Earth-rock mixture embankment dynamic response analysis and verification method

Abstract

The invention discloses an earth-rock mixture embankment dynamic response analysis and verification method, and belongs to the technical field of embankment stability analysis. The method comprises the steps that a pseudo-three-dimensional discrete-continuous coupling model of the earth-rock mixture embankment is established, a discrete element method is adopted to simulate discrete attributes of earth-rock mixtures, and a finite difference method is adopted to simulate pavement continuous attributes and fluid seepage characteristics; an inclined foundation, lateral penetration erosion and a particle migration effect are considered in the model; carrying out seepage-stress coupling analysis; a cyclic vehicle load and a seepage field are applied to the model, and the dynamic response of the embankment under the cyclic load and seepage coupling effect is simulated. The invention further provides a step for verifying the reasonability of the model through a field vibration test. According to the method, the internal mechanism of embankment degradation caused by rainfall erosion can be revealed more truly, and the calculation efficiency is considered.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of embankment stability analysis in civil engineering, and particularly relates to a method for analyzing and verifying dynamic response of soil-rock mixture embankment. BACKGROUND

[0002] Soil-rock mixture (SRM) is widely used as embankment filler in mountainous areas due to its high strength, low deformation and good water permeability. However, under the coupling action of cyclic vehicle load and strong rainfall seepage, uneven settlement, collapse and even instability are easily induced in long-term operation of mountain embankment.

[0003] To study this problem, the existing technology mainly adopts two types of methods: one is large-scale indoor model test (such as centrifuge test, full-size model test) or in-situ vibration test. These tests can directly reflect the response of the embankment, but they have the problems of boundary effect, high cost, long cycle and difficulty in completely reproducing complex field conditions. The second is numerical simulation method. Existing researches mainly focus on the strength reduction caused by rainfall based on continuous medium theory (such as finite element method, finite difference method (FDM)) to establish water-force coupling model. For example, patent document CN112345678A discloses a method for analyzing dynamic response of embankment, but it only uses finite element method to simulate continuous medium and does not consider the effect of particle migration. For another example, the DEM-FDM coupling model proposed by Zhang et al. (2023) in Computers and Geotechnics considers the particle behavior, but the calculation efficiency is low and it is difficult to apply to practical engineering. These models regard soil as a continuum, or consume a large amount of computing resources, making it difficult to accurately simulate the key physical process of strong rainfall erosion induced fine particle migration, loss, and the resulting change in filler gradation and mechanical property degradation.

[0004] Therefore, the existing technology cannot effectively balance the calculation efficiency and the simulation of the key mechanism of particle migration. For the dynamic response analysis of soil-rock mixed embankment under the coupling action of cyclic load-seepage, especially considering the inclined foundation condition, there is still a lack of an efficient and physically complete means. SUMMARY

[0005] The present application aims to solve the deficiencies of the existing technology in analyzing the dynamic response of soil-rock mixture embankment under the coupling action of cyclic vehicle load and rainfall seepage. Specifically, the existing technology has the following problems: Incomplete physical mechanism: numerical models based on continuous medium theory (such as finite element method) are difficult to accurately simulate the key physical process of strong rainfall erosion induced fine particle migration, loss, and the resulting change in filler gradation and mechanical property degradation.

[0006] Computational efficiency and authenticity are difficult to balance: large indoor model test or in-situ test can directly reflect the embankment response, but the cost is high, the cycle is long, and there is a boundary effect; and the high-precision three-dimensional discrete element model consumes huge computing resources, which is difficult to apply to practical engineering.

[0007] Lack of effective verification means: the existing method lacks systematic comparison and verification of field tests consistent with the geometric conditions of the numerical model, especially containing rainfall conditions, which limits the credibility and engineering guidance value of the model.

[0008] In order to solve the above technical problems, the present application is implemented as follows: The embodiment of the present application provides a soil and rock mixture embankment dynamic response analysis and verification method, comprising the following steps: Step S1: establishing a pseudo three-dimensional discrete-continuous coupled model of the soil and rock mixture embankment, wherein the discrete element method is used to simulate the discrete properties of the soil and rock mixture, and the finite difference method is used to simulate the continuous properties of the road surface and the fluid seepage characteristics; the pseudo three-dimensional discrete-continuous coupled model is constructed by distributing unit length in a two-dimensional vertical plane; Step S2: considering the inclined foundation, lateral seepage erosion and particle migration effect in the pseudo three-dimensional discrete-continuous coupled model; Step S3: performing seepage-stress coupling analysis, including flow field calculation and particle motion calculation; Step S4: applying cyclic vehicle load and seepage field in the model to simulate the dynamic response of the embankment under the coupling action of cyclic load and seepage.

