CN106980723A - The discrete particle SPH coupled simulation methods that gravity retaining wall antiskid is analyzed in earthquake - Google Patents

Abstract

A discrete particle-SPH coupling simulation method for the anti-sliding analysis of gravity retaining walls in earthquakes, including the following steps: (1) matching numerical tests on the macroscopic parameters of particle aggregates and continuous soil; (2) establishing the finite element method of retaining walls Model, establish the discrete particle model of the soil near the retaining wall, and establish the SPH continuous soil model away from the retaining wall: (3) establish the cross-scale connection between the discrete particle and the continuous soil; (4) the finite element of the retaining wall The model is coupled with the discrete particle model; (5) Calculate the anti-sliding stability safety factor of the retaining wall during the earthquake. Compared with the discrete particle-continuous soil coupling method of the seismic response of the existing retaining wall, the coupling method of the present invention is more suitable for the analysis of large seismic deformation, and at the same time overcomes the separation of the discrete particles and the continuous soil on the coupling boundary in the existing method. The problem.

Description

Discrete Particle-SPH Coupling Simulation Method for Sliding Analysis of Gravity Retaining Wall During Earthquake

technical field

The invention belongs to the field of geotechnical engineering research, in particular to a discrete particle-SPH coupling simulation method for anti-sliding analysis of gravity retaining walls during earthquakes.

Background technique

As a support structure in geotechnical engineering, gravity retaining wall is widely used in slope support in our country. However, the theory of its seismic design is not mature. The current analysis method is mainly the pseudo-static method. Under the earthquake, the gravity retaining wall has horizontal acceleration, that is, the horizontal inertial force is simplified to static force to analyze the retaining wall. anti-skid stability. In order to deeply obtain the anti-sliding stability of the retaining wall during the whole earthquake process, the seismic response of the retaining wall can be simulated by establishing a continuum such as finite element or finite difference, but this type of continuum model is difficult to analyze the relationship between discrete particles and the retaining wall. Discontinuous dynamic contact action. Therefore, in order to finely analyze the anti-sliding stability of the gravity retaining wall during the whole earthquake process, the soil mass can be simulated based on discrete particles, but due to the limitation of the number of discrete particles and computer performance, it is difficult to use discrete particle simulation in the whole domain The mechanical behavior of soil, for this reason, people have developed a solid discrete-continuous soil coupling method to reduce the scale of discrete element simulation, and use this method to simulate the seismic response of retaining walls (see the literature "Zhou Jian, Jin Weifeng. Based on the coupling method Numerical Simulation of Seismic Response of Retaining Wall [J]. Rock and Soil Mechanics, 2010, 31(12): 3949-3957."). However, in these coupling models, continuous solids are discretized based on finite element or finite difference grids, and there are numerical instability problems such as grid distortion in earthquake large deformation simulations. Soil and discrete particles are easily separated on coupled boundaries.

Smooth particle hydrodynamics method (SPH) is a kind of meshless method, which can adapt to the simulation of large earthquake deformation of soil, so it can be considered to use SPH method to couple with discrete particles, and the soil near the retaining wall can be used Discrete particle simulation, the soil far away from the retaining wall is simulated by the SPH method, which can consider the discontinuous contact between the retaining wall and discrete particles, and can effectively reduce the discrete element simulation scale, and the continuous soil can also adapt to large deformation analysis , but it is still necessary to construct a cross-scale connection method to couple the discrete particles around the retaining wall and the SPH continuous soil, so as to ensure that the continuous soil and discrete particles will not be separated in the coupling transition domain.

Contents of the invention

In order to overcome the existing discrete particle-continuous soil coupling method, it is difficult to take into account the large deformation of the continuous soil and the coupling between the continuous soil and the discrete particles when analyzing the anti-sliding stability of the gravity retaining wall in the earthquake. To solve the problem of easy separation on the boundary, the present invention proposes a discrete particle-SPH coupling simulation method for the anti-sliding analysis of gravity retaining walls in earthquakes, so that not only the discontinuous contact between the retaining wall and discrete particles can be considered and the effect can be effectively reduced. Discrete element simulation scale, while overcoming the difficulty in existing methods that continuous soil is difficult to adapt to large deformation analysis, and the problem that continuous soil and discrete particles will be separated on the coupling boundary.

