Dynamic disturbance simulation method based on discrete element and peridynamic coupling model

Abstract

The present invention provides a method for simulating dynamic disturbances based on a discrete element method and a peridynamic coupling model, comprising constructing a peridynamic coupling model; calculating particle force information based on the discrete element method and the peridynamic coupling model; calculating particle velocity and displacement according to the particle force information to obtain calculation results; outputting the calculation results and drawing a cloud map. The present invention adopts a peridynamic and static coupling model to divide the specimens of the simulation test into different areas, and applies different calculation rules to ensure the calculation accuracy of the fine calculation area and the calculation efficiency of the rough calculation area. The present invention constructs a peridynamic coupling model for the destruction state of the slope model during the influence of dynamic loads, forming a method for describing the dynamic disturbance destruction characteristics of rocks; the present invention can provide a reference for the mechanical characteristics of the dynamic disturbance simulation test, reflect the destruction and instability of models such as slopes under dynamic load conditions, and ensure production safety during construction.

Description

Technical Field

[0001] The present invention relates to the field of geotechnical engineering technology, and in particular to a dynamic disturbance simulation method based on a discrete element and peridynamic coupling model. Background Art

[0002] The discrete element method (DEM) is well-suited for problems involving discontinuous media and is relatively mature in studying large displacements and deformations and nonlinear relationships. It has been widely applied in fields such as geotechnical engineering, structural geology, geophysics, and mining engineering, achieving numerous important results. Peridynamics not only considers the mechanical effects of interparticle bonding but also considers the connections between other particles within a particle's neighborhood. This method has demonstrated promising results in characterizing fracture failure and dynamic testing.

[0003] Existing discrete element methods have limitations when simulating dynamic problems, and cannot fully reproduce the process and results of a model's changes under dynamic loads. To better demonstrate the mechanical behavior of materials under dynamic loads, peridynamic methods can be introduced to obtain more accurate simulation results of dynamic load changes.

[0004] In discrete element simulations, peridynamics usually consumes more computing power, which makes the calculation process longer. Summary of the Invention

[0005] In response to the shortcomings of the existing technology, the present invention provides a dynamic disturbance simulation method based on a discrete element and peridynamic coupling model. The present invention adopts a peridynamic and static coupling model to divide the specimens of the simulation test into different areas and applies different calculation rules to ensure the calculation accuracy of the fine calculation area and the calculation efficiency of the rough calculation area.

[0006] The technical solution of the present invention is: a dynamic disturbance simulation method based on a discrete element and peridynamic coupling model, comprising the following steps:

[0007] S1), building a peridynamic coupling model;

[0008] S2), based on the discrete element method and the peridynamic coupling model, input parameters and conditions, and determine whether the time step is reached;

[0009] If the time step is not reached, the particle force information is calculated according to the calculation rules of the peridynamic coupling model;

[0010] If the time step has been reached, the calculation results are directly output and the cloud map is drawn;

[0011] S3) Determine whether all particles have been traversed. If all particles have been traversed, calculate the particle velocity and displacement according to the particle force information to obtain a calculation result; output the calculation result and draw a cloud map.

[0012] Preferably, in step S1), constructing a peridynamic coupling model specifically includes the following steps:

[0013] S11), applying bonding to the generated particle model;

[0014] S12), dividing the particles in the area selected for peridynamic calculation into neighborhoods, and applying peridynamic bonding to the particles and other particles in the neighborhood;

[0015] S13), applying static bonding to other areas;

[0016] S14) The boundary between the two regions is bonded using the coupling of peridynamics and statics.

[0017] Preferably, in step S2), based on the discrete element method and the peridynamic coupling model, parameters and conditions are input; if the time step is not reached, particle force information is calculated; specifically, the following steps are included:

[0018] S21), initializing parameters of the peridynamic coupling model, inputting material parameters, and determining the model size;

[0019] S22), determining the coordinates of discrete particles;

[0020] S23), numbering the discrete particles and inputting corresponding data information;

[0021] S24), applying initial boundary conditions and determining the time step;

[0022] S25) Calculate the particle force information according to the calculation rules of the peridynamic coupling model.

[0023] Preferably, in step S2), the peridynamic coupling model is divided into different calculation areas, including a statics area, a dynamics area, and a static-dynamic coupling simulation area.

[0024] Preferably, in step S2), in the statics region, the rock material is statically bonded and exhibits linear elastic behavior.