[0009] Further, it further comprises step S5: verifying the rationality of the pseudo three-dimensional discrete-continuous coupled model through field vibration test, including comparing the simulation results with the measured data.

[0010] Further, in step S1, the discrete element method is realized by PFC3D software, and the finite difference method is realized by LoadFLAC3D module.

[0011] Further, in step S1, the pseudo three-dimensional discrete-continuous coupled model adopts a "wall-area" interface coupling method, and realizes real-time exchange of force and displacement data through SocketI / O interface.

[0012] Further, in step S3, the flow field calculation is based on Darcy's law and Biot's theory, and the particle motion calculation is based on Newton's second law.

[0013] Further, in step S1, the geometric size of the pseudo three-dimensional discrete-continuous coupled model is set based on the actual road section, the embankment height is 5.0m, the slope gradient is 1:1, and the cross slope gradient is 2°.

[0014] Further, in step S4, the cyclic vehicle load is simulated by rBlock, rBlock is an inverted cylinder, height 0.22m, diameter 0.5m, group spacing is 1.8m.

[0015] Further, in step S4, the initial permeability of the seepage field is set to at least one of 40kPa, 50kPa, 60kPa and 70kPa.

[0016] Further, in step S5, the field vibration test adopts SBZ30 variable frequency variable torque vibrator, and is carried out under rainfall and non-rainfall conditions, and measures pore pressure, flow velocity, vertical dynamic stress and displacement.

[0017] Further, the mesoscopic parameters and fluid-structure coupling parameters of the coupling model are calibrated through cyclic triaxial tests and seepage erosion tests.

[0018] Further, in step S3, the permeability parameters are updated through the Kozeny-Carman equation to realize dynamic adjustment of the seepage-stress coupling field.

[0019] Compared with the prior art, the present application has the beneficial effects that: 1. More complete physical mechanism: through the coupling of discrete elements and finite difference method, the stress-seepage coupling of continuous medium and the migration effect of discrete particles are considered at the same time in the analysis of embankment dynamic response for the first time, which can more truly reveal the internal mechanism of rainfall erosion leading to fine particle loss, gradation deterioration and then causing embankment deterioration, and overcome the inherent limitations of traditional continuous medium model.

[0020] 2. Model efficiency and authenticity: by constructing a pseudo three-dimensional model (assigning a unit thickness in a two-dimensional vertical plane), the actual three-dimensional embankment problem is effectively simplified under the software limitation that PFC3D only supports three-dimensional calculation, which significantly reduces the consumption of computing resources, while maintaining the authenticity of the model in key mechanical and hydraulic behaviors, providing an efficient analysis tool for engineering applications.

[0021] 3. High verification reliability: in-situ vibration tests consistent with the geometric conditions of the numerical model are used for verification, especially the field tests under rainfall conditions, which make the verification results direct and reliable, and significantly improve the credibility and engineering guidance value of the coupling model.

[0022] 4. Strong engineering practicability: The model parameters are calibrated based on cyclic triaxial tests and seepage erosion tests, and the boundary conditions are set by fully considering the actual engineering characteristics (such as inclined foundation, stress wave absorbing boundary), and the load setting covers different vehicle speeds, axle loads and overload working conditions, so that the analysis results are closer to the actual engineering, and can provide accurate and practical technical support for the design, safety evaluation and disaster prevention and control of SRM embankments of mountainous highways and railways. BRIEF DESCRIPTION OF DRAWINGS

[0023] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings. Figure 1 A fluid FDM-SRMDEM area coupling analysis model provided by the present application is shown in the figure; Figure 2 A fluid-particle coupling analysis schematic diagram based on the DEM-FDM method provided by the present application is shown in the figure; Figure 3 A barycentric interpolation scheme in the coupling calculation provided by the present application is shown in the figure; Figure 4 A typical section of a highway in hilly areas provided by the present application is shown in the figure; Figure 5 A pseudo-three-dimensional model mesh division schematic diagram provided by the present application is shown in the figure; Figure 6 A particle size distribution diagram provided by the present application is shown in the figure; Figure 7 A boundary setting diagram in the DEM-FDM coupling model provided by the present application is shown in the figure; Figure 8 A rheological component diagram of "linear pbond" provided by the present application is shown in the figure; Figure 9 A rheological component diagram of "linear" model provided by the present application is shown in the figure; Figure 10 A DYNTTS cyclic triaxial test system diagram provided by the present application is shown in the figure; Figure 11 A stress-strain hysteresis loop diagram provided by the present application is shown in the figure; Figure 12 A seepage erosion simulation test device diagram provided by the present application is shown in the figure; Figure 13 A hydraulic gradient and flow velocity relationship diagram provided by the present application is shown in the figure; Figure 14 A sensor installation schematic diagram provided by the present application is shown in the figure; Figure 15A complete time history graph before rainfall provided by the present application; Figure 16 A local time history graph before rainfall provided by the present application; Figure 17 A complete time history graph after rainfall provided by the present application; Figure 18 A local time history graph after rainfall provided by the present application; Figure 19 A vertical dynamic stress distribution contrast graph along the depth direction provided by the present application. DETAILED DESCRIPTION