The present invention involves some abbreviations and symbols, the following are notes:

SPH: refers to the smooth particle hydrodynamics method (SPH) in the meshless method. The continuous soil model established by this method can be adapted to the analysis of large earthquake deformation.

{u ^C } _int : column vector of the SPH particle displacement combination on the coupled transition domain, where the superscript C is used to indicate the variable on the continuous soil, and the subscript int is used to indicate the coupling.

{f ^C } _int : column vector of the combination of coupling forces of discrete particles on the SPH particle on the coupled transition domain.

{u ^C } _uin : the column vector of the SPH particle displacement combination not on the coupled transition domain, where the subscript uin means uncoupled.

Column vector of combinations of SPH particle velocities that are not on the coupled transition domain.

Column vector of combinations of SPH particle accelerations that are not on the coupled transition domain.

{f ^C } _uin : the column vector of the external force on the SPH particle not on the coupled transition domain.

[M]: Mass matrix obtained by SPH discrete continuous solid differential equation.

[C]: Damping matrix obtained by discretizing continuous solid differential equations in SPH.

[K]: Stiffness matrix obtained by SPH discrete continuous solid differential equation.

The translational displacement column vector of the ith discrete particle on the coupled transition domain, where the superscript M represents the variable on the discrete particle.

The column vector of the translational acceleration of the ith discrete particle on the coupled transition domain.

The overall displacement column vector formed by combining the displacement column vectors of n discrete particles on the coupled transition domain.

{f _i ^M } _contact : the i-th discrete particle on the coupling transition domain is subjected to the resultant force column vector of other discrete particles, where the subscript contact indicates particle contact.

{f ^M } _contact : A column vector composed of {f _i ^M } _contacts of n discrete particles on the coupled transition domain.

{f _i ^M } _int : The i-th discrete particle on the coupling transition domain is subjected to the i-th SPH particle coupling force column vector.

{f ^M } _int : A column vector composed of {f _i ^M } _int of n discrete particles on the coupled transition domain.

[m]: The overall mass matrix formed by combining the balance equations of n discrete particles in the coupled transition domain.

n ^slip : the number of finite element boundary segments on the side of the retaining wall in contact with the particles, where the superscript slip means sliding;

F _i ^slip : On the side of the retaining wall in contact with the particles, the horizontal thrust of the particles on the finite element boundary of the i segment.

F ^slip : the resultant force of the horizontal thrust of the retaining wall by the soil, that is, the resultant force of the sliding force of the retaining wall.

n ^anti-slip : the number of finite element boundary segments in contact with the particles at the bottom of the retaining wall, where the superscript anti-slip means anti-slip.

F _i ^anti-slip : the finite element boundary of the i-th segment at the bottom of the retaining wall is subject to the horizontal friction of discrete particles.

F ^anti-slip : The bottom of the retaining wall is subjected to the combined force of the anti-slip force of the soil.

K: Anti-sliding stability safety factor of the retaining wall.

In order to solve the above technical problems, the following technical solutions are adopted:

The invention provides a discrete particle-SPH coupling simulation method for the anti-sliding analysis of a gravity retaining wall in an earthquake, which includes the macroscopic parameters of the aggregate of scattered particles and the matching numerical test of the continuous soil body, and establishes the finite element model of the retaining wall and the retaining wall in different regions. The discrete particle model near the soil wall and the SPH continuous soil model far away from the retaining wall. At the same time, there is a partially overlapping coupling transition domain between the discrete particles and the continuous soil, so as to realize the anti-sliding stability safety factor of the gravity retaining wall in the earthquake Calculation, the specific steps are as follows:

Step 1: Numerical test of macroscopic parameters of granular aggregates and continuous soil matching;

Step 2: Establish the finite element model of the retaining wall, establish the discrete particle model of the soil near the retaining wall, and establish the SPH continuous soil model far away from the retaining wall;

Step 3: Establish cross-scale connection between discrete particles and continuous soil;

Step 4: The finite element model of the retaining wall is coupled with the discrete particle model;

Step 5: Calculate the safety factor of anti-sliding stability of the retaining wall during the earthquake.

in,

(1) In the step 1, the macroscopic parameter of the particle aggregate and the matching numerical test of the continuous soil include:

