CN110008599B - Water-soil coupling landslide simulation method based on high-order double-sleeve double-phase object particle method - Google Patents

Water-soil coupling landslide simulation method based on high-order double-sleeve double-phase object particle method Download PDF

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CN110008599B
CN110008599B CN201910279829.2A CN201910279829A CN110008599B CN 110008599 B CN110008599 B CN 110008599B CN 201910279829 A CN201910279829 A CN 201910279829A CN 110008599 B CN110008599 B CN 110008599B
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soil
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CN110008599A (en
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孙政
周晓敏
郭钟群
金解放
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Jiangxi University of Science and Technology
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Abstract

The invention provides a simulation method of water-soil coupling landslide based on a high-order double-set double-phase object particle method, which adopts two sets of object dot division to respectively disperse solid soil particles and pore fluid, and adopts a regular background grid to realize the solution of a control equation; under the continuous medium mechanical framework, the establishment of a control equation of a solid-liquid two-phase object particle method for dividing double sets of substances is realized; realizing interaction between solid-liquid two-phase object particles and background grid nodes through a high-order B spline basis function; updating the information such as acceleration, speed and position of the solid-liquid two-phase material point based on the B spline basis function, mapping the calculated node information to the material point, updating the material information of the latest solid-liquid two-phase material point, and finally outputting simulation information. The invention can accurately simulate the large deformation damage process and the water-soil coupling mechanism of the water-soil coupling soil landslide, and provides data support for disaster assessment and prevention of the water-soil coupling soil landslide problem.

Description

Water-soil coupling landslide simulation method based on high-order double-sleeve double-phase object particle method
Technical Field
The invention relates to a geological disaster simulation technology, in particular to a water-soil coupling landslide simulation method.
Background
Landslide is a sudden geological disaster with extremely high destructiveness, is one of three geological disaster sources at present, accounts for more than 60% of all-scale landslide, and is widely distributed and large in scale due to rainfall in rainy seasons, so that huge disaster losses are brought to engineering such as civil engineering, water conservancy, traffic and mining.
At present, the stability of the soil slope is generally studied by adopting a limit balance method or an intensity folding method, namely, the safety coefficient and the initial unstability sliding surface of the slope are mainly analyzed. However, the formation and development of soil landslide is a complex dynamic process, and the failure mechanism involves the whole process from peristaltic movement, extrusion, slow sliding, acceleration sliding and deceleration sliding of the landslide body to re-stabilization. Therefore, only analyzing the stability of the slope can not fully reflect and recognize the movement process of the instability damage of the slope, and the movement characteristics of the slope after the instability large deformation damage of the slope induced by rainfall are difficult to effectively characterize, if the landslide is stabilized for the first time, secondary landslide can be generated, and if the landslide is blocked by the river valley to form a barrier lake in the movement process, so that secondary disasters are caused. Meanwhile, the rainfall-induced soil landslide relates to the interaction of solid soil particles and pore liquid, wherein the change of pore water pressure can cause the change of effective stress of soil body, thereby causing the change of physical properties of the soil body, and adversely affecting the pore water pressure, and the water-soil coupling effect is an important factor for causing the shearing sliding of the slope body and further developing and penetrating to form the landslide.
