CN117034689A - Soil liquefaction large deformation analysis method based on gridless RBF mapping technology - Google Patents
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Abstract
A soil liquefaction large deformation analysis method based on a gridless RBF mapping technology belongs to the technical field of geotechnical engineering numerical analysis. The steps are as follows: 1) Adopting grid-free nodes to discrete potential soil liquefaction large deformation areas, and setting boundary conditions; 2) Constructing fixed Gaussian points in the background grid, and assembling matrixes and vectors required by a balance equation and a continuity equation; 3) Regenerating a set of motion Gaussian points in the background grid, recording field variable information obtained by solving an equation in the motion Gaussian points, and updating coordinates of the motion Gaussian points; 4) And mapping the field variable information of the moving Gaussian points back to the fixed Gaussian points, and realizing the redistribution of the soil stress state and the pore pressure information in space in the large deformation process. The invention cooperatively plays the advantages of precision and stability of any Lagrange-Euler frame in large deformation analysis and the characteristic that no grid method is not needed for unit topology, establishes an effective stress-pore water pressure coupling large deformation analysis method of saturated soil, realizes coupling analysis with finite elements, and provides a powerful technical means for simulating the problem of large deformation of soil liquefaction.
Description
Technical Field
The invention belongs to the technical field of geotechnical engineering numerical analysis methods, and relates to a soil liquefaction large deformation analysis method based on a gridless RBF mapping technology.
Background
Large deformation phenomenon exists widely in geotechnical engineering, and the induced soil body and structures are destroyed to seriously threaten the normal life of human beings and cause immeasurable economic loss. The soil body has pores and cracks on the microstructure, is a typical saturated porous medium under a water level line, and under the action of dynamic load, the pore water pressure of the saturated soil body is rapidly increased, so that the effective stress of a soil skeleton is reduced or even eliminated, and the local weakening-liquefying phenomenon of the soil body is induced. Actual earthquake damage shows that the large soil liquefaction deformation seriously affects the safe operation of the structure: in 1995, the daily raiser wharf in the sakagu had replaced the sandy soil area and the backfill soil area to be liquefied on a large scale, so as to cause the caisson to incline forwards; lower San Fernando soil dam in 1971 earthquake has obvious sliding deformation of upstream dam slopes due to certain liquefaction of soil body at the junction surface area of the dam foundation. Therefore, the soil liquefaction large deformation analysis method is one of hot problems in numerical simulation in engineering, and the liquefaction analysis method at the present stage mainly focuses on the strength of the soil and cannot meet urgent requirements of engineering on the liquefaction deformation characteristics of the soil. Meanwhile, the problem of large liquefaction deformation in geotechnical engineering often relates to the problem of strong nonlinearity of materials, and higher requirements are also provided for the existing analysis method of large liquefaction deformation.
The Finite Element (FEM) small deformation analysis method commonly adopted in geotechnical engineering is mature in development and high in calculation stability, but the model geometry, the soil stress state and the pore pressure information are not considered in the deformation process, so that the development process of soil liquefaction is difficult to truly reproduce. The large deformation analysis method in early geotechnical engineering is mainly based on grids and developed under the Lagrange framework and comprises the following steps: complete Lagrangian (TL) and Updated Lagrangian (UL). The method has wide application by virtue of good adaptability to the constitutive model and the advantages of easily capturing and solving domain boundaries and applying surface load. However, the TL/UL method may distort the grid during large deformation, thereby affecting simulation accuracy and even causing an unsolvable phenomenon, so that the method is gradually replaced by a RITSS method based on an arbitrary lagrangian-euler framework (ALE) and a coupled euler-lagrangian method (CEL). The RITSS method introduces a grid re-splitting process and a variable mapping technology based on standard FEM small deformation analysis, successfully simulates the problem of large deformation, but the RITSS method can have the problems of splitting failure or error accumulation in the continuous re-splitting and mapping processes; compared with the RITSS method, the CEL adopts the reference points to replace material points, so that the initial grid is ensured to be fixed in the deformation process, but the initial grid is difficult to develop deeply and secondarily and only supports total stress analysis due to the built-in commercial program, and the requirement of soil liquefaction large deformation analysis cannot be met. At present, research results of RITSS and CEL in seismic liquefaction large deformation simulation are irrelevant.
