Abstract
Some of the methods commonly used for analyzing slopes utilizing the principles of limit equilibrium are the Ordinary method, the Janbu method, the Bishop method, the Morgenstern-Price method, and the Spencer methods.
Spencer proposed two general limit equilibrium methods of slices, the method (1967) of the resultant inter-slice force Q in a slice and the other method (1973) of divided two inter-slice forces Z in a slice. The Spencer method (1967) is simply introduced in an assumption of constant angle θ of inter-slice force Q in all slices. The property of moment equilibrium equation in conversing calculation is simple and this method is sometimes used in tree-dimensional analysis. On the other hand, the Spencer method (1973) is introduced in an assumption of different angles θ; of inter-slice forces Z in each slice and is more general and advanced than the Spencer method (1967). However, the property of moment equilibrium equation of the Spencer method (1973) is complicated like that of the Morgenstern-Price method and this has a disadvantage of computer programming.
It is considered mainly on the moment equilibrium equation of the Spencer method (1973) that is ∑ [J] =0. It is shown that the equation is sum of the moment of inter-slice forces Z in all slices about the start point of a slip surface, although this is introduced from the principle that moment equilibrium condition is satisfied if sum of the moments of all forces in each slice about a middle point of base is zero and these conditions are realized in all slices of a slip surface. A general moment equilibrium equation is proposed, and the statical signification is discussed. The properties of these equations and relative merits are discussed.
