A high-speed railway subgrade structure design method based on dynamic stability

Abstract

The high-speed railway subgrade structure design method based on dynamic stability includes: the design process starts with: clarifying the design load and control conditions; constructing a high-speed railway vehicle-track-subgrade layered structure lumped parameter dynamic coupling model; based on the design parameter system, setting parameter input and verification for the model; solving the subgrade layer dynamic response results through the dynamic coupling model; judging the critical conditions of the first and second design thresholds; substituting various design parameters that meet the first and second design control thresholds into the dynamic coupling model for recalculation, verifying that various dynamic response laws meet the design requirements, and finally achieving the design goal. The present invention is aimed at the typical high-speed railway subgrade structure base surface graded gravel and base bottom coarse-grained soil filler types, and combines the long-term deformation development laws and hysteresis energy characteristics of different fillers under the action of train dynamics to establish a high-speed railway subgrade filler dynamic stability critical state judgment standard, providing support for the high-speed railway subgrade structure stability design.

Description

Technical Field

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

[0002] High-speed railway subgrade structures are crucial for the safe and smooth operation of high-speed trains. Scientific subgrade design is the fundamental guarantee for their long-term service life and technical and economic viability. By the end of 2023, China's high-speed railway operating mileage reached 45,000 kilometers, ranking first in the world. High-speed railway subgrade structures are subjected to cyclic dynamic loads during both their formation and service life. Dynamic forces persist throughout the structure's lifecycle. The dynamic performance and deformation control of high-speed railway subgrade structures are key technologies for ensuring safe, high-speed, and smooth train operation. Their dynamic deformation state is closely related to post-construction settlement control, structural vertical stiffness matching, and longitudinal stiffness coordination. These factors are complex, and precise control and long-term maintenance of dynamic deformation of subgrade structures remain global technical challenges. Currently, the cumulative length of my country's high-speed railway subgrades is approximately 13,300 kilometers, with high-speed rail lines accounting for nearly 30%. A number of representative high-speed railway subgrade projects have been completed in diverse regions and climates. High-standard structural design and filler selection ensure the high-quality construction of large-scale high-speed railway subgrades in my country. 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 in the subgrade and providing a solid and stable foundation for the upper track structure is a prerequisite for maintaining high-speed, safe, and smooth train operation. Establishing a scientific and effective high-speed railway subgrade structural design method is a fundamental theoretical challenge that must be overcome to achieve high-precision deformation control and long-term service life for high-speed railway subgrades. In design practice, my country's high-speed railway subgrade design has achieved a transition from strength control such as bearing capacity to refined structural deformation control. To ensure the long-term stability of subgrade deformation, existing design methods have established design criteria for controlling the total deformation of the subgrade surface and the critical strain of the subgrade. Using a simplified equivalent load analysis method, the subgrade is assumed to be a semi-infinite elastic space body. The Boussinesq formula is used to calculate the stress and strain of the subgrade. The dynamic strain of the subgrade layer and the deformation of the subgrade surface are then compared with the design values ​​to achieve long-term deformation stability control of the subgrade. This method has laid an important foundation for large-scale high-speed railway construction in my country and has played a significant role in the application of subgrade structural design. However, this design method simplifies the dynamic process of the subgrade structure during its service life, transforming it into a pseudo-static problem through theoretical assumptions. It is inadequate in characterizing the dynamic service state of each layer of subgrade filler material. It also lacks scientific and effective consideration of the long-term dynamic performance of high-speed railway subgrade structures. The selection of design parameters involves the simultaneous use of dynamic and static parameters, resulting in a certain discrepancy between the calculated structural load distribution and filler stress and deformation characteristics and the service state of the subgrade structure under dynamic excitation. Establishing a new high-speed railway subgrade structure design method that meets these refined functional requirements will help further improve and develop high-speed railway subgrade structure design theory, optimize high-speed railway subgrade structures, and ultimately ensure the design goal of durable and stable subgrades over a century of service life under higher speeds and complex environments.

