CN115099119A

CN115099119A - Surge simulation method and system based on landslide body motion model and mesh-free SPH

Info

Publication number: CN115099119A
Application number: CN202210773382.6A
Authority: CN
Inventors: 缪吉伦; 袁浩; 周家俞; 黄成林; 段金宏; 王小蓉
Original assignee: Chongqing Jiaotong University
Current assignee: Chongqing Jiaotong University
Priority date: 2022-07-01
Filing date: 2022-07-01
Publication date: 2022-09-23

Abstract

The invention discloses a surge simulation method and system based on a landslide body motion model and a mesh-free SPH (sinusoidal pulse height), which comprises the steps of calculating the slip time of the landslide body motion model and the slip speed and the slip distance at each moment to obtain the motion process of a landslide body on water and/or under water; constructing an SPH surge fluid particle expression and a control equation of water body motion under the impact of a landslide body, and constructing a discretized SPH surge numerical calculation model; carrying out iterative solution on the SPH surge numerical calculation model to obtain physical and mechanical parameters of the water body and a propagation motion process of the water body at each moment; the method comprises the steps of carrying out imaging processing on the movement process of a landslide body and the propagation movement process of a water body to obtain the simulated evolution process of the surge of the landslide body at each moment, further quickly determining a disaster area possibly caused by surge and climbing, and providing a more comprehensive and accurate scientific basis for real-time forecasting and prevention of the landslide surge.

Description

Surge simulation method and system based on landslide body motion model and non-grid SPH

Technical Field

The invention relates to the technical field of reservoir bank surge simulation, in particular to a method and a system for simulating surge based on a landslide body motion model and a meshless SPH.

Background

Landslides are widely distributed in China and other regions in the world, rock-soil bodies can induce landslides under certain natural factors or artificial conditions, and direct disasters and secondary disasters caused by large landslides are huge. On one hand, the landslide body directly destroys farmlands, plants, residences and other infrastructure of the landslide area; on the other hand, in the reservoir area, waves generated by high-speed water entering of a landslide body can cause huge damage to residents and infrastructure along the shore; in coastal areas, underwater landslides are a second important source of tsunami production, sometimes with even greater intensity of damage than earthquake-induced tsunamis. The dam break is likely to be disastrous due to various factors such as poor stability of a dam body of a dammed lake formed by a large amount of landslide accumulation bodies and continuously rising water level. The destructive power of surge and dam break secondary disasters caused by large landslides even far exceeds the direct destructive power of the large landslide.

At present, the following three methods are generally adopted for calculating landslide surge: physical model tests, numerical simulation and empirical formula methods. Although the physical model test overcomes some defects of prototype observation, the physical model test has many self limitations, such as similar simulation of sliding body materials, speed per hour control of sliding body models, site limitation, precision of measuring instruments and the like. The method is simple and easy to implement, but cannot provide complete and systematic landslide surge information. Although numerical simulation can provide relatively complete and systematic information, is not limited by space and time, and the model can be repeatedly debugged and replayed, so that time, manpower, material resources, financial resources and the like are greatly saved, in practical problems, certain parameters need to be provided through prototype observation or model tests to verify the established numerical model.

Disclosure of Invention

In view of the above, the present invention provides a method and a system for simulating swell based on a landslide body motion model and a mesh-free SPH, so as to solve the problems of poor simulation accuracy, incomplete simulated swell information, incomplete parameters caused by lack of prototype observation data, and the like in the prior art due to limitations of landslide body materials, model speed per hour control, fields, instruments, and the like.

In order to achieve the above object, a first aspect of the present invention provides a method for simulating swell based on a landslide body motion model and a meshless SPH, comprising the following steps:

s1: establishing a landslide body motion model according to the bank landslide geological section, and performing evolution calculation on the slip time of the landslide body motion model and the slip speed and the slip distance at each moment to obtain the motion process of the landslide body on water and/or under water;

s2: constructing an SPH surge fluid particle expression and a control equation of water body motion under the impact of a landslide body, dispersing the control equation by the SPH surge fluid particle expression, and constructing a discretized SPH surge numerical calculation model by combining a constructed state equation and a fluid particle displacement change equation;

s3: setting parameters of an SPH surge numerical calculation model, and carrying out iterative solution on the SPH surge numerical calculation model to obtain physical and mechanical parameters of the water body and a propagation motion process of the water body at each moment;

s4: and carrying out imaging processing on the motion process of the landslide body and the propagation motion process of the water body to obtain the simulated evolution process of the surge of the landslide body at each moment.

Further, the step S1 includes the following sub-steps:

s101: collecting a geological section image of a bank landslide, and acquiring position coordinates of a sliding surface, a landslide body and a water body surface;

s102: dividing the landslide body into a preset number of blocks based on a strip division method, and establishing a landslide body motion model;

s103: and from the initial moment, iteratively calculating the motion parameters of each block in each sliding preset unit distance until the speed of each block is zero, and outputting the total sliding time and the sliding distance of the sliding body motion model and the sliding speed at each moment to obtain the motion process of the sliding body on the water and/or under the water.

Further, the step S103 includes the following substeps:

s1031: acquiring an initial time and an initial speed of the sliding body sliding at a current preset unit distance and initial position coordinates of the sliding body and the water body surface at the initial time of the current preset unit distance;

s1032: judging whether the landslide body moves underwater, calculating the stress of each block to obtain the gliding force of the movement of the block in the current preset unit distance, and calculating the unit acceleration of the block according to the gliding force of the block in the current preset unit distance;

s1033: calculating the unit horizontal velocity of the bar block after sliding for a preset unit distance according to the initial velocity and the unit acceleration, and calculating the unit time increment of the bar block during sliding for the preset unit distance;

s1034: judging whether the unit horizontal speed is zero, if so, continuing to execute the step S1035, otherwise, skipping to execute the step S1036;

s1035: outputting the total sliding time and the sliding distance of the sliding mass motion model and the sliding speed at each moment to obtain the motion process of the sliding mass on the water and/or under the water;

s1036: updating the initial time and the initial speed of the sliding of the bar block in the next preset unit distance according to the unit horizontal speed and the unit time increment of the current preset unit distance, acquiring the initial time of the starting time of the sliding body and the water body surface in the next preset unit distance, and then skipping to execute the step S1032.

