Multiple Choice with Justification: 07-Str-A3, May 2014, Q1

Question 1: Multiple Choice with Justification (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.

Given. Five short statements covering gradation and shear strength, gradation and permeability, the Proctor behaviour of three USCS groups, the effective friction angles of four soil types, and the fabric produced by compaction on the wet side of optimum.

Find. The correct selection in each case together with the soil-mechanics reasoning that decides it — the marks here are carried entirely by the justification, not by the choice.

Summary of answers
Part	Question (abbreviated)	Answer
(i)	Greater shear strength: Sand A ($C_u = 4$) or Sand B ($C_u = 1$)	Sand A
(ii)	Lower coefficient of permeability: Sand A, B or C	Sand C
(iii)	Higher dry density and higher optimum moisture content: GW, ML or CH	No single soil — GW gives the higher $\gamma_{d,\max}$, CH the higher OMC
(iv)	Higher $\phi'$ from a CD triaxial test: expansive clay, glacial till, silt or sand	Soil B — glacial till
(v)	Fabric of a clay compacted wet of optimum	Dispersed (oriented)

(i) Sand A, with $C_u = 4$

The coefficient of uniformity $C_u = D_{60}/D_{10}$ measures the spread of grain sizes. Sand B with $C_u = 1$ is the limiting case of a perfectly uniform soil: every grain is the same size, so the packing is that of equal spheres and no smaller particle is available to sit in the void between three larger ones. Sand A at $C_u = 4$ carries a range of sizes, the finer fraction occupies part of the void space, and at the same compactive effort the soil reaches a markedly lower void ratio.

Shear resistance in a cohesionless soil has two components. The first is sliding friction between mineral surfaces, which depends on mineralogy and surface roughness and is essentially identical for two quartz sands. The second is the work that must be done to lift grains over one another before they can slide — interlocking and dilatancy — and that component grows rapidly as the void ratio falls. Writing the peak angle as $\phi_{\text{peak}} = \phi_{cv} + \psi$, where $\phi_{cv}$ is the constant-volume angle and $\psi$ the dilatancy angle, the two sands share $\phi_{cv}$ but the well-graded Sand A develops the larger $\psi$. In practice a dense well-graded sand reaches $\phi_{\text{peak}} \approx 38^\circ$ to $45^\circ$, while a uniform sand at comparable effort rarely exceeds $32^\circ$ to $36^\circ$. Sand A is therefore the stronger soil in shear.

(ii) Sand C

Permeability in a granular soil is controlled not by the average grain size but by the size of the narrowest pore throats along the flow path, and those throats are set by the finest fraction present. Hazen’s relation $k \approx C\,D_{10}^{2}$ and the more general Kozeny–Carman expression, in which $k$ varies as $e^{3}/(1+e)$ divided by the square of the specific surface, both say the same thing: fines and a low void ratio each drive $k$ down.

Sand A is a uniform coarse sand — large grains, large voids, large $D_{10}$ — and is by far the most permeable of the three. Sand B is gap-graded: it has coarse grains and fine grains but nothing in between, so the fines are too few to fill the coarse skeleton completely and a network of open voids survives. Sand C is continuously (well) graded from coarse down to very fine, so each size fraction occupies the voids left by the fraction above it. That gives Sand C both the smallest $D_{10}$ and the lowest void ratio, and therefore the lowest coefficient of permeability. This is exactly why a well-graded material is specified for a compacted core or a low-permeability liner, and why filter and drainage layers are deliberately specified as uniform.

(iii) GW gives the higher dry density, CH the higher optimum moisture content — no one soil gives both

Maximum dry density and optimum moisture content are inversely related, so the question as posed has no single-soil answer, and saying so is the answer. Water in a Proctor test acts as a lubricant that lets particles slide into a denser arrangement; the finer and more plastic the soil, the more water its specific surface must first satisfy before any is left to lubricate, and the more water is held in the compacted mass at peak density. Consequently the soils that need the most water reach the lowest dry density.

Taking standard-Proctor values typical of Canadian practice: a well-graded gravel GW reaches $\gamma_{d,\max} \approx 20$ to $22\ \text{kN/m}^3$ at an optimum moisture content of roughly 7 % to 11 %; a low-plasticity silt ML reaches about $17$ to $18\ \text{kN/m}^3$ at 14 % to 18 %; and a high-plasticity clay CH reaches only $13$ to $16\ \text{kN/m}^3$ at 22 % to 30 %. GW therefore has the highest dry density and the lowest optimum moisture content, CH the reverse, and ML sits between them. The correct examination answer is to name GW for dry density, CH for optimum moisture content, and to state that no soil can be highest in both because the two quantities move in opposite directions along the USCS sequence.

