Hehua Zhu

Effect of Model Scale and Particle Size Distribution on PFC3D Simulation Results

This paper investigates the effect of model scale and particle size distribution on the simulated macroscopic mechanical properties, unconfined compressive strength (UCS), Young’s modulus and Poisson’s ratio, using the three-dimensional particle flow code (PFC3D). Four different maximum to minimum particle size (dmax/dmin) ratios, all having a continuous uniform size distribution, were considered and seven model (specimen) diameter to median particle size ratios (L/d) were studied for each dmax/dmin ratio. The results indicate that the coefficients of variation (COVs) of the simulated macroscopic mechanical properties using PFC3D decrease significantly as L/d increases. The results also indicate that the simulated mechanical properties using PFC3D show much lower COVs than those in PFC2D at all model scales. The average simulated UCS and Young’s modulus using the default PFC3D procedure keep increasing with larger L/d, although the rate of increase decreases with larger L/d. This is mainly caused by the decrease of model porosity with larger L/d associated with the default PFC3D method and the better balanced contact force chains at larger L/d. After the effect of model porosity is eliminated, the results on the net model scale effect indicate that the average simulated UCS still increases with larger L/d but the rate is much smaller, the average simulated Young’s modulus decreases with larger L/d instead, and the average simulated Poisson’s ratio versus L/d relationship remains about the same. Particle size distribution also affects the simulated macroscopic mechanical properties, larger dmax/dmin leading to greater average simulated UCS and Young’s modulus and smaller average simulated Poisson’s ratio, and the changing rates become smaller at larger dmax/dmin. This study shows that it is important to properly consider the effect of model scale and particle size distribution in PFC3D simulations.

HIGH ROCK SLOPE STABILITY ANALYSIS USING THE ENRICHED MESHLESS SHEPARD AND LEAST SQUARES METHOD

The meshless methods are particularly suitable for modeling problems with discontinuities such as joints in rock mass. The meshless Shepard and least squares (MSLS) method is a newly developed meshless method, which overcomes some limitations with other meshless methods. In the present paper, the MSLS method is extended for modeling jointed rock mass and the joint is modeled as discontinuity governing the near-field stress. A substantial high rock slope by the dam shoulder of Jinping Hydropower Station is analyzed by the developed method. Safety factors are evaluated based on the stress results along potential slip surfaces and compared with the conventional slice methods. The results demonstrate the feasibility of using the MSLS method in rock slope stability analysis and also reveal some interesting differences from the conventional slice methods. Some findings and outstanding issues demonstrated in this study are discussed in the end, which can be the topics for future development.

A two-dimensional micromechanical damage-healing model on microcrack-induced damage for microcapsule-enabled self-healing cementitious composites under compressive loading

Concretes with micro-encapsulated healing agents are very appealing due to the advantages of self-healing and the potential for controllable quantifiable healing on a large scale with little initial damage. Based on experimental observation and Taylors model, a two-dimensional micromechanical damage-healing model of microcapsule-enabled self-healing cementitious materials under tensile loading has been proposed. The healing effect on microcrack-induced damage can now be predicted quantitatively by its microscopic healing mechanism. The kinetic equations of damage-healing evolution and the formulations of compliance after healing are developed. Subsequently, simple and efficient numerical simulations are presented and different system parameters of microcapsule-enabled self-healing concretes, such as the radius and volume fraction of microcapsules, fracture toughness of healing agents and initial damage degree, are investigated. In particular, the proposed micromechanical damage-healing model demonstrates the potential capability to explain and simulate the physical behavior of microcapsule-enabled self-healing materials on the mesoscale.

Improved Prediction of Lateral Deformations due to Installation of Soil-Cement Columns

A modified method is proposed for predicting the lateral displacements of the ground caused by installation of soil-cement columns. The method is a combination of the original method derived on the basis of the theory of cylindrical cavity expansion in an infinite medium and a correction function introduced to consider the effect of the limited length of the columns. The correction function has been developed by comparing the solutions obtained using the spherical and the cylindrical cavity expansion theories for a single column installation. Both the original and the modified methods have been applied to a case history reported in the literature, which involves clay soils, and the predictions are compared with field measurements. The advantage of the modified method over the original method is demonstrated. Finally, the modified method has also been applied to a case history involving loose sandy ground, and the calculations show that the method can also be used for this type of soil provided that appropriate consideration is given to the volumetric strain occurring in the plastic zone of soil surrounding the soil-cement columns.

Multiscale modelling of hydro-mechanical couplings in quasi-brittle materials

A multiscale computational homogenization method for the modeling of hydro-mechanical coupling problem for quasi-brittle materials is developed. The present method is based on an asymptotic expansion homogenization combined with the semi-concurrent finite element modelling approach. Modified periodic boundary conditions and a molecular dynamics (MD) based inclusion or filler generation procedure are devised for the hydro-mechanical coupling problem. A modified elastic damage constitutive model and a damage induced permeability law have been developed for the hydraulic fracturing. The statistical convergence of the microscale representative volume element (RVE) model regarding the RVE characteristic size is studied. It was found that the RVE characteristic size is determined by both the mechanical and hydraulic properties of the RVE simultaneously. The present method is validated by the experimental results for brittle material. The damage zone and crack propagation path captured by the present method is compared with the experimental results (Chitrala et al. in J Pet Sci Eng 108:151–161, 2013). The results show that the present method is an effective for the modelling of hydro-mechanical coupling for brittle materials.

