16-Civ-B3 Geotechnical Design · May 2015

Question 2 of 9: Does the Bearing Capacity of a Strip Footing on Sand Change with Time?

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 2: Does the Bearing Capacity of a Strip Footing on Sand Change with Time? (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 bearing capacity of a footing on sand is not a fixed soil property; it will change during the design life, and it can change in both directions. The general bearing capacity equation shows why, because every term in it contains a quantity that the site can alter:

$$q_u = c'N_cF_{cs}F_{cd} + q\,N_qF_{qs}F_{qd} + \tfrac{1}{2}\gamma B N_{\gamma}F_{\gamma s}F_{\gamma d}$$

For a clean sand $c' = 0$, so the capacity rests entirely on the surcharge term $q$, the unit weight $\gamma$ beneath the footing, and the friction angle $\phi'$ that fixes $N_q$ and $N_{\gamma}$. Each of these is time-dependent in a real ground.

Changes that reduce the capacity. The single largest effect is a rise in the groundwater table. If water rises from below the failure zone to the level of the foundation base, the effective unit weight in the $N_{\gamma}$ term falls from $\gamma$ to $\gamma' \approx \gamma - 9.81$, roughly halving it; if it rises further, to ground surface, the surcharge term is reduced in the same proportion. For a typical sand the ultimate capacity is cut by 40 to 50 per cent, which is why the design case is always the highest credible water level, not the level recorded on the day of drilling. Second, loss of embedment removes the surcharge term directly: scour beside a bridge pier or an abutment, erosion of a slope crest, an adjacent service trench or a neighbouring basement excavation each reduce $D_f$, and the $N_q$ term falls in proportion. Third, cyclic and dynamic loading can reduce $\phi'$ where the sand is loose and saturated; in the limit, earthquake shaking generates enough excess pore pressure to liquefy the layer and the capacity falls essentially to zero. Fourth, a loose, dry, weakly cemented sand or silty sand can collapse on first wetting from a leaking service or from irrigation, producing sudden settlement at unchanged load. Finally, a change in the structure itself — a new eccentricity or a horizontal thrust — reduces the effective width $B' = B - 2e$ and brings in the inclination factors, so the available capacity for the actual load falls even though the soil has not changed.

Changes that increase the capacity. Sands densify under sustained and repeated loading. Traffic, machine vibration and simple ageing (silica dissolution and re-precipitation at grain contacts, plus rearrangement into a more stable fabric) all raise the relative density and the interlocking component of $\phi'$; measured cone resistances in hydraulic fills commonly increase by 50 to 100 per cent over the first year or two. A falling water table, a fill placed alongside, or the confinement provided by a new adjacent structure all raise $q$ and $\gamma$ and therefore the capacity.

Practical consequence. Because the sand under a strip footing is stiff enough that shear failure is rarely reached, the design of footings on sand is almost always governed by settlement rather than by bearing capacity; but the same water-table rise that halves the capacity also roughly doubles the settlement, so both limit states move together. Canadian practice (CFEM 4th ed. Ch. 10) therefore requires the geotechnical resistance to be evaluated for the seasonally highest groundwater level, with the minimum embedment taken below the frost depth and below any credible scour depth — the design capacity is the capacity of the worst state the ground will pass through, not its state at construction.

Topic. Time-dependence of the bearing resistance of shallow foundations on granular soil.

Key relations. General bearing capacity equation as above; effective unit weight $\gamma' = \gamma_{sat} - \gamma_w$; $N_q = e^{\pi\tan\phi'}\tan^2(45+\phi'/2)$ and $N_{\gamma} = 2(N_q+1)\tan\phi'$, both extremely sensitive to $\phi'$; effective width $B' = B - 2e$ for eccentric load.

Why this works. The bearing capacity equation is a statement about the stresses available on a shear surface, and every stress in it is an effective stress. Anything that changes pore pressure, overburden or density therefore changes the answer. Because $N_q$ and $N_{\gamma}$ grow roughly exponentially with $\phi'$, a change of only two or three degrees in the mobilised friction angle moves the capacity by tens of per cent, which is why densification and liquefaction both have such large effects.

Common pitfall. Using the water level measured in the borehole during the site investigation as the design level, and forgetting that the $N_{\gamma}$ term needs $\gamma'$ whenever the water table is within a depth $B$ below the base while the $N_q$ term needs the effective surcharge at base level — the two corrections are separate.

Source. Das, Principles of Foundation Engineering 9th ed. §3.5–3.9; CFEM 4th ed. Ch. 10; Coduto, Foundation Design 3rd ed. Ch. 6.

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