Seepage Beneath Hydraulic Structures – Streamline Shape Without a Floor If there is no impervious floor or boundary provided at the bottom of a hydraulic structure (e.g., a weir without a floor), the seepage streamlines tend to follow which idealized path beneath the structure?

Introduction / Context:
Design of hydraulic structures on permeable foundations requires understanding seepage patterns. Classical flow approximations (e.g., Bligh’s creep theory and potential flow analogies) provide intuitive shapes for flow lines when structural floors or cutoffs are absent.

Given Data / Assumptions:

• Homogeneous, isotropic pervious foundation.
• No impervious floor at the structure's base.
• Two-dimensional seepage under the structure is considered.

Concept / Approach:

Without a floor, the equipotential and streamlines under a narrow obstruction approximate circular arcs due to symmetry and boundary conditions. The idealized streamline beneath the structure tends toward a semi-circular path connecting upstream and downstream faces, a result consistent with potential flow solutions for obstacles on a pervious half-space.

Step-by-Step Solution:

Verification / Alternative check:

Flow nets drawn for structures without floors show nearly circular flow tubes under the base, while adding floors or cutoffs distorts these into elongated paths.

Why Other Options Are Wrong:

Straight or parabolic paths do not satisfy boundary conditions; semi-elliptical forms are more representative when floors/cutoffs exist and geometry is elongated, not for a bare base.

Common Pitfalls:

Confusing idealized streamline shapes with actual, more complex patterns when anisotropy or layered foundations are present.

Final Answer:

A semi-circle