16-Civ-B3 Geotechnical Design · December 2014

Question 1 of 10: In-situ determination of bearing capacity, and the right test for a sand

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 2014 — 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 five design questions of 24 marks each (answer any three); the examinable total is 4 × 7 + 3 × 24 = 100 marks. All ten 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).
B. M. Das, Principles of Geotechnical Engineering, 9th ed. — lateral earth pressure (Ch. 13), shear strength (Ch. 12), slope stability (Ch. 15), subsurface exploration (Ch. 17).
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, 8th ed. — earth pressure theory and slope stability.
D. P. Coduto, Foundation Design: Principles and Practices, 2nd ed. — in-situ testing and SPT correlations.
J. E. Bowles, Foundation Analysis and Design, 5th ed. — bearing capacity factors and retaining-wall stability tables.

Sources of charts and assumed values (page-1 Note 6). Note 6 of this paper requires the candidate to identify the source of every design chart and every assumed value. Each chart reading and each assumption below is therefore named where it is used, and the values assumed in the absence of data are collected here:

Q6 — adhesion factor α from Das, Principles of Foundation Engineering, Table 11.6 (Terzaghi, Peck & Mesri form, α against $c_u/p_a$); $\lambda$ from Vijayvergiya & Focht (1972) as tabulated by Das, Table 11.7.
Q7 — overburden correction $C_N$ from Liao & Whitman (1986); $\phi'$ from Wolff (1989) and from Hatanaka & Uchida (1996), both reproduced in Das, Ch. 2; settlement-controlled bearing pressure from Meyerhof (1965) as given by Das, Ch. 5, used only as a serviceability check because the question forbids direct correlations of bearing capacity to penetration index. Table I prints the blow counts as field values $N_f$; with no hammer data they are converted as $N_{60} = N_f$, i.e. a safety hammer at the reference 60 per cent energy ratio with borehole, sampler and rod-length factors of 1 (Das, Ch. 2, hammer-efficiency and correction-factor tables).
Q8 — embankment influence factor from Osterberg (1957), reproduced as Das Fig. 6.24; the closed form of that chart is used so the reading carries no chart-scaling error.
Q9 — Meyerhof general bearing-capacity equation with the shape factors of De Beer (1970) and the depth factors of Hansen (1970), as set out in Das, Ch. 3.
Q10 — Coulomb active earth-pressure coefficient, Das Eq. 13.31; unit weight of the mass-concrete wall assumed $\gamma_c = 24\ \text{kN/m}^3$ (CFEM 4th ed., normal-density concrete), the only value the figure does not supply.

Question 1: In-situ determination of bearing capacity, and the right test for a 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.

Bearing capacity is never measured directly in the ground; what an in-situ test measures is either a penetration resistance, a stress–deformation response, or a strength, from which bearing resistance is then computed. The methods available in Canadian practice, in the order they appear in CFEM Chapter 4, are the following.

Standard penetration test (SPT). Blow count $N$ in a driven split-spoon, corrected to $N_{60}$ and $(N_1)_{60}$, then correlated to $\phi'$ or $D_r$ and fed into a bearing-capacity equation.
Cone penetration test (CPT / CPTu). Continuous measurement of cone tip resistance $q_c$, sleeve friction $f_s$ and, in the piezocone, pore pressure $u_2$. Interpreted for $\phi'$, $D_r$, constrained modulus and soil behaviour type.
Plate load test. A rigid plate (typically 300 to 750 mm) is loaded in a test pit and the pressure–settlement curve is measured directly.
Pressuremeter test (PMT). A borehole probe expands radially; gives the limit pressure $p_L$ and the pressuremeter modulus $E_p$, from which bearing resistance follows directly through the Menard rules.
Flat dilatometer test (DMT). Gives the material index, horizontal stress index and dilatometer modulus, hence $K_0$, $\phi'$ and a settlement modulus.
Field vane shear test (FVT). Direct measurement of undrained shear strength $c_u$ — but only meaningful in soft to firm clays and silts.
Screw-plate and borehole shear tests, and geophysical methods (seismic cross-hole, down-hole, MASW) for the small-strain modulus $G_{max}$.
Full-scale prototype load test on the actual footing — the only truly direct measurement, and correspondingly the most expensive.