Further, in step S1032, regarding the blocks as rigid bodies having a mass property, each block receives a supporting force in a direction perpendicular to the sliding surface and a sliding force in a direction parallel to the sliding surface when the sliding body slides along the sliding surface on or under water; when the landslide body slides along the sliding surface underwater, each block is also subjected to flow field resistance from a water body and surface friction force of the water body acting on the upstream surface of the landslide body respectively;

when the sliding body slides on water and/or underwater, the acceleration of the sliding body in the direction vertical to the sliding surface is zero, the supporting force and the sliding force are respectively represented by the movement of the bar in the direction vertical to the sliding surface and the direction parallel to the sliding surface, and the movement of the bar in the direction vertical to the sliding surface is represented as:

∑F _y ＝W _i cosα _i -(U _i+1 -U _i )sinα _i -U _bi -N _i ；

the motion of the bar in a direction parallel to the sliding surface is represented by:

∑F _x ＝W _i sinα _i +ΔT _i -(U _i+1 -U _i )cosα _i -(C _i L _i +N _i tanφ _i )-M _i a _i ；

wherein: sigma F _y For the supporting force of the bar i in the direction perpendicular to the sliding surface, Sigma F _x The downward sliding force of the bar block i in the direction parallel to the sliding surface is shown, and i is the number of the divided bar blocks; w _i And M _i Weight and mass of the bar i, respectively; alpha is alpha _i The inclination of the sliding surface of the bar i; u shape _i And U _i+1 The buoyancy force borne by the strips i and i + 1; u shape _bi The osmotic water pressure experienced by the bar i; n is a radical of _i A counter force acting on the bar i for the sliding surface; delta T _i The resultant force of the downward sliding force between the bars; c _i Is the cohesive force of the bar i; l is _i The sliding distance of the bar i along the sliding surface; phi is a _i The dynamic friction angle between the bar i and the sliding surface; a is _i Acceleration of bar i;

when the sliding mass slides underwater, the sliding mass is taken as a whole to respectively analyze the flow field resistance and the surface friction of the sliding mass, and the flow field resistance is expressed as:

the surface friction is expressed as:

wherein: f _f Flow field resistance of the landslide mass, F _s The surface friction of the landslide body; g is the mass of the landslide body; v is the slip speed of the slip mass; t is the slip time of the slip mass; c. C _d Is a constant; ρ is a unit of a gradient _s Is the density of the water body; r is a viscous drag coefficient; and S is the surface area of the upstream surface of the landslide body.

Further, the step S2 includes the following sub-steps:

s201: dispersing a water body into a series of fluid particles based on an SPH method, obtaining a state expression of the water body at any point in space by utilizing a kernel function approximation method, dispersing the state expression, and constructing an SPH surge fluid particle expression;

s202: constructing a Lagrange type control equation for the water body motion under the impact of the landslide body, utilizing the SPH surge fluid particle expression to disperse the control equation, and expressing the control equation into an SPH discrete form; wherein the governing equations include a continuity equation and an energy equation;

s203: constructing an equation of state based on fluid compressibility;

s204: and combining the control equation expression to construct a discretized SPH surge numerical calculation model for the SPH discrete form, the state equation and the fluid particle displacement change.

Further, in step S201, the SPH surge fluid particle expression is:

wherein: a (r) _I ) And A (r) _J ) The coordinates r of the corresponding positions of the fluid particles I and the fluid particles J respectively _I And position coordinates r _J A kernel estimate of (I ≠ J), where I ≠ 1, 2., N, J ≠ 1, 2.., N, where N is the number of discrete fluid particles within the computational domain; m is a unit of _J And ρ _J Mass and density of the fluid particles J, respectively; k (r) _I -r _J H) is a kernel function, r _I -r _J H is the smooth length of the kernel function, which is the distance between the fluid particle I and the fluid particle J.

Further, in step S204, the SPH swell numerical calculation model is expressed as:

wherein: rho _I And ρ _J Density of fluid particles I and J, I ≠ 1, 2., N, J ≠ 1, 2., N, where I ≠ J, N is the number of discrete fluid particles within a computational domain; t is time; v _IJ Is the velocity difference, V, between fluid particles I and fluid particles J _IJ ＝V _I -V _J ，V _I And V _J The movement speeds of the fluid particles I and the fluid particles J respectively; m is _J Is the mass of the fluid particle J; k _IJ For the kernel function, K, of the influence of the fluid particles J on the fluid particles I _IJ ＝K(r _I -r _J ,h)，r _I -r _J Is the distance between the fluid particle I and the fluid particle J, and h is the smooth length of the kernel function; r is _I And r _J Position coordinates of the fluid particles I and the fluid particles J respectively; p is a radical of _I And p _J Pressures of fluid particles I and fluid particles J, respectively; n shape _IJ Is a diffusion term variable between the fluid particle J and the fluid particle I;

is the acceleration of gravity; p is artificially applied fluid particle pressure; rho ₀ Is a reference density constant; ρ is the fluid particle density; c. C ₀ Is artificial soundSpeed; gamma is a constant;

is a coordinate vector of the fluid particle;

is the motion velocity vector of the fluid particles.

Further, the step S3 includes the following sub-steps:

s301: determining a kernel function and a smooth length range thereof, the total number of fluid particles and a boundary position, assigning an initial value to each fluid particle, determining iteration time steps, and initializing the SPH surge numerical value calculation model;

s302: searching each fluid particle for a nearest neighbor fluid particle within its computational domain based on a nearest neighbor particle search algorithm and computing the kernel function based on the fluid particle and its nearest neighbor fluid particle;

s303: respectively calculating the density change, the pressure and the acceleration of the fluid particles according to the SPH swell numerical calculation model and the kernel function, correcting the density and the speed of the fluid particles, and then repeatedly executing the step S302 to iteratively update the density, the speed and the position of the fluid particles until convergence or the maximum iteration time step number is reached;

s304: and outputting physical and mechanical parameters of each fluid particle to obtain the propagation motion process of surge at each moment.

Further, in step S301, a specific method for determining the boundary position of the fluid particle is as follows:

for the particles of the solid-wall boundary, discretizing the solid-wall boundary into boundary virtual fluid particles, and assuming that the boundary fluid particles exert a central repulsive force acting only within a preset distance range on the fluid particles close to the boundary fluid particles, wherein the central repulsive force prevents the fluid particles from crossing the solid-wall boundary and does not participate in the density calculation of the fluid particles; the central repulsive force is expressed as:

wherein: f (r') is the central repulsive force of the solid-wall boundary particles; q, n, n' are adjustable parameters; r' ₀ Is the initial separation of the solid wall boundary particles from the fluid particles; r' is the distance between the solid wall boundary particles and the fluid particles at the current moment;

for free surface particles, the particle density of the free surface is made equal to the actual density of the free surface water body.

The second aspect of the present invention provides a landslide body motion model and mesh-free SPH based surge simulation system for implementing the landslide body motion model and mesh-free SPH based surge simulation method, which includes:

the landslide body motion model calculation module is used for establishing a landslide body motion model, and performing evolution calculation on the sliding time of the landslide body motion model, the sliding speed and the sliding distance at each moment to obtain the motion process of the landslide body on water and/or under water;

the system comprises a surge numerical calculation model building module, a control equation generation module, a state equation generation module and a fluid particle displacement variation equation generation module, wherein the surge numerical calculation model building module is used for building an SPH surge fluid particle expression and a control equation of water motion under the impact of a landslide body, the control equation is dispersed by the SPH surge fluid particle expression, and a discretized SPH surge numerical calculation model is built by combining a structural state equation and a fluid particle displacement variation equation;

the SPH numerical value calculation module is used for carrying out iterative solution on the SPH surge numerical value calculation model according to the set SPH surge numerical value calculation model parameters to obtain physical and mechanical parameters of the water body and a propagation motion process of the physical and mechanical parameters at each moment; and

and the surge simulation module is used for carrying out imaging processing on the movement process of the landslide body and the propagation movement process of the water body to obtain the simulated evolution process of the landslide body surge at each moment, including real scenes such as bubble formation, collapse and the like.