Take soil samples around the gravity retaining wall, conduct indoor triaxial tests to determine the internal friction angle and cohesion of the soil, and conduct indoor dynamic triaxial tests to determine the dynamic modulus of the soil. The cohesion and dynamic modulus are assigned to the continuous soil model; the mesoscopic parameters of the discrete particles are continuously adjusted to carry out the biaxial compression test and the cyclic biaxial numerical test of the discrete particles, so that the internal friction angle and viscosity obtained from the biaxial compression numerical test The cohesion force is consistent with the actual test, so that the dynamic modulus obtained by the cyclic biaxial numerical test is consistent with the measured dynamic modulus, so as to determine the mesoscopic parameters of the particles such as the normal phase stiffness k _n , the tangential stiffness k _s and the friction coefficient f _c . These mesoscopic parameters are assigned to the discrete particle model.

(2) In the step 2, the retaining wall finite element model, soil discrete particle model, and SPH continuous soil model are described as follows:

(2.1) The finite element model of the retaining wall uses the four-node isoparametric element in the finite element method.

(2.2) In the discrete particle model of soil, the motion equation of particles includes translation equation and rotation equation.

(2.3) In the SPH continuous soil model, the smooth particle hydrodynamics method (SPH) is used to establish the continuous soil model, and the SPH kernel function used adopts the existing Gaussian kernel function.

(3) In step 3, the cross-scale connection between discrete particles and continuous soil is established, the specific method is as follows:

There is a partially overlapping coupling transition domain between the discrete particles and the continuous soil. Each discrete particle and the continuous soil SPH particle in the coupling transition domain are coupled one-to-one and the displacement, velocity and acceleration are equal, and the discrete particles and the continuous soil are established. The coupling force algorithm between SPH particle coupling transition domains is as follows:

Assuming that there are n SPH particles and corresponding n discrete particles in the coupling transition domain, then the continuous soil SPH particles are divided into two parts, and the n SPH particle displacements in the coupling transition domain are combined into a column vector {u ^C } _int , the SPH particle is combined into a column vector {f ^C } _int by the coupling force of discrete particles, where the superscript C is used to indicate the variable on the continuous soil, and the subscript int is used to indicate the coupling; for the SPH particle not on the coupling transition domain, its displacement , velocity, acceleration and external force are respectively combined into a column vector {u ^C } _uin , and {f ^C } _uin , where the subscript uin means uncoupling; at the same time [M], [C] and [K] are used to represent the mass matrix, damping matrix and stiffness matrix obtained from the SPH discrete continuous solid differential equation, respectively. Then the kinetic equation can be obtained based on the SPH discretization:

Let the mass of the i-th discrete particle on the coupled transition domain be m _i , and the column vector of translational displacement be The corresponding acceleration column vector is The resultant force by other discrete particles is the column vector {f _i ^M } _contact , and the column vector of the i-th SPH particle coupling force is {f _i ^M } _int , where the superscript M represents the variable on the discrete particle, and the subscript contact here Indicates particle contact; regardless of particle rotation, the equilibrium equation for a single discrete particle is:

Combine the equilibrium equations of n discrete particles on the coupling transition domain, set the overall mass matrix as [m], and the n particles’ {f _i ^M } _contact and {f _i ^M } _int are respectively combined as {f ^M } _contact and {f ^M } _int , so the overall equilibrium equation of discrete particles on the coupled transition domain can be written as:

Solve for the coupling force as follows:

(a) Find the displacement on the coupling particle by eliminating the unknown coupling force

The SPH particle and the discrete particle have the same acceleration in the coupling transition domain, and the coupling force is a pair of counterforces, we have {f ^C } _int ＝-{f ^M } _int , substituting formula (3) into formula (1) can eliminate the unknown coupling force {f ^C } _int and {f ^M } _int , as follows:

In the above formula, [M _int ] is the coupling mass matrix after substituting [m] into [M]. In the above formula, the unknown coupling forces {f _i ^C } _int and {f _i ^M } _int have been eliminated, and the coupling transition domain can be solved Acceleration of SPH particle speed and displacement {u ^c } _int .

(b) Calculate the coupling force on the coupled transition domain

will solve the obtained speed and the displacement {u ^c } _int are substituted into formula (1) to calculate the coupling force column vector {f ^c } _int acting on the SPH particle, and then the coupling force column vector {f ^M } _int acting on the discrete particle particle can be obtained = -{f ^c } _int .