While the grid-based large deformation simulation method is developed, another type of node-based large deformation method is also developed, wherein the most representative method is a non-grid method (MFM), and the method can be further divided into: smooth particle flow mechanics (SPH), cell-free galerkin's method (EFGM), and Radial Point Interpolation (RPIM). The method gets rid of the dependence of interpolation and integration in FEM on units, essentially avoids the problem of grid distortion, and has natural advantages in large deformation. However, the grid-free large deformation method is mainly poor in stability under the UL/TL framework, and in addition, compared with the grid-based analysis method, the application of the grid-free method in practical engineering is restricted due to the defect of low calculation efficiency of the grid-free method. Meanwhile, there are also a large deformation analysis method between grid-based and node-based, such as: the object point method (MPM) adopts background grid points to replace nodes to establish a balance equation, and adopts substance points to replace Gaussian points to carry out numerical integration, so that the problem of large deformation is successfully solved. However, the method has a large difference from the finite element in the numerical flow, is difficult to realize efficient coupling analysis, and cannot fully utilize the advanced calculation method and the abundant material constitutive library in the FEM program.
Disclosure of Invention
Aiming at the defects of the analysis method, the invention aims to provide a soil liquefaction large deformation analysis method based on a gridless RBF mapping technology. The invention is realized under any Lagrange-Euler frame, and establishes a gridless-finite element coupling large deformation analysis method. The method solves the problem that the accuracy of the large deformation method based on the units is limited by the grid quality, and provides a powerful technical means for simulating the problem of large deformation of soil liquefaction.
In order to achieve the purpose, the invention adopts the following technical scheme:
a soil liquefaction large deformation analysis method based on a gridless RBF mapping technology comprises the following steps:
s1, dispersing a potential soil liquefaction large deformation area by adopting mesh-free nodes, and setting displacement/pore pressure boundary conditions;
s2, generating a background grid covering the large deformation area in the step S1, constructing fixed Gaussian points in the background grid, and calculating a displacement/hole pressure shape function and a bias guide of each fixed Gaussian point;
s3, based on the calculation result of the step S2, assembling matrixes and vectors required by the balance equation and the continuity equation, and solving the equation;
s4, regenerating a set of motion Gaussian points in the background grid, recording field variable information obtained by solving the equation in the step S3 in the motion Gaussian points, and updating the coordinates of the motion Gaussian points according to the solved node displacement;
s5, constructing a Radial Basis Function (RBF), and mapping field variable information of the moving Gaussian points in the step S4 back to fixed Gaussian points to realize the redistribution of soil stress states and pore pressures in space in the large deformation process.
Further, the initial and deformed positions of the large deformed area in the step S1 need to be estimated, so as to ensure that the area can be always covered by the background grid in the step S2.
In (x) gi,k ,y gi,k ) Representing the coordinates of each fixed Gaussian point location within the kth background grid, (x) bi,k ,y bi,k ) Representing the kth background grid corner coordinates.
Further, the balance equation and the continuity equation in the step S3 may be represented by corresponding vectors and matrices:
in the method, in the process of the invention,u represents the acceleration, velocity and displacement matrix of the node, respectively, +.>p represents the pore pressure and the first derivative matrix of the pore pressure with respect to time, M, K, C, Q fs (Q sf ) S, H are respectively a mass matrix, an overall stiffness matrix, a damping matrix, a fluid-solid coupling matrix, a seepage matrix and a compression matrix which are obtained by calculating the displacement/pore pressure shape function of each fixed Gaussian point in the step S2 and the partial derivatives thereof, F f Representing the solid and fluid force vectors.