Because the large deformation movement process and the damage mechanism of the landslide are complex, the direct modeling analysis is difficult in theory; experimental studies are limited by various objective conditions, such as: test period, manpower, material resources, safety factors and the like, and the problem of rainfall landslide is difficult to develop and efficiently and systematically study and analyze; the existing numerical calculation method commonly used in the geotechnical engineering field comprises the following steps: the finite element method, the finite difference method and the like can be used for simulating and determining the initial instability and the safety coefficient of the side slope, but the large deformation movement process after the instability and the damage of the side slope is difficult to effectively analyze due to the existence of grid distortion. The object point method is a gridless method combining Lagrange and Euler dual description, the establishment of a control equation is independent of grids, the grid distortion problem is effectively avoided, and the method can be used for analyzing the soil landslide large deformation problem. However, the traditional object point method only adopts one set of object point division, and cannot effectively represent the water-soil coupling effect of the rainfall landslide; meanwhile, the traditional object point method adopts a linear interpolation shape function, and the derivative at the grid boundary is discontinuous, so that when the object point passes through the grid boundary, a larger numerical error, namely a grid passing error, is caused, and the solving precision of pore water pressure and effective stress is lower.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a water-soil coupling landslide simulation method based on a high-order double-sleeve double-phase object particle method, which can effectively analyze the large deformation motion process of the soil landslide problem and the water-soil coupling effect thereof, and improve the solving precision; the large deformation damage process and the water-soil coupling mechanism of the rainfall type soil landslide are accurately provided, and data basis and simulation prediction are provided for disaster evaluation and prevention and control of the rainfall type soil landslide.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a water-soil coupling landslide simulation method based on a high-order double-set double-phase object particle method comprises the following steps:
step 1, determining calculation parameters through site survey, wherein the calculation parameters comprise geometrical configuration, soil distribution and hydrogeological conditions of a slope body are determined through soil exploration;
step 2, dividing based on a double Lagrangian material point method, respectively dispersing a soil body skeleton and pore fluid, wherein solid phase material points and liquid phase material points are overlapped with each other at the initial moment, but are kept independent geometrically, relative movement is allowed to exist, the Lagrangian material points carry all material information and move along with the soil body movement to avoid grid distortion, and a set of regular Euler background grids are arranged to solve a control equation;
step 3, under the continuous medium mechanics framework, based on Darcy law and Biot theory, establishing a control equation of a solid-liquid two-phase material particle method divided by two sets of materials:
conservation of mass of solid phase:
Figure BDA0002021292170000021
conservation of mass of liquid phase:
Figure BDA0002021292170000022
conservation of mass for solid-liquid biphase coupling:
Figure BDA0002021292170000023
wherein: ρ is density, v i Is the speed; n is the porosity; s and w represent the solid and liquid phase medium respectively,
momentum conservation equation for liquid phase:
Figure BDA0002021292170000024
wherein: k is the permeability coefficient.
Momentum conservation equation for solid-liquid dual-phase coupling:
Figure BDA0002021292170000025
middle sigma ij ＝σ′ ij -p w δ ij Is full stress, sigma' ij Is effective stress acting on the soil body framework;
and 4, a solving process of a B spline basis function, namely discretizing a mass conservation equation and a momentum conservation equation of a solid-liquid dual-phase coupling material particle method based on a higher-order B spline basis function, wherein the B spline interpolation shape function is established in a node degree of freedom space rather than a background grid space, the B spline basis function on each node degree of freedom is obtained on a parameter grid space through a Cox-de Boor recursion formula, and the recursion formula is as follows:
Figure BDA0002021292170000026
Figure BDA0002021292170000027
wherein: zeta type toy i For the space nodes of the parameter grid, p is the order of the B spline basis function, N i,p Representing a p-th order B spline basis function in the degree of freedom of the ith node;
step 5, the B spline interpolation shape function realizes the mutual mapping of the material point information and the node information, and the mass, momentum and stress strain information of the solid-phase material particles and the liquid-phase material particles are mapped to the background grid nodes respectively based on the B spline interpolation shape function; applying displacement boundary conditions on the background grid nodes, and realizing explicit solution of a control equation; mapping node information obtained by solving back to corresponding solid-phase and liquid-phase object points through a B spline interpolation shape function;
step 6, applying boundary conditions on the background grid nodes, and realizing explicit solution of a control equation;
step 7: respectively updating the speed and position information of solid-phase material points and liquid-phase material points;
step 8: updating stress, strain, density and porosity information of solid-phase material points according to the soil body constitutive model;
step 9: updating the porosity, volume and pore water pressure of the liquid phase material points;
step 10: and outputting the simulation information, and entering the next calculation flow or ending the calculation.