The method is based on the strip division thought and combines the mechanics principle to establish a bank high-speed sliding mass motion model, divides the sliding mass into a plurality of strips with certain quality, treats each strip as a rigid body, decomposes the motion of each strip into motion along two directions vertical to a sliding surface and parallel to the sliding surface, reduces excessive stress decomposition of the strips, can clearly and quickly obtain the maximum speed of the sliding mass, the change rule of the speed and the accelerated speed in the motion process, further obtains the turning point of the sliding mass from acceleration to deceleration, avoids complex and complex numerical analysis in the whole process, and is quick in calculation without setting excessive parameters; in addition, the water body is dispersed into a plurality of fluid particles to represent the whole continuous medium water body based on the SPH method, the density, the pressure intensity, the pressure, the speed and the like of the fluid particles are calculated by establishing an SPH swell numerical calculation model, and then the motion trail of the fluid particles is simulated, so that the swell evolution process under the impact of a landslide body is obtained, the mesh division or iterative divergence process caused by establishing a two-dimensional mesh model or a dispersion model can be avoided, the simulation precision is improved, and the simulation fidelity is increased.

Drawings

Fig. 1 is a flowchart of a swell simulation method based on a landslide body motion model and a meshless SPH according to embodiment 1 of the present invention.

Fig. 2 is a flowchart of step S1 in fig. 1.

Fig. 3 is a bank landslide geological section image of the target area of step S101 in fig. 2.

Fig. 4 is a flowchart of step S103 in fig. 1.

FIG. 5 is a force analysis of a bar.

Fig. 6 is a flowchart of step S2 in fig. 1.

Fig. 7 is a flowchart of step S3 in fig. 1.

Fig. 8 is a schematic view of a mesh region of fluid particles and its immediate vicinity.

Fig. 9 to 14 are schematic diagrams of deformation motions of the landslide body and the swell at various time points.

FIG. 15 is a graph of acceleration of a sliding mass over time

FIG. 16 is a graph showing the change of speed of a sliding mass with time

Fig. 17 is a system block diagram of a swell simulation system based on a landslide body motion model and a meshless SPH according to embodiment 2 of the present invention.

Detailed Description

The following is further detailed by way of specific embodiments:

example 1

Fig. 1 is a flowchart of a swell simulation method based on a landslide body motion model and a meshless SPH according to this embodiment. The landslide mass surge is the result of the interaction between the landslide mass and the water body, so the simulation of the landslide mass surge comprises the movement and the interaction between the landslide mass (solid phase) and the water body (liquid phase), and the embodiment adopts the strip method thought and the mechanical principle to calculate the movement process of the landslide mass; and then dispersing the water body into a plurality of fluid particles by adopting an SPH method, and calculating the physical and mechanical parameters of each fluid particle so as to carry out the propagation motion process of the water body under the impact of the landslide body, thereby obtaining the evolution process of the surge at each moment. Specifically, the present embodiment includes the following steps:

s1: and constructing a motion model of the landslide body, calculating the motion parameters of the landslide body and obtaining the motion process of the landslide body.

Because the landslide body will generate more or less deformation in the sliding process, for the landslide body deformation prediction, not only the conditions of landscapes of sliding in a landslide area, rock and soil bodies, strength parameters of soft and weak zones and the like need to be considered, but also the parameter changes (such as speed, acceleration and the like) caused by the sliding surface of the landslide body sliding in the moving process and the changes of the stress conditions (such as water movement, underwater movement and the like) of the landslide body need to be considered, and therefore, the moving process and the moving rule of the landslide body need to be determined.

Specifically, firstly, collecting a geological section image of a bank landslide, dividing a landslide body in the image into a plurality of vertical strips, and establishing a landslide body motion model after assigning attributes to each strip; and then analyzing the motion condition of each block, and calculating the slip time of the motion model of the landslide body, the slip speed and the slip distance at each moment to obtain the motion process of the landslide body on the water and/or under the water.

As shown in fig. 2, the step S1 includes the following sub-steps:

s101: and acquiring the position coordinates of the sliding surface, the sliding mass and the water body surface.

As shown in fig. 3, collecting a bank landslide geological section image of a certain target area, and acquiring elevation data of the bank landslide geological section image; and then establishing a coordinate system for the bank landslide geological section image, and acquiring position coordinates of a sliding surface, a landslide body and a water body surface in the bank landslide geological section image, so as to conveniently determine the position relation between the sliding surface and the landslide body, the initial position of the landslide body and the water level of the water body.

S102: and dividing the landslide body into blocks, and establishing a landslide body motion model.

Referring to fig. 3, first, based on the idea of the segmentation method, the landslide mass is vertically divided into a preset number of segments according to the landform and geological conditions of the target area. Then, assuming that each block is stressed, and after the sliding mass is divided into a plurality of vertical blocks, regarding each block as a rigid body, namely, the blocks are still vertical blocks after sliding downwards along the sliding surface, and neglecting shearing force and other resistance among the blocks; and when the sliding mass slides down along the broken sliding surface, the static stability of the sliding mass is still planar during analysis, so that a sliding mass motion model is established.

S103: and (5) iteratively calculating the motion parameters of the bar blocks to obtain the motion process of the landslide mass.

From the initial moment of sliding of the landslide body (namely when the landslide body is at the highest point of the sliding surface), regarding a preset unit distance delta L of each sliding of the landslide body along the sliding surface as a sliding step, stepping the landslide body according to the sliding step, iteratively calculating the motion parameters of each sliding step of each strip block until the speed of each strip block is zero, stopping the movement of the landslide body at the moment, and then outputting the total sliding time and sliding distance of the landslide body motion model and the sliding speed of each moment to obtain the motion process of the landslide body on the water and/or under the water so as to clearly obtain the maximum speed of the landslide body during the motion, the change rule of the speed and the acceleration in the motion process and the turning point of the landslide body from acceleration to deceleration.

As shown in fig. 4, the step S103 includes the following sub-steps:

s1031: and acquiring initial position parameters of the landslide body and the water body.

And acquiring initial position coordinates of the landslide body and the water body surface when the landslide body slides by a preset unit distance of the current step, and an initial sliding moment and a corresponding initial speed of the landslide body according to the bank landslide geological section image of the target area.

In this embodiment, if the sliding mass slides in a first sliding step (i.e., a first sliding preset unit distance), the initial position coordinate of the sliding mass is the position coordinate of the sliding mass at the highest point of the sliding surface, the initial position coordinate of the water surface is the water level when the sliding mass starts to slide (i.e., at the highest point of the sliding surface), the initial time of the sliding mass is zero, and the initial speed is also zero; if the sliding body slides in a non-first sliding step (i.e., a second sliding step to a later sliding step), the initial position coordinate of the sliding body is the position coordinate at the end of the previous sliding step (i.e., the position coordinate of the sliding body at the end of the previous preset unit distance), the position coordinate of the water surface is also corresponding to the water level at the end of the previous sliding step, the initial time of sliding of the sliding body is the time when the current sliding step starts (i.e., the time when the sliding body ends in the previous sliding step), and the initial speed of the sliding body is the speed of the sliding body at the start of the current sliding step (i.e., the last speed of the sliding body at the end of the previous sliding step).

