Geotechnical Engineering

DHARM

SOIL MOISTURE–PERMEABILITY AND CAPILLARITY 145

If the degree of saturation is S, Darcy’s Law for a particular value of x, gives:

S. v = k. i

In terms of seepage velocity vs, this reduces to:

S. n. vs = k. i, n being the porosity.

Here, vs = the seepage velocity parallel to X-direction = dx/dt

∴ S. n. dx/dt = k

hh

x

.()^0 + c

or xdx =

k

Sn.

(h 0 + hc)dt

Integrating between the limits x 1 and x 2 for x, and t 1 and t 2 for t,

x

x

t sc

t

xdx

k

Sn

hhdt

1

2

1

2

zz. =+. ()

∴

xx

tt

k

Sn

(^2) hhc
2
1
2
21
0
− 2
−
F
HG
I
KJ
=+
.
() ...(Eq. 5.40)
The degree of saturation, may be found from the dry weight, volume, grain specific
gravity, and the wet weight at the end of the test. The porosity may also be computed from
these.
In case the degree of saturation is assumed to the 100%, we may write:
xx
tt
k
n
(^2) hhc
2
1
2
21
0
−^2
−
F
HG
I
KJ
=+() ...(Eq. 5.41)
There are two unknowns k and hc in this equation. The usual procedure recommended
for their solution is as follows :
The first stage of the test is done with a certain value of the head, h 01 when the sample
is saturated for about one-half of its length, the values of x being recorded for different time
lapses t. The second stage of the test is conducted with a much larger value of the head, h 02 ;
this large value of the head is best imposed by clamping a head water tube to the left end of the
glass tube containing the soil sample.
A plot of t versus x^2 gives a straight line which has different slopes for the two stages as
shown in Fig. 5.19.
First
stage
(slope
m)^1
First stage(slope m )
1
Second
stage
(slope
m)^2
Second stage(slope m )
2
Time, t
Square of saturated length, x
2
Fig. 5.19 Plot of t vs. x^2 in horizontal capillarity test