16-Civ-B3 Geotechnical Design · December 2017

Question 2 of 9: Short-term stability of a natural slope in soft clay

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. National Examinations, December 2017 — 16-Civ-B3 Geotechnical Design; three hours, open book, any non-communicating calculator. Section A holds five discussion questions worth 7 marks each of which four are marked; Section B holds four design questions worth 24 marks each of which three are marked, so the examinable total is 4 × 7 + 3 × 24 = 100 marks. All nine questions are worked below, because the set is a study resource rather than a marked script.

Reference texts. B. M. Das, Principles of Foundation Engineering, 8th–9th ed. (Cengage); B. M. Das, Principles of Geotechnical Engineering, 9th ed.; R. F. Craig / J. Knappett, Craig's Soil Mechanics, 9th ed.; Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed.; D. P. Coduto, Foundation Design: Principles and Practices; J. E. Bowles, Foundation Analysis and Design; ASTM D1586 (SPT), D5778 (CPTu), D2573 (field vane).

Source of design charts and assumed values (page 1, Note 6). Rankine active and passive coefficients from Das, Principles of Foundation Engineering, Ch. 7 (Eqs. 7.11 and 7.30); cantilever-wall stability procedure from Das Ch. 8 (Eqs. 8.11–8.14). Drilled-shaft adhesion factor alpha* = 0.55 and the 1.5 m surface exclusion from Reese & O'Neill (1989), tabulated in Das Ch. 12; bearing factor Nc* = 9 from Skempton (1951); block-failure check from Das Ch. 11 (Eq. 11.55). Compression index from Skempton's Cc = 0.009(LL − 10). Strain-influence factors and the C1, C2 corrections from Schmertmann, Hartman & Brown (1978) as presented in Das Ch. 5; Es = 500(N60 + 15) kPa from Das Table 5.7 (Bowles). Friction angle from the SPT via Wolff (1989), phi' = 27.1 + 0.3(N1)60 − 0.00054[(N1)60]², with the Liao & Whitman (1986) overburden correction; Vesic bearing-capacity, shape and depth factors from Das Tables 4.2 and 4.3. Every assumed value (unit weights of concrete, specific gravity for the void ratio, pile spacing, factors of safety) is stated in a callout beside the step that uses it.

Question 2: Short-term stability of a natural slope in soft clay (7 marks)

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.

What "short term" means, and what it requires. Immediately after a change in loading — a toe excavation, a fill placed at the crest, rapid erosion — a soft clay of low permeability has not drained, so the volume of the clay is unchanged and its shear strength is the undrained strength that existed before the change. The stability analysis is therefore a total-stress (phi_u = 0) analysis, and the pore pressures do not need to be known because they are carried implicitly inside c_u. This is the critical case for a cut or an excavation in clay, because subsequent swelling reduces the strength with time; it is not the critical case for an embankment on clay, where consolidation gains strength and the long-term condition is safer.

The parameters needed. Six groups: (i) the undrained shear strength profile c_u(z), including its increase with depth, its anisotropy and whether a desiccated or fissured crust caps the deposit; (ii) the bulk unit weight gamma, which supplies the driving weight and, with c_u, the tension-crack depth z₀ = 2c_u/gamma over which no shear resistance can be counted; (iii) the slope geometry — height H, angle beta, berms, and the depth to a firm stratum, since a deep-seated toe circle in a soft deposit is often more critical than a slope circle; (iv) the stratigraphy, in particular any thin silt or sand seams which would drain and invalidate the undrained assumption; (v) the sensitivity S_t and remoulded strength, because in a sensitive Champlain Sea or Leda clay a local failure can retrogress catastrophically; and (vi) external effects — surcharge at the crest, water in a tension crack, and the seismic coefficient if the case is a rapid loading event. Groundwater levels and effective-strength parameters c' and phi' are not needed for the short-term check itself, but they are collected in the same investigation because the long-term case must also be examined.

