The self-supporting capacity of undermined, discontinuous excavation roofs has been studied through the application of voussoir beam theory since 1941. A voussoir beam is a jointed beam that self-stabilizes and is considered fully elastic, carries no tensile loads, and does not displace at its abutments. Previous research has developed analytical solutions to predict deflection and stress development in elastic voussoir beams based on geometry and material properties. The research presented herein expands the application of the voussoir beam analog to understand the influence of more complex (i.e. realistic) loading conditions on voussoir beam mechanics. Others have considered, through the use of physical and numerical models, the effects of multiple joints, discontinuity shear strength, excavation sequence, surcharge loading, and horizontal stress. This study presents unique numerical models utilizing the discrete element method that incrementally relate increased complexity to deviations in predicted stress and displacement of voussoir beams. Model results are compared to analytical predictions of roof factors of safety and empirical observations of voussoir beam behavior. Potential practical applications of this research include: (1) roof support design optimization that considers self-supporting capacity, and (2) predicting changes in roof factor of safety with changing stress conditions and rockmass properties.


Flat-roof excavations in bedded sedimentary geologic units are commonly implemented in underground mining and civil-infrastructure projects. Typical fracture networks in these formations consist of a combination of parallel bedding planes and sets of conjugate cross-joints. The earliest conceptual models of such excavations considered roof layers as continuous, homogeneous, isotropic, and linearly elastic (CHILE) simply-supported or fixed-end beams (Fayol, 1885).

CHILE assumptions do not account for many observed in-situ rock mass and material properties such as: (1) fracture influence, (2) variation in rock strength and stiffness, (3) anisotropy, and (4) temporal effects of cyclical loading (Hudson et al., 2002). Removing the "continuous" assumption and introducing a single vertical joint at midspan brings the simple stacked beam analog one step closer to capturing the in-situ mechanical behavior of deformation in an excavation roof. This segmented beam geometry is known as a voussoir beam, first theorized by Evans (1941) based on previous observations and experimentation by Fayol (1885), Jones & Llewellyn-Davies (1929), and Bucky & Taborelli (1938). Since then, voussoir beam behavior and its application to excavation roof stability has been studied via analytical, laboratory, field, and numerical methods by Wright & Mirza (1963), Wright (1972), and many others (Sterling, 1980; Beer & Meek, 1982; Ran et al., 1994; Sofianos, 1996; Sofianos & Kapenis, 1998; Hatzor & Benary, 1998; Diederichs & Kaiser, 1999; Talesnick et al., 2007; Nomikos et al., 2007; Alejano et al., 2008; Stimpson & Ahmed, 2009; Bakun-Mazor et al., 2009; Tsesarsky, 2012; Shabanimashcool & Li, 2015; Abousleiman et al., 2019).

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