[0004] In recent years, shakedown design has become a key concept in the design of structures such as transportation infrastructure. Unlike conventional elastoplastic incremental analysis and critical state design methods, it not only requires that structures meet bearing capacity and transient deformation requirements 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 determining plastic failure criteria in engineering strength design codes, providing a powerful analytical tool for selecting critical dynamic stress, assessing structural safety, and controlling long-term deformation. In recent years, shakedown design has been increasingly applied in geotechnical engineering, such as in the analysis of pavement rutting deformation, offshore platform foundations, slope stability, and ballastless track structures. For high-speed railway subgrade structures subjected to high-frequency dynamic cyclic traffic loads, this method can effectively determine whether the deformation can reach a stable state under different stress-strain states, and thus provide a critical envelope for satisfying structural dynamic shakedown, thereby determining the appropriate design threshold for the high-speed railway subgrade to meet long-term service durability requirements.

[0005] The Railway Architectural Research Institute of the China Academy of Railway Sciences Group Co., Ltd. has developed a high-speed railway subgrade structural design method (CN 202010329656.3). This method, based on multi-layer system design theory, determines the load distribution structure of the subgrade surface, constructs analytical expressions for the stress and strain of a single soil layer, and proposes stress and displacement expressions for each subgrade layer. This method then iteratively solves the problem by comparing it with the control criteria for the dynamic deformation of the subgrade surface and the dynamic strain of the subgrade layer, achieving optimal adjustment of the parameters of each subgrade structure layer. The main shortcomings of this technical solution are: ① The load pattern and distribution within the subgrade are primarily based on the assumption of vertical concentrated forces. Static methods are used to analyze the dynamic strain of a single soil layer and the stress and displacement expressions of each layer. This approach fails to account for dynamic effects such as varying train speeds, dynamic action frequencies, and damping. ② The critical values ​​for its core design control indicators—subgrade surface dynamic deformation, subgrade substratum dynamic strain, and maximum strain constraint criteria—are primarily determined by methods based on the critical strain value described in foreign literature as preventing deformation accumulation. These values ​​are defined as 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 fillers for high-speed railway subgrade structures remains to be studied. ③ The approach used to determine the design threshold is limited to comparing the average and maximum dynamic strains of the subgrade substratum and the magnitude of the subgrade surface dynamic deformation to see if they meet the requirements. While these three indicators are representative, there is room for improvement in reflecting the stable state of service deformation at different points along the subgrade depth. Furthermore, this method does not properly 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 subgrade filling materials (CN202310356164.7). This method mainly considers the typical layered interfaces of the subgrade structure and the differences in the physical and mechanical properties of materials between different layers from the perspectives of wave dynamics and micromechanics, as well as the propagation behaviors such as stress wave signal waveform distortion, transflection, etc., to establish a stress wave interface transflection effect model. The effective frequency response range of the subgrade is determined by calculating the circular frequency of the stress wave. The key parameters of each layer of filling material are adjusted to reduce the vibration deformation of the upper layer and suppress the amplification effect of the vibration deformation of the subgrade layered interface. From the perspective of filling material design parameter optimization, relevant technologies for subgrade structure deformation control are proposed. The main shortcomings of this technical solution are: ① Its core model is mainly based on the one-dimensional layered viscoelastic granular material interface contact model, and calculations are carried out based on the assumption of an ideal viscoelastic interface. Although it can reflect the dynamic characteristics and fluctuation characteristics of the 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 cannot consider the influence of dynamic stress-strain and cumulative deformation of the bed filler, and is difficult to apply to the design requirements 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. The dynamic load of the train on the top of the subgrade is calculated through the track-subgrade dynamic analytical model. The dynamic stress distribution within the subgrade is calculated based on a 2.5-dimensional or 3D finite element analysis model. Then, the cumulative deformation of the subgrade is obtained based on the mechanical-empirical model of cyclic cumulative deformation of the soil. The main shortcomings of this technical solution are: ① This method is mainly aimed at the design goal of cumulative settlement deformation of high-speed railway subgrades, taking into account static deformation requirements, but it is unable to verify and compare 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, which calculates the cumulative deformation of different layers in the subgrade at various automatic stress levels using the cumulative strain empirical formula. It does not specify the impact of the key parameter of the number of cycles N, that is, it still needs to be optimized in terms of considering the number or duration of load application; ③ The design concept of ensuring that the total deformation of the subgrade structure does not exceed the limit has reference value for short-term post-construction settlement calculations. However, for high-speed railway subgrade structures with a service life of 100 years, the magnitude of their total settlement is difficult to accurately estimate and is not solely due to the deformation of the subgrade structure itself. Therefore, it is more critical to determine whether the long-term deformation of the subgrade structure can converge rapidly rather than continuously accumulate. The total deformation judgment concept proposed by this method cannot consider the impact of long-term stability in this regard. Summary of the Invention

