and
k(kvkh)1/2. (2.14)The seepage flow, q(equation (2.10) should be referred to), is defined
by
qkH (2.15)whereHis the head differential and the ratio Nf/Ndis the flownet shape
factor, i.e. the number of flow channels, Nf, in relation to the number of
decrements in potential, Nd(NfandNdneed not be integers).
For the unconfined flow situation applicable to seepage througha
homogeneous embankment the phreatic surface is essentially parabolic.
The curve can be constructed by the Casagrande–Kozeny approximation,
defined in the references previously detailed, or from interpretation of
piezometric data (Casagrande, 1961). In the case of a central core and/or
zoned embankment, construction of the flownet is based upon considera-
tion of the relative permeability of each element and application of the
continuity equation:
qupstream shoulderqcore zoneqdownstream shoulderqdrains. (2.16)An illustrative flownet for seepage underan embankment is given in Fig.
2.11. (The figure forms the transform scale solution to worked example
2.1.) In Fig. 2.12 is shown the flownet for a simple upstream core two-zone
profile, where piezometric data have been interpreted to define the
phreatic surface within the core (Fig. 2.12 is the flownet solution to worked
example 2.2).
The thickness of horizontal blanket drain, td, required to discharge
the seepage flow and shown in Fig. 2.12 can be estimated from
td(qL/kd)1/21.5H(kc/kd)1/2 (2.17)whereLis the downstream shoulder width at drain level and kdandkcare
the drain and core permeabilities respectively (the factor 1.5 in equation
(2.17) is derived from a representative embankment geometry).
Nf
Nd