Factor of Safety Against Shearing-Sliding for Dams With Inclined Post-Tensioned Anchors

In accordance with current Federal Energy Regulatory Commission (FERC) dam safety regulations, a stability evaluation of an existing rigid body dam must be made in order to establish its stability and also to provide the basis for determining the need for further engineering review and studies. As a result of this evaluation many dams are found to require stability improvement. To increase the sliding and overturning stability for older dams, the common approach is to install post-tensioned anchors. When the anchor's opposing active force is applied to the dam, it may be accounted for in calculations of the Factor of Safety in two ways:
1. The horizontal component of the anchor total post-tensioned force is added directly to the summation of the resisting forces and it is included in the numerator of the factor of safety equation.
2. The horizontal component of the post-tensioned force is subtracted directly from the summation of the shear (driving) forces and it is included in the denominator of the factor of safety equation.
Definition 1 appears to be a more conservative approach and therefore has been accepted as a current procedure for calculating the factor of safety against sliding. Nevertheless, there is disagreement in the engineering community over which of these two definitions is correct and most importantly results in improved and reliable safety at lower cost, when post-tensioned anchors are included in a stability improvement program. This article attempts to provide justification for the recommended use of Definition 2 in the evaluation of post-tensioned anchors to stabilize rigid body dams. Comparable analyses are presented using both definitions based on the results of a numerical example. The example further illustrates how the computed factor of safety varies when using the two definitions, and suggests that reliance on Definition 1 may result in the use of overly large anchor forces at higher costs compared to the Definition 2 approach. In addition, the use of Definition 1 may in some cases actually reduce overall dam stability by overstressing the dam in the upstream direction, a condition which may be detrimental if the reservoir level is substantially reduced. This article also helps define Active and /or Reactive shear (driving) and resisting forces based on the movement of the dam when the dam is subjected to the external loads. 12 pp.