Seepage through earth dams: The shape of the phreatic line (upper seepage line) within a homogeneous earth dam with a horizontal drainage filter is typically:

Introduction / Context:
Estimating seepage and pore-pressure distribution in earth dams is vital for stability and filter design. The phreatic line represents the top boundary of saturated flow, separating saturated and unsaturated zones inside the embankment.

Given Data / Assumptions:

• Homogeneous earth dam with a drainage filter (toe drain).
• Steady-state seepage conditions.
• Darcian flow and Dupuit assumptions commonly used.

Concept / Approach:
Under Dupuit–Forchheimer assumptions for homogeneous isotropic media and horizontal drainage, the free seepage surface (phreatic line) becomes approximately parabolic. Graphical methods such as Casagrande’s construction are based on this property, facilitating routine design checks.

Step-by-Step Solution:

Verification / Alternative check:
Finite element seepage analyses for homogeneous sections reproduce a near-parabolic free surface for moderate slopes and steady states.

Why Other Options Are Wrong:

• Circular/Elliptical/Straight line: not consistent with theory or practice for homogeneous dams with toe drains.
• “Depends only on upstream slope”: many factors influence the line; and the canonical shape under these assumptions is parabolic.

Common Pitfalls:
Ignoring anisotropy and zoning; in zoned dams or anisotropic conditions, the shape deviates from a simple parabola.

Final Answer:
Parabolic