16-Civ-B3 Geotechnical Design · May 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. EGBC / Engineers Canada National Examination 16-Civ-B3 Geotechnical Design, May 2018. Three hours, open book, any non-communicating calculator. Section A — five discussion questions of 7 marks each, answer any four. Section B — four design questions of 24 marks each, answer any three. Examinable total $4\times 7 + 3\times 24 = 100$ marks. Page 1 Note 6 requires the candidate to identify clearly the source of every design chart and assumed value used, so the provenance of each correlation is named where it is used, not only in the concept notes. All nine questions are solved below, because the set is a study resource rather than a three-hour sitting.
Reference texts for this subject. B. M. Das, Principles of Foundation Engineering, 9th ed. (Cengage) — Ch. 3 (subsurface exploration and SPT corrections), Ch. 4 (bearing capacity), Ch. 5 (settlement, Schmertmann), Ch. 8 (retaining walls), Ch. 11–12 (pile foundations and drilled shafts); B. M. Das, Principles of Geotechnical Engineering, 9th ed. — Ch. 8 (shear strength), Ch. 15 (slope stability); R. D. Holtz, W. D. Kovacs & T. C. Sheahan, An Introduction to Geotechnical Engineering, 2nd ed.; Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed. — the Canadian design authority for the factors of safety and serviceability limits quoted here; L. C. Reese & M. W. O'Neill, Drilled Shafts: Construction Procedures and Design Methods (FHWA-HI-88-042).
Check — figure readings. Two dimensions are read from the drawings, as follows. (1) In Figure 2 the “1 m” dimension is the height of the bell: its arrows point inward at the flare, and scaling against the 4 m dimension on the same figure puts the bell base exactly on the 12 m line. The pile is therefore $L = 12$ m long with the bell top at 11 m, not 11 m long with its base floating 1 m clear of the layer base. (2) In Figure 3 the “0.35 m” label carries extension lines from the top and bottom corners of the base slab, so it is the base thickness; the “0.5 m” at the left is measured to the base underside, so only 0.15 m of soil covers the toe. The toe projection is not dimensioned and follows from the printed values as $4.0 - 0.3 - 2.0 = 1.7$ m. Figure 3 is not drawn to scale — its toe is drawn about half its dimensioned length — so the printed numbers govern, as page 1 Note 1 anticipates.
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 normally justified for the short-term condition of an excavated slope — typically 1.2 to 1.3 against the 1.5 demanded of the permanent slope — but only when the clay is intact and the undrained strength has been measured properly. In a stiff fissured clay, a sensitive clay, or where a short-term failure would be dangerous, the short-term factor must be raised back toward the long-term value. Both halves of that statement come out of the same mechanics, so the reasoning has to be set out before the number is chosen.
Excavating a slope unloads the ground. For a saturated clay of low permeability the removal of total stress occurs far faster than water can flow, so the response is undrained: the change in mean total stress generates a negative excess pore pressure, $\Delta u = B[\Delta\sigma_3 + A(\Delta\sigma_1-\Delta\sigma_3)]$, which for an unloading path is negative. The effective stresses on the potential slip surface are therefore temporarily higher than they will eventually be, and the available shear strength is correspondingly higher. As time passes the negative excess pore pressures dissipate, water flows toward the newly exposed face, the clay swells, effective stresses fall, and the factor of safety decreases monotonically with time. This is the exact opposite of an embankment built on soft clay, where the positive excess pore pressures generated by loading dissipate and the factor of safety rises with time. For a cut, the critical case is the long-term drained condition analysed in effective stresses with $c'$ and $\phi'$; the short-term undrained case analysed with $c_u$ and $\phi_u = 0$ is the safest moment in the life of the slope.
Three practical consequences follow. First, because the design is governed by the long-term case, the short-term check is not the controlling calculation, and demanding 1.5 of it wastes batter and money for a condition that will never be critical. Second, the exposure is brief and controllable: a temporary cut can be monitored, dewatered, protected from surface water, and backfilled on a known date, so the probability of the design event coinciding with the vulnerable period is low. Third, the consequence of a temporary failure is usually smaller. Those three arguments justify accepting $FS \approx 1.2$–$1.3$ for the short-term condition, which is the range the Canadian Foundation Engineering Manual and common provincial excavation practice recognise for temporary works.
The countervailing argument must be stated with equal force, because it is where short-term slopes actually fail. The undrained analysis rests entirely on $c_u$, and $c_u$ is not a soil constant: it depends on sampling disturbance, on the rate of shearing, on anisotropy, and above all on the presence of fissures. In a stiff fissured clay the strength of a 38 mm triaxial specimen may be two or three times the strength of the fissured mass, and progressive failure along fissures has produced short-term collapses in excavations that the $\phi_u = 0$ analysis declared safe by a wide margin. Sensitive clays behave the same way once strain localises. In addition, a saturated clay slope that is nominally undrained may in fact be partly drained by silt or sand laminations, so the true condition sits somewhere between the two analyses. Where any of these conditions applies, the short-term factor must be lifted back to 1.4–1.5, or the undrained analysis abandoned in favour of an effective-stress analysis with measured pore pressures.
Recommendation. Adopt $FS = 1.3$ for the short-term undrained condition of an excavated slope in an intact, well-characterised saturated clay, and check the long-term drained condition at $FS = 1.5$ as the governing case. Raise the short-term value to 1.5 for fissured, sensitive or laminated clays, or where failure would endanger people or adjacent structures.