Compared with the prior art, the invention adopts two sets of material dot division to respectively disperse solid soil particles and pore fluid; solving a control equation by adopting a regular background grid; under the continuous medium mechanical framework, the establishment of a control equation of a solid-liquid two-phase object particle method for dividing double sets of substances is realized; realizing interaction and connection between solid-liquid two-phase object particles and background grid nodes through a high-order B spline basis function; based on B spline basis function, updating acceleration, speed and position information of solid-liquid two-phase material points, stress, strain, density, volume, pore water pressure and porosity information of solid-phase material points, mapping the calculated node information onto the material points, finally outputting simulation information according to requirements (a simulation result can be output at each period of time, a plurality of groups of simulation results at different time can be output, and then entering a calculation process until the simulation time is finished, for example, the total simulation time is 60s, the simulation result can be output every 5s until the whole simulation is finished, and the water-soil coupling effect of rainfall landslide is effectively represented and simulated.
The method solves the problem of grid distortion when the traditional grid-based method solves the problem of landslide due to water-soil coupling, and solves the problem that the traditional object point method only adopts one set of object point division and cannot effectively represent the water-soil coupling effect of the rainfall landslide, and the traditional object point method adopts a linear interpolation shape function, so that the derivative at the grid boundary is discontinuous, and when the object point passes through the grid boundary, larger numerical error is caused, so that the solution precision to pore water pressure and effective stress is lower; the method is used for simulating and analyzing various soil landslide problems under the action of water-soil coupling, can accurately simulate the large deformation damage process of the water-soil coupling soil landslide and the water-soil coupling mechanism thereof, and provides data support for disaster assessment and prevention of the water-soil coupling soil landslide problems.
Drawings
FIG. 1 is a schematic diagram of the recursive solution of the spline basis function of step 4B of the present invention;
FIGS. 2 (a) and 2 (B) are graphs of linear interpolation shape function and 3-degree B spline interpolation shape function of the conventional object point method under the same background meshing in step 4 of the present invention;
FIG. 3 is a schematic diagram of the algorithm mapping process of step 5 of the present invention;
FIG. 4 is a flowchart of an algorithm of the present invention;
FIG. 5 is a calculation model of embodiment 1 of the present invention;
FIG. 6 shows the kinetic energy variation law of the landslide mass in the large deformation motion process of the embodiment 1 of the invention;
FIG. 7 is a graph showing the displacement clouds at different moments during the landslide process of the slope body according to embodiment 1 of the present invention;
fig. 8 is a simulation result of example 1 of the present invention, and a cloud chart of equivalent shaping strain and pore water pressure of the obtained slope body is simulated at the time t=60 s.
Detailed Description
A water-soil coupling landslide simulation method based on a high-order double-set double-phase object particle method comprises the following steps:
step 1, determining calculation parameters including geometrical configuration, soil distribution and hydrogeological conditions of a slope body through site survey; establishing a numerical calculation model;
step 2: based on the division of a double set of Lagrangian material point method, respectively dispersing a soil body framework and pore fluid, wherein solid phase material points and liquid phase material points are overlapped with each other at the initial moment, but are kept independent geometrically, relative movement is allowed to exist, and Lagrangian material points carry all material information and move along with the soil body so as to avoid grid distortion; meanwhile, a set of regular Euler type background grids are arranged to solve a control equation;
step 3: under the continuous medium mechanics framework, based on Darcy law and Biot theory, a control equation of a solid-liquid two-phase particle method with double material divisions is established:
conservation of mass of solid phase:
Figure BDA0002021292170000041
conservation of mass of liquid phase:
Figure BDA0002021292170000042
conservation of mass for solid-liquid biphase coupling:
Figure BDA0002021292170000043
wherein: ρ is density, v i Is the speed; n is the porosity; s and w represent solid and liquid phase media, respectively.
Momentum conservation equation for liquid phase:
Figure BDA0002021292170000044
wherein: k is the permeability coefficient.
Momentum conservation equation for solid-liquid dual-phase coupling:
Figure BDA0002021292170000045
middle sigma ij ＝σ′ ij -p w δ ij Is full stress, sigma' ij To act on the soil bodyEffective stress on the skeleton.