Further, the step S5 specifically includes the following steps in each load step:
s51, calculating the average distance between the fixed Gaussian points and taking the average distance as the radius of the supporting domain;
s52, calculating the distance between the fixed Gaussian point and the moving Gaussian point, and judging the number of the moving Gaussian points in the supporting domain of the fixed Gaussian point according to the size relation of the supporting domain radius in S51;
s53, calculating an RBF mapping function based on the supporting intra-domain motion Gaussian points in the S52, and transmitting the motion Gaussian point field variable information recorded in the S4 to the fixed Gaussian points through the mapping function;
s54, resetting the motion Gaussian point;
and S55, ending the calculation if the current load step is the last step, otherwise, circulating the S51-S54 process.
Further, the RBF mapping function in the step S53 is calculated as follows:
R(r) ij ＝(r ij +cd av ) q
wherein R (R), p (x) are a radial basis matrix and a linear additional basis matrix, respectively, a i ,b j To solve for the constant, n is the number of motion Gaussian points (equal to the radial basis matrix dimension) in the fixed Gaussian point support domain, m is the linear additional basis matrix dimension, and m=3 additional basis matrices in the project are [1, x, y ]]，d av To fix the average distance of Gaussian points, r ij The distance between a fixed Gaussian point and a certain motion Gaussian point is represented, c and q are shape parameters of a shape function, and the matrix expression of the above formula is as follows:
furthermore, the numerical value implementation flow is basically consistent with the finite element, seamless coupling with the finite element method can be realized on the level of the matrix in a mode of sharing nodes, and then a gridless-finite element coupling large deformation analysis method is established, so that the application range of the method is greatly expanded, and the defect of low calculation efficiency of the method is overcome.
Further, the stiffness matrix and the external force vector of the mesh-free finite element coupling large deformation analysis method can be expressed as follows:
in the formula, a subscript couple represents a coupling matrix or vector, Ω 1 ,Ω 2 The model mesh-free region and the finite element region, respectively.
The invention discloses a soil liquefaction large deformation analysis method based on a gridless RBF mapping technology, which cooperatively plays the advantages of precision and stability of an arbitrary Lagrange-Euler framework in large deformation analysis and the characteristic that a gridless method does not need unit topology, establishes a saturated soil effective stress-pore water pressure coupling large deformation analysis method, and realizes coupling analysis with finite elements based on a c++ language and an object-oriented programming method. The method solves the problem that the accuracy of the large deformation method based on the units is limited by the grid quality, and provides a powerful technical means for simulating the problem of large deformation of soil liquefaction.
Compared with the prior art, the project has the following advantages:
(1) The method is realized under any Lagrangian-Euler frame, and has higher precision and stability in large deformation analysis;
(2) The problem that the accuracy of a large deformation method based on the unit is limited by the quality of the grid is solved without the need of unit topology information;
(3) The method has good applicability to the soil elastoplastic constitutive model, and can more effectively capture complex mechanical behaviors such as soil liquefaction deformation and the like under the action of an earthquake;
(4) Based on a gridless RBF mapping technology, the soil body stress state and the hole pressure redistribution in space in the liquefaction deformation process are considered, and the soil body liquefaction development process is simulated more truly and reasonably;
(5) The numerical value implementation flow is basically consistent with the finite element, is convenient for coupling analysis with the finite element, greatly expands the application range of the method, and makes up the defect of lower calculation efficiency.
