Question 7 of 7: Effective Stress Beneath a Sand-and-Clay Site, Before and After Construction

Question 7: Effective Stress Beneath a Sand-and-Clay Site, Before and After Construction (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Approach. With no "moist" unit weight given, use γ_dry for soil above the water table and γ_sat below it, sum γ×thickness down to the bottom of the clay for σ, get u = γ_w×(depth below the water table), and take σ′ = σ − u. Stage (c) additionally requires recognizing that, immediately after construction, a saturated clay carries a fresh surface load undrained.

1. a) Prior to any work. Above the 4 m water table: 2 m dry sand + 2 m dry clay; below it: 3 m saturated clay down to the 7 m base: $$\sigma = \gamma_{d,\text{sand}}(2) + \gamma_{d,\text{clay}}(2) + \gamma_{sat,\text{clay}}(3) = 15.7(2)+16.7(2)+17.9(3) = \boxed{118.5\ \text{kPa}}$$ $$u = \gamma_w(7-4) = 9.81(3) = \boxed{29.43\ \text{kPa}}, \qquad \sigma' = \sigma - u = 118.5-29.43 = \boxed{89.07\ \text{kPa}}$$
2. b) After excavating 1 m of sand. The water table's elevation is unchanged, so it is now only 3 m below the new (lower) surface; the clay base is still 3 m below the water table (that vertical distance is fixed by the clay-base and water-table elevations, neither of which moved), while the profile above the W.T. has lost 1 m of sand: $$\sigma = \gamma_{d,\text{sand}}(1) + \gamma_{d,\text{clay}}(2) + \gamma_{sat,\text{clay}}(3) = 15.7(1)+16.7(2)+17.9(3) = \boxed{102.8\ \text{kPa}}$$ $$u = \gamma_w(3) = 29.43\ \text{kPa}\ (\text{unchanged: still 3 m below the W.T.}), \qquad \sigma' = 102.8-29.43 = \boxed{73.37\ \text{kPa}}$$ Removing overburden lowers both σ and σ′ (u is unaffected because it depends only on depth below the water table) — the clay is unloaded and tends to rebound/swell, exactly the "stress relief" a preload fill (Question 3c) is meant to guard against re-occurring under later construction.
3. c) Immediately after construction. The building's 48 kPa dead load is applied at the new surface. Check: assumes a saturated clay responds to a sudden surface load essentially undrained immediately after construction (Skempton B ≈ 1), so the entire stress increment initially appears as excess pore pressure rather than as a change in effective stress. Total stress rises by the full surcharge; pore pressure rises by the same amount (Δu = Δσ); effective stress is therefore, for this instant, unchanged from stage (b): $$\sigma = 102.8+48 = \boxed{150.8\ \text{kPa}}, \qquad u = 29.43+48 = \boxed{77.43\ \text{kPa}}$$ $$\sigma' = 150.8-77.43 = \boxed{73.37\ \text{kPa}}\ (\text{unchanged from stage b})$$ Over time, as this excess pore pressure dissipates through consolidation, u will fall back toward its hydrostatic value (29.43 kPa) and σ′ will rise to 150.8−29.43 = 121.4 kPa, producing the settlement a preload strategy is designed to pre-empt.