CN110008599A - A kind of analogy method on the water and soil coupling landslide based on the double set two-phase object particle methods of high-order - Google Patents
A kind of analogy method on the water and soil coupling landslide based on the double set two-phase object particle methods of high-order Download PDFInfo
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Abstract
The present invention provides a kind of analogy method on water and soil coupling landslide based on the double set two-phase object particle methods of high-order, and this method is used two sets of substance points to divide to distinguish discrete solid soil particle and pore-fluid, the solution of governing equation is realized using the background grid of rule；Under Continuum Mechanics frame, the foundation of double set substances divide solid-liquid double-phase object particle method governing equation is realized；The interaction between solid-liquid double-phase substance point and background grid node is realized by high order B-spline basic function；The information such as acceleration, speed and the position of solid-liquid two-phase substance point are updated based on B-spline basic function, the nodal information being calculated is mapped on substance point, the material information of newest solid-liquid two-phase substance point, final output analog information are updated.The present invention is capable of the large deformation destructive process and its water and soil coupling mechanism of accurate simulation water and soil coupling landslide o earth slope, couples the Disaster Assessment of landslide o earth slope problem for water and soil and prevention and treatment provides data supporting.
Description
Technical field
The present invention relates to geological disaster analogue techniques, and in particular to a kind of analogy method on water and soil coupling landslide.
Background technique
Landslide is a kind of great research of abrupt geological hazard of destructiveness, is one of current three big geology disaster sources, various
Landslide o earth slope accounts for 60% or more in the landslide of scale, and the distribution of the landslide o earth slope caused by rainy season, rainfall that mostly occurs is wide, scale
Greatly, huge casualty loss is brought to engineerings such as building, water conservancy, traffic and minings.
Currently, generally studying the stability of soil-slope using limit equilibrium method or Strength Reduction Method, i.e., to analyze side
Based on the safety coefficient on slope and initial unstability slide surface.But the formation and development of landslide o earth slope is a complicated dynamics mistake
Journey, failure mechanism be related to slip mass by wriggling, extruding, slowly sliding, accelerate sliding, slow down that it is stable entire again to be slid onto
Process.Therefore, the only stability of analysis of slope will be unable to the motion process reflected comprehensively and understanding slope instability destroys, it is difficult to
Efficient Characterization rainfall induces the motion feature after slope instability large deformation destroys, if any landslide can also be produced after first stablize
Raw secondary landslide, the landslide having can block river valley during the motion and form barrier lake and cause secondary disaster.Meanwhile in rainfall
The landslide o earth slope of induction is related to the interaction of solid soil particle and pore liquid, and the variation of Pore Pressure will cause
The change of soil body effective stress, and then lead to the change of physical properties of soil, and pore water pressure is influenced in turn, this water and soil
Coupling effect is an important factor for leading to slopes shearing slip and further development perforation and form landslide.
Since the large deformation motion process and failure mechanism on landslide are complicated, it is difficult to which theoretically Direct Modeling is analyzed；Test
Research due to being limited by various objective condition, such as: test period, human and material resources and safety factor, it is also difficult to rainfall
Efficient, systematically research and analysis are unfolded in type Landslide Problems；The existing numerical computation method for being usually used in geotechnical engineering field, such as:
FInite Element and finite difference calculus etc., although can be used for simulating and determining the initial unstability and safety coefficient of side slope, due to net
Lattice distortion presence and be difficult to the large deformation motion process after effective analysis of slope unstable failure.Object particle method is that one kind combines
The non-mesh method of Lagrange and the dual description of Euler, the foundation of governing equation effectively prevent net independent of grid
Lattice aberration problems can be used for analyzing landslide o earth slope large deformation problem.But conventional matter point method is divided only with a set of substance point, nothing
The water and soil coupling effect of method Efficient Characterization rain-induced landslide；Meanwhile conventional matter point method due to use linear interpolation shape function,
Derivative at net boundary is discontinuous, therefore when substance point passes through net boundary, will cause biggish numerical error, i.e. " net
Lattice underrun error " causes the solving precision to pore water pressure and effective stress lower.
