Estimating landslide sliding distance based on an improved Heim sled model

Abstract

Part of the gravitational potential energy of a landslide is converted into heat or other forms of energy via irreversible processes such as inelastic collisions and fragmentation between particles. In this study, we define the gravitational potential energy component as additional work W, which is numerically equivalent to Mgc. Based on the model proposed by Heim (1932), we conceptualize landslide movement as the movement of particles, and the concept of extra work is used to establish a model to estimate landslide sliding distance. Twenty-seven irrigation-induced loess landslides were used to build a model for the Heitai terrace in the upper reaches of the Yellow River in Gansu Province, China. Considering the additional work W, the average relative error and average error between the estimated value and the measured value were significantly reduced (the average relative error was reduced from 11.21% to 6.27%, and the average error was reduced from 20.4 m to 9.6 m). Ten landslides in the Heitai terrace and 13 landslides on the south bank of the Jing River in northwest China were used to verify the model. The average relative errors between the estimated and observed values are 5.55% and 7.78%, respectively. In addition, based on data from earthquake-induced loess landslides, we use the model to further explore the significance of additional work in the construction of a sliding distance prediction model. The results of the model show that the introduction of additional work improved the accuracy of the predicted sliding distance. The model has a good applicability to loess landslides with volumes <106 m3, but the applicability to loess slide is relatively poor.