A numerical simulation method for fluid-solid coupling of surface water and soft soil subgrade soil

Abstract

The present invention discloses a fluid-solid coupling numerical simulation method for the coupling of surface water and soft soil subgrade soil, including: setting the simulation time and time step, and inputting the collected surface water data and the physical property parameters of the subgrade soil into the simulation model; establishing the coupling action equation of surface water and soil: describing the movement of surface water through the Stokes equation including boundary conditions, describing the soil through the Biot equation, and coupling the Stokes equation and the Biot equation through the interface condition to obtain a coupling system; constructing the Robin boundary condition, and reconstructing and decoupling the coupling system through the Lagrangian-Eulerian method; ending the simulation when the simulation time is reached, and outputting the deformation displacement, seepage flow pressure and seepage flow velocity of the subgrade for judging the stability of the subgrade. The present invention solves the problems of difficulty in judging the stability according to the coupling action of surface water and soft soil subgrade and consuming a large amount of resources.

Description

Technical Field

[0001] The present invention relates to the technical field of fluid - solid coupling numerical simulation, and particularly to a fluid - solid coupling numerical simulation method for the coupling of surface water and soft soil subgrade soil. Background Technique

[0002] Regions dominated by saturated soft clay deposits are called soft soil regions, and soft soil includes saturated soft clay and silt. There is generally extensive distribution of soft soil along coasts, lakes, and rivers. When building roads on soft soil foundations, problems such as embankment instability or excessive settlement are likely to occur; in heavy rainfall weather, long - term rainwater scouring can also cause waterlogging of the subgrade, thereby reducing the service strength of the subgrade. When the bearing capacity of the subgrade decreases, accidents such as road surface subsidence and collapse may occur. Therefore, in - depth understanding of the coupling effect of surface water and soft soil subgrade has important practical significance for guiding road construction and preventing disasters. In existing research, it mainly focuses on measuring the water depth on the road surface, pays less attention to the profound impact of seepage water on the stability of the road surface structure, and ignores that the accumulation of long - term seepage water may lead to subgrade softening, road surface subsidence, and even serious safety hazards such as subgrade collapse; moreover, existing technologies generally require direct experiments with a large amount of materials and special experimental equipment, collect a large amount of data, consume a large amount of funds and human resources, and although existing monitoring equipment (such as lidar, water level sensors, video monitoring) can obtain the water depth and distribution on the road surface, it is difficult to directly obtain data on underground seepage water, unless measured by destructive ground excavation, which further damages the soft soil subgrade. Therefore, it is crucial to develop a fluid - solid coupling numerical simulation method for the coupling of surface water and soft soil subgrade soil. Summary of the Invention

[0003] (I) Technical Problems to be Solved

[0004] Based on the above problems, the present invention provides a fluid - solid coupling numerical simulation method for the coupling of surface water and soft soil subgrade soil, which solves the problems of difficulty in stability judgment based on the coupling effect of surface water and soft soil subgrade and the consumption of a large amount of resources.

[0005] (II) Technical Solutions

[0006] Based on the above - mentioned technical problems, the present invention provides a fluid - solid coupling numerical simulation method for the coupling of surface water and soft soil subgrade soil, including the following steps:

[0007] S1. Set the simulation time T and the time step Δ t , the current time t is initially 0, and the average water level height h 0 of the collected surface water and the water surface velocity v, and the physical property parameters of the subgrade soil are input into the simulation model. The physical property parameters of the subgrade soil include: the lame constant of the flexible vegetation μ s and λ s , the constrained unit storage coefficient C 0, the permeability tensor κ , the foundation density ρ p and the Beavers-Joseph condition coefficient α BJ ;

[0008] S2. Establish the coupling equation between surface water and soil;

[0009] S21. According to the fact that the viscous force, pressure gradient and body force of the fluid conform to the law of conservation of momentum, and the inflow and outflow of the fluid conform to the law of conservation of mass, construct the Stokes equation including boundary conditions to describe the movement of surface water;

[0010] S22. Take the soil as a poroelastic model. According to the elastic equation of the poroelastic model, and the law of conservation of mass that the change rate of the volume of the poroelastic medium is equal to the divergence of the seepage fluid velocity and the linear relationship between the seepage velocity of water in the saturated soil and the pressure gradient, combined with the physical property parameters of the subgrade soil, construct the Biot equation to describe the soil;

[0011] S3. Construct the Robin boundary condition, and reconstruct and decouple the coupling system by the Lagrangian-Euler method;

[0012] S4. Judge whether the current time t is greater than or equal to the set simulation time T . If so, the simulation ends and proceeds to step S5. Otherwise, t = t +Δ t , and return to step S3;

[0013] S5. End the simulation and output the deformation displacement , the seepage flow pressure and the seepage flow velocity u p for judging the stability of the subgrade.

