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.
Every remedial measure available to a geotechnical engineer acts on one of the two terms in the definition of the factor of safety, FS = (shear strength available along the surface) / (shear stress mobilised along it). Figure 2 shows a slope whose curved slip surface passes through the slope mass and daylights near the toe, with an interface at the crest, so the mechanism is a rotational slide. That geometry means the driving term is dominated by the weight of the upper part of the mass and the resisting term by the strength along the lower part of the arc. Four genuinely different measures follow, and it is worth grouping them by which term they attack.
1. Change the geometry — flatten, bench or unload the crest. Cutting the face back to a gentler angle, or removing a wedge of soil from the head of the slide, reduces the driving moment directly because the material removed is the material with the longest lever arm about the centre of rotation. Benching adds the further benefit of intercepting surface runoff. This is normally the cheapest option where land is available, and the only one that improves stability without introducing anything that can later deteriorate.
2. Add resisting weight at the toe — a counterweight berm or shear key. Placing free-draining granular fill over the toe increases the normal stress on the lower part of the arc, where the surface is close to horizontal and additional weight therefore adds much more resistance than driving force. A berm is quick, uses locally available material, and can be combined with toe drainage. Its limitation is that it must not load a soft stratum enough to trigger a deeper mechanism, and it consumes land at the toe where roads or watercourses often sit.
3. Lower the pore water pressure — surface and subsurface drainage. Discussed in detail below.
4. Add tensile or structural reinforcement. Soil nails, ground anchors tied to a facing, a row of stabilising piles through the slip surface into the firm base, or a toe retaining structure all add a resisting force that the soil itself cannot supply. Geosynthetic reinforcement layers do the same in a reconstructed slope. Reinforcement is the option of choice where the geometry cannot be changed and the slide is shallow enough to pin, but it is the most expensive per metre and needs the most design attention, because the reinforcement must be long enough to reach beyond every plausible surface, not just the one analysed.
Two further measures deserve mention even though the question asks only for four: ground improvement of the sliding mass itself (lime or cement stabilisation, jet grouting, stone columns, or in a cohesive slope electro-osmosis) raises the strength term, and protection of the toe against erosion (riprap, gabions, a revetment) prevents the loss of the passive support on which the whole slope depends. A slope that has already reached FS < 1 has usually failed for a combination of reasons, so the remedy is commonly a combination too — typically regrading plus drainage.
Measure 3 in detail — drainage. Drainage is discussed here because it is almost always the most cost-effective intervention, and because it is the one whose mechanism is most often stated loosely. Along any element of the slip surface the available shear strength is governed by effective stress:
$$\tau_f = c^{\prime} + (\sigma_n - u)\tan\varphi^{\prime}$$Draining the slope does not change cʹ, φʹ or the total normal stress σn — the soil is the same soil and the geometry is unchanged. What it changes is u. Every kilopascal of pore pressure removed adds tanφʹ kilopascals of shear strength along the whole surface, and it does so without adding a single kilonewton of driving weight. That asymmetry is the reason drainage buys more factor of safety per dollar than anything else: in a slope with φʹ = 30° and a piezometric level 3 m above the slip surface, drawing that level down to the surface recovers roughly 17 kPa of shear strength at every point on the arc. Expressed through the pore pressure ratio ru = u/(γh), the same statement is that a reduction in ru from 0.4 to 0.2 typically lifts FS by 20 to 30 per cent for a cohesive-frictional slope.
In practice the works come in two layers. Surface drainage stops water entering: the crest is graded away from the slope, a lined interceptor ditch is cut behind the crest, tension cracks are sealed, and the face is vegetated or membrane-covered to limit infiltration and protect against erosion. Subsurface drainage removes water that is already in the ground: sub-horizontal drains drilled into the face and discharging by gravity are the standard tool for a slide of this size, supplemented where necessary by a counterfort or trench drain running down the slope, a granular blanket under a berm, or relief wells and pumped wells where the water is under artesian pressure from a deeper aquifer. Filter protection is essential at every interface, or the drains silt up and the measure quietly reverses.
Two cautions belong with the recommendation. First, drainage acts over time — in a clay slope the pore pressures may take months to respond, so it is not an emergency measure for a slope already moving. Second, its benefit persists only as long as the drains do, which makes piezometric monitoring and a maintenance commitment part of the design rather than an optional extra. On a Canadian site the seasonal cycle matters as well: the critical case is usually spring thaw with a perched water table on still-frozen ground, and discharge points must be detailed so they do not freeze shut in winter.