For the reliable determination of in-situ bearing capacity in a sandy soil the recommended method is the electric cone penetration test (CPT), supplemented by one plate or full-scale load test where the project size justifies it.

The governing reason is that a clean sand cannot be sampled undisturbed. Any strength or stiffness measured on a reconstituted laboratory specimen has lost the in-situ density, fabric, ageing and cementation that actually control bearing resistance, so laboratory testing is not an option and the assessment must be made in the ground. Among the in-situ options, the CPT is the one that combines a continuous profile with the tightest repeatability: the cone is pushed at a standardised 20 mm/s, the tip and sleeve resistances are logged every 10 to 50 mm, and the result is essentially independent of the operator and of the drilling method. That continuity matters in sand because loose seams and weak lenses a few hundred millimetres thick will govern settlement and can be stepped straight over by an SPT sampled at 1.5 m centres.

The CPT also gives the two quantities a bearing-capacity calculation actually needs. Cone resistance correlates directly with $\phi'$ (Robertson & Campanella, 1983) and with relative density, and $q_c$ converts to a constrained modulus for settlement through well-established coefficients, so a single sounding supports both the strength check and the settlement check — and in sand it is settlement, not shear failure, that almost always governs the design pressure.

The competing methods are weaker for this soil type for specific reasons. The SPT is crude and energy-dependent; hammer efficiency ranges from about 45 to 90 per cent between rigs, gravel particles inflate the blow count, and the correlation to $\phi'$ carries a scatter of several degrees. The plate load test, although it measures the pressure–settlement response directly, stresses only about twice the plate width of soil, so in a sand — where stiffness increases with confining stress and any deep loose layer is entirely outside the plate's influence zone — the result cannot be scaled to a real footing without a size correction that is itself uncertain. The field vane is inapplicable: it measures undrained strength, and a sand loaded by a footing drains essentially as fast as it is loaded. The pressuremeter is an excellent alternative where a specialist rig is available, but pre-bored PMT in a clean sand suffers borehole disturbance and is slower and dearer than the cone.

Topic: in-situ testing and the selection of the appropriate test for a given soil type.

Key relations: $N_{60} = N\,\dfrac{E_r}{60}$; $(N_1)_{60} = C_N N_{60}$ with $C_N = \sqrt{p_a/\sigma'_v}$; $q_{ult} = c' N_c F_{cs} F_{cd} + q N_q F_{qs} F_{qd} + \tfrac{1}{2}\gamma B N_\gamma F_{\gamma s} F_{\gamma d}$.

Why this works: the choice of in-situ test follows from what can and cannot be sampled. In clays an undisturbed tube sample is obtainable, so laboratory triaxial and oedometer testing carries the design and the in-situ test is largely a profiling tool. In sands and gravels no undisturbed sample exists at commercial cost, so the in-situ test is the strength measurement, and the premium therefore goes to whichever test is most repeatable and most continuous. That is the cone.

Common pitfall: quoting a bearing capacity straight from an SPT correlation chart without checking settlement. In a sand a 3 m wide footing on $N_{60} = 20$ can satisfy a bearing-capacity factor of safety of 3 at a pressure that produces well over 25 mm of settlement. The two checks are independent and both must be made.

Source: Canadian Geotechnical Society, Canadian Foundation Engineering Manual, 4th ed., Ch. 4 (In-situ testing); B. M. Das, Principles of Foundation Engineering, 9th ed., Ch. 2 (Subsoil exploration); D. P. Coduto, Foundation Design, 2nd ed., Ch. 4.

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