F [cb(W uwb)tan] . (2.26a)
In the above iterative expression bis the width of any slice. Alternatively,
expressing porewater pressure uwin terms of predicted pore pressure
ratio,ru, for convenience in initial analysis, with ruuw/ zuwb/Wfor any
slice:
F [cbW(1 ru)tan] . (2.26b)
On the assumption of a saturated fill, the further substitution of B ̄forru
may be made in equation (2.26b).
In applying this method an appropriate trial value of F is first
selected, subsequent iteration resulting in the expression converging
rapidly to a solution. The Bishop expression may, with discretion,
be applied to a non-circular arc failure surface, as shown in Fig. 2.15,
which refers also to worked example 2.3. Charts of m
cos[1(tantan)/F] for use with equation (2.26) are presented in
Fig. 2.16.
More exhaustive circular arc analyses include the Bishop rigorous
solution (Bishop, 1955): solutions to the analysis of non-circular and irregu-
lar failure surfaces are provided in Janbu (1973) and by Morgenstern and
Price (1965). Parametric initial studies of the stability of homogeneous
shoulders can be made using stability charts (Bishop and Morgenstern,
1960; O’Connor and Mitchell, 1977). Stability charts for rapid drawdown
analysis are presented in Morgenstern (1963).
sec
1 (tantan)/F1
∑Wsinsec
1 (tantan)/F1
∑WsinSTABILITY AND STRESS 87
Fig. 2.15 Stability analysis: non-circular arc failure surface (Worked
example 2.3 should also be referred to)