07-Str-A3 · December 2015

Question 2 of 6: Choice of shear strength tests and samples for an earth dam

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

Notes on this paper

Paper format. Engineers Canada / PEO National Examinations, December 2015 — 07-Str-A3 Geotechnical Materials and Analysis. Closed book, three hours, 100 marks, one approved Casio or Sharp calculator, drawing instruments required. All six questions are compulsory and are weighted 20 / 10 / 10 / 20 / 20 / 20. The paper carries its own appendix: a formula sheet, the rectangular-loading m–n influence chart and a Newmark influence chart whose influence value is printed as $I_N = 0.005$ (200 elements). Values quoted below are taken from those sheets.

Reference texts.

B. M. Das & K. Sobhan, Principles of Geotechnical Engineering, 9th ed. — Ch. 6 (compaction), Ch. 7 (permeability), Ch. 9 (stresses in a soil mass), Ch. 10 (consolidation), Ch. 12 (shear strength).
R. F. Craig / J. A. Knappett, Craig’s Soil Mechanics, 8th ed. — Ch. 3 (effective stress, artesian profiles), Ch. 4 (pore pressure coefficients $A$ and $B$), Ch. 5 (shear strength and the choice of test), Ch. 6 (stress distribution).
Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed. — Ch. 4 (site investigation and sampling categories), Ch. 6 (excavations and base stability). The Canadian reference for practice, sampling classes and terminology.
K. Terzaghi, R. B. Peck & G. Mesri, Soil Mechanics in Engineering Practice, 3rd ed. — Art. 15–17 (consolidation and seepage), Art. 19–20 (shear strength of clays).

Check — three readings of the printed paper, carried as stated. (1) Question 1 is headed “(4 x 5 = 20 marks)” but prints five lettered parts (i)–(v); all five are answered and the header total of 20 marks is kept. (2) The section figure for Question 5 is captioned “Figure 2” on page 4 although the stem of Question 5 calls it Figure 3 — the same drawing, mislabelled in the source. (3) On that figure the “3.0 m” dimension is drawn with its arrowhead at the top of the sand, but at the figure’s own vertical scale (calibrated on the 2 m of clay left beneath the cut) the dimensioned distance is $3.1$ m from the piezometric surface down to the base of the cut, and $5.1$ m down to the sand. The piezometric surface is therefore taken as $3.0$ m above the base of the cut, i.e. $5.0$ m above point $A$; this is also the only reading for which a positive depth of water $h$ exists, and it reproduces the depth of water drawn in the figure. The alternative reading is worked through and dismissed in Question 5.

Question 2: Choice of shear strength tests and samples for an earth dam (10 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 choice of test is dictated by the drainage condition that governs the design, and for a 10 m embankment placed on a deep, saturated, normally consolidated clay that condition is the end of construction. The fill is placed in weeks or months; the clay beneath it has a coefficient of consolidation of order $1$ to $5\ \text{m}^{2}$/year and a drainage path measured in tens of metres, so essentially none of the excess pore pressure raised by the fill has dissipated by the time the last lift is placed. The foundation is at its weakest at that instant and gains strength thereafter as it consolidates. The figure shows the pattern.

The Bishop and Bjerrum picture of an embankment on a normally consolidated clay: excess pore pressure peaks at the end of construction and the factor of safety passes through its minimum there, then recovers as consolidation transfers load to the soil skeleton.

Tests proposed. The central test is the consolidated undrained triaxial test with pore-water pressure measurement (CU-bar, ASTM D4767), run on a set of undisturbed specimens from several depths. Each specimen is back-pressure saturated until Skempton’s $B$ exceeds about $0.95$, consolidated to the in-situ effective stress appropriate to its depth — anisotropically, at $K_0$, if the equipment allows, because a normally consolidated clay is not isotropically consolidated in the ground — and then sheared undrained with the pore pressure recorded. A single test series then yields three things at once: the effective-stress parameters $c' \approx 0$ and $\phi'$ for the long-term analysis, the undrained strength $s_u$ mobilised at the end of construction, and the pore pressure parameter $A_f$ needed to predict the excess pressure the fill will raise. Nothing else gives all three.

