Question 1 of 6: Multiple statements with justification

Question 1: Multiple statements with justification (4 × 5 = 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.

Each part is a conceptual (state-and-justify) item; no computation is required, so the reasoning is given as prose.

(i) Sand A ($C_u = 4$) has the greater shear strength. The coefficient of uniformity $C_u = D_{60}/D_{10}$ measures the spread of particle sizes. $C_u = 1$ means a single (uniform) grain size — a poorly graded sand (SP) that cannot pack tightly, so it has a high void ratio and a lower peak friction angle. $C_u = 4$ is a better-graded sand in which finer grains occupy the voids between the coarser grains, giving denser packing, more inter-particle contacts and greater interlock. Since the drained strength of sand is purely frictional, $\tau_f = \sigma' \tan\phi'$, the denser, well-graded Sand A mobilises the larger $\phi'$ and therefore the greater shear strength.

(ii) Sand C has the lowest coefficient of permeability. Figure 1 draws each sand as a row of its grain sizes. Sand A is a row of near-equal grains: a uniform (poorly graded) sand whose single-sized grains leave large, well-connected voids, so it is the most permeable. Sand B is gap graded: a few coarse grains and a separate group of much finer grains, with the intermediate sizes missing, so the fines only partly fill the voids between the coarse grains. Sand C runs continuously from coarse to very fine: a well-graded sand in which each smaller size fits the voids left by the next larger one, giving the densest packing and the smallest, most tortuous pore channels. Permeability is controlled by pore-channel size, which Hazen’s relation ties to the fine end of the grading ($k \approx C\,D_{10}^{2}$), and continuous grading removes the large open voids. Sand C is therefore the least permeable, gap-graded Sand B is intermediate and uniform Sand A is the most permeable.

(iii) These two properties do not occur together in one soil — they are inversely related, so GW gives the higher maximum dry density (with a low optimum moisture content) while CH gives the higher optimum moisture content (with a low dry density). A well-graded gravel (GW) compacts to a high $\gamma_{d,\max}$ at a low optimum water content because its wide gradation packs efficiently with little lubricating water. A highly plastic clay (CH) has a large specific surface, needs much more water to reach its optimum, and reaches only a low $\gamma_{d,\max}$; silt (ML) lies between the two. Because $\gamma_{d,\max}$ and $w_{opt}$ move in opposite directions along the line of optimums, no single soil maximises both — the correct answer is to identify GW for dry density and CH for optimum moisture content.

(iv) Soil B, glacial till, has the highest effective friction angle $\phi'$. The drained (CD) friction angle increases with density, angularity and range of grain sizes. Glacial till is a dense, well-graded, angular granular deposit and typically develops $\phi' \approx 35^\circ$–$45^\circ$, higher than a clean uniform sand ($\approx 30^\circ$–$36^\circ$) or a silt. The expansive clay has the lowest $\phi'$ because its platy, low-friction clay minerals slide readily. Order: glacial till $\gt$ sand $\gt$ silt $\gt$ expansive clay.

(v) A dispersed (oriented) structure — option B in Figure 2. When a fine-grained clay is compacted wet of optimum there is enough pore water to develop repulsive double-layer forces between particles, so the compactive effort shears the clay plates into a parallel, face-to-face (dispersed / oriented) arrangement. Compaction dry of optimum instead produces the edge-to-face, random flocculated fabric. The dispersed fabric gives lower permeability and lower as-compacted strength — which is why clay liners are placed slightly wet of optimum.