07-Str-A3 · December 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC / Engineers Canada National Examination — Structural Engineering (legacy), 07-Str-A3 Geotechnical Materials and Analysis, December 2013. Three hours; closed book; one Casio or Sharp approved calculator; drawing instruments required; all required charts and equations are supplied at the back of the paper (Fadum influence chart, Newmark chart with $I_N = 0.005$, and a two-page formula sheet). Total value 100 marks over six compulsory questions (20 + 10 + 10 + 20 + 20 + 20). Every question and every sub-part is solved in full below.
Reference texts: Das, Principles of Geotechnical Engineering, 9th ed. (Ch. 3 weight–volume relationships, Ch. 6 compaction, Ch. 7 permeability, Ch. 8 seepage, Ch. 9 in-situ stresses, Ch. 10 stresses in a soil mass, Ch. 11 consolidation, Ch. 12 shear strength); Knappett & Craig, Craig’s Soil Mechanics, 8th ed. (Ch. 3 effective stress and artesian profiles, Ch. 5 shear strength and stress-path plots); Holtz, Kovacs & Sheahan, An Introduction to Geotechnical Engineering, 2nd ed. (compacted-fill fabric); Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed. — the governing Canadian practice document for settlement, excavation heave and factors of safety; ASTM D698 / D1557 (Proctor compaction), ASTM D7181 (consolidated-drained triaxial).
Check — two printing slips in the source, carried as stated. (a) The Question 1 header reads “(4 × 5 = 20 marks)” but five statements (i)–(v) are printed; the solution treats the question as 5 × 4 = 20 marks and answers all five. (b) Question 5 is valued at 20 marks while its printed sub-part marks are 5 + 7 + 7 = 19; the missing mark is assumed to sit with part (a), and all three parts are answered in full. Neither slip changes any calculation.
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. A fine-grained soil compacted at a fixed compactive effort over a range of moulding water contents, producing the standard Proctor curve of dry unit weight against water content.
Find. (i) the curve with the dry side, the optimum and the wet side identified; (ii) a definition of the two sides in no more than thirty words; (iii) a comment on how unconfined shear strength differs between the two.
Approach. Locate the peak of the curve, define the two branches relative to it, then explain the strength difference through the fabric the two branches produce rather than through the density alone — because at equal dry density one specimen from each branch can be found, and they still behave quite differently.
At a fixed compactive effort the dry unit weight rises with water content up to a maximum $\gamma_{d,\max}$ at the optimum moisture content (OMC), then falls away, running roughly parallel to and below the zero-air-voids line. Everything to the left of the OMC is the dry side; everything to the right is the wet side. The zero-air-voids curve,
$$\gamma_{zav} = \frac{G_s\gamma_w}{1 + wG_s}$$
is the theoretical limit at $S = 100\ \%$; a real compaction curve can approach it on the wet side but can never touch or cross it, and a data point that appears to do so means the water content or $G_s$ is in error. The specimen of Question 2, at $S = 65\ \%$, sits on the dry side.
Dry side: water content below optimum, air-filled voids, flocculated random fabric. Wet side: water content above optimum, near-saturated, particles dispersed parallel; added water now displaces solids and lowers density. (30 words)
The unconfined compression test gives $q_u$, and the undrained shear strength is $s_u = q_u/2$. Two effects pull in opposite directions across the curve. Density rises to the OMC and falls after it, which alone would make strength peak at the optimum. But suction falls monotonically as water is added: on the dry side the air–water menisci in the partly saturated voids generate a large negative pore pressure that acts as an extra effective confining stress, and on the wet side that suction has all but vanished.
The two effects combine so that the strength maximum sits slightly dry of optimum, typically 1 % to 3 % below OMC, not at it. Moving further wet of optimum, $q_u$ falls steeply — commonly by a factor of two to four between 2 % dry and 3 % wet — even though the dry density has changed only slightly. The behaviour differs in kind as well as in magnitude:
| Property | Compacted dry of optimum | Compacted wet of optimum |
|---|---|---|
| Fabric | Flocculated, random, edge-to-face | Dispersed, particles oriented parallel |
| Unconfined compressive strength $q_u$ | Higher (peaks ~1–3 % dry of OMC) | Lower, falling steeply with added water |
| Stress–strain response | Stiff, brittle, distinct peak then softening | Soft, ductile, plastic, no sharp peak |
| Permeability | Higher (by up to two orders of magnitude) | Lower — the reason liners are placed wet |
| Volume-change risk | Swells on wetting; collapse potential | Shrinks on drying; higher compressibility |
| Typical use | Structural fill, embankment shoulders | Clay cores, landfill and pond liners |
The engineering consequence is that “which side of optimum” is a design decision, not a construction accident. A structural fill that must be stiff and strong is specified dry of optimum; a dam core or a landfill liner that must be tight and must tolerate differential movement without cracking is specified 1 % to 3 % wet of optimum, deliberately accepting the lower strength in exchange for the lower permeability and the ductile response. Canadian practice states the requirement as a percentage of standard or modified Proctor maximum density together with an allowable water-content window relative to OMC, precisely so that both effects are controlled.
Check — the plotted curve is illustrative. The question asks for a typical Proctor curve and supplies no test data, so the figure above uses representative values ($\gamma_{d,\max} = 18.3\ \text{kN/m}^3$ at OMC = 14 %, $G_s = 2.70$ for the zero-air-voids line). Only the shape and the position of the two branches relative to the peak are being examined.