Drawings
FIG. 1 is a schematic diagram of the main flow of the method of the present invention;
FIG. 2 is a schematic diagram of a model background grid and a fixed Gaussian distribution;
FIG. 3 is a schematic diagram of a model motion Gaussian point distribution;
FIG. 4 is a schematic diagram of RBF-based inter-Gaussian point field variable mapping;
FIG. 5 is a schematic diagram of a grid-less finite element coupling analysis;
FIG. 6 (a) is a one-dimensional saturated earth column geometry model;
FIG. 6 (b) is a one-dimensional saturated earth column mesh-free model;
FIG. 6 (c) is a finite element model of a one-dimensional saturated earth column;
FIG. 7 is a comparison of vertical final sedimentation values under multi-load conditions of a saturated column;
FIG. 8 (a) is a plot of vertical settlement at the top of a saturated column as a function of consolidation time factor (finite element small deformation calculation result);
FIG. 8 (b) is a plot of vertical settlement at the top of a saturated column as a function of consolidation time factor (calculation result of no grid large deformation);
FIG. 9 is a diagram of a San Fernando dam geometry model and material partitioning;
FIG. 10 is a schematic representation of the actual jolt of a San Fernando dam (Wu Q, li DQ, liu Y, et al semiconductor performance of Earth dams founded on liquefiable soil layer subjected to near-fault group movements, soil Dyn Earth Eng,2021, 143:106623.);
FIG. 11 is a San Fernando mesh-free finite element coupling model;
fig. 12 (a) is a dam node deformation graph when t=5s;
fig. 12 (b) is a dam node deformation graph when t=8s;
fig. 12 (c) is a dam node deformation map at t=12s;
fig. 12 (d) is a diagram of dam node deformation at t=15 s (post-earthquake);
fig. 13 is a graph showing the pore pressure ratio distribution of the dam at t=15 s (post-earthquake).
Detailed Description
The invention will be further described with reference to the drawings and the specific embodiments, but the scope of the invention is not limited thereto.
Referring to fig. 1, a soil liquefaction large deformation analysis method based on a gridless RBF mapping technology comprises the following steps:
s1, dispersing a potential soil liquefaction large deformation area by adopting mesh-free nodes, and setting displacement/pore pressure boundary conditions;
s2, generating a background grid covering the large deformation area in the S1, constructing fixed Gaussian points in the background grid, and calculating a displacement/hole pressure shape function and a bias guide of each fixed Gaussian point;
s3, based on the calculation result of the S2, assembling matrixes and vectors required by a balance equation and a continuity equation, and solving the equation;
s4, a set of generated motion Gaussian points are re-generated in the background grid, the field variable information obtained by solving the equation in the S3 is recorded in the motion Gaussian points, and the coordinates of the motion Gaussian points are updated according to the solved node displacement;
s5, constructing a Radial Basis Function (RBF), and mapping field variable information of the moving Gaussian points in the S4 back to fixed Gaussian points to realize the redistribution of soil stress states and pore pressures in space in the large deformation process.
Referring to fig. 2, the initial and deformed positions of the large deformation area in step S1 are estimated, so as to ensure that the area can be covered by the background grid in step S2 all the time, in the present invention, a rectangular background grid is adopted, and 2×2 fixed gaussian points are generated inside (only one gaussian point is set in each background grid in the figure for convenience of representation), the background grid is kept unchanged in the large deformation simulation, and the size of the rectangular background grid is calculated according to the following formula:
wherein, I x ,l y Respectively representing the size of the background grid in the x and y directions, n represents the number of nodes in the solution domain, (x) i ,y i ) Representing node coordinates, each gaussian point coordinate is calculated as:
in (x) gi,k ,y gi,k ) Representing the coordinates of each fixed Gaussian point location within the kth background grid, (x) bi,k ,y bi,k ) Representing the kth background grid corner coordinates.
The balance equation and the continuity equation in the step S3 may be represented by corresponding vectors and matrices:
in the method, in the process of the invention,u represents the acceleration, velocity and displacement matrix of the node, respectively, +.>p represents the pore pressure and the first derivative matrix of the pore pressure with respect to time, M, K, C, Q fs (Q sf ) S, H are respectively a mass matrix, an overall stiffness matrix, a damping matrix, a fluid-solid coupling matrix, a seepage matrix and a compression matrix which are obtained by calculating the displacement/pore pressure shape function of each fixed Gaussian point in the step S2 and the partial derivatives thereof, F f Representing the solid and fluid force vectors.