[0008] In order to solve the defects 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: Design process begins: Define the design objectives, including determining the line grade, operating speed, basic line geometry requirements, and design-related standards, which provide prerequisites for determining design loads and basic parameters;

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

[0012] Step 3: Construct a lumped parameter dynamic coupling model of the high-speed railway vehicle-track-subgrade layered 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 dynamic response results of the subgrade layer through the dynamic coupling model;

[0015] Step 6: Use the dynamic response of the roadbed layer as the first design threshold critical condition to verify the stability characteristics of the filler. If it meets the requirements, proceed to step 7. If not, readjust the design parameters of the layer and return to step 4 to re-assign 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 meets the critical condition, proceed to Step 7. If not, readjust 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 to verify that the dynamic response laws meet the design requirements. Conduct scheme comparison and optimization analysis to ultimately 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 ideas, from the perspective of structural stability design, considering the changing law of the dynamic characteristics of fillers under long-term service conditions, combining the deformation convergence law and the energy dissipation law, a filler stability state judgment standard based on equivalent volume dissipated energy is proposed. Based on the stability theory, a method for determining the critical thresholds of dynamic stress and dynamic strain 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 subgrade bottom layer and subgrade surface layer in the refined design of high-speed railway subgrade.

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

[0022] It breaks through the limitations of traditional design methods such as quasi-static assumptions and empirical design control standards. Starting from the dynamic equation, the layered structure of high-speed railway trains, tracks, and roadbed is regarded as design elements that jointly affect the dynamic response of the system. A lumped parameter dynamic generalization model of the high-speed railway vehicle-track-roadbed layered structure is constructed, and the calculation and analysis of the vehicle-track-layered roadbed dynamic response under different parameters such as train running speed, smoothness, layer stiffness, and damping are realized. The design control thresholds of 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 comprehensive design parameter system was proposed from three aspects: the upper train, track structure parameters, design load input parameters, and layered roadbed structure parameters, including vehicle type, suspension properties of each system, vehicle speed, roughness, and various geometric parameters and static and dynamic parameters of the subgrade surface, sub-layer, and main body layers. A critical strain design threshold based on the stability characteristics of the subgrade filler and a vibration response design threshold based on the train's running comfort were proposed. A design process was established: initial assignment of design indicators - construction of a coupling model - calculation of dynamic response - comparison of discriminant indicators - iterative optimization of parameters - and updating of design solutions. This supports the refined design of high-speed railway subgrade layered composite structures suitable for different filler types, different static and dynamic smoothness control levels, and meeting long-term stability requirements. 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 the 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 a typical filler for a high-speed railway subgrade, including (a) coarse-grained soil filler in the bottom layer of the subgrade; (b) graded crushed stone in the surface layer of the subgrade;

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

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

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

[0033] Figure 9 Critical threshold curve of dynamic stress stability of filler, including (a) Group A filler; (b) Group B filler; c) Group C filler; (d) Group D filler; (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] Figure 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] Figure 11 Schematic diagram of wheel-rail forces under different roadbed settlement irregularities;

[0036] Figure 12 Schematic diagram of vehicle acceleration under different roadbed settlement irregularities;

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

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

[0039] Figure 15 Schematic diagram of wheel-rail forces under different roadbed camber irregularities;

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

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

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

[0043] The high-speed railway subgrade structure design method based on dynamic stability has the following main steps: initial assignment of design indicators - construction of coupling model - calculation of dynamic response - comparison of discrimination indicators - iterative optimization of parameters - updating of design scheme, 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 Define the design load and control conditions, specify the design load under the corresponding vehicle model, speed, and other conditions, and assign the dynamic modulus parameters and initial values ​​of the layer thickness to each layer (the dynamic modulus of each layer is related to the strain level and is assigned by the critical threshold strain);

[0047] ③Construct a lumped parameter dynamic coupling model of the 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 layer through the dynamic coupling model;

[0050] ⑥ Identification 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, the critical dynamic stress and dynamic strain design thresholds of different layers are clarified, and the obtained dynamic stress and dynamic strain are specifically substituted into the dynamic stability threshold of each layer of fillers for judgment. If they meet the requirements, the next step is entered. If not, the design parameters of the layer are readjusted, including increasing the modulus to reduce the strain, changing the design thickness, etc., and returning to step ④ to re-assign the model design parameters.