[0025] Preferably, in step S2), when located in the dynamic region, the simulation is performed using the calculation rules of peridynamics.

[0026] Preferably, in step S2), when located in the static-dynamic coupling simulation area, statics and peridynamics simulations are simultaneously adopted.

[0027] As a preference, in step S1), for the statics region, the parallel bonding force between particles is divided into normal force and tangential force

[0028] Preferably, in step S2), for the kinetic region, the equilibrium equation is expressed as follows:

[0029] ρü(x,t)=∫{ T [x,t]<x′-x> - T [x′,t]<x-x′>}dV x′ +b(x,t)

[0030] Where ρ is density, u is displacement, b is body density, T is the vector state of the bond force; T It is a function of both the bond length ξ and the position x and time t; dV x′ represents the volume element at point x′; ü represents acceleration; x and x′ represent the coordinates of two different points in space respectively;

[0031] Preferably, in step S2), for each individual particle, the area near it is regarded as its neighborhood, and other particles in the neighborhood will form a bond with the particle; the expression of the force information of the individual particle is:

[0032]

[0033] in, T is the vector state of the bond force, t is the scalar state of the force, is the vector state of the force along the bond deformation direction.

[0034] Preferably, in step S3), the particle velocity v is calculated according to the particle force result:

[0035]

[0036] Among them, f is the final calculated particle force, d m is the damping coefficient, Δt is the unit time step, and m is the unit mass of the particle.

[0037] Preferably, in step S3), based on the particle velocity result, the relative particle displacement Δs at each time step is obtained by multiplying the particle velocity by the unit time step:

[0038] Δs=vΔt.

[0039] The beneficial effects of the present invention are:

[0040] 1. The present invention constructs a peridynamic coupling model for the failure state of the slope model under the influence of dynamic loads, forming a method for describing the characteristics of rock dynamic disturbance failure;

[0041] 2. The present invention can provide a reference for the mechanical characteristics of dynamic disturbance simulation tests, reflecting the damage and instability of models such as slopes under dynamic load conditions, and ensuring production safety during construction.

[0042] 3. The present invention adopts a coupling model of peridynamics and statics, divides the specimens of the simulation test into different areas, and applies different calculation rules to ensure the calculation accuracy of the fine calculation area and the calculation efficiency of the rough calculation area. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Schematic diagram of the process of the present invention;

[0044] Figure 2 Schematic diagram of the peridynamic principle of the present invention;

[0045] Figure 3 Schematic diagram of the coupling between the peridynamics calculation area and the statics calculation area of ​​the present invention;

[0046] Figure 4 This is a rendering of the regional division of the present invention;

[0047] Figure 5 This is a slope model diagram for simulating earthquake load input test of the present invention;

[0048] Figure 6 This is a schematic diagram of seismic wave filtering and baseline correction according to the present invention;

[0049] Figure 7 The slope damage cloud map of the present invention simulates the seismic wave input;

[0050] Figure 8 This is a diagram showing the results of the indoor test of seismic wave input in the present invention. DETAILED DESCRIPTION

[0051] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0052] like Figure 1 As shown, this embodiment provides a dynamic disturbance simulation method based on a discrete element and peridynamic coupling model, comprising the following steps:

[0053] S1) Constructing a peridynamic coupling model; specifically including the following steps:

[0054] S11), applying bonding to the generated particle model;

[0055] S12), dividing the particles in the area selected for peridynamic calculation into neighborhoods, and applying peridynamic bonding to the particles and other particles in the neighborhood;

[0056] S13), applying static bonding to other areas;

[0057] S14) The boundary between the two regions is bonded using the coupling of peridynamics and statics.

[0058] S2), based on the discrete element method and the peridynamic coupling model, input parameters and conditions, and determine whether the time step is reached; if the time step is not reached, calculate the particle force information according to the peridynamic coupling model calculation rules; specifically comprising the following steps:

[0059] S21) Initialize the parameters of the peridynamic coupling model, input material parameters, and determine the model size; in this embodiment, the input parameters include but are not limited to damping coefficient, stiffness, calculation boundary radius, neighborhood radius, elastic modulus, bulk modulus, critical elongation, boundary conditions, etc.

[0060] The dimensions of the model include but are not limited to length, width, elastic modulus, density, and damping coefficient;

[0061] S22), determining the discrete particle coordinates according to the initial generation coordinates of the particles and the displacement information in each time step;

[0062] S23), numbering the discrete particles and inputting corresponding data information, including but not limited to coordinates, radius, speed, force, torque, bonding state, etc.;

[0063] S24), applying initial boundary conditions and determining the time step;

[0064] S25) Calculate the particle force information according to the calculation rules of the peridynamic coupling model.