And (3) obtaining stress distribution under the balanced state of the soil slope body by linearly loading gravity acceleration, so as to introduce landslide induction-rainfall factor of water-soil coupling.
Step 4: based on a high-order B-spline basis function, discretizing a mass conservation equation and a momentum conservation equation of a solid-liquid dual-phase coupling mass point method, wherein:
the discrete format of the liquid phase equation of motion is:
Figure BDA0002021292170000051
wherein:
Figure BDA0002021292170000052
indicating the acceleration of the liquid phase object point in the I background grid node and in the I direction in the n+1th calculation step; />
Figure BDA0002021292170000053
Representing the mass of liquid phase material points on the ith background grid node in the nth calculation step; />
Figure BDA0002021292170000054
And->
Figure BDA0002021292170000055
Respectively representing the internal force and the external force components of the liquid phase object point on the ith background grid node in the I direction in the nth calculation step. The above amounts can be obtained by interpolation and summation of corresponding information on liquid phase object points respectively, and the method comprises the following steps:
the discrete format of the solid phase equation of motion is:
Figure BDA0002021292170000056
/>
step 5: and mapping the mass, momentum and stress strain information of the solid-phase object particles and the liquid-phase object particles to the background grid nodes respectively based on the B spline interpolation shape function.
Figure BDA0002021292170000057
Figure BDA0002021292170000058
Figure BDA0002021292170000059
Figure BDA00020212921700000510
Figure BDA00020212921700000511
Figure BDA00020212921700000512
Wherein: superscript s represents the solid phase; subscript sp represents a solid phase particle;
Figure BDA00020212921700000513
representing a B spline interpolation function of the wp liquid phase object point on the I node in the nth calculation step; />
Figure BDA00020212921700000514
Representing the gradient of the B spline interpolation function of the wp liquid phase object point on the I node in the I direction in the n-th calculation step; />
Figure BDA00020212921700000515
Representing the porosity of the wp-th liquid phase object point in the nth calculation step; />
Figure BDA00020212921700000516
Representing the water pressure on the wp liquid phase object point in the nth calculation step; />
Figure BDA0002021292170000061
Representing the volume of the wp liquid phase object point in the nth calculation step; />
Figure BDA0002021292170000062
Representing the permeability tensor on the wp liquid phase object point in the nth calculation step; />
Figure BDA0002021292170000063
Representing the water body speed on the wp liquid phase object point in the nth calculation step; />
Figure BDA0002021292170000064
Representing the value of the solid velocity field on the wp liquid phase object point in the nth calculation step; />
Figure BDA0002021292170000065
Representing the component force of the water phase boundary force on the wp liquid phase object point in the ith direction in the nth calculation step; h is the boundary layer thickness; />
Figure BDA0002021292170000066
For the nth calculation step, the physical force components in the i directions.
Step 6: boundary conditions are imposed on the background mesh nodes and explicit solution to the control equations is achieved.
The boundary conditions are:
Figure BDA0002021292170000067
wherein: h (X, t) is the pressure head; h 1 Is of known boundary head, i.e. Γ 1 Is a first type of boundary condition; q n Boundary normal flow per unit time (rainfall intensity),
Figure BDA0002021292170000068
is the direction cosine of the direction of the normal outside the boundary, i.e. Γ 2 Is a second type of boundary condition; z is the exudation boundary condition, Γ 3 A third type of boundary condition.
The explicit solution format is:
Figure BDA0002021292170000069
Figure BDA00020212921700000610
step 7: and respectively updating the speed and position information of the solid-phase material dot and the liquid-phase material dot. The speed and displacement of pi-phase (pi=s, w) object points are obtained through corresponding node information interpolation respectively:
Figure BDA00020212921700000611
Figure BDA00020212921700000612
step 8: updating information such as stress, strain, density, porosity and the like of solid-phase material points according to the soil body constitutive model, wherein the distribution is as follows:
the strain rate and rotation rate tensors of the soil skeleton are respectively as follows:
Figure BDA0002021292170000071
Figure BDA0002021292170000072
the update format of the strain and effective stress on the solid phase material point is as follows:
Figure BDA0002021292170000073
Figure BDA0002021292170000074
wherein:
Figure BDA0002021292170000075
the time derivative of the material, which is the effective stress on the solid particle framework, has the expression:
Figure BDA0002021292170000076
Figure BDA0002021292170000077
for objective Jaumann strain rates, the effect of stiffness transition can be eliminated in large deformations.