[0051] ⑦ Second design threshold critical condition judgment (verification of vehicle-track-road overall coupled dynamic response) - the obtained wheel-rail force, roadbed surface dynamic displacement and other indicators are substituted into the thresholds under different comfort control conditions for judgment. If they meet the requirements, the next step is entered. If not, the design parameters are readjusted, including increasing the modulus to reduce the strain, changing the design thickness, etc., and returning 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 transferred to the roadbed surface through the absorption and attenuation of the track when the train is running. 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 design. The main reason for the generation of vertical wheel-rail force is due to 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 (0.5-10Hz), which is almost entirely caused by the relative movement of the vehicle body to the suspension part; (2) medium frequency range (30-60Hz), which is caused by the rebound effect of the unsprung wheelset mass on the rail; (3) high frequency range (100-400Hz), which is caused by the resistance of the rail movement to 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 factors affecting the wheel-rail force are track unevenness and the corrugated wear effect of the rail surface. 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 aforementioned theoretical research results and measured patterns, this invention uses a train load expressed in the form of a Fourier series for multiple wheelsets, applicable to wave transmission units. This represents an excitation force that reflects periodic characteristics. It includes a static load and a dynamic load formed by the superposition of a series of sinusoidal functions. The individual components of the excitation force correspond to high, medium, and low frequencies, respectively, reflecting the effects of irregularity, additional dynamic load, and rail corrugation. 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 Ⅰ, Ⅱ and Ⅲ in Table 1; ω i 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] Where, 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 railway, taking a 17t axle weight train as an example, the single wheel weight P0 is taken as 85kN. The unsprung mass is taken as M0 = 750kg = 750N·s 2 / m. The corresponding three control conditions Ⅰ, Ⅱ and Ⅲ take the typical uneven vibration wavelength and the corresponding arrow 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 are in line with the above-mentioned 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 below Figure 2 shown.

[0071]

[0072] 3. Construction of a lumped parameter dynamic coupling model for the hierarchical structure of high-speed railway vehicles, tracks, and subgrade

[0073] The present invention constructs the coupled dynamic relationship control equations of the vehicle, rails, lower track structure, and layered roadbed structure under 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 layer of the vehicle-track-roadbed structure through iterative solution. The model diagram of a single train wheel set is shown in the figure below. Figure 3 shown.

[0074] The model primarily considers the vertical vibration coupling relationship between vehicle, track, and filler, combining the filler deformation mechanics model with the dynamic equations of the layered structure under train load. The upper part of the model consists of the vehicle body, bogie, wheelset, and primary and secondary suspensions, while the lower part is the elastic-plastic deformation mechanics model of each layer of filler in the roadbed. Vibration coupling and response transmission are achieved between the two through the wheel-rail contact relationship and wheel-rail force.

[0075] The basic model unit of the layered roadbed structure lumped parameter is the filler compaction deformation mechanics model, which consists 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 uses 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 packing and is often used to analyze the dynamic characteristics of the packing. The hyperbola in the form of equation (5) is selected as the load-deformation relationship of the plastic spring.

[0076]

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

[0078] To describe the temporal evolution of plastic deformation, the model connects a plastic spring in parallel with a viscometer. The viscometer describes the time dependence of plastic deformation and the energy dissipated during plastic deformation. A larger plastic damping coefficient slows down the plastic deformation and consumes more energy.

[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 respectively, 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 deformations of the primary and secondary suspensions, rails and supporting structures, and the ith (i=1, 2, 3, …, n) layer of roadbed, are the deformation rates of the primary and secondary suspensions, 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 i-th 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 respectively. are the accelerations of the car body, bogie, wheelset, rail, track plate and supporting structure respectively, F N is the reaction force of the rail on the wheelset, and F(t) is the irregularity excitation load in the design load and control conditions determined in step ②.