Summary of the invention
In view of the deficiencies of the prior art, the present invention provides a kind of water and soil coupling cunning based on the double set two-phase object particle methods of high-order
The analogy method on slope, the large deformation motion process and its water and soil coupling effect, raising that can effectively analyze landslide o earth slope problem are asked
Solve precision；The large deformation destructive process and water and soil coupling mechanism of Rainfall landslide o earth slope are accurately provided, it is sliding for Rainfall soil property
The Disaster Assessment on slope and prevention and treatment provide data foundation and simulation and forecast.
To achieve the above object, the technical solution adopted by the present invention is as follows:
A kind of analogy method on the water and soil coupling landslide based on the double set two-phase object particle methods of high-order, includes the following steps:
Step 1 passes through on-site land survey, determines that calculating parameter, the calculating parameter include that soil property reconnoitres the several of determining slopes
What configuration, soil property distribution and hydrogeologic condition；
Step 2 covers Lagrangian object particle method division based on double, respectively discrete soil body skeleton and pore-fluid, wherein solid
Phase substance point and liquid phase object particle initial time are overlapped, but geometrically keep independent, allow there are relative motion, glug is bright
Day substance point carries all substances information and follows the soil body to move and move and avoid mesh distortion, is simutaneously arranged set of rule
Euler's type background grid is to realize the solution of governing equation；
Step 3, under Continuum Mechanics frame, it is theoretical based on Darcy law and Biot, establish double set substances and divide
, the governing equation of solid-liquid double-phase object particle method:
The conservation of mass of solid phase:
The conservation of mass of liquid phase:
The conservation of mass of solid-liquid double-phase coupling:
In formula: ρ is density, viFor speed；N is porosity；S and w respectively indicate solid phase and liquid phase medium,
The momentum conservation equation of liquid phase:
In formula: k is infiltration coefficient.
The momentum conservation equation of solid-liquid double-phase coupling:
σ in formulaij=σ 'ij-pwδijFor resultant stress, σ 'ijFor the effective stress acted on soil body skeleton；
The solution procedure of step 4, B-spline basic function is based on high order B-spline basic function, couples substance to solid-liquid double-phase
The mass-conservation equation of point method and momentum conservation equation progress are discrete, and wherein B-spline interpolating shape functions are built upon node freedom
Spend space rather than background grid space, the B-spline basic function in each degree of freedom on a node basis is to pass through Cox- on parametric grid space
De Boor recurrence formula obtains, recurrence formula are as follows:
In formula: ξiFor parametric grid space nodes, p is the order of B-spline basic function, Ni,pIndicate i-th of degree of freedom on a node basis
On p rank B-spline basic function；
Step 5, B-spline interpolating shape functions realize the mutual mapping of substance point information and nodal information, are based on B-spline interpolation
Shape function, respectively by the quality of solid formation particle and liquid phase object particle, momentum, ess-strain information MAP to background grid section
Point；Apply displacement boundary conditions on background grid node, and realizes the explicit solution to governing equation；Gained node will be solved
Information maps back corresponding solid phase and liquid phase object particle by B-spline interpolating shape functions；
Step 6 applies boundary condition on background grid node, and realizes the explicit solution to governing equation；
Step 7: updating solid phase, the speed and location information of liquid phase object particle respectively；
Step 8: stress, strain, density and the porosity information of solid formation particle are updated according to soil constitutive model；
Step 9: updating porosity, volume and the pore water pressure of liquid phase object particle；
Step 10: output analog information into next calculation process or terminates to calculate.
Compared to the prior art, the present invention uses two sets of substance points to divide to distinguish discrete solid soil particle and hole clearance flow
Body；The solution of governing equation is realized using the background grid of rule；Under Continuum Mechanics frame, realize that double set substances divide
, the foundation of solid-liquid double-phase object particle method governing equation；Solid-liquid double-phase substance point and back are realized by high order B-spline basic function
Interaction and connection between scape grid node；Acceleration, the speed of solid-liquid two-phase substance point are updated based on B-spline basic function
And stress, strain, density, volume and pore water pressure, the porosity information of location information and solid formation particle, it will calculate
Obtained nodal information is mapped on substance point, and the last analog information of output as needed (can export mould each a period of time
It is quasi- as a result, the analog results of many group different times can be exported, then enter back into calculation process until simulated time knot
Beam, such as: simulation total time is 60s, an analog result can be exported every 5s, until knot is entirely simulated in simulation to 60s
Beam), Efficient Characterization and simulate the water and soil coupling effect of rain-induced landslide.
