131 Transportation Research Record: Journal of the Transportation Research Board, No. 2522, Transportation Research Board, Washington, D.C., 2015, pp. 131–136. DOI: 10.3141/2522-13 Unreinforced-masonry underground structures are composed of a finite number of distinct interacting blocks that have length scales relatively comparable with the underground openings of interest. Therefore, these structures are ideal candidates for modeling as discrete systems instead of as continuous systems. The discrete finite element method (DFEM) developed by the author to model discontinuous media consisting of blocks of arbitrary shapes was adopted for the static analysis of unre- inforced masonry underground structures. The developed DFEM was based on the principles of the finite element method incorporating con- tact elements. The DFEM considers blocks as subdomains and represents them by solid elements. Contact elements, which are far superior to joint or interface elements, are used to model block interactions such as sliding or separation. In this study, the DFEM is briefly reviewed; then, through some illustrative examples, the applicability of the DFEM to the analysis of unreinforced-masonry underground structures is examined and discussed. It is shown that the DFEM provides an efficient tool for researchers and practical engineers in designing, analyzing, and studying the behavior of unreinforced masonry underground structures under static loading. Analysis of unreinforced-masonry underground structures is of par- ticular interest among civil engineers. In recent years, several tech- niques have been developed to analyze rock masses consisting of distinct blocks in the field of rock mechanics. A comprehensive review of these techniques was presented by Kawamoto and Aydan (1). The limiting equilibrium analysis by Hoek and Bray (2) and Aydan et al. (3) as well as some numerical analysis methods, such as the finite element method (FEM) with joint or interface elements by Goodman et al. (4), among others, the distinct element method (DEM) by Cundall (5), and discontinuities deformation analysis (DDA) by Shi (6), have all been proposed. In spite of all these tech- niques, it is difficult to say that a unique technique that guarantees satisfactory results has been developed. Although the DEM and DDA can be used for static and dynamic analyses of discontinu- ous media, the treatment of rate-dependent behavior of materials in these methods is inconsistent with actual behavior. For example, the 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. The author proposed the discrete FEM (DFEM), which is based on the principles of the FEM, for analysis of blocky systems under static and dynamic loading (7–10). The DFEM consists of a mechanical model to represent the deformable blocks and contact models that specify the interaction among them. In the DFEM, a viscoelastic con- stitutive law for linear behavior and a viscoelastoplastic constitutive law for nonlinear behavior of blocks and contacts are used together with the updated Lagrangian scheme. The DFEM can handle large block motions within the framework of the FEM. In this paper, first the modeling of underground opening discontinuities and DFEM for- mulation are briefly presented. Then, the applicability of the DFEM to static analysis of unreinforced-masonry underground structures is verified and discussed. MODELING OF UNDERGROUND OPENING DISCONTINUITIES A discontinuum is distinguished from a continuum by the existence of discontinuities at contacts between the discrete bodies that com- prise the system. The actual geometry of contacts is never smooth and has asperities of varying amplitude and wavelength (3). Relative sliding or separational movements in such localized zones present an extremely difficult problem in mechanical modeling and numeri- cal analysis. The most suitable and mechanically sound approach in modeling underground opening discontinuities is band-type model- ing. In this approach, contacts between neighboring blocks are treated as bands with a finite thickness. The thickness of the bands is related to the thickness of shear bands observed in tests or in nature and, if data exist, the height of asperities along the plane (3). For an idealized contact as shown in Figure 1, the average normal and shear stresses and strains are defined as follows: (1) F A n n σ= (2) A n n ε= δ (3) F A s s τ= (4) F h s s γ= Discrete Finite Element Method Application for Analysis of Unreinforced-Masonry Underground Structures Iraj H. P. Mamaghani Department of Civil Engineering, University of North Dakota, 243 Centennial Drive, Grand Forks, ND 58202-8115. iraj.mamaghani@engr.und.edu.