[0091] Wheel-rail contact interaction force F s The depth is transferred downward from rails to supporting structure and then to layered roadbed, which can be expressed as:

[0092]

[0093] During train operation, wheelsets and rails are not always in contact. When the wheel-rail interaction force is large, the wheelset may separate from the rail. Since only compressive forces, not tensile forces, can be generated between the wheelset and rail, the interaction force is zero when the rail and wheelset separate.

[0094]

[0095] Considering the diffusion effect of load as the depth increases, the load-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 stiffness k of the first layer parameter element located on the surface of the subgrade e1 , damping coefficient c e1 And 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 train model 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 terminal mainly refer to the relevant methods in step ② to determine the design load and control conditions. The time history curve of the train wheel-rail interaction force under different track irregularity spectra and line irregularity conditions caused by the roadbed foundation structure is constructed as the initial excitation input for the relevant design model.

[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. These parameters 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 2, 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] Where 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 respectively. s1 , Δ s2 are the areas of regions S1 and S2 in the figure respectively.

[0111] For the typical filling types of high-speed railway subgrade, the following 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 gradation curves and dynamic modulus determination methods of type I and II graded gravel of the subgrade surface layer.

[0112] The value of the dynamic modulus of the filler is closely related to the stress and 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 a 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 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 six 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 parameter of the dynamic modulus changing with confining pressure and the initial dynamic modulus parameter 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 calculation equations for dynamic parameters of six typical high-speed railway subgrade fillers

[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, the vehicle-track-filler coupled dynamic system was established based on the dynamic equations described in Step 3 (Constructing a Lumped Parameter Dynamic Coupling Model for the High-Speed ​​Railway Vehicle-Track-Subgrade Layered Structure). Under the excitation of a given track irregularity, the train load's effects on the vehicle, track, track support structure, and subgrade layered structure were dynamically calculated. The vibration state responses and deformation patterns, such as acceleration, of each layer were determined. The above calculation steps were then repeated for the next time step. To facilitate the extraction and analysis of the model's output signals, a fixed-step ode4 algorithm was used for the iterative calculations, with a simulation step size of 0.001 seconds.

[0128] Acceleration of each layer of the car body, bogie, wheelset, rails and supporting structure in the model The dynamic displacement x is calculated using 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 determined by the width W and length L of the upper support structure, the thickness h of the surface and bottom layers of the subgrade, and the load of the interlayer filler. 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 discretization of the layer is analyzed i The ratio of is related, expressed as:

[0134]

[0135] 6. First design threshold

[0136] The design thresholds in the design method described in the present invention are 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 defined as the first design threshold critical judgment condition and the second design threshold critical judgment condition respectively.

[0137] The first design threshold is primarily based on the long-term deformation stability of each layer of the roadbed filler. It is necessary to ensure that it meets the dynamic stability state and does not accumulate deformation during its service life, thereby ensuring the durability and stability of the roadbed structure. Accordingly, the dynamic stress and dynamic strain of each layer of the roadbed should be less than the critical dynamic stress and dynamic strain thresholds of the filler in the corresponding layer, which are specifically expressed as follows:

[0138]

[0139]

[0140] Where λ σ基床表层 ,λ σ基床底层 ,λ σ路基本体层 are the critical thresholds of dynamic stress stability of the filler of the subgrade surface layer, subgrade layer and subgrade body layer, respectively, ε基床表层 ,λ ε基床底层 ,λ ε路基本体层 σ is the critical threshold value 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. 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 The confining pressure of the filler material of the subgrade surface layer, subgrade layer and roadbed body layer is the third principal stress. * is the critical cyclic stress ratio, which is related to the confining pressure of the filler, that is, 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 stability 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, and is the influencing term reflecting the magnitude of the dissipated energy value. The superscript d represents the influence of the circulation dynamics. is the final unit volume dissipation energy reached at the maximum vibration order m, is the dissipated energy per unit volume corresponding to the characteristic vibration order m / 10, and the term in brackets is a dimensionless influence term reflecting the upward 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 method for determining the upper and lower limits of the critical stability state is adopted. The equivalent unit volume dissipated energy is divided 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 plastic stable state A The minimum dissipated energy per unit volume equivalent to the 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, the stable state judgment criterion is given:

[0148]

[0149]

[0150]

[0151] Where: A-B ,λ B-C These correspond to the critical values ​​of equivalent unit volume dissipation energy between states AB and BC, respectively. Different filler types and loading test conditions may affect these values, but the above criteria and threshold calculation methods remain applicable. Table 5 shows the critical thresholds for typical filler types in my country's high-speed railway subgrades.

