The friction circle method is a two-dimensional limiting equilibrium technique of stability analysis which requires a potential failure mass to be in moment equilibrium as well as force equilibrium and gives a safety factor based on shear strength. A generalized procedure for friction circle analyses of foundation sliding stability of gravity dams is outlined then applied to an idealized triangular dam and two actual gravity dams. The friction circle method is a useful tool for gravity dam foundation sliding stability assessments. Friction circle analyses are simple enough that the user retains contact with physical reality but detailed enough (in terms of moment equilibrium as well as force equilibrium) to model the limiting equilibrium problem for purposes of guiding engineering judgement.
Concrete gravity dams, along with concrete gravity spillways and powerplant intake structures for embankment dams, are commonly constructed on rock foundations. In many cases, there is concern about sliding stability along the concrete-rock contact or along discontinuities in rock beneath this contact. Foundation sliding stability of gravity dams is generally analyzed with two-dimensional limiting equilibrium procedures based on considerations of force equilibrium. More sophisticated limiting equilibrium stability analyses and finite element stress and displacement analyses have also been used for gravity dam foundations. Most of these sophisticated methods have found limited application. Reasons for this include status quo attitudes among dam engineers; requirements for large, complex computer programs and, in some cases, extensive rock property data; and difficulties in interpreting results. Some of the older gravity dam foundation sliding analyses, developed more than forty years ago, are still being used. These traditional procedures treat horizontal sliding and give a factor of safety defined as the ratio of resisting forces to driving forces in the horizontal direction. More recently, two-dimensional multiwedge sliding analyses have been developed for non-planar failure surfaces. These multi-wedge analyses employ a factor of safety defined as the ratio of available shear strength to shear strength required for limiting equilibrium (Corps of Engineers, 1981). The newer, multi-wedge analyses for gravity dams are similar to those which have been used for some time in rock mechanics analyses of slope and foundation stability. The new definition of safety factor in terms of shear strength is consistent with contemporary practice in soil mechanics as well as rock mechanics. Many of the newer gravity dam foundation sliding analyses, like the older ones, consider only force equilibrium and neglect moment equilibrium of the potential failure mass (Corps of Engineers, 1981). The importance of moment considerations in two-dimensional limiting equilibrium procedures of slope analysis has been known for many years (Wright, 1969). The importance of moment equilibrium in foundation sliding stability analyses for gravity dams has not yet been widely recognized. Several years ago, the writer applied the general two-dimensional limiting equilibrium procedure of Morgenstern and Price (1965) to gravity dam foundation sliding analyses (Hamel, et al., 1976). This work demonstrated that consideration of moment equilibrium along with force equilibrium gave much higher safety factors (based on shear strength) than those obtained with traditional horizontal force equilibrium procedures.