

[0165]

[0166] In the formula λ U1 , U2 They are the design threshold of the wheel-rail force of the high-speed railway foundation and the dynamic displacement control threshold that meets the management value of the allowable deviation of dynamic quality of level I and II. n is the safety factor proposed according to the requirements of different deformation stability levels. The larger the value, the stricter the design requirements. It is mainly determined according to different line grades, design speeds and control targets.

[0167] Combined with the control limits of various indicators of vehicles, tracks, roadbeds and other structures in the current specifications, typical indicators such as wheel-rail force and vehicle acceleration are selected to determine the control thresholds of static and dynamic deformation of roadbed unevenness under different smoothness and different dynamic quality tolerance management values. According to the relevant control parameters in the "High-speed Railway Design Specifications" (TB10621-2014), "High-speed Railway Track Engineering Construction Quality Acceptance Standards" (TB 10754-2018), "High-speed Railway Engineering Dynamic Acceptance Technical Specifications" (TB10761-2013), "High-speed Railway Ballastless Track Line Maintenance Rules (Trial)" (TGGW115-2023) and other standards, the control limit of the wheel-rail vertical force of high-speed railway ballastless track and ballasted track is 170kN. The track dynamic quality tolerance management values ​​are shown in Table 8, and the management values ​​in the table are the half-peak values ​​of the actual amplitude of track unevenness. For vehicle acceleration, the vertical acceleration is judged by a 20Hz low-pass filter, and the lateral acceleration of the vehicle body is judged by a 0.5-10Hz band-pass filter for level I and II standards, and a 10Hz low-pass filter for level III and IV standards.

[0168] Table 8 Permissible deviation management values ​​of line track dynamic quality

[0169]

[0170]

[0171] (1) Uneven roadbed settlement conditions

[0172] For the uneven settlement condition, the wheel-rail force cloud diagram under different settlement wavelengths and amplitudes is as follows: Fig.11 As shown. It can be seen that when the settlement wavelength is 5m and 40m, the wheel-rail vertical force is less sensitive to the settlement amplitude; when the wavelength is 10m and 30m, the wheel-rail vertical force is highly sensitive to the settlement amplitude. As the settlement amplitude increases, the wheel-rail vertical force increases significantly, but has not yet exceeded the limit. When the wavelength is 15m and 20m, the wheel-rail vertical force has exceeded the limit of 170kN under larger settlement amplitudes. In order to ensure that the wheel-rail force does not exceed the limit, the amplitude limit is 22mm under the 15m settlement wavelength, and the amplitude limit is 27mm under the 20m settlement wavelength.

[0173] The vehicle vertical acceleration is managed at level I, which is 1.0 m / s 2 , at 15m, 20m, 30m wavelength conditions, the settlement limits are 14.9mm, 20.9mm, 38.7mm; for the vehicle body vertical acceleration level II management standard, that is, 1.5m / s 2 , under the conditions of 15m and 20m wavelength, the settlement limit is 32.6mm and 35.7mm. Different smoothness control threshold divisions under the corresponding conditions of Level I and Level II management standards are as follows Fig.13 shown.

[0174] The relationship between vehicle acceleration and roadbed surface dynamic deformation under uneven settlement conditions is as follows: Fig.14 As shown in Figure 2, it can be seen that the vehicle acceleration is roughly linearly positively correlated with the dynamic deformation of the roadbed surface. Compared with the vertical acceleration of the vehicle under the management standards of Level I and Level II, the critical design thresholds of the dynamic displacement amplitude of the roadbed surface are λ U1 =0.200mm,λ U2 =0.292mm.

