Dynamic disturbance simulation method based on discrete element and near-field dynamics coupling model

Abstract

The invention provides a dynamic disturbance simulation method based on discrete elements and a near-field dynamics coupling model. The dynamic disturbance simulation method comprises the following steps: constructing the near-field dynamics coupling model; calculating particle stress information based on a discrete element method and the near-field dynamics coupling model; calculating the particle speed and displacement according to the particle stress information to obtain a calculation result; and outputting a calculation result and drawing a cloud picture. According to the method, a near-field dynamics and statics coupling model is adopted, a test sample of a simulation test is divided into different regions, and different calculation rules are applied, so that the calculation accuracy of a region subjected to fine calculation and the calculation efficiency of a region subjected to rough calculation are ensured. According to the method, a near-field dynamic coupling model is constructed according to the damage state of a slope model in the dynamic load influence process, and a method for describing rock dynamic disturbance damage characteristics is formed; according to the method, reference can be provided for mechanical characteristics of a dynamic disturbance simulation test, damage and instability of models such as a side slope under the dynamic load condition are reflected, and production safety in the construction process is guaranteed.

Description

Technical Field

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

[0002] The discrete element method has a good adaptability to discontinuous medium problems and is relatively mature in studying problems of large displacement deformation and non-linear relationships. It is widely used in various fields such as geotechnical engineering, structural geology, geophysics, mining engineering, etc., and many important results have been achieved. Peridynamics not only pays attention to the mechanical influence of particle bonding, but also considers the connection between other particles within the particle neighborhood. This method shows good results in reflecting crack failure and dynamic tests.

[0003] Existing discrete element software has certain limitations in simulating dynamic problems and cannot fully reproduce the change process and results of the model under dynamic loads. To better display the mechanical behavior of materials under dynamic action, the peridynamics method can be introduced to obtain more accurate simulation results of dynamic load changes.

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

[0005] In view of the deficiencies of the prior art, the present invention provides a dynamic disturbance simulation method based on a coupled model of discrete element and peridynamics. The present invention adopts a coupled model of peridynamics and statics, divides different regions of the specimen for the simulation test, and applies different calculation rules to ensure the calculation accuracy of the fine calculation region and the calculation efficiency of the rough calculation region.

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

[0007] S1), construct a peridynamics coupled model;

[0008] S2), based on the discrete element method and the peridynamics coupled model, input parameters and conditions, and judge whether the time step is reached;

[0009] If the time step is not reached, calculate the particle force information according to the calculation rules of the peridynamics coupled model;

[0010] If the time step is reached, directly output the calculation result and draw a contour map;

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

[0012] Preferably, in step S1), a peridynamic coupling model is constructed, specifically including the following steps:

[0013] S11): Apply bonds to the generated particle model.

[0014] S12): Divide the neighborhood of the particles in the area selected for peridynamic calculation, and apply peridynamic bonds between the particles and other particles in the neighborhood.

[0015] S13): Apply static bonds to other areas.

[0016] S14): Use peridynamic and static coupling bonds at the boundary between the two areas.

[0017] Preferably, in step S2), based on the discrete element method and the peridynamic coupling model, input parameters and conditions are provided. If the time step is not reached, the force information of the particles is calculated, specifically including the following steps:

[0018] S21): Initialize the parameters of the peridynamic coupling model, input material parameters, and determine the model size.

[0019] S22): Determine the coordinates of the discrete particles.

[0020] S23): Number the discrete particles respectively and input the corresponding data information.

[0021] S24): Apply initial boundary conditions and determine the time step.

[0022] S25): Calculate the force information of the particles 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 static area, a dynamic area, and a static-dynamic coupling simulation area.

[0024] Preferably, in step S2), in the static area, the rock material uses static bonds and exhibits linear elastic behavior.

[0025] Preferably, in step S2), when in the dynamic area, the calculation rules of peridynamics are used for simulation.

[0026] Preferably, in step S2), when in the static-dynamic coupling simulation area, both static and peridynamic simulations are used.

[0027] Preferably, in step S1), in the static area, the parallel bond force between particles is divided into a normal force and a tangential force

[0028] Preferably, in step S2), for the kinetic region, its 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] In the formula, ρ is the density, u is the displacement, b is the body force density, T is the vector state of the bond force; T 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 the acceleration; x and x′ respectively represent the coordinates of two different points in space;

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

[0032]

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

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

[0035]

[0036] Where f is the finally 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), according to 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 during the influence process of dynamic loads, forming a method for describing the dynamic disturbance failure characteristics of rocks;

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

[0042] 3. The present invention adopts a coupled model of peridynamics and statics, divides different regions of the specimen for the simulation test, and applies different calculation rules to ensure the calculation accuracy of the region for fine calculation and the calculation efficiency of the region for rough calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a schematic flow chart of the method of the present invention;

[0044] Figure 2 is a schematic diagram of the peridynamics principle of the present invention;

[0045] Figure 3 is a schematic diagram of the coupling of the peridynamics calculation region and the statics calculation region of the present invention;

[0046] Figure 4 is an effect diagram of the region division of the present invention;

