Toppling failure occurs by tensile stress caused by moment due to weight of rock columns. Since the geostructural weaknesses (natural microcracks) are very frail against tensile stresses, hence, they might be highly affected by these stresses. In this paper, magnitude and location of maximum tensile stress in rock columns with potential of flexural toppling failure are determined. Geostructural weaknesses that might naturally exist in rock columns are modeled by a series cracks in maximum tensile stress plane. Then, the minimum safety factor of rock columns by means of principles of solid and fracture mechanics, independently, are computed. In fracture mechanics approach, the two parameters such as length of geostructural weaknesses and joint persistence are very effective on flexural toppling failure, whereas, in solid mechanics approach the safety factor is merely related to joint persistence parameter. Finally, for stabilization of the prescribed rock slopes, some new equations are suggested for determination of lengths of the required fully grouted rock bolts.


Rock masses are natural materials which are formed in the course of million of years. Since during their formation and afterwards, they have been subjected to high pressure, usually, they are not continuous and may contain plenty cracks and fractures. The exerted pressure, sometimes, causes to produce joint sets. Since, these pressures sometimes may not be that high to create separate joint sets in rock masses, it causes to produce micro joints and micro cracks. However, the results can not be considered as independent joint sets. Although the effects of these micro cracks are not that pronounced as compared with large size joint sets, they may cause a drastic change of in-situ geomechanical properties of rock masses. Also, in many instances, due to dissolution of in-situ rock masses, minute bobble like cavities …etc, are produced which causes a severe reduction of insitu tensile strength. Therefore, one should not replace this in-situ strength by that obtained laboratorial. On the other hand, measuring the insitu rock tensile strength due to the interaction of complex parameters that involved is impractical. Hence, an appropriate approach for estimation this strength should be sought. In this paper by means of principles of solid and fracture mechanics, a new approach for determination of the effect of geostructural weaknesses on flexural toppling failure is proposed.

A brief review of historical development

Though considerable research has been carried out in the field of flexural toppling failure as yet [1, 2, 3, 4, 5, 6], even so the first applied research was due to Goodman and Bray [2]. These researchers proposed the indispensable condition for flexural toppling failure. In 1992, Aydan and Kawamato, by employing the equation of limit equilibrium and the boundary conditions, had proposed an equation for determination of intercolumn forces of rock masses in open excavations and underground openings environment as well [4].

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