[0175] (2) Unsmooth arching condition

[0176] For the uneven camber condition, the wheel-rail force cloud diagram under different camber wavelength and amplitude conditions is as follows: Fig.15 As shown. When the wavelength of the camber is greater than 40m, the wheel-rail vertical force is less sensitive to the camber amplitude; when the wavelength is 30m, the wheel-rail vertical force is somewhat sensitive to the change of the camber amplitude. As the camber amplitude increases, the wheel-rail vertical force increases significantly, but has not yet exceeded the limit. When the wavelength of the camber is 5m, 10m, 15m, and 20m, at a larger camber amplitude, the wheel-rail vertical force has exceeded the limit of 170kN. In order to ensure that the wheel-rail force does not exceed the limit, the lower amplitude limit of the 5m camber wavelength is 16mm, the lower amplitude limit of the 10m camber wavelength is 18mm, the lower amplitude limit of the 15m camber wavelength is 19mm, and the lower amplitude limit of the 20m camber wavelength is 22mm.

[0177] The vehicle vertical acceleration is managed at level I, which is 1.0 m / s 2 , at 5m, 10m, 15m, 20m, and 30m wavelengths, the camber limits are 11.9mm, 12.2mm, 13.6mm, 17.5mm, and 25.0mm; for the vehicle body vertical acceleration level II management standard, that is, 1.5m / s 2 , under the wavelength conditions of 5m, 10m, and 15m, the upper arch limit is 20.8mm, 21.5mm, and 22.1mm. Different smoothness control threshold divisions under the corresponding conditions of Level I and Level II management standards are as follows Fig.17 shown.

[0178] The relationship between vehicle acceleration and roadbed surface dynamic deformation under the condition of camber unevenness is as follows: Fig.18 As shown in Figure 2, it can be seen that the vehicle acceleration is roughly linearly positively correlated with the dynamic deformation of the roadbed surface. Compared with the vertical acceleration of the vehicle under the management standards of Level I and Level II, the critical design thresholds of the dynamic displacement amplitude of the roadbed surface are λ U1 =0.199mm,λ U2 =0.288mm.

[0179] Table 9 gives the control threshold values ​​of the dynamic displacement of the roadbed surface. The level I dynamic quality tolerance management corresponds to the daily control state in the "Technical Specifications for Dynamic Acceptance of High-speed Railway Projects" (TB10761-2013), and the level II dynamic quality tolerance management corresponds to the control state of planned maintenance. Different control values ​​are given for different roadbed irregularities such as settlement and arching, but the difference between the two is not large. In most cases, they can be regarded as the same control threshold, that is, the level I control value of the roadbed surface dynamic displacement can be 0.20 mm, and the level II control value can be 0.29 mm.

[0180] Table 9 Threshold values ​​for dynamic displacement control of roadbed surface

[0181]

[0182] 8. Complete the design and verify the solution

[0183] According to the previous design process, the design results are verified, and the design parameters that meet the first and second design control thresholds are substituted into the model for recalculation to verify that the various dynamic response laws meet the design requirements. Scheme comparison and optimization analysis are carried out to ultimately achieve the design goals.

[0184] The purpose of the present invention is to provide a design method for the stability performance of high-speed railway subgrade structures based on the dynamic stability theory framework. This method is aimed at the typical high-speed railway subgrade structure surface graded crushed stone and subgrade bottom coarse-grained soil filling types, combined with the long-term deformation development law and hysteresis energy characteristics of different filling materials under the action of train power, and establishes a high-speed railway subgrade filling material dynamic stability critical state judgment standard based on the equivalent volume dissipated energy index, proposes a dynamic stability design threshold calculation method for different filling material types, and constructs a high-speed railway subgrade structure design method flow considering the dynamic stability performance of the filling material, which provides support for the high-speed railway subgrade structure stability design.

[0185] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions only describe the principles of the present invention. The present invention may be subject to various changes and improvements without departing from the spirit and scope of the present invention. These changes and improvements fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the attached claims and their equivalents.

