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From the microperspective, this paper presents a model based on a new type of noncontinuous theoretical mechanical method, molecular dynamics (MD), to simulate the typical soil granular flow. The Hertzian friction formula and viscous damping force are introduced in the MD governing equations to model the granular flow. To show the validity of the proposed approach, a benchmark problem of 2D viscous material flow is simulated. The calculated final flow runout distance of the viscous material agrees well with the result of constrained interpolated profile (CIP) method as reported in the literature. Numerical modeling of the propagation of the collapse of three-dimensional axisymmetric sand columns is performed by the application of MD models. Comparison of the MD computational runout distance and the obtained distance by experiment shows a high degree of similarity. This indicates that the proposed MD model can accurately represent the evolution of the granular flow. The model developed may thus find applications in various problems involving dense granular flow and large deformations, such as landslides and debris flow. It provides a means for predicting fluidization characteristics of soil large deformation flow disasters and for identification and design of appropriate protective measures.

As a kind of typical granular material, soil causes the common flow forms mainly for earthwork excavation, flow of soil slope by filling, and sudden slip on a weak foundation soil. The large deformation disasters caused by the flow of soil particles have received considerable attention and researches both at home and abroad.

Molecular dynamics originated in the 50s and began to be widely concerned in the mid-70s. In 1957, the state equations of gas and liquid were studied, firstly using molecular dynamics in the hard sphere model, thus setting a precedent for studying the macroscopic properties in the molecular dynamics method [

Molecular dynamics method, which is a combination of physics, mathematics, and chemistry, mainly relies on Newtonian mechanics to simulate the movement of molecular system and can simulate the movement of a single particle in a large number of particle collection system (solid, gas, or liquid). Its key is the concept of movement, that is, to compute the evolution of the position, velocity, and orientation of particles over time. The particle in molecular dynamics can be atom, molecule, or larger set of particles [

At present, the molecular dynamics simulation researches mostly focus on physics, biology, and chemistry, but the application in the field of geotechnical engineering is rare. The molecular dynamics approach is suitable to model granular material and to observe the trajectory of a single particle, so as to possibly identify its dynamical properties. Thus, the molecular dynamics method is tried to be applied to the granular flow characteristics research, and a 3D MD model that simulates granular flow is presented in this work, which is dedicated to provide a strong scientific basis for solving geotechnical engineering problem.

The accuracy of the model depends on the accuracy of description of external forces acting on the particle and the treatment of collisions. The particles can be either rigid and/or soft. A soft particle model [

Viscous damping force calculation formula of the particle is based on the Stokes drag law of fluid mechanics [

At present, in the field of molecular dynamics, the integral of the motion equation mainly adopts Verlet algorithm [

The calculation formulas of Verlet algorithm are as follows:

The performance of the new model will be verified in this section. It is essential to create an input script containing the desired commands before running LAMMPS. The Verlet algorithm is applied to the integral of motion equation in the input scripts. When numerical calculation starts, LAMMPS reads the input script, and the displacement, velocity, and acceleration of every granular particle are calculated and updated, thus obtaining the evolution trajectory of the whole calculation system over time. A two-dimensional simulation of viscous material flow was conducted to verify the reliability of the MD method.

Viscous materials flow on the plane under its own gravity, and a literature [

Calculation model [

Based on the molecular dynamics model mentioned above, the viscous material flow process was simulated. In MD simulation, the calculation area of 50 m long and 20 m wide and the viscous material size of 12 m long and 10 m wide were set up. The particles were idealized as circle with ignoring particle size distribution. The boundary conditions were fixed, and the interaction between particles in the system was calculated according to the Hertzian friction formula. The initial velocity was set to zero.

Calculation parameters and simulation results are shown in Table

Calculation parameters.

Parameters | Value |
---|---|

Grain diameter (m) | 0.05 [ |

Density (kg/m^{3}) |
2000.0 [ |

Elastic constant for normal contact (MPa) | 1 [ |

Elastic constant for tangential contact (MPa) | 0.29 |

Damping constant for normal contact | 0.001 [ |

Damping constant for tangential contact | 0.0005 |

Cohesion (Pa) | 800 [ |

Time step (s) | 1.0 × 10^{−4} |

Particle number | 57,251 |

Simulated propagation of the viscous material flow. (a)

Comparisons of MD and CIP results. (a)

Figure

This section discusses the three-dimensional simulation of the propagation of sand flow as the application of MD modeling to real large deformation of geomaterials. The motions of sands after collapse were represented in the MD simulation. This study can produce preliminary results for the prediction fluidization characteristics of large deformation flow disasters of geomaterials.

