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Three-dimensional stability of roofs in deep flat-ceiling cavities is analyzed. The stability number, factor of safety, and required supporting stress are used as measures of roof stability. Despite the simplicity of the flat roof geometry, the three-dimensional stability analysis presents some complexities owed to the shape of the failure surface geometry in the collapse mechanism. The failure mode assumes a rock block moving downward into the cavity, and the study aims to recognize the most critical shape of the failing block. Three specific block shapes are described in some detail, but more have been analyzed. Blocks defined by a special case of a 4th order conical surface (quartic) on a rectangular base, and a 2nd order elliptic surface (quadric) are found to be the most critical in the stability analysis. The kinematic approach of limit analysis was used, with the rock strength governed by the Hoek-Brown failure criterion. The parametric form of the Hoek-Brown function was employed. Interestingly, an absence of diagonal symmetries in the most critical failure mechanisms was observed in roof collapse of square-ceiling cavities. Computational results in terms of dimensionless measures of stability are presented in charts and tables.
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Three-dimensional stability assessment of slopes in intact rock governed by the Hoek-Brown failure criterion
Three-dimensional failure analyses of slopes are rather elaborate, and for rock slopes, where the rock strength is defined by nonlinear failure envelopes, they are particularly intricate. This is why many earlier approaches used a linear approximation of the strength envelope prior to carrying out the stability analysis. This approximation is avoided in this paper, thanks to using the parametric form of the Hoek-Brown failure criterion. The kinematic approach of limit analysis is used as the method of study. An argument is brought forward that even though rocks tend to fracture at low confining stresses, the ductility of deformation prior to a brittle drop in stress during failure may be sufficient for limit analysis theorems to be applicable. Two measures of rock slope stability are evaluated: the stability number and the factor of safety. Numerical results are presented in the form of charts and tables. Because the limit analysis used allows one to evaluate the rigorous bounds on true solutions, it was possible to demonstrate that the method employed in the paper yields more accurate results than the approaches used formerly in the subject literature. A new and efficient mechanism of failure was devised for very narrow rock slopes.
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- Award ID(s):
- 1901582
- PAR ID:
- 10319882
- Date Published:
- Journal Name:
- International journal of rock mechanics and mining sciences
- Volume:
- 137
- ISSN:
- 1873-4545
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.ijrmms.2020.104522
