16-Civ-B3 Geotechnical Design · December 2016

Question 2 of 9: Shear-strength parameters for short-term slope stability in clay

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

Notes on this paper

Paper format. Professional Engineers Ontario / Engineers Canada National Examinations, December 2016 — 98-Civ-B3 Geotechnical Design. Three hours, OPEN BOOK, any non-communicating calculator. Section A carries five discussion questions of 7 marks each (answer any four); Section B carries four design questions of 24 marks each (answer any three); 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 timed attempt.

Reference texts (98-Civ-B3 / 16-Civ-B3 Geotechnical Design).

B. M. Das, Principles of Foundation Engineering, 9th ed. — subsurface exploration (Ch. 2), bearing capacity of shallow foundations (Ch. 3), settlement of shallow foundations including Schmertmann's strain-influence method (Ch. 5), retaining walls (Ch. 8), pile foundations (Ch. 11), drilled shafts (Ch. 12).
B. M. Das, Principles of Geotechnical Engineering, 9th ed. — shear strength (Ch. 12), lateral earth pressure (Ch. 13), slope stability (Ch. 15).
Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed. — the governing Canadian practice document for site investigation, in-situ testing, bearing resistance, deep foundations and earth-retaining structures.
R. F. Craig, Craig's Soil Mechanics, 9th ed. — effective stress, undrained versus drained behaviour, earth pressure, and the total-stress circular-arc slope analysis.
M. J. Tomlinson & J. Woodward, Pile Design and Construction Practice, 6th ed. — shaft adhesion in clay and under-reamed (belled) bored piles.
P. K. Robertson & K. L. Cabal, Guide to Cone Penetration Testing, 6th ed. — CPT interpretation and CPT-versus-SPT selection.

Sources of design charts and assumed values (page-1 Note 6). Note 6 requires the candidate to identify the source of every design chart and of every value assumed where the paper supplies none. They are named at the point of use and collected here:

Adhesion factor α = 0.55 for a drilled shaft in clay (Q6) — O'Neill and Reese (1999), reproduced in Das, Principles of Foundation Engineering, 9th ed., Section 12.9; the exclusion of the top 1.5 m and of one shaft diameter above the bell comes from the same source.
Bearing-capacity factor N_c^* = 9 (Q6) — Skempton (1951), as tabulated in Das, Section 11.11.
Overburden correction C_N = √(p_a/σ'_o) (Q7) — Liao and Whitman (1986), Das Principles of Geotechnical Engineering, Section 17.6.
SPT-to-friction-angle correlation (Q7) — Peck, Hanson and Thornburn (1974) as fitted by Wolff (1989); cross-checked against Kulhawy and Mayne (1990). Both are tabulated in Das, Principles of Foundation Engineering, 9th ed., Section 2.9.
Bearing-capacity factors and shape/depth factors (Q7) — Vesic (1973) and De Beer (1970), Das Sections 3.6 and 3.7.
Strain-influence diagram and the C₁, C₂ factors (Q7) — Schmertmann, Hartman and Brown (1978), Das Section 5.6; the modulus correlation E_s = 500(N₆₀ + 15) kPa is Bowles (1996), reproduced in the same section.
Rankine active coefficient for an inclined backfill (Q9) — Das, Principles of Geotechnical Engineering, 9th ed., Eq. (13.35); the base friction and adhesion reductions k₁ = k₂ = 2/3 are Das Section 8.4.
Unit weight of the submerged backfill (Q9) — assumed equal to the printed moist unit weight, 18 kN/m³, in the absence of a saturated value; the consequence of that assumption is bounded in the Q9 callout.

Section A

Question 2: Shear-strength parameters for short-term slope stability in 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.

For short-term stability of a slope in clay the appropriate parameters are the undrained parameters, c_u with φ_u = 0, used in a total-stress analysis. No pore-pressure term appears anywhere in the calculation, and the mobilised strength along the trial surface is simply c_u at the depth concerned.

