CN106980723A - The discrete particle SPH coupled simulation methods that gravity retaining wall antiskid is analyzed in earthquake - Google Patents
The discrete particle SPH coupled simulation methods that gravity retaining wall antiskid is analyzed in earthquake Download PDFInfo
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Abstract
A kind of discrete particle SPH coupled simulation methods that gravity retaining wall antiskid is analyzed in earthquake, comprise the following steps：(1) aggregates body macroparameter and continuous soil body matching numerical experimentation；(2) retaining wall FEM model, the soil body discrete particle method set up near retaining wall are set up, the continuous soil models of SPH away from retaining wall are set up：(3) the span yardstick linking of discrete particle and the continuous soil body is set up；(4) retaining wall FEM model is coupled with discrete particle method；(5) factor against sliding of retaining wall in earthquake is calculated.Compared with the continuous soil body coupling process of the discrete particle of existing retaining wall seismic response, coupling process of the invention more adapts to earthquake analysis on Large Deformation, while overcoming the problem of discrete particle and the continuous soil body can depart from coupling boundary in existing method.
Description
Technical Field
The invention belongs to the field of geotechnical engineering research, and particularly relates to a discrete particle-SPH coupling simulation method for anti-slip analysis of a gravity retaining wall in earthquake.
Background
The gravity retaining wall is used as a supporting structure in geotechnical engineering and has wide application in slope support in China. However, the theory of the anti-seismic design is not mature, the current analysis method is mainly a quasi-static method, and the gravity retaining wall has horizontal acceleration under the action of an earthquake, namely, the horizontal inertia force is simplified into static force to analyze the anti-slip stability of the retaining wall. In order to deeply obtain the anti-sliding stability of the retaining wall in the whole earthquake process, the earthquake response of the retaining wall can be simulated by establishing a finite element or finite difference and other continuous bodies, but the discontinuous dynamic contact action of the discrete particles and the retaining wall is difficult to analyze by the continuous body model. Therefore, in order to analyze the anti-sliding stability of the gravity type retaining wall in the whole earthquake process in a refined way, a soil body can be simulated based on discrete particles, but because of the limitation of the quantity of the discrete particles and the computer performance, the mechanical behavior of the soil body is difficult to simulate on the whole area by adopting the discrete particles, so that a solid discrete-continuous soil body coupling method is developed to reduce the discrete element simulation scale and simulate the earthquake response of the retaining wall by adopting the method (see the literature, "Zhoujian, Jinweifeng. numerical simulation of the earthquake response of the retaining wall based on the coupling method [ J ]. geotechnical mechanics, 2010, 31 (12): 3949-. However, in these coupling models, continuous solids are based on finite element or finite difference grid dispersion, and numerical instability problems such as grid distortion exist in the seismic large deformation simulation, so that the method is not suitable for seismic large deformation analysis by a meshless method and discrete particles, and continuous soil and discrete particles are easy to separate on the coupling boundary.
Smooth particle dynamics (SPH) is a meshless method, and can adapt to earthquake large deformation simulation of soil, so that coupling of the SPH method and discrete particles can be considered, soil close to a retaining wall is simulated by the discrete particles, soil far away from the retaining wall is simulated by the SPH method, discontinuous contact effect of the retaining wall and the discrete particles can be considered, the simulation scale of discrete elements can be effectively reduced, meanwhile, continuous soil can also adapt to large deformation analysis, but a cross-scale connection method needs to be constructed to couple the discrete particles around the retaining wall and the SPH continuous soil, and therefore the continuous soil and the discrete particles cannot be separated in a coupling transition region.
Disclosure of Invention
The invention provides a discrete particle-SPH coupling simulation method for earthquake gravity type retaining wall anti-skid analysis, aiming at overcoming the problems that the large deformation problem of a continuous soil body is difficult to consider and the continuous soil body and discrete particles are easy to separate on a coupling boundary when the existing discrete particle-continuous soil body coupling method is used for finely analyzing the earthquake gravity type retaining wall anti-skid stability.
The invention relates to some abbreviations and symbols, the following are notes:
SPH: the method refers to a Smooth particle dynamics (SPH) method in a meshless method, and a continuous soil body model established by the method can adapt to large deformation analysis of earthquake.