[0065] If the time step has been reached, the calculation results are directly output and the cloud map is drawn.

[0066] In this embodiment, the overlap variable between particles is defined as follows according to the discrete element method: Select any particle and traverse other particles. When the overlap variable between the traversed particles and the selected particles is When it is greater than zero, the particles overlap and are judged to be in contact. For the contact between particles and walls, the overlap is calculated using the particle coordinates and the wall coordinates.

[0067] like Figure 2 As shown in , for each individual particle, the area around it is regarded as its neighborhood. Other particles in the neighborhood will form bonds with the particle, and its constitutive relationship is:

[0068]

[0069] in, Tis the vector state of the bond force, t is the scalar state of the force, is the vector state of the force along the bond deformation direction.

[0070] Figure 2 In the equation, R represents the radius of the neighborhood; x and x′ represent the coordinates of two different points in the space; T ' represents the bond force received at another point, which is considered to be the same as T Vectors of equal magnitude and opposite direction; ξ represents the relative position vector, usually expressed as ξ = x′-x.

[0071] For the scalar state of the force t , whose expression is:

[0072]

[0073] In the formula, λ, θ and τ are all fixed parameters that can be obtained according to actual conditions, m is the unit mass, ω is a weight function with non-zero value in the action neighborhood, x is the vector state of the particle position, e is the scalar state of the bond stretch.

[0074] In this embodiment, when the particles are in equilibrium, the peridynamic coupling model is divided into different calculation regions, including the static region, the dynamic region, and the static-dynamic coupling simulation region. In the static region, the rock material adopts static bonding and exhibits linear elastic behavior. In the static region, the parallel bonding force between particles is divided into the normal force and tangential force Right now:

[0075]

[0076] in, is the normal force; is the tangential force; represents the contact normal unit vector.

[0077] The calculation formula of the normal force of the parallel bond force is as follows:

[0078]

[0079] Where, represents the normal force in the step at that time; is the normal force in the previous time step, is the normal stiffness, is the cross-sectional area, which is generally set to the diameter of the smaller particle of the two particles; c bond Indicates the calculated boundary radius; Δδ nis the relative normal displacement increment, which can be obtained by the overlap When the particles overlap, the normal force can continue to increase with the increase of the overlap; when the particles do not overlap, the normal force increases with the increase of the distance between the particles until it exceeds the calculation boundary, and the normal force returns to zero after fracture.

[0080] The calculation formula of the tangential force of the parallel bonding force is as follows:

[0081]

[0082] Where, represents the tangential force in the current step; represents the tangential force in the previous time step; is the tangential stiffness, is the cross-sectional area, Δδ s is the relative tangential displacement increment; 0<δ s <τ bond When δ s As the force increases, when it exceeds the failure limit, the bond breaks and the tangential force returns to zero. s <0, there is no tangential force; τ bond Indicates the calculated border radius.

[0083] For the statics region, the force on the particle is expressed as:

[0084]

[0085] Among them, f x,ST 、f y,ST are the x- and y-direction components of the particle in the statics region, l n is the bonding number of particles, F n and F s are the normal force and tangential force of bonding, θ l is the bonding tilt angle.

[0086] When located in the dynamic region, the peridynamics calculation rules are used for simulation. The peridynamics equilibrium equation is expressed as follows:

[0087] ρü(x,t)=∫{ T [x,t]<x′-x> - T [x′,t]<x-x′>}dV x′ +b(x,t)

[0088] Where ρ is density, u is displacement, b is body density, T is the vector state of the bond force; T It is a function of both the bond length ξ and the position x and time t; dVx′ represents the volume element at point x′; ü represents acceleration; x and x′ represent the coordinates of two different points in space respectively;

[0089] The bond forces in the dynamic region are calculated as:

[0090]

[0091] in, t is the scalar state of the force, is the vector state of the force along the bond deformation direction.

[0092] t The expression is:

[0093]

[0094] In the formula, λ, θ and τ are all fixed parameters that can be obtained according to actual conditions, m is the unit mass, ω is a weight function with non-zero value in the action neighborhood, x is the vector state of the particle position, e is the scalar state of the bond stretch.

[0095] For the particle forces in the dynamic region, the sum of all bond forces is taken, that is:

[0096]

[0097] Among them, f x,PD 、f y,PD are the x- and y-direction components of the particle in the dynamic region, respectively.

