Seepage force in soils — identify the complete and correct description of seepage force with respect to flow-net geometry and hydraulic parameters.

Introduction / Context:
Seepage force is the drag exerted by flowing water on the soil skeleton. It influences piping, heave beneath excavations, and stability of filters and drains. Recognizing its direction and how its magnitude scales with hydraulic quantities is central to safe geotechnical design near exits and interfaces.

Given Data / Assumptions:

• Flow is steady and laminar (Darcy’s law applies).
• A valid flow net exists with orthogonal flow lines and equipotential lines.
• Unit weight of water is gamma_w; hydraulic gradient is i.

Concept / Approach:

The seepage force per unit volume is f = i * gamma_w, acting in the direction of flow. Flow lines are by definition perpendicular to equipotential lines; hence the force is perpendicular to equipotentials. The gradient i can be written as delta_h / delta_l for a given flow path length, so for a fixed path the force is proportional to head loss delta_h. Near the exit boundary, i approximates the exit gradient, making the force particularly sensitive there and explaining why critical gradients govern piping risk.

Step-by-Step Solution:

Verification / Alternative check:

Compute effective stress under upward seepage: sigma_prime = sigma_total - u - i * gamma_w * z_effective (conceptually). When i approaches the critical gradient i_c = (Gs - 1)/(1 + e), quick conditions occur, validating the link between gradient and destabilizing force.

Why Other Options Are Wrong:

Each of A, B, C is individually true but incomplete; only “all the above” covers direction and both proportionalities.

Common Pitfalls:

Confusing flow direction with equipotential orientation; ignoring exit gradients in design; assuming seepage force is negligible in coarse filters without checking i.

Final Answer:

all the above