16-Civ-B3 Geotechnical Design · May 2016

Question 2 of 9: Unsupported cuts in clay, and strength gain in clay embankments (7 marks)

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 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 method (Ch. 5), retaining walls (Ch. 8), pile foundations (Ch. 11).
B. M. Das, Principles of Geotechnical Engineering, 9th ed. — shear strength (Ch. 12), lateral earth pressure (Ch. 13), slope stability including the planar-surface analysis (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 slope stability.
D. P. Coduto, Foundation Design: Principles and Practices, 3rd ed. — CPT correlations and settlement of shallow foundations on sand.
M. J. Tomlinson & J. Woodward, Pile Design and Construction Practice, 6th ed. — shaft adhesion in clay and driven displacement piles in sand.

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

Strain-influence diagram and the C₁, C₂ correction factors (Q6) — Schmertmann, Hartman and Brown (1978), as tabulated in Das, Principles of Foundation Engineering, 9th ed., Section 5.6.
Rankine active coefficient for an inclined backfill (Q7) — Das, Principles of Geotechnical Engineering, 9th ed., Eq. (13.35).
Bearing-capacity factors N₢, Nᵤ, Nγ and the depth and load- inclination factors (Q7) — Vesic / Meyerhof as tabulated in Das, Principles of Foundation Engineering, 9th ed., Tables 3.3 and 3.4, applied to a retaining-wall base in Section 8.6.
Meyerhof bearing-capacity factor Nᵤ* for a driven pile point and the limiting point resistance (Q8) — Das, 9th ed., Section 11.9 and its interpolated Nᵤ* table; Nᵤ* = 143 at φ′ = 35°.
Adhesion factor α against cu/p₀ (Q8) — Das, 9th ed., Table 11.6 (after Terzaghi, Peck and Mesri); α = 0.68 at cu/p₀ = 0.5.
Earth-pressure coefficient K and interface friction angle δ′ for a driven high-displacement pile (Q8) — Das, 9th ed., Section 11.11: K ≈ 1.4K₀ and δ′ ≈ 0.8φ′ are assumed, and the critical-depth rule L′ = 15D is Das Eq. (11.42).
Unit weight of water γᵣ = 9.81 kN/m³ and g = 9.81 m/s² throughout; atmospheric pressure p₀ = 100 kPa.

Section A — discussion questions (7 marks each)

Question 2 — Unsupported cuts in clay, and strength gain in clay embankments (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.

Both halves of this question are answered by the same idea, applied with opposite signs: a saturated clay has such a low permeability that a change of total stress is carried at first entirely by the pore water, and the drainage that follows either helps or harms the soil depending on whether the total stress went down or up.

Why a cut in clay stands unsupported for a while. Excavation is an unloading. Removing the soil from the cut reduces the total vertical and horizontal stresses on the remaining clay, and because the clay cannot draw in water quickly, the volume cannot change; the pore-water pressure falls, often to values well below hydrostatic and frequently negative (a suction). Since effective stress is the difference between total stress and pore pressure, that fall in u keeps the effective stress — and therefore the mobilised shear strength — high even though the total stress has dropped. In the short term the clay behaves as a purely cohesive material of undrained strength $c_u$ with $\phi_u = 0$, and a vertical cut of height H is stable so long as

$$H \;\lt\; H_c = \frac{4c_u}{\gamma}\qquad\text{(no tension crack)},$$

which for a stiff clay with $c_u = 100$ kPa and $\gamma = 19$ kN/m³ is over 20 m. Allowing for the tension crack that forms at the crest reduces the coefficient from 4 to about 3.85, and in practice a working factor of safety is applied, but the point stands: the temporary strength is large.

