Deformation mechanisms and stability analysis of undermined sedimentary rocks in the shallow subsurface

The deformation mechanisms and the stability of an undermined sedimentary rock layers were studied using the numerical model FLAC (Itasca, 2006), specifically validated for such configurations. The lowermost stratum in a sequence of successive layers is modeled as multi-fractured Voussoir beam. Boundary conditions, material properties and geometrical constraints for the numerical modeling were chosen to reflect rock mass properties that are characteristic to sedimentary rock masses. A series of ordered models, spanning over a representative range is presented. The indeterminacy parameters of the Voussoir beam model are determined using non-linear regression of the numerical results over a dimensionless space. The results show that the thickness coefficient of the compressive arch, n, formed within the deflecting beam is non uniform: at the abutment na ranges from 0.3 to 0.4 inversely proportional to beam stiffness, at the mid-span nm ranges from 0.4 to 0.5. Snap-trough failure of the beam occurs for beams of normalized composite stiffness EN < 1.25 · 103, for which na < 0.2. Finally, a straightforward procedure for determining the stability of the Voussoir beam and the Factors of Safety against different failure modes is proposed and the associated uncertainties are discussed. The procedure is applied for back analysis of the roof failure in the ancient underground water reservoir of the UNESCO world heritage site of Tel Beer-Sheva, excavated in discontinuous sedimentary rock mass. It is shown that the proposed procedure can be successfully extrapolated to natural rock masses.

► Voussoir beam mechanics were studied using specifically validated numerical model.
► Analysis is constrained by structural properties of sedimentary rock masses.
► Improvement over previous Voussoir beam analyses is presented.
► Stability assessment procedure based on non-linear regression is presented.
► Extrapolation to field-scale is demonstrated using an illustrative case study.