Geotechnical Engineering

DHARM

178 GEOTECHNICAL ENGINEERING

From the transformed section, the rate of seepage can be determined using Eq. 6.1 with

exception that ke is to be substituted for k (see Fig. 6.12):

l

b

kx

kz

Flow Flow

Natural scale Transformed scale

l.k/kÖxz

Fig. 6.12 Flow in anisotropic soil

Transformed Section:

qT = ke .iA = ke.

∆h

l

. b = ke. ∆h
Natural Section:

qN = kx. iN. A = kx.

∆h

lkkxz/

. b = kx.

∆h

kkxz/

Since qT = qN,

ke ∆h = kx. ∆h

kkxz/

...(Eq. 6.12)

ke is said to be the effective permeability.

The transformed section can also be used to determine the head at any point. However,

when determining a gradient, it is important to remember that the dimensions on the trans-

formed section must be corrected while taking the distance over which the head is lost. To

compute the gradient, the head loss between equipotentials is divided by the distance lN, the

perpendicular distance between equipotentials on the natural scale, and not by lT, the distance

between equipotentials on the transformed scale (Fig. 6.13).

Square

lT

Flow

Transformed section Natural section

Flow

lN

Parallelograms

kz

kx

Fig. 6.13 Portion of flow net in anisotropic soil

Also, note that flow is perpendicular to equipotentials in only isotropic soils.

6.6 Top Flow Line in an Earth Dam

The flow net for steady seepage through an earth dam can be obtained by any one of the

methods available, including the graphical approach. However, since this is the case of an