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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Measures of Stability for Roofs over Cavities in Rock
Engineered cavities in rock formations are often part of an underground transportation infrastructure. Three measures of roof stability in such cavities are discussed: the stability number, the factor of safety, and the support pressure needed to prevent cavity roof failure in weak rock. The stability number is a dimensionless combination of the rock properties and the size of the cavity when roof failure becomes imminent. While there exists substantial experience in application of the stability number and the factor of safety to soil structures, their use to define the safety of rock structures is intricate. This is because the strength envelope for rocks is a non-linear function of the mean stress. The specific function used in the analysis is the Hoek-Brown failure criterion. The kinematic approach of limit analysis is used, and the results are presented in charts. All measures of stability are strongly dependent on the Geological Strength Index, and, to a lesser degree, on other parameters in the Hoek-Brown failure criterion.
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- Award ID(s):
- 1901582
- PAR ID:
- 10402309
- Date Published:
- Journal Name:
- Geo-Congress 2022 GSP 336
- Page Range / eLocation ID:
- 629 to 638
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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