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

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

[0049] Figure 7 is a cloud diagram of slope failure of the present invention for simulating the input of seismic waves;

[0050] Figure 8 is a diagram of the test results of the indoor input of seismic waves of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0051] The following further describes the specific embodiments of the present invention with reference to the drawings:

[0052] As Figure 1 shown, this embodiment provides a dynamic disturbance simulation method based on a coupled model of discrete element and peridynamics, including the following steps:

[0053] S1). Construct a peridynamics coupled model; specifically including the following steps:

[0054] S11). Apply bonds to the generated particle model;

[0055] S12). Divide the neighborhood of the particles in the region selected for peridynamics calculation, and apply peridynamics bonds to the particles and other particles in the neighborhood;

[0056] S13), Apply static bonding to other regions;

[0057] S14), For the boundary between the two regions, use the coupling bonding of peridynamics and statics.

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

[0059] S21), Initialize the parameters of the peridynamics 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] Among them, the size of the model includes but is not limited to length, width, elastic modulus, density, damping coefficient;

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

[0062] S23), Number the discrete particles respectively and input the corresponding data information, including but not limited to coordinates, radius, velocity, force, moment, bonding state, etc.;

[0063] S24), Apply initial boundary conditions and determine the time step;

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

[0065] If the time step has been reached, directly output the calculation result and draw the contour map.

[0066] In this embodiment, 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 particle and the selected particle is greater than zero, the particles overlap, and at this time, it is determined that the particles are in contact. For the contact between particles and the wall, calculate the overlap using the particle coordinates and the wall coordinates

[0067] As Figure 2 shown, for each individual particle, regard the area near it as its neighborhood. Other particles within the neighborhood will form bonds with this particle, and its constitutive relationship is:

[0068]

[0069] Among them, TIs the vector state of the bond force, t Is the scalar state of the magnitude of the force, Is the vector state of the force along the bond deformation direction.

[0070] Figure 2 In, R represents the radius of the neighborhood; x and x′ represent the coordinates of two different points in space respectively; T ′ represents the bond force received by another point, which is regarded as a vector with the same magnitude and opposite direction as T in the present invention; ξ represents the relative position vector, usually expressed as ξ = x′ - x.

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

[0072]

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

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

[0075]

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

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

[0078]

[0079] In the formula, represents the normal force within the current time step; is the normal force within the previous time step, is the normal stiffness, is the cross-sectional area, generally set as the diameter of the smaller particle among the two particles; c bond represents the calculation boundary radius; Δδ nis the increment of relative normal displacement, which can be obtained from the magnitude of the overlap . When the particles overlap, as the overlap increases, the normal force can continuously increase; 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 for the tangential force of the parallel bond force is as follows:

[0081]

[0082] In the formula, represents the tangential force within the current time step; represents the tangential force within the previous time step; is the tangential stiffness, is the cross-sectional area, Δδ s is the increment of relative tangential displacement; 0 < δ s <τ bond When, the tangential force increases with the increase of δ s . When it exceeds the failure limit, the bond fractures and the tangential force returns to zero. If δ s < 0, there is no tangential force; τ bond represents the calculation boundary radius.

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

[0084]

[0085] Among them, f x,ST and f y,ST are the component forces of the particle in the x and y directions in the static region respectively, l n is the bond number generated by the particle, F n and F s are the normal force and tangential force of the bond respectively, θ l is the bond inclination angle.

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

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

[0088] In the formula, ρ is the density, u is the displacement, b is the body force density, T is the vector state of the bond force; T is a function of both the bond length ξ and the position x and time t; dVx′ Denote the volume element at point x'; ü denotes the acceleration; x and x' represent the coordinates of two different points in space respectively;

[0089] The calculation method of the bond force in the kinetic region is as follows:

[0090]

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

[0092] t The expression of is:

[0093]

[0094] In the formula, λ, θ and τ are all fixed parameters, which can be obtained according to the actual situation, m is the unit mass, ω is the 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 elongation.

[0095] For the force on the particles in the kinetic region, take the sum of all bond forces, that is:

[0096]

[0097] Wherein, f x,PD 、f y,PD are the component forces of the particles in the x and y directions in the kinetic region respectively.

[0098] When located in the static-dynamic coupling simulation region, both static mechanics and peridynamics simulations are adopted. The force on the particles in the static-dynamic coupling simulation region is expressed as:

[0099]

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

[0101] As Figure 3 shown, for the boundary of the peridynamics and static mechanics coupling model, for the particles in the static mechanics region, ordinary bonding, that is, static mechanics bonding, will be adopted for calculation; for the particles in the peridynamics region, peridynamics bonding will be adopted for calculation, and the influence of the neighborhood will be considered at the same time; when the particles are in the static mechanics region and are affected by the neighborhood of the particles in the peridynamics region at the same time, peridynamics bonding is formed and the peridynamics calculation rules are given.

[0102] As shown Figure 4 in the figure, the area for forming the specimen in the discrete element software is divided. The peridynamic calculation is adopted where fractures are applied, and rough calculation is carried out in places far from the fractures, and ordinary bonding is used here.