(4) In the step 4, the specific method of coupling the finite element model of the retaining wall with the discrete particle model is as follows:

The finite element-discrete particle coupling is realized by ensuring the continuity of force and velocity on the coupling boundary. On the contact surface between the finite element model of the retaining wall and the discrete particle, the contact surface is the line boundary of the finite element model, and the contact surface is in the discrete element model. The middle _is the wall _boundary of discrete particles, and the velocity of the finite element node on the contact surface is extracted as the velocity of the wall boundary _node in the discrete element model; F _x , F _y and M _xy are transformed into nodal forces, which are applied to the boundary nodes of the finite element model of the retaining wall as force boundaries:

(5) in described step 5, the concrete method of the anti-sliding stability safety factor of retaining wall in calculating earthquake is:

The load is applied at the bottom of the retaining wall-discrete particle-SPH continuous soil coupling system, that is, the seismic acceleration is loaded at the bottom of the continuous soil. It is assumed that there are n ^slip segment finite element boundaries on the side where the retaining wall contacts with the particles. Let The particle horizontal thrust on the finite element boundary of section i is F _i ^slip , and the resultant horizontal thrust force F ^slip of the soil on the retaining wall is assumed to be the resultant sliding force of the retaining wall. Here the superscript slip means sliding; at the bottom of the retaining wall, there are n ^anti-slip segment finite element boundaries in contact with particles, and the i-th segment of the wall is assumed to be F _i ^anti-slip in horizontal friction force of discrete particles, so that the retaining wall is affected by soil The resultant anti-slip force of the body is Here the superscript anti-slip means anti-sliding; in this way, the anti-sliding stability safety factor of the retaining wall can be calculated as the ratio of the anti-sliding force resultant force to the sliding force, and the anti-sliding stability safety factor is K,

Compared with the prior art, the present invention adopts the above technical scheme and has the following technical effects: compared with the discrete particle-continuous soil coupling method of the seismic response of the existing retaining wall, there are two advantages (a): the method adopts discrete The smooth particle hydrodynamics method (SPH) method is used for simulation on granular and continuous soils, which is more suitable for large deformation analysis and overcomes the difficulty of grid distortion in large deformation analysis of finite element or finite difference grids in existing coupling methods. Adapt to the problem of seismic large deformation analysis; (b) This method sets a coupling transition domain in the discrete particle-SPH continuous soil, the coupled discrete particle and SPH particle displacement are the same, and overcomes the coupling between the discrete particle and the continuous soil in the existing method The problem of detachment at the border.

Description of drawings

Figure 1 is a prototype diagram of the retaining wall and soil;

Figure 2 is a coupling model diagram of retaining wall-discrete particles-SPH continuous soil;

Fig. 3 is the transition domain diagram of discrete particle-SPH continuous soil coupling;

Fig. 4 is the coupling diagram of discrete particles and finite element boundary of retaining wall.

In the figure 1. Soil, 2. Retaining wall, 3. Earthquake load, 4. Discrete particle model of soil, 5. Discrete particle-SPH continuous soil coupling transition domain, 6. Continuous soil SPH particle, 7. Retaining The finite element model of the soil wall.

detailed description

In order to make the technical means, innovative features, goals and effects achieved by the present invention easy to understand, the present invention will be further described below in conjunction with specific illustrations.

The present invention involves some abbreviations and symbols, the following are notes:

SPH: refers to the smooth particle hydrodynamics method (SPH) in the meshless method. The continuous soil model established by this method can be adapted to the analysis of large earthquake deformation.

{u ^C } _int : column vector of the SPH particle displacement combination on the coupled transition domain, where the superscript C is used to indicate the variable on the continuous soil, and the subscript int is used to indicate the coupling.

{f ^C } _int : column vector of the combination of coupling forces of discrete particles on the SPH particle on the coupled transition domain.

{u ^C } _uin : the column vector of the SPH particle displacement combination not on the coupled transition domain, where the subscript uin means uncoupled.

Column vector of combinations of SPH particle velocities that are not on the coupled transition domain.

Column vector of combinations of SPH particle accelerations that are not on the coupled transition domain.

{f ^C } _uin : the column vector of the external force on the SPH particle not on the coupled transition domain.