Each matrix in the above equation is calculated as follows:
C＝αM+βK
wherein D represents a material constitutive model matrix, k represents a material permeation matrix, N,for displacement and pore pressure shape function matrix, B, < ->Bias guide matrix for displacement and pore pressure shape functions, ρ represents material density, Ω is integral domain, I d The two-dimensional identity matrix, a represents a scaling factor, alpha and beta are constants irrelevant to frequency, and the quality matrix calculated according to the formula can avoid negative values of the mesh-free high-order function at the corner nodes, so that the problems of reduced solving precision and even divergence are solved.
The external force vectors in the above equation are calculated as follows:
in the formula, v n For flow velocity in normal direction outside the water permeable boundary, f and f b Respectively representing the solid surface force and the physical load, f b,f Indicating fluid physical load.
The step S5 specifically comprises the following steps in each load step:
s51, calculating the average distance between the fixed Gaussian points and taking the average distance as the radius of the supporting domain;
s52, calculating the distance between the fixed Gaussian point and the moving Gaussian point, and judging the number of the moving Gaussian points in the supporting domain of the fixed Gaussian point according to the size relation of the supporting domain radius in S51;
s53, calculating an RBF mapping function based on the supporting intra-domain motion Gaussian points in the S52, and transmitting the motion Gaussian point field variable information recorded in the S4 to the fixed Gaussian points through the mapping function;
s54, resetting the motion Gaussian point;
and S55, ending the calculation if the current load step is the last step, otherwise, circulating the S51-S54 process.
Referring to fig. 3, a set of motion gaussian points is regenerated in the background grid, the motion gaussian point coordinates are consistent with the fixed gaussian points, the motion gaussian point coordinates are updated according to the node displacement calculated in step S2, and the motion gaussian point coordinates are moved in the background grid with field variable information in the large deformation simulation process. Referring to fig. 4, the RBF mapping function is used to transfer the field variable information from the motion gaussian point back to the fixed gaussian point, and the RBF mapping function is calculated by first determining the radius of each fixed gaussian point supporting domain, and calculating the radius according to the following formula:
wherein r is mi,k Representing the supporting domain diameter of the ith fixed gaussian point in the kth background grid, the moving gaussian point is considered to be within the supporting domain of a certain fixed gaussian point for all temporal gaussian cycles if:
in the formula, (x' g,i ,y’ g,i ) Representing coordinates after deformation of the temporary Gaussian points, taking alfs as a supporting domain parameter, wherein the alfs in the project takes a value of 3, and calculating RBF mapping functions according to the distance between the moving Gaussian points and the fixed Gaussian points:
R(r) ij ＝(r ij +cd av ) q
wherein R (R), p (x) are a radial basis matrix and a linear additional basis matrix, respectively, a i ,b j To solve for the constant, n is the number of motion Gaussian points (equal to the radial basis matrix dimension) in the fixed Gaussian point support domain, m is the linear additional basis matrix dimension, and m=3 additional basis matrices in the project are [1, x, y ]]，d av To fix the average distance of Gaussian points, r ij The distance between a fixed Gaussian point and a certain motion Gaussian point is represented, c and q are shape parameters of a shape function, and the matrix expression of the above formula is as follows:
wherein each matrix is:
f＝{f(x 1 )f(x 2 )f(x 3 )...f(x n )} T
A T ＝{a 1 a 2 ...a n } T ,B T ＝{b 1 b 2 ...b m } T
referring to fig. 5, the method has great potential in the processes of matrix vector calculation, gaussian point number value integration, equation solving and the like, and therefore has great potential in the coupling analysis with finite elements, firstly, a node discrete model is adopted for a potential liquefaction large deformation area, the rest part still adopts a finite element grid, the coupling analysis with a finite element method on a rigidity array level is realized by sharing nodes, and the method is convenient to integrate into commercial/autonomous research and development finite element software, so that the application range of the method is greatly expanded, and the defect of low calculation efficiency of the method is overcome.
The stiffness matrix and the external force vector of the non-grid-finite element coupling large deformation analysis method can be expressed as follows:
in the formula, a subscript couple represents a coupling matrix or vector, Ω 1 ,Ω 2 The model mesh-free region and the finite element region, respectively.