The present invention solves the problems, such as that tradition is based on the mesh distortion when solving water and soil coupling Landslide Problems of grid class method,
Solve conventional matter point method simultaneously and divided only with a set of substance point, can not the water and soil coupling of Efficient Characterization rain-induced landslide imitate
It answers and conventional matter point method is due to using linear interpolation shape function, the derivative at net boundary is discontinuous, when substance is brought out into the open
More net boundary when, biggish numerical error will be caused, cause the solving precision to pore water pressure and effective stress lower
Problem；The present invention is used to simulating and analyzing all kinds of landslide o earth slope problems under water and soil coupling, being capable of accurate simulation water and soil coupling
Close landslide o earth slope large deformation destructive process and its water and soil coupling mechanism, for water and soil couple landslide o earth slope problem Disaster Assessment and
Prevention and treatment provides data supporting.
Detailed description of the invention
Fig. 1 is step 4B spline base function recursive resolve schematic diagram of the present invention；
Fig. 2 (a), 2 (b) for conventional matter point method under step 4 same background grid dividing of the present invention linear interpolation shape letter
Several and 3 B-spline interpolating shape functions figures；
Fig. 3 is step 5 Algorithm mapping process schematic of the present invention；
Fig. 4 is inventive algorithm flow chart；
Fig. 5 is the computation model of the embodiment of the present invention 1；
Fig. 6 is the changing rule of 1 slopes of embodiment of the present invention landslide large deformation motion process kinetic energy；
Fig. 7 is the displacement cloud atlas of 1 slopes process of landslides different moments of the embodiment of the present invention；
Fig. 8 is 1 analog result of the embodiment of the present invention, and the T=60s moment simulates the equivalent moulding strain of gained slopes and pore water
Pressure cloud atlas.
Specific embodiment
A kind of analogy method on the water and soil coupling landslide based on the double set two-phase object particle methods of high-order, includes the following steps:
Step 1 passes through on-site land survey, determines calculating parameter, reconnoitres the geometrical configuration for determining slopes, soil property point including soil property
Cloth and hydrogeologic condition；Establish mathematical calculation model；
Step 2: Lagrangian object particle method division is covered based on double, respectively discrete soil body skeleton and pore-fluid, wherein solid
Phase substance point and liquid phase object particle initial time are overlapped, but geometrically keep independent, allow there are relative motion, glug is bright
Day substance point carries all substances information and follows the soil body to move and move and avoid mesh distortion；It is simutaneously arranged set of rule
Euler's type background grid is to realize the solution of governing equation；
Step 3: it is theoretical based on Darcy law and Biot under Continuum Mechanics frame, it establishes double set substances and divides
, the governing equation of solid-liquid double-phase object particle method:
The conservation of mass of solid phase:
The conservation of mass of liquid phase:
The conservation of mass of solid-liquid double-phase coupling:
In formula: ρ is density, viFor speed；N is porosity；S and w respectively indicate solid phase and liquid phase medium.
The momentum conservation equation of liquid phase:
In formula: k is infiltration coefficient.
The momentum conservation equation of solid-liquid double-phase coupling:
σ in formulaij=σ 'ij-pwδijFor resultant stress, σ 'ijFor the effective stress acted on soil body skeleton.
By linear loading acceleration of gravity, the stress distribution under soil property slopes equilibrium state is obtained, and then introduces water and soil
Landslide inducement -- the rain factor of coupling.