[M]: Mass matrix obtained by SPH discrete continuous solid differential equation.

[C]: Damping matrix obtained by discretizing continuous solid differential equations in SPH.

[K]: Stiffness matrix obtained by SPH discrete continuous solid differential equation.

The translational displacement column vector of the ith discrete particle on the coupled transition domain, where the superscript M represents the variable on the discrete particle.

The column vector of the translational acceleration of the ith discrete particle on the coupled transition domain.

The overall displacement column vector formed by combining the displacement column vectors of n discrete particles on the coupled transition domain.

{f _i ^M } _contact : the i-th discrete particle on the coupling transition domain is subjected to the resultant force column vector of other discrete particles, where the subscript contact indicates particle contact.

{f ^M } _contact : A column vector composed of {f _i ^M } _contacts of n discrete particles on the coupled transition domain.

{f _i ^M } _int : The i-th discrete particle on the coupling transition domain is subjected to the i-th SPH particle coupling force column vector.

{f ^M } _int : A column vector composed of {f _i ^M } _int of n discrete particles on the coupled transition domain.

[m]: The overall mass matrix formed by combining the balance equations of n discrete particles in the coupled transition domain.

n ^slip : the number of finite element boundary segments on the side of the retaining wall in contact with the particles, where the superscript slip means sliding;

F _i ^slip : On the side of the retaining wall in contact with the particles, the horizontal thrust of the particles on the finite element boundary of the i segment.

F ^slip : the resultant force of the horizontal thrust of the retaining wall by the soil, that is, the resultant force of the sliding force of the retaining wall.

n ^anti-slip : the number of finite element boundary segments in contact with the particles at the bottom of the retaining wall, where the superscript anti-slip means anti-slip.

F _i ^anti-slip : the finite element boundary of the i-th segment at the bottom of the retaining wall is subject to the horizontal friction of discrete particles.

F ^anti-slip : The bottom of the retaining wall is subjected to the combined force of the anti-slip force of the soil.

K: Anti-sliding stability safety factor of the retaining wall.

As shown in Figures 1-4, the present invention designs a discrete particle-SPH coupling simulation method for the anti-sliding analysis of gravity retaining walls in earthquakes. Through the matching numerical experiments of the macroscopic parameters of particle aggregates and continuous soil, the retaining walls are established in different regions. The finite element model of the soil wall, the discrete particle model near the retaining wall, and the SPH continuous soil model far away from the retaining wall, and there is a partially overlapping coupling transition domain between the discrete particles and the continuous soil. Based on the above content, the earthquake mid-retaining The safety factor of anti-sliding stability of the earth wall, the specific steps are as follows:

Step 1: Numerical test on the matching of macroscopic parameters of discrete particle aggregates and continuous soil: take soil samples around the gravity retaining wall, conduct indoor triaxial tests to determine the internal friction angle and cohesion of the soil, and conduct indoor dynamic triaxial tests The dynamic modulus of the soil is determined by the test, and the internal friction angle, cohesion and dynamic modulus obtained here are assigned to the SPH continuous soil model; the mesoscopic parameters of the discrete particles are continuously adjusted to carry out the biaxial compression test and cycle of the discrete particles Biaxial numerical test, so that the internal friction angle and cohesion obtained by the biaxial compression numerical test are consistent with the actual test, and the dynamic modulus obtained by the cyclic biaxial numerical test is consistent with the measured dynamic modulus, so as to determine the microscopic parameters of the particles Such as normal phase stiffness k _n , tangential stiffness k _s and friction coefficient f _c , these mesoscopic parameters are assigned to the discrete particle model;

Step 2: As shown in Figure 2, establish the finite element model of the retaining wall 7, establish the discrete particle model of the soil near the retaining wall 4, and establish the SPH continuous soil model 6 away from the retaining wall:

(2.1) The finite element model 7 of the retaining wall uses the four-node isoparametric element in the finite element method, and the shape functions on the four nodes are respectively N ₁ , N ₂ , N ₃ and N ₄ , and the variables in the shape function r and s, the specific form of the shape function on the four nodes of the isoparametric element is:

(2.2) In the soil discrete particle model 4, the motion equation of the particle includes a translational equation and a rotational equation:

Translation equation:

Rotation equation:

In the above formula, m is the particle mass, with is the translational acceleration of the particle in the x and y directions, F _x and F _x are the resultant forces acting on the particle in the x and y directions, M _xy is the torque in the xy direction of the particle, I is the moment of inertia, is the angular acceleration.