[0014] Furthermore, in S3, for the Robin condition, it is discretized in time, and the backward Euler discretization is used for the coupling system. The following discrete system is obtained at each moment:

[0015] The reconstructed Biot equation obtained:

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022] The equations of the Lagrangian-Eulerian method include:

[0023]

[0024]

[0025]

[0026] The obtained reconstructed Stokes equations:

[0027]

[0028]

[0029]

[0030] Wherein, is the ALE mapping, ω f is the ALE velocity, and all superscripts n +1 represents the quantity at the n +(1)th step, and all superscripts n represent the quantity at the n th step.

[0031] Furthermore, in S5, the calculation formula for the stability of the roadbed is:

[0032]

[0033] Wherein, S is the stability score, and a, b, and c are the weight coefficients of the deformation displacement, seepage flow pressure, and seepage flow velocity respectively, are the maximum allowable values of the deformation displacement, seepage flow pressure, and seepage flow velocity respectively; the higher the stability score, the worse the stability of the roadbed.

[0034] Furthermore, if the stability score exceeds the set stability score threshold, the roadbed needs to be reinforced or repaired.

[0035] Furthermore, in S5, the fluid velocity uf and fluid pressure p f 。

[0036] Furthermore, in S3, the ranges of L1, L2, and L3 are 500 - 2000.

[0037] (III) Beneficial Effects

[0038] The above technical solutions of the present invention have the following advantages:

[0039] (1) The present invention numerically simulates the mutual coupling effect between surface water seepage and soft soil subgrade soil, and outputs the deformation displacement, seepage flow pressure, and seepage flow velocity related to the subgrade stability, analyzes the influence of seepage water on the subgrade structure stability, provides scientific guidance and decision-making support for road design, construction optimization, and disaster prevention, and has important practical significance for ensuring road safety and extending road service life; moreover, the present invention only needs to obtain the average water level height and water surface velocity of surface water that are simple and easy to obtain, and can work by using computer simulation. The data acquisition is simple and convenient, reduces the difficulty of judging the stability according to the coupling effect between surface water and soft soil subgrade, and saves equipment cost and labor cost;

[0040] (2) The present invention decouples the fluid-elastic subgrade by the Lagrangian-Euler method, enabling the coupling system established by the present invention to be discretely decoupled in time and overcoming the difficulty of decoupling according to the coupling system. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The features and advantages of the present invention will be more clearly understood by referring to the accompanying drawings. The drawings are schematic and should not be construed as limiting the present invention in any way. In the drawings:

[0042] Figure 1 is a schematic flow chart of the fluid-solid coupling numerical simulation method for the coupling of surface water and soft soil subgrade soil in an embodiment of the present invention;

[0043] Figure 2 is a simulation interface diagram of the original surface water and subgrade in an embodiment of the present invention;

[0044] Figure 3 is a simulation interface diagram of the deformation result of the subgrade in an embodiment of the present invention;

[0045] Figure 4 is a simulation interface diagram of the movement trajectory of surface water in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] The following will further describe in detail the specific embodiments of the present invention in conjunction with the drawings and embodiments. The following embodiments are used to illustrate the present invention but are not used to limit the scope of the present invention.

[0047] An embodiment of the present invention is a fluid-solid coupling numerical simulation method for the coupling of surface water and soft soil subgrade soil. As Figure 1 shown, it includes the following steps:

[0048] S1. Set the simulation time T and the time step Δ t . The current time t is initially 0. The data input into the simulation model includes: the average water level height h 0 of the surface water and the water surface velocity v , as well as the physical property parameters of the subgrade soil: the lame constants μ s and λ s of the flexible vegetation, the unit storage coefficient C 0 of the constraint, the permeability tensor κ , the foundation density ρ p and the Beavers-Joseph condition coefficient α BJ ;

[0049] S2. Establish the coupling equation of surface water and soil:

[0050] S21. According to the fact that the viscous force, pressure gradient and volume force of the fluid conform to the law of conservation of momentum, and the inflow and outflow of the fluid conform to the law of conservation of mass, construct the Stokes equation including boundary conditions to describe the movement of surface water:

[0051] And

[0052] The boundary conditions are:

[0053] Among them: σ f represents the stress of the fluid, represents the strain tensor of the fluid, ρ f represents the density of the fluid, μ f represents the viscosity coefficient of the fluid, u f represents the fluid velocity, p f represents the fluid pressure, f f represents the source term, such as gravitational force or other volume forces, which is user-defined, represents the gradient operator, represents the σ f divergence ofI represents the identity matrix, represents the region where the fluid is located, which is related to the current moment t and changes continuously with time. The upper surface (water surface) of the fluid calculation region is Г1, and it is assumed that the water surface velocity v flows from left to right. Denote the left surface as Г2 and the right surface as Г3 (if the flow velocity is opposite, swap the labels of the left and right surfaces). In the boundary conditions, the fluid velocity u f is a vector function. Here, it is assumed that there is only a horizontal flow component on the upper boundary and no vertical velocity component; y refers to the ordinate of each point on Г2, indicating that the velocity at the left end boundary is related to the depth in the water and is in the shape of a parabola; h 0 is the average height of the initial water level of the input quantity, v is the water surface velocity of the input quantity. A free boundary condition is applied on the right side, n Г3 represents the unit outer normal vector of this surface.

[0054] The Stokes equation is a simplified version of the Navier - Stokes equation after neglecting the inertial term. It is applicable to low - Reynolds - number flows and is suitable for describing the motion of surface free flows. The Stokes equation is a system of equations consisting of two equations. Among them, the first equation is the momentum equation, which represents that the fluid flow conforms to the law of conservation of momentum, and there is a dynamic equilibrium relationship among viscous forces, pressure gradients, and body forces; the first term of the equation is the transient inertial term, which characterizes the dynamic inertial effect of the momentum of fluid micro - elements changing with time. When the flow velocity field has significant time - dependence, this term reflects the rate of change of momentum corresponding to the acceleration of fluid micro - elements; the second term of the equation is the divergence term of the stress tensor, which represents the net surface force per unit volume. This term contains two core contributions: one is the pressure stress term, and the negative gradient direction of ∇ represents the stress that drives the fluid to flow from the high - pressure area to the low - pressure area; the other is the viscous stress term, which describes the viscous dissipation of the fluid's resistance to deformation and reflects the shear stress diffusion effect caused by the velocity gradient inside the fluid. The viscous resistance generated by the molecular momentum transfer between fluid layers is quantified in this term. The second - order spatial derivative of the velocity field ( ) reflects the intensity of the viscous drag effect of the fluid micro - element by adjacent fluid layers. The greater the dynamic viscosity μ, the more significant the blocking effect of the viscous force on the flow. The right - hand side of the equation is the body - force term, which can be used here to represent the action of gravity on the fluid and is generally expressed as f f = rho*g, where rho is the fluid density and g is the acceleration due to gravity.

[0055] The second equation is the continuity equation, indicating that the fluid obeys the law of conservation of mass. The divergence of the velocity field being zero represents an incompressible fluid, meaning that the mass flux of the fluid flowing into and out of any control volume is strictly balanced, reflecting the characteristic that the volume of fluid parcels remains unchanged during motion.

[0056] S22. Consider the soil as a poroelastic model. According to the elastic equation of the poroelastic model, and the law of conservation of mass where the rate of change of the volume of the poroelastic medium is equal to the divergence of the seepage fluid velocity and the linear relationship between the seepage velocity of water in the saturated soil and the pressure gradient, combined with the physical property parameters of the subgrade soil, construct the Biot equation to describe the soil:

[0057] For the soil part, consider it as an elastic porous medium region and describe it by the Biot equation:

[0058] while

[0059] where: σ p represents the stress tensor of the dense elastic vegetation area, ρ p represents the foundation density, μ s , λ s represents the lame constant of the flexible vegetation, C 0 represents the constrained unit storage coefficient, α represents the Biot-Willis constant of the model, κ represents the permeability tensor, represents the deformation displacement, represents the seepage flow pressure, u p represents the seepage flow velocity, f s represents the source term of the elastic equation, Ω p represents the soil calculation area, independent of the current time t independent.

