16-Civ-B3 Geotechnical Design · May 2016

Question 1 of 9: Governing criterion for a shallow foundation on dense sand (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 1 — Governing criterion for a shallow foundation on dense sand (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.

Settlement governs. For a shallow foundation founded in a dense sand, the serviceability limit state — total and differential settlement — is reached at a contact pressure far below the pressure that would cause a bearing-capacity failure, so the allowable pressure is fixed by settlement and the stability check merely confirms an ample reserve.

The reason lies in the two bearing-capacity terms. A dense sand has a peak effective friction angle typically in the range 38° to 45°, and both Nᵤ and Nγ grow roughly exponentially with φ′. At φ′ = 40° the Vesic factors are already Nᵤ ≈ 64 and Nγ ≈ 109, so even a modest strip footing 1.5 m wide at 1.5 m depth develops an ultimate bearing pressure of the order of 3000 kPa. Dividing by a global factor of safety of 3 still leaves an allowable stability pressure of about 1000 kPa, which is an order of magnitude more than the 150 to 300 kPa that ordinary building footings actually apply.

Settlement, by contrast, is not so generous. Sand is a stiff but not rigid skeleton; its deformation is essentially immediate, elastic-plastic distortion of the grain structure, and the strains are concentrated within about two footing widths below the base. The tolerable movement, not the soil, sets the limit: Canadian practice (CFEM, 4th ed.) and the usual Skempton and MacDonald criteria restrict total settlement of an isolated footing on sand to about 25 mm and angular distortion to about 1/500, and those limits are typically reached at 150 to 250 kPa. That is why every classical design chart for footings on sand — Terzaghi and Peck, Meyerhof, Burland and Burbidge, the Schmertmann method used in Question 6 — is a settlement chart that returns the pressure for 25 mm of movement, not a strength chart.

Three further practical reasons reinforce the conclusion. First, settlement of a footing on sand occurs essentially as the load is applied, so most of it is already in the ground before the superstructure is finished and cannot be corrected later; there is no delayed reserve to fall back on. Second, sand deposits are variable in density over short distances, so differential settlement between adjacent footings, rather than the average value, usually controls, and differential movement is only weakly related to strength. Third, the settlement of a footing on sand grows with width for a given contact pressure while the bearing capacity per unit area also grows with width, so widening a footing to solve a stability problem is very effective whereas widening it to solve a settlement problem is not — further evidence that the two criteria are far apart in this material.

The exceptions are worth naming because a marker looks for them. Stability can govern a dense sand if the footing is very narrow and very shallow (a strip footing at the ground surface has almost no surcharge term), if the footing sits on or near a slope crest so that the passive wedge is truncated, if the loading is strongly eccentric or inclined so that the effective width and the inclination factors collapse the capacity (exactly what happens to the retaining wall in Question 7), or if the sand is only a thin dense crust over a soft compressible layer, in which case punching through the crust is the real mechanism. Absent those, design the footing for settlement and check stability.

Topic. Ultimate limit state versus serviceability limit state for shallow foundations on granular soil.

Key relations. Ultimate bearing capacity $q_u = c'N_c F_{cs}F_{cd}F_{ci} + qN_q F_{qs}F_{qd}F_{qi} + \tfrac{1}{2}\gamma B N_\gamma F_{\gamma s}F_{\gamma d}F_{\gamma i}$, with $c' = 0$ in a clean sand so that capacity comes entirely from the surcharge and self-weight terms; against this, $q_{\text{all,settlement}}$ is whatever pressure produces the tolerable movement, in Canadian practice about 25 mm of total settlement for an isolated footing.

Why this works. The strength terms scale with $N_q$ and $N_\gamma$, which are exponential in $\phi'$, whereas the stiffness of a sand scales only roughly linearly with relative density and confining stress. Increasing the density of a sand therefore multiplies its strength much faster than it multiplies its stiffness, and the gap between the two limit states widens as the sand gets denser. In a soft clay the position is reversed at short term (undrained strength is low, so stability governs) and reversed again at long term (consolidation settlement is large), which is why the same question asked about a soft clay has the opposite answer.

Common pitfall. Quoting a factor of safety of 3 on bearing capacity and stopping there. A dense sand will pass that check by a wide margin and the footing will still be unserviceable; the settlement calculation is the design, not an afterthought. The mirror-image error is to assume settlement always governs: an eccentrically or obliquely loaded footing on the same sand can fail the stability check outright.

Source. Das, Principles of Foundation Engineering, 9th ed., Ch. 3 (bearing capacity) and Ch. 5 (elastic settlement of shallow foundations); Canadian Geotechnical Society, Canadian Foundation Engineering Manual, 4th ed., Ch. 10 (shallow foundations) and its tolerable-movement guidance.

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