Hydraulic Structures: Fourth Edition

GRAVITY DAM ANALYSIS 141

ofFSFrequired under alternative load combinations are summarized in
Table 3.6 (USBR, 1987).
Acceptance of the marginal stability permissible under extreme load
combination is a question of engineering judgement, and should only be
contemplated for smaller structures and after the most rigorous investiga-
tion. For major dams it is recommended practice to relax the values of FSF
required for normal load combination by 33% for any load combination
which includes seismic effects.

LIMIT EQUILIBRIUM FACTOR, FLE

The limit equilibrium approach to sliding stability follows conventional
soil mechanics logic in defining the limit equilibrium factor, FLE, as the
ratio of shear strength to mean applied shear stress across a plane, i.e.

FLEf/ (3.28)

wherefis the shear strength available, and is the shear stress generated
under the applied loading.
f is expressed by the Mohr–Coulomb failure criterion (Section
2.3.2), and equation (3.28) may be rewritten accordingly:

FLE. (3.29)

In the foregoing expression, nis the stress acting normal to the plane of
sliding.
Referring to Fig. 3.5, which illustrates a single-plane sliding mode,
application of equation (3.29) with appropriate substitutions yields

FLE. (3.30)

Note that for the case of a horizontal sliding plane (
0), equation (3.30)
simplifies to the expression given in equation (3.25), i.e. FLEFSF(
0).

cAh[∑Vcos
∑Hsin
] tan



∑Hcos
 ∑Vsin

cntan





Table 3.6 Recommended shear friction factors, FSF(USBR, 1987)

Location of sliding plane Load combination

Normal Unusual Extreme

Dam concrete/base interface 3.0 2.0 1.0
Foundation rock 4.0 2.7 1.3