Modeling stress wave propagation in rocks by distinct lattice spring model

In this paper, the ability of the distinct lattice spring model （DLSM） for modeling stress wave propagation in rocks was fully investigated. The influence of particle size on simulation of different types of stress waves （e.g. one-dimensional （1D） P-wave, 1D S-wave and two-dimensional （2D） cylindrical wave） was studied through comparing results predicted by the DLSM with different mesh ratios （It） and those obtained from the corresponding analytical solutions. Suggested values of lr were obtained for modeling these stress waves accurately. Moreover, the weak material layer method and virtual joint plane method were used to model P-wave and S-wave propagating through a single discontinuity. The results were compared with the classical analytical solutions, indicating that the virtual joint plane method can give better results and is recommended. Finally, some remarks of the DLSM on modeling of stress wave propagation in rocks were provided.

On the four-dimensional lattice spring model for geomechanics

Recently, a four-dimensional lattice spring model(4D-LSM) was developed to overcome the Poisson’s ratio limitation of the classical LSM by introducing the fourth-dimensional spatial interaction. In this work, some aspects of the 4D-LSM on solving problems in geomechanics are investigated, such as the ability to reproduce elastic properties of geomaterials, the capability of solving heterogeneous problems,the accuracy on modelling stress wave propagation, the ability to solve dynamic fracturing and the parallel computational efficiency. Our results indicate that the 4D-LSM is promising to deal with problems in geomechanics.

Stability analysis on tunnels with karst caves using the distinct lattice spring model

The effects of karst caves on tunnel stability were numerically investigated using the distinct lattice spring model(DLSM).The DLSM was validated by investigating the mechanical behavior of Brazilian discs with various sizes of central circular holes.Then,the effects of karst cave on U-shaped tunnel were investigated under various karst caves positions(top,bottom,and right side of the tunnel),tunnelcave distances(0.5-4 times the radius of the tunnel arc),and cave shapes(circular,rectangular flat,and rectangular vertical caves).The failure processes of the tunnel under those various conditions were analyzed and both the failure process and the final failure patterns of the tunnel were discussed.Numerical simulation demonstrated that karst caves around the tunnel could weaken the stability of the tunnel,indicating tunnel-cave distance effects.The closer the cave to the tunnel,the weaker the tunnel under loading.This effect was not significant when the tunnel-cave distance(d)was larger than three times the tunnel arc radius(R).In addition,the final failure pattern of the tunnel and its surrounding rock mass were dependent on both the position and the size of the cave.The larger the cave,the weaker the tunnel and its surrounding rock mass.Furthermore,compared with those cases with top and bottom caves,the tunnel with a right side cave had more impacts on tunnel stability.The main research finding could help engineers carry out stability analysis on tunnels in karst areas and take effective measures to enhance tunnel stability.

Elastic Characteristics of Digital Cores from Longmaxi Shale Using Lattice Spring Models

Effective medium methods for the attribution of micro-structures to macro elastic properties of shales are important for the prediction of sweet spots in the shale-gas production.With X-ray micro-computed tomography(XMCT),the micro-structures of shale core samples from Longmaxi Formation are visualized and characterized by 3D digital images.As an efficient alternative to conventional effective medium methods for estimating elastic properties,we propose a consistent workflow of lattice spring modeling(LSM)to emulate the digital cores using three types of lattices.Particular attention is paid to investigate the effective Young’s moduli,Poisson’s ratios,and preferred orientations,by uniaxial compression tests along two directions.Within elastic deformation,the impact of lattice arrangements on the anisotropy is even more than those of stress disturbances and micro-structural features.Compared with analytical approximations and theoretical predictions,the LSM numerical scheme shows general applicability for heterogeneous porous rocks.

High-performance computing of 3D blasting wave propagation in underground rock cavern by using 4D-LSM on TianHe-3 prototype E class supercomputer

Parallel computing assigns the computing model to different processors on different devices and implements it simultaneously.Accordingly,it has broad applications in the numerical simulation of geotechnical engineering and underground engineering,of which models are always large-scale.With parallel computing,the computing time or the memory requirements will be reduced by splitting the original domain of the numerical model into many subdomains,which is thus named as the domain decomposition method.In this study,a cubic and equal volume domain decomposition strategy was utilized to realize the parallel computing on the distributed memory system of four-dimensional lattice spring model(4D-LSM)based on the message passing interface.With a more efficient communication strategy introduced,this study aimed at operating an one-billion-particle model on a supercomputer platform.The preprocessing procedure of the parallelized 4D-LSM was restructured and the particle generation strategy suitable for the supercomputer platform was employed to minimize the time consumption in preprocessing and calculation.On this basis,numerical calculations were performed on TianHe-3 prototype E class supercomputer at the National Supercomputer Center in Tianjin.Two fieldscale three-dimensional blasting wave propagation models were carried out,of which the numerical results verify the computing power and the advantage of the parallelized 4D-LSM in the simulation of large-scale three-dimension models.Subsequently,the time complexity and spatial complexity of 4D-LSM and other particle discrete element methods were analyzed.

Mechanical behavior and wrinkling patterns of phaseseparated binary polymer blend film

The wrinkling of phase-separated binary polymer blend film was studied through combining the Monte Carlo(MC)simulation for morphologies with the lattice spring model(LSM)for mechanical properties.The information of morphology and structure obtained by use of MC simulation is input to the LSM composed of a three-dimensional network of springs,which allows us to determine the wrinkling and the mechanical properties of polymer blend film,such as strain,stress,and Young’s modulus.The simulated results show that the wrinkling of phase-separated binary polymer blend film is related not only to the structure of morphology,but also to the disparity in elastic moduli between polymers of blend.Our simulation results provide fundamental insight into the relationship between morphology,wrinkling,and mechanical properties for phase-separated polymer blend films and can yield guidelines for formulating blends with the desired mechanical behavior.The wrinkling results also reveal that the stretching of the phase-separated film can form the micro-template,which has a wide application prospect.