[0024] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0025] The terms "first", "second", and the like in the specification and claims of the present application are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the present application can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first", "second", etc. are generally a category, and are not limited to the number of objects, for example, the first object can be one or more. In addition, "and / or" in the specification and claims indicates at least one of the connected objects, and the character " / ", generally indicates that the objects before and after are in an "or" relationship.

[0026] The embodiment of the present application provides a soil and stone mixture embankment dynamic response analysis and verification method, comprising the following steps: Step S1: a pseudo three-dimensional discrete-continuous coupling model of the soil and stone mixture embankment is established. Specifically, the discrete properties of the soil and stone mixture embankment are simulated by using the discrete element method, and the continuous properties of the road surface and the fluid characteristics of the rainwater are simulated by using the finite difference method. The pseudo three-dimensional discrete-continuous coupling model is constructed by distributing unit length in the vertical plane in the two-dimensional domain, so as to effectively approximate the three-dimensional mechanical behavior while ensuring the calculation efficiency, effectively bridge the size constraints, and maintain the calculation efficiency.

[0027] Step S2: the effects of inclined foundation, lateral seepage erosion and particle migration are considered in the pseudo three-dimensional discrete-continuous coupling model.

[0028] Step S3: Perform seepage-stress coupling analysis, which includes flow field calculation based on Darcy's law and Biot's theory, and particle motion calculation based on Newton's second law.

[0029] Step S4: Apply cyclic vehicle load and seepage field in the pseudo three-dimensional discrete-continuous coupling model to simulate the dynamic response of the embankment under the action of cyclic load-seepage coupling.

[0030] Step S5: Verify the reasonableness of the pseudo three-dimensional discrete-continuous coupling model through field vibration test, including comparing simulation results with measured data such as pore pressure, flow velocity, vertical dynamic stress and displacement.

[0031] In step S1, the discrete element method is realized by PFC3D software, and the finite difference method is realized by LoadFLAC3D module.

[0032] The finite difference method is realized by LoadFLAC3D module, and its principle is as follows: The "LoadFLAC3D" module is used for fluid-structure coupling calculation, and the description of mechanical deformation and fluid dissipation is introduced under the framework of quasi-static Biot theory. It is designed to solve single-phase seepage problems in porous media, while following Darcy's law. Assuming that the volume strain is known, the mass balance equation is replaced by the fluid intrinsic relationship. Then, an equation relating pore pressure and saturation can be introduced according to Darcy's law, as shown in formulas (1)-(9).

[0033] Fluid motion can be described by Darcy's law: (1) In the formula, is the Darcy's specific flow vector component (m / s); k ij a is the apparent hydraulic flowability coefficient tensor; P represents the pore water pressure (Pa); g k is the component of gravitational acceleration in the k th coordinate direction (m / s 2 ), used to represent the potential energy direction of fluid in the gravitational field; p w represents the density of liquid phase (kg / m 3 ); x j and x k and

[0034] For small deformation problems, the mass balance equation of fluid can be expressed as formula (2): (2) wherein, z is the volumetric flow rate; q v is the fluid volume or fluid capacity per unit volume of the porous medium; t is the time variable; x i denotes the spatial coordinate components. The momentum balance equation is given by equation (3): (3) wherein, p = (1- n ) p s + n p w is the volumetric density (kg / m 3 ); n is the grid porosity; p s denotes the density of the solid phase (kg / m 3 ); u i is the displacement component (m) representing the displacement of the medium in x i direction; s ij is the total stress tensor component (Pa) reflecting the stress distribution in each direction; g i is the component of the gravitational acceleration in the i coordinate direction (m / s 2 ) and is used to represent the overall gravitational effect on the solid-liquid mixed medium.

[0035] Saturation s determines the porosity-permeability response equation. In the fully saturated state, s = 1, the fluid can withstand a tension of up to T f (flow tension limit, representing the maximum tensile stress that the pore water can withstand in the fully saturated state). For s = 1, the response equation is given by equation (4): (4) wherein, M is the Biot modulus (Pa), α is the Biot effective stress coefficient, e is the volumetric strain.