{uC}int: column vectors of SPH particle displacement combinations over the coupling transition domain, where the variable on the continuous soil is denoted by superscript C and the coupling is denoted by subscript int.
{fC}int: the SPH particles on the coupling transition domain are subjected to column vectors that are a combination of the coupling forces of the discrete particles.
{uC}uin: column vectors of SPH particle displacement combinations that are not on the coupling transition domain, where the subscript uin denotes no coupling.
Column vectors for SPH particle velocity combinations that are not on the coupling transition domain.
Not in the coupling transition regionColumn vectors of SPH particle acceleration combinations above.
{fC}uin: the column vector of the external force to which the SPH particles are not on the coupling transition region.
[ M ]: the mass matrix obtained by SPH discrete continuous solid differential equation.
[C] The method comprises the following steps And (4) obtaining a damping matrix by SPH discrete continuous solid differential equation.
[K] The method comprises the following steps And (3) a rigidity matrix obtained by SPH discrete continuous solid differential equation.
The translational displacement column vector of the ith discrete particle on the transition domain is coupled, where the superscript M denotes the variable on the discrete particle.
And coupling the translational acceleration column vector of the ith discrete particle on the transition domain.
And the displacement column vectors of the n discrete particles on the coupling transition domain are combined to form an overall displacement column vector.
{fi M}contact: the ith discrete particle in the coupling transition region is subjected to the action of other discrete particles to produce a resultant column vector, where the subscript contact indicates particle contact.
{fM}contact: coupled with n discrete particles in the transition regioni M}contactA column vector formed by the union.
{fi M}int: the ith discrete particle in the coupling transition region is coupled by the ith SPH particleThe resultant force column vector.
{fM}int: coupled with n discrete particles in the transition regioni M}intA column vector formed by the union.
[ m ]: and (3) forming an overall quality matrix by combining balance equations of the n discrete particles in the coupling transition domain.
nslip: the number of finite element boundary segments on the side of the retaining wall in contact with the particles, where the upper label slip indicates slip;
Fi slip: the side of the retaining wall in contact with the particles, wherein the particle horizontal thrust is experienced by the i-th section finite element boundary.
Fslip: the soil retaining wall is subjected to the horizontal thrust resultant force of the soil body, namely the slip force resultant force of the soil retaining wall.
nanti-slip: the number of finite element boundary segments at the bottom of the retaining wall in contact with the particles, where the superscript anti-slip indicates the slip resistance.
Fi anti-slip: the ith section of finite element boundary at the bottom of the retaining wall is subjected to the horizontal friction force of discrete particles.
Fanti-slip: the bottom of the retaining wall is subjected to the resultant force of the anti-sliding force of the soil body.
K: the anti-skidding of retaining wall stabilizes factor of safety.
In order to solve the technical problems, the following technical scheme is adopted:
the invention provides a discrete particle-SPH coupling simulation method for anti-slip analysis of a gravity type retaining wall in an earthquake, which comprises a macro parameter and continuous soil body matching numerical test of a bulk particle aggregate, a finite element model of the retaining wall, a discrete particle model near the retaining wall and an SPH continuous soil body model far away from the retaining wall are established in different areas, and meanwhile, a coupling transition area which is partially overlapped is arranged between discrete particles and the continuous soil body, so that the anti-slip stable safety coefficient calculation of the gravity type retaining wall in the earthquake is realized, and the specific steps are as follows:
step 1: performing a particle aggregate macroscopic parameter and continuous soil body matching numerical test;
step 2: establishing a retaining wall finite element model, establishing a soil discrete particle model near the retaining wall, and establishing an SPH continuous soil model far away from the retaining wall;
and step 3: establishing cross-scale connection between discrete particles and a continuous soil body;
and 4, step 4: coupling the retaining wall finite element model with the discrete particle model;
and 5: and calculating the anti-skid stability safety factor of the earth retaining wall in the earthquake.
