Fluid-solid coupling numerical simulation method for coupling surface water and soft soil roadbed soil

Abstract

The invention discloses a fluid-solid coupling numerical simulation method for coupling surface water and soft soil roadbed soil, which comprises the following steps of: setting simulation time and time step length, and inputting acquired surface water data and physical property parameters of roadbed soil into a simulation model; the method comprises the following steps: establishing a coupling function equation of surface water and soil: describing the movement of the surface water through a Stokes equation containing boundary conditions, describing the soil through a Biot equation, and coupling the Stokes equation and the Biot equation through interface conditions to obtain a coupling system; constructing a Robin boundary condition, and reconstructing and decoupling the coupling system through a Lagrange-Euler method; when the simulation time is up, simulation is ended, and deformation displacement, seepage flow pressure and seepage flow speed of the roadbed are output and used for judging the stability of the roadbed. The method solves the problems that stability judgment according to the coupling effect of the surface water and the soft soil roadbed is difficult, and a large number of resources are consumed.

Description

Technical Field

[0001] The invention relates to the technical field of fluid-solid coupling numerical simulation, and in particular to a fluid-solid coupling numerical simulation method for coupling surface water with soft soil roadbed soil. Background Art

[0002] Areas dominated by water-saturated soft clay deposits are called soft soil areas. Soft soil includes water-saturated soft clay and silt. Coastal, lakeside, and riverside areas generally have extensive soft soil distribution. When building roads on soft soil foundations, problems such as embankment instability or excessive settlement are prone to occur. In heavy rainfall weather, long-term rain erosion will also cause water accumulation on the roadbed, thereby reducing the use strength of the roadbed. When the bearing capacity of the roadbed decreases, accidents such as road surface decline and collapse may occur. Therefore, in-depth understanding of the coupling effect of surface water and soft soil roadbed has important significance for guiding road construction and preventing disasters. In existing research, the main focus is on the measurement of road surface water depth, and less attention is paid to the profound impact of seepage water on the stability of pavement structure, ignoring that the accumulation of long-term seepage water may lead to softening of the roadbed, road subsidence, and even cause serious safety hazards such as roadbed collapse; and the existing technology generally requires a large amount of materials and direct experiments with special experimental equipment, collects a large amount of data, and consumes a lot of funds and human resources. Although the existing monitoring equipment (such as lidar, water level sensor, video monitoring) can obtain the water depth and distribution of the road surface, it is difficult to directly obtain data on underground seepage water unless it is measured through destructive ground excavation, which further destroys the soft soil roadbed. Therefore, it is crucial to develop a fluid-solid coupling numerical simulation method for coupling surface water with soft soil roadbed soil. Summary of the invention

[0003] 1. Technical issues to be resolved Based on the above problems, the present invention provides a fluid-solid coupling numerical simulation method for coupling surface water and soft soil roadbed soil, which solves the problem that stability judgment based on the coupling effect of surface water and soft soil roadbed is difficult and consumes a lot of resources.

[0004] (II) Technical solution Based on the above technical problems, the present invention provides a fluid-solid coupling numerical simulation method for coupling surface water with soft soil subgrade soil, comprising the following steps: S1. Set simulation time T and time step Δ t , current moment t Initially 0, the average height of the collected surface water level h 0 and surface speed v , and the physical property parameters of the roadbed soil are input into the simulation model, wherein the physical property parameters of the roadbed soil include: the lame constant of the flexible vegetation ms and l s , Unit storage coefficient of constraints C 0. Permeability Tensor k , foundation density r p and the Beavers-Joseph conditional coefficient α BJ ; S2. Establish the coupling equation between surface water and soil; S21. Based on the fact that the viscosity, pressure gradient and volume force of the fluid conform to the law of conservation of momentum, and the fact that the inflow and outflow of the fluid conform to the law of conservation of mass, the Stokes equations with boundary conditions are constructed to describe the movement of surface water. S22, taking soil as a poroelastic model, constructing a Biot equation to describe the soil according to the elastic equation of the poroelastic model, the mass conservation law that the rate of change of the volume of the poroelastic medium is equal to the divergence of the velocity of the seepage fluid, the linear relationship between the seepage velocity of water in saturated soil and the pressure gradient, and the physical property parameters of the roadbed soil; S3, constructing Robin boundary conditions, and reconstructing and decoupling the coupled system by Lagrange-Euler method; S4. Determine the current moment t Is it greater than or equal to the set simulation time? T If yes, the simulation ends and goes to step S5. Otherwise, t = t +Δ t , return to step S3; S5. End the simulation and output the deformation displacement of the roadbed , permeate pressure and permeate flow rate u p , used to judge the stability of the roadbed.