[0036] When sWhen =1, the porosity flow characteristics are shown in equations (5)~(7).

[0037] (1) Saturation equation: (5) (2) Saturation and pore water pressure relationship: (6) where, h ( s ) is a function of saturation s , which represents the pressure head or matric suction head corresponding to the pore water under different saturation states.

[0038] (3) Relative permeability and saturation relationship: (7) where, k ij a represents the effective (unsaturated) permeability tensor under a given water content state; k ij represents the components of the intrinsic permeability (or saturated hydraulic conductivity) tensor; represents the relative permeability (dimensionless).

[0039] In the "LoadFLAC3D" module, when h ( s )=0, it corresponds to the unsaturated region, where the flow is mainly affected by gravity. This function has a specific form as shown in equation (8).

[0040] (8) The relationship between strain rate and velocity gradient is shown in equation (9): (9).

[0041] where, u i is the displacement component (m) representing the displacement of the medium in x j direction; The discrete element method is implemented through PFC3D software, and its principle is as follows: In the traditional discrete element method (DEM), the motion calculation of granular particles in bulk materials is based on Newton's second law, mainly considering the interaction between particles, fluid forces, and various volume forces, as shown in equations (10)~(11).

[0042] (10) (11) in, m i and I i Particles i Mass and moment of inertia; n i c For particles i The number of contacts; U i p and w i Particles i The advection velocity and angular velocity; F i f,p and F i g Acting on particles i Force and gravity; F ij c and M ij Particles i For particles j The contact force and rotational torque are determined by the “linear pbond” contact model (for a detailed explanation of the “linear pbond” contact model, please refer to the section on constitutive models below).

[0043] In this case, the fluid force acting on the particle (denoted as ) F i f,p Including drag force F i d and water pressure gradient force F i ▽p (Including buoyancy), as shown in formula (12): (12) The drag applied to a single particle is calculated by equation (13).

[0044] (13) In the formula, C D This is the traction coefficient, which is related to the Reynolds number Re. d P The particle diameter; U f The fluid velocity within the grid; U P Particle velocity; n1-x This is a correction factor designed to account for the influence of other particles on the drag force of the particles. C D and n 1-x The specific values ​​are shown in formula (14): (14) In the formula, m f is the fluid dynamic viscosity coefficient.

[0045] The osmotic force acting on each particle can be calculated using formula (15): (15) In the formula, r Particle size; g w This is the unit weight of water.

[0046] The buoyant force on a particle in a saturated state can be calculated using formula (16): (16) As mentioned above, the fluid-particle coupling analysis is performed in the "LoadFLAC3D" module, while the micromechanical analysis is performed in PFC3D. The key steps of the coupling analysis are summarized below (see...). Figure 1 As shown in the diagram: A boundary wall is set as a mechanical transfer interface at the contact surface between the fluid FDM region and the SRM DEM region. Specifically, the wall surface (particle boundary) in the DEM region is aligned with the surface of the adjacent continuum mesh to ensure coordinated deformation between the particle wall surface and the mesh, thereby achieving contact surface deformation. Simultaneously, feedback data of permeability parameters is obtained from the corresponding region using the overlapping area of ​​the mesh and the sphere, thereby achieving dynamic adjustment of the overall seepage-stress coupling field.

[0047] Real-time data exchange between grids and particles is mainly achieved through Figure 2 The steps shown are to be followed.

[0048] Step (1) Use the “Load” module of FLAC3D to perform an initial seepage-stress coupling solution on the entire domain at a specific time step to establish the initial seepage field and stress field.

[0049] Step (2): The pore pressure information within the FDM domain mesh is transferred to the particles surrounded by the wall within the DEM domain, and then converted into permeability force, which is applied to all particles within the wall as the input external force ① for DEM analysis. The deformation information (node ​​coordinates) of the mesh at the contact boundary within the FDM domain is assigned to the corresponding boundary wall within the DEM domain. The wall coordinates are adjusted to update the particle-boundary contact force, which is then used as the input external force ② for DEM analysis. These external forces ② are then applied to the DEM domain ensemble for detailed mechanical analysis.

[0050] Step (3) After completing the specific analysis steps in the DEM domain, obtain the force of the particles acting on the boundary wall and use it as the boundary load of the adjacent grid in the FDM domain. Obtain the real-time permeability parameters in the wall region of the DEM domain and use the Kozeny-Carman equation (see Equation (17)) to feed them back to the FDM domain grid and update the permeability parameters of the grid.

[0051] Step (4) Restart the global integrated seepage analysis using the “LoadFLAC3D” module, and repeat steps (2) to (4).

