16-Civ-B3 Geotechnical Design · December 2015

Question 1 of 9: Rationale for SPT Results in Foundation Design in Coarse-Grained Soils

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 1: Rationale for SPT Results in Foundation Design in Coarse-Grained Soils (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 rationale begins with a sampling problem rather than a testing preference. Clean sands and gravels cannot be recovered undisturbed by any routine technique: pushing a thin walled tube into a cohesionless deposit densifies it, the sample drains and loses its capillary bonding on withdrawal, and whatever arrives in the laboratory has a fabric, density and stress history unrelated to the ground. Because the two parameters that actually govern the design of a footing on sand — the effective friction angle $\phi'$ and the compressibility — both depend almost entirely on relative density and fabric, a laboratory test on a reconstituted sample measures the technician's compaction effort, not the deposit. An in-situ index that is taken while the soil is still in the ground and still under its own overburden stress is therefore the only honest measurement available, and the SPT is the index for which the profession has the longest and broadest calibration record.

The second element of the rationale is empirical rather than theoretical. The blow count is a crude dynamic penetration index with no closed-form relation to any soil property, but it correlates well with relative density, and through relative density with $\phi'$, with elastic modulus, with liquefaction resistance and — through Terzaghi and Peck's original settlement charts and Meyerhof's later revisions — directly with the settlement of a footing of a given width at a given pressure. Sixty years of case records underpin those correlations, so a designer using them is leaning on observed foundation performance rather than on a constitutive model. The test is also cheap, is performed in the same borehole that is being advanced for stratigraphy, recovers a disturbed sample for classification at every increment, and can be carried out in gravelly soils that defeat the cone. That combination of coverage, cost and calibration is why the SPT survives in coarse-grained work long after it was abandoned for clays.

The Canadian Foundation Engineering Manual accepts the test on these terms and then attaches a set of conditions to its use. Its recommendations may be summarised as follows.

Correct for energy first. The raw blow count depends on the hammer system, so $N$ must be converted to $N_{60}$, the value corresponding to a rod energy ratio of 60 percent of the theoretical free-fall energy, using a measured or published efficiency for the rig. Automatic-trip hammers common in Canada deliver 55 to 80 percent, and an uncorrected count from a modern rig can overstate density substantially.
Then correct for overburden. For any relative-density or $\phi'$ correlation, normalise to a vertical effective stress of 100 kPa, giving $(N_1)_{60}$. Without this correction a uniform deposit appears to gain strength with depth purely through the confinement of the test.
Use it as an index, not as a measurement. CFEM presents SPT-based values of $\phi'$ and of settlement as preliminary or comparative estimates, appropriate for routine light and moderate structures, and recommends that important or settlement-sensitive works be supported by the cone penetration test, pressuremeter, plate load tests or full-scale load tests.
Respect the soils in which it is unreliable. The manual cautions against SPT-based design in gravels and cobbly soils (blow counts inflated by particles larger than the sampler shoe), in silts and fine sands below the water table (where negative pore pressures or, at the other extreme, boiling of the base can distort $N$ either way), and in soft and sensitive clays, for which vane, cone or laboratory testing is preferred.
Control the procedure. Standard sampler dimensions, a clean stabilised borehole, adequate drilling fluid head to prevent base heave, rod lengths accounted for in short holes, and a test interval close enough to define the profile.

In practice, then, the CFEM position is that SPT results are used because nothing better survives sampling in a coarse-grained deposit, that they must be corrected before they mean anything, and that they define a design that is then confirmed — by a second in-situ method, or by observation — whenever the consequences of being wrong are serious.

Topic. In-situ index testing of cohesionless soils and its place in Canadian foundation practice.

Key relations. $N_{60} = N \cdot (E_r/60)$; $(N_1)_{60} = C_N N_{60}$ with $C_N = \sqrt{p_a/\sigma'_v}$ (Liao & Whitman, 1986); $\phi' = 27.1 + 0.3(N_1)_{60} - 0.00054[(N_1)_{60}]^2$ (Peck, Hanson & Thornburn as fitted by Wolff, 1989).

Why this works. The blow count is a measure of the work required to displace a fixed volume of soil, which for a cohesionless material is controlled by dilatancy, and dilatancy is controlled by relative density at the prevailing effective stress. Removing the energy variability and the confinement variability leaves a number that tracks relative density alone, and relative density is the single state variable that governs both the strength and the stiffness of a clean sand. The correlations are therefore not arbitrary curve fits; they are the visible consequence of a real physical chain.

Common pitfall. Two mistakes recur. The first is using raw field $N$ values in a $\phi'$ correlation and so importing the drill rig's hammer efficiency into the design. The second is applying an SPT settlement chart in a gravelly soil, where a single cobble on the sampler shoe can double the blow count and produce a dangerously optimistic bearing pressure.

Source. Canadian Geotechnical Society, Canadian Foundation Engineering Manual, 4th ed., §4 (in-situ testing) and §10; Das, Principles of Foundation Engineering, 9th ed., §2.8–2.10.

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