[0005] Furthermore, in S3, the Robin condition is discretized in time, and backward Euler discretization is used for the coupled system to obtain the following discrete system at each moment: The reconstructed Biot equation obtained is:

[0006] The equations of the Lagrange-Euler method include: The resulting reconstructed Stokes equations are: in, For ALE mapping, oh f ALE speed, all superscript n +1 means n +1 step amount, all superscripts n Indicates n The amount of steps.

[0007] Further, in S5, the stability calculation formula of the roadbed is: Among them, S is the stability score, a, b, and c are the weight coefficients of deformation displacement, seepage pressure, and seepage velocity, respectively. They are the maximum allowable values ​​of deformation displacement, seepage flow pressure and seepage flow velocity respectively; the higher the stability score, the worse the stability of the roadbed.

[0008] Furthermore, if the stability score exceeds a set stability score threshold, the roadbed needs to be reinforced or repaired.

[0009] Furthermore, in S5, the fluid velocity is also output u f and fluid pressure p f .

[0010] Furthermore, in S3, the range of L1, L2, and L3 is 500~2000.

[0011] (III) Beneficial effects The above technical solution of the present invention has the following advantages: (1) The present invention simulates the mutual coupling between surface water infiltration and soft soil roadbed soil through numerical simulation, and outputs deformation displacement, seepage flow pressure and seepage flow velocity related to roadbed stability, analyzes the influence of seepage water on roadbed structure stability, and provides scientific guidance and decision-making support for road design, construction optimization and disaster prevention, which has important practical significance for ensuring road safety and extending road service life; and the present invention only needs to obtain the simple and easy-to-obtain average water level height and water surface velocity of surface water, and can work by computer simulation. Data acquisition is simple and convenient, which reduces the difficulty of stability judgment based on the coupling effect of surface water and soft soil roadbed, and saves equipment cost and labor cost; (2) The present invention decouples the fluid-elastic roadbed through the Lagrange-Euler method, so that the coupling system established by the present invention is discretely decoupled in time, thereby overcoming the difficulty of decoupling the coupling system. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The features and advantages of the present invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the present invention in any way. In the accompanying drawings: Figure 1 It is a flow chart of a fluid-solid coupling numerical simulation method for coupling surface water and soft soil subgrade soil according to an embodiment of the present invention; Figure 2 The simulated interface diagram of the original surface water and roadbed of the embodiment of the present invention; Figure 3 A simulation interface diagram of the deformation result of the roadbed according to an embodiment of the present invention; Figure 4 This is a simulation interface diagram of the movement trajectory of surface water according to an embodiment of the present invention. DETAILED DESCRIPTION

[0013] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0014] The embodiment of the present invention is a fluid-solid coupling numerical simulation method for coupling surface water with soft soil subgrade soil, such as Figure 1 As shown, the following steps are included: S1. Set simulation time T and time step Δ t , current moment t Initially 0, the data input to the simulation model include: average height of surface water level h 0 and surface speed v , and physical property parameters of roadbed soil: lame constant of flexible vegetation m s and ls , Unit storage coefficient of constraints C 0. Permeability Tensor k , foundation density r p and the Beavers-Joseph conditional coefficient α BJ ; S2. Establish the coupling equation between surface water and soil: S21. Based on the fact that the viscosity, pressure gradient and volume force of the fluid conform to the law of conservation of momentum, and the fact that the inflow and outflow of the fluid conform to the law of conservation of mass, the Stokes equations with boundary conditions are constructed to describe the movement of surface water: and The boundary conditions are: in: s f represents the stress of the fluid, represents the strain tensor of the fluid, r f represents the density of the fluid, m f represents the viscosity coefficient of the fluid, u f represents the fluid velocity, p f represents the fluid pressure, f f Represents source terms, such as gravity or other body forces, which are defined by the user. represents the gradient operator, Express s f Find the divergence, I represents the identity matrix, Indicates the area where the fluid is located, and the current time t The upper surface (water surface) of the fluid calculation area is Г1, and the water surface velocity is assumed to be v For flow from left to right, the left surface is Г2 and the right surface is Г3 (if the flow velocities are opposite, the labels of the left and right surfaces are swapped). In the boundary conditions, the fluid velocity u f is a vector function, where the upper boundary assumes that there is only horizontal flow and no vertical velocity component; y Refers to the ordinate of each point on Г2, indicating that the left boundary velocity is related to the depth in the water and is a parabola shape; h 0 is the average height of the initial water level of the input, v is the input water surface velocity. A free boundary condition is applied on the right side. nГ3 Represents the unit external normal vector of this face.