The justification is a permeability argument. Clay has a hydraulic conductivity of the order of 10⁻⁹ m/s or less, so the time needed for the excess pore pressures generated by excavation or by placing a fill to dissipate is measured in years or decades, while construction takes weeks. Immediately after the change of total stress the clay therefore deforms essentially at constant volume: whatever the change in total stress, the change in effective stress is very small because the water carries it. Under those conditions the shear strength that can be mobilised is a fixed value set by the water content that existed before construction, and that value is c_u. Choosing total-stress parameters is not an approximation of convenience — it is the correct constitutive description of a saturated clay loaded faster than it can drain, and it has the practical advantage that the pore pressures, which are exactly what cannot be predicted reliably in the short term, never enter the equations.

The values are obtained from a field vane test (with Bjerrum's plasticity correction applied), from unconsolidated-undrained triaxial tests on good-quality tube samples, from unconfined compression tests, or from a CPTu using c_u = (q_t − σ_vo) / N_kt. The profile of c_u with depth matters more than any single number, and sensitivity S_t should be recorded because a sensitive clay that is sheared past peak loses most of its strength.

The statement in the question is true for an excavated slope or cut, and false for an embankment built on soft clay, and the reason is the sign of the excess pore pressure. In a cut, the total stresses are reduced by removing soil, which generates negative excess pore pressures. Immediately after excavation the pore pressures are low, the effective stresses are correspondingly high, and the slope is strong. As those negative excess pressures dissipate the pore pressures rise towards their long-term steady-seepage values, effective stresses fall, and the available strength falls with them; the clay also swells and softens. The factor of safety therefore decreases with time and the long-term (drained, effective-stress) case governs — which is precisely why cut slopes in stiff clay so often fail years after they were dug. For that geometry the statement is true.

For an embankment or fill placed on soft clay the argument reverses. Loading generates positive excess pore pressures, so the end-of-construction condition is the weakest the foundation will ever be. As consolidation proceeds the pore pressures dissipate, effective stresses and strength both increase, and the factor of safety rises with time. Here the short-term case governs and the statement is false; it is exactly this behaviour that staged construction exploits.

Two qualifications complete the answer. First, the long-term analysis must use c' and φ' with realistic pore pressures, and in stiff fissured clay the operational value of c' should be taken as zero or close to it, with φ' at or near the fully softened or residual value, because progressive failure prevents the peak cohesion intercept from being mobilised everywhere at once. Second, because the two conditions govern different geometries, competent practice checks both: undrained for the end of construction, drained for the design life, and for a fill on soft clay also the intermediate partially-consolidated stages.

Topic. Total-stress versus effective-stress slope analysis, and which of the two is critical for cuts and for fills.

Key relations. Undrained: $\tau_f = c_u$, $\phi_u = 0$, and for a circular arc $FS = c_u L_a R / (W \bar{x})$. Drained: $\tau_f = c' + (\sigma - u)\tan\phi'$. The link between them is $\Delta u = B\left[\Delta\sigma_3 + A(\Delta\sigma_1 - \Delta\sigma_3)\right]$, whose sign follows the sign of the total-stress change.

Why this works. A saturated clay sheared without drainage cannot change volume, so its strength is locked to its pre-construction water content and is a single number rather than a function of the applied normal stress. That is what makes φ_u = 0 legitimate. The long-term case is different only because the pore pressures have had time to reach a steady state that can be estimated from a flow net or a piezometric line, at which point the effective-stress strength law applies directly.

Common pitfall. Answering "the short-term case is always critical". That is true for embankments on soft clay and false for cuts, and stating it without the qualification is the most common way of losing marks on this question. A second pitfall is mixing the two systems — using c_u together with a pore-pressure term, which double-counts the water.

Source. Craig, Craig's Soil Mechanics, 9th ed., Section 9.2 (slope-stability analysis types) and Section 4.7 (undrained versus drained shear strength); Das, Principles of Geotechnical Engineering, 9th ed., Sections 12.10 and 15.6.

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