Rock mass consists of distinct blocks produced by discontinuities. The geometry and orientation of pre-existing discontinuities show a larger impact on the behavior of slopes that is often used to describe the measurement of the steepness, incline, gradient, or grade of a straight line. There are numerous analytical methods for the rock slope stability including limit equilibrium, stress analysis and stereographic methods. This paper has tried to explore the effects of forces due to water pressure on discontinuity surfaces in plane failure through applying the improved equations by Hoek & Bray, Goodman & Shi, Priest & Vutukuri and Katsuyama. It has studied the effect of water flow velocity on sliding surfaces in safety factor, as well. New equations for consideration water velocity (fluid dynamics) are presented. The suggested equations have higher validity rate comparing to the current equations.


Rock mass classification system was proposed about 60 years ago for tunneling with steel support but later developed for non-steel support underground excavation, slope and foundation engineering. So far as slope stability is concerned, it is an extreme consideration by Priest (1976) [1], Hoek & Bray (1981) [2], Goodman & Shi (1985) [3] and Vutukuri & Katsuyama (1994) [4]. Problem of slope stability is an important issue in soil and rock engineering and therefore, much works have been done to solve this problem by employing different methods such as limit equilibrium using slices, limit analysis, method of characteristics, and more recently, the finite element technique [5]. Slope stability is usually assessed under the framework of limiting equilibrium [6], an analysis that is a simplification of the more rigorous limit theory, and has become the most preferred method for routine slope stability analysis in rock and soil mechanics. In this particular analysis, an assumption of the slip-line field is made, usually, as a geometrically fairly simple failure surface [7]. However, none of the basic equations of continuum mechanics regarding equilibrium, deformation and constitutive behavior are satisfied completely. Safety factors, in these methods, are calculated using one or more of the equations of static equilibrium applied to material bounded by an assumed potential slip surface and surface of slope. Limit equilibrium method is based on efficient force condition on slip surface. Two major categories can be identified as follow: a. Forces that cause failure, and b. Forces that resist failure. In equilibrium conditions, ratio of these forces is an equivalent one. Due to inaccurate estimation and determination, the ratio of resisting forces to slip forces is mostly considered bigger than one. In this research firstly equilibrium equation is studied then the effect of forces due to water pressure on discontinuity in two cases of static and fluid dynamics are discussed.

Equilibrium Equation

Many of the limit equilibrium methods such as ordinary method of slices, simplified Bishop [8] and Spencer [9] are considered static equilibrium by dividing the soil or rock mass above an 1218 assumed slip surface into a finite number of vertical slices.

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