Question 6 of 7: Standard Proctor Compaction — Zero-Air-Voids Line and Air Content

Question 6: Standard Proctor Compaction — Zero-Air-Voids Line and Air Content (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. The zero-air-voids (saturation) line gives the maximum possible dry unit weight at each moisture content (S = 100%, no air in the voids); plot it from γ_zav = G_sγ_w/(1+wG_s) and compare it with the actual compacted point to get the void ratio, degree of saturation, and hence the air content at w = 10%.

1. a) Zero-air-voids line. At any moisture content w (decimal), the maximum possible dry unit weight with zero air voids is $$\gamma_{zav}(w) = \frac{G_s\gamma_w}{1+wG_s}$$ Evaluated at w = 10% and 11% (bracketing the peak) with γ_w = 9.81 kN/m³: $$\gamma_{zav}(0.10) = \frac{2.60(9.81)}{1+0.10(2.60)} = \boxed{20.24\ \text{kN/m}^3}, \qquad \gamma_{zav}(0.11) = \frac{2.60(9.81)}{1+0.11(2.60)} = 19.83\ \text{kN/m}^3$$ Plotted across the moisture range, this curve lies everywhere above the compaction curve (shown in the figure), as it must — no compacted point can exceed the density a fully saturated sample of the same soil would have.
2. b) % of void volume filled with air, w = 10%. From the actual point on the curve, γ_d = 19.0 kN/m³ at w = 10%, the void ratio follows from G_sγ_w/γ_d = 1 + e: $$e = \frac{G_s\gamma_w}{\gamma_d}-1 = \frac{2.60(9.81)}{19.0}-1 = 0.342$$ The degree of saturation actually achieved, S = wG_s/e, and the fraction of the void volume that is not water is air: $$S = \frac{wG_s}{e} = \frac{0.10(2.60)}{0.342} = 0.759\ (75.9\%)$$ $$\text{air, \% of void volume} = (1-S)\times100\% = \boxed{24.1\%}$$ (Equivalently, as a fraction of the total sample volume rather than of the void volume alone, the air content is n(1−S) ≈ 6.1%.)

c) Effects of compaction. Hydraulic: compaction collapses macropores and reduces the void ratio, which sharply lowers saturated hydraulic conductivity and infiltration capacity — useful for a liner or subgrade, but it also increases surface runoff. Structural: the denser, better-interlocked particle arrangement raises shear strength, stiffness (modulus) and bearing capacity, and reduces post-construction settlement (compressibility) — the entire purpose of specifying a target relative compaction (e.g. 95% of Proctor maximum) for engineered fill. Erosive: the denser surface is more resistant to particle detachment and piping, but because infiltration is suppressed, more rainfall converts to surface runoff, which can increase erosive shear stress at the surface and on downslope, un-compacted ground unless drainage is specifically managed.