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1、International Journal of Rock Mechanics and Mining SciencesAnalysis of geo-structural defects in flexural toppling failure Abbas Majdi and Mehdi AminiAbstractThe in-situ rock structural weaknesses, referred to herein as geo-structural defects, such as naturally induced micro-cracks, are extremely re
2、sponsive to tensile stresses. Flexural toppling failure occurs by tensile stress caused by the moment due to the weight of the inclined superimposed cantilever-like rock columns. Hence, geo-structural defects that may naturally exist in rock columns are modeled by a series of cracks in maximum tensi
3、le stress plane. The magnitude and location of the maximum tensile stress in rock columns with potential flexural toppling failure are determined. Then, the minimum factor of safety for rock columns are computed by means of principles of solid and fracture mechanics, independently. Next, a new equat
4、ion is proposed to determine the length of critical crack in such rock columns. It has been shown that if the length of natural crack is smaller than the length of critical crack, then the result based on solid mechanics approach is more appropriate; otherwise, the result obtained based on the princ
5、iples of fracture mechanics is more acceptable. Subsequently, for stabilization of the prescribed rock slopes, some new analytical relationships are suggested for determination the length and diameter of the required fully grouted rock bolts. Finally, for quick design of rock slopes against flexural
6、 toppling failure, a graphical approach along with some design curves are presented by which an admissible inclination of such rock slopes and or length of all required fully grouted rock bolts are determined. In addition, a case study has been used for practical verification of the proposed approac
7、hes.Keywords Geo-structural defects, In-situ rock structural weaknesses, Critical crack length1. IntroductionRock masses are natural materials formed in the course of millions of years. Since during their formation and afterwards, they have been subjected to high variable pressures both vertically a
8、nd horizontally, usually, they are not continuous, and contain numerous cracks and fractures. The exerted pressures, sometimes, produce joint sets. Since these pressures sometimes may not be sufficiently high to create separate joint sets in rock masses, they can produce micro joints and micro-crack
9、s. However, the results cannot be considered as independent joint sets. Although the effects of these micro-cracks are not that pronounced compared with large size joint sets, yet they may cause a drastic change of in-situ geomechanical properties of rock masses. Also, in many instances, due to diss
10、olution of in-situ rock masses, minute bubble-like cavities, etc., are produced, which cause a severe reduction of in-situ tensile strength. Therefore, one should not replace this in-situ strength by that obtained in the laboratory. On the other hand, measuring the in-situ rock tensile strength due
11、to the interaction of complex parameters is impractical. Hence, an appropriate approach for estimation of the tensile 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 geo-structural defects on flexural
12、 toppling failure is proposed. 2. A brief review of previous workConsiderable research has been performed in the field of flexural toppling failure 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. The first applied research was due to Goodman and Bray 2. These researchers proposed the indispensable condition for f
13、lexural toppling failure. In 1987, Aydan and Kawamoto, by employing the equations of limit equilibrium and the boundary conditions, proposed an equation for determination of inter-column forces of rock masses in open excavations and underground openings environment 5. They verified the method by car
14、rying out laboratory base friction modeling. On the basis of these experiments, the total failure plane of flexural toppling is normal to the discontinuities. Hence, the angle between the total failure plane and the normal to the discontinuities is zero. It is also seen that they assumed that if the
15、 rock layers are stable under a given load condition in the upper part, the inter-column forces will be zero. Based on the aforementioned assumptions the factor of safety of all rock columns should be computed and consequently the extension of total failure plane can be determined. Adhikary et al.,
16、by carrying centrifuge modeling, made some changes to Aydan and Kawamotos equation for flexural toppling failure in open excavations 7, 8 and 9. On the basis of these experiments, the total failure plane of flexural toppling failure is around 10 above normal to the discontinuities. In , Majdi and Amini 10 and Amini et al. 11, using the principles of compatibility and the equations of equilibrium along with the governing equations to ela