[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: Figure 9 、 Figure 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 Parameter values ​​of the critical threshold curve of dynamic strain stability of typical high-speed railway subgrade fillers

[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 need to be controlled so that the train wheel-rail force F s Not exceeding the limit, and the dynamic displacement of the roadbed surface U d The corresponding train acceleration meets the dynamic quality tolerance management values ​​of levels I and II. The specific expressions are as follows:

[0164]

[0165]

[0166] In the formula λ U1 ,λ U2 The values ​​are the design thresholds for high-speed railway subgrade wheel-rail forces and the dynamic displacement control thresholds required to meet the tolerances for dynamic quality at levels I and II, respectively. n is a safety factor based on different deformation stability requirements; larger values ​​indicate stricter design requirements. These values ​​are primarily determined based on different line grades, design speeds, and control objectives.

[0167] Based on the control limits for various structural indicators such as vehicles, tracks, and roadbeds in current standards, representative indicators such as wheel-rail forces and vehicle acceleration were selected to determine the control thresholds for static and dynamic deformation of roadbed irregularities under different conditions of smoothness and dynamic quality tolerances. Based on the relevant control parameters in the "High-Speed ​​Railway Design Specification" (TB10621-2014), the "High-Speed ​​Railway Track Engineering Construction Quality Acceptance Standard" (TB 10754-2018), the "High-Speed ​​Railway Engineering Dynamic Acceptance Technical Specification" (TB10761-2013), and the "High-Speed ​​Railway Ballastless Track Maintenance Rules (Trial)" (TGGW115-2023), the control limit for the wheel-rail vertical force for both ballastless and ballasted tracks on high-speed railways is 170 kN. The control values ​​for track dynamic quality tolerances are shown in Table 8, where the control values ​​are the half-peak values ​​of the actual track irregularity amplitudes. For vehicle acceleration, vertical acceleration is judged by 20Hz low-pass filtering, and lateral acceleration of vehicle level I and II is judged by 0.5-10Hz band-pass filtering, while level III and IV is judged by 10Hz low-pass filtering.

[0168] Table 8 Permissible deviation management values ​​for 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: Figure 11 As shown in the figure, the wheel-rail vertical force is less sensitive to the settlement amplitude when the settlement wavelength is 5m and 40m. At wavelengths of 10m and 30m, the wheel-rail vertical force is highly sensitive to the settlement amplitude, significantly increasing with the settlement amplitude, but still remaining within the limit. At wavelengths of 15m and 20m, the wheel-rail vertical force exceeds the 170kN limit at larger settlement amplitudes. To ensure that the wheel-rail force does not exceed the limit, the amplitude limit is 22mm for a 15m settlement wavelength and 27mm for a 20m settlement wavelength.

[0173] The vehicle vertical acceleration is managed at level I, which is 1.0 m / s 2 , at 15m, 20m, and 30m wavelengths, the settlement limits are 14.9mm, 20.9mm, and 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 Figure 13 shown.

[0174] The relationship between vehicle acceleration and roadbed surface dynamic deformation under uneven settlement conditions is as follows: Figure 14 As shown. It can be seen that the vehicle acceleration is roughly linearly positively correlated with the dynamic deformation of the roadbed surface. Compared with the vehicle vertical acceleration under the Level I and Level II management standards, 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: Figure 15 As shown. When the camber wavelength 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 changes in the camber amplitude. As the camber amplitude increases, the wheel-rail vertical force increases significantly, but has not yet exceeded the limit. When the camber wavelength is 5m, 10m, 15m, and 20m, the wheel-rail vertical force exceeds the 170kN limit at larger camber amplitudes. To ensure that the wheel-rail force does not exceed the limit, the lower amplitude limit for the camber wavelength of 5m is 16mm, the lower amplitude limit for the camber wavelength of 10m is 18mm, the lower amplitude limit for the camber wavelength of 15m is 19mm, and the lower amplitude limit for the camber wavelength of 20m 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 respectively; 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 Figure 17 shown.