[0052] (17) In the formula, k Permeability coefficient, c is a coefficient.

[0053] The pseudo-3D discrete-continuous coupling model employs a "wall-region" interface coupling method, using a Socket I / O interface to achieve real-time exchange of force and displacement data. This interface coupling method offers higher computational efficiency than direct coupling methods. Specifically, in each calculation cycle of the Discrete Element Model (DEM) region, the force-displacement criterion is strictly applied to each contact point, following Newton's second law to precisely control the motion of individual particles. Simultaneously, the positions of particles and boundary walls are continuously updated to ensure accuracy and consistency. Unbalanced forces acting on interconnecting walls are efficiently transmitted to the Finite Element Model (FDM) region via the embedded Socket I / O interface. Upon receiving updated stresses and forces, the model iteratively calculates new velocities and displacements by invoking equilibrium (motion) equations. Subsequently, the nodal displacements within the coupling region are converted into new displacement boundary conditions via the Socket I / O interface. This process drives the displacement of particles within the discrete domain, enabling seamless iteration calculation cycles.

[0054] It must be emphasized that the mechanical calculations in the coupled analysis must employ a large deformation mode, and the coupling and importing walls must be finely meshed using triangular elements. Assume the particle establishes contact with the triangular wall, denoted as C. CP i This represents the point on the wall closest to point C. From...CP i To reach the vertices of the triangle, extrapolation is performed using centroid interpolation, such as... Figure 3 As shown, where, V 1 (i) , V 2 (i) and V 3 (i) These represent the three vertices of the triangle. A 1. A 2 and A 3 represents the area of ​​the triangle corresponding to these vertices. Centroid weighted term. w i Defined as w i = A i / A ,in A i Indicates the relationship with vertex V i The area of ​​the corresponding triangle, A Let represent the total area of ​​the triangle. R 1. R 2. R 3 is CP i Vectors to the three vertices F 1. F 2. F 3 represents the force acting on the node. F This represents the force applied at contact point C. M b This represents the torque generated by adhesion at contact point C.

[0055] The geometric dimensions of the pseudo-three-dimensional discrete-continuous coupled model are set based on the actual embankment cross section, with an embankment height of 5.0m, a slope of 1:1, and a cross slope of 2°.

[0056] In step S3, the permeability parameters are updated using the Kozeny-Carman equation to achieve dynamic adjustment of the seepage-stress coupling field.

[0057] The flow field calculation is based on Darcy's law and Biot's theory, and the particle motion calculation is based on Newton's second law.

[0058] In step S4, the cyclic vehicle load is simulated by rBlock, which is an inverted cylinder with a height of 0.22m, a diameter of 0.5m, and a group spacing of 1.8m.

[0059] The initial permeability intensity of the seepage field is set to at least one of 40 kPa, 50 kPa, 60 kPa, and 70 kPa.

[0060] In step S5, the field vibration test is conducted using an SBZ30 variable frequency and variable torque vibrator under both rain and non-rain conditions, measuring pore pressure, flow velocity, vertical dynamic stress, and displacement.

[0061] The method also includes calibrating the microscopic parameters and fluid-structure interaction parameters of the coupled model through cyclic triaxial tests and permeation erosion tests.

[0062] The following is a detailed description of a method for dynamic response analysis and verification of soil-rock mixture embankments provided by the present invention, using specific embodiment 1 as an example.

[0063] Example 1 provides a method for dynamic response analysis and verification of soil-rock mixture embankments, specifically including: Step 1: Establish a pseudo-3D FDM-DEM coupled model First, determine the geometric dimensions of the target embankment. Using a typical cross-section of the hilly area of ​​the Hangzhou Second Ring Road project in Zhejiang Province, China, as an example, such as... Figure 4 As shown. The embankment is constructed on a sloping limestone foundation with a gradient of 2°. The embankment is 5.0m high, the upper road surface is 33.5m wide, and the slope is 1:1. The road surface structure, from bottom to top, consists of a 0.20m thick 4% cement-stabilized crushed stone subbase, a 0.34m thick 5% cement-stabilized crushed stone base course, and an asphalt layer with a total thickness of 0.18m (from top to bottom: 0.04m SMA-13, 0.06m Sup-25, 0.08m Sup-20).

