A stability analysis of landslides based on random fields - Part I: Toe circle slope

The stability analysis of toe circle slopes is studied using random field theory from the perspective of probability, and the relationship between the failure probability of toe circle slopes and the correlation length is analyzed. The closed-form solutions of the safety factor and the failure probability of toe circle slopes are derived using the integration method. The accuracy of the safety factor of toe circle slopes is improved when the slice method is replaced by the integration method. The effects of spatial correlation length on the safety factor and failure probability of toe circle slopes are investigated. The results show that the spatial correlation length significantly affects the failure probability, and the vertical integration model is more suitable for the homogeneous toe circle slopes than the horizontal integration model.