Application of Discrete Finite Element Method for Analysis of Unreinforced Masonry Structures

Introduction

Masonry structures, consisting of interacting distinct blocks, have been constructed since the earliest days of civilization, are still commonly built in many countries all over the world, and constitute a significant percentage of current structures. Many of these structures are located in seismically active regions and were built before the establishment of any design code requirements for earthquake-resistant construction. Compared with modern structures built of materials with well-understood constitutive laws, the mechanics of masonry structures are still not clearly understood in spite of their long use. The failures and damage reported in recent earthquakes attest to the need for efficient strengthening procedures and therefore an efficient analytical method for analysis of masonry structures.

The analysis of unreinforced masonry and rock engineering structures excavated in discontinuous rock masses has been receiving particular interest among civil engineers, rock mechanics, and rock engineers. Since rock masses consist of distinct blocks due to geological discontinuities, several techniques have been developed to analyze masses consisting of distinct blocks. A literature review shows that during the last three decades, the limiting equilibrium analysis (Aydan et al., 1989; Hoek & Bray, 1977) and some numerical analysis methods such as the finite element method (FEM) (Aydan et al., 1990; Barbosa & Ghaboussi, 1990; Ghaboussi et al., 1973; Goodman et al., 1968; Kawamoto & Aydan, 1999; Oda et al., 1993), distinct element method (DEM) (Cundall, 1971), and discontinuities deformation analysis (DDA) (Shi, 1988) have been developed for the analysis of problems involving discontinuities in rock mechanics. The DEM has been used for years in different industries (e.g., mining, civil engineering, and nuclear waste disposal) for the solution of problems involving deformation, damage, fracturing, and stability of fractured rock masses and masonry structures (among others: Baggio & Trovalusci, 1993, 1998; Cundall, 2011; Itasca Consulting Group, Inc., 2014; Lermos, 2007; Mamaghani, 1994, 2006). Recently, a number of modeling techniques have been developed to simulate coupled hydro-mechanical problems with the DEM; these methods have been reviewed by Furtney et al. (2013). For example, the Universal Distinct Element Code (UDEC), developed by Itasca Consulting Group, Inc. (2014), utilizes an explicit solution scheme that can model the complex, non-linear behavior of media containing multiple intersecting joint structures. Joint models and properties can be assigned separately to individual discontinuities or sets thereof. The analysis of rock mass stimulation by fluid injection requires analytical tools, such as numerical models based on DEM, which can represent discontinuities explicitly (Damjanac et al., 2015). A similar approach for simulation of fracturing and hydraulic fracturing of rocks is based on the combined finite element method (FEM) and DEM. The formulation of the method and some example applications are found in Rougier et al. (2011, 2012), Zhao et al. (2015), and Lisjak et al. (2015). In spite of all these techniques, it is difficult to say that a unique technique that guarantees satisfactory results has been developed. Although DEM and DDA can be used for the static and dynamic analysis of discontinuous media, the treatment of rate-dependent behavior of materials in these methods is not realistic. For example, DEM introduces a forced damping to suppress oscillations, while DDA adopts very large time steps so that artificial damping occurs as a result of numerical integration.