Seepage through soils (Darcy’s law in geotechnical engineering): The quantity (discharge) of seepage water through a soil mass is proportional to which factors?

Introduction / Context:

In civil engineering hydraulics of soils, predicting how much water seeps through an earth mass is essential for the design of filters, earth dams, cutoffs, and dewatering systems. The governing relation for laminar flow through porous media is Darcy’s law, which ties seepage discharge to soil properties and the energy gradient driving flow.

Given Data / Assumptions:

• Steady, laminar flow through a saturated soil (typical of fine and medium sands, silts under modest gradients).
• Homogeneous soil with constant coefficient of permeability k.
• Flow occurs under a measurable total head loss across a specimen or field section.

Concept / Approach:

Darcy’s law states: q = k * i * A, where q is discharge, k is coefficient of permeability, i is hydraulic gradient (head loss per unit length), and A is flow area. Thus, for a given geometry, the seepage is directly proportional to both k and the head loss (since i scales with total head loss across a fixed length).

Step-by-Step Solution:

Verification / Alternative check:

Laboratory constant-head and falling-head tests confirm linear proportionality between discharge and head loss for laminar regimes and a constant k for a given soil and packing.

Why Other Options Are Wrong:

• Coefficient of permeability alone (a) is incomplete—no flow occurs without a head loss.
• Total head loss alone (b) ignores that highly impermeable soils transmit far less water.
• “Neither” and “area only” contradict Darcy’s relation for laminar flow.

Common Pitfalls:

• Applying Darcy’s law outside its range (very high gradients or coarse gravels where flow may be non-Darcian).
• Confusing elevation head and pressure head—total head loss drives seepage.

Final Answer:

both (a) and (b)