Geotechnical Engineering

DHARM

194 GEOTECHNICAL ENGINEERING

The upward force of seepage is h. γw A, as is in the left hand side of Eq. 6.32. In uniform
flow it is distributed uniformly throughout the volume of soil L. A, and hence the seepage force
j per unit volume is hγw. A/LA, which equals i. γw.
j = i. γw ...(Eq. 6.33)
Thus, the seepage force in an isotropic soil acts in the direction of flow and is given by
i.γw per unit volume. The vector sum of seepage forces and gravitational force is called the
resultant body force. This combination may be accomplished either by a combination of the
total weight and the boundary neutral force or by a combination of the submerged weight and
the seepage force. The two approaches give identical results.

6 .11 Effective Stress in a Soil Mass Under Seepage

The effective stress in the soil at any point is decreased by an amount equal to the seepage

force at that point for upward flow; correspondingly, the neutral pressure is increased by the

same amount, the total stress remaining unaltered.

Similarly, the effective stress is increased by an amount equal to the seepage force for

the downward flow; correspondingly, the neutral pressure is decreased by the same amount,

the total stress remaining unaltered.

This is due to the fact that the seepage force is the viscous drag transmitted to the

particles while the seeping water is being pushed through the pores, the surfaces of the parti-

cles serving as the walls surrounding the pores. This, in addition to the fact that seepage force

acts in the direction of flow, will enable one to determine the effective stress in a soil mass

under steady state seepage.

6.12 ILLUSTRATIVE EXAMPLES

Example 6.1: What is the critical gradient of a sand deposit of specific gravity = 2.65 and void

ratio = 0.5? (S.V.U.—B.Tech., (Part-Time)—Sep., 1982)

G = 2.65, e = 0.50

Critical hydraulic gradient, ic = (G – 1)(1 + e).

=

(. )

(.)

.

.

265 1

1050

165

150

−

+

= = 1.1.

Example 6.2: A 1.25 m layer of the soil (G = 2.65 and porosity = 35%) is subject to an upward
seepage head of 1.85 m. What depth of coarse sand would be required above the soil to provide
a factor of safety of 2.0 against piping assuming that the coarse sand has the same porosity
and specific gravity as the soil and that there is negligible head loss in the sand.

(S.V.U—B.E.(R.R.)—Sep., 1978)

G = 2.65; n = 35% = 0.35; e =

n

()n

.

.1

035

− 065

= = 7/13

Critical hydraulic gradient, ic = ()

()

(. )

(/)

G

e

−

+

= −

+

1

1

265 1

1713

=

1.65× 13

20

= 1.0725