[0064] Secondly, a pseudo-3D numerical model was constructed. The geometric contour of the embankment cross-section was drawn using Rhino software (version 7.0) and its plugin Gridle (version 2.00.12). Since this invention aims to study the embankment response within a two-dimensional plane strain problem framework, but the PFC3D software used only supports three-dimensional calculations, a unit thickness of 0.5m was set in the y-direction perpendicular to the two-dimensional cross-section to construct a pseudo-3D model, as shown below. Figure 5 As shown. In Gridle, irregular 8-node hexahedral meshes are generated for the pavement structure layer (physical unit region) and the SRM embankment fill region (fluid mesh region), and the mesh is refined for the "wall-zone" coupling interface region and the slope infiltration region. The generated mesh models are then imported into the PFC3D and "LoadFLAC3D" modules to generate the corresponding discrete element particles and finite difference meshes.

[0065] In PFC3D, spherical elements are used to simulate SRM filler particles. To balance calculation accuracy and efficiency, the original gradation particles are subjected to isocyanate analysis. u C c Magnification, minimum particle size after magnification d min The maximum particle size is 1.0 mm. dmax The uniformity coefficient C is 20mm. u =7.47, curvature coefficient C c =2.29, compared to the original gradation (C u =7.49, C c =2.31) is basically consistent, so the gradation characteristics can be considered not significantly affected. The particle size distribution is as follows: Figure 6 As shown.

[0066] Step 2: Set model boundary conditions and constitutive parameters Boundary condition settings, such as Figure 7 As shown: The bottom of the embankment is made of rigid, impermeable limestone, and is designed with fixed displacement boundaries (no vertical displacement) and impermeable boundaries.

[0067] The junction between the embankment and the road surface is designed as an impermeable boundary.

[0068] The short slope (infiltration side) is set as the seepage boundary, with an initial saturation of s=1.

[0069] The long slope (seepage side) is set as the seepage boundary, with an initial saturation of s=0.

[0070] To eliminate the reflection of dynamic stress waves at the side boundaries, a viscous damped free field boundary is set at the side boundary of the FDM region; and a viscoelastic artificial boundary is set at the side boundary of the DEM region for the particles in contact with the sidewall.

[0071] The constitutive model and parameter settings are as follows: FDM region (pavement structure layer): Assumed to be a homogeneous elastic material, following the generalized Hooke's law, and with Rayleigh damping. The corresponding parameters can be derived using formulas (18)~(20): (18) (19) (20) In the formula, E It is the elastic modulus; m Poisson's ratio; E s It is the compressibility modulus; K Bulk modulus; G The shear modulus is given. Rayleigh damping is specified for the FDM region (see Equation (21)).

[0072] (twenty one) In the formula, [ C [ is the damping matrix;] M ] is the mass matrix; [ K [ ] represents the stiffness matrix;α Let be the mass damping constant; β Here is the stiffness damping constant; α and β Each with the system's natural frequency w i and w j and the corresponding damping ratio x i and x j Related. Let. x i = x j = x (Dynamic local damping), then α and β It satisfies equation (22).

[0073] (twenty two) Specific parameters are given in Table 1, including the thickness of each layer of material. h ,density p Elastic modulus E bulk modulus K shear modulus G Poisson's ratio m and damping coefficient α and β .

[0074] Table 1 Constitutive Model Parameters In the Discrete Element Model (DEM) region, the contact between spheres is described using a "linear p-bond" model, while the interaction between particles and the wall is described using a "linear" model. Furthermore, local damping coefficients are assigned to the particles (see...). Figure 8 and Figure 9 ).

[0075] Parameter calibration The "linear pbond" contact model and local damping parameters were calibrated using the GDSDYNTTS system through cyclic triaxial tests (see...). Figure 10 (As shown). The diameter of the triaxial specimen used in the experiment. d It is 100mm high. h The minimum particle size was set to 200 mm, and the original particle size of the SRM was adjusted to address size effects and improve computational efficiency. Specifically, for this modification, a minimum particle size of 200 mm is recommended. d min The maximum particle size is 1.0 mm. d max 20mm h / dmax =5), such as Figure 9 (Minimum particle size) is shown. It is worth noting that C before and after the modification... c and C u The values ​​remain unchanged, meaning the effect of the modification is negligible. The loading frequency is set to 5.0 Hz, the confining pressure to 30 kPa, and the cyclic deviation stress amplitudes to 40, 60, and 80 kPa, respectively. Figure 11 The dynamic stress-strain curves of experimental and simulation results were compared under three different amplitude cyclic deviation stresses.

[0076] The initial permeability coefficient of the original graded SRM was determined using a permeation erosion test apparatus (see...). Figure 12 (As shown). Compacted saturated SRM specimens with optimum moisture content were subjected to permeation erosion tests under different gradient pressures. The resulting pore water pressure, water flow rate, and duration of the erosion process were measured, and the permeability coefficient of the specimens was calculated accordingly (see...). Figure 13 (As shown). The mesoscopic parameters and fluid-structure interaction parameters of the contact model are detailed in Tables 2-3.