[0178] The relationship between vehicle acceleration and roadbed surface dynamic deformation under the camber condition is as follows: Figure 18 As shown. It can be seen that the vehicle acceleration is roughly linearly positively correlated with the dynamic deformation of the roadbed surface. Compared with the vehicle vertical acceleration under the Level I and Level II management standards, 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 lists the control thresholds for subgrade surface dynamic displacement. Level I dynamic quality tolerance management corresponds to the daily maintenance control state specified in the "Technical Specifications for Dynamic Acceptance of High-Speed ​​Railway Projects" (TB10761-2013), while Level II dynamic quality tolerance management corresponds to the planned maintenance control state. Different control values ​​are assigned for subgrade irregularities such as settlement and camber, but the differences between the two are not significant. In most cases, these thresholds can be considered the same: 0.20 mm for Level I control value of subgrade surface dynamic displacement, and 0.29 mm for Level II control value.

[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 this invention is to provide a design method for the stability performance of high-speed railway subgrade structures based on a dynamic stability theory framework. This method targets typical high-speed railway subgrade structure filler types, including graded crushed stone on the surface layer and coarse-grained soil on the bottom layer. Combining the long-term deformation development patterns and hysteretic energy characteristics of different fillers under train dynamics, this method establishes a critical state discrimination standard for the dynamic stability of high-speed railway subgrade fillers based on the equivalent volume dissipated energy index. A method for calculating the dynamic stability design thresholds for different filler types is proposed, and a high-speed railway subgrade structure design method flow that considers the dynamic stability performance of fillers is constructed, providing support for the design of high-speed railway subgrade structures.

[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 merely illustrate the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A high-speed railway subgrade structure design method based on dynamic stability is characterized by: Step 1: Design process begins: Define 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 type 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 layered structure. The dynamic coupling model considers the vibration coupling relationship between the vehicle, track, and filler in the vertical direction, combining the filler deformation mechanics model with the dynamic equations of the layered structure under the action of train loads. The upper part of the dynamic coupling model includes the car body, bogie, wheelset, and primary and secondary suspension. The lower part of the coupling model is the elastic-plastic deformation mechanics model of each layer of the roadbed filler. The vibration coupling and response transmission between the two are achieved by the wheel-rail contact relationship and wheel-rail force. The structural lumped parameter dynamic coupling model of each roadbed layer is a filler compaction deformation mechanics model, which consists of two parts, viscoelasticity and viscoplasticity, connected in series. The hyperbola in the form of formula (5) is selected as the load-deformation relationship of the plastic spring: （5） Where F is the load, x is the plastic spring deformation, and A and B are the two plastic parameters in the hyperbola. According to the form of the filler deformation mechanics model, the load-deformation relationship is as shown in formula (6); （6） in: （7） Where: is the load at time t; is the total strain at time t; is the elastic stiffness; is the elastic deformation at time t; is the elastic damping coefficient; is the plastic deformation at time t; is the elastic deformation rate at time t; is the plastic damping coefficient; is the plastic deformation rate at time t; The plastic deformation rate is calculated according to formula (8): （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 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: （9） （10） 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 respectively, 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, ..., nth layer of roadbed, 、 、 、 are the deformation rates of the primary and secondary suspensions, rails, supporting structures, and the i-th layer of roadbed, respectively. 、 is the elastic deformation and elastic deformation rate of the i-th layer of roadbed, is the plastic deformation of the i-th 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 respectively. 、 、 、 、 are the accelerations of the car body, bogie, wheelset, rail, track plate and supporting structure respectively, F N is the reaction force of the rail on the wheelset, F(t) is the irregularity excitation load in the design load and control conditions determined in step 2; Wheel-rail contact interaction force F s The depth is transferred downward from rails to supporting structure and then to layered roadbed, which can be expressed as: （11） 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 zero when the rail and wheelset separate from each other. （12） Considering the diffusion effect of load as the depth increases, the load-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 stiffness k of the first layer parameter element located on the surface of the subgrade e1 , damping coefficient c e1 And the relationship between the layer width d1 is: （13）； 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 dynamic response results of the subgrade layer through the dynamic coupling model; Step 6: Use the dynamic response as the first design threshold critical condition to verify the filler stability characteristics. If it meets the requirements, proceed to step 7. If not, re-adjust the design parameters of the subgrade position that does not meet the requirements 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, proceed 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 to verify that the dynamic response laws meet the design requirements. Conduct scheme comparison and optimization analysis to ultimately 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: using a plurality of wheel set train loads F(t) based on the Fourier series form, wherein the train load F(t) includes a static load and a dynamic load formed by the superposition of a series of sinusoidal functions, and each sub-item corresponds to high, medium, and low frequencies, respectively, to reflect the effects of unevenness, additional dynamic load, and rail corrugation. The expression of F(t) is: （1） is the static load of the wheel; 、 、 Each corresponds to a typical value of vibration load; Let the unsprung mass of the train be , then the corresponding vibration load amplitude is: （2） in, Corresponding to a typical sagitta; 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: （3） in, is the running speed of the train; 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 2, wherein step 4 further comprises the following: The design parameter index system includes the following three aspects: (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~L3 and irregularity amplitudes η1~η3 within three typical frequency response ranges; track irregularity related parameters including irregularity wavelength L4 and irregularity amplitude η4 caused by subgrade; (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.