A new method for automated discontinuity trace mapping on rock mass 3D surface model

This paper presents an automated discontinuity trace mapping method on a 3D surface model of rock mass. Feature points of discontinuity traces are first detected using the Normal Tensor Voting Theory, which is robust to noisy point cloud data. Discontinuity traces are then extracted from feature points in four steps: (1) trace feature point grouping, (2) trace segment growth, (3) trace segment connection, and (4) redundant trace segment removal. A sensitivity analysis is conducted to identify optimal values for the parameters used in the proposed method. The optimal triangular mesh element size is between 5cm and 6cm; the angle threshold in the trace segment growth step is between 70? and 90?; the angle threshold in the trace segment connection step is between 50? and 70?, and the distance threshold should be at least 15 times the mean triangular mesh element size. The method is applied to the excavation face trace mapping of a drill-and-blast tunnel. The results show that the proposed discontinuity trace mapping method is fast and effective and could be used as a supplement to traditional direct measurement of discontinuity traces. An automated discontinuity trace mapping method is presented.The method is robust on noisy point cloud data of rock mass surface.Segmentation of extracted traces is overcomed.Smooth and continuous discontinuity traces can be achieved.This method is applied to excavation face mapping of a rock tunnel.

ARBITRARY DISCONTINUITIES IN THE NUMERICAL MANIFOLD METHOD

An overview of modeling arbitrary discontinuities within the numerical manifold method (NMM) framework is presented. The NMM employs a dual cover system, namely mathematical covers (MCs) and physical covers (PCs), to describe a physical problem. MCs are constructed totally independent of geometries of the problem domain, over which a partition of unity is defined. PCs are the intersections of MCs and the problem domain, over which local approximations with unknowns to be determined are defined. With such a dual cover system, arbitrary discontinuities involving jumps, kinks, singularities, and other nonsmooth features can be modeled in a convenient manner by constructing special PCs and designing tailored local approximations. Several typical discontinuities in solid mechanics are discussed. Among them are the simulations of material boundaries, voids, brittle cracks, cohesive cracks, material interfaces, interface cracks, dislocations, shear bands, high gradient zones, etc.

Modeling microcapsule-enabled self-healing cementitious composite materials using discrete element method

Concrete with a micro-encapsulated healing agent is appealing due to its self-healing capacity. The discrete element method (DEM) is emerging as an increasingly used approach for investigating the damage phenomenon of materials at the microscale. It provides a promising way to study the microcapsule-enabled self-healing concrete. Based on the experimental observation and DEM, a three-dimensional damage-healing numerical model of microcapsule-enabled self-healing cementitious materials under compressive loading is proposed. The local healing effect can be simulated in our model, as well as the stress concentration effect and the partial healing effect. The healing variable of the DEM model is developed to describe the healing process. We examine the dependence of the mechanical properties of the microcapsule-enabled self-healing material on (a) the stiffness of the solidified healing agent, (b) the strength of the solidified healing agent, (c) the initial damage of specimens, and (d) the partial healing effect. In particular, the proposed numerical damage-healing model demonstrates the potential capability to explain and simulate the physical behavior of microcapsule-enabled self-healing materials on the microscale.

Automatic extraction of discontinuity orientation from rock mass surface 3D point cloud

This paper presents a new method for extracting discontinuity orientation automatically from rock mass surface 3D point cloud. The proposed method consists of four steps: (1) automatic grouping of discontinuity sets using an improved K-means clustering method, (2) discontinuity segmentation and optimization, (3) discontinuity plane fitting using Random Sample Consensus (RANSAC) method, and (4) coordinate transformation of discontinuity plane. The method is first validated by the point cloud of a small piece of a rock slope acquired by photogrammetry. The extracted discontinuity orientations are compared with measured ones in the field. Then it is applied to a publicly available LiDAR data of a road cut rock slope at Rockbench repository. The extracted discontinuity orientations are compared with the method proposed by Riquelme et al. (2014). The results show that the presented method is reliable and of high accuracy, and can meet the engineering needs. An improved K-means algorithm based on sample density and clustering validity index is proposed to group discontinuities automatically.Discontinuity segmentation is optimized by redistributing misclassified vertices and facets which are caused by undulating DSM surfaces.This discontinuity orientation extraction method is automated, fast and effective in field application.

Phase field modelling of crack propagation, branching and coalescence in rocks

We present a phase field model (PFM) for simulating complex crack patterns including crack propagation, branching and coalescence in rock. The phase field model is implemented in COMSOL and is based on the strain decomposition for the elastic energy, which drives the evolution of the phase field. Then, numerical simulations of notched semi-circular bend (NSCB) tests and Brazil splitting tests are performed. Subsequently, crack propagation and coalescence in rock plates with multiple echelon flaws and twenty parallel flaws are studied. Finally, complex crack patterns are presented for a plate subjected to increasing internal pressure, the (3D) Pertersson beam and a 3D NSCB test. All results are in good agreement with previous experimental and numerical results.