(2.3) In the SPH continuous soil model 6, the smooth particle hydrodynamics method (SPH) is used to establish the continuous soil model, and the SPH kernel function used adopts the existing Gaussian kernel function. Let the SPH kernel function be W(R ,h), R is the distance between two SPH particles, h is the smooth length, and the kernel function is W(R,h) in the following form:

Step 3: Establish the cross-scale connection between the discrete particles 4 and the continuous soil 6, the specific method is as follows: Establish the coupling transition domain 5 with partial overlap between the discrete particles 4 and the continuous soil 6, the characteristics of the coupling transition domain 5 and the coupling The force calculation method is as follows:

As shown in Fig. 3, in the coupling transition domain 5 where discrete particles partially overlap with the continuous soil, the continuous soil is simulated by smooth particle hydrodynamics method (SPH), and it is required that each continuous The SPH particles of the soil coincide with the discrete particles and the displacements are equal; at this time, the key to the coupling problem is to strengthen the compatibility of the force in the coupling transition domain to realize the cross-scale coupling of the discrete particles-continuous soil. The particles correspond to the SPH particles of the continuous soil, so this problem can be expressed as solving the coupling force between the discrete particles and the continuous soil on the coupling transition domain, and this coupling force makes the displacement of the SPH particle and the discrete particle the same;

Assuming that there are n SPH particles and corresponding n discrete particles in the coupling transition domain, then the continuous soil SPH particles are divided into two parts, and the n SPH particle displacements in the coupling transition domain are combined into a column vector {u ^C } _int , the SPH particle is combined into a column vector {f ^C } _int by the coupling force of discrete particles, where the superscript C is used to indicate the variable on the continuous soil, and the subscript int is used to indicate the coupling; for the SPH particle not on the coupling transition domain, its displacement , velocity, acceleration and external force are respectively combined into a column vector {u ^C } _uin , and {f ^C } _uin , where the subscript uin means uncoupling; at the same time [M], [C] and [K] are used to represent the mass matrix, damping matrix and stiffness matrix obtained from the SPH discrete continuous solid differential equation, respectively. Then the kinetic equation can be obtained based on the SPH discretization:

Let the mass of the i-th discrete particle on the coupled transition domain be m _i , and the column vector of translational displacement be The corresponding acceleration column vector is The resultant force by other discrete particles is the column vector {f _i ^M } _contact , and the column vector of the i-th SPH particle coupling force is {f _i ^M } _int , where the superscript M represents the variable on the discrete particle, and the subscript contact here Indicates particle contact; regardless of particle rotation, the equilibrium equation for a single discrete particle is:

Combine the equilibrium equations of n discrete particles on the coupling transition domain, set the overall mass matrix as [m], and the n particles’ {f _i ^M } _contact and {f _i ^M } _int are respectively combined as {f ^M } _contact and {f ^M } _int , so the overall equilibrium equation of discrete particles on the coupled transition domain can be written as:

Solve for the coupling force as follows:

(a) Find the displacement on the coupling particle by eliminating the unknown coupling force

The SPH particle and the discrete particle have the same acceleration in the coupling transition domain, and the coupling force is a pair of counterforces, we have {f ^C } _int ＝-{f ^M } _int , substituting equation (7) into equation (5) can eliminate the unknown coupling force {f ^C } _int and {f ^M } _int , as follows:

In the above formula, [M _int ] is the coupling mass matrix after substituting [m] into [M]. In the above formula, the unknown coupling forces {f _i ^C } _int and {f _i ^M } _int have been eliminated, and the coupling transition domain can be solved Acceleration of SPH particle speed and displacement {u ^c } _int .

(b) Calculate the coupling force on the coupled transition domain

will solve the obtained speed and the displacement {u ^c } _int can be substituted into formula (5) to obtain the coupling force column vector {f ^c } _int acting on the SPH particle, and then the coupling force column vector {f ^M } _int acting on the discrete particle particle can be obtained = -{f ^c } _int .

