The critical failure surface for a given slope can be determined by comparing factor of safety of several trial slip surfaces. To find the minimum factor of safety, it is important to get critical failure surface for the given slope. Different searching and optimization methods that had the difficulty in using them for hand calculations have been used in the past. In this study, effect of soil strength parameters; cohesion (c), internal friction angle (ϕ), and unit weight () on the failure surface and factor of safety of the slope were studied. GEO5 software program were used to calculate the length of failure and determine the critical failure surface. An equation was introduced in to locate the critical failure surface by using soils strength and slope geometry parameters. The results of the study showed that the factor of safety of the slope changes with varying cohesion c, internal friction angle ϕ, and the unit weight  of the soil. Moreover, the slip surface is affected by the dimensionless function (), which is related to the cohesion, internal friction angle and unit weight. Model was introduced in to locate the critical failure surface by using soils strength and slope geometry.

This study shows the comparative analysis engineering, the physical and mechanical properties of river sand concrete with quarry dust concrete. The selected materials were batched by weight and volume. The water-cement ratio was opted as 0.50 1:2:4 for mix ratio was selected for the experimental investigation respectively. The specimens were cured for 7, 14, 21 and 28 days. For the purpose Slump, density and compressive strength tests were carried out. The river sand concrete showed better results and greater density and compressive strength than quarry dust concrete for all curing ages. The 28 days of curing, river sand concrete rise the required compressive strength by 36%, whereas quarry dust concrete was less than the limit compressive strength by 12%. Both river sand concrete and quarry dust concrete for the selected water/cement ratio and mix ratio has been found suitable for non-structural applications and lightly-loaded members where high strength is not a prerequisite.