The collapse test of three-dimensional axisymmetric sand columns was carried out on the basis of the apparatus developed independently, which was made of steel with the inner diameter of 10 cm, the height of 10 cm, and the thickness of 1 cm.

Firstly, the collapse device was placed on a smooth horizontal plane to ensure that there was no gap between the experimental device and the contact surface. Secondly, the dry sand was slowly sprinkled into apparatus to keep uniform distribution. When the sand sample reached the height of the design of 10 cm, it was stopped and made to stand for a period of time, until the sand was compacted under its own gravity. Then, the camera was opened, and the collapse device was vertically and quickly removed. Finally, configuration images of sand were collected and analyzed. In the experiment, the frictional effects between individual grains on granular flow play a role only in the last instant of the flow, as it comes to an abrupt halt.

The final configuration of sand after collapse is conical in the experiment, as shown in Figure

The final configuration of sand flow.

The time-history curve of the cone diameter.

The developed and validated MD model was used to simulate the collapse propagation of an initially vertical 3D axisymmetric sand column in the work. The MD input file for 3D simulation of sand columns collapse was compiled, and then the diameter of the bottom circle formed by the final flowing configuration was calculated using the LAMMPS package. In the proposed model, the sand materials were discretized into a series of MD particles with a certain diameter. In the numerical simulation, sands were regarded as the uniformly distributed spherical particles, the calculation area was a cylinder with the diameter of 10 cm and the height of 10 cm, and the initial velocity of every sand particle was set to zero. The parameters used in the MD simulation were listed in Table ^{−5} s, and there were about 118,700 MD particles used to represent the sand column in the simulations conducted. The final runout distance was investigated and compared with the experimental observation, and the result was presented subsequently.

The parameters used in the MD simulation of a sand slump.

Parameters | Value |
---|---|

Grain diameter (mm) | 2 |

Density (kg/m^{3}) |
2650 |

Elastic constant for normal contact (MPa) | 10 |

Elastic constant for tangential contact (MPa) | 2.86 |

Damping constant for normal contact | 0.1 |

Damping constant for tangential contact | 0.05 |

Time step (s) | 1.0 × 10^{−5} |

Particle number | 118,700 |

Comparisons of MD numerical simulation results and the experimental results are shown in Figure

The change of the diameter of the cone bottom with time in MD simulation.

Thus, the MD method can describe well the granular flow of sand columns after collapse, and the correctness and applicability of the model and algorithm of molecular dynamics are verified again.

Application of the MD method to the simulation of soil granular materials under large deformation is the subject of this paper. The Hertzian friction formula and viscous damping force are implemented in the MD framework to model the granular flow.

The model developed is validated by the collapse of viscous material flow as reported in the available literature. Excellent agreement is observed between the MD model simulations and CIP simulations with respect to the flow distance, thus verifying the performance of the MD modeling scheme.

Simulation of the collapse of 3D axisymmetric sand columns is also conducted. Numerical results for the granular flow pattern and final runout distance are in good agreement with the experimental observations. The flow velocity of the simulated deformed region within a sand column during the collapse is bigger than the experimental observation. The likely cause is that MD numerical simulations ignore the influence of the evacuation of collapse device on the sand, whereas the collapse device has created the friction on the sand particles when it is removed in the experiment process.

This study indicates that the MD model developed can be used to effectively simulate large deformation of granular materials, and geomaterials in general, if proper calculation models are implemented. This is due to the fact that the MD method is a particle-based mesh-free numerical method. In the MD method, the variables of particles are calculated through the integration procedure. If an appropriate integration step is chosen, the MD model developed is capable of presenting many discrete characteristics of dense granular flow for granular materials under large deformation. Thus, the MD model may find extensive applications in various problems involving granular flow such as landslides and debris flow.

The authors declare that they do not have any commercial or associative interest that represents a conflicts of interest in connection with the work submitted.

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant no. 51608316), the Research Fund of the Key Laboratory of Transportation Tunnel Engineering, Ministry of Education (Grant no. TTE2014-05), and the Traffic Science and Technology Program in Shanxi Province (Grant no. 2017-1-20). The authors would like to express their gratitude for the financial support.