16-Civ-B3 Geotechnical Design · May 2015

Question 5 of 9: Investigation and Design of a Highway Embankment Slope 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, May 2015 — 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. — bearing capacity (Ch. 3), stress increase in a soil mass (Ch. 6), retaining walls (Ch. 8), pile foundations (Ch. 11), subsurface exploration (Ch. 2).
B. M. Das, Principles of Geotechnical Engineering, 9th ed. — consolidation (Ch. 11), shear strength (Ch. 12), lateral earth pressure (Ch. 13).
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, 9th ed. — earth pressure theory, effective stress and slope stability.
D. P. Coduto, Foundation Design: Principles and Practices, 3rd ed. — in-situ testing, settlement of shallow and deep foundations.
M. J. Tomlinson & J. Woodward, Pile Design and Construction Practice, 6th ed. — shaft adhesion in clay, pile-group behaviour, load testing.

Sources of design charts and assumed values (page-1 Note 6). Note 6 of this paper requires the candidate to identify the source of every design chart used and of every value assumed in the absence of data. They are named where used and collected here:

Q6 — bearing capacity factors $N_c$, $N_q$, $N_{\gamma}$ from Das, Principles of Foundation Engineering, Table 3.3 (Prandtl–Reissner $N_q$, Vesic $N_{\gamma}=2(N_q+1)\tan\phi'$); shape factors after De Beer (1970) and depth factors after Hansen (1970), Das Table 3.4. Assumed: unit weight of water $\gamma_w = 9.81$ kN/m$^3$; general shear failure; the sand extends at least $2B$ below the base.
Q7 — adhesion factor $\alpha = 1.0$ for soft clay ($c_u \le 50$ kPa) from NAVFAC DM-7.2 Fig. 1 and Tomlinson & Woodward Table 4.6; $\lambda = 0.24$ at an embedded length of 12 m from Vijayvergiya & Focht (1972) as tabulated by Das, Table 11.7; bearing factor $N_c^{*}=9$ for $L/D \ge 4$ (Skempton). Assumed: pile spacing $s = 3d = 1.5$ m centre to centre, driven closed-end concrete piles, clay $\gamma_{sat} = 17$ kN/m$^3$ with the water table at ground level.
Q8 — compression index from the Skempton correlation $C_c = 0.009\,(LL-10)$, Das Principles of Geotechnical Engineering Eq. (11.42); $2{:}1$ stress distribution, Das Eq. (6.31); Boussinesq rectangular influence factor (Das Table 6.6) used as the cross-check.
Q9 — Coulomb active pressure coefficient, Das Principles of Foundation Engineering Eq. (8.13) with the wall friction angle prescribed by the question, $\delta = 0.6\phi' = 18^{\circ}$. Assumed: unit weight of reinforced concrete $\gamma_c = 24$ kN/m$^3$ (CSA A23.3 nominal); passive resistance in front of the toe neglected; the backfill surface is horizontal and carries no surcharge.

Question 5: Investigation and Design of a Highway Embankment Slope 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.

The investigation. The programme has to characterise the same material twice: as a foundation beneath the embankment and as a fill within it. Continuous sampling along the alignment, by hollow-stem auger with thin-walled tube samples and test pits to the depth of seasonal moisture change, should establish the classification and swell potential of the deposit: Atterberg limits, grain-size and hydrometer analysis, linear shrinkage, and free-swell or swell-index tests. Plasticity index is the primary screening index (a $PI$ above about 35 with a liquid limit above 50 signals high swell potential), and it should be supported by mineralogical work — X-ray diffraction and methylene-blue or cation-exchange-capacity tests to confirm smectite content — and by Skempton's activity $A = PI/(\text{clay fraction})$. The magnitude of the problem is then quantified directly in the oedometer: a one-dimensional free-swell test gives the swell percentage under a given surcharge, and a constant-volume test gives the swell pressure. Because expansive-soil behaviour is a suction problem rather than a saturated one, I would also profile the natural water content and matric suction with depth (filter paper method, tensiometers or thermal conductivity sensors) at least twice, in the wettest and driest seasons, to define the depth of the active zone; and determine the soil-water characteristic curve on representative samples. Field mapping of desiccation cracks, existing slope failures along nearby cuts, and the depth to any perched water table completes the picture.

