Abstract
Taylor’s φ-circle method is a classical method for slope stability calculation, which has analytical solutions. Taylor derived equations in two cases separately, namely, (i) the outlet of the critical failure surface is at the slope toe and (ii) the outlet of the failure surfaces is not at the slope toe. The method is only appropriate for two conditions (without underground water table in slopes or totally submerged slopes). In this study, a general equation that unifies the equations of the two cases is proposed and partially submerged condition is introduced. The critical failure surfaces corresponding to the minimum factor of safety are determined using the computer program proposed by the authors. The general expression of the safety factor of slopes under the following four conditions is derived, namely, (i) partly submerged, (ii) completely submerged, (iii) water sudden drawdown, and (iv) water slow drawdown. The corresponding charts for practical use are available.
Highlights
Taylor’s φ-circle method is a classical method for slope stability calculation, which has analytical solutions
A general equation that unifies the equations of the two cases is proposed and partially submerged condition is introduced. e critical failure surfaces corresponding to the minimum factor of safety are determined using the computer program proposed by the authors. e general expression of the safety factor of slopes under the following four conditions is derived, namely, (i) partly submerged, (ii) completely submerged, (iii) water sudden drawdown, and (iv) water slow drawdown. e corresponding charts for practical use are available
It is assumed that the potential failure surface is a circular arc and the resultant force of the friction and normal stress on the entire failure surface is tangent to the φ-circle. e φ-circle is a circle which is concentric with the failure surface. e radius of the φ-circle is the product of the radius of failure surface arc R and sinφ. us, this method is termed the φ-circle method. is φ-circle method regards the whole mass above the failure surface as a research object and has strict mathematical derivation and analytical solution
Summary
Deduction of the gravity and gravity moment for the latter two models is listed in Appendix A. e polygon of force equilibrium in the case of water declining is shown, in which there is an added pore water pressure Pw on the failure surface compared with Taylor’s original model. For the slope having water sudden drawdown, the soil between the water levels before and after drawdown is saturated and the pore water pressure on the failure arc has not dissipated. In this case, ru cw/c, c2 csat − c1, and c3 −cw, and equation (15) can be simplified as c F. It is easy and practical to figure out using the computer program
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