Seepage Analysis MCQ with answer and solution

Concept

Critical Hydraulic Gradient

Formula

ic = γ' / γw

Step-by-step solution

- Step 1: Find submerged unit weight: γ' = γsat - γw = 19.62 - 9.81 = 9.81 kN/m³ - Step 2: Calculate critical hydraulic gradient: ic = γ' / γw = 9.81 / 9.81 = 1

Explanation

The critical hydraulic gradient (ic) is calculated using the formula ic = γ' / γw, where γ' is the submerged unit weight of the soil and γw is the unit weight of water (9.81 kN/m³). First, calculate the submerged unit weight: γ' = γsat - γw = 19.62 - 9.81 = 9.81 kN/m³ Then, calculate the critical hydraulic gradient: ic = 9.81 / 9.81 = 1

Shortcut

Since 19.62 kN/m³ is exactly twice the unit weight of water (9.81 kN/m³), use the direct ratio shortcut: ic = (γsat / γw) - 1 = (19.62 / 9.81) - 1 = 2 - 1 = 1.

Common mistake

Students often forget to subtract the unit weight of water (9.81 kN/m³) from the saturated unit weight to find the submerged unit weight, mistakenly using the saturated unit weight directly in the critical hydraulic gradient formula.