Calculating the parameters of stratified rock slopes

Abstract

Let us consider the condition for limiting equilibrium of a stratified rock mass. Caving of the slope will occur at a certain height H and a corresponding thickness m of the rock stratum along a broken surface which partly passes along the contact between the strata DC (Fig. I) and partly across the stratification over a surface which intersects the strata at the base of the slope at an angle E = 45 ~ --p/2 to the surface of the slope (stratification) --AD.The slope of the surface of slip at the base of the bank is governed by the conditions of the state of stress of the caving strata compressed in this zone.Note that caving over surface CDA unavoidably leads to formation of a surface of detachment DE, inclined at 90 ~ --P to AD and, according to the terminology of V. V. Sokolovskii, belonging to the category of the second family of slip surfaces.The caving prism at limiting equilibrium can be arbitrarily divided into two, BCDE and AED, interacting over surface DE.Under these conditions the most reliable results in estimation of the stability of a slope can be obtained by using the graphical method of the polygon of forces [i]. However, a reliable solution by determinination of the parameters of stable banks with a graphical variant of the polygon of forces involves repeated calculations and constructions, owing to the lack of an analytical expression for the relation between the height of the slope in its limiting position and the thickness of the caving strata (the width of the prism of possible caving), and requires much time.In this article I will suggest an analytical method, based on the graphical polygon of forces, for calculating the stability of stratified rock slopes, by which we can take account of the mechanical characteristics of the contacts: 0', the angle of friction at a contact, and k', the cohesion at the contact between strata.The scheme of action of the forces on the prism of possible caving is shown in Fig. 2. On the prism of active pressure BCDE there act the following forces:Px, the weight of the prism; E2, the reaction from prism AED; and Ex, the reaction at the contact between the surrounding strata and the stable rock mass.The forces of reaction E~ and E2 are equal to the vector sum of the forces N, normal to the surfaces bounding the prism of active pressure, th_e forces of friction T, and the forces of cohesion kL: = ~, +~,+k'L = R, +k'L1, ~= N2+ r~+k-LS~ = ~,+~--s where k' is the cohesion at the contact between the rock strata, k is the cohesion of the mass across the stratification, and Lx and L2 are respectively the