Hydraulic Structures: Fourth Edition

GRAVITY DAM ANALYSIS 139

SHEAR FRICTION FACTOR, FSF

FSFis defined as the ratio of the total resistance to shear and sliding which
can be mobilized on a plane to the total horizontal load. With this
approach both cohesion and the frictional components of shear strength
are accounted for and

FSFS/∑H. (3.22)

In the above expression Sis the maximum shear resistance which can be
mobilized. Referring to Fig. 3.5 it may be defined as

S∑Vtan (
) (kN m^1 ) (3.23)

whereAhis the area of plane of contact or sliding (Ahis the thickness, T,
for a two-dimensional section).
For the case of a horizontal plane (
0), equation (3.23) simplifies
to

ScAh∑Vtan. (3.24)

Substitution in equation (3.22) then gives the standard expression for the
shear friction factor, i.e.

FSF. (3.25)

cAh∑Vtan



∑H

cAh



cos
(1 tantan
)

Fig. 3.5 Sliding and shearing resistance: shear friction factor