4. The high-speed railway subgrade structure design method based on dynamic stability according to claim 3 is characterized by: Said step 4 further comprises 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; then, various dynamic response values ​​are obtained through iterative solution; the acceleration of each layer of the vehicle body, bogie, wheelset, rail and support structure in the model is calculated; , dynamic displacement Calculated using the following formula: （18） （19） The dynamic stress of the roadbed layer is caused by the interaction force between the layered soils 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 of the upper support structure. and length , thickness of the surface and bottom layers of the subgrade , load diffusion angle The factors are comprehensively determined; the simplified formula is: （20） Dynamic strain of roadbed layers Soil deformation through layered filling The filler thickness after discretization analysis of this layer The ratio of is related, expressed as: （21）。 5. The high-speed railway subgrade structure design method based on dynamic stability according to claim 4 is characterized in that step 5 further includes the following contents: the first design threshold is mainly based on the long-term deformation stability of each layer of subgrade filler, which needs to meet the dynamic stability state and prevent deformation accumulation during the service life, thereby ensuring the durability and stability of the subgrade structure; the dynamic stress of each layer of the subgrade is mainly based on the long-term deformation stability of each layer of the subgrade filler, which needs to meet the dynamic stability state and prevent deformation accumulation during the service life, thereby ensuring the durability and stability of the subgrade structure; , dynamic strain They should all be less than the critical dynamic stress and dynamic strain thresholds of the filler dynamic stability at the corresponding layer, as shown below: （22） （23） In the formula 、 、 are the critical thresholds of dynamic stress stability of the filler of the subgrade surface layer, subgrade layer and roadbed body layer, respectively. 、 、 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 targets; 、 、 are the confining pressures of the filler materials of the subgrade surface layer, subgrade layer and roadbed body layer, i.e. the third principal stress; CSR * is the critical cyclic stress ratio, which is related to the confining pressure of the filler, that is, the third principal stress Related, expressed as: （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 stability state as the basis for judging the critical threshold of power stability, and proposing the equivalent unit volume dissipated energy As the basic indicator for judging the critical stability of fillers, the calculation formula is: （25） Where: is the mean value of the dissipated energy per unit volume under the action of the circulation dynamics, and is the influencing term reflecting the magnitude of the dissipated energy value. The superscript d represents the influence of the circulation dynamics. is the final unit volume dissipation energy reached at the maximum vibration order m, is the dissipated energy per unit volume corresponding to the characteristic vibration order m / 10, and the term in brackets is a dimensionless influence term reflecting the upward trend of the dissipated energy.

6. 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, smooth and comfortable train operation, that is, it is necessary to control the static and dynamic irregularities of the subgrade so that the train wheel-rail force F s Not exceeding the limit, and the dynamic displacement of the roadbed surface U d The corresponding train acceleration meets the dynamic quality tolerance management values ​​of levels I and II; the specific expressions are as follows: ； ； In the formula 、 、 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 deformation stability requirements. The larger the value, the stricter the design requirement. It is determined according to different line grades, design speeds and control objectives.

7. A non-volatile storage medium, characterized in that: The non-volatile storage medium includes a stored program, wherein when the program is run, it controls the device where the non-volatile storage medium is located to execute the high-speed railway subgrade structure design method based on dynamic stability as described in any one of claims 1 to 6.

8. A high-speed railway subgrade 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 6.

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