16-Civ-B3 Geotechnical Design · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examinations, December 2019 — 16-Civ-B3 Geotechnical Design. Three hours, open book, any non-communicating calculator. Section A holds five discussion questions worth 7 marks each (answer any four); Section B holds four design questions worth 24 marks each (answer any three). The examinable total is therefore 4 × 7 + 3 × 24 = 100 marks. Page-1 Note 3 sets the answer-any-four / any-three rule, and Note 6 requires the candidate to name the source of every design chart and of every assumed value — so every chart read, correlation and assumption below is attributed where it is used. All nine questions are solved here, because the set is a study resource rather than a timed sitting.
Reference texts. B. M. Das, Principles of Foundation Engineering, 9th ed. (bearing capacity, elastic settlement, retaining walls, drilled shafts); B. M. Das, Principles of Geotechnical Engineering, 9th ed. (shear strength, lateral earth pressure, slope stability); Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed. (Canadian practice, factors of safety, in-situ testing); R. F. Craig, Craigʹs Soil Mechanics, 9th ed. (effective stress, undrained strength); D. P. Coduto, Foundation Design: Principles and Practices, 2nd ed. (shallow-foundation design, settlement serviceability).
Check — conventions used throughout this paper. Unit weights printed on the figures are treated as bulk (saturated below any water table); effective unit weights use γw = 9.81 kN/m3. Reinforced concrete is taken at γc = 24 kN/m3 (CFEM 4th ed.; the exam gives no value), and Question 8 shows that the conclusion is unchanged anywhere in the 23–25 kN/m3 range. Where the paper omits a number the solution needs, the assumption is stated at the point of use and its influence on the answer is quantified, as page-1 Notes 1 and 7 invite.
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.
Why sand is the reference material. A free-draining granular backfill does three things for a retaining wall, and it is easiest to see the problems with an expansive clay by noting that it fails at all three. Sand dissipates water so no pore pressure builds against the stem; it has no volume change with moisture content, so the pressure the wall was designed for is the pressure it receives for the life of the structure; and it reaches its active state with a small wall movement, so a wall designed for Ka genuinely experiences Ka. An expansive clay — a high-plasticity clay rich in smectite, of which the Regina, Winnipeg and Lake Agassiz clays are the familiar Canadian examples — provides none of these.
The problems, in order of severity. The first and worst is swelling pressure. On wetting, a compacted expansive clay confined by a wall cannot expand, so it develops a horizontal pressure that bears no relation to Kaγz. Swelling pressures of 100 to 400 kPa are routinely measured in oedometer tests on such clays, which for a 6 m wall can exceed the active thrust several times over; the pressure is also nearly uniform with depth rather than triangular, so it produces a much larger overturning moment than the same resultant applied at H/3. Second is cyclic shrink–swell ratcheting: the clay swells in the wet season and pushes the wall out, then shrinks in the dry season and leaves a gap that fills with debris and water, so the wall walks progressively outward and never recovers its position. Third, the clayʹs low permeability means water that reaches the backfill cannot escape, so full hydrostatic pressure can develop behind the wall — and water pressure is not reduced by any earth-pressure coefficient, so it typically doubles the design thrust.
Beyond those, desiccation cracks open to depths of a metre or more in dry weather and then act as direct conduits for surface water to the base of the wall, applying a hydrostatic wedge pressure in the crack itself; the clay loses strength on wetting, so the φʹ assumed in design may not be there when it is needed and the long-term operative strength drifts towards a residual value; the material is frost susceptible and can generate ice-lens pressures in the upper metres of a Canadian wall; it creeps, so lateral pressure tends towards at-rest or higher over decades rather than staying at active; it is difficult to compact within a narrow acceptable moisture band, and over-compaction dry of optimum guarantees later swelling; and its low permeability plus high compressibility make long-term settlement of anything founded on or behind the wall a separate problem.
Precautions and design measures. The single most effective measure, and the one to lead with, is to keep the clay away from the stem. A wedge of imported free-draining granular fill placed against the back face, wide enough that its inner boundary lies outside the active failure plane (a rule of thumb is a width of at least H/2, and never less than about 1 m for constructability), means the wall is loaded by sand and the clay merely surcharges the granular wedge. Only a small fraction of the total backfill volume has to be imported, so the cost is far below that of replacing the whole backfill. A geotextile filter on the clay/granular interface stops the fines migrating in and clogging the wedge, and a geocomposite drainage sheet against the stem is a compact alternative where space is tight.
Drainage must then be positive and redundant: a perforated collector pipe in a filter surround at the base of the wedge, discharging to a positive outlet clear of the footing; weep holes through the stem at 1.5 to 3 m centres as a second path; and the whole system detailed so it can be inspected and rodded. The surface behind the wall should be sealed — paved, or capped with a metre of low-permeability fill and graded to fall away — so that infiltration, and with it the moisture cycling that drives the swelling, is minimised. A vertical moisture barrier or capillary break at the outer edge of the granular wedge is a proven detail in expansive-soil regions.
The wall itself should then be designed for the pressure it will actually receive, not for Ka. Where clay remains within the zone of influence, design for at-rest pressure K0 = 1 − sinφʹ, or for the measured swelling pressure from an oedometer test on the compacted clay at its placement condition, whichever is larger, and treat that pressure as approximately uniform with depth. Full hydrostatic pressure should be carried as a design case unless drainage is demonstrably reliable. If the clay must be reused in bulk, treat it: lime stabilisation at 4 to 6 per cent by mass reduces plasticity index and swell potential markedly and is the standard remedy, with cement or a lime–flyash blend as alternatives; compact wet of optimum to a moderate density, since a clay placed dense and dry has the greatest swell potential; and consider geogrid-reinforced granular layers to build a reinforced-soil block that carries the load independently of the clay. Finally, prefer a wall system that tolerates movement — a reinforced-soil wall with a flexible facing, or a cantilever wall with articulated joints — over a rigid gravity wall, and instrument an important wall with inclinometers and pressure cells so that ratcheting is detected before it becomes structural damage.
Check — order of magnitude. For the 6 m wall in question, an active thrust on a granular backfill (γ = 19 kN/m3, φʹ = 34°, Ka = 0.283) is about 97 kN/m acting at 2 m above the base, giving roughly 194 kN·m/m of overturning moment. An expansive clay developing a uniform 150 kPa of swelling pressure over the same height applies 900 kN/m at 3 m, i.e. about 2700 kN·m/m — roughly fourteen times the moment. That ratio, not any refinement of Ka, is the reason the granular wedge is the answer rather than a thicker stem.
