16-Civ-B3 Geotechnical Design · May 2016

Question 4 of 9: Field methods for soil strength, and their limitations (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 4 — Field methods for soil strength, and their limitations (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.

Methods available in the field. The in-situ tests in ordinary Canadian practice, in roughly increasing order of sophistication, are: the standard penetration test (SPT) with split-spoon sampling; the cone penetration test and its piezocone variant (CPT / CPTu), optionally with a seismic module; the field vane shear test (VST); the flat dilatometer test (DMT); the pressuremeter test, either pre-bored (Menard) or self-boring; the plate load test and the screw plate test; the borehole shear test; the Becker penetration test for gravels and tills; and geophysical methods (seismic cross-hole, down-hole and surface-wave surveys) that return the small-strain shear modulus $G_{\max} = \rho V_s^{2}$ rather than a strength. To these should be added the quasi-field index tools used on recovered samples at the borehole — the pocket penetrometer and the torvane — which are useful for logging but are not design tests.

The rapid method for a dense sand: the cone penetration test. The CPT pushes a 10 cm² cone at 20 mm/s and logs tip resistance $q_c$ and sleeve friction $f_s$ continuously, so a 20 m profile is obtained in well under an hour and the friction angle follows from established correlations such as $\phi' = \tan^{-1}\!\left[0.1 + 0.38\log\left(q_c/\sigma'_{v0}\right)\right]$ (Robertson and Campanella — the same source as the profile used in Question 6). Where the sand is gravelly or contains cobbles the SPT is the practical alternative, with $\phi'$ taken from $N_{60}$ corrected for overburden to $\left(N_1\right)_{60}$.

The rapid method for a soft clay: the field vane test. The vane is pushed into undisturbed clay below the borehole and rotated at about 6° per minute; the peak torque gives the undrained strength directly, $c_u = \dfrac{T}{\pi d^{2}\left(h/2 + d/6\right)}$ for a rectangular vane, and rotating the vane rapidly through ten turns and re-testing gives the remoulded strength and hence the sensitivity in the same operation. CPTu is the natural companion, giving a continuous profile through $c_u = \left(q_t - \sigma_{v0}\right)/N_{kt}$.

Limitations of each.

CPT / CPTu. No sample is recovered, so the soil must be classified from the friction ratio and pore-pressure response rather than seen; the strength values are correlations, not measurements, and the cone factor $N_{kt}$ ranges from about 10 to 20 so the derived $c_u$ carries a real uncertainty; a heavy reaction mass (typically a 15 to 20 tonne truck or anchored rig) is needed and access can be impossible; the cone refuses in dense gravel, cobbles or till and can be damaged; readings must be corrected for unequal end area to $q_t$, and in a very dense sand the tip load may exceed the rating of the cone.
SPT. The single most variable test in geotechnics: the energy actually delivered to the rods depends on the hammer, and raw N must be converted to $N_{60}$; results are affected by rod length, borehole diameter, sampler liners, and by disturbance or base heave in the borehole; gravel or cobbles jamming the shoe give spuriously high blow counts; in soft clay N is near zero and carries no useful information; the sample is disturbed, so it serves only for classification; and every strength interpretation is empirical, with no modulus obtained at all.
Field vane. Applicable only to soft to firm clays — it cannot be pushed into stiff clay, sand or till; it measures strength on a vertical cylindrical surface, so it reflects anisotropy in an unrepresentative way; it systematically over-estimates the strength mobilised in a field embankment failure, which is why Bjerrum's correction factor $\mu\!\left(\text{PI}\right)$ (falling from 1.0 at low plasticity to about 0.6 at PI = 60) must be applied; sand or silt partings and fissures in the clay give erratically high torques; the result is rate dependent; and it gives only the undrained strength, never $c'$, $\phi'$ or any stiffness.
Pressuremeter and dilatometer (mentioned for completeness). Both give strength and stiffness in one test, but the pre-bored pressuremeter is highly sensitive to the quality of the pocket, the self-boring version is expensive and slow, and both require skilled operators and careful interpretation.
Plate load test. Direct and easy to interpret, but it stresses only about twice the plate width of soil, so it misses deeper compressible layers entirely, and the scale effect between a 300 mm plate and a real footing must be corrected for; it is slow and costly and is normally reserved for confirming a design rather than making one.

The practical conclusion is that no single test is sufficient. Canadian practice, and the CFEM, recommend a combination: continuous CPTu profiling to define the stratigraphy and the trend of strength with depth, calibrated at intervals by boreholes with SPT and sampling in coarse soils and by field vane tests in soft clays, with laboratory triaxial and oedometer testing on the best samples to anchor the correlations.

Topic. In-situ testing for shear strength: what each test actually measures and what it cannot.

Key relations. $N_{60} = \dfrac{N\,E_r}{60}$ and $\left(N_1\right)_{60} = C_N N_{60}$ with $C_N = \sqrt{p_a/\sigma'_{v0}}$ (Liao and Whitman); $c_u = \left(q_t - \sigma_{v0}\right)/N_{kt}$; vane strength $c_u = T/\left[\pi d^{2}\left(h/2 + d/6\right)\right]$ with the corrected design value $c_{u,\text{design}} = \mu\,c_{u,\text{vane}}$; sensitivity $S_t = c_{u,\text{peak}}/c_{u,\text{remoulded}}$.

Why this works. Every in-situ test imposes a different stress path, strain rate and drainage condition on the soil, so each is trustworthy over a narrow band of materials: the vane shears a soft clay slowly enough to stay undrained but not so slowly that it drains, while the cone at 20 mm/s is undrained in clay and drained in sand, which is precisely why the same instrument needs two different interpretation frameworks. Matching the test to the material and to the limit state being checked is the whole skill.

Common pitfall. Using an uncorrected vane strength in an embankment stability analysis. Bjerrum's correction exists because back-analysed field failures mobilise appreciably less strength than the vane reports, and omitting it can turn a computed factor of safety of 1.4 into a real one below unity. The parallel error on the granular side is quoting raw SPT blow counts without the energy and overburden corrections.

Source. Das, Principles of Foundation Engineering, 9th ed., Ch. 2 (subsurface exploration: SPT, CPT, vane, pressuremeter, dilatometer, plate load test); Canadian Geotechnical Society, Canadian Foundation Engineering Manual, 4th ed., Ch. 4; Robertson and Campanella (1983, 1988) for the CPT correlations.

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