16-Civ-B3 Geotechnical Design · May 2016

Question 5 of 9: Influence of the water table on bearing capacity in 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 5 — Influence of the water table on bearing capacity in 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.

The strength of a sand comes entirely from friction between grains, and friction depends on how hard the grains are pressed together — that is, on the effective stress, not on the total weight of soil overhead. Water sitting in the pores carries part of the total stress itself and presses the grains apart, so wherever the sand is below the water table the grains are effectively buoyant and the weight that counts is roughly halved: a sand weighing about 20 kilonewtons per cubic metre in bulk counts for only about 10 once it is submerged.

That single fact drives everything. The bearing capacity of a footing on sand is built from two contributions. The first is the weight of the soil lying beside the footing, between the ground surface and the founding level, which acts as a surcharge holding down the ground into which the failure wedge has to push. The second is the weight of the sand within the failure wedge itself, immediately below and beside the footing, which has to be lifted and pushed aside for a failure to develop. Both are weights, so both are cut roughly in half wherever the water table submerges the soil they refer to. The depth of the water table matters only through which of those two blocks of soil it touches.

Case (a) — water table five footing widths below. The zone of soil that participates in a bearing-capacity failure is shallow: the wedge and the log-spiral and passive zones beneath a footing extend only about one to two footing widths below the base, and essentially all of the useful surcharge lies above the base. A water table five widths down is therefore far outside the region that matters. The sand in the failure zone and the sand providing the surcharge are both moist or dry, both act at their full bulk unit weight, and the bearing capacity is the same as it would be if there were no water table at all. In design terms, no correction is applied.

Two qualifications belong in the answer. The first is that "five widths" is generous for a small footing but not for a large one; the practical rule is that the water table has no effect once it lies more than about the footing width below the base, and the case given is comfortably beyond that. The second is that the sand above a water table often carries a little capillary moisture, which adds a small apparent cohesion; ignoring it, as is normal, is conservative.

Case (b) — water table at the natural ground surface. Now everything is submerged. Both the surcharge alongside the footing and the sand in the failure wedge act at buoyant weight, so both contributions to the bearing capacity are reduced by roughly one half, and the ultimate bearing capacity of the footing is about half what it would be with a deep water table. This is the single largest environmental correction made to a shallow foundation on sand, and it is not a refinement: halving the capacity halves the allowable pressure for a given factor of safety.

Several secondary effects push in the same direction and should be mentioned. Any apparent cohesion from capillary suction is destroyed by full saturation, so a fine sand that appeared to stand in a trench loses that strength entirely. A loose saturated sand becomes vulnerable to liquefaction or to collapse settlement under cyclic or seismic loading, a mechanism that simply does not exist above the water table. Upward seepage, if the site is being dewatered or if there is an artesian pressure below, reduces the effective stress further and in the limit can cause quick conditions and remove the bearing capacity altogether. Construction is also harder: excavation below water requires dewatering, and dewatering elsewhere on the site can draw the water table down temporarily and mislead the designer.

The engineering conclusion is that the water table must be designed for over the life of the structure, not as found on the day of the investigation. Design for the highest credible level — seasonal high, flood level, the level after a nearby dewatering scheme is switched off, or the recovered regional level if pumping ceases — because a water table that rises beneath an existing footing reduces its bearing capacity and, in a loose sand, can itself trigger settlement. Between the two cases given, the answer is therefore that (a) requires no correction at all, while (b) roughly halves the ultimate bearing capacity and is the governing design condition.

Topic. Water-table correction to the bearing capacity of a shallow foundation on granular soil.

Key relations. Although the question forbids equations in the answer, the underlying rule is that the surcharge term uses the effective overburden $q = \sum\gamma_i h_i$ with $\gamma' = \gamma_{\text{sat}} - \gamma_w$ below the water table, and the width term uses an effective unit weight $\bar{\gamma}$ that equals $\gamma$ if the water table is more than $B$ below the base, $\gamma'$ if it is at or above the base, and a linear interpolation in between (Das Eqs. 3.14 to 3.16). Since $\gamma' \approx \gamma/2$ for a typical sand, full submergence roughly halves both terms.

Why this works. Mohr-Coulomb strength in a clean sand is $\tau_f = \sigma'\tan\phi'$ with no cohesion intercept, so every kilopascal of pore pressure is a kilopascal of lost normal effective stress on every potential slip surface. The bearing-capacity factors themselves are unchanged — $\phi'$ does not depend on saturation — which is why the effect appears purely as a change of unit weight.

Common pitfall. Applying the correction to only one of the two terms, usually remembering the surcharge and forgetting the width term, or vice versa. Question 7 of this paper is the worked counter-example in the other direction: the same effective-stress logic, applied to a retaining wall, changes the thrust, the resisting weight and the base pressure all at once.

Source. Das, Principles of Foundation Engineering, 9th ed., Section 3.5 (effect of the water table on bearing capacity); Canadian Geotechnical Society, Canadian Foundation Engineering Manual, 4th ed., Ch. 10.

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