An Extension Of Taylor’s φ-circle Method To Stability Calculation For Submerged Slopes

Taylor’s φ-circle method is a classical method to stability calculation in homogenous soil slopes, with less hypothesis and strict analytic results. The paper aims to extend the φ-circle method to calculate the factor of safety in submerged slopes. The main contents and achievements are as follows.(1) Based on Taylor’s derivation and superimposition of three independent slopes with appropriate unit weight, then reduce the cohesion and angle of internal friction at the same time, the general expression for the factor of safety in water drawdown case can be obtained. The expression includes several specific slope cases, such as water sudden or slow drawdown, unsubmerged and completely submerged.(2) The paper writes a VB programm with the expression to search the critical sliding surface and the corresponding minimum factor of safety. By giving parameters of water level, use the programm to calculate the factor of safety in three specific slope cases, there are: unsubmerged slopes(Taylor’s model), water slow drawdown slopes and water sudden drawdown slopes. The design charts for the factor of safety of three slope cases are presented here, based on which the influence of water on the slope stability can be summarized.(3) In unsubmerged slopes, a further derivation shows that the factor of safety F has a linear relationship with the parameter c/?H1. Therefore, choose two sets of c/?H1 values 0.1 and 0.2, draw the relationship charts between the factor of safety, slope angle and angle of internal friction. Based on the charts and the linear relationship between F and c/?H1, it is easy to calculate the factor of safety F for any value of c/?H1. It provides a direct and simple way to determine the factor of safety, which avoids the tedious process in using Taylor’s chart.(4) In water slow drawdown slopes, the pore water pressure on the critical sliding surface can be ignored. The program is used to calculate the factor of safety of slopes under different water levels. Given 6 slope examples, draw the relationship charts between the factor of safety and water levels, based on which to summarize the influence law of water level on slope stability: stability factor decreases monotonously with the water level decline in steep slopes(generally slope angle≥60°); in gentle slopes, the factor of safety decreases firstly and then increases with the decline of water level, and the water level leading to the minimum F lies in 1/5-1/3 of slope height above the slope toe.(5) In water sudden drawdown slopes, when the slope soil is hardly permeable, the pore water pressure on the slide surface can not be neglected. The program is used to calculate 2 slopes, draw the relationship chart between the factor of safety in water sudden drawdown. To summarize the influence law of water sudden drawdown on slope stability: the factor of safety in sudden drawdown is significantly smaller than that in water slow drawdown case, and the larger water level suddenly declines, the lower the factor of safety is.Through the comparison for the results by these three methods: Taylor’s φ-circle method in this paper, Morgenstern-Price method and Bishop method, shows that the factor of safety and critical slip surface calculated by the three methods is similar.