Wherein,
(1) in the step 1, the particle aggregate macroscopic parameter and continuous soil body matching numerical test comprises the following steps:
sampling soil around a gravity type retaining wall, carrying out an indoor triaxial test to determine the internal friction angle and the cohesion force of the soil, carrying out an indoor dynamic triaxial test to determine the dynamic modulus of the soil, and assigning the obtained internal friction angle, the cohesion force and the dynamic modulus to a continuous soil model for use; continuously adjusting the mesoscopic parameters of the discrete particles to perform a biaxial compression test and a cyclic biaxial numerical test of the discrete particles, making the internal friction angle and the cohesive force obtained by the biaxial compression numerical test consistent with those obtained by the actual test, and making the dynamic modulus obtained by the cyclic biaxial numerical test consistent with that obtained by the actual test, thereby determining the mesoscopic parameters of the particles, such as the normal phase stiffness knTangential stiffness ksAnd coefficient of friction fcThe mesoscopic parameters are assigned for use by the discrete particle model.
(2) In the step 2, the retaining wall finite element model, the soil discrete particle model and the SPH continuous soil model are as follows:
and (2.1) using four-node isoparametric units in a finite element method for the retaining wall finite element model.
And (2.2) in the soil discrete particle model, the motion equation of the particles comprises a translation equation and a rotation equation.
(2.3) in the SPH continuous soil model, a continuous soil model is established by Smooth particle dynamics (SPH), and the used SPH kernel function adopts the existing Gaussian kernel function.
(3) In the step 3, the cross-scale connection between the discrete particles and the continuous soil body is established, and the specific method is as follows:
the method comprises the following steps that a partially overlapped coupling transition domain is formed between discrete particles and a continuous soil body, each discrete particle and a SPH particle of the continuous soil body on the coupling transition domain are correspondingly coupled one by one, the displacement, the speed and the acceleration are equal, and a coupling force algorithm between the discrete particles and the SPH particle coupling transition domain of the continuous soil body is established as follows:
the coupling transition region is provided with n SPH particles and n corresponding discrete particles, then the continuous soil body SPH particles are divided into two parts, and the n SPH particles on the coupling transition region are combined into a column vector { u }C}intThe coupling forces of the SPH particles by the discrete particles are combined into a column vector { f }C}intHere, the superscript C denotes the variable on the continuous soil mass and the subscript int denotes the coupling; for SPH particles not on the coupling transition region, the displacement, the velocity, the acceleration and the external force are respectively combined into a column vector { u }C}uin、And { fC}uinHere, the subscript uin denotes no coupling; simultaneously using [ M]、[C]And [ K ]]Respectively representing a mass matrix, a damping matrix and a rigidity matrix obtained by an SPH discrete continuous solid differential equation. The equation of power can then be derived based on SPH dispersion:
let the ith discrete in the coupling transition regionThe mass of the particles is miThe translational displacement column vector isCorresponding acceleration column vector ofThe resultant force from the action of other discrete particles is the column vector fi M}contactThe column vector of the I-th SPH particle coupling force is { fi M}intWhere superscript M denotes a variable on a discrete particle, where subscript contact denotes particle contact; regardless of particle rotation, the equilibrium equation for a single discrete particle is:
the equilibrium equations of n discrete particles in the coupling transition domain are combined, and the overall quality matrix is set as [ m]N particles of{fi M}contactAnd { fi M}intAre respectively combined in a simultaneous manner{fM}contactAnd { fM}intThus, the overall equilibrium equation for discrete particles over the coupled transition region can be written as:
the coupling force is solved as follows:
(a) displacement on coupled particles by cancelling unknown coupling forces
The acceleration of SPH particles and discrete particles in the coupling transition region is the same, and the coupling force is a pair of counter forces, one{fC}int＝-{fM}intSubstitution of equation (3) for equation (1) eliminates the unknown coupling force { fC}intAnd { fM}intAs follows:
in the above formula [ Mint]Is [ m ]]Substitution of [ M]The subsequent coupling mass matrix, where the unknown coupling force f has been cancelledi C}intAnd { fi M}intThe acceleration of the SPH particles in the coupling transition domain can be solvedSpeed of rotationAnd a displacement { u }c}int。
(b) Determining the coupling force in the coupling transition region
Will be solved toSpeed of rotationAnd a displacement { u }c}intThe coupling force column vector { f) acting on the SPH particles can be calculated by substituting formula (1)c}intThe column vector of coupling forces acting on the discrete particle spots { fM}int＝-{fc}int。