Step 4: high order B-spline basic function is based on, to the mass-conservation equation of solid-liquid double-phase couplings particle method and dynamic
It is discrete to measure conservation equation progress, in which:
The discrete scheme of the liquid phase equation of motion are as follows:
Wherein:Indicate in (n+1)th calculating step, liquid phase object particle in I background grid node, on the direction i
Acceleration；It indicates in n-th of calculating step, quality of the liquid phase object particle on I background grid node；WithIt respectively indicates in n-th of calculating step, liquid phase object particle is on I background grid node, the internal force on the direction i and outer
Force component.Above each amount, can sum to obtain, have by the corresponding information interpolation on liquid phase object particle respectively:
The discrete scheme of the solid phase equation of motion are as follows:
Step 5: be based on B-spline interpolating shape functions, respectively by the quality of solid formation particle and liquid phase object particle, momentum, answer
Stress-strain information MAP is to background grid node.
In formula: subscript behalf solid phase；Subscript sp indicates solid formation particle；It indicates in n-th of calculating step, wp
B-spline interpolating shape functions of the liquid phase object particle on i-th node；It indicates in n-th of calculating step, the wp liquid phase substance
Point is in gradient of the B-spline interpolating shape functions on the direction i on i-th node；It indicates in n-th of calculating step, the wp liquid
Porosity on phase substance point；It indicates in n-th of calculating step, the water pressure on the wp liquid phase object particle；Indicate the
In n calculating step, the volume of the wp liquid phase object particle；It indicates in n-th of calculating step, on the wp liquid phase object particle
Coefficient Tensor of Permeability；It indicates in n-th of calculating step, the water body speed on the wp liquid phase object particle；It indicates n-th
It calculates in step, value of the solid speed field on the wp liquid phase object particle；It indicates in n-th of calculating step, the wp liquid phase
Component of the water phase boundary force in i-th of direction on substance point；H is boundary layer thickness；It is walked for n-th of calculating, on i direction
Physical strength component.
Step 6: applying boundary condition on background grid node, and realize the explicit solution to governing equation.
Boundary condition are as follows:
In formula: h (X, t) is pressure head；H1For known boundaries head, i.e. Γ1For First Boundary Condition；qnFor unit
Time boundary normal direction flow (rainfall intensity),For the direction cosines in boundary exterior normal direction, i.e. Γ2For the second class side
Boundary's condition；Z is exudation boundary condition, i.e. Γ3For third boundary condition.
Explicit solution format are as follows:
Step 7: updating solid phase, the speed and location information of liquid phase object particle respectively.Wherein π phase (π=s, w) substance point
Speed and displacement are obtained by corresponding node information interpolation respectively:
Step 8: the information such as stress, strain, density and the porosity of solid formation particle are updated according to soil constitutive model, point
Cloth are as follows:
The strain rate and speed of rotation tensor of soil body skeleton are respectively as follows:
The more format of strain and effective stress on solid formation particle are as follows:
Wherein:For the material time derivative of effective stress on solid particle skeleton, expression formula are as follows:
For objective Jaumann strain rate, the influence rigidly gone to can be eliminated in large deformation.
According to solid phase mass-conservation equation, soil body grain skeleton is homogenized densityIn the expression formula of t moment
Are as follows:
Wherein J (Xsp, t) and it is solid deformation gradient tensorDeterminant, XspFor the coordinate vector of solid formation particle；Become
Shape gradient tensorMore new formula are as follows:
Since the change of homogenizing solid Density all is from the variation of porosity, then porosity is at the substance point of solid phase position
More format are as follows:
Since porosity parameter is present on solid formation particle, to acquire porosity in the value of liquid phase object particle positionIt then needs to construct porosity field first, i.e., first calculates value of the porosity on background grid node:
Step 9: updating porosity, volume and the pore water pressure of liquid phase object particle.
At this point, porosity can be by obtaining in the value of liquid phase object particle in background grid knot interpolation:
According to liquid phase quality conservation equation, the volume of liquid phase object particle more format are as follows:
Under isothermal saturated conditions, the situation of change of pore water pressure are as follows:
In formula: KwFor the bulk compressibility modulus of liquid phase water body.Since pore water pressure is stored by liquid phase object particle, then in liquid
The incremental update format of pore water pressure on phase substance point are as follows:
In formula:Characterization is value of the solid phase speed Divergence Field in liquid phase object particle position, i.e., at liquid phase object particle
Solid volume strain rate；Characterize the liquid phase volume strain rate at liquid phase object particle.
