Stresses And Deformations Of Vertical Slopes In Elasto-Plastic Rocks

In many civil or mining engineering works, the stresses and deformations of natural or excavated slopes due to the combined effect of self-weight and initial stresses are of interest. Because of the mathematical complexities of this problem, however, no complete exact solution exists for the simplest case, that of assuming the stress-strain relation of the rock to be perfectly elastic. Efforts have therefore been directed toward numerical and experimental technique. The stresses within an elastic slope have been obtained by LaRochelle,1 using the photoelastic and finite difference method to determine the difference and sum of principal stresses. Subsequently, Finn,2 Hoyaux and Ladanyi,3 and Duncan and Dunlop4 attempted to solve the same problem by using the finite element method. The problem was also investigated by Brown and Goodman5 and Brown and King6 who emphasize the importance of the effect of loading or unloading procedure on the stress distribution within the slope. Although the geometry of the slope and the boundary conditions involved are identical or similar, the results obtained by these various authors by no means agree. It is therefore necessary to review briefly the results of elastic analysis in order to lend credence to the methods used in the solution. Although the stress-strain behavior of some rocks may be reasonably approximated by the elastic modrl, other rocks generally exhibit an elasto-plastic behavior with strain hardening or strain softening as shown in Fig. 1. Experiments show that for most rocks, the stress-strain relationship is approximately linear from the origin to the point P (neglecting the small concave region under low stresses). At P, the curve deviates