That programme is supported rather than replaced by the following. Unconsolidated undrained triaxial tests (UU, ASTM D2850) and unconfined compression tests give a quick $s_u$ profile for the immediate stability check, but they measure the strength of the sample as it arrives in the laboratory and so are unforgiving of disturbance. In-situ field vane shear tests (ASTM D2573, CFEM Ch. 4) are the reliable way to obtain the $s_u$ profile with depth, because they sample nothing and therefore disturb nothing; the raw vane strength must be multiplied by Bjerrum’s correction factor $\mu$, which falls from about $1.0$ at a plasticity index of 20 to roughly $0.6$ at a plasticity index of 100. Oedometer (consolidation) tests are indispensable even though they are not strength tests: they confirm that the deposit really is normally consolidated by locating the preconsolidation pressure $\sigma_p'$ relative to the present overburden, and they supply $c_v$, which sets the rate at which the design strength gain actually occurs. Finally, consolidated drained triaxial tests (CD) or slow direct shear tests give $c'$ and $\phi'$ directly for the long-term, steady-seepage condition and for the reservoir drawdown case; they are slow, but on a dam they are worth running as a check on the effective-stress parameters back-figured from the CU-bar series.

Two further points earn marks because they are specific to a normally consolidated deposit. First, the undrained strength of such a clay is not a constant — it increases with depth in proportion to the effective overburden, typically $s_u/\sigma_v' \approx 0.20$ to $0.25$ — so a single design value is meaningless and the test programme must sample the profile. Second, because the foundation gains strength as it consolidates, staged construction with piezometric monitoring is the natural way to build the dam, and the CU-bar and oedometer results are exactly the data that let the designer set the height of each stage and the waiting period between stages.

Samples required. High-quality undisturbed samples are essential, because every laboratory strength quoted above is destroyed by remoulding: a normally consolidated clay derives part of its strength from a structure built during deposition and ageing, and a sensitivity of 4 to 8 (much higher in a Champlain Sea clay) means that disturbance can halve or quarter the measured strength. In practice that means thin-walled fixed-piston sampling (ASTM D1587, Shelby tubes of 75 mm diameter or larger) with an area ratio below about ten per cent, a sharp cutting edge, zero inside clearance, pushed continuously rather than driven, sealed in the tube, kept vertical and at constant humidity in transit, and extruded in the direction of sampling shortly before testing. For a structure of this consequence, Laval or Sherbrooke block samples are the CFEM category-1 option where the deposit is soft and sensitive. Alongside these, ordinary disturbed samples from split-spoon or auger sampling are adequate and cheap for the classification work — water content, Atterberg limits, particle size, specific gravity, organic content — that the Bjerrum correction and the $s_u/\sigma_v'$ correlation both depend on. Continuous piezocone soundings between boreholes tie the discrete samples into a continuous profile and identify any silt or sand seams, which would change the drainage path assumption completely.

Test	What it delivers	Sample required
CU triaxial with pore-pressure measurement (primary)	$c'$, $\phi'$, $s_u$, $A_f$ at the correct consolidation stress	Undisturbed, thin-walled piston or block
UU triaxial and unconfined compression	Immediate undrained strength, rapid profile	Undisturbed, thin-walled piston
Field vane (with Bjerrum correction)	Undisturbed $s_u$ profile with depth	None — in situ
Oedometer	$\sigma_p'$ (confirms normally consolidated), $c_v$, rate of strength gain	Undisturbed
CD triaxial or slow direct shear	Long-term $c'$, $\phi'$ for steady seepage and drawdown	Undisturbed
Classification suite	$w$, $w_L$, $I_p$, grading, $G_s$ for correlations	Disturbed

Topic. Matching the laboratory drainage condition to the field loading rate, and the sample quality that makes the result meaningful.

Key relations. $\tau_f = c' + \sigma_n'\tan\phi'$ (effective stress); $\tau_f = s_u$ (total stress, $\phi_u = 0$, saturated undrained); $s_u/\sigma_v' \approx 0.22$ for a normally consolidated clay; $s_u(\text{design}) = \mu\, s_u(\text{vane})$; area ratio $A_r = (D_o^{2} - D_i^{2})/D_i^{2}$.

Why this works. A saturated clay loaded faster than it can drain responds at constant volume, so its strength at that instant is fixed by the effective stress it had before loading, not by the new total stress. That is the definition of the undrained case and it is why $\phi_u = 0$ analysis is legitimate at the end of construction. The CU-bar test reproduces exactly that history — consolidate to the in-situ state, then shear without drainage — which is why it is the primary test rather than the quicker UU. Everything else in the programme either confirms the stress history, converts a field measurement into a design value, or covers the long-term condition the undrained analysis does not address.

Common pitfall. Proposing UU tests alone and treating the result as the design strength: a disturbed 50 mm tube sample from a soft normally consolidated clay can return half the true $s_u$, and UU gives no effective-stress parameters at all, so the long-term case cannot be checked. The second common error is quoting the uncorrected vane strength, which is unconservative in a plastic clay by up to forty per cent.

Source. Craig’s Soil Mechanics 8th ed., §5.2–5.5 and §5.9 (choice of test, vane, Bjerrum correction); Das & Sobhan 9th ed., §12.5–12.12; CFEM 4th ed., Ch. 4 (sampling categories and disturbance).

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