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24-Bld-A6 Geotechnical Materials and Analysis · December 2017

Question 1 of 7

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

07-Bld-A6 Geotechnical Materials and Analysis — National Exam, December 2017. Closed book, 3 hours; drawing instruments and either a Casio or Sharp approved calculator required; the formula sheet and influence charts printed at the back of the exam are reproduced/used inline where needed. Section A (Questions 1–3, 40 marks, answer all) and Section B (Questions 4–7, 20 marks each, the paper asks for any three of four) — all seven questions are answered below.

Reference texts: B. M. Das, Principles of Geotechnical Engineering, 9th ed. (phase relations, seepage/flow nets, stress distribution, consolidation, shear strength); R. F. Craig / J. Knappett, Craig's Soil Mechanics, 9th ed. (flow nets, effective-stress strength parameters); Canadian Foundation Engineering Manual (CFEM), 4th ed.

Check — assumptions and source notes for this paper. (1) Question 4's flow net (Nf = 5 flow channels, Nd = 14 equipotential drops, point A read as three drops upstream of the downstream exit, exit-field length ≈ 2 m) is used with a soil total unit weight of 20 kN/m³. (2) Question 5(ii)'s "approximate" method is extended from the formula sheet's centre-of-rectangle formula to a corner point (point A here is not centred on the loaded area) using the standard mirror/quartering superposition trick, valid because the approximate formula is linear in load exactly like the exact one. (3) Question 6's least-squares fit through the three effective-stress points gives an intercept of −0.7 kPa — not distinguishable from zero with only three data points — so c′ is taken as 0, consistent with the expected behaviour of a normally consolidated clay. (4) Question 7's figure shows three distinct layer thicknesses — H1 = 1.5 m (sand above the water table), H2 = 1.5 m (sand below the water table), H3 = 2 m (the clay layer, void ratio e = 0.75) — and all three values are used below.

Question 1 (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.

(i) Answer: True. The submerged (buoyant) unit weight follows $$\gamma' = \frac{(G_s-1)\gamma_w}{1+e},$$ and for a normal mineral soil ($G_s\approx2.65$–2.80) this is lower than $\gamma_w$ only when the void ratio is large. Question 2 of this very paper supplies exactly such a soil ($G_s=2.75$, $e=9.0$, a highly expansive clay): substituting gives $\gamma'=(1.75)(9.81)/10=1.72$ kN/m³, well below $\gamma_w=9.81$ kN/m³. So the statement is demonstrably true for high-void-ratio soils, even though for a typical medium-dense sand ($e\approx0.6$) $\gamma'\approx10.8$ kN/m³ is above $\gamma_w$ — the statement only requires that it CAN be lower, not that it always is.

(ii) Answer: False. There is no physical upper bound of 100% on the liquid limit; LL is simply the water content at which a remoulded soil-water paste closes a standard groove after 25 blows, and highly plastic clay minerals (montmorillonite/bentonite-rich clays) routinely test at LL well above 100%, in some cases several hundred percent. The "highly expansive clay" of Question 2 (with a natural water content of 311%) is itself a strong hint that such soils exist on this exam — a soil that can hold over three times its dry mass in water at its natural state plainly has a liquid limit far above 100%.

(iii) Answer: True. Permeability in a granular/coarse soil is governed almost entirely by the size of the smallest interconnected pore throat, which in turn is set by the finest particles present, not by the average particle size. A well-graded soil has a continuous range of particle sizes, so smaller grains settle into the voids between larger ones, producing a denser packing with a smaller effective pore diameter and hence lower permeability. A poorly graded (uniformly sized) soil has no such infilling: its pores stay large, open, and well-connected, giving a distinctly higher coefficient of permeability for the same nominal particle size range.

(iv) Answer: False (taking the statement, in the context of this paper's own Question 6 on CU triaxial testing, to mean the EXCESS pore pressure generated during undrained shear loading). A normally consolidated clay is contractive under shear: as it is sheared undrained it "wants" to compress, and because undrained loading prevents any volume change, that tendency is expressed instead as a rise in pore pressure. The excess pore pressure generated by an NC clay under undrained shear is therefore always positive, never negative — Question 6's own data (deviator stress increments of 103, 202, 305 kPa producing pore-pressure increments of 82, 169, 252 kPa, all positive and all a large fraction of the deviator stress) is a direct illustration. Negative excess pore pressure (dilation) under undrained shear is the signature of a heavily OVER-consolidated clay, not a normally consolidated one.

(v) Answer: True. The triaxial cell is the most versatile shear-strength apparatus in routine use: by controlling the drainage valves and the rate of loading, the same equipment performs unconsolidated-undrained (UU), consolidated-undrained (CU, with or without pore-pressure measurement), and consolidated-drained (CD) tests, and specimens can be prepared from sands (usually tested CD or CU with saturation by back-pressure) as readily as from clays. This flexibility — independent control of confining stress, drainage condition, and loading rate on one apparatus — is exactly why it is the standard laboratory shear test referenced throughout this exam (Question 6 uses it in CU mode).

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