16-Civ-A4 Geotechnical Materials and Analysis · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Examinations (Engineers Canada / PEO), 98-Civ-A4 Geotechnical Materials and Analysis, December 2014. Closed book, 3 hours, 100 marks. Six questions — answer all. Charts and equations supplied at the back of the paper.
Reference texts: Das & Sobhan, Principles of Geotechnical Engineering (9th ed.), Cengage; Holtz, Kovacs & Sheahan, An Introduction to Geotechnical Engineering (2nd ed.), Pearson; Craig’s Soil Mechanics (Knappett & Craig, 8th ed.), CRC Press.
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.
Each part is a single concept; the mark is earned by the justification, not the letter.
(i) Highest OMC → (C) clay. Optimum moisture content rises with fineness and plasticity. Clay particles carry an enormous specific surface and a diffuse double layer, so a great deal of water is needed to lubricate the platelets and let them reorient into their densest packing under a given compactive effort. A clean sand, with negligible surface area, reaches its maximum dry density at only a few percent water content, silt is intermediate, and clay is highest (typical OMC: sand ≈ 8–12 %, silt ≈ 12–18 %, clay ≈ 18–30 %).
(ii) Highest permeability → (A) sand. The coefficient of permeability is governed by the size of the pore channels, which scale with the grain size. Hazen’s rule $k \approx C\,D_{10}^{2}$ makes $k$ vary with the square of the effective size, so the coarse, single-grained sand (large $D_{10}$, large interconnected voids) is orders of magnitude more permeable than silt, which in turn far exceeds clay. Representative values: sand $10^{-2}$–$10^{-5}$ m/s, silt $10^{-5}$–$10^{-8}$ m/s, clay $10^{-9}$ m/s or lower.
(iii) Highest unconfined compressive strength → (C) dry of optimum. At a fixed compactive effort a clay compacted dry of optimum develops a flocculated fabric (edge-to-face particle contacts) and retains large negative pore-water pressures (matric suction). Both effects stiffen the soil, so the as-compacted, undrained unconfined strength $q_u$ is highest on the dry side. Wet of optimum the fabric becomes dispersed (parallel platelets) and the suction is largely destroyed, giving a lower $q_u$ (though a lower permeability — which is why clay liners are placed slightly wet of optimum).
(iv) Higher compression index $C_c$ → (A) normally consolidated clay. A normally consolidated clay has never carried a stress greater than its present overburden, so any load increment moves it down the steep virgin compression line in $e$–$\log\sigma'$ space, whose slope is $C_c$. An over-consolidated clay first travels along the much flatter recompression line (slope $C_r \approx \tfrac{1}{5}$ to $\tfrac{1}{10}\,C_c$) until the applied stress reaches the pre-consolidation pressure. For working stresses below $\sigma'_p$ the OC clay is far less compressible; hence the NC clay has the larger $C_c$ and settles more.
(v) Higher effective cohesion $c'$ → (B) over-consolidated clay. The effective-stress failure envelope of a normally consolidated clay passes essentially through the origin ($c' \approx 0$): its strength is purely frictional. An over-consolidated clay carries a genuine cohesion intercept because unloading has locked the particles into a dense, interlocked fabric and because stress history / light cementation give it strength at zero effective stress. Therefore $c'_{OC} > c'_{NC} \approx 0$.
