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• A state of art approach to study 3D sinkhole stability due to underground cavities. • Advanced 3D finite element limit analysis for circular and square openings. • Rigorous 3D upper bound and lower bound solutions of active and passive trapdoors. • Comprehensive design charts, tables and equations presented. • Stability numbers and factors of safety for a wide range of design parameters. There has been an increasing interest in the study of sinkhole occurrences due to frequent underground activities. Most of the research direction are related to the detection of the underground cavity using geophysics techniques. Very little is done in the area of soil stability. This paper investigates the three-dimensional stability of circular and square trapdoors. The combined effect of surcharge pressure, soil weight and supporting pressure is considered in Broms and Bennermarks' original stability number for a cohesive soil. The study uses the finite element limit analysis to compute upper bound and lower bound minimum supporting pressures for both collapse and blowout scenarios. The obtained critical stability numbers and factor of safety are compared with other published results in both two- and three- dimensions. Design charts, tables and equations are presented to cover a wide range of design parameters and a practical example is introduced to illustrate how to use the them. [ABSTRACT FROM AUTHOR]

This paper investigates the use of stability factors to estimate tunnel heading pressures. The primary method adopted is a conventional equation based on the soil property and stability factors, analogous to the bearing capacity factors (N c , N s and N γ) of strip footings. The finite element limit analysis (FELA) is employed to determine rigorous upper bound (UB) and lower bound (LB) solutions of stability factors (F c , F s and F γ), which are functions of the depth ratio (C/D) and soil internal friction angle (Ø). The obtained results are compared and validated by using the finite difference analysis as well as other available published results in the literature. A number of examples are illustrated on how to use the factors to estimate tunnel heading pressures. [ABSTRACT FROM AUTHOR]