[0015] The Stokes equations are a simplified version of the Navier-Stokes equations after ignoring the inertia term. They are applicable to low Reynolds number flows and are suitable for describing the movement of surface free streams. The Stokes equations are a set of equations consisting of two equations. Among them, the first equation is the momentum equation, which means that the fluid flow complies with the law of conservation of momentum, and there is a dynamic equilibrium relationship between the viscous force, the pressure gradient and the volume force; the first term of the equation is the transient inertia term, which characterizes the dynamic inertia effect of the fluid micro-group momentum changing with time. When the flow velocity field has a significant time dependence, this term reflects the momentum change rate corresponding to the acceleration of the fluid micro-group; the second term of the equation is the stress tensor divergence term, 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 that the stress 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 against deformation, reflecting 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, and the second-order spatial derivative of the velocity field ( ) reflects the intensity of the viscous drag on the fluid microelement by the adjacent flow layer. The larger the dynamic viscosity μ, the more significant the viscous force's blocking effect on the flow. The right side of the equation is the volume force term, which can be used here to represent the effect of gravity on the fluid, and can generally be expressed as f f = rho*g, rho is the fluid density and g is the acceleration due to gravity.

[0016] The second equation is the continuity equation, which means that the fluid obeys the law of conservation of mass. The divergence of the velocity field is zero, which means that the fluid is incompressible, which means 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 the fluid micro-group remains unchanged during movement.

[0017] S22. Taking soil as a porous elastic model, according to the elastic equation of the porous elastic model, the mass conservation law that the rate of change of the volume of the porous elastic medium is equal to the divergence of the velocity of the seepage fluid, the linear relationship between the seepage velocity of water in saturated soil and the pressure gradient, and the physical property parameters of the roadbed soil, a Biot equation is constructed to describe the soil: For the soil part, it is regarded as an elastic porous medium region and described by the Biot equation: and in: s p represents the stress tensor in the dense elastic vegetation area, r p represents the ground density, ms , l s The lame constant representing the flexible vegetation, C 0 indicates a unit storage factor for the constraint, α represents the Biot-Willis constant of the model, k represents the permeability tensor, represents the deformation displacement, represents the permeate flow pressure, u p represents the permeate flow velocity, f s represents the source term of the elasticity equation, Oh p Indicates the calculated soil area, which is different from the current time t Not relevant.

[0018] The Biot equation, also known as the poroelastic model, is used to describe the interaction between fluid and matrix deformation in porous media. It is a system of three equations. The third equation is the famous Darcy theorem, which is used to describe the linear relationship between the seepage velocity and pressure gradient of water in saturated soil, also known as the linear seepage law.

[0019] The first equation is the elastic part of the Biot equation. Since fluid-solid coupling studies the transient changes between the two, we need to retain the second-order time derivative of the elastic equations with respect to deformation (the Biot equation ignoring the second-order time derivative becomes a quasi-static equation, which is usually used in a separate porous elastic problem), that is, the first term of the equation. The second term is the stress divergence of the porous elastic medium, which describes the resultant force acting on the solid microelement due to the uneven stress distribution. The stress term mainly consists of two parts: represents the Cauchy stress tensor. Conventional linear elastic materials use this formula to describe the relationship between deformation and stress. In the porous elastic model, the fluid in the medium also exerts a force on the matrix. Here we use the seepage pressure to measure it, which produces The right side of the equation is the volume force, which can be used here to represent the effect of gravity on the substrate.

[0020] The second equation is called the Darcy equation, which is also the mass conservation equation. Since the density is assumed to be constant, the rate of change of the volume of the entire porous elastic medium is equal to the divergence of the velocity of the seepage fluid. It represents the increment of the unit volume of the fluid and the unit volume of the solid. The derivative with respect to time represents the rate of change of the increment of the unit volume of the fluid and the unit volume of the solid per unit time. The second term combined with Darcy's law is the velocity of the seepage fluid.

[0021] S23, coupling the Stokes equation and the Biot equation through the interface condition to obtain a coupled system: in, n Гfp represents the unit normal vector of the interface, t Гfp represents the unit tangent vector of the interface, α BJ is the Beavers-Joseph condition coefficient.

