In an oedometer test, a 20 mm thick clay sample drained at top and bottom reaches 50% consolidation in 10 minutes. In the field, the same clay forms a 4 m thick layer between two sand layers. How long will the field layer take to reach 50% consolidation? How would the answer change if the clay rested on impervious rock instead?
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Time factor T_v = c_v t / H_dr². For the same clay and same degree of consolidation, t ∝ H_dr².
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Worked answer.
Theory. Terzaghi's one-dimensional consolidation theory gives the time factor
T_v = c_v t / H_dr²,
where c_v is the coefficient of consolidation and H_dr is the drainage path length (the longest distance water must travel to reach a drainage boundary). For the same clay (same c_v) and the same degree of consolidation (same T_v), t is proportional to H_dr².
Step 1: Drainage paths.
- Lab sample, double drainage: H_dr = 20/2 = 10 mm.
- Field layer between two sand layers, double drainage: H_dr = 4000/2 = 2000 mm.
Step 2: Scale the time.
t_field = t_lab × (H_field / H_lab)² = 10 min × (2000/10)² = 10 × 200² = 10 × 40,000 = 400,000 minutes.
Converting: 400,000 / 60 ≈ 6667 hours, and 6667 / 24 ≈ 278 days (about 9 months).
Step 3: Single drainage (on impervious rock). Water can drain only upward, so H_dr = 4000 mm.
t = 10 × (4000/10)² = 10 × 160,000 = 1,600,000 min ≈ 1111 days (about 3 years), four times longer.
Check via c_v. For U = 50%, T_v ≈ 0.197. From the lab: c_v = 0.197 × 10² / 10 = 1.97 mm²/min. In the field: t = 0.197 × 2000² / 1.97 = 400,000 min. This matches Step 2.
Why clay is slow and sand is fast. Settlement under load requires water to be squeezed out of the pores. Clay has very low permeability, so excess pore pressure dissipates slowly over months to years (primary consolidation). Sand is highly permeable, so its settlement is practically immediate.
Common mistake. Using the full thickness of a doubly drained layer as H_dr, which overestimates the time four times. Another is scaling linearly with thickness instead of with its square.
Likely follow-up. "Does the magnitude of settlement depend on drainage?" No. Drainage controls the rate; the final settlement depends on compressibility (C_c or m_v), stress increase and layer thickness.
Original UniCircle question. Last reviewed 28 Oct 2026.