S1032: and (4) iteratively calculating the slip force of each block in each step, and calculating the unit acceleration of the corresponding block.

When sliding down along the sliding surface, the sliding mass first slides on the sliding surface above the horizontal plane, and after entering water, slides on the sliding surface below the horizontal plane until stopping. When the landslide body slides on water, the landslide body is only under the action of self gravity and a sliding surface, and when the landslide body slides under water, the landslide body is under the action of self gravity and the sliding surface, and besides the self gravity and the sliding surface, the landslide body is also under the action of flow field resistance of a water body and friction force between an upstream surface of the landslide body and the water body. Therefore, it is necessary to determine whether the sliding mass is moving on water or under water according to the current position coordinates of the sliding mass and the water body, so as to further analyze the sliding force exerted on each block of the sliding mass in the current sliding step, and further calculate the unit acceleration of the block according to the corresponding sliding force.

In the embodiment, when the sliding body slides along the sliding surface on water or under water, each bar is subjected to a supporting force in a direction perpendicular to the sliding surface and a sliding force in a direction parallel to the sliding surface, wherein the supporting force and the sliding force are represented by the movement of the bar in the direction perpendicular to the sliding surface and the direction parallel to the sliding surface respectively; when the landslide body slides along the sliding surface under water, each block is also subjected to flow field resistance from a water body and surface friction force of the water body acting on the upstream surface of the landslide body.

Fig. 5 is a schematic view of the stress analysis of the bar. When the sliding body slides on water and/or underwater along the sliding surface, according to Newton's second motion law, the motion of the sliding body can be decomposed into motion in the direction vertical to the sliding surface and motion in the direction parallel to the sliding surface when the sliding body slides under the action of the gravity of the sliding body and the action force of the sliding surface. Since the sliding mass slides down along the sliding surface, the acceleration of the sliding mass in the direction perpendicular to the sliding surface is zero, and the resultant force (i.e. the supporting force) applied to the sliding mass is balanced in the direction perpendicular to the sliding surface, and at this time, the motion of the bar in the direction perpendicular to the sliding surface is represented as:

∑F _y ＝W _i cosα _i -(U _i+1 -U _i )sinα _i -U _bi -N _i ＝0 (1)

wherein: sigma F _y The supporting force of the bar i in the direction perpendicular to the sliding surface, i being the number of divided bars, W _i Is the weight of bar i; alpha is alpha _i Is the inclination of the sliding surface of the bar i; u shape _i And U _i+1 The buoyancy force borne by the strips i and i + 1; u shape _bi The osmotic water pressure experienced by the bar i; n is a radical of _i Is a counter force of the sliding surface acting on the bar i.

For the direction parallel to the sliding surface, the resultant external force borne by the sliding mass is unbalanced, and the sliding mass slides downwards, at this time, the motion of the bar in the direction parallel to the sliding surface is represented as:

W _i sinα _i +ΔT _i -(U _i+1 -U _i )cosα _i -(C _i L _i +N _i tanφ _i )＝M _i a _i (2)

further, it is possible to obtain:

∑F _x ＝W _i sinα _i +ΔT _i -(U _i+1 -U _i )cosα _i -(C _i L _i +N _i tanφ _i )-M _i a _i (3)

wherein: sigma F _x The downward sliding force of the bar block i in the direction parallel to the sliding surface is shown, and i is the number of the divided bar blocks; w _i And M _i Weight and mass of the bar i, respectively; alpha is alpha _i The inclination of the sliding surface of the bar i; u shape _i And U _i+1 The buoyancy force borne by the strips i and i + 1; n is a radical of _i A counter force acting on the bar i for the sliding surface; delta T _i The resultant force of the downward sliding force between the bars; c _i Is the cohesive force of the bar i; l is _i The sliding distance of the bar i along the sliding surface; phi is a _i The dynamic friction angle between the strip block i and the sliding surface is related to the soil body internal friction angle of the target area; a is _i The acceleration of the bar i.

When the landslide body slides underwater, at least two resistance functions need to be overcome, one resistance function is flow field resistance, whether the water body has viscosity or not exists all the time, and the other resistance function is that the landslide body needs to overcome the friction force between the upstream surface and the water body to do work.

In this embodiment, the flow field resistance and the surface friction of the sliding mass are respectively analyzed as a whole, and the flow field resistance is expressed as:

wherein: f _f The flow field resistance of the landslide body; g is a landslide bodyThe mass of (c); v is the slip speed of the slip mass; and t is the slip time of the slip mass.

The surface friction is expressed as:

wherein: f _s The surface friction of the landslide body; c. C _d Is constant, in this embodiment, c _d The value range is 0.15-0.18; rho _s Is the density of the water body; r is a viscous drag coefficient; and S is the surface area of the upstream surface of the landslide body.

Considering the bars as rigid bodies with certain mass, the vertical force between the bars may be ignored, so that the acceleration of each block at a certain moment is equal, the total force between the blocks is zero according to the dynamic balance condition, at this time, the acceleration of the bars at a certain moment when sliding on water can be calculated according to the above formulas (1), (4), (5) and (2) or (3), and the acceleration of the bars at a certain moment when sliding underwater can be calculated according to the formulas (1), (4), (5) and (2) or (3).

S1033: and calculating the unit horizontal speed and the unit time increment of the sliding mass in each sliding step.

Firstly, calculating the unit horizontal speed of the bar block after sliding for a preset unit distance according to the initial speed of the sliding body in the current sliding step and the unit acceleration. In the present embodiment, the unit horizontal velocity is calculated by the following formula:

wherein: v. of _t The unit horizontal speed reached after the sliding mass slides within the current sliding step by the preset unit distance is also used as the initial speed of the next sliding step to participate in the calculation of the unit horizontal speed in the next sliding step; v. of ₀ The initial speed of the sliding body at the starting moment of the current sliding step (namely, the unit horizontal speed of zero or the last sliding step); a is the addition of a landslide bodyVelocity, which can be dependent on the acceleration a of the bars _i Calculating to obtain; and the delta L is a preset unit distance for the sliding body to slide.

Then, the unit time increment of the sliding body in the current sliding step (namely the time required for the sliding body to slide at the current initial speed and the acceleration by the preset unit distance delta L) is calculated according to the initial speed, the unit horizontal speed and the acceleration of the sliding body in the current sliding step. In this embodiment, the increment per unit time is calculated by the following formula:

Δt＝(v _t -v ₀ )/a (7)

wherein: Δ t is a unit time increment.

S1034: it is determined whether the unit horizontal velocity is zero.

Judging whether the unit horizontal speed is zero, if so, indicating that the sliding mass has slid to the farthest distance and stops moving, and at the moment, continuing to execute the step S1035; otherwise, it indicates that the landslide mass still slides down, the movement of the landslide mass is not stopped, and the landslide mass still can impact the water body to form surge, and at this time, the step S106 is executed by skipping.

S1035: and outputting the motion parameters and the motion process of the motion model of the landslide body.