According to the solid phase mass conservation equation, the soil body particle skeleton homogenizes the density
Figure BDA0002021292170000078
The expression at time t is:
Figure BDA0002021292170000079
wherein J (X) sp T) is the solid phase deformation gradient tensor
Figure BDA00020212921700000710
Determinant, X sp Is the coordinate vector of solid phase object points; deformation gradient tensor->
Figure BDA00020212921700000711
The update formula is:
Figure BDA00020212921700000712
since the change in density of the homogenized solid phase is all from the change in porosity, the updated format of the porosity at the solid phase location object points is:
Figure BDA00020212921700000713
because the porosity parameter exists on the solid phase material point, the value of the porosity at the position of the liquid phase material point is obtained
Figure BDA00020212921700000714
It is necessary to construct the porosity field first, i.e. calculate the value of the porosity at the background mesh node first:
Figure BDA00020212921700000715
Figure BDA00020212921700000716
step 9: updating the porosity, volume and pore water pressure of the liquid phase material point.
At this time, the value of the porosity in the liquid phase material point can be obtained by interpolation in the background grid node:
Figure BDA0002021292170000081
according to the liquid phase mass conservation equation, the volume update format of the liquid phase material points is as follows:
Figure BDA0002021292170000082
under the isothermal saturation condition, the change condition of pore water pressure is as follows:
Figure BDA0002021292170000083
wherein: k (K) w Is the bulk compression modulus of the liquid phase water body. Since pore water pressure is stored by liquid phase material points, the incremental update format of pore water pressure on liquid phase material points is as follows:
Figure BDA0002021292170000084
wherein:
Figure BDA0002021292170000085
the characteristic is the value of the solid phase velocity divergence field at the position of the liquid phase material particles, namely the solid phase volume strain rate at the position of the liquid phase material particles; />
Figure BDA0002021292170000086
Characterizing the liquid phase volume strain rate at the liquid phase object point.
Step 10: outputting a simulation result, entering the next calculation flow or finishing calculation, and outputting calculation result information including the positions, the quality, the speed, the stress, the strain and the pore water pressure of each solid phase and liquid phase material point at intervals of a period of simulation time (such as 1/12 of the total simulation time) according to the requirement; further, the next calculation flow (from step 5 to step 10) is entered until the simulation total time is reached, that is, the calculation is ended.
The calculation procedure of example 1 is as follows:
as shown in fig. 5, the soil slope body is initially stationary, and the landslide is induced by rainfall, and the landslide large deformation process and pore water pressure of the problem are simulated by using the invention. The simulation time is 60s, wherein 0-10s is gradually and linearly loaded from 0 to 9.81m/s for gravity acceleration 2 I.e. t=10s time is the stationary equilibrium state of the slope; at T>10s, consider the falling of soil cohesion caused by rainfall to induce landslide, and the simulation results of the invention are shown in fig. 6-8.