[0098] When located in the static-dynamic coupling simulation area, statics and peridynamics simulations are used simultaneously. The force on the particles in the static-dynamic coupling simulation area is expressed as:

[0099]

[0100] Among them, f x,DS 、f y,DS are the component forces of particles in the x and y directions in the dynamic-static coupling simulation area, respectively.

[0101] like Figure 3 As shown in the figure, for the boundary of the peridynamic and statics coupling model, ordinary bonding, i.e., static bonding, is used for the calculation of particles in the statics region; peridynamic bonding is used for the calculation of particles in the peridynamic region, while the effect of the neighborhood is taken into account. When a particle is in the statics region and is affected by the neighborhood of particles in the peridynamic region, peridynamic bonding is formed and the peridynamic calculation rules are assigned.

[0102] like Figure 4 The area where the specimen is formed is divided within the discrete element software. Peridynamic calculations are performed where the cracks are applied, while rough calculations are performed away from the cracks, where ordinary bonding is used.

[0103] S3) Determine whether all particles have been traversed. If all particles have been traversed, calculate the particle velocity and displacement according to the particle force information to obtain a calculation result; output the calculation result and draw a cloud map.

[0104] According to the particle force results, the particle velocity v is calculated:

[0105]

[0106] Among them, f is the final calculated particle force, d m is the damping coefficient, Δt is the unit time step, and m is the unit mass of the particle.

[0107] Among them, the calculation formula of the particle force f is as follows:

[0108]

[0109] Preferably, in step S3), based on the particle velocity result, the relative particle displacement Δs at each time step is obtained by multiplying the particle velocity by the unit time step:

[0110] Δs=vΔt.

[0111] In order to verify the simulation accuracy and rationality of the constitutive model of this embodiment, a comparison between the numerical simulation data and the experimental data was performed.

[0112] like Figure 5 As shown, a slope model was constructed using discrete element software and calculated to equilibrium under its own weight, resulting in a force cloud diagram of the particles. At this point, particles near the bottom are subject to greater forces, appear darker, and are more compressed at the bottom of the slope. After equilibrium, bonds are established between the particles. For the trapezoidal regions of the slope, peridynamic bonding is employed, with a defined radius for the particles and calculations performed using peridynamic calculation rules. For other regions, static bonding is employed to establish force bonds between contacting particles, and the commonly used parallel bonding model along the path is used for calculations. At the interface between the two, a bond generation method combining peridynamics and statics is employed.

[0113] like Figure 6 As shown, the constructed slope model requires the input of seismic wave loads. KOBE seismic waves are used here, and the raw data is filtered and baseline corrected to reduce interference waves, resulting in the final seismic wave input. The seismic wave applies a numerical value to the bottom wall, which then propagates to the slope, causing damage.

[0114] like Figure 7 As shown in the figure, the damage of the slope when it is subjected to earthquake load is calculated using the peridynamic coupling model in the discrete element software.

[0115] like Figure 8 As shown in Figure 2, the damage of the slope model in the test box when KOBE seismic waves are applied under the same conditions.

[0116] The above embodiments and descriptions are only for explaining the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, which shall fall within the scope of the invention to be protected.