And integrating the unit horizontal speed, unit time increment and the like of the landslide body motion model obtained by calculation according to each sliding step at each moment, and outputting the total sliding time, the sliding distance and the sliding speed of the landslide body motion model at each moment to obtain the motion process of the landslide body on the water and/or under the water.

S1036: and updating the initial motion parameters of the sliding mass in the next sliding step, and performing iterative solution.

Updating the initial time and initial speed of the sliding step at the next sliding step (i.e. the sliding of the sliding body at the next preset unit distance) and the initial time of the starting time of the sliding body and the water body surface at the next preset unit distance by the unit horizontal speed and the unit time increment of the current sliding step (i.e. the sliding of the sliding body at the current preset unit distance) calculated in the step S1034, and then skipping to execute the step S1032 until the sliding body stops moving.

S2: and constructing a discretized SPH surge numerical calculation model based on the SPH method.

Specifically, an SPH surge fluid particle expression of the water body is constructed based on an SPH method, a control equation of the water body motion under the impact of the landslide body is constructed based on the landslide body motion model, the control equation is dispersed through the SPH surge fluid particle expression, and a discretized SPH surge numerical calculation model is constructed by combining a constructed state equation and a fluid particle displacement change equation.

As shown in fig. 6, the step S2 includes the following sub-steps:

s201: and constructing an SPH surging fluid particle expression.

The water body in the calculation domain is dispersed into N small volume units and replaced by fluid particles (or interpolation particles) based on an SPH method, the SPH method is based on a partial differential equation system taking the density, the speed, the energy and the like of the fluid particles as variables, and a function describing a fluid field is approximately expressed as an integral of the product of an arbitrary function and an accounting number by kernel function approximation. The state parameters (such as density, pressure, velocity, etc.) of the simulated water body (fluid particles) at any point in space can be obtained by integrating the values of various points on a kernel function, and the state parameters are represented as kernel estimation values of certain fluid particles at space position coordinates. In this embodiment, the kernel estimate of the fluid particle at the spatial position coordinates is expressed in the form of:

wherein: a (r) _I ) And A (r) _J ) Respectively the coordinates r of the fluid particles I and the fluid particles J at the corresponding positions _I And position coordinates r _J A kernel estimate of (I) ═ 1, 2., N, J ═ 1, 2., N is the number of discrete fluid particles in the computational domain; d is a calculation domain; d is a spatial dimension; k (r) _I -r _J H) is a kernel function, r _I -r _J The distance between the fluid particle I and the fluid particle J, and h is the effective range of the defined kernel functionI.e. the smooth length of the kernel function.

The N fluid particles each have a mass, denoted m ₁ ,m ₂ ,..,m _N And the coordinates of the mass center positions of the N fluid particles are expressed as r ₁ ,r ₂ ,..,r _N Then, the contribution of the jth fluid particle (or fluid particle J) to the kernel estimate of the fluid particle at the spatial position coordinates is:

wherein: m is _J And ρ _J Respectively the mass and density of the fluid particles J.

From the contribution of the jth fluid particle (or fluid particle J) to the estimated value of the kernel of the fluid particle at the spatial position coordinate, in the numerical integral calculation of the kernel function, the integral may be expressed in the form of a finite series sum, and then the estimated value of the kernel of the fluid particle at the spatial position coordinate in the equation (8) may be approximated as:

thus, an expression of the SPH surging fluid particles is obtained.

S202: and constructing a water body motion control equation under the impact of the landslide body and dispersing the equation into an SPH (discrete particle ph) discrete form.

Firstly, a mesh-free SPH method based on Lagrange is adopted to construct the water motion construction N-S control equation under the impact of the landslide mass. In the present embodiment, the lagrangian-type governing equation includes a continuity equation and a momentum equation; wherein the continuous equation is expressed as:

wherein: ρ is the density of the fluid particles; t is time;

is the motion velocity vector of the fluid particles.

The momentum equation is expressed as:

wherein: ρ is the density of the fluid particles; t is time;

is the motion velocity vector of the fluid particle; p is the particle pressure;

is the acceleration of gravity; r' is the kinematic viscosity coefficient, which in this example is 10 ^-6 m ² /s。

In other embodiments, euler control may also be used to characterize the movement of the body of water.

And then, discretizing the governing equation by using the SPH surging fluid particle expression, and expressing the governing equation in an SPH discrete form. In this embodiment, the SPH discrete form of the continuous equation is represented as:

wherein: ρ is a unit of a gradient _I And ρ _J Density of fluid particles I and J, I1, 2, N, J1, 2, N being the number of discrete fluid particles within a computational domain; t is time; v _IJ Is the velocity difference, V, between fluid particles I and fluid particles J _IJ ＝V _I -V _J ，V _I And V _J The movement speeds of the fluid particles I and the fluid particles J respectively; m is _J Is the mass of the fluid particle J; k is _IJ For the kernel function, K, of the influence of the fluid particles J on the fluid particles I _IJ ＝K(r _I -r _J ,h)，r _I -r _J Is the distance between the fluid particle I and the fluid particle J, and h is the smooth length of the kernel function; r is _I And r _J Respectively, the position coordinates of the fluid particles I and the fluid particles J.

The SPH discrete form of the momentum equation is represented as:

wherein: rho _I And ρ _J Density of fluid particles I and J, I1, 2, N, J1, 2, N being the number of discrete fluid particles within a computational domain; t is time; v _I Is the moving speed of the fluid particles I; m is _J Is the mass of the fluid particle J; k _IJ For the kernel function, K, of the influence of the fluid particles J on the fluid particles I _IJ ＝K(r _I -r _J ,h)，r _I -r _J Is the distance between the fluid particle I and the fluid particle J, and h is the smooth length of the kernel function; r is a radical of hydrogen _I And r _J Position coordinates of the fluid particles I and the fluid particles J respectively; p is a radical of _I And p _J Pressures of fluid particles I and fluid particles J, respectively; n shape _IJ Is a diffusion term variable between the fluid particle J and the fluid particle I;

is the acceleration of gravity.

To avoid non-physical oscillations in the solution domain, a diffusion term variable is introduced in the discrete course of the above momentum equations to reduce non-physical oscillations and prevent non-physical penetration of the fluid particles in the vicinity, in this embodiment, the diffusion term variable pi between the fluid particles J and the fluid particles I _IJ The formula proposed by Morris is used, which is expressed as:

wherein: r' is kinematic viscosity coefficient;

is the vector distance between the fluid particle I and the fluid particle J; v _IJ Is the velocity difference between fluid particle I and fluid particle J; rho _I And ρ _J The densities of fluid particles I and fluid particles J, respectively.

S203: an equation of state is constructed based on the fluid compressibility.

In the SPH method, the motion of fluid particles is generated by the gradient effect of pressure, in the embodiment, a theoretically incompressible fluid is regarded as a compressible fluid by adopting a method of artificially increasing the compressibility of the fluid, and the compressibility is introduced into the equation of state of a water body to simulate the fluid with a free surface. In this embodiment, the equation of state is expressed as:

wherein: p is artificially applied fluid particle pressure; rho ₀ Is a reference density constant; ρ is the fluid particle density; c. C ₀ Is an artificial sound velocity, in this embodiment, an artificial sound velocity c ₀ Taking about 10 times of the maximum flow velocity of the flow field to ensure that the density calculation error caused by the compressibility is controlled within 1 percent so as to improve the simulation truth; γ is a constant, and in the present embodiment, γ is 7.

