SOIL AND GROUNDWATER - Introduction to Soft Soil Geotechnique: Content, Context and Application - page 54

N subsequent other equipotential lines to reach the other boundary with known
potential head

2 , then

= k ( 2 1 )/ N . Hence, also = k ( 2 1 )/ N .

y y y

Q tube = Q tube = Q tube = =q =q =q n n n

s s s

q q q

n n n

q = q s q = q s q = q s q = q s

x x x

q y q y q y q y

s s s

n n n

q x q x q x q x

q n =0 q n =0 q n =0 q n =0

Figure 4.1b Principle of square flow net

From (4.12), the local discharge, expressed in finite differentials, is q = / n .

This implies q 2 )/ N . If the 2D flow field reflects groundwater

flow in a layer with thickness B (perpendicular to the ( s,n )-plane), the meaning of
qB

n = = k ( 1

n is the discharge Q tube through the tube bounded by two subsequent
streamlines. Thus, Q tube = is a constant: through every flow tube in the

sketched square net the same amount of flow occurs. If the total flow field counts
M flow tubes, then the total discharge in m 3 /s becomes

B

Q = MkB (

2 )/ N

(4.13)

1

By just sketching a flow field and counting the number of flow tubes M and
equipotential intervals N , the total discharge can be estimated by formula (4.13).
One needs not to be an artist; for a rough drawing, the resulting Q will be accurate
within 20%.

Model tests
The essential parameter for groundwater flow is the permeability k . It can be
determined in the laboratory or in the field. In the laboratory, for sandy soils a
cylinder test is performed (Fig 4.2). The sandy sample, height L and cross-section
A , is placed on a permeable raster and subjected to a constant water drop H . The
cylinder test was first performed by Darcy, published in 1856. Darcy found a
discharge Q proportional to HA/L , or Q = kHA/L . With the definition of the
specific discharge q = Q/A , the formula becomes q = k ( H/L ), known as Darcy's
law. Here H/L is the water-head gradient, usually represented as dh/ds

or i . The minus sign indicates flow runs to the lower pressure. Note that effective
stresses is affected by the drag force of the flowing pore fluid (see page 63).

d /dz or