The main method of estimating the stability of slopes is a determination of their factor of safety against sliding by the following equation:K=A/8;(1) in engineering practice this factor is understood to he the ratio of the ultimate failure stresses A to the operating stresses B. Such a definition permits referring the concept of safety factor* to the acting forces or to the characteristics of the strength of the investigated section, However, it is necessary to bear in mlnd that a determination of the absolute value of the factor of safety against sliding for a natural rock slope is a quite complex problem and the results obtained usually have an extremely low reliability. This is explained by the large number of always llttle-studled factors which must he taken into account in the calculation. The main factors are the slope angles of the surface of weakness to the horizontal ~x, ..., ~n and the parameters of the shear strength along these potential sur~ faces of sliding ~,, "'',~n and c,, ..., c n (n is the number of calculated surfaces of weakness),The parameters ui, Bi, and c i are assigned on the basis of numerous hut not always sufficiently accuracte field measurements and experiments giving, as a rule, a scatter of the readings within 5-10% and more. Under these conditions a calculation of the factor of safety against sliding Just with the use of the average values of the parameters without consideration of their dispersion does not lead to reliable results for Judging the actual stability of the investigated rock mass, As a rule, the indices of the shear strength along the surfaces of weakness in the rock mass are the most uncertain, Since the number of experimental points is always very limited, various reducing coefficients are introduced into the experimental results to preclude the possible effect of "chance~" or methods of treating these results for the purpose of obtaining the lower confidence limit of the values with a certain percent of frequency [i] are used.The proposed method of prohabilistic estimation of the reliability of the initial information permits separate consideration and analysis of the effect on the stability of the rock mass of not only the average values of ~ and c but also their possible dispersions. As the random variahles we will examine ~,, .,., ~n and c,, ..., c n whose distribution will he assumed normal,The proposed probabilistic approach can be used in practically any method of calculating stability in which the factor of safety against sliding is expressed by Eq. (i).In the general case functions A and B can be functions of all random arguments, namely:(2) (3) *The new specifications SNiP II-16-75 "Foundations of Hydraulic Structures" introduce separated coefficients: reliability Kr, load combination nc, and working conditions m, in terms of which the factor of safety against sllding being considered is expressed so: K = (Krnc)/ m~ Translated from Gidrotekhnicheskoe Stroltel'stvo, No. 3, pp, 38-41, March, 1978.