Step 4: The finite element model 7 of the retaining wall is coupled with the discrete particle model 4. The specific coupling method is as follows: as shown in Figure 4, the finite element-discrete particle coupling is realized by ensuring the continuity of force and velocity on the coupling boundary. The contact surface between the soil wall finite element model 7 and discrete particles 4, the contact surface is the line boundary of the finite element model, and the contact surface is the wall boundary of discrete particles in the discrete element model, the velocity of the finite element node on the contact surface is extracted as the discrete The velocity of the wall boundary nodes in the element model; the finite element model counts the resultant force F _x , F _y and resultant moment M _xy of particles on the contact surface, transforms F _x , F _y and M _xy into node force, and applies it to the barrier as a force boundary On the boundary nodes of the soil wall finite element model:

Step 5: Calculating the anti-sliding stability safety factor of the retaining wall during the earthquake, the specific method is: apply a load 3 at the bottom of the retaining wall-discrete particle-SPH continuous soil coupling system shown in Figure 2, that is, in the continuous soil Earthquake acceleration is loaded on the bottom of the body. It is assumed that there are n ^slip finite element boundaries on the side where the retaining wall is in contact with the particles. It is assumed that the horizontal thrust of particles on the i-th finite element boundary is F _i ^slip , and the retaining wall is affected by soil The resultant force F ^slip of the horizontal thrust is the resultant force of the sliding force of the retaining wall. Here the superscript slip means sliding; at the bottom of the retaining wall, there are n ^anti-slip segment finite element boundaries in contact with particles, and the i-th segment of the wall is assumed to be F _i ^anti-slip in horizontal friction force of discrete particles, so that the retaining wall is affected by soil The resultant anti-slip force of the body is Here the superscript anti-slip means anti-sliding; in this way, the anti-sliding stability safety factor of the retaining wall can be calculated as the ratio of the anti-sliding force resultant force to the sliding force, and the anti-sliding stability safety factor is K,

Claims (6)

