Guidelines for Safety Inspection of Dams - Central Water Commission

α = Angle between inclined plane and horizontal (positive
for uphill sliding).
for sliding downhill, the angle α is negative and equation (1)
becomes:
RR = V tan (φ - α) + CA …………(4)
cos α (1+ tan φ tan α )
when the plane of investigation is horizontal, and the angle is
zero and equation (4) reduced to the following:
RR = V tan φ + CA
4.4.4.5.2 Downstream resistance
When the base of a concrete structure is embedded in rock or
the potential failure plane lies below the base, the passive
resistance of the downstream layer of rock may sometimes be
utilized for sliding resistance. Rock that may be subjected to
high velocity water scouring should not be used. The
magnitude of the downstream resistance is the lesser of (a)
the shearing resistance along the continuation of the potential
sliding plane until it daylights or (b) the resistance available
from the downstream rock wedge along an inclined plane.
The theoretical resistance offered by the passive wedge can be
computed by a formula equivalent to formula (3) :
PP = W tan (φ + α ) + CA ……….(5)
cos α (1- tan φ tan α )
PP
= Passive resistance of rock wedge
W = Weight (buoyant weight, if applicable) of downstream
rock wedge above inclined plane of resistance, plus
any superimposed loads.
α = Angle of internal friction or, if applicable, angle of
sliding friction.
α = Angle between inclined failure plane and horizontal.
C = Unit shearing strength at zero normal load along failure
plane.
A = Area of inclined plane of resistance.
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