(4) In the step 4, the specific method for coupling the retaining wall finite element model and the discrete particle model comprises the following steps:
realizing finite element-discrete particle coupling by ensuring the continuity of force and speed on a coupling boundary, wherein on a contact surface of a finite element model and discrete particles of the retaining wall, the contact surface is a line boundary of the finite element model, the contact surface is a wall boundary of the discrete particles in the discrete element model, and the speed of a finite element node on the contact surface is extracted as the speed of a wall boundary node in the discrete element model; finite element model statistics of resultant force F of particles on contact surfacex、FySum and resultant moment MxyWill Fx、FyAnd MxyAnd (3) converting into node force, and applying the node force as a force boundary to a boundary node of the finite element model of the retaining wall:
(5) in the step 5, the specific method for calculating the anti-skid stability safety coefficient of the earth retaining wall in the earthquake comprises the following steps:
applying load at the bottom of the retaining wall-discrete particle-SPH continuous soil body coupling system, namely loading seismic acceleration at the bottom of the continuous soil body, and setting n on the side edge of the retaining wall in contact with the particlesslipSegment finite element boundary, wherein the particle horizontal thrust to which the i-th segment finite element boundary is subjected is set as Fi slipSetting the resultant force F of horizontal thrust of soil body on retaining wallslipThe resultant force is the sliding force of the retaining wall, and hasHere the superscript slip indicates slip; n is arranged at the bottom of the retaining wallanti-slipThe section finite element boundary is contacted with the particles, and the horizontal friction force of the i-th section wall subjected to the discrete particles is set as Fi anti-slipSo that the anti-slip force of the earth mass on the retaining wall is the total forceThe superscript anti-slip here indicates anti-slip; therefore, the anti-skid stability safety factor of the retaining wall can be calculated as the ratio of the resultant force of the anti-skid force to the sliding force, and an anti-skid stability safety system is arrangedA number of K, have
Compared with the prior art, the invention adopting the technical scheme has the following technical effects: compared with the existing discrete particle-continuous soil body coupling method for seismic response of the retaining wall, the method has two advantages (a) that the method adopts a Smooth particle dynamics (SPH) method to simulate on the discrete particles and the continuous soil body, is more suitable for large deformation analysis, and overcomes the problem that the grid distortion of a finite element or a finite difference grid in the existing coupling method is difficult to adapt to the large deformation analysis of the earthquake in the large deformation analysis; (b) the method sets a coupling transition region in the discrete particle-SPH continuous soil body, the coupled discrete particles and the SPH particle displacement are the same, and the problem that the discrete particles and the continuous soil body can be separated from each other on the coupling boundary in the existing method is solved.
Drawings
FIG. 1 is a diagram of a retaining wall and a soil prototype;
FIG. 2 is a diagram of a retaining wall-discrete particle-SPH continuous soil mass coupling model;
FIG. 3 is a diagram of a discrete particle-SPH continuous soil coupling transition region;
FIG. 4 is a diagram of discrete particle to retaining wall finite element boundary coupling.
In the figure, 1, soil body, 2, retaining wall, 3, seismic load, 4, soil body discrete particle model, 5, discrete particle-SPH continuous soil body coupling transition region, 6, continuous soil body SPH particle, and 7, retaining wall finite element model.
Detailed Description
In order to make the technical means, innovative features, objectives and effects of the present invention apparent, the present invention will be further described with reference to the following detailed drawings.
The invention relates to some abbreviations and symbols, the following are notes:
SPH: the method refers to a Smooth particle dynamics (SPH) method in a meshless method, and a continuous soil body model established by the method can adapt to large deformation analysis of earthquake.
{uC}int: column vectors of SPH particle displacement combinations over the coupling transition domain, where the variable on the continuous soil is denoted by superscript C and the coupling is denoted by subscript int.
{fC}int: the SPH particles on the coupling transition domain are subjected to column vectors that are a combination of the coupling forces of the discrete particles.
{uC}uin: column vectors of SPH particle displacement combinations that are not on the coupling transition domain, where the subscript uin denotes no coupling.
Column vectors for SPH particle velocity combinations that are not on the coupling transition domain.
Column vectors of SPH particle acceleration combinations that are not on the coupling transition domain.
{fC}uin: the column vector of the external force to which the SPH particles are not on the coupling transition region.
