ABSTRACT
The conventional engineering methods for prediction of slope stability are directed to evaluation of conditions of limit equilibrium of rock mass immediately preceding ultimate failure and practically do not consider a possibility of partial losing of partial losing of strength of rock mass far before failure. Such an approach is valid in case when a slope is composed of homogeneous unlayered rocks. In other case if a slope is composed of layered rocks the losing of slope stability may be connected not with the failure of rocks themselves, but with the failure of week contacts between layers, what provoked bending deformations due to lack of bending rigidity in foliated rock mass. There is a characteristic case of such a process-an undrained slope composed of subvertical dipping strata-under consideration in this report. The main condition of limit equilibrium moments of bending forces and strength(friction and cohesion), resisting to sliding layers on each other, is the following:
Here y0 is the density of water, hcr is the critical height of the slope, hi is the height of the i-th layer, mi is the thickness of the i-th layer, φci, cci, σci are the angle of friction, cohesion and the effective normal stress on the contact between the i-th and the i+1-th layer, correspondingly, n is the number of layers, composing the slope, z is the vertical distance form the base of the slope. In the important for the practical use case of supposingly homogeneous structure of the slope, composed of layers with equal thickness and strength
where α is the angle of slope inclination, φc, cc are the strength caracteristics of the contacts between the layers. Calculation of the horizontal displacement v of the slope points may be fulfilled using the following formulae:
Correspondingly, for the cases when the layers are dipping outside(3a) and inside (3b) the rock mass. Here A = γ 0 ⋅ h 4 ( tan α - tan ϕ c ) 6 E m 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429087813/e28ca3aa-05c6-4b83-b55b-11b100aac0f8/content/inline-math1.tif"/> , h is the height of the slope, m is the thickness of a layer, zn = z/h, z is the height of the layer.