The soil liquefaction large deformation analysis method based on the gridless RBF mapping technology has the following advantages:
(1) The method is realized under any Lagrangian-Euler frame, and has higher precision and stability in large deformation analysis;
(2) The problem that the accuracy of a large deformation method based on the unit is limited by the quality of the grid is solved without the need of unit topology information;
(3) The method has good applicability to the soil elastoplastic constitutive model, and can more effectively capture complex mechanical behaviors such as soil liquefaction deformation and the like under the action of an earthquake;
(4) Based on a gridless RBF mapping technology, the soil body stress state and the hole pressure redistribution in space in the liquefaction deformation process are considered, and the soil body liquefaction development process is simulated more truly and reasonably;
(5) The numerical value implementation flow is basically consistent with the finite element, is convenient for coupling analysis with the finite element, greatly expands the application range of the method, and makes up the defect of lower calculation efficiency.
In order to prove the effectiveness of the technical scheme, the technical scheme is adopted to respectively carry out numerical simulation on the consolidation problem of the one-dimensional saturated soil column (the first embodiment) and the liquefaction deformation problem of the san fermi dam (the second embodiment).
Embodiment one: one-dimensional saturated soil column consolidation problem
Step 1, referring to the earth column geometric model in fig. 6 (a), establishing a mesh-free node model in fig. 6 (b) for large deformation analysis, and establishing a finite element model in fig. 6 (c) for comparison and development of small deformation analysis.
And 2, setting the parameters of the soil column materials, wherein the elastic modulus of the solid phase medium is E=1GPa, the Poisson ratio v=0.0, the porosity n=0.3, the permeability coefficient k=0.01 m/s, and the liquid phase is regarded as incompressible.
And 3, restraining all nodes of the earth column model in the horizontal direction, restraining the nodes at the bottom in the vertical direction, wherein the two side edges and the bottom edge are both non-drainage boundaries, and the top is a drainage boundary.
And 4, uniformly distributing loads on the top, wherein the total of four working conditions is T=0.2E, T=0.4E, T=0.6E and T=0.8E.
And 5, summarizing simulation results of the two models under four working conditions, wherein the simulation results comprise a vertical final sedimentation value and a change curve of vertical sedimentation at the top of the soil column along with a consolidation time factor.
Fig. 7 summarizes the comparison of the vertical final sedimentation values of the mesh-free large deformation and the finite element small deformation under different working conditions, and introduces the analytic solution of the one-dimensional finite elastic consolidation problem given by Gibson and considering the large deformation, and the result shows that: compared with the traditional FEM small deformation analysis, the simulation result of the grid-free large deformation has good anastomosis, and the accuracy of the method is verified.
As can be seen from fig. 8 (a) and (b), when the top load is small, the calculation result of the large deformation and the small deformation has small deviation, but the relative deviation of the two gradually increases with the increase of the load, so that the necessity of considering the soil state and the redistribution of the pore pressure information in space in the fluid-solid coupling large deformation problem is verified.
Embodiment two: liquefaction deformation problem of san fern dam
Step 1, fig. 9 shows the geometric model and material partition of the san frandol dam, where l=6.1 m, d=320 m, d 1 ＝88.3m，D 2 ＝40.1m，D 3 ＝88.3m，D 4 ＝60.5m，H 1 ＝12.9m，H 2 ＝3.8m，H 3 ＝27.2m，H 4 ＝10m。
Step 2, actual shock damage (fig. 10) shows that the dam body mainly sinks and slides and deforms towards the upstream, and almost no deformation occurs in the bedrock and the downstream weighting area, so that a grid-free and finite element coupling model (fig. 11) is established for the potential liquefaction large deformation area.
Step 3, calibrating the dam material by adopting a generalized elastoplastic model, wherein the dry density is 2690kg/m 3 The porosity was 0.397, the permeability coefficient was 0.0001m/s, and the remaining material parameters are shown in Table 1.
