NONCIRCULAR CURVE SEARCHING FOR DETERMINING THE MINIMUM SAFETY FACTOR IN DESIGNING A HOMOGENEOUS SLOPE

The goal of design for an excavated slope is to determine a slope angle and a slope height within a design value of safety factor. Therefore, the purpose of searching for the potential slip surface is to find out a plane where the minimum ratio of shear resistance and force occurs under the design value of safety factor. This paper presents a very simple exponential curve searching method. It can be used to search for the minimum value of safety factor in a slope with groundwater and determine the corresponding slope angle and height. The curve searching starts from the slope shoulder. The searching continues along the upper slope at an equal interval and generates a family of curves going through the slope toe and the specified point on the upper slope as the power continues to increase from 1. They can be treated as potential shear surfaces, which will allow us to delineate a potential sliding body. The sliding body is then divided into a number of vertical slices so that shear forces and shear resistance and their horizontal and vertical components of forces can be calculated for each slice. According to parallelogram law of forces, one can find the resultant force from the horizontal and vertical components of forces from all the slices and the resultant strength in a similar way. By comparing the shear strength and shear force along this sliding surface, one can obtain the ratio of the shear resistance and shear force. By comparing the ratios between those potential sliding surfaces, a minimum ratio can be found for each family of curves. The searching continues until the minimum ratio is equal to the design factor of safety. For comparison we use the Sarma method to calculate the minimum safety factor of the slope body delineated by the exponential curve searching method. Three case studies are used to demonstrate the applicability of the exponential curve searching method in comparison with other methods. At the end we recommend that the minimum safety factor be used as a major standard guideline for slope design.