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. A lower factor of safety is appropriate for the short-term condition — typically 1.2 to 1.3 against the 1.5 that the permanent condition must carry. The reason is not that the short-term case is unimportant but that for an excavated slope in clay it is not the critical case: the slope is at its strongest the moment the cut is finished and gets weaker with every month that passes.
The pore-pressure argument. Excavation removes total stress from the ground beneath and behind the cut face. In a saturated clay of low permeability the water cannot move quickly enough to respond, so the volume is held constant and the reduction in mean total stress is taken by the pore water as a negative excess pore pressure, $\Delta u \lt 0$. Effective stress on the potential slip surface is therefore temporarily higher than its long-term equilibrium value, the mobilised shear strength $\tau_f = c' + \sigma'\tan\phi'$ is correspondingly higher, and the computed factor of safety is at its maximum. With time the negative excess pore pressure dissipates — water is drawn into the clay from the exposed face, from rainfall and from any permeable layers — the pore pressures rise towards the long-term steady seepage values, the effective stresses fall, the clay swells and softens, and the factor of safety falls with them. The governing design case for a cut is therefore the long-term drained analysis in effective stresses, and that is where the full 1.5 belongs.
Why the short-term case can nevertheless be relaxed. Three practical reasons support the lower number. The exposure period is short and definable, so the probability of the design load or a design storm occurring while the temporary slope stands is much lower. The condition can be observed: a temporary cut can be instrumented with inclinometers and piezometers, walked daily, and closed or bermed if movement starts, so there is a warning mechanism that a permanent slope does not have. And the consequence of failure is generally smaller, because the works are under the control of the contractor and the public is excluded.
Where the relaxation is not safe. The undrained analysis is a $\phi_u = 0$ total-stress calculation, and it is only as good as $c_u$. In a fissured stiff clay the mass strength is far below the strength of an intact 38 mm triaxial specimen, softening along fissures begins within days rather than years, and progressive failure can propagate at an average mobilised strength well under the peak — London Clay cuttings are the classic record of exactly this. In a sensitive or quick clay an undrained failure is brittle and gives no warning at all. Sample disturbance, strength anisotropy and strain-rate effects all bias $c_u$, and a temporary works design usually rests on very few tests. So the rule is: 1.3 rather than 1.5 for a genuinely temporary, monitored cut in an intact clay of known strength; do not go below 1.3, and do not use the short-term case at all if the excavation will stand open through a wet season, will be surcharged by spoil or plant near the crest, or is in a fissured or sensitive clay.
The contrast worth stating. The reasoning reverses for an embankment built on soft clay. There the loading is positive, the excess pore pressure is positive, effective stress and strength are at their lowest immediately after construction, and the factor of safety increases as consolidation proceeds. For a fill the short-term undrained case is critical and must carry the full factor of safety; for a cut it is the long-term drained case. Confusing the two is the single most common error on this question.
