16-Civ-B3 Geotechnical Design · December 2014

Question 2 of 10: Shear-strength parameters for long-term slope stability in expansive soil

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 2014 — 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 five design questions of 24 marks each (answer any three); the examinable total is 4 × 7 + 3 × 24 = 100 marks. All ten 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. — bearing capacity (Ch. 3), stress increase in a soil mass (Ch. 6), retaining walls (Ch. 8), pile foundations (Ch. 11).
B. M. Das, Principles of Geotechnical Engineering, 9th ed. — lateral earth pressure (Ch. 13), shear strength (Ch. 12), slope stability (Ch. 15), subsurface exploration (Ch. 17).
Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed. — the governing Canadian practice document for site investigation, bearing resistance, deep foundations and earth-retaining structures.
R. F. Craig, Craig's Soil Mechanics, 8th ed. — earth pressure theory and slope stability.
D. P. Coduto, Foundation Design: Principles and Practices, 2nd ed. — in-situ testing and SPT correlations.
J. E. Bowles, Foundation Analysis and Design, 5th ed. — bearing capacity factors and retaining-wall stability tables.

Sources of charts and assumed values (page-1 Note 6). Note 6 of this paper requires the candidate to identify the source of every design chart and every assumed value. Each chart reading and each assumption below is therefore named where it is used, and the values assumed in the absence of data are collected here:

Q6 — adhesion factor α from Das, Principles of Foundation Engineering, Table 11.6 (Terzaghi, Peck & Mesri form, α against $c_u/p_a$); $\lambda$ from Vijayvergiya & Focht (1972) as tabulated by Das, Table 11.7.
Q7 — overburden correction $C_N$ from Liao & Whitman (1986); $\phi'$ from Wolff (1989) and from Hatanaka & Uchida (1996), both reproduced in Das, Ch. 2; settlement-controlled bearing pressure from Meyerhof (1965) as given by Das, Ch. 5, used only as a serviceability check because the question forbids direct correlations of bearing capacity to penetration index. Table I prints the blow counts as field values $N_f$; with no hammer data they are converted as $N_{60} = N_f$, i.e. a safety hammer at the reference 60 per cent energy ratio with borehole, sampler and rod-length factors of 1 (Das, Ch. 2, hammer-efficiency and correction-factor tables).
Q8 — embankment influence factor from Osterberg (1957), reproduced as Das Fig. 6.24; the closed form of that chart is used so the reading carries no chart-scaling error.
Q9 — Meyerhof general bearing-capacity equation with the shape factors of De Beer (1970) and the depth factors of Hansen (1970), as set out in Das, Ch. 3.
Q10 — Coulomb active earth-pressure coefficient, Das Eq. 13.31; unit weight of the mass-concrete wall assumed $\gamma_c = 24\ \text{kN/m}^3$ (CFEM 4th ed., normal-density concrete), the only value the figure does not supply.

Question 2: Shear-strength parameters for long-term slope stability in expansive soil (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.

Long-term stability is by definition a drained condition, so the analysis must be carried out in effective stresses using the drained parameters $c'$ and $\phi'$, with the pore pressures taken from the steady-state seepage condition rather than from the end of construction. That much is common to every clay slope. What is specific to an expansive clay is which drained parameters, because the peak drained envelope measured on an intact specimen is not the strength that will be available on a slip surface decades later.

The parameters recommended are therefore:

Where no pre-existing shear surface exists: the fully softened strength, that is $c' = 0$ with the fully softened friction angle $\phi'_{fs}$, measured on a normally consolidated, remoulded specimen in a drained direct shear or consolidated-undrained triaxial test with pore-pressure measurement.
Where a pre-existing slip surface, bedding-plane shear or old landslide is present: the residual strength, $c'_r = 0$ and $\phi'_r$, measured in a ring-shear apparatus (Bromhead) or by reversal direct shear.

Three mechanisms make the peak parameters unsafe in this soil. First, an expansive clay is a high-plasticity clay whose volume changes with water content. Seasonal wetting and drying opens a network of fissures to depths of several metres; each fissure is a plane of near-zero cohesion, and the mass strength collapses towards the strength of the fissure walls. Any $c'$ intercept measured on an intact 38 mm triaxial specimen simply does not exist at the scale of a slope.

Second, swelling on wetting destroys the suction and the diagenetic bonding that produced the cohesion intercept in the first place. Skempton's classic observation on Brown London Clay is that a cut slope in a stiff fissured clay stands for years and then fails at a mobilised strength corresponding to $c' = 0$ — the fully softened condition — because water has slowly entered the fissures and swelled the clay to a normally consolidated state. The delay between excavation and failure is exactly the delay required for negative excess pore pressures to dissipate and for softening to progress.

Third, stiff clays are strain-softening: peak strength occurs at a small strain and falls away as displacement continues. Along a curved slip surface the local displacement is not uniform, so the peak cannot be mobilised everywhere at once. Progressive failure propagates from the toe, and the average strength available at collapse lies between peak and residual. Where movement has already occurred — a reactivated slide, a bedding-plane shear, a slope showing tension cracks — the clay platelets on the shear plane are fully aligned and the residual value, which for a high-plasticity clay can be as low as 8° to 12°, is the only defensible choice.

Two practical points complete the answer. The pore pressures must correspond to the long-term steady seepage regime, taken from piezometers and a flow net, and should include the worst credible condition (a wet-season perched water table, a blocked drain). And in an expansive clay the seasonal swelling pressure itself imposes a horizontal stress that can approach the passive value in the active zone; where a structure is founded within that zone this must be carried as a load, not ignored.

Topic: drained shear-strength parameters, peak against fully softened against residual, in stiff fissured and expansive clays.

Key relations: $\tau_f = c' + \sigma' \tan\phi'$ (peak); $\tau_{fs} = \sigma' \tan\phi'_{fs}$ (fully softened, $c' = 0$); $\tau_r = \sigma' \tan\phi'_r$ (residual); factor of safety $FS = \dfrac{\sum \left[c' \ell + (W\cos\alpha - u\ell)\tan\phi'\right]} {\sum W \sin\alpha}$ for the ordinary method of slices.

Why this works: effective-stress analysis is mandatory in the long term because the pore pressures are known (steady seepage) whereas in the short term they are not. The choice between fully softened and residual is then a question of shear history: fully softened corresponds to first-time failure in a fissured mass, residual to a surface that has already been sheared through large displacement.

Common pitfall: carrying the peak $c'$ intercept into a long-term analysis. A cohesion intercept of even 10 kPa contributes an enormous resisting moment on a long slip surface and can double the computed factor of safety; it is the single most common cause of over-optimistic slope design in stiff clays.

Source: B. M. Das, Principles of Geotechnical Engineering, 9th ed., Ch. 12 (Shear strength — residual strength) and Ch. 15 (Slope stability); Skempton (1970, 1977, 1985) on first-time slides and residual strength; CFEM 4th ed., Ch. 6.

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