TABLE 1
And step 4, the bottom and two sides of the model are watertight boundaries, the rest are watertight boundaries, and the initial stress is calculated by the dam body under the action of dead weight.
And 5, dynamically calculating an acceleration time-course curve by using a Pacoima acceleration spectrum, wherein the peak acceleration is 0.6g, the holding time is 15s, and the integration interval is 0.005s.
And 6, sorting the dam deformation graph at typical moment and the post-earthquake pore pressure ratio distribution.
As can be seen from fig. 12 (a) - (d), the whole dam is not greatly deformed in the early stage of the earthquake, but as the earthquake continues, the effective stress is reduced, the dam body is obviously vertically sunk, the maximum sinking is positioned at the top of the dam, the maximum value is 15.6m, the dam slope is subjected to sliding deformation pointing upstream, the maximum horizontal displacement can reach 19.3m, the deformation after the earthquake of the dam is matched with the actual earthquake damage trend, and the effectiveness of the mesh-free finite element coupling method and the applicability of the elastoplastic constitutive model of the soil body are verified.
As can be seen from fig. 13, there is a large range of high hole pressure ratio area (greater than 0.85) in the dam foundation junction area, which indicates that the area has a large liquefaction risk, the decrease of the effective soil stress can cause insufficient resistance to continue to bear the driving force, and further sliding deformation can occur, however, due to the existence of the downstream weighting area, the further development of the deformation of the downstream dam slope is hindered, the sliding damage of the downstream dam slope similar to the upstream dam slope is not ensured, and the method is verified to provide an effective technical means for the problem of large soil liquefaction deformation.
The above description is illustrative of the best possible embodiment of the invention and is not intended to limit the invention to the particular embodiments disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.
Claims (5)
1. The soil body liquefaction large deformation analysis method based on the gridless RBF mapping technology is characterized by comprising the following steps of:
s1, dispersing a potential soil liquefaction large deformation area by adopting mesh-free nodes, and setting displacement/pore pressure boundary conditions;
s2, generating a background grid covering the large deformation area in the step S1, constructing fixed Gaussian points in the background grid, and calculating a displacement/hole pressure shape function and a bias guide of each fixed Gaussian point;
s3, based on the calculation result of the step S2, assembling matrixes and vectors required by the balance equation and the continuity equation, and solving the equation;
s4, regenerating a set of motion Gaussian points in the background grid, recording field variable information obtained by solving the equation in the step S3 in the motion Gaussian points, and updating the coordinates of the motion Gaussian points according to the solved node displacement;
s5, constructing a radial basis function RBF, and mapping field variable information of the moving Gaussian points in the step S4 back to the fixed Gaussian points to realize the redistribution of soil stress states and pore pressures in space in the large deformation process.
2. The method for analyzing the soil liquefaction large deformation based on the gridless RBF mapping technology according to claim 1, wherein the step S2 is to estimate the initial and deformed positions of the large deformation area in the step S1, so as to ensure that the background grid in the step S2 can always cover the area; a rectangular background grid is adopted, 2×2 fixed gaussian points are generated internally, and the coordinates of each gaussian point are calculated according to the following formula:
in (x) gi,k ,y gi,k ) Representing the coordinates of each fixed Gaussian point location within the kth background grid, (x) bi,k ,y bi,k ) Representing the kth background grid corner coordinates.
3. The method for analyzing soil liquefaction large deformation based on the gridless RBF mapping technology according to claim 1, wherein the balance equation and the continuity equation in the step S3 can be represented by corresponding vectors and matrices:
in the method, in the process of the invention,respectively representing the acceleration, the speed and the displacement matrix of the node; node->Respectively representing the first derivative matrix of pore pressure and time; m, K, C, Q fs (Q sf ) S, H are respectively a mass matrix, an overall stiffness matrix, a damping matrix, a fluid-solid coupling matrix, a seepage matrix and a compression matrix which are obtained by calculating the displacement/pore pressure shape function of each fixed Gaussian point and the partial derivatives thereof in the step S2; f, F f Representing the solid and fluid force vectors.