Shear strength parameters for the stability analysis. The critical point is that peak strength measured on an intact or freshly compacted specimen is the wrong parameter for this slope. A compacted expansive fill swells and softens on wetting, and the desiccation cracks that form each dry season propagate and then fill with water, so within a few seasons the operative strength on any potential slip surface has fallen from peak to the fully softened value — the drained strength of the same soil in the normally consolidated, remoulded state, with $c' = 0$. This is exactly the mechanism behind the well-documented shallow slides that appear in compacted high-plasticity embankments five to fifteen years after construction, and it must be the basis of the long-term analysis. I would therefore obtain:

Fully softened strength from drained direct shear or CU triaxial tests with pore-pressure measurement on specimens remoulded at the liquid limit and normally consolidated, giving $\phi'_{fs}$ with $c' = 0$ — the parameter for the long-term, post-swelling condition.
Residual strength from ring-shear (Bromhead) or repeated direct-shear tests, needed wherever a pre-existing shear surface, a fissure set or an old landslide plane exists in the foundation, since strength there is already at residual.
Undrained strength $c_u$ from UU triaxial tests and field vane in the foundation clay, for the end-of-construction case in which the embankment is placed faster than pore pressures can dissipate.
Effective peak parameters $c'$, $\phi'$ from CU triaxial tests with pore-pressure measurement on samples compacted to the specified placement condition, for comparison and for the intermediate-term case.
Unsaturated strength from suction-controlled shear tests to quantify the $\tan\phi^b$ contribution, useful for understanding the as-built condition but not to be relied on in the long-term design, because suction is destroyed by the first prolonged wet period.

Other design criteria. Stability against sliding is only one limit state. The dominant serviceability problem is volume change: shrink-swell cycles in the active zone crack the pavement, distort shoulders and open longitudinal cracks along the crest, so compaction must be specified wet of optimum and to a moderate rather than a maximum dry density (typically 95 per cent of standard Proctor at 2 to 4 per cent above optimum), which deliberately trades strength for a lower swell potential. Chemical stabilisation of the upper metre or two with lime (2 to 6 per cent quicklime or hydrated lime), or with lime plus fly ash, converts the smectite surface chemistry and largely removes the plasticity; a non-expansive capping layer, a moisture barrier or a geomembrane apron beneath the shoulders serves the same purpose by keeping the moisture regime constant. Side slopes should be flattened to 1V:3H or flatter to guard against the shallow fully-softened slides described above, and geogrid reinforcement or a granular drainage-and-filter blanket at the base can be used where the alignment cannot afford the width. Positive surface drainage away from the crest, sealed shoulders, vegetated slopes (chosen so that deep-rooted trees do not themselves desiccate the fill), toe drains and maintenance access all matter. In the Canadian context the design must also address freeze-thaw and frost heave, since repeated freezing further degrades an expansive clay fill and the pavement structure must be founded below the frost depth; and the long-term factor of safety should be checked at 1.5 for the drained fully-softened case, 1.3 for end-of-construction, and against the pseudo-static seismic case where the NBCC hazard warrants it.

Topic. Expansive (smectitic) soils as embankment fill: characterisation, strength selection and slope design.

Key relations. Activity $A = PI/CF$; free swell and swell pressure from the oedometer; fully softened envelope $\tau_f = \sigma'_n\tan\phi'_{fs}$ with $c'=0$; residual envelope $\tau_r = \sigma'_n\tan\phi'_r$; unsaturated strength $\tau_f = c' + (\sigma_n - u_a)\tan\phi' + (u_a-u_w)\tan\phi^b$.

Why this works. A high-plasticity clay derives much of its peak strength from a fabric and a suction that seasonal wetting destroys. Analysing the long-term slope with peak parameters therefore predicts a factor of safety that the slope never possesses after its first few wet seasons, which is why fully softened strength — the strength the soil returns to when remoulded and normally consolidated — is the honest long-term parameter, and residual strength is the honest one wherever a slip surface already exists. Specifying compaction wet of optimum works for the same reason in reverse: placing the clay at a water content close to its eventual equilibrium leaves it little suction to lose and little room to swell.

Common pitfall. Designing the slope with peak $c'$ and $\phi'$ from CU tests on freshly compacted specimens, which typically overstates the long-term factor of safety by 30 to 60 per cent; and compacting the fill hard and dry to meet a density specification, which maximises both the strength on the day and the swell pressure two years later.

Source. Das, Principles of Geotechnical Engineering 9th ed. §12.15 (residual strength) and Ch. 15 (slope stability); Fredlund & Rahardjo, Soil Mechanics for Unsaturated Soils; Transportation Association of Canada, Pavement Asset Design and Management Guide, for Canadian subgrade practice.

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