Claims

1. A high-speed railway subgrade structure design method based on dynamic stability is characterized by: Step 1: Start of the design process: clarify the design objectives, including determining the line grade, operating speed, basic line geometry requirements and design-related standards, providing prerequisites for design loads and basic parameters; Step 2: Define the design load and control conditions, define the design load under the corresponding vehicle model and speed conditions, and assign the modulus dynamic parameters and initial values ​​of layer thickness to each layer; Step 3: Construct a dynamic coupling model of the lumped parameters of the high-speed railway vehicle-track-roadbed hierarchical structure; Step 4: Based on the design parameter index system, set the parameters for the dynamic coupling model and perform calculation verification; Step 5: Solve the subgrade layered dynamic response results through the dynamic coupling model; Step 6: Use the dynamic response as the first design threshold critical condition to verify the stability characteristics of the filler. If it is satisfied, proceed to step 7. If not, re-adjust the design parameters of the subgrade position that does not meet the conditions, and return to step 4 to re-assign the design parameters of the dynamic coupling model. Step 7: Use the total dynamic displacement of the roadbed surface as the second design threshold critical condition to verify the vehicle-track-road overall coupled dynamic response. If it is satisfied, go to step 8; if not, return to step 4 and re-assign the design parameters of the dynamic coupling model. Step 8: Substitute the design parameters that meet the first and second design control thresholds into the dynamic coupling model for recalculation, verify that the dynamic response laws meet the design requirements, conduct scheme comparison and optimization analysis, and finally achieve the design goal.

2. The high-speed railway subgrade structure design method based on dynamic stability according to claim 1 is characterized by: The step 2 further includes the following contents: using multiple sets of wheel set train loads F(t) based on the Fourier series form, the train load F(t) includes a static load and a dynamic load formed by superposition of a series of sinusoidal functions, and each sub-item corresponds to high, medium and low frequencies, respectively used to reflect the influence of unevenness, additional dynamic load and rail surface corrugation effect, and the expression of F(t) is: F(t)=P0+P1sinω1t+P2sinω2t+P3sinω3t (1) P0 is the static load of the wheel; P1, P2, and P3 correspond to a typical value of vibration load respectively; Let the unsprung mass of the train be M0, then the corresponding vibration load amplitude is: P i =M0a i ω i 2 (2) Among them, a i Corresponding to a typical vector height; ω i is the circular frequency at the wavelength of the uneven vibration corresponding to different vehicle speed conditions. The calculation formula of the circular frequency is: Among them, υ is the running speed of the train; L i is the typical wavelength corresponding to different situations; according to different line smoothness and control level requirements, the parameter values ​​under the corresponding control conditions in formulas (1), (2) and (3) should be adjusted accordingly.

3. The high-speed railway subgrade structure design method based on dynamic stability according to claim 1, characterized in that step 3 further comprises the following contents: The dynamic coupling model considers the vibration coupling relationship of vehicle-track-filler in the vertical direction, combines the filler deformation mechanical model with the dynamic equation of the layered structure under the train load, the upper part of the dynamic coupling model includes the car body, bogie, wheelset and primary and secondary suspension, and the lower part of the coupling model is the elastic-plastic deformation mechanical model of each layer of filler in the roadbed, and the vibration coupling and response transmission between the two are realized by the wheel-rail contact relationship and wheel-rail force; The structural lumped parameter dynamic coupling model of each layer of the roadbed is a filler compaction deformation mechanics model, which is composed of two parts in series: viscoelasticity and viscoplasticity. The hyperbola in the form of formula (5) is selected as the load-deformation relationship of the plastic spring: Where F is the load, x is the plastic spring deformation, A and B are two plastic parameters in the hyperbola; according to the form of the packing deformation mechanics model, its load-deformation relationship is as shown in formula (6); in: Where: σ(t) is the load at time t; ε(t) is the total strain at time t; k e is the elastic stiffness; ε ve (t) is the elastic deformation at time t; c e is the elastic damping coefficient; ε vp (t) is the plastic deformation at time t; is the elastic deformation rate at time t; c p is the plastic damping coefficient; is the plastic deformation rate at time t; The plastic deformation rate is calculated according to formula (8): During the operation of the train, the track plate can only produce pressure on the filler, not tension, and the plastic deformation of the filler can only develop in one direction. can only be positive when σ(t)-f(ε vp When (t))≤0, no plastic deformation occurs, that is, Taking the free state of each basic unit as the reference zero point, the dynamic equation of the "vehicle-track-roadbed" coupling system is: Where m c 、m z 、m l 、m g 、m d are the masses of the car body, bogie, wheelset, rail, track plate and supporting structure, g is the acceleration of gravity, k c , k z are the stiffness of the primary suspension and the secondary suspension, k g is the stiffness between the rail and the supporting structure, c c 、c z are the damping coefficients of the primary suspension and the secondary suspension, c g is the damping coefficient between the rail and the supporting structure, λ1, λ2, λ3, λ soil-i are the deformation of the primary and secondary suspensions, rails and supporting structures, and the ith, i=1, 2, 3, …, nth layer of roadbed, respectively. are the deformation rates of the primary and secondary suspension, rails, supporting structures, and the i-th roadbed, respectively, soil-ie , is the elastic deformation and elastic deformation rate of the i-th layer of roadbed, λ soil-ip is the plastic deformation of the ith layer of roadbed, x c 、x z 、x l 、x g 、x d are the displacements of the car body, bogie, wheelset, rail, track plate and supporting structure, are the accelerations of the car body, bogie, wheelset, rail, track plate and supporting structure, respectively, N is the reaction force of the rail on the wheelset, F(t) is the irregularity excitation load in the design load and control condition determined in step 2; The interaction force F between wheel and rail s The depth is transferred downward from rails-support structure-layered roadbed in sequence, expressed as: When the wheel-rail interaction force is large, the wheelset will separate from the rail; since only pressure but no tension can be generated between the wheelset and the rail, the interaction force is 0 when the rail and wheelset separate from each other; Considering the diffusion effect of load as the depth increases, the bearing area and system parametric mass of each layer of the layered roadbed change accordingly, and the stiffness and damping coefficient of each layer also change; considering the layer width d i , layer thickness h i , diffusion angle θ i The influence of parameters, the stiffness k of the lumped parameter unit corresponding to the i-th layer of roadbed ei and the damping coefficient c ei The first layer parameter unit stiffness k located on the surface of the subgrade e1 , damping coefficient c e1 The relationship between the layer width d1 is:

4. The high-speed railway subgrade structure design method based on dynamic stability according to claim 3 is characterized in that the step 4 further comprises the following contents: Consider the following three aspects to design the parameter index system: (1) Upper train and track structure parameters: basic train parameters such as car body mass m0, bogie mass m1, wheelset mass m2, and related structural dimension parameters, primary suspension and secondary suspension stiffness, damping coefficients k0, k1, c0, c1; track mass, track plate and support layer mass m3, m4, and related structural dimensions; rail-support layer fastener connection stiffness and damping coefficients k2, c2; (2) Design load input parameters: train speed v, track irregularity spectrum related parameters including irregularity wavelengths L1 to L3 and irregularity amplitudes η1 to η3 within three typical frequency response ranges; track irregularity related parameters including irregularity wavelength L4 and irregularity amplitude η4 caused by the roadbed; (3) Layered roadbed parameters: including the dynamic modulus E of each layer d , damping ratio ζ, density ρ, diffusion angle θ, and design thickness h are defined for the subgrade surface layer, subgrade bottom layer, and roadbed body layer respectively.

5. The high-speed railway subgrade structure design method based on dynamic stability according to claim 4 is characterized by: The step 4 further includes the following contents: firstly, according to the dynamic equations in the construction of the high-speed railway vehicle-track-roadbed layered structure lumped parameter dynamic coupling model in step 3, a vehicle-track-filler coupling dynamic system is established; under the excitation of the set track irregularity, the train load is dynamically calculated on the vehicle, track, track support structure and layered roadbed structure to obtain the acceleration vibration state response and deformation law of each layer, and then the dynamic response values ​​of each layer are obtained through iterative solution; the acceleration of each layer of the car body, bogie, wheelset, rail and support structure in the model is calculated; The dynamic displacement x is calculated by the following formula: The dynamic stress of the roadbed layer is determined by the interlayer interaction force F between the layered soils. N The interlayer interaction force between the layered soils is related to the wheel-rail interaction force transmission law, and the interlayer filler load equivalent action area is obtained by dividing by the interlayer filler load equivalent action area, where the interlayer interaction force between the layered soils is related to the wheel-rail interaction force transmission law, and the interlayer filler load equivalent action area is determined by the width W and length L of the upper support structure, the thickness h of the surface layer and the bottom layer of the subgrade i , load diffusion angle α i The factors are combined to determine the simplified formula: Dynamic strain of roadbed layer ε i The deformation of the soil mass by layered filling i The filler thickness h after the layer is discretized i The ratio of is related, expressed as:

6. The high-speed railway subgrade structure design method based on dynamic stability according to claim 4 is characterized in that the step 5 further includes the following contents: the first design threshold is mainly based on the long-term deformation stability of each layer of the subgrade filler, and it is necessary to make it meet the dynamic stability state and not accumulate deformation during the service life, so as to ensure the durability and stability of the subgrade structure; the dynamic stress σ of each layer of the subgrade d 、Dynamic strain ε d They should all be less than the critical dynamic stress and dynamic strain thresholds of the dynamic stability of the filler at the corresponding layer, as shown below: Where λ σ基床表层 , σ基床底层 , σ路基本体层 are the critical thresholds of dynamic stress stability of the filler materials of the subgrade surface layer, subgrade layer and subgrade body layer, respectively, ε基床表层 , ε基床底层 , ε路基本体层 are the critical thresholds of dynamic strain stability of the filler of the subgrade surface layer, subgrade layer and subgrade body layer, respectively; n is the safety factor proposed according to different deformation stability requirements; the larger the value, the stricter the design requirement, which is determined according to different line grades, design speeds and control objectives; 3基床表层 , σ 3基床底层 , σ 3路基本体层 CSR is the confining pressure of the filler material of the subgrade surface layer, subgrade layer and subgrade body layer, i.e. the third principal stress; * is the critical cyclic stress ratio, which is related to the confining pressure of the filler, i.e., the third principal stress σ3, and is expressed as: CSR=Aσ3 b (24) Where A and b are fitting parameters obtained based on indoor test of different types of fillers; The first design threshold is proposed by constructing the relationship between dissipated energy and stable state as the basis for judging the critical threshold of power stability, and proposing an equivalent unit volume dissipated energy As the basic indicator for judging the critical stability of fillers, the calculation formula is: Where: is the mean value of the dissipated energy per unit volume under the action of the circulation dynamics, is the influencing term reflecting the magnitude of the dissipated energy value, and the superscript d represents the influence of the circulation dynamics; is the final unit volume dissipated energy corresponding to the maximum vibration order m, is the energy dissipated per unit volume corresponding to the characteristic vibration order m / 10, and the term in brackets is a dimensionless influence term reflecting the increasing trend of the dissipated energy.

7. The high-speed railway subgrade structure design method based on dynamic stability according to claim 4 is characterized by: The step 6 further includes the following contents: the second design threshold needs to make the coupled dynamic response of the high-speed railway subgrade meet the requirements of safe, stable and comfortable train operation, that is, the static and dynamic unevenness of the subgrade needs to be controlled so that the train wheel-rail force F s The roadbed surface dynamic displacement U d The corresponding train acceleration meets the dynamic quality tolerance management values ​​of level I and II; the specific expressions are as follows: In the formula λ U1 , U2 They are the design threshold of the wheel-rail force on the high-speed railway subgrade and the dynamic displacement control threshold that meets the management value of the allowable deviation of dynamic quality of levels I and II. n is the safety factor proposed according to different requirements of deformation stability. The larger the value, the stricter the design requirement. It is determined according to different line grades, design speeds and control objectives.

8. A non-volatile storage medium, characterized in that: The non-volatile storage medium includes a stored program, wherein when the program is run, the device where the non-volatile storage medium is located is controlled to execute the high-speed railway subgrade structure design method based on dynamic stability as described in any one of claims 1 to 7.

9. A high-speed railway roadbed structure electronic device based on dynamic stability, characterized in that: It comprises a processor and a memory; the memory stores computer-readable instructions, and the processor is used to run the computer-readable instructions, wherein the computer-readable instructions, when running, execute the high-speed railway subgrade structure design method based on dynamic stability as described in any one of claims 1 to 7.

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