Theoretical investigation on the initiation and propagation behavior of dominant cracks in valley slopes

The stability of rock slopes is frequently controlled by the initiation and propagation of inherent dominant cracks. This study systematically investigated these processes in valley slopes by combining fracture-mechanics analysis with transparent soil model tests. An analytical expression for the stress field at the dominant crack tip was derived from the slope stress distribution by superposing the corresponding stress intensity factors (SIFs). The theoretical predictions were then validated against observations from transparent soil model tests. The influences of slope angle (β), crack inclination angle (α), crack position parameter (b), and crack length parameter (h) on crack initiation and propagation were quantified. The results indicated that: (1) cracks at the slope crest tended to propagate in shear mode, and the shear crack initiation angle (θs) was approximately 8°. Cracks at the slope toe might propagate in either tensile or shear mode. (2) θs at the slope crest increased with β, b, and l, and decreased with α. The maximum change in θs induced by the considered parameters was approximately 30°. (3) The tensile crack initiation angle (θt) at the slop toe decreased with β, α, and l, while the influence of b was comparatively minor. The maximum change in θt caused by individual parameters ranged approximately from 25° to 60°. Predicted crack propagation modes and directions showed good agreement with experimental results. These findings provide theoretical guidance for stability assessments of valley slopes controlled by dominant crack propagation.