4. The method for analyzing the soil liquefaction large deformation based on the gridless RBF mapping technology according to claim 1, wherein the step S5 specifically comprises the following steps in each loading step:
s51, calculating the average distance between the fixed Gaussian points and taking the average distance as the radius of the supporting domain;
s52, calculating the distance between the fixed Gaussian point and the moving Gaussian point, and judging the number of the moving Gaussian points in the supporting domain of the fixed Gaussian point according to the size relation of the supporting domain radius in S51;
s53, calculating an RBF mapping function based on the supporting intra-domain motion Gaussian points in the S52, and transmitting the motion Gaussian point field variable information recorded in the S4 to the fixed Gaussian points through the mapping function;
s54, resetting the motion Gaussian point;
and S55, ending the calculation if the current load step is the last step, otherwise, circulating the S51-S54 process.
5. The method for analyzing the large deformation of the soil body liquefaction based on the gridless RBF mapping technology according to claim 4, wherein the RBF mapping function in the step S53 is calculated according to the following formula:
R(r) ij ＝(r ij +cd av ) q
wherein R (R), p (x) are a radial base matrix and a linear additional base matrix respectively; a, a i ,b j Is a substitution constant; n is the number of moving Gaussian points in the fixed Gaussian point support domain, and is equal to the radial basis matrix dimension; m is the linear additional base matrix dimension; d, d av Is the average distance between fixed Gaussian points; r is (r) ij Representing the distance between a fixed Gaussian point and a certain motion Gaussian point; c, q is a shape parameter of a shape function; the matrix expression of the above formula is:
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110298105A (en) * | 2019-06-26 | 2019-10-01 | 大连理工大学 | The CCPDI-IMPM method of saturated porous media analysis on Large Deformation |
| CN110457790A (en) * | 2019-07-26 | 2019-11-15 | 顾鑫 | The discontinuous golden finite element method of gal the Liao Dynasty of near field dynamics for malformation analysis |
| US20210012046A1 (en) * | 2019-07-12 | 2021-01-14 | Beihang University | Meshless method for solid mechanics simulation, electronic device, and storage medium |
| US11232648B1 (en) * | 2020-11-23 | 2022-01-25 | Bentley Systems, Incorporated | Systems, methods, and media for modifying a mesh for a material point method utilized for geotechnical engineering |
| CN115410663A (en) * | 2022-08-16 | 2022-11-29 | 大连理工大学 | Dynamic impact/contact elastoplasticity large deformation fracture analysis explicit phase field material point method |
-
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- 2023-08-02 CN CN202310964065.7A patent/CN117034689B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110298105A (en) * | 2019-06-26 | 2019-10-01 | 大连理工大学 | The CCPDI-IMPM method of saturated porous media analysis on Large Deformation |
| US20210012046A1 (en) * | 2019-07-12 | 2021-01-14 | Beihang University | Meshless method for solid mechanics simulation, electronic device, and storage medium |
| CN110457790A (en) * | 2019-07-26 | 2019-11-15 | 顾鑫 | The discontinuous golden finite element method of gal the Liao Dynasty of near field dynamics for malformation analysis |
| US11232648B1 (en) * | 2020-11-23 | 2022-01-25 | Bentley Systems, Incorporated | Systems, methods, and media for modifying a mesh for a material point method utilized for geotechnical engineering |
| CN115410663A (en) * | 2022-08-16 | 2022-11-29 | 大连理工大学 | Dynamic impact/contact elastoplasticity large deformation fracture analysis explicit phase field material point method |
Non-Patent Citations (2)
| Title |
|---|
| 荚颖;唐小微;栾茂田;杨庆;: "液化场地桩-土相互作用大变形无网格法分析", 大连理工大学学报, no. 04 * |
| 邹德高等: "深厚覆盖层上土质心墙坝防渗墙-心墙接头局部无网格大变形分析", 岩土工程学报, vol. 45, no. 9, pages 1 - 9 * |
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