Overview of the numerical methods for the modelling of rock mechanics problems

Abstract

Subject reviewThe numerical methods have their origin in the early 1960s and even at that time it was noted that numerical methods can be successfully applied in various engineering and scientific fields, including the rock mechanics. Moreover, the rapid development of computers was a necessary background for solving computationally more demanding problems and the development process of the methods in general. Thus, we have many different methods presently, which can be separated into two main branches: continuum and discontinuum-based numerical methods. Some problems require the strengths of both main approaches which brought the hybrid continuum/discontinuum methods. The first goal of this paper is to present the state of the art numerical methods and approaches for solving the rock mechanics problems, as well as to give the brief explanation about the theoretical background of each method. The second goal is to emphasise the area of applicability of the methods in rock mechanics. Keywords: numerical methods; numerical modelling; rock mechanics Pregled numeričkih metoda za modeliranje u mehanici stijenaPregledni rad Počeci numeričkih metoda sežu u rane 1960-e. Već tada je bilo jasno da numeričke metode mogu biti uspješno upotrijebljene za različita inženjerska i znanstvena područja, uključujući i primjenu u mehanici stijena. Ubrzan razvoj računala je omogućavao razvoj numeričkih metoda i rješavanje računalno zahtjevnijih sustava. Takav razvoj doveo je do velikog broja različitih metoda i pristupa koji se mogu svrstati u dvije skupine: metode kontinuuma i metode diskontinuuma. Određene zadaće zahtijevaju prednosti oba pristupa, što je dovelo do razvoja kombiniranih konačno-diskretnih metoda. Prvi cilj ovog rada je predstavljanje numeričkih metoda i pristupa koji se koriste za rješavanje zadaća u mehanici stijena, kao i kratko objašnjenje osnovnih teorijskih postavki svake od metoda. Drugi cilj je osvrt na primjenjivost pojedine metode u mehanici stijena.

An overview on advances in computational fracture mechanics of rock

“…However, the conventional FDM suffers from the use of regular grid system for the description of material heterogeneity, complex boundary conditions and fractures (Elmo, 2006;Jing and Hudson, 2002). To overcome these shortcomings, the general FDM has been improved particularly thanks to the development of finite volume methods, which make it capable of using irregular quadrilateral, triangular and Voronoi grids (Figure 6) (Nikolic, et al, 2016). The commercial FLAC code is the most common FDM tool for stress analysis in geomechanics problems.…”

“…Jing and Hudson (2002) and Jing (2003) reviewed numerical methods and their application in rock mechanics engineering. Their state of art review has been recently updated by Nikolic et al (2016) and Zhao et al (2011a). Meanwhile, Ingraffea (2007) reviewed different computational fracture mechanics codes.…”

A critical review on coupled geomechanics and fluid flow in naturally fractured reservoirs

“…On the other hand, the conventional FDMs have several shortcomings such as material heterogeneity, complicated boundary conditions, and inflexibility in dealing with fractures (Shojaei et al, 2019;Wang, 2020). In general, the FDMs are incompatible for modelling rock mechanics problems (Nikolić et al, 2016).…”

A Novel Method of Calibrating Micro-Scale Parameters of PFC Model and Experimental Validation

“…With the rapid development of information technology and computational mechanics theory, more and more commercial software based on finite element method (FEM), discrete element method (DEM), boundary element method (BEM), or finite difference method (FDM) has been developed [1][2][3][4][5][6], such as Abaqus [7], Ansys [8,9], FLAC (Fast Lagrangian Analysis of Continua) [10,11], Rocscience [12], UDEC (Universal Distinct Element Code) [13], and PFC (Particle Flow Code) [14]. Since these pieces of software possess significant merits like low cost, high efficiency, and broad range of applications [15][16][17], they have been widely applied to investigate both the macroscopic and microscopic mechanical behavior of large-scale rock engineering or small-size rock specimens.…”