1. a discrete particle-SPH coupling simulation method of gravity type retaining wall anti-sliding analysis in an earthquake, it is characterized in that comprising the steps: Step 1: Numerical test of macroscopic parameters of granular aggregates and continuous soil matching; Step 2: Establish the finite element model of the retaining wall, establish the discrete particle model of the soil near the retaining wall, and establish the SPH continuous soil model far away from the retaining wall; Step 3: Establish cross-scale connection between discrete particles and continuous soil; Step 4: The finite element model of the retaining wall is coupled with the discrete particle model; Step 5: Calculate the safety factor of anti-sliding stability of the retaining wall during the earthquake. 2. The discrete particle-SPH coupling simulation method for the anti-sliding analysis of gravity retaining walls in a kind of earthquake according to claim 1, characterized in that: in the step 1, the macroscopic parameters of the particle aggregates are matched with the continuous soil mass Numerical experiments include: Take soil samples around the gravity retaining wall, conduct indoor triaxial tests to determine the internal friction angle and cohesion of the soil, and conduct indoor dynamic triaxial tests to determine the dynamic modulus of the soil. The cohesion and dynamic modulus are assigned to the continuous soil model; the mesoscopic parameters of the discrete particles are continuously adjusted to carry out the biaxial compression test and the cyclic biaxial numerical test of the discrete particles, so that the internal friction angle and viscosity obtained from the biaxial compression numerical test The cohesion force is consistent with the actual test, so that the dynamic modulus obtained by the cyclic biaxial numerical test is consistent with the measured dynamic modulus, so as to determine the mesoscopic parameters of the particles such as the normal phase stiffness k _n , the tangential stiffness k _s and the friction coefficient f _c . These mesoscopic parameters are assigned to the discrete particle model. 3. the discrete particle-SPH coupling simulation method of gravity retaining wall anti-sliding analysis in a kind of earthquake according to claim 1, is characterized in that: in described step 2, retaining wall finite element model uses finite element method The four-node isoparametric unit in the model; in the discrete particle model of soil, the motion equation of the particles includes the translation equation and the rotation equation; in the SPH continuous soil model, the smooth particle hydrodynamics method (SPH) is used to establish the continuous soil Volume model, the SPH kernel function used adopts the existing Gaussian kernel function. 4. The discrete particle-SPH coupling simulation method for the anti-sliding analysis of a gravity retaining wall in an earthquake according to claim 1, characterized in that: in the step 3, there is a part between the discrete particles and the continuous soil Overlapped coupling transition domains, each discrete particle and continuous soil SPH particle in the coupling transition domain are coupled one-to-one, and the displacement, velocity and acceleration are equal. 5. the discrete particle-SPH coupling simulation method of gravity retaining wall anti-sliding analysis in a kind of earthquake according to claim 1, it is characterized in that: in the described step 3, the discrete particle and continuous soil SPH mass point coupling force The calculation method is as follows: Assuming that there are n SPH particles and corresponding n discrete particles in the coupling transition domain, then the continuous soil SPH particles are divided into two parts, and the n SPH particle displacements in the coupling transition domain are combined into a column vector {u ^C } _int , the SPH particle is combined into a column vector {f ^C } _int by the coupling force of discrete particles, where the superscript C is used to indicate the variable on the continuous soil, and the subscript int is used to indicate the coupling; for the SPH particle not on the coupling transition domain, its displacement , velocity, acceleration and external force are respectively combined into a column vector {u ^C } _uin , and {f ^C } _uin , where the subscript uin means uncoupling; at the same time [M], [C] and [K] are used to represent the mass matrix, damping matrix and stiffness matrix obtained from the SPH discrete continuous solid differential equation, respectively. Then the kinetic equation can be obtained based on the SPH discretization: Let the mass of the i-th discrete particle on the coupled transition domain be m _i , and the column vector of translational displacement be The corresponding acceleration column vector is The resultant force by other discrete particles is the column vector {f _i ^M } _contact , and the column vector of the i-th SPH particle coupling force is {f _i ^M } _int , where the superscript M represents the variable on the discrete particle, and the subscript contact here Indicates particle contact; regardless of particle rotation, the equilibrium equation for a single discrete particle is: Combine the equilibrium equations of n discrete particles on the coupling transition domain, set the overall mass matrix as [m], and the n particles’ {f _i ^M } _contact and {f _i ^M } _int are respectively combined as {f ^M } _contact and {f ^M } _int , so the overall equilibrium equation of discrete particles on the coupled transition domain can be written as: Solve for the coupling force as follows: (a) Find the displacement on the coupling particle by eliminating the unknown coupling force The SPH particle and the discrete particle have the same acceleration in the coupling transition domain, and the coupling force is a pair of counterforces, we have {f ^C } _int ＝-{f ^M } _int , substituting formula (3) into formula (1) can eliminate the unknown coupling force {f ^C } _int and {f ^M } _int , as follows: In the above formula, [M _int ] is the coupling mass matrix after substituting [m] into [M]. In the above formula, the unknown coupling forces {f _i ^C } _int and {f _i ^M } _int have been eliminated, and the coupling transition domain can be solved Acceleration of SPH particle speed and displacement {u ^c } _int ; (b) Calculate the coupling force on the coupled transition domain will solve the obtained speed and the displacement {u ^c } _int are substituted into formula (1) to calculate the coupling force column vector {f ^c } _int acting on the SPH particle, and then the coupling force column vector {f ^M } _int acting on the discrete particle particle can be obtained = -{f ^c } _int . 6. the discrete particle-SPH coupling simulation method of gravity type retaining wall anti-sliding analysis in a kind of earthquake according to claim 1, it is characterized in that: in the described step 5, calculate the anti-sliding stability security of retaining wall in earthquake The specific method of the coefficient is: The load is applied at the bottom of the retaining wall-discrete particle-SPH continuous soil coupling system, that is, the seismic acceleration is loaded at the bottom of the continuous soil. It is assumed that there are n ^slip segment finite element boundaries on the side where the retaining wall contacts with the particles. Let The particle horizontal thrust on the finite element boundary of section i is F _i ^slip , and the resultant horizontal thrust force F ^slip of the soil on the retaining wall is assumed to be the resultant sliding force of the retaining wall. Here the superscript slip means sliding; at the bottom of the retaining wall, there are n ^anti-slip segment finite element boundaries in contact with particles, and the i-th segment of the wall is assumed to be F _i ^anti-slip in horizontal friction force of discrete particles, so that the retaining wall is affected by soil The resultant anti-slip force of the body is Here the superscript anti-slip means anti-sliding; in this way, the anti-sliding stability safety factor of the retaining wall can be calculated as the ratio of the anti-sliding force resultant force to the sliding force, and the anti-sliding stability safety factor is K,