[ M ]: the mass matrix obtained by SPH discrete continuous solid differential equation.
[C] The method comprises the following steps And (4) obtaining a damping matrix by SPH discrete continuous solid differential equation.
[K] The method comprises the following steps And (3) a rigidity matrix obtained by SPH discrete continuous solid differential equation.
The translational displacement column vector of the ith discrete particle on the transition domain is coupled, where the superscript M denotes the variable on the discrete particle.
And coupling the translational acceleration column vector of the ith discrete particle on the transition domain.
And the displacement column vectors of the n discrete particles on the coupling transition domain are combined to form an overall displacement column vector.
{fi M}contact: the ith discrete particle in the coupling transition region is subjected to the action of other discrete particles to produce a resultant column vector, where the subscript contact indicates particle contact.
{fM}contact: coupled with n discrete particles in the transition regioni M}contactA column vector formed by the union.
{fi M}int: the ith discrete particle in the coupling transition region is subjected to the ith SPH particle coupling force column vector.
{fM}int: coupled with n discrete particles in the transition regioni M}intA column vector formed by the union.
[ m ]: and (3) forming an overall quality matrix by combining balance equations of the n discrete particles in the coupling transition domain.
nslip: the number of finite element boundary segments on the side of the retaining wall in contact with the particles, where the upper label slip indicates slip;
Fi slip: the side of the retaining wall in contact with the particles, wherein the particle horizontal thrust is experienced by the i-th section finite element boundary.
Fslip: the soil retaining wall is subjected to the horizontal thrust resultant force of the soil body, namely the slip force resultant force of the soil retaining wall.
nanti-slip: the number of finite element boundary segments at the bottom of the retaining wall in contact with the particles, where the superscript anti-slip indicates the slip resistance.
Fi anti-slip: the ith section of finite element boundary at the bottom of the retaining wall is subjected to the horizontal friction force of discrete particles.
Fanti-slip: the bottom of the retaining wall is subjected to the resultant force of the anti-sliding force of the soil body.
K: the anti-skidding of retaining wall stabilizes factor of safety.
As shown in figures 1-4, the invention designs a discrete particle-SPH coupling simulation method for anti-slip analysis of a gravity type retaining wall in an earthquake, which comprises the following steps of establishing a retaining wall finite element model, a discrete particle model near the retaining wall and an SPH continuous soil body model far away from the retaining wall in different regions through particle aggregate macroscopic parameters and continuous soil body matching numerical tests, and simultaneously obtaining an anti-slip stable safety coefficient of the retaining wall in the earthquake based on simulation of the coupling transition regions which are partially overlapped between discrete particles and the continuous soil body, wherein the method comprises the following specific steps:
step 1: discrete particle aggregate macroscopic parameter and continuous soil body matching numerical test: sampling soil around a gravity type retaining wall, carrying out an indoor triaxial test to determine the internal friction angle and the cohesion force of the soil, carrying out an indoor dynamic triaxial test to determine the dynamic modulus of the soil, and assigning the obtained internal friction angle, the cohesion force and the dynamic modulus to an SPH continuous soil model for use; continuously adjusting the microscopic parameters of the discrete particles to perform a biaxial compression test and a cyclic biaxial numerical test of the discrete particles, making the internal friction angle and the cohesive force obtained by the biaxial compression numerical test consistent with those of an actual test, and making the dynamic modulus obtained by the cyclic biaxial numerical test consistent with that of an actual test, thereby determining the particlesMicroscopic parameters such as normal phase stiffness knTangential stiffness ksAnd coefficient of friction fcAssigning the microscopic parameters to the discrete particle model for use;
step 2: as shown in fig. 2, a retaining wall finite element model 7 is established, a soil discrete particle model 4 near the retaining wall is established, and an SPH continuous soil model 6 far from the retaining wall is established:
(2.1) the retaining wall finite element model 7 uses four-node isoparametric units in the finite element method, and the shape functions on the four nodes are respectively set as N1、N2、N3And N4Setting variables in the shape function as r and s, and the concrete form of the shape function on four nodes of the equal parameter unit as follows:
(2.2) in the soil discrete particle model 4, the motion equation of the particles comprises a translation equation and a rotation equation:
translation equation:
equation of rotation:
in the above formula, m is the mass of the particles,andis the translational acceleration of the particle in the x and y directions, FxAnd FxFor the resultant forces acting on the particles in the x and y directions, MxyThe xy-direction torque applied to the particles, I is the moment of inertia,is the angular acceleration.
