Water: Surface and Subsurface - Geotechnical Engineering Investigation - page 643

is the void ratio, or the discharge velocity divided by the effective porosity ( n e ),
expressed as

v s k i/ n e ft/day or cm/sec (8.5)

The practical significance of seepage velocity lies in the field evaluation of k , using dye trac-
ers and measuring the time for the dye to travel the distance between two holes, and in
estimating the rate of movement in pollution-control studies. Some relationships between
permeability, hydraulic gradient, and the rate of groundwater flow are given in Table 8.2.

Pressures and Liquefaction
Seepage pressures j are stresses in the soil caused by the flow of water. They are equal to
the hydraulic gradient i times the unit weight of water, expressed as

j h / L γ w i γ w (8.6)

and act in the direction of the flow.
Where the flow tends to be upward, as at the toe of a dam, along slopes, or at the bot-
toms of excavations, the pressure is resisted by the weight of the overlying soil column.
“Quick conditions” (boiling or liquefaction) occur when the upward gradient increases
until the seepage pressure exceeds the submerged weight of the soil, and the soil column
is uplifted. The result is a complete loss of intergranular friction and the supporting capac-
ity of the soil. (“Cyclic” liquefaction occurs under dynamic loadings; see Section 11.3.3).
Critical gradient is the hydraulic gradient required to produce liquefaction and equals
the ratio of the submerged unit weight of the soil to the unit weight of water:

i cr ( γ t γ w )/ γ w γ b / γ w (8.7)

In coarse to fine sand, i cr is about 0.9 to 1.0, and in layman's terms results in “quicksand.”
The example given in Figure 8.26 is barely stable ( i cr

1.04).
The factor of safety against liquefaction, usually taken as 3 or more because of the disas-
trous nature of such a failure, is defined as

FS i cr / i (8.8)

TABLE 8.2
Permeability, Hydraulic Gradient, and Groundwater Flow-Rate Relationships for Various Soil
Gradations

Soil Type Permeability (cm/sec) Gradient i Time to Move 30 cm n e

Clean sand 1.0 10 −2 0.10 2.5 h 0.30

0.01 25.0 h

Silty sand 1.0 10 −3 0.10 1.4 days 0.40

0.01 14.0 days

Silt 1.0 10 4 0.10 14.0 days 0.40

0.01 140.0 days

Clayey sand 1.0 10 5 0.10 174 days 0.50

0.01 4.8 years

Silty clay 1.0 10 6 0.10 4.8 years 0.50

0.01 48.0 years

Clay (intact) 1.0 10 7 0.10 48.0 years 0.50

0.01 480 years