Claims

1. A dynamic disturbance simulation method based on a discrete element and peridynamic coupling model, characterized by: The steps include: S1), building a peridynamic coupling model; S2), based on the discrete element method and the peridynamic coupling model, input parameters and conditions, and determine whether the time step is reached; If the time step is not reached, the particle force information is calculated according to the calculation rules of the peridynamic coupling model; If the time step has been reached, the calculation results are directly output and the cloud map is drawn; Based on the discrete element method and the peridynamic coupling model, parameters and conditions are input; if the time step is not reached, the particle force information is calculated. Specifically, the steps include: S21), initializing parameters of the peridynamic coupling model, inputting material parameters, and determining the model size; S22), determining the coordinates of discrete particles; S23), numbering the discrete particles and inputting corresponding data information; S24), applying initial boundary conditions and determining the time step; S25), calculating the particle force information according to the calculation rules of the peridynamic coupling model in different calculation areas; According to the discrete element method, the overlap variable between particles is defined as Select any particle and traverse other particles. When the overlap variable between the traversed particles and the selected particles is When it is greater than zero, the particles overlap and are judged to be in contact. For the contact between particles and walls, the overlap is calculated using the particle coordinates and the wall coordinates. When the particles are in equilibrium, the peridynamic coupling model is divided into different computational regions, including a static region, a dynamic region, and a static-dynamic coupling simulation region; In the statics region, the rock material adopts static bonding and exhibits linear elastic behavior; In the static region, the parallel bonding forces between particles are divided into normal forces and tangential force Right now: in, is the normal force; is the tangential force; represents the contact normal unit vector; For the statics region, the force on the particle is expressed as: Among them, f x 、f y are the forces on the particle in the x and y directions, l n is the bonding number of particles, F n and F s are the normal force and tangential force of the parallel adhesion force, θ l is the bonding tilt angle; When located in the dynamic region, the peridynamics calculation rules are used for simulation. For the dynamic region, the equilibrium equation is expressed as follows: ρü(x,t)=∫{ T [x,t]<x′-x>- T [x′,t]<x-x′>}dV x′ +b(x,t) Where ρ is density, u is displacement, b is body force density, and T is the vector state of bond force; T is a function of both bond length ξ and position x and time t; dV x′ represents the volume element at point x′; ü represents acceleration; x and x′ represent the coordinates of two different points in space respectively; For the particle forces in the dynamic region, the sum of all bond forces is taken, that is: Among them, f x,PD 、f y,PD are the component forces on the particle in the x and y directions in the dynamic region, respectively; S3) Determine whether all particles have been traversed. If all particles have been traversed, calculate the particle velocity and displacement according to the force information of the particles to obtain the calculation results; output the calculation results and draw a cloud map.

2. The dynamic disturbance simulation method based on the discrete element and peridynamic coupling model according to claim 1 is characterized in that: The calculation formula of the normal force of the parallel bond force is as follows: Where, represents the normal force in the step at that time; is the normal force in the previous time step, is the normal stiffness, is the cross-sectional area; c bond Indicates the calculated boundary radius; Δδ n is the relative normal displacement increment, through the overlap When the particles overlap, the normal force increases with the increase of the overlap; when the particles do not overlap, the normal force increases with the increase of the distance between the particles until it exceeds the calculation boundary, and the normal force returns to zero after fracture.

3. The dynamic disturbance simulation method based on the discrete element and peridynamic coupling model according to claim 1 is characterized in that: The calculation formula of the tangential force of the parallel bonding force is as follows: Where, represents the tangential force in the current step; represents the tangential force in the previous time step; is the tangential stiffness, is the cross-sectional area, Δδ S is the relative tangential displacement increment; 0<δ s <τ bond When δ s As the force increases, when it exceeds the failure limit, the bond breaks and the tangential force returns to zero; if δ s <0, there is no tangential force; τ bond Indicates the threshold value of bond strength.

4. The dynamic disturbance simulation method based on the discrete element and peridynamic coupling model according to claim 1 is characterized in that: In step S2), when the particles are located in the static-dynamic coupling simulation area, statics and peridynamics simulations are used simultaneously. The force on the particles in the static-dynamic coupling simulation area is expressed as: Among them, f x,DS 、f y,DS are the component forces of particles in the x and y directions in the dynamic-static coupling simulation area, respectively; f x,ST 、f y,ST are the x- and y-direction components of the particle in the statics region; f x,PD 、f y,PD are the x- and y-direction components of the particle in the dynamic region, respectively.

5. The dynamic disturbance simulation method based on the discrete element and peridynamic coupling model according to claim 4 is characterized in that: In step S2), for the boundary of the peridynamic and statics coupled model, ordinary bonding, i.e., static bonding, is used for the calculation of particles in the statics region; peridynamic bonding is used for the calculation of particles in the peridynamic region, while the effect of the neighborhood is taken into account. When a particle is in the statics region and is affected by the neighborhood of particles in the peridynamic region, peridynamic bonding is formed and the peridynamic calculation rules are assigned.

6. The dynamic disturbance simulation method based on the discrete element and peridynamic coupling model according to claim 5 is characterized in that: In step S2), for each individual particle, the area around it is considered as its neighborhood, and other particles in the neighborhood will form a bond with the particle; the expression of the force information of the individual particle is: in, T is the vector state of the bond force, t is the scalar state of the force, is the vector state of force along the bond deformation direction; For the scalar state of the force t , whose expression is: In the formula, λ, θ and τ are all fixed parameters that can be obtained according to actual conditions, m is the unit mass, ω is a weight function with non-zero value in the action neighborhood, x is the vector state of the particle position, e is the scalar state of the bond stretch.

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