(2.3) in the SPH continuous soil model 6, Smooth particle dynamics (SPH) is used to build the continuous soil model, the used SPH kernel function adopts the existing gaussian kernel function, the SPH kernel function is set as W (R, h), R is the distance between two SPH particles, h is the Smooth length, and the kernel function is in the form of W (R, h):
and step 3: the method for establishing the cross-scale connection between the discrete particles 4 and the continuous soil body 6 comprises the following specific steps: establishing a coupling transition region 5 with partial overlap between the discrete particles 4 and the continuous soil body 6, wherein the characteristics of the coupling transition region 5 and the coupling force calculation method are as follows:
as shown in fig. 3, in the coupling transition region 5 where the discrete particles and the continuous soil body partially overlap, the continuous soil body is simulated by Smooth particle dynamics (SPH), and each continuous soil body SPH particle is required to be overlapped with the discrete particle and have equal displacement on the coupling transition region 5; the key of the coupling problem is that the cross-scale coupling of the discrete particles and the continuous soil body is realized by strengthening the force compatibility on the coupling transition domain, and the discrete particles and the SPH particles of the continuous soil body correspond to each other on the coupling transition domain, so the problem can be expressed as solving the coupling force of the discrete particles and the continuous soil body on the coupling transition domain, and the coupling force enables the SPH particles and the discrete particles to have the same displacement;
the coupling transition region is provided with n SPH particles and n corresponding discrete particles, then the continuous soil body SPH particles are divided into two parts, and the n SPH particles on the coupling transition region are combined into a column vector { u }C}intThe coupling forces of the SPH particles by the discrete particles are combined into a column vector { f }C}intHere, the superscript C denotes the variable on the continuous soil mass and the subscript int denotes the coupling; for SPH particles not on the coupling transition region, the displacement, the velocity, the acceleration and the external force are respectively combined into a column vector { u }C}uin、And { fC}uinHere, the subscript uin denotes no coupling; simultaneously using [ M]、[C]And [ K ]]Respectively representing a mass matrix, a damping matrix and a rigidity matrix obtained by an SPH discrete continuous solid differential equation. The equation of power can then be derived based on SPH dispersion:
let the mass of the ith discrete particle in the coupling transition region be miThe translational displacement column vector isCorresponding acceleration column vector ofThe resultant force from the action of other discrete particles is the column vector fi M}contactThe column vector of the I-th SPH particle coupling force is { fi M}intWhere superscript M denotes a variable on a discrete particle, where subscript contact denotes particle contact; regardless of particle rotation, the equilibrium equation for a single discrete particle is:
the equilibrium equations of n discrete particles in the coupling transition domain are combined, and the overall quality matrix is set as [ m]N particles of{fi M}contactAnd { fi M}intAre respectively combined in a simultaneous manner{fM}contactAnd { fM}intThus, the overall equilibrium equation for discrete particles over the coupled transition region can be written as:
the coupling force is solved as follows:
(a) displacement on coupled particles by cancelling unknown coupling forces
The acceleration of SPH particles and discrete particles in the coupling transition region is the same, and the coupling force is a pair of counter forces, one{fC}int＝-{fM}intSubstitution of equation (7) for equation (5) eliminates the unknown coupling force { fC}intAnd { fM}intAs follows:
in the above formula [ Mint]Is [ m ]]Substitution of [ M]The subsequent coupling mass matrix, where the unknown coupling force f has been cancelledi C}intAnd { fi M}intThe acceleration of the SPH particles in the coupling transition domain can be solvedSpeed of rotationAnd a displacement { u }c}int。
(b) Determining the coupling force in the coupling transition region
Will be solved toSpeed of rotationAnd a displacement { u }c}intThe coupling force column vector { f) acting on the SPH particles can be calculated by substituting equation (5)c}intThe column vector of coupling forces acting on the discrete particle spots { fM}int＝-{fc}int。