Claims (1)

1. A water-soil coupling landslide simulation method based on a high-order double-set double-phase object particle method is characterized by comprising the following steps:
step 1, determining calculation parameters through site survey, wherein the calculation parameters comprise geometrical configuration, soil distribution and hydrogeological conditions of a slope body are determined through soil exploration;
step 2, dividing based on a double Lagrangian material point method, respectively dispersing a soil body skeleton and pore fluid, wherein solid phase material points and liquid phase material points are overlapped with each other at the initial moment, but are kept independent geometrically, relative movement is allowed to exist, the Lagrangian material points carry all material information and move along with the soil body movement to avoid grid distortion, and a set of regular Euler background grids are arranged to solve a control equation;
step 3, under the continuous medium mechanics framework, based on Darcy law and Biot theory, establishing a control equation of a solid-liquid two-phase material particle method divided by two sets of materials:
conservation of mass of solid phase:
Figure FDA0004194100260000011
conservation of mass of liquid phase:
Figure FDA0004194100260000012
conservation of mass for solid-liquid biphase coupling:
Figure FDA0004194100260000013
wherein: ρ is density, v i Is the speed; n is the porosity; s and w represent the solid and liquid phase medium respectively,
momentum conservation equation for liquid phase:
Figure FDA0004194100260000014
wherein: k is the permeability coefficient;
momentum conservation equation for solid-liquid dual-phase coupling:
Figure FDA0004194100260000015
wherein: sigma (sigma) ij ＝σ′ ij -p w δ ij Is full stress; sigma'. ij Is effective stress acting on the soil body framework;
step 4, solving a B spline basis function: discretizing a mass conservation equation and a momentum conservation equation of a solid-liquid dual-phase coupling material particle method based on a higher-order B spline basis function, wherein the B spline interpolation shape function is established in a node degree of freedom space instead of a background grid space, the B spline basis function on each node degree of freedom is obtained on a parameter grid space through a Cox-de Boor recursion formula, and the recursion formula is as follows:
Figure FDA0004194100260000021
Figure FDA0004194100260000022
wherein: zeta type toy i For the space nodes of the parameter grid, p is the order of the B spline basis function, N i,p Representing a p-th order B spline basis function in the degree of freedom of the ith node;
the discrete format of the liquid phase equation of motion is:
Figure FDA0004194100260000023
wherein:
Figure FDA0004194100260000024
indicating the acceleration of the liquid phase object point in the I background grid node and in the I direction in the n+1th calculation step; />
Figure FDA0004194100260000025
Representing the mass of liquid phase material points on the ith background grid node in the nth calculation step; />
Figure FDA0004194100260000026
And->
Figure FDA0004194100260000027
Respectively representing the internal force and external force components of the liquid phase object particles on the ith background grid node in the I direction in the nth calculation step; the above amounts can be obtained by interpolation and summation of corresponding information on liquid phase object points respectively:
the discrete format of the solid phase equation of motion is:
Figure FDA0004194100260000028
step 5, the B spline interpolation shape function realizes the mutual mapping of the material point information and the node information: mapping the mass, momentum and stress strain information of the solid-phase object particles and the liquid-phase object particles to background grid nodes respectively based on a B spline interpolation shape function; applying displacement boundary conditions on the background grid nodes, and realizing explicit solution of a control equation; mapping node information obtained by solving back to corresponding solid-phase and liquid-phase object points through a B spline interpolation shape function;
Figure FDA0004194100260000029
Figure FDA00041941002600000210
Figure FDA00041941002600000211
Figure FDA00041941002600000212
Figure FDA00041941002600000213
Figure FDA0004194100260000031
wherein: superscript s represents the solid phase; subscript sp represents a solid phase particle;
Figure FDA0004194100260000032
representing a B spline interpolation function of the wp liquid phase object point on the I node in the nth calculation step; />
Figure FDA0004194100260000033
Representing the gradient of the B spline interpolation function of the wp liquid phase object point on the I node in the I direction in the n-th calculation step; />
Figure FDA0004194100260000034
Representing the porosity of the wp-th liquid phase object point in the nth calculation step; />
Figure FDA0004194100260000035
Representing the water pressure on the wp liquid phase object point in the nth calculation step; />
Figure FDA0004194100260000036
Representing the volume of the wp liquid phase object point in the nth calculation step; />
Figure FDA0004194100260000037
Representing the permeability tensor on the wp liquid phase object point in the nth calculation step; />
