16-Civ-B3 Geotechnical Design · December 2015

Question 4 of 9: Foundation Selection for a Shopping Complex on 5 m of Expansive Clay

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. Professional Engineers Ontario / Engineers Canada National Examinations, December 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. — subsurface exploration (Ch. 2), bearing capacity (Ch. 3), settlement of shallow foundations (Ch. 5), stress increase in a soil mass (Ch. 6), retaining walls (Ch. 8), pile foundations (Ch. 11).
B. M. Das, Principles of Geotechnical Engineering, 9th ed. — consolidation (Ch. 11), shear strength (Ch. 12), lateral earth pressure (Ch. 13), slope stability (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, earth-retaining structures and expansive soils.
R. F. Craig, Craig's Soil Mechanics, 9th ed. — effective stress, earth pressure theory and slope stability.
D. P. Coduto, Foundation Design: Principles and Practices, 3rd ed. — in-situ testing correlations and settlement of shallow foundations.
M. J. Tomlinson & J. Woodward, Pile Design and Construction Practice, 6th ed. — shaft adhesion in clay, bored and augered piles, 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 — Rankine active coefficient for a sloping backfill, Das, Principles of Foundation Engineering, Eq. (8.5); base friction and adhesion mobilisation factors $k_1 = k_2 = \tfrac{2}{3}$ after Das §8.5; Rankine passive coefficient $K_p = \tan^2(45^{\circ} + \phi'_2/2)$. Assumed: stem height $H = 10.0$ m (the exam omits it — see the callout in Q6); reinforced concrete $\gamma_c = 24$ kN/m$^3$ (CFEM §4; CSA A23.3 normal-density concrete); the backfill is fully drained so no water force acts.
Q7 — overburden correction $C_N$ after Liao & Whitman (1986); $\phi'$ from $(N_1)_{60}$ after Peck, Hanson & Thornburn (1974) as fitted by Wolff (1989), cross-checked against Hatanaka & Uchida (1996); bearing capacity factors from Das 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; settlement from Meyerhof's (1965) SPT expression, Das Eq. (5.42), cross-checked by Schmertmann's strain-influence method with $E_s = 500(N_{60}+15)$ kPa. Assumed: founding depth $D_f = 2.0$ m; the sand is uniform to at least $2B$ below the base; tolerable settlement 25 mm.
Q8 — compression index from Terzaghi & Peck (1967), $C_c = 0.009(LL-10)$; stress increase by the 2:1 method (Das §6.2) with a Boussinesq rectangular-area cross-check (Das Table 6.6); Simpson weighting of $\Delta\sigma'$ prescribed on the exam paper itself. Assumed: $\gamma_w = 9.81$ kN/m$^3$; the clay is saturated so $e_0 = wG_s$; the sand layers are incompressible relative to the clay.
Q9 — undrained ($\phi_u = 0$) mass procedure, Das, Principles of Geotechnical Engineering, §15.5; drained comparison by the ordinary method of slices and Bishop's simplified method, Das §15.11–15.12, and by the infinite-slope criterion, Das Eq. (15.10). Assumed: no external water force and no seismic loading; the sliding mass is homogeneous.

Section A — discussion questions (7 marks each; answer any four)

Question 4: Foundation Selection for a Shopping Complex on 5 m of Expansive Clay (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.

Recommendation. Support the structure on straight-shafted or belled drilled piers (cast-in-place concrete caissons) founded in the sand below the expansive clay, with the pier shafts sleeved or slip-coated through the active zone, tied together by grade beams cast on a void form so that they bear on nothing, and with all ground-supported floor slabs either structurally suspended over a void or accepted as sacrificial. This is the standard Canadian solution for a substantial structure over a shallow expansive deposit, and it is what CFEM recommends where the swelling soil is thin enough to be penetrated economically.