That state is not permanent. Over days to months, water is drawn in from the surrounding ground and from rainfall, the negative excess pore pressures dissipate towards the new steady-state seepage condition, the clay swells and softens, and the strength that governs becomes the drained strength $\tau_f = c' + \sigma'\tan\phi'$ with a very small (in a fissured clay, effectively zero) $c'$. The factor of safety therefore falls with time, which is the classical explanation of the delayed failures of cuttings in London Clay documented by Skempton. Fissuring, desiccation cracking, softening at the face and the build-up of water pressure in tension cracks all accelerate the process. This is why unsupported excavations are permitted only as short-term works, why the occupational health and safety regulations in every Canadian province limit unsupported depths (in British Columbia, excavations deeper than 1.2 m must be sloped, benched or shored unless a professional engineer certifies otherwise), and why a cut that has stood open over a wet winter is far more dangerous than one opened yesterday.

Why a clay embankment gains strength with time. Filling is a loading, so every sign reverses. As each lift of compacted clay is placed, the total stress on the underlying material rises faster than the water can escape, so a positive excess pore pressure is generated. Effective stress therefore rises very little during construction, the available shear strength is essentially the undrained strength of the compacted fill and of the foundation clay, and the end of construction is the critical case for an embankment. If the rate of filling outruns the rate of dissipation the embankment can fail as it is being built — hence staged construction, wick drains and piezometric monitoring on soft ground.

After construction the excess pore pressures dissipate by consolidation: water is squeezed out, the void ratio falls, the effective stress rises towards the new total stress, and the shear strength rises with it through $\tau_f = c' + \sigma'\tan\phi'$. The clay also becomes stiffer and, having been consolidated to a higher stress than it has ever carried, lightly overconsolidated on any subsequent unloading. The factor of safety therefore increases with time, and the long-term drained condition is the safe one. The time scale follows from the coefficient of consolidation, $t = T_v H_{dr}^{2}/c_v$, so a thick homogeneous clay core may take years, which is exactly why the rapid-drawdown and end-of-construction cases, not the steady-seepage case, control the design of a clay-cored earth dam.

Stated compactly: an excavation is safest when it is new and grows more dangerous; an embankment is most dangerous when it is new and grows safer. Both follow from the sign of the excess pore pressure generated by the change in total stress.

Topic. Undrained versus drained behaviour of saturated clay, and the time-dependence of the factor of safety after unloading and after loading.

Key relations. Terzaghi's effective-stress principle $\sigma' = \sigma - u$; undrained strength envelope $\tau_f = c_u$, $\phi_u = 0$; drained envelope $\tau_f = c' + \sigma'\tan\phi'$; critical height of a vertical cut $H_c = 4c_u/\gamma$ (Das Eq. 15.10, reduced to $3.85c_u/\gamma$ with a tension crack); degree of consolidation through $T_v = c_v t/H_{dr}^{2}$.

Why this works. Skempton's pore-pressure equation $\Delta u = B\left[\Delta\sigma_3 + A(\Delta\sigma_1 - \Delta\sigma_3)\right]$ shows that for a saturated soil ($B = 1$) the sign of the excess pore pressure follows the sign of the applied total-stress change. Excavation gives $\Delta\sigma \lt 0$ and therefore $\Delta u \lt 0$, so $\sigma'$ is temporarily higher than its equilibrium value; filling gives $\Delta u \gt 0$, so $\sigma'$ is temporarily lower. Equilibration in either direction moves the soil towards its drained strength, which is below the temporary value in the first case and above it in the second.

Common pitfall. Writing that a clay cut stands because of "cohesion" as though cohesion were a permanent material property. The temporary strength is a consequence of the negative excess pore pressure, not of true cohesion, and it disappears as the pore pressures equalise; a design that relies on $c_u$ for a permanent slope is unsafe. The matching pitfall on the embankment side is to check only the long-term steady-seepage case and miss the end-of-construction condition that actually governs.

Source. Craig, Craig's Soil Mechanics, 9th ed., Ch. 4 and Ch. 5 (effective stress, shear strength) and Ch. 12 (stability of slopes); Das, Principles of Geotechnical Engineering, 9th ed., Ch. 12 and Ch. 15.

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