Site investigation. Begin with a desk study: geological maps, air photographs and LiDAR hillshade to identify old landslide scarps, hummocky ground and seepage lines, plus any records of previous instability. Follow with boreholes on at least two sections through the slope — crest, mid-slope and toe — taken to a depth well below the deepest plausible slip surface and continued into the firm stratum. Recover continuous undisturbed samples with thin-walled Shelby or, better, fixed-piston samplers of 75 mm or larger (an area ratio below 10 per cent), because SPT split-spoon samples are useless for strength testing in soft clay and the SPT N value itself is unreliable there. In parallel run field vane shear tests (ASTM D2573) at 0.5 to 1.0 m intervals, taking both peak and remoulded readings so the sensitivity is measured directly, and correct the peak values by Bjerrum's factor mu, which falls from about 1.0 at a plasticity index of 20 to about 0.6 at PI = 100. Push a CPTu profile beside the boreholes: it gives a continuous record that finds the thin drainage seams the boreholes miss, yields c_u = (q_t − sigma_v0)/N_kt with N_kt in the range 10 to 20 calibrated against the vane, and supplies the coefficient of consolidation from pore-pressure dissipation tests. Install standpipe piezometers and, where the slope is already moving, slope inclinometers to locate the active surface directly.

Laboratory programme and the analysis. On the recovered tubes run classification tests (water content, Atterberg limits, unit weight, grain size) on every sample, because w and PI anchor the Bjerrum correction and the c_u/sigma'_v0 normalisation; unconsolidated-undrained (UU) triaxial tests and unconfined compression tests for c_u; fall-cone or remoulded vane for the remoulded strength and hence S_t; consolidated-undrained triaxial tests with pore-pressure measurement on a few specimens to obtain c' and phi' for the long-term check and to confirm the stress history; and oedometer tests to establish the preconsolidation pressure, since for a normally consolidated clay c_u/sigma'_v0 should fall near 0.11 + 0.0037 PI (Skempton) and a measured value far from that flags disturbance. The stability itself is then evaluated with a total-stress circular-arc analysis, FS = c_uL_aR/(Wx), searching for the critical circle, or read directly from Taylor's stability number for a homogeneous deposit; the tension crack is introduced by terminating the arc at depth z₀. A short-term factor of safety of about 1.3 is normally required for a temporary condition, and 1.5 for a permanent one.

Topic. Total-stress (undrained, phi_u = 0) slope stability in soft clay, and the investigation that supplies its parameters.

Key relations. FS = c_uL_aR/(Wx) for a circular arc; Taylor's stability number N_s = c_u/(FS gamma H); tension-crack depth z₀ = 2c_u/gamma; Bjerrum's correction c_u(design) = mu c_u(vane); c_u = (q_t − sigma_v0)/N_kt from the CPTu; Skempton's c_u/sigma'_v0 = 0.11 + 0.0037 PI.

Why this works. In a saturated clay of very low permeability, loading applied over days produces essentially no drainage, so the effective stresses on the potential slip surface are the same as before the load was applied and the mobilised strength equals the pre-existing undrained strength. Because that strength is a single measured quantity rather than a friction law, the analysis needs no pore pressures — which is precisely why it is robust: pore pressures in a soft clay under transient loading are the hardest thing in the whole problem to predict, and the undrained formulation sidesteps them.

Common pitfall. Using uncorrected field-vane strengths, which over-predict the mobilised strength in plastic clays by up to 40 per cent, and assuming undrained behaviour across a deposit that contains silt partings, which drain in hours and make the short-term case a partly drained one. A third error is neglecting the fissured crust: it contributes almost no shear resistance and is where the tension crack forms.

Source. Das, Principles of Geotechnical Engineering, Ch. 15 (slope stability) and Ch. 12 (shear strength); Craig's Soil Mechanics, Ch. 12; Canadian Foundation Engineering Manual, 4th ed., Ch. 4 (site investigation) and Ch. 6.

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