Why the obvious alternatives fail. The governing problem here is not bearing capacity and it is not settlement; it is differential vertical movement driven by moisture change. A highly expansive clay changes volume with water content, and water content changes seasonally at the perimeter, permanently under a heated slab, and catastrophically if a service leaks or landscape irrigation is installed. The movement is seasonal at the edges and cumulative in the centre, and it is measured in tens of millimetres. A conventional spread footing at, say, 1.5 m depth sits inside that active zone: it will be lifted in a wet cycle, dropped in a dry cycle, and the differential between a shaded north perimeter and a heated interior column will distort the frame far beyond anything the structure can tolerate. A raft is better because it bridges local variation, but a stiffened raft thick enough to resist the centre-heave and edge-lift bending moments generated by a highly expansive clay across a shopping-centre footprint is very expensive, and it does not remove the movement — it only makes the movement uniform enough to survive, which is a bet on the moisture regime staying uniform. It is a defensible solution for a small, single-storey, lightly loaded building, not for a multi-storey complex with column loads and a long design life. Removing and replacing 5 m of clay under a large footprint is technically valid and is sometimes done for roads, but the excavation volume, the disposal of a problem soil and the dewatering make it uncompetitive under a building.

Why drilled piers work. Piers carry the load past the entire active zone into a sand that does not change volume with water content, so the founding level is stable by construction. The sand is described as very deep, so end bearing is reliable and a belled base can develop a large capacity in a single element; where the sand is dense the bell may be unnecessary and a straight shaft with side resistance in the sand will do. Crucially, the design must then deal with the one mechanism that still couples the structure to the clay: uplift by shaft heave. When the clay swells it grips the pier and drags it upward, mobilising a tensile force over the whole thickness of the active zone. The design consequences are as follows.

Isolate the shaft in the active zone. Use a permanent sleeve, a double-casing detail, or a bond-breaking coating over the full 5 m so that the swelling clay slides past the concrete rather than gripping it.
Reinforce the shaft for tension. Carry full-length vertical steel capable of resisting the uplift that survives the sleeving, and anchor it into the bell or into the sand socket. Piers that are reinforced only in the top few metres, as a compression element would be, fail by tensile fracture at mid-height.
Provide dead load and anchorage. Size the embedment in the sand so that shaft resistance plus structural dead load exceeds the uplift with an adequate margin, recognising that uplift is greatest under the lightly loaded piers — canopy columns, entrance features, exterior walls — not under the heavily loaded ones.
Void everything that touches the clay. Grade beams on collapsible void formers with a clear gap beneath; a structurally suspended ground floor over a crawl space or void former for the trading floor, or, if a slab-on-grade is accepted for back-of-house areas, a slab fully isolated from the columns and understood to be replaceable.
Control the moisture regime. Positive grading away from the building, sealed and accessible services with flexible connections, no irrigated planting adjacent to the structure, and perimeter moisture barriers. Most expansive-soil damage in practice is initiated by a leak or by landscaping, not by climate.

Investigation required to complete the design. Swell–consolidation oedometer tests to obtain the swelling pressure and the free-swell strain, Atterberg limits and clay-fraction data to classify the expansive potential, natural water-content profiles in both a wet and a dry season to establish the depth of the active zone, and confirmation by borehole or CPT that the sand is continuous and competent at the founding level.

Topic. Foundations on expansive soils; deep foundations used as a displacement-control measure rather than a capacity measure.

Key relations. Uplift on a pier shaft in the active zone $Q_{up} = \alpha_{sw}\,c_u\,p\,Z_a$, resisted by $W_{dead} + Q_{s,anchor} + Q_{bell}$; swelling pressure $p_s$ from a swell–consolidation test; active-zone depth $Z_a$ from seasonal water-content profiles.

Why this works. Expansive clay imposes a displacement, not a load. A foundation that resists displacement must either be stiff enough to redistribute it (a heavily stiffened raft) or be founded outside the zone in which it occurs (piers into sand). The second is cheaper and far more robust when the swelling stratum is only a few metres thick, because it removes the mechanism rather than accommodating it.

Common pitfall. Designing the pier as a compression element only. Uplift from shaft heave routinely exceeds the dead load on lightly loaded piers, and an under-reinforced shaft with a properly designed bell will simply pull apart in tension partway up the active zone. The second recurring pitfall is casting grade beams directly on the clay, which reintroduces the entire problem at the beams.

Source. CFEM 4th ed., §16 (special soil conditions — swelling and shrinking soils) and §18; Das, Principles of Foundation Engineering, 9th ed., Ch. 12 (foundations on difficult soils); Coduto, Foundation Design, 3rd ed., Ch. 19.

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