From this, the displacement variation of the fluid particles can be obtained as:

wherein:

is the vector of the change in displacement of the fluid particles,

is the velocity change vector of the fluid particle;t is time.

S204: and constructing a discretized SPH surge numerical calculation model.

Integrating the control equation and the state equation in the SPH discrete form and the displacement change of the fluid particles to form a discretized N-S equation set, adding solution conditions to form an iterative equation set, and constructing a discretized SPH surge numerical calculation model by simultaneous equations (13), (14), (16) and (17).

In this embodiment, the SPH swell numerical calculation model is represented as:

s3: and carrying out iterative solution on the SPH surge numerical calculation model to obtain a surge propagation motion process.

Setting parameters of an SPH surge numerical calculation model, assigning attributes to each fluid particle, determining the nearest fluid particle of each fluid particle based on a nearest particle search algorithm, and performing iterative solution on the SPH surge numerical calculation model based on the fluid particles and the nearest fluid particles thereof to obtain physical and mechanical parameters (at least comprising the density, pressure, speed and the like of the fluid particles) of a water body and a propagation motion process of the physical and mechanical parameters at each moment.

As shown in fig. 7, the step S3 includes the following sub-steps:

s301: setting model parameters and initializing an SPH surge numerical calculation model.

First, the kernel function and its smooth length range are determined. In an embodiment, the number of computations is chosen as a quadratic kernel function, which is expressed as:

wherein: q ═ r (r) _I -r _J ) K is a normalized constant, and k is 2/(pi h) for two-dimensional problem ² ) The smooth length range is case specific.

The total number of discrete fluid particles is then determined and the discrete boundary locations are processed. After the water body is dispersed into fluid particles with mass attributes, the fluid particles close to the reservoir bank boundary are regarded as being composed of fixed fluid particles (namely, a fixed wall boundary), when the sliding mass moves underwater, the surface of the sliding mass is regarded as being composed of movable boundary fluid particles (namely, a free surface), and in order to avoid the fluid particles from crossing the boundary, the boundary needs to be processed.

For the processing of fluid particles at solid wall boundaries, the Lennard-Jones repulsion force method was introduced, discretizing the solid wall boundaries into boundary virtual fluid particles, and assuming that the boundary fluid particles exert a central repulsion force on the fluid particles close to them that only works within a preset distance range, so that the fluid particles cross the solid wall boundaries and the particles at the boundaries do not participate in the density calculation of the fluid particles. In the present embodiment, the center repulsive force is expressed as:

wherein: f (r') is the central repulsive force of the solid-wall boundary particles; q, n, n 'are adjustable parameters, wherein Q is determined according to specific conditions, in the embodiment, the parameter Q is in the same magnitude as the square of the maximum speed value, and the parameters n and n' are respectively 12 and 4; r' ₀ Is the initial separation of the solid wall boundary particles from the fluid particles; r 'is the distance between the solid wall boundary particle and the fluid particle at the current moment, when r'>r' ₀ When f (r') is 0.

For the particles with free surfaces, a Koshizuka algorithm is adopted to realize the Dirichlet condition if the density rho of the fluid particles _a Satisfies the condition ρ _a <βρ ₀ (wherein ρ is ₀ Beta is a parameter less than 1, in this embodiment, the value of beta ranges from 0.8 to 0.99), and the fluid particles are considered as free surface particles, and the density of the fluid particles is equal to the actual density of the free surface water.

And finally, assigning an initial value to each fluid particle, determining iteration time steps, and finishing initialization of the SPH surge numerical calculation model. In this embodiment, the initial values of the fluid particles at least include initial density, pressure, velocity, particle type, and the like. The iteration time step number is an interval based on water motion change caused by the impact of a landslide body, namely the frequency or times of iterative solution.

S302: the kernel function is computed based on a nearest neighbor search algorithm.

Based on the nearest particle searching algorithm, each fluid particle is searched for the nearest fluid particle in the calculation domain, and the distance between the nearest fluid particle and the calculated fluid particle, namely r, is calculated _I -r _J And then based on the distance r between the nearest neighboring fluid particle and the calculated fluid particle _I -r _J The values of the kernel function are solved.

As shown in fig. 8, when the smooth length of the kernel function is very constant for all fluid particles, the entire computational domain may be divided into a series of square grid regions. For the nearest fluid particle of any fluid particle in the region, it must be in the mesh region to which it belongs or in the directly adjacent mesh region of the mesh region, so that only the fluid particles in the mesh region of the fluid particle or the directly adjacent mesh region of the mesh region need to be searched (9 mesh regions in the two-dimensional case and 27 mesh regions in the three-dimensional case), and all the fluid particles in the full calculation region need not to be searched, which greatly reduces the calculation amount and improves the calculation efficiency.

In other embodiments, if variable smoothing lengths are used, the smoothing length may be updated by using the average density, but when the smoothing length h is initially sized, sufficient fluid particles are ensured within a limited kernel. With variable smooth lengths, the population is typically about 12-20 for the two-dimensional case.

S303: and (5) iteratively solving the physical and mechanical parameters of the fluid particles.

The acceleration of fluid particles is generally divided into acceleration due to internal forces and acceleration due to external forces.

First, the density change of the fluid particles is calculated by the continuous equation of the SPH discrete form in the SPH swell numerical calculation model according to the initial density, velocity, mass, position coordinates of the particles, and the value of the kernel function of the corresponding fluid particles calculated in step S302.

In this embodiment, since the particles at the solid wall boundary do not participate in the density calculation, but the free surface particles participate in the density calculation, after the calculation is completed, the free surface particles need to be captured, and the density of the free surface particles needs to be corrected, that is, the density of the free surface particles is forced to be equal to the actual density of the free surface water body.

Then, according to the initial density of the fluid particles and the set reference density constant, the pressure on the fluid particles is calculated through the state equation in the SPH swell numerical calculation model, and at the same time, the acceleration caused by the external force is calculated.

Then, according to the initial density, velocity, pressure, mass, position coordinates of the fluid particles, and the value of the kernel function of the corresponding fluid particles calculated in step S302, the total acceleration of the fluid particles is calculated by using the momentum equation in the SPH discrete form in the SPH surging numerical calculation model, and then the final velocity of the fluid particles is calculated according to the set iteration time step, the initial velocity of the fluid particles, and the total acceleration.

In order to increase the numerical viscosity, the arrangement of the whole fluid particle system is more ordered, and the mutual penetration among the fluid particles is avoided, so that the calculated speed needs to be corrected. In this embodiment, the XSPH method is used to correct the speed, which is expressed as:

wherein:

the position coordinate correction value of the fluid particle I is obtained;

the corrected value of the velocity of the fluid particles I is obtained; epsilon is a correction coefficient, the value range of epsilon is 0-1, and epsilon is 0.02 in the embodiment;

the corrected value is the velocity difference between the fluid particles I and the fluid particles J.