[0060] The Biot equation, also known as the poroelastic model, is used to describe the interaction between the fluid and the matrix deformation in the porous medium. It is a system of equations consisting of three equations. The third equation is the famous Darcy's theorem, which is used to describe the linear relationship between the seepage velocity of water in the saturated soil and the pressure gradient, also known as the linear seepage law.

[0061] The first equation is the elastic part of the Biot equation. Since the transient changes between the two are studied in fluid-structure interaction, we need to retain the second-order time derivative of the elastic deformation in the elastic equations (neglecting the second-order time derivative, the Biot equation becomes a quasi-static equation, which is usually used in separate poroelastic problems), that is, the first term of the equation. The second term is the divergence of the stress in the poroelastic medium, which describes the resultant force acting on the solid microelement due to the non-uniform stress distribution. The stress term mainly consists of two parts, represents the Cauchy stress tensor, and the relationship between deformation and stress of conventional linear elastic materials is described by this formula. In the poroelastic model, the fluid in the medium also exerts a force on the matrix. Here, we use the seepage pressure to measure it, resulting in term. The right side of the equation is the body force, which can be used here to represent the action of gravity on the matrix.

[0062] The second equation is called the Darcy equation, which is also the mass conservation equation. Assuming constant density, the rate of change of the volume of the entire poroelastic medium is equal to the divergence of the seepage fluid velocity. Among them, the in the first term represents the increment of the fluid unit volume and the solid unit volume. Taking the derivative with respect to time represents the rate of change of the increment of the fluid unit volume and the solid unit volume per unit time. The second term combined with Darcy's law is the velocity of the seepage fluid.

[0063] S23. Couple the Stokes equation and the Biot equation through the interface conditions to obtain a coupled system:

[0064]

[0065] Among them, n Гfp represents the unit normal vector of the interface, τ Гfp represents the unit tangent vector of the interface, α BJ is the Beavers-Joseph condition coefficient.

[0066] S3. Construct the Robin boundary condition and reconstruct and decouple the coupled system through the Lagrangian-Eulerian method;

[0067] The above Stokes equation holds in the Eulerian coordinate system, and the Biot equation holds in the Lagrangian coordinate system. Under the action of the fluid stress, elastic deformation will occur in the subgrade area, resulting in a change in the fluid calculation area (that is, is related to time). However, the Biot equation holds in the Lagrangian coordinate system, and its physical quantities such as elastic displacement are expressed by the function values on a fixed area (that is, Ωp independent of time). The governing equations of the two physical processes hold in different coordinate systems and are coupled together through a common interface, which brings great difficulties to the solution by traditional numerical methods, such as the time derivative in the fluid equation cannot be discretized properly. To overcome these difficulties, we consider designing a fluid-elastic subgrade decoupling algorithm based on the Arbitrary Lagrangian-Eulerian (ALE) method. The basic idea of the ALE method: In order to be able to discretize the time derivative on a time-varying region consider a fixed reference region such as the initial region) to the time-varying region construct a family of mappings and define the mesh deformation velocity:

[0068]

[0069]

[0070] which is the ALE mapping. Based on this, define the ALE time derivative:

[0071]

[0072] Substitute it into the Stokes equation to obtain the ALE form of the Stokes equation (in the reference coordinate system):

[0073]

[0074] where ω f is the ALE velocity.

[0075] To solve the above coupling problem, construct 5 Robin boundary conditions to reconstruct the above coupling system, so that the whole coupling system is completely decoupled:

[0076]

[0077] where the interface term function R 1, R 2, R 3, R 4, R 5 is:

[0078]

[0079] where, L 1, L 2, L 3 are Robin parameters, recommended to be in the range of 500 - 2000; n p represents the unit normal vector of the interface; ξDenotes the deformation velocity, i.e., the time derivative of the deformation displacement; ; P f Denotes the projection operator of the fluid region; P p Denotes the projection operator of the Biot region; u Denotes the fluid velocity; τ f,j Denotes the unit tangent vector of the interface of the fluid region; j Denotes the subscript. For two-dimensional problems, there is only one tangent vector, while for three-dimensional problems, there are tangent vectors in two directions. Therefore, j in two dimensions, it only takes 1, while in three dimensions, it can take 1 and 2; d Denotes the dimension, which can be two-dimensional or three-dimensional; Г denotes the interface;

[0080] For the above Robin condition, we discretize in time and use backward Euler discretization for the entire system to obtain the following discrete system at each time step:

[0081] The reconstructed Biot equation for the subgrade region:

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] The ALE equation:

[0089]

[0090]

[0091]

[0092] The reconstructed Stokes equation for the fluid region:

[0093]

[0094]

[0095]

[0096] Among them, all superscripts n +1 represents then The quantity of +1 step n represents the quantity of the n step.

