16-Civ-A4 Geotechnical Materials and Analysis · December 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Reference texts: Das & Sobhan, Principles of Geotechnical Engineering (Cengage); Knappett & Craig, Craig’s Soil Mechanics; Holtz, Kovacs & Sheahan, An Introduction to Geotechnical Engineering. Canadian practice: effective-stress, seepage and consolidation methods as summarised in the Canadian Foundation Engineering Manual (CFEM, 4th ed.).
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.
(i) Correct answer: (a). The zero-air-voids (ZAV) line is the theoretical relationship between dry unit weight and water content for a fully saturated soil ($S = 100\%$). It is obtained purely from the definition of the phase relations, $$\gamma_{d,\text{zav}} = \dfrac{G_s\,\gamma_w}{1 + w\,G_s},$$ so once the specific gravity $G_s$ is assumed it can be plotted directly — no compaction test is required. Because field or laboratory compaction can never expel every air void, the actual compaction curve always lies below and to the left of the ZAV line (the two only approach one another on the wet side of optimum). Option (b) is therefore wrong: the ZAV line can never fall below the compaction curve, and it needs no tests to construct.
(ii) Sand A has the higher saturated permeability. Figure 1 shows Sand A as a uniform (poorly graded) assemblage of similarly sized grains, whereas Sand B is well graded, its finer particles occupying the pore space between the coarse grains. Well grading lowers the void ratio and, more importantly, greatly reduces the size of the interconnected flow channels. Since permeability is dominated by the smallest pore throats — Hazen’s rule $k \approx C\,D_{10}^{2}$ and the Kozeny–Carman relation $k \propto \dfrac{e^{3}}{1+e}\cdot\dfrac{1}{S_s^{2}}$ — a small drop in the effective grain size $D_{10}$ produces a large drop in $k$. Uniform Sand A retains large, open, well-connected voids and so conducts water far more readily than the void-filled Sand B.
(iii) GW has the higher angle of internal friction. A well-graded gravel (GW) is a coarse, angular, granular material whose strength comes from dense particle interlock and rolling/sliding friction; its effective friction angle is typically $\phi' \approx 38^\circ$–$45^\circ$. A high-plasticity clay (CH) derives its shear resistance from clay-mineral surface friction and is much weaker in friction, with $\phi'$ commonly only $15^\circ$–$22^\circ$ (its strength is largely cohesive/undrained). Hence GW $\gg$ CH in $\phi'$.
(iv) Soil B (expansive clay) has the higher swelling index. The swelling (recompression) index $C_s$ measures the reversible volume change on unloading/reloading and correlates directly with clay-mineral activity. An expansive clay is dominated by smectite (montmorillonite), whose lattice adsorbs and expels large volumes of interlayer water, giving a steep swelling line; an ordinary silty clay contains far less active mineral. Therefore $C_s$(expansive) $>$ $C_s$(silty clay), often by a factor of several.
(v) Normally consolidated clays — answer (a). When sheared, a normally consolidated (NC) clay is contractive: it tends to reduce in volume, and under undrained conditions that suppressed contraction is carried by the pore water as a positive excess pore pressure. An over-consolidated (OC) clay is dilatant: it tends to expand on shearing, generating small or even negative pore pressures. This is reflected in Skempton’s pore-pressure parameter at failure, $A_f \approx 0.5$–$1.0$ for NC clays but $A_f \approx 0$ to $-0.5$ for heavily OC clays. Hence the shear-induced positive pore pressures are higher in NC clays.
