Generation of Numerical Models of Anisotropic Columnar Jointed Rock Mass Using Modified Centroidal Voronoi Diagrams

Qingxiang Meng,Yulong Chen,Qiang Zhang,Long Yan

doi:10.3390/sym10110618

Abstract

A columnar joint network is a natural fracture pattern with high symmetry, which leads to the anisotropy mechanical property of columnar basalt. For a better understanding the mechanical behavior, a novel modeling method for columnar jointed rock mass through field investigation is proposed in this paper. Natural columnar jointed networks lies between random and centroidal Voronoi tessellations. This heterogeneity of columnar cells in shape and area can be represented using the coefficient of variation, which can be easily estimated. Using the bisection method, a modified Lloyd’s algorithm is proposed to generate a Voronoi diagram with a specified coefficient of variation. Modelling of the columnar jointed rock mass using six parameters is then presented. A case study of columnar basalt at Baihetan Dam is performed to demonstrate the feasibility of this method. The results show that this method is applicable in the modeling of columnar jointed rock mass as well as similar polycrystalline materials.

Highlights

Columnar jointed rock is a typical geological structure formed by a lot of ordered colonnades like the world famous natural wonders of Fingal’s Cave and Giant’s Causeway [1,2]
Because of its adverse geologic conditions, study on the mechanical properties of columnar jointed rock mass is very important in engineering projects
A Voronoi diagram is a classical domain partitioning method named after Georgy Voronoi, a generation ispartitioning the dual algorithm of Delaunay triangulation

Summary

Introduction

Columnar jointed rock is a typical geological structure formed by a lot of ordered colonnades like the world famous natural wonders of Fingal’s Cave and Giant’s Causeway [1,2]. Being a miraculous natural phenomenon, the study on the geological structure of columnar jointed rock can be dated back to the 17th century [3]. With the increase of human activities, some engineering projects have encountered columnar jointing, and a large hydropower station is even founded on it [11]. Because of its adverse geologic conditions, study on the mechanical properties of columnar jointed rock mass is very important in engineering projects. King et al studied elastic-wave propagation in columnar joints with a series of cross-hole acoustic measurements made between four horizontal boreholes drilled from a near-surface underground opening situated in a basaltic rock mass [12].

Objectives

Methods

Conclusion