[0097] By successively solving the above three equations at each moment t the simulation of the coupled action between groundwater and subgrade can be completed.

[0098] S4. Determine whether the current moment t is greater than or equal to the set simulation time T . If so, the simulation ends and step S5 is entered; otherwise t = t +Δ t , and return to step S3;

[0099] S5. End the simulation and output the deformation displacement , seepage flow pressure and seepage flow velocity u p of the subgrade to judge the stability of the subgrade.

[0100] As Figure 2 shown, the original surface water and subgrade are presented. The notch on the subgrade represents the pothole; as Figure 3 shown, the deformation result of the simulated subgrade is presented. The arrow represents the deformation direction; as Figure 4 shown, the movement trajectory of the simulated surface water is presented. The arrow represents the movement direction of the surface water.

[0101] The calculation formula for the stability of the subgrade is:

[0102]

[0103] where S is the stability score, a, b, and c are the weight coefficients of the deformation displacement, seepage flow pressure, and seepage flow velocity respectively are the maximum allowable values of the deformation displacement, seepage flow pressure, and seepage flow velocity respectively; the higher the stability score, the worse the stability of the subgrade. If the set stability score threshold is exceeded, the subgrade needs to be reinforced or repaired.

[0104] In addition, the fluid velocity u f and fluid pressure p f can also be output for the monitoring of surface water.

[0105] Finally, it should be noted that the above numerical simulation method can be converted into software program instructions, which can be implemented by running a numerical simulation system including a processor and a memory, or can be implemented by computer instructions stored in a non-transitory computer-readable storage medium. The integrated unit implemented in the form of a software functional unit can be stored in a computer-readable storage medium. The above software functional unit is stored in a storage medium, including several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor to execute some steps of the methods described in the embodiments of the present invention. The foregoing storage medium includes: various media such as USB flash drives, external hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical discs that can store program codes.

[0106] In summary, through the above fluid-solid coupling numerical simulation method for the coupling of surface water and soft soil subgrade soil, the following beneficial effects are obtained:

[0107] (1) The present invention simulates the mutual coupling effect between surface water infiltration and soft soil subgrade soil through numerical simulation, and outputs the deformation displacement, seepage flow pressure, and seepage flow velocity related to the subgrade stability, analyzes the influence of the infiltrating water on the subgrade structure stability, provides scientific guidance and decision-making support for road design, construction optimization, and disaster prevention, and has important practical significance for ensuring road safety and extending the service life of the road; and the present invention only needs to obtain the average water level height and water surface velocity of surface water that are simple and easy to obtain, and can work by using computer simulation. The data acquisition is simple and convenient, reducing the difficulty of judging the stability according to the coupling effect between surface water and soft soil subgrade, and saving equipment costs and labor costs;

