DHARM176 GEOTECHNICAL ENGINEERING
Functions φ and ψ are termed ‘Conjugate harmonic functions’. In such a case, the curves
‘‘φ(x, z) = a constant’’ will be orthogonal trajectories of the curves ‘‘ψ(x, z) = a constant’’.
Flow nets will be useful for the determination of rate of seepage, hydrostatic pressure,
seepage pressure and exit gradient. These aspects have already been discussed in Sec. 6.2.
The following important properties of the flow nets are useful to remember:
(i) The flow lines and equipotential lines intersect at right angles to each other.
(ii) The spaces between consecutive flow and equipotential lines form elementary squares
(a circle can be inscribed touching all four lines).
(iii) The head drop will be the same between successive equipotentials; also, the flow in
each flow channel will be the same.
(iv) The transitions are smooth, being elliptical or parabolic in shape.
(v) The smaller the size of the elementary square, the greater will be the velocity and
the hydraulic gradient.
These are correct for homogeneous and isotropic soils.*6.5 Seepage Through Non-Homogeneous and Anisotropic Soil
Although Eq. 6.2 was derived fro general conditions, the preceding examples considered only
soil that does not vary in properties from point horizontally or vertically–homogeneous soil–
and one that has similar properties at a given location on planes at all inclination–isotropic
soil. Unfortunately, soils are invariably non-homogeneous and anisotropic.
The process of formation of sedimentary soils is such that the vertical compression is
larger than the horizontal compression. Because of the higher vertical effective stress in a
sedimentary soil, the clay platelets tend to have a horizontal alignment resulting in lower
permeability for vertical flow than for horizontal flow.
In man-made as well as natural soil, the horizontal permeability tends to be larger than
the vertical. The method of placement and compaction of earth fills is such that stratification
tend to be built into the embankments leading to anisotropy.
Non-homogeneous Soil
In case of flow perpendicular to soil strata, the loss of head and rate of flow are influenced
primarily by the less pervious soil whereas in the case of flow parallel to the strata, the rate of
flow is essential controlled by comparatively more pervious soil.
Figure 6.11 shows a flow channel and part of a flow net, from soil A to soil B. The
permeability of soil A is greater than that of soil B. By the principle of continuity, the same
rate of flow exists in the flow channel in soil A as in soil B. By means of this, relationship
between the angles of incidence of the flow paths with the boundary of the two flow channels
can be determined. Not only does the direction of flow change at the boundary between soils
with different permeabilities, but also the geometry of the figures in the flow net changes. As
can be seen from Fig. 6.11, the figures in soil B are not squares as in soil A, but are rectangles.