And 4, step 4: the retaining wall finite element model 7 is coupled with the discrete particle model 4, and the specific coupling mode is as follows: as shown in fig. 4, the finite element-discrete particle coupling is realized by ensuring the continuity of the force and the speed on the coupling boundary, on the contact surface of the retaining wall finite element model 7 and the discrete particle 4, the contact surface is the line boundary of the finite element model, the contact surface is the wall boundary of the discrete particle in the discrete element model, and the speed of the finite element node on the contact surface is extracted as the speed of the wall boundary node in the discrete element model; finite element model statistics of resultant force F of particles on contact surfacex、FySum and resultant moment MxyWill Fx、FyAnd MxyAnd (3) converting into node force, and applying the node force as a force boundary to a boundary node of the finite element model of the retaining wall:
and 5: the method for calculating the anti-skid stability safety coefficient of the earth retaining wall in the earthquake comprises the following steps: applying a load 3 to the bottom of the retaining wall-discrete particle-SPH continuous soil coupling system shown in FIG. 2, namely applying a seismic acceleration to the bottom of the continuous soil, and setting n on the side where the retaining wall is contacted with the particlesslipSegment finite element boundary, wherein the particle horizontal thrust to which the i-th segment finite element boundary is subjected is set as Fi slipSetting the resultant force F of horizontal thrust of soil body on retaining wallslipThe resultant force is the sliding force of the retaining wall, and hasHere the superscript slip indicates slip; n is arranged at the bottom of the retaining wallanti-slipThe section finite element boundary is contacted with the particles, and the horizontal friction force of the i-th section wall subjected to the discrete particles is set as Fi anti-slipSo that the anti-slip force of the earth mass on the retaining wall is the total forceThe superscript anti-slip here indicates anti-slip; therefore, the anti-skid stability safety factor of the retaining wall can be calculated as the ratio of the resultant force of the anti-skid force to the sliding force, the anti-skid stability safety factor is K, and
Claims (6)
1. A discrete particle-SPH coupling simulation method for earthquake gravity type retaining wall skid resistance analysis is characterized by comprising the following steps:
step 1: performing a particle aggregate macroscopic parameter and continuous soil body matching numerical test;
step 2: establishing a retaining wall finite element model, establishing a soil discrete particle model near the retaining wall, and establishing an SPH continuous soil model far away from the retaining wall;
and step 3: establishing cross-scale connection between discrete particles and a continuous soil body;
and 4, step 4: coupling the retaining wall finite element model with the discrete particle model;
and 5: and calculating the anti-skid stability safety factor of the earth retaining wall in the earthquake.
2. The discrete particle-SPH coupling simulation method for the sliding resistance analysis of the gravity retaining wall in the earthquake according to claim 1, wherein: in the step 1, the particle aggregate macroscopic parameter and continuous soil body matching numerical test comprises the following steps:
sampling soil around a gravity type retaining wall, carrying out an indoor triaxial test to determine the internal friction angle and the cohesion force of the soil, carrying out an indoor dynamic triaxial test to determine the dynamic modulus of the soil, and assigning the obtained internal friction angle, the cohesion force and the dynamic modulus to a continuous soil model for use; continuously adjusting the mesoscopic parameters of the discrete particles to perform a biaxial compression test and a cyclic biaxial numerical test of the discrete particles, making the internal friction angle and the cohesive force obtained by the biaxial compression numerical test consistent with those obtained by the actual test, and making the dynamic modulus obtained by the cyclic biaxial numerical test consistent with that obtained by the actual test, thereby determining the mesoscopic parameters of the particles, such as the normal phase stiffness knTangential stiffness ksAnd coefficient of friction fcThe mesoscopic parameters are assigned for use by the discrete particle model.
3. The discrete particle-SPH coupling simulation method for the sliding resistance analysis of the gravity retaining wall in the earthquake according to claim 1, wherein: in the step 2, the retaining wall finite element model uses four-node isoparametric units in a finite element method; in the soil discrete particle model, the motion equation of the particles comprises a translation equation and a rotation equation; in the SPH continuous soil model, a continuous soil model is established using Smooth particle dynamics (SPH), and the used SPH kernel function uses an existing gaussian kernel function.
4. The discrete particle-SPH coupling simulation method for the sliding resistance analysis of the gravity retaining wall in the earthquake according to claim 1, wherein: in the step 3, a partially overlapped coupling transition region is formed between the discrete particles and the continuous soil body, each discrete particle on the coupling transition region is correspondingly coupled with the SPH particle of the continuous soil body one by one, and the displacement, the speed and the acceleration are equal.