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

[0104] Calculate the particle velocity v according to the particle force result:

[0105]

[0106] where f is the finally 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] where the calculation formula of the finally calculated particle force f is as follows:

[0108]

[0109] Preferably, in step S3), according to 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] To verify the simulation accuracy of this embodiment and the rationality of the constitutive model, a comparison between the numerical simulation data and the experimental data is carried out.

[0112] As shown Figure 5 in the figure, a slope model is constructed using the discrete element software, and it is calculated to equilibrium under its own weight to obtain the particle force contour map. At this time, the particles are more stressed and the color is deeper when approaching the bottom end, and the particles at the bottom of the slope are more compressed. After the particles are balanced, bonds are constructed between the particles. For the trapezoidal area at the slope, peridynamic bonding is adopted, the domain radius is set for the particles, and the peridynamic calculation rule is used for calculation; for other areas, static bonding is used to construct force bonds for the particles in contact, and the commonly used parallel bond model along the way is used for calculation. The coupling bonding generation method of peridynamics and statics is adopted at the junction of the two.

[0113] As shown Figure 6 in the figure, it is necessary to input the seismic wave load to the constructed slope model. The KOBE seismic wave is adopted here, and the original data of the seismic wave is filtered and baseline corrected to reduce the interference wave to obtain the finally used seismic wave for input. The seismic wave applies the value to the bottom wall, and the wave propagates to the slope and causes damage.

[0114] As shown Figure 7 in the figure, the failure condition of the slope under seismic load is calculated by using the peridynamics coupling model in the discrete element software.

[0115] As shown Figure 8 in the figure, the failure condition of the slope model in the test box under the application of the KOBE seismic wave under the same conditions.

[0116] The above embodiments and descriptions in the specification only illustrate the principles and the best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements fall within the scope of the present invention claimed.

Claims

1. A dynamic disturbance simulation method based on a discrete element and peridynamic coupling model, characterized in that: The steps include: S1), constructing 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; S3), determine whether all particles have been traversed, if all particles have been traversed, calculate the particle speed and displacement according to the particle force information, and obtain the calculation result; output the calculation result and draw a cloud map.

2. The dynamic disturbance simulation method based on discrete element and peridynamic coupling model according to claim 1 is characterized in that: 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, the particle force information is calculated; specifically, the following steps are included: S21), initializing parameters of the peridynamic coupling model, inputting material parameters, and determining model dimensions; S22), determining the coordinates of discrete particles; S23), numbering the discrete particles respectively 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.

3. The dynamic disturbance simulation method based on discrete element and peridynamic coupling model according to claim 2 is characterized in that: In step S2), 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 particle is When it is greater than zero, the particles overlap and are considered 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.

4. The method for simulating dynamic disturbances based on a discrete element and peridynamic coupling model according to claim 3, characterized in that: In step S2), 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 normal force 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 of the particle in the x and y directions, respectively, and l n is the bonding number of particles, F n and F S are the normal force and tangential force of the parallel adhesion, θ l is the bonding tilt angle.

5. The method for simulating dynamic disturbances based on a discrete element and peridynamic coupling model according to claim 4, characterized in that: The calculation formula of the normal force of the parallel bonding force is as follows: In the formula, represents the normal force in the current step; 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, which can be obtained by the overlap It is obtained from the size of the particle that when the particles overlap, the normal force can continue to increase with the increase of the overlap amount; 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.

6. The method for simulating dynamic disturbances based on a discrete element and peridynamic coupling model according to claim 4, characterized in that: The calculation formula of the tangential force of the parallel bonding force is as follows: In the formula, represents the tangential force in the step at that time; 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 , the tangential force increases with 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.

7. The method for simulating dynamic disturbances based on a discrete element and peridynamic coupling model according to claim 3, characterized in that: In step S2), when located in the dynamic region, the calculation rules of peridynamics 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 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; For the particle forces in the dynamic region, take the sum of all bond forces, that is: Among them, f x,PD 、f y,PD are the x- and y-direction components of the particle in the dynamic region, respectively.

8. The method for simulating dynamic disturbances based on a discrete element and peridynamic coupling model according to claim 3, characterized in that: In step S2), when the particles are in the static-dynamic coupling simulation area, statics and peridynamics simulation are used simultaneously, and 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 x- and y-direction components of the particles in the dynamic-static coupling simulation area, respectively.

9. The method for simulating dynamic disturbances based on a discrete element and peridynamic coupling model according to claim 8, characterized in that: In step S2), for the boundary of the peridynamic and static coupling model, for the particles in the static region, ordinary bonding, i.e., static bonding, will be used for calculation; for the particles in the peridynamic region, peridynamic bonding will be used for calculation, while considering the effect of the neighborhood; when the particles are in the static region and are affected by the neighborhood of the particles in the peridynamic region, peridynamic bonding is formed and the peridynamic calculation rules are assigned.

10. The method for simulating dynamic disturbances based on a discrete element and peridynamic coupling model according to claim 9, characterized in that: 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: 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 fixed parameters, which can be obtained according to the actual situation, 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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