Figure 1.1 — A standard-Proctor curve, showing why the fabric question in part (v) and the density question in part (iii) are two views of the same curve. Compacting dry of optimum leaves the clay platelets flocculated; compacting wet of optimum leaves them dispersed.

(iv) Soil B — glacial till

In a consolidated-drained triaxial test the pore pressure stays at its back-pressure value throughout, so the measured strength is a genuine effective-stress strength and $\phi'$ reflects gradation, angularity, density and mineralogy alone. Ranking the four soils on those grounds:

Soil B, glacial till — a very well-graded, angular, over-consolidated deposit that has already been compressed under an ice sheet. Its wide gradation gives dense packing, its angularity gives strong interlocking, and both feed the dilatancy term. Canadian tills routinely give $\phi' = 34^\circ$ to $45^\circ$; this is the highest of the four.
Soil D, sand — frictional but usually more uniform and more rounded than a till, giving $\phi' \approx 30^\circ$ to $36^\circ$.
Soil C, silt — low plasticity but a much larger specific surface and rounder, smaller grains, so interlocking is weak: $\phi' \approx 27^\circ$ to $32^\circ$.
Soil A, expansive clay — dominated by smectite platelets whose faces slide over one another on adsorbed water layers. This is the lowest of the four, with $\phi' \approx 12^\circ$ to $20^\circ$ and a residual angle that can fall below $10^\circ$.

The general rule the examiner is testing is that $\phi'$ falls as particles become smaller, rounder, more uniform and more platy, and glacial till is the only one of the four candidates that scores well on every count.

(v) A dispersed (oriented) structure

The fabric of a compacted clay is decided by the electrical forces between platelets at the moment of compaction, and those forces depend on how thick the diffuse double layer is. Compacting dry of optimum leaves the pore water in short supply, the double layers are suppressed, inter-particle attraction at the platelet edges dominates, and the compactive effort cannot overcome it — the particles lock into the random edge-to-face “card house” of Figure 2(A), the flocculated structure.

Compacting wet of optimum supplies enough water for the double layers to expand fully. Repulsion between the negatively charged platelet faces then dominates, inter-particle contact is lubricated, and the shear strains imposed by the roller or rammer are free to rotate the platelets into parallel alignment — the face-to-face arrangement of Figure 2(B), the dispersed or oriented structure. That is the answer to part (v).

The distinction matters in design as well as in theory. A clay compacted wet of optimum is less permeable (the parallel platelets close off the flow paths), more ductile, less prone to swelling, and less brittle on shearing, which is why liners and dam cores are specified 1 % to 3 % wet of optimum. A clay compacted dry of optimum is stiffer and stronger at small strain but is more permeable, more brittle and much more swell-prone on later wetting.

Topic: Gradation, compaction fabric and the drained friction angle — the four descriptors that a geotechnical engineer reads off an index test before any strength testing is done.

Key relations: $C_u = D_{60}/D_{10}$ and $C_c = D_{30}^2/(D_{10}D_{60})$ for gradation; Hazen $k \approx C\,D_{10}^2$ and Kozeny–Carman $k \propto e^3/[(1+e)S^2]$ for permeability; $\phi_{\text{peak}} = \phi_{cv} + \psi$ for the split between sliding friction and dilatancy; and the inverse pairing of $\gamma_{d,\max}$ with the optimum moisture content along the USCS sequence GW → ML → CH.

Why this works: All five parts reduce to one physical idea — how tightly the grains can be packed, and what fills the space between them. A wide gradation lets small grains occupy the voids left by large ones, which simultaneously raises density, raises interlocking and strength, and lowers permeability. A large specific surface (silt, and much more so clay) means a large volume of water is bound to particle surfaces rather than being available to lubricate, which simultaneously raises the optimum moisture content, lowers the achievable dry density and lowers $\phi'$. Fabric follows the same logic at the platelet scale: the amount of pore water present at compaction decides whether repulsion or edge attraction wins, and therefore whether the platelets end up parallel or randomly stacked.

Common pitfall: Answering part (iii) by naming a single soil. The pairing of high dry density with high optimum moisture content does not exist, and an answer that names one soil for both scores badly regardless of which soil is named. The second pitfall is part (ii): candidates often pick the soil with the visibly smallest grains rather than the one with the widest gradation, forgetting that it is the fines combined with the low void ratio of a continuous gradation that shuts down the flow paths.

Source: Das, Principles of Geotechnical Engineering, 9th ed., Ch. 2 (gradation parameters), Ch. 6 (compaction, structure of compacted clay), Ch. 7 (Hazen and Kozeny–Carman) and Ch. 12 (drained strength of granular soils); Holtz, Kovacs & Sheahan, An Introduction to Geotechnical Engineering, 2nd ed., Ch. 5, for the flocculated / dispersed fabric of compacted clays and its engineering consequences.