[0077] Table 2. Microscopic parameters of particles in the DEM region Table 3 Fluid-structure Interaction Calculation Parameters in the FDM Region Step 3: Simulation Process – Applying Seepage Field and Circulating Vehicle Load 1. Applying a seepage field: Apply hydrostatic pressure vertically to the short slope of the embankment model to simulate heavy rainfall infiltration. The fluid is considered to be incompressible and isotropic. The short slope is set as the saturated infiltration boundary (…). s =1), the long slope is an unsaturated seepage boundary ( s =0), forming a hydraulic gradient within the embankment and establishing a free seepage field. Based on Darcy's law and measured parameters, the initial seepage erosion intensity corresponding to 24-hour rainfall intensities of 3.1250–7.2875 mm / h was calculated. The range is 35.736–83.337 kPa (calculated using formula 23 below).

[0078] (twenty three) In the formula, p 0 represents the penetration erosion intensity (kPa); p w The density of water is taken as 1000 kg / m³; g The acceleration due to gravity is taken as 9.81 m / s². 2 ; I Rainfall intensity (mm / h); t 0 represents the duration of rainfall, taken as 24 hours;h For an effective infiltration rate, the present invention preferably uses 0.85; k The permeability coefficient of the SRM specimen is calculated to be approximately 0.012642 m / s.

[0079] In the simulation, select p The working conditions were analyzed at four levels: 40, 50, 60, and 70 kPa. When the system reached a critical state (particles on the short slope were on the verge of erosion, and particles on the long slope may have begun to migrate), the application of seepage force was stopped.

[0080] 2. Apply cyclic vehicle load: Two sets of rBlocks are placed on the upper road surface of the model to simulate truck tires. Each rBlock is an inverted cylinder with a height of 0.22m and a diameter of 0.5m. The two sets of rBlocks are spaced 1.8m apart, with the center of the first set located at... x At a distance of 12.185m, the second group is located x =28.935m. Cyclic loads are applied to rBlock according to vehicle dynamics formulas (24)-(26).

[0081] (twenty four) (25) (26) In the formula, P 0 represents the static load on the wheel (kN); P dmax The amplitude of the vibration load (kN); w The angular frequency of vibration (Hz); M 0 represents the unsprung mass (120 N·s) 2 / m); h 0 represents the geometric irregularity height (0.2 mm); v Speed ​​(km / h); L The wavelength of the geometric curve is 6m; t It is a time variable.

[0082] The load settings are shown in Table 4. The axle load is set at 100kN. In current design specifications, the load borne by a single tire is... P 0 represents 50 kN. Key variables include axle load (single tire static load). P 0 represents 50, 55, 60, and 65 kN, corresponding to overload rates of 0%, 10%, 20%, and 30%, respectively, and vehicle speed ( v (Using speeds of 100, 110, 120, and 150 km / h) and initial permeability. p 0.

[0083] Table 4 Load settings for this simulation Step 4: Model Validation To verify the accuracy of the established pseudo-3D coupled model, a field vibration test was conducted. The test embankment cross-section was consistent with the numerical model. The SBZ30 variable frequency and torque vibrator developed by the China Academy of Railway Sciences was used as the excitation source, mounted on a counterweight to simulate tire contact (two rectangular contact surfaces, 1.8m apart). Eight dynamic earth pressure cells were embedded within the embankment. Figure 14 Vertical dynamic stress was monitored in four layers (depths of 0m, 0.9m, 1.7m, and 2.5m).

[0084] The test was conducted under two operating conditions: Non-rainfall conditions: Tested after 7 consecutive days without rainfall.

[0085] Rainfall conditions: The average rainfall intensity is 4.58 mm / h (corresponding to...) p The test was conducted after 2 days (0=52.375kPa).

[0086] In both operating conditions, a vibration load of 10t and 13.7Hz was applied to simulate the passage of a truck with an axle load of 100kN and a speed of 100km / h.

[0087] Verification results Figure 15~Figure 18 The time-history curves of vertical dynamic stress at sensor 5 before and after rainfall are shown. During rainfall, the vertical dynamic stress amplitude at location 5 was approximately 15.8 kPa, slightly higher than the 13.7 kPa recorded without rainfall. The waveforms indicate that fluctuations in non-significant peaks were more pronounced during rainfall than without rainfall. The increase in vertical dynamic stress amplitude and the enhancement of waveform fluctuations during rainfall can be attributed to changes in moisture content, interparticle interactions, and pore pressure effects. Rainfall increases soil moisture, thereby altering soil mechanical properties and redistributing stress. Furthermore, rainfall may reduce interparticle friction and alter interaction modes, leading to changes in the propagation velocity and amplitude of stress waves. The effects of water flow and pore pressure further enhance the sensitivity of the stress response, especially in the non-significant peak region, resulting in intensified waveform fluctuations.