[0022] S3, constructing Robin boundary conditions, and reconstructing and decoupling the coupled system by Lagrange-Euler method; The above Stokes equation is valid in the Euler coordinate system, and the Biot equation is valid in the Lagrangian coordinate system. Under the action of fluid stress, the roadbed area will undergo elastic deformation, which will cause the fluid calculation area to change (i.e. However, the Biot equation is valid in the Lagrangian coordinate system, and its physical quantities such as elastic displacement are expressed by function values ​​on a fixed area (i.e. Oh p The control equations of the two physical processes are established in different coordinate systems and are coupled to each other through a common interface, which brings great difficulties to the traditional numerical method. For example, the time derivative in the fluid equation cannot be discretized normally. In order to overcome these difficulties, we consider designing a fluid-elastic roadbed decoupling algorithm based on the arbitrary Lagrangian-Euler (ALE) method. The basic idea of ​​the ALE method is: in order to be able to discretize the time-varying region The time derivative of (such as the initial region) to the time-varying region Construct a family of mappings and define the mesh deformation rate: This is the ALE mapping. Based on this, the ALE time derivative is defined as: Substituting into the Stokes equation, we get the ALE form of the Stokes equation (in the reference coordinate system): in oh f is the ALE speed.

[0023] In order to solve the above coupling problem, five Robin boundary conditions are constructed to reconstruct the above coupling system so that the entire coupling system is completely decoupled: The interface function R 1, R 2, R 3, R 4, R 5 is: in, L 1. L 2. L 3 is the Robin parameter, the recommended range is 500~2000; n p represents the normal vector outside the interface; x Indicates the deformation velocity, that is, the deformation displacement The time derivative of P f The projection operator representing the fluid region; P p represents the projection operator of the Biot region; u represents the fluid velocity; t f,j represents the unit tangent vector of the fluid region interface; j Indicates the subscript. For a two-dimensional problem, there is only one tangent vector, while for a three-dimensional problem, there are tangent vectors in two directions. j In two dimensions, it can only take 1, but in three dimensions, it can take 1 and 2; d It indicates dimension, which can be two-dimensional or three-dimensional; Г indicates the interface; For the above Robin conditions, we discretize in time and use backward Euler discretization for the entire system to obtain the following discrete system at each moment: Biot equation for reconstruction of roadbed area: ALE equation: Reconstructed Stokes equations for the fluid region: Among them, all superscript n +1 represents n +1 step amount, n Representative n The amount of steps.

[0024] Through every moment t By solving the above three equations in sequence, the simulation of the coupling effect between groundwater and roadbed can be completed.

[0025] S4. Determine the current moment t Is it greater than or equal to the set simulation time? T If yes, the simulation ends and goes to step S5. Otherwise, t = t +Δ t , return to step S3; S5. End the simulation and output the deformation displacement of the roadbed , permeate pressure and permeate flow rate u p , used to judge the stability of the roadbed.

[0026] like Figure 2 Shown are the original surface water and roadbed, with gaps in the roadbed indicating potholes; Figure 3 The deformation result of the simulated roadbed is shown in Fig. Figure 4 The figure shows the simulated movement trajectory of surface water, and the arrows represent the movement direction of surface water.

[0027] The formula for calculating the stability of the roadbed is: Among them, S is the stability score, a, b, and c are the weight coefficients of deformation displacement, seepage pressure, and seepage velocity, respectively. They are the maximum allowable values ​​of deformation displacement, seepage flow pressure and seepage flow velocity respectively; the higher the stability score, the worse the stability of the roadbed. If it exceeds the set stability score threshold, the roadbed needs to be reinforced or repaired.

[0028] In addition, the fluid velocity can also be output u f and fluid pressure p f , used for monitoring of surface water.

[0029] Finally, it should be noted that the above-mentioned numerical simulation method can be converted into software program instructions, which can be implemented by using 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 above-mentioned integrated unit implemented in the form of a software functional unit can be stored in a computer-readable storage medium. The above-mentioned software functional unit is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor to perform some steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), disk or optical disk and other media that can store program codes.

