07-Str-B1 · Undated paper
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Examinations — May 2019 — 07-Str-B1 Geotechnical Design. Three-hour, OPEN-BOOK exam; any calculator is permitted provided the candidate records its make and model. Format: Section A carries five discussion questions of 7 marks each, of which the candidate answers any four; Section B carries four problems of 24 marks each, of which the candidate answers any three (4 × 7 + 3 × 24 = 100 marks). Every question is worked here, because the set is a study resource rather than a marked script.
Reference texts: Das, B.M., Principles of Foundation Engineering (9th ed., Cengage) — SPT-based allowable bearing pressure, Terzaghi bearing capacity, drilled-shaft capacity, retaining walls, sheet-pile walls; Das, B.M., Principles of Geotechnical Engineering (9th ed., Cengage) — effective stress, shear strength, lateral earth pressure; Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM, 4th ed., 2006) — Canadian practice for site investigation, SPT and CPT interpretation, tolerable settlement, raft and deep foundations; Craig, R.F. / Knappett, J.A., Craig's Soil Mechanics (8th ed., CRC Press) — undrained strength, slope stability, anchored sheet-pile design; Reese, L.C. and O'Neill, M.W., Drilled Shafts: Construction Procedures and Design Methods (FHWA) — the alpha method for shafts in clay.
Assumptions declared once, applied throughout. Unit weight of water $\gamma_w = 9.81\ \text{kN/m}^3$; atmospheric reference pressure $p_a = 101.3\ \text{kPa}$; the SPT blow counts quoted in Question 6 are already corrected to $N_{60}$, as the paper states, so no further energy or overburden correction is applied. All wall and sheet-pile results are per metre run of wall. Where the paper says "make suitable assumptions providing justification", the assumption is stated in a highlighted note beside the step that uses it, in the form the exam rubric asks for.
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.
Answer: FALSE as the statement is written, because it asserts the result for two named soils rather than for a stated condition. The $\phi_u = 0$ result is a consequence of full saturation, not of a soil being a clay, and neither an expansive clay nor a glacial till can be assumed to be fully saturated in the state in which either is normally sampled and tested.
Why full saturation gives a horizontal envelope. In an unconsolidated undrained test the drainage line is closed from the moment the cell pressure is applied. If the specimen is saturated, Skempton's pore-pressure parameter $B$ is unity, so an increase in cell pressure $\Delta\sigma_3$ produces an equal increase in pore pressure, $\Delta u = \Delta\sigma_3$, and the effective confining stress is unchanged. Every specimen of the same clay, tested at any cell pressure, therefore fails at the same effective stress state and the same deviator stress. The total-stress Mohr circles all have the same diameter, the common tangent is horizontal, and the interpretation is $\phi_u = 0$ with $c_u = q_f/2$. This is a statement about the test and the degree of saturation, not a material property.
Soil A, expansive clay. If a saturated specimen is recovered from below the water table, the argument above applies exactly and $\phi_u \approx 0$. But expansive clays are engineering problems precisely because they are found above the water table in the seasonally active zone, desiccated, with a degree of saturation well below 100 per cent and a large negative pore-water pressure. In an unsaturated specimen $B \lt 1$: part of every cell-pressure increment compresses the air voids and passes into the soil skeleton, so the effective stress rises with cell pressure, the Mohr circles grow, and the envelope is a curve of decreasing slope with an apparent $\phi_u$ that can be 10 to 20 degrees at low cell pressures. Only once the air has been driven into solution at high cell pressure does the envelope flatten to the horizontal.
Soil B, glacial till. Till is the harder case for the statement. It is a dense, heavily over-consolidated, extremely well-graded deposit containing everything from clay to cobbles, and it very commonly has a degree of saturation of 85 to 95 per cent rather than 100. The same partial-saturation argument therefore applies, and unconsolidated undrained tests on till routinely return an apparent $\phi_u$ of the order of 5 to 20 degrees. There is a second, independent reason: a 38 mm or 50 mm triaxial specimen of a gravelly till is not a representative element of the deposit at all. Individual gravel particles produce interlock and dilation during shear, the failure is not a clean single plane, and the measured "undrained strength" is partly frictional in the mechanical sense. The scatter between nominally identical till specimens is often larger than the difference the question is asking about.
The complete answer. The correct statement is conditional: $\phi_u = 0$ for any soil, clay or otherwise, that is fully saturated and sheared without drainage, and the result fails for any soil that is not. For a desiccated expansive clay and for a typical unsaturated glacial till the statement as printed is false. In practice, the safe design route for both soils is to measure the effective-stress parameters $c'$ and $\phi'$ in consolidated tests with pore-pressure measurement, and to use the undrained strength only where the field problem is genuinely undrained and the ground genuinely saturated.