Figure FDA0004194100260000038
Representing the water body speed on the wp liquid phase object point in the nth calculation step; />
Figure FDA0004194100260000039
Representing the value of the solid velocity field on the wp liquid phase object point in the nth calculation step; />
Figure FDA00041941002600000310
Representing the component force of the water phase boundary force on the wp liquid phase object point in the ith direction in the nth calculation step; h is the boundary layer thickness; />
Figure FDA00041941002600000311
For the nth calculation step, the physical force components in the i directions;
step 6, applying boundary conditions on the background grid nodes, and realizing explicit solution of a control equation;
the boundary conditions are:
Figure FDA00041941002600000312
wherein: h (X, t) is the pressure head; h 1 Is of known boundary head, i.e. Γ 1 Is a first type of boundary condition; q n Is the boundary normal flow per unit time,
Figure FDA00041941002600000313
direction cosine of the direction of the normal outside the boundaryI.e. Γ 2 Is a second type of boundary condition; z is a exudation boundary condition; Γ -shaped structure 3 Is a third class boundary condition;
the explicit solution format is:
Figure FDA00041941002600000314
Figure FDA00041941002600000315
step 7: respectively updating the speed and position information of solid-phase material points and liquid-phase material points; the speed and displacement of the alpha phase alpha=s and w object points are obtained through interpolation of corresponding node information respectively:
Figure FDA0004194100260000041
Figure FDA0004194100260000042
step 8: updating stress, strain, density and porosity information of solid-phase material points according to the soil body constitutive model; the distribution is as follows:
the strain rate and rotation rate tensors of the soil skeleton are respectively as follows:
Figure FDA0004194100260000043
Figure FDA0004194100260000044
the update format of the strain and effective stress on the solid phase material point is as follows:
Figure FDA0004194100260000045
Figure FDA0004194100260000046
wherein:
Figure FDA0004194100260000047
the time derivative of the material, which is the effective stress on the solid particle framework, has the expression:
Figure FDA0004194100260000048
Figure FDA0004194100260000049
for objective Jaumann strain rate, the influence of rigidity transition can be eliminated in large deformation;
according to the solid phase mass conservation equation, the soil body particle skeleton homogenizes the density
Figure FDA00041941002600000410
The expression at time t is:
Figure FDA00041941002600000411
/>
wherein J (X) sp T) is the solid phase deformation gradient tensor
Figure FDA00041941002600000412
Determinant, X sp Is the coordinate vector of solid phase object points; deformation gradient tensor->
Figure FDA00041941002600000413
The update formula is:
Figure FDA00041941002600000414
since the change in density of the homogenized solid phase is all from the change in porosity, the updated format of the porosity at the solid phase location object points is:
Figure FDA0004194100260000051
because the porosity parameter exists on the solid phase material point, the value of the porosity at the position of the liquid phase material point is obtained
Figure FDA0004194100260000052
It is necessary to construct the porosity field first, i.e. calculate the value of the porosity at the background mesh node first:
Figure FDA0004194100260000053
Figure FDA0004194100260000054
step 9: updating the porosity, volume and pore water pressure of the liquid phase material points;
at this time, the value of the porosity in the liquid phase material point can be obtained by interpolation in the background grid node:
Figure FDA0004194100260000055
according to the liquid phase mass conservation equation, the volume update format of the liquid phase material points is as follows:
Figure FDA0004194100260000056
under the isothermal saturation condition, the change condition of pore water pressure is as follows:
Figure FDA0004194100260000057
wherein: k (K) w For the bulk compression modulus of a liquid phase body of water, because pore water pressure is stored by liquid phase material points, the incremental update format of pore water pressure on the liquid phase material points is as follows:
Figure FDA0004194100260000058
wherein:
Figure FDA0004194100260000059
the characteristic is the value of the solid phase velocity divergence field at the position of the liquid phase material particles, namely the solid phase volume strain rate at the position of the liquid phase material particles; />
Figure FDA00041941002600000510
Characterizing a liquid phase volume strain rate at the liquid phase object point;
step 10, outputting a simulation result, entering the next calculation flow or finishing calculation, and outputting calculation result information including the positions, the quality, the speed, the stress, the strain and the pore water pressure of each solid phase and liquid phase material point at intervals of one section of simulation time, such as 1/12 of the total simulation time according to the requirement; further, the next calculation flow is entered from step 5 to step 10 until the simulation total time is reached, i.e., the calculation is completed.
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