And finally, calculating to obtain the displacement change vector of the fluid particles according to the final velocity of the fluid particles and a displacement calculation formula of the fluid particles in the SPH surge numerical calculation model.

Updating the next iteration time step by using the calculated fluid particle density change, speed, pressure intensity, acceleration and position change vector update, and skipping to the step S302 to execute repeatedly until convergence or the maximum iteration time step number is reached.

After the solution of the SPH surge numerical calculation model is completed, the position, speed, pressure, density and other related physical and mechanical parameters of each fluid particle can be obtained, and further the propagation motion process of the surge at each moment can be obtained.

In other embodiments, for the flow condition of the non-compressible fluid free surface, in order to avoid oscillation generated by explicit calculation and ensure the convergence of the result, for the time integration of the SPH method, a leap-frog method, a pre-estimation correction method and a Verlet velocity correction method can be generally adopted, and it is only necessary to satisfy the CFL condition that the time step Δ t should be satisfied.

S4: and processing the motion process of the landslide body and the propagation motion process of the water body.

In order to facilitate the intuitive observation of the water body motion under the impact of the landslide body, after the motion process of the landslide body and the propagation motion process of the water body are obtained through calculation, the motion process of the landslide body and the propagation motion process of the water body need to be subjected to imaging processing, and the simulated evolution process of the surge of the landslide body at each moment is obtained.

Specifically, firstly, the calculated movement process of the sliding mass and the propagation movement process of the water body are output as DXF format files by adopting a FORTRAN language programming, so that the exchange between the FORTRAN and the AutoCAD is realized, and further editing is facilitated. In an embodiment, the DXF file is a representation of the marking data of all the information contained in a particular version of the AutoCAD graphic file, which may be in ASCII format or in binary format.

Then, ignoring unnecessary entries in the DXF file (the required graphics are still available in AutoCAD), tracing such as swells using only the segments of entites, defining layer names, defining linetypes, colors, etc., taking care to satisfy the necessary group codes for each block, and having to have EOF entries at the end of the file, can also be run to generate CAD drawings.

Finally, the FORTRAN and software such as AutoCAD, MATLAB and the like are used for realizing interaction, secondary development is carried out, processing of graphic images is completed, the whole model has a strong data processing function and a dynamic demonstration function, generated related graphics can be processed by the TECPLOT, the MATLAB and the like in a later period, a seamless interface with common modeling software can be achieved, and the effect of double results with half effort can be achieved.

To further explain the swell simulation method based on the landslide body motion model and the mesh-free SPH in the embodiment, taking the bank landslide geological section image of the target region shown in fig. 3 as an example, the landslide body area is about 1.82 × 102m ² Maximum thickness of about 10m, and internal friction angle of soil body in target area

Cohesion force C _i 9KPa, the soil mass volume weight is 20.0kN/m ³ (ii) a According to the landform and geological condition, the landslide body is divided into 15 strips from top to bottom along the sliding surface, and therefore a landslide body motion model is established.

In the SPH swell numerical calculation model, the body of water is divided into a number of fluid particles with mass properties, and the bank slope is considered to be composed of immobilized particles. When the landslide body moves underwater, the surface of the landslide body is considered as a movable boundary particle. In order to avoid the 'penetration' phenomenon of water body particles, the bank slope wall-fixing particles are arranged in two lines in a staggered mode, and the distance between the particles is consistent with the distance between the water body particles. The inter-particle distance Δ x ═ Δ z ═ 1m, the total number of particles is 6806, and the iteration time step Δ t is 0.001 s.

Through calculation, the deformation motions of the sliding mass and the swell at each time point are shown in fig. 9 to 14, and the temporal changes of the acceleration and the speed of the sliding mass are shown in fig. 15 and 16. From this, it is clear that the maximum height of the wave formed when t is 14.2s is 9.63 m. The maximum slip distance was 79.5m and the maximum slip speed was 17.6 m/s.

According to the surge simulation method based on the landslide mass motion model and the mesh-free SPH, the bank high-speed landslide mass motion model is established based on the strip division method thought and combined with the mechanical principle, excessive stress decomposition on strips is reduced, and the maximum speed of the landslide mass and the change rule of the speed and the acceleration in the motion process can be clearly and quickly obtained; meanwhile, the water body is dispersed into a plurality of fluid particles to represent the whole continuous medium water body based on the SPH method, the density, the pressure, the speed and the like of the fluid particles are calculated by establishing an SPH surge numerical calculation model, and then the motion trail of the fluid particles is simulated, so that the surge evolution process under the impact of a landslide body is obtained, the surge climbing heights of different river sections are further determined, the action range of the landslide body on the surge climbing is displayed, the disaster area possibly caused by the surge climbing is determined, and more comprehensive and accurate scientific basis is provided for real-time forecasting and prevention of the surge of the landslide.

Example 2

Fig. 17 is a system block diagram of the swell simulation system based on the landslide body motion model and the meshless SPH according to this embodiment. The embodiment is used for realizing the landslide body motion model and mesh-free SPH-based surge simulation method described in embodiment 1, and includes a landslide body motion model calculation module 1, a surge numerical value calculation model construction module 2, an SPH numerical value calculation module 3, and a surge simulation module 4. Wherein:

the landslide mass motion model 1 calculation module is used for dividing a landslide mass in an image into a plurality of vertical strips by acquiring a geological section image of a bank landslide, and establishing a landslide mass motion model after attributing each strip; and analyzing the motion condition of each block, and calculating the slip time of the motion model of the landslide body, the slip speed and the slip distance at each moment to obtain the motion process of the landslide body on the water and/or under the water. The specific calculation process of the sliding mass motion model calculation module 1 refers to the related description of step S1 in embodiment 1, which is not described in detail in this embodiment.

The surging numerical calculation model construction module 2 constructs an SPH surging fluid particle expression of the water body based on an SPH method, constructs a control equation of the water body motion under the impact of the landslide body based on the landslide body motion model, disperses the control equation by the SPH surging fluid particle expression, and constructs a discretized SPH surging numerical calculation model by combining a constructed state equation and a fluid particle displacement change equation. For the specific construction process of the SPH surge numerical calculation model, the surge numerical calculation model construction module 2 refers to the related description of step S2 in embodiment 1, which is not described in detail in this embodiment.

The SPH numerical calculation module 3 sets SPH swell numerical calculation model parameters and assigns attributes to each fluid particle, then determines the nearest fluid particle of each fluid particle based on a nearest particle search algorithm, and iteratively solves the SPH swell numerical calculation model based on the fluid particles and the nearest fluid particles thereof to obtain the physical and mechanical parameters (at least including the density, pressure, speed and the like of the fluid particles) of the water body and the propagation motion process of the fluid particles at each moment. The specific calculation process of the SPH value calculation module 3 refers to the related description of step S3 in embodiment 1, which is not described in detail in this embodiment.

The surge simulation module 4 performs imaging processing on the movement process of the landslide body and the propagation movement process of the water body to obtain the simulated evolution process of the landslide body surge at each moment. The specific processing procedure of the surge simulation module 4 is described in the related description of step S4 in embodiment 1, and is not described in detail in this embodiment.