[0108] (2) The present invention decouples the fluid-elastic subgrade through the Lagrangian-Euler method, enabling the coupling system established by the present invention to be discretely decoupled in time, and overcoming the difficulty of decoupling according to the coupling system.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the embodiments of the present invention are described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A numerical simulation method for fluid-solid coupling of surface water and soft soil subgrade soil, characterized in that Including the following steps: S1. Set the simulation time T and the time step Δ t . The current time t is initially 0. Input the average water level height h 0 and the water surface velocity v of the collected surface water, as well as the physical property parameters of the subgrade soil into the simulation model. The physical property parameters of the subgrade soil include: the lame constants μ s and λ s of the flexible vegetation, the unit storage coefficient of the constraint C 0, the permeability tensor κ , the foundation density ρ p and the Beavers-Joseph condition coefficient ; S2. Establish the coupling equation of surface water and soil; S2 includes: S21. Based on the fact that the viscous force, pressure gradient, and body force of the fluid conform to the law of conservation of momentum, and the inflow and outflow of the fluid conform to the law of conservation of mass, construct the Stokes equation including boundary conditions to describe the movement of surface water; the Stokes equation includes: The boundary conditions: Among them, σ f is the stress of the fluid, is the strain tensor of the fluid, ρ f is the density of the fluid, μ f is the viscosity coefficient of the fluid, u f is the fluid velocity, p f is the fluid pressure, f f is the source term, is the gradient operator, is for σ f taking the divergence, I is the identity matrix, is the region where the fluid is located, Г1 is the upper surface of the fluid calculation region, Г2 is the left surface of the fluid calculation region, Г3 is the right surface of the fluid calculation region, y is the ordinate of each point on Г2, is the unit outer normal vector of the Г3 surface; S22. Take the soil as a poroelastic model. According to the elastic equation of the poroelastic model, the change rate of the volume of the poroelastic medium is equal to the divergence of the seepage flow velocity, and the linear relationship between the seepage flow velocity of water in the saturated soil and the pressure gradient, combined with the physical property parameters of the subgrade soil, construct the Biot equation to describe the soil; S23. Couple the Stokes equation and the Biot equation through the interface conditions to obtain a coupled system; S3. Construct the Robin boundary condition, and reconstruct and decouple the coupled system by the Lagrangian-Eulerian method; S4. Determine the current time t whether it is greater than or equal to the set simulation time T , if so, end the simulation and proceed to step S5, otherwise t = t +Δ t , return to step S3; S5. End the simulation and output the deformation displacement of the subgrade , seepage flow pressure and seepage flow velocity u p for judging the stability of the subgrade.

2. The fluid-solid coupling numerical simulation method for the coupling of surface water and soft soil subgrade soil according to claim 1, wherein The Biot equation includes: where σ p is the stress tensor of the dense elastic vegetation area, α is the Biot-Willis constant of the model, is the deformation displacement, is the seepage flow pressure, u p is the seepage flow velocity, f s is the source term of the elastic equation, Ω p is the soil calculation area.

3. The fluid-solid coupling numerical simulation method for coupling surface water and soft soil subgrade soil according to claim 1, characterized in that, The coupling system includes: wherein, is the unit normal vector of the interface, is the unit tangent vector of the interface.

4. The fluid-solid coupling numerical simulation method for the coupling of surface water and soft soil subgrade soil according to claim 3, characterized in that, In S3, the Robin boundary condition includes: where the interface term function R 1, R 2, R 3, R 4, R 5 is: where, L 1, L 2, L 3 are Robin parameters; n p is the unit normal vector outside the interface; ξ is the deformation velocity; P f is the projection operator of the fluid region; P p is the projection operator of the Biot region; u is the fluid velocity; is the unit tangent vector of the interface of the fluid region, j is a subscript, j takes 1 in two dimensions and takes 1 and 2 in three dimensions; d represents the dimension, including two dimensions and three dimensions; Г represents the interface, and Г(t) represents the interface corresponding to the current time t.

5. The fluid-solid coupling numerical simulation method for coupling surface water and soft soil subgrade soil according to claim 4, characterized in that, In S3, for the Robin boundary condition, discretize it in time, use backward Euler discretization for the coupled system, and obtain the following discrete system at each moment: The obtained reconstructed Biot equation: The equations of the Lagrangian-Eulerian method include: The obtained reconstructed Stokes equation: where is the ALE mapping, ω f is the ALE velocity, and all superscripts n +1 denote the quantity at the n +1-th step, and all superscripts n denote the quantity at the n -th step.

6. The fluid-solid coupling numerical simulation method for the coupling of surface water and soft soil subgrade soil according to claim 1, characterized in that, In S5, the calculation formula for the stability of the roadbed is as follows: where S is the stability score, and a, b, and c are the weight coefficients of the deformation displacement, seepage flow pressure, and seepage flow velocity respectively, are the maximum allowable values of the deformation displacement, seepage flow pressure, and seepage flow velocity respectively; the higher the stability score, the worse the stability of the roadbed.

7. The fluid-solid coupling numerical simulation method for coupling surface water and soft soil subgrade soil according to claim 6, wherein If the stability score exceeds the set stability score threshold, the subgrade needs to be reinforced or repaired.

8. The fluid-solid coupling numerical simulation method for the coupling of surface water and soft soil subgrade soil according to claim 1, wherein In S5, the fluid velocity is also output u f and the fluid pressure p f .

9. The fluid-solid coupling numerical simulation method for coupling surface water and soft soil subgrade soil according to claim 4, characterized in that In S3, the ranges of L1, L2, and L3 are 500 - 2000.

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