Stability of layered soil slope with tension crack: a closed-form solution

Evaluating the stability of layered slopes, a common type of terrain in nature and engineering practice, poses a fundamental challenge in the field of geotechnique. The emergence and extension of tension cracks play a crucial role in the failure process of layered slopes, but accurately predicting the location of layered slope cracking and assessing its impact on layered slopes remains a challenge using conventional analytical methods. Herein, we present a closed-form solution for evaluating the layered slope stability with tension cracks without any priori assumptions. The presented closed-form solution enables the location and depth of tension crack, the critical failure surface in different soil layers, and the corresponding normal stress distribution to be determined for all single/layered slopes. Effects of tension cracks on layered slopes are investigated, considering slope inclination, soil properties, layer thickness, and dominant failure mechanism. Note that, the results show that the dominant failure mode of layered slopes could change from toe failure (without cracks) to face/base failure (with tension cracks), which has not been previously reported. Multiple cracks are possible to develop in layered slopes. The proposed closed-form solution can be applied to improve the stability assessment and engineering design of layered slopes considering tension crack.