ABSTRACT

The resistant Cedarville Dolomite forms natural cantilevers with overhangs of up to 3.7 m. Since the cantilevers are self-loaded, tensile stresses may be computed. Cantilevers measured in the field suggest a tensile strength of 0.33 MPa, while laboratory tests give an average strength of 17.45MPa. The difference was modeled as a size effect using the laboratory tests to calibrate a Weibull analysis. This accounted for only a small part of the difference in strength. A fracture mechanics analysis was more successful in explaining the discrepancy, and in defining the mode of failure. It is suggested that these cantilevers fail catastrophically due to joints extending through 50 to 90% of their depth. This critical condition may be attained by stable crack propagation, with stress corrosion a possible mechanism.

INTRODUCTION

Natural cantilevers in the Cedarville Dolomite (Figures 1 and 2) are fortuitous examples of long-term tensile loading in that the magnitude of the loading may be computed. This allows an analysis of the mechanism of failure in the cantilevers. Of particular interest is the very low apparent strength of the cantilevers in the field relative to the strength predicted by laboratory tensile tests. A plausible explanation is found in high stress intensities at the tips of preexisting cracks. Given a high stress intensity, progressive failure may result from frost wedging or stress corrosion. Results from this relatively controlled environment have potential applications in understanding the development of natural joints and progressive failure in underground openings. The implications with regard to roof falls in bedded rock are particularly clear.

GEOLOGIC RELAT IONSHIPS

Steep slopes and cliffs are prominently developed in Middle Silurian dolomite along Yellow Springs Creek and the Little Miami River near Yellow Springs and Clifton, Ohio. The massive Cedarville Dolomite which is locally more than 15 m thick is the primary cliff-forming unit. It is underlain by the Springfield Dolomite which is 2.1 m thick. The Springfield weathers more rapidly than the Cedarville, leading to overhangs protruding up to 3.7m beyond the face of the Springfield.

Separation Plane of Failed Cantilevers

The fracture surfaces found in these rocks may be divided into three differentiable classes. A) Regional joints which are planar on a large scale and exhibit extensive solutioning and sometimes secondary deposition of calcite. B) Joints associated with near-surface weathering. Some of these joints have also experienced solutioning or deposition of secondary calcite. C) Fractures which have not been subjected to significant weathering. Type C fractures tend to be irregular, reflecting the inhomogeneity of the rock. They are unfortunately lacking in hackle marks or other surface textures which might indicate direction of propagation or the presence during propagation of free surfaces above or below. Fracture types A and B existed before cantilever failure. Type C fractures are young but their character does not indicate whether they antedate cantilever failure or formed at the time of failure. The separation fracture plane in some cases is more than half type A or B. The remainder is type C. It is apparent that the overhangs failed due to cantilever loading.

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