[0030] In summary, the above-mentioned fluid-solid coupling numerical simulation method for coupling surface water with soft soil embankment has the following beneficial effects: (1) The present invention simulates the mutual coupling between surface water infiltration and soft soil roadbed soil through numerical simulation, and outputs deformation displacement, seepage flow pressure and seepage flow velocity related to roadbed stability, analyzes the influence of seepage water on roadbed structure stability, and provides scientific guidance and decision-making support for road design, construction optimization and disaster prevention, which has important practical significance for ensuring road safety and extending road service life; and the present invention only needs to obtain the simple and easy-to-obtain average water level height and water surface velocity of surface water, and can work by computer simulation. Data acquisition is simple and convenient, which reduces the difficulty of stability judgment based on the coupling effect of surface water and soft soil roadbed, and saves equipment cost and labor cost; (2) The present invention decouples the fluid-elastic roadbed through the Lagrange-Euler method, so that the coupling system established by the present invention is discretely decoupled in time, thereby overcoming the difficulty of decoupling the coupling system.

[0031] 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 it. Although the embodiments of the present invention are described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations shall fall within the scope defined by the appended claims.

Claims

1. A fluid-solid coupling numerical simulation method for coupling surface water with soft soil embankment soil, characterized in that: The following steps are involved: S1. Set simulation time T and time step Δ t , current moment t Initially 0, the average height of the collected surface water level h 0 and surface speed v , and the physical property parameters of the roadbed soil are input into the simulation model, wherein the physical property parameters of the roadbed soil include: the lame constant of the flexible vegetation μ s and λ s , Unit storage coefficient of the constraint C 0. Permeability Tensor κ , foundation density ρ p and the Beavers-Joseph conditional coefficient α BJ ; S2. Establish the coupling equation between surface water and soil; S21. Based on the fact that the viscosity, pressure gradient and volume force of the fluid conform to the law of conservation of momentum, and the fact that the inflow and outflow of the fluid conform to the law of conservation of mass, the Stokes equations with boundary conditions are constructed to describe the movement of surface water. S22, taking soil as a poroelastic model, constructing a Biot equation to describe the soil according to the elastic equation of the poroelastic model, the mass conservation law that the rate of change of the volume of the poroelastic medium is equal to the divergence of the velocity of the seepage fluid, the linear relationship between the seepage velocity of water in saturated soil and the pressure gradient, and the physical property parameters of the roadbed soil; S23, coupling the Stokes equation and the Biot equation through an interface condition to obtain a coupled system; S3, constructing Robin boundary conditions, and reconstructing and decoupling the coupled system by Lagrange-Euler method; S4. Determine the current moment t Is it greater than or equal to the set simulation time? T If yes, the simulation ends and goes to step S5. Otherwise, t = t +Δ t , return to step S3; S5. End the simulation and output the deformation displacement of the roadbed , permeate pressure and permeate flow rate u p , used to judge the stability of the roadbed.

2. The fluid-solid coupling numerical simulation method for coupling surface water and soft soil subgrade according to claim 1 is characterized in that: The Stokes equations include: and The boundary conditions are: in, 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, For σ f Find the divergence, I is the identity matrix, is the area where the fluid is located, Г1 is the upper surface of the fluid calculation area, Г2 is the left surface of the fluid calculation area, and Г3 is the right surface of the fluid calculation area. y is the ordinate of each point on Г2, n Г3 is the unit external normal vector of the Г3 surface.

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

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

5. The fluid-solid coupling numerical simulation method for coupling surface water and soft soil subgrade according to claim 4 is characterized in that: In S3, the Robin boundary conditions include: The interface function R 1, R 2, R 3, R 4, R 5 is: in, L 1. L 2. L 3 is the Robin parameter; n p is the normal vector outside the interface; ξ is the deformation speed; 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; τ f,j is the unit tangent vector of the fluid region interface, j is a subscript, j In two dimensions, it takes 1, and in three dimensions, it takes 1 and 2; d represents dimension, including two-dimensional and three-dimensional; Г represents the interface.

6. The fluid-solid coupling numerical simulation method for coupling surface water and soft soil subgrade according to claim 5 is characterized in that: In S3, for the Robin boundary condition, discretization is performed in time, and backward Euler discretization is used for the coupled system to obtain the following discrete system at each moment: The reconstructed Biot equation obtained is: The equations of the Lagrange-Euler method include: The resulting reconstructed Stokes equations are: in, For ALE mapping, ω f ALE speed, all superscript n +1 means n +1 step amount, all superscripts n Indicates n The amount of steps.

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

8. The fluid-solid coupling numerical simulation method for coupling surface water and soft soil subgrade according to claim 7 is characterized in that: If the stability score exceeds a set stability score threshold, the roadbed needs to be reinforced or repaired.

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

10. The fluid-solid coupling numerical simulation method for coupling surface water and soft soil subgrade according to claim 5, characterized in that: In S3, the range of L1, L2, and L3 is 500~2000.

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