The landslide body motion model and mesh-free SPH based surge simulation system provided by the embodiment calculates the motion process of the landslide body motion model by arranging the landslide body motion model calculation module 1, constructs the SPH surge numerical value calculation model of water motion under the impact of the landslide body by arranging the surge numerical value calculation model construction module 2, calculates the physical and mechanical parameters of the water body by arranging the SPH numerical value calculation module 3, obtains the propagation motion process of the surge, and further simulates the motion trail of fluid particles, thereby obtaining the surge evolution process under the impact of the landslide body, and realizing the simulation of the water surge under the impact of the landslide body. In addition, the method of the embodiment can be used for simulating surge caused by large-volume high-speed bank collapse and landslide, can also be used for simulating the motion process of complex tsunamis, avalanches and volcanoes, and has a wide application range.

Claims

1. The swell simulation method based on the landslide body motion model and the meshless SPH is characterized by comprising the following steps of:

s3: setting parameters of an SPH surge numerical calculation model, and carrying out iterative solution on the SPH surge numerical calculation model to obtain physical and mechanical parameters of a water body and a propagation motion process of the physical and mechanical parameters at each moment;

2. The method for simulating swell based on the landslide body motion model and the mesh-free SPH according to claim 1, wherein the step S1 comprises the following sub-steps:

s101: collecting a geological section image of the bank landslide, and acquiring position coordinates of a sliding surface, a landslide body and a water body surface;

s102: dividing a sliding mass into a preset number of blocks based on a strip division method, and establishing a sliding mass motion model;

3. The method for simulating swell based on the landslide body motion model and the mesh-free SPH according to claim 2, wherein the step S103 comprises the following sub-steps:

4. The method for simulating a surge based on a landslide body motion model and a grid SPH according to claim 3, wherein in step S1032, the blocks are regarded as rigid bodies with a mass property, and each block is subjected to a supporting force in a direction perpendicular to the sliding surface and a sliding force in a direction parallel to the sliding surface when the landslide body slides along the sliding surface on or under water; when the landslide body slides along the sliding surface underwater, each block is also subjected to flow field resistance from a water body and surface friction force of the water body acting on the upstream surface of the landslide body respectively;

∑F _y ＝W _i cosα _i -(U _i+1 -U _i )sinα _i -U _bi -N _i ；

wherein: sigma F _y For the supporting force of the bar i in the direction perpendicular to the sliding surface, Sigma F _x The downward sliding force of the bar block i in the direction parallel to the sliding surface is shown, and i is the number of the divided bar blocks; w _i And M _i Weight and mass of the bar i, respectively; alpha is alpha _i Is the inclination of the sliding surface of the bar i; u shape _i And U _i+1 The buoyancy force borne by the strips i and i + 1; u shape _bi The osmotic water pressure experienced by the bar i; n is a radical of hydrogen _i Acting as a sliding surface against the bar iForce; delta T _i The resultant force of the downward sliding force between the bars; c _i Is the cohesive force of the bar i; l is a radical of an alcohol _i The sliding distance of the bar i along the sliding surface; phi is a _i The dynamic friction angle between the bar i and the sliding surface; a is _i Acceleration of bar i;

the surface friction is expressed as:

5. The method for simulating swell based on the landslide body motion model and the mesh-free SPH according to claim 1, wherein the step S2 comprises the following sub-steps:

s202: constructing a Lagrange type control equation for the water body motion under the impact of the landslide body, utilizing the SPH surge fluid particle expression to disperse the control equation, and expressing the control equation into an SPH discrete form; wherein the governing equations comprise a continuity equation and an energy equation;

s203: constructing an equation of state based on fluid compressibility;

6. The method for simulating swell based on the landslide body motion model and the meshless SPH according to claim 5, wherein in step S201, the SPH swell fluid particle expression is:

wherein: a (r) _I ) And A (r) _J ) Respectively the coordinates r of the fluid particles I and the fluid particles J at the corresponding positions _I And position coordinates r _J A kernel estimate of (I ≠ J), where I ≠ 1, 2., N, J ≠ 1, 2.., N, where N is the number of discrete fluid particles within the computational domain; m is _J And ρ _J Mass and density of the fluid particles J, respectively; k (r) _I -r _J H) is a kernel function, r _I -r _J H is the smooth length of the kernel function, which is the distance between the fluid particle I and the fluid particle J.

7. The landslide body motion model and mesh-free SPH based surge simulation method of claim 5 wherein in step S204, said SPH surge numerical computation model is represented as:

wherein: rho _I And ρ _J Density of fluid particles I and J, I ≠ 1, 2., N, J ≠ 1, 2., N, where I ≠ J, N is the number of discrete fluid particles within a computational domain; t is time; v _IJ Is the difference in velocity, V, between the fluid particle I and the fluid particle J _IJ ＝V _I -V _J ，V _I And V _J The movement speeds of the fluid particles I and the fluid particles J respectively; m is a unit of _J Is the mass of the fluid particle J; k is _IJ For the kernel function, K, of the influence of the fluid particles J on the fluid particles I _IJ ＝K(r _I -r _J ,h)，r _I -r _J Is the distance between the fluid particle I and the fluid particle J, and h is the smooth length of the kernel function; r is _I And r _J Position coordinates of the fluid particles I and the fluid particles J respectively; p is a radical of _I And p _J Pressures of fluid particles I and fluid particles J, respectively; n shape _IJ Is a diffusion term variable between the fluid particle J and the fluid particle I;

is the acceleration of gravity; p is artificially applied fluid particle pressure; rho ₀ Is a reference density constant; ρ is the fluid particle density; c. C ₀ Artificial sound velocity; gamma is a constant;

is a coordinate vector of the fluid particle;

is the motion velocity vector of the fluid particles.

8. The method for simulating swell based on the landslide body motion model and the mesh-free SPH according to claim 5, wherein the step S3 comprises the following sub-steps:

s303: respectively calculating the density change, the pressure and the acceleration of the fluid particles according to the SPH swell numerical calculation model and the kernel function, correcting the density and the speed of the fluid particles, and then repeatedly executing the step S302 to iteratively update the density, the speed and the position of the fluid particles until convergence or the maximum iteration time step is reached;

9. The method for simulating swell based on the landslide body motion model and the mesh-free SPH according to claim 8, wherein in step S301, the specific method for determining the boundary position of the fluid particle is as follows:

10. The landslide body motion model and mesh-free SPH based surge simulation system is characterized in that the landslide body motion model and mesh-free SPH based surge simulation method is used for realizing any one of claims 1-9, and comprises the following steps:

the landslide body motion model calculation module is used for establishing a landslide body motion model, and performing evolution calculation on the sliding time of the landslide body motion model and the sliding speed and the sliding distance at each moment to obtain the motion process of the landslide body on water and/or under water;

the surging numerical calculation model building module is used for building an SPH surging fluid particle expression and a control equation of water body motion under the impact of a landslide body, dispersing the control equation by the SPH surging fluid particle expression, and building a discretized SPH surging numerical calculation model by combining a constructed state equation and a fluid particle displacement change equation;

and the surge simulation module is used for carrying out imaging processing on the movement process of the landslide body and the propagation movement process of the water body to obtain the simulated evolution process of the landslide body surge at each moment.