Statistical Estimation of Loess Landslide Impact by Multivariate Normal Distribution Models with Consideration of Transformation Methods

The Loess Plateau is the world's largest loess accumulation region, where landslides often threaten residents. To reduce the loss caused by loess landslides, numerous approaches have been developed to gain insight into the processes that cause landslide or to identify sensitive areas via landslide susceptibility mapping. None of these approaches, however, can statistically assess the impact of a potential landslide, which is critical for landslide risk management. To address this issue, this study first constructs a loess landslide database by field investigation, from which a multivariate Gaussian distribution model was developed. The model consists of landslides' data (e.g., height, width, area, and length) transformed using Johnson's transformation, Box-Cox, and Nataf transformation. Given the height of an unstable slope, the width, length, and area of a potential landslide is then statistically predicted. Database complied in Baoji city, Shaanxi, is used to demonstrate the proposed method. Results show that Johnson's transformation has satisfactory accuracy and robustness compared with the other two methods.