5. The discrete particle-SPH coupling simulation method for the sliding resistance analysis of the gravity retaining wall in the earthquake according to claim 1, wherein: the method for calculating the coupling force of the discrete particles and the continuous soil body SPH particles in the step 3 comprises the following steps:
the coupling transition region is provided with n SPH particles and n corresponding discrete particles, then the continuous soil body SPH particles are divided into two parts, and the n SPH particles on the coupling transition region are combined into a column vector { u }C}intThe coupling forces of the SPH particles by the discrete particles are combined into a column vector { f }C}intHere, the superscript C denotes the variable on the continuous soil mass and the subscript int denotes the coupling; for SPH particles not on the coupling transition region, the displacement, the velocity, the acceleration and the external force are respectively combined into a column vector { u }C}uin、And { fC}uinHere, the subscript uin denotes no coupling; simultaneously using [ M]、[C]And [ K ]]Respectively representing a mass matrix, a damping matrix and a rigidity matrix obtained by an SPH discrete continuous solid differential equation. The equation of power can then be derived based on SPH dispersion:
let the mass of the ith discrete particle in the coupling transition region be miThe translational displacement column vector isCorresponding acceleration column vector ofThe resultant force from the action of other discrete particles is the column vector fi M}contactThe column vector of the I-th SPH particle coupling force is { fi M}intWhere superscript M denotes a variable on a discrete particle, where subscript contact denotes particle contact; regardless of particle rotation, the equilibrium equation for a single discrete particle is:
the equilibrium equations of n discrete particles in the coupling transition domain are combined, and the overall quality matrix is set as [ m]N particles of{fi M}contactAnd { fi M}intAre respectively combined in a simultaneous manner{fM}contactAnd { fM}intThus, the overall equilibrium equation for discrete particles over the coupled transition region can be written as:
the coupling force is solved as follows:
(a) displacement on coupled particles by cancelling unknown coupling forces
The acceleration of SPH particles and discrete particles in the coupling transition region is the same, and the coupling force is a pair of counter forces, one{fC}int＝-{fM}intSubstitution of equation (3) for equation (1) eliminates the unknown coupling force { fC}intAnd { fM}intAs follows:
in the above formula [ Mint]Is [ m ]]Substitution of [ M]The subsequent coupling mass matrix, where the unknown coupling force f has been cancelledi C}intAnd { fi M}intThe acceleration of the SPH particles in the coupling transition domain can be solvedSpeed of rotationAnd a displacement { u }c}int；
(b) Determining the coupling force in the coupling transition region
Will be solved toSpeed of rotationAnd a displacement { u }c}intThe coupling force column vector { f) acting on the SPH particles can be calculated by substituting formula (1)c}intThe column vector of coupling forces acting on the discrete particle spots { fM}int＝-{fc}int。
6. The discrete particle-SPH coupling simulation method for the sliding resistance analysis of the gravity retaining wall in the earthquake according to claim 1, wherein: the specific method for calculating the anti-skid stability safety factor of the retaining wall in the earthquake in the step 5 comprises the following steps:
applying load at the bottom of the retaining wall-discrete particle-SPH continuous soil body coupling system, namely loading seismic acceleration at the bottom of the continuous soil body, and arranging the retaining wall and the particlesThe side edge of the particle contact has nslipSegment finite element boundary, wherein the particle horizontal thrust to which the i-th segment finite element boundary is subjected is set as Fi slipSetting the resultant force F of horizontal thrust of soil body on retaining wallslipThe resultant force is the sliding force of the retaining wall, and hasHere the superscript slip indicates slip; n is arranged at the bottom of the retaining wallanti-slipThe section finite element boundary is contacted with the particles, and the horizontal friction force of the i-th section wall subjected to the discrete particles is set as Fi anti-slipSo that the anti-slip force of the earth mass on the retaining wall is the total forceThe superscript anti-slip here indicates anti-slip; therefore, the anti-skid stability safety factor of the retaining wall can be calculated as the ratio of the resultant force of the anti-skid force to the sliding force, the anti-skid stability safety factor is K, and
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