[0088] Figure 19 The vertical dynamic stress distribution inside the SRM embankment was summarized under two conditions: 10t-13.7Hz vibration load (with and without rainfall) and simulated load of 100kN~100km / h (corresponding to seepage erosion intensity). p(0 is 52.375 kPa). It can be seen that under both rainfall (seepage erosion) and non-rainfall (no erosion) conditions, the vertical dynamic stress amplitude at shallow locations varies relatively little, but gradually increases along the depth direction. Furthermore, in the absence of rainfall (no seepage erosion), the difference in vertical dynamic stress amplitude obtained from vibration tests and pseudo-3D simulations at different locations does not exceed 26.8%. Conversely, under rainfall (seepage erosion) conditions, the maximum difference in vertical dynamic stress amplitude obtained by the two methods reaches 44.5%. The observed differences may be attributed to the high complexity of the seepage field inside the SRM embankment under actual rainfall conditions. In contrast, the seepage field constructed by the pseudo-3D model represents an idealized scenario and cannot completely replicate real-world conditions. However, regardless of whether seepage erosion (rainfall) occurs, the vertical dynamic stress amplitudes at various locations inside the embankment obtained through numerical simulation and field vibration tests remain within the same order of magnitude. Therefore, the pseudo-3D response model can provide a more realistic characterization within the allowable error range.

[0089] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0090] Furthermore, it should be noted that the scope of the methods and systems in the embodiments of the present invention is not limited to performing functions in the order shown or discussed, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. In addition, features described with reference to certain examples may be combined in other examples.

[0091] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of the present invention.

Claims

1. A method for dynamic response analysis and verification of soil-rock mixture embankments, characterized in that, Includes the following steps: Step S1: Establish a pseudo-three-dimensional discrete-continuous coupled model of soil-rock mixture embankment, wherein the discrete element method is used to simulate the discrete properties of soil-rock mixture, and the finite difference method is used to simulate the continuous properties of pavement and fluid seepage characteristics; the pseudo-three-dimensional discrete-continuous coupled model is constructed by allocating unit lengths in a two-dimensional vertical plane; Step S2: Consider the effects of tilted foundation, lateral seepage erosion, and particle migration in the pseudo-three-dimensional discrete-continuous coupling model; Step S3: Perform seepage-stress coupling analysis, including flow field calculation and particle motion calculation; Step S4: Apply cyclic vehicle loads and seepage fields to the model to simulate the dynamic response of the embankment under the coupled action of cyclic loads and seepage.

2. The method as described in claim 1, characterized in that, It also includes step S5: verifying the rationality of the pseudo-three-dimensional discrete-continuous coupling model through field vibration tests, including comparing the simulation results with the measured data.

3. The method as described in claim 1, characterized in that, In step S1, the discrete element method is implemented using PFC3D software, and the finite difference method is implemented using the LoadFLAC3D module.

4. The method as described in claim 1, characterized in that, In step S1, the pseudo-three-dimensional discrete-continuous coupling model adopts the "wall-region" interface coupling method and realizes real-time exchange of force and displacement data through the SocketI / O interface.

5. The method as described in claim 1, characterized in that, In step S3, the flow field calculation is based on Darcy's law and Biot's theory, and the particle motion calculation is based on Newton's second law.

6. The method as described in claim 1, characterized in that, In step S1, the geometric dimensions of the pseudo-three-dimensional discrete-continuous coupled model are set based on the actual embankment cross section, with an embankment height of 5.0m, a slope ratio of 1:1, and a cross slope of 2°.

7. The method as described in claim 1, characterized in that, In step S4, the cyclic vehicle load is simulated by rBlock, which is an inverted cylinder with a height of 0.22m, a diameter of 0.5m, and a group spacing of 1.8m.

8. The method as described in claim 1, characterized in that, In step S4, the initial permeability intensity of the seepage field is set to at least one of 40 kPa, 50 kPa, 60 kPa and 70 kPa.

9. The method as described in claim 1, characterized in that, In step S5, the field vibration test is conducted using an SBZ30 variable frequency and variable torque vibrator under both rain and non-rain conditions, measuring pore pressure, flow velocity, vertical dynamic stress, and displacement.

10. The method as described in claim 1, characterized in that, It also includes calibrating the microscopic parameters and fluid-structure interaction parameters of the coupled model through cyclic triaxial tests and permeation erosion tests.

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