Step 10: output analog result into next calculation process or terminates to calculate, as needed when one section of simulation
Between (such as every the 1/12 of simulation total time) calculated result information of output, position including each solid phase and liquid phase object particle,
Quality, speed, stress, strain and pore water pressure；In turn, into next calculation process (from step 5 to step 10) up into
To simulation total time, that is, calculate terminates row.
The calculating process of implementation 1 is as follows:
As shown in figure 5, soil property slopes, slopes rest, inducement rainfall and induced landslide, using the present invention to the problem
Landslide large deformation process and pore water pressure simulated.Simulated time is 60s altogether, and wherein 0-10s is acceleration of gravity from 0
Gradually linear loading is to 9.81m/s2, i.e., the T=10s moment be slopes rest equilibrium state；In T > 10s, consider that rainfall causes
The decline of soil body cohesive strength and induced landslide, Fig. 6-Fig. 8 give analog result of the invention.
Claims (1)
1. a kind of analogy method on the water and soil coupling landslide based on the double set two-phase object particle methods of high-order, which is characterized in that including such as
Lower step:
Step 1 passes through on-site land survey, determines that calculating parameter, the calculating parameter include that soil property reconnoitres the geometry structure for determining slopes
Shape, soil property distribution and hydrogeologic condition；
Step 2 covers Lagrangian object particle method division based on double, respectively discrete soil body skeleton and pore-fluid, wherein solid formation
Particle and liquid phase object particle initial time are overlapped, but geometrically keep independent, allow there are relative motion, Lagrangian object
Particle carries all substances information and follows the soil body to move and move and avoid mesh distortion, is simutaneously arranged the Euler of set of rule
Type background grid is to realize the solution of governing equation；
Step 3, under Continuum Mechanics frame, it is theoretical based on Darcy law and Biot, establish that double set substances divide, solid
The governing equation of liquid two-phase object particle method:
The conservation of mass of solid phase:
The conservation of mass of liquid phase:
The conservation of mass of solid-liquid double-phase coupling:
In formula: ρ is density, viFor speed；N is porosity；S and w respectively indicate solid phase and liquid phase medium,
The momentum conservation equation of liquid phase:
In formula: k is infiltration coefficient.
The momentum conservation equation of solid-liquid double-phase coupling:
σ in formulaij=σ 'ij-pwδijFor resultant stress, σ 'ijFor the effective stress acted on soil body skeleton；
The solution procedure of step 4, B-spline basic function: it is based on high order B-spline basic function, to solid-liquid double-phase couplings particle method
Mass-conservation equation and momentum conservation equation carry out it is discrete, wherein B-spline interpolating shape functions be built upon the degree of freedom on a node basis sky
Between rather than background grid space, the B-spline basic function in each degree of freedom on a node basis is to pass through Cox-de on parametric grid space
Boor recurrence formula obtains, recurrence formula are as follows:
In formula: ξiFor parametric grid space nodes, p is the order of B-spline basic function, Ni,pIndicate the p in i-th of degree of freedom on a node basis
Rank B-spline basic function；
Step 5, B-spline interpolating shape functions realize the mutual mapping of substance point information and nodal information: being based on B-spline interpolation shape letter
Number, respectively by the quality of solid formation particle and liquid phase object particle, momentum, ess-strain information MAP to background grid node；?
Apply displacement boundary conditions on background grid node, and realizes the explicit solution to governing equation；Gained nodal information will be solved
Corresponding solid phase and liquid phase object particle are mapped back by B-spline interpolating shape functions；
Step 6 applies boundary condition on background grid node, and realizes the explicit solution to governing equation；
Step 7: updating solid phase, the speed and location information of liquid phase object particle respectively；
Step 8: stress, strain, density and the porosity information of solid formation particle are updated according to soil constitutive model；
Step 9: updating porosity, volume and the pore water pressure of liquid phase object particle；
Step 10: output analog information into next calculation process or terminates to calculate.
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| CN112818574A (en) * | 2021-01-27 | 2021-05-18 | 江西理工大学 | Numerical method for simulating start-up formation, flow development and re-siltation of debris flow |
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