Probabilistic slope stability analysis of side wall of river under water level changes and correlation of soil random variables

Introduction
Stability analysis of earthen slopes is important for the investigation of road embankments, river walls and upstream and downstream slopes of earthen dams. The sloping earthen walls of the river are always subject to instability and failure caused by various factors such as floods, variations of the water level in the river. In investigating the stability of the earthen sloping walls of rivers, the role of hydraulic and geotechnical variables and their correlations are important as factors of creating uncertainty in the analyzes. The aim of current research is to investigate the effect of water level changes on the stability of the soil slopes of the river wall under the conditions of applying the correlation of effective random geotechnical variables with the use of copula functions. Also, comparing the performance of copula functions used in combination with limit equilibrium methods is another goal of this research.

Methodology
The uncertainty and correlation of the random soil properties including the internal friction angle and the cohesion of the river sloping wall were investigated at four cross-sections of Shalmanrood river in Guilan province of Iran. To this end, a computer code was developed in MATLAB and five copula functions were applied to the soil properties and the calculated correlations and distributions were compared using Akaike and Bayesian information criteria to determine the best copula. Then in GeoStudio software, using three limit equilibrium methods including Bishop, Spencer and Morgenstern-Price the slope stability was approximated. The distributions of factor of safety were obtained for three scenarios of water level including the maximum observed level and the water level decline by 20 and 40 %.

Results and discussion
For the maximum water level in the river cross-section 1, the distribution of factor of safety was obtained in the range of 1.4-3.6 using the limit equilibrium method. By decreasing the water level by 20%, the factor of safety changes to 1.2-1.9 and declining the water level by 40% , the range is obtained 1.06-2.8. The same trends of decreasing the factor of safety by the water level decline in the river are observed in three other cross-sections. For the maximum river water level in cross-section 1, the maximum error of normal and GEV distributions were obtained equal to 7.8 and 11.4%, respectively. In addition, the error of normal and GEV distributions for water level decline by 20% were13.4% and 13.6% respectively. Finally, the error of 9% and 14.5% were obtained for the water level decline by 40% for the normal and GEV, respectively. It is observed that normal distribution offers better performance for all water levels and the errors of both distributions increase with water level decline. This trend is also observed in the all studied cross-sections.

Conclusions
The performance of the Morgenstern-Price method compared to other limit equilibrium methods is not affected by the variations of the water level in the river and always offers acceptable results. Three limit equilibrium methods used (Bishop, Spencer, and Morgenstern-Price) provide similar results at lower values of the factor of safety (with lower cumulative probability, CDF). Frank copula is the best function to model the correlation of random variables affecting the studied sloping walls of the river. The highest rate of change in factor of safety is observed for the water level decline by 20%.