EXISTENCE AND REASON OF A GLOBAL MINIMUM FACTOR OF SAFETY OF SOIL SLOPES

This study reveals the different contributions of soil cohesion and internal friction angle on factor of safety(FOS) of soil slope. It shows the existence and reason of a critical slip surface with a global minimum factor of safety(FOS)value in soil slopes. It selects a large number of potential slip surfaces in soil slopes,and then defines four types of FOS values(FOS^c×φ,FOS^c,FOS^φ and FOS^c+φ)for each potential slip surface. It calculates these FOS values by conventional slice methods under the limited equilibrium principle,and then plots these FOS values against their associated slip depths and finds their variation features in terms of the slip depth d. The FOS^c×φ is defined as the conventional FOS value contributed by both soil cohesion and internal frictional angle of a soil slope. The plots show that local FOS^c×φ value decreases and then increases as slip depth increases. Therefore,FOS^c×φ have a global minimum value. The FOS^c is defined as the FOS value contributed by only the internal cohesion of a soil slope. The plots show that local minimum FOS^c value decreases as slip depth increases. The FOS^φ is defined as the FOS value contributed by only internal friction angle of a soil slope. The plots show that local minimum FOS^φ value always near-linearly increases as slip depth increases. The FOS^c+φ is defined as the sum of FOS^c and FOS^φ. The results show FOS^c+φ value is approximately equal to FOS^c×φ value for each potential slip surface. The above four features are further shown in the results of the five conventional slice methods,the slopes with ground water effect,and the slopes comprising of heterogeneous soils. Hence,this paper shows that a general soil slope has a global minimum value among its numerous FOS values associated with numerous potential slip surfaces. The reasons for the existence of a global minimum FOS value are (1)the individual contributions of the cohesion and friction angle to FOS values against the depth d and (2)the approximate equal values of FOS^c+φ to FOS^c×φ for any potential slip surface.