07-Str-B1 · May 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Examinations — May 2013 — 07-Str-B1 Geotechnical Design. Three-hour, OPEN-BOOK exam; any non-communicating calculator permitted (the candidate must record its make and model). Format: Section A carries five short-answer questions of 7 marks each, of which any FOUR are to be answered; Section B carries the long design questions at 24 marks each, of which any THREE are to be answered. The paper instructs candidates to state any interpretive assumptions and to identify the source of every design chart or assumed value used. Every question in both sections is worked below, because the set is intended as a study resource.
Reference texts: Das, B.M., Principles of Foundation Engineering (9th ed., Cengage) — shallow foundations, consolidation settlement, sheet-pile walls, retaining walls and drilled shafts; Das, B.M., Principles of Geotechnical Engineering (9th ed., Cengage) — method of slices, lateral earth pressure, consolidation theory; Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM, 4th ed., 2006) — Canadian practice for SPT interpretation, pile design, limit-states design and tolerable settlement; Craig, R.F. / Knappett, J.A., Craig's Soil Mechanics (8th ed., CRC Press) — effective stress, shear strength and slope stability; Duncan, J.M., Wright, S.G. & Brandon, T.L., Soil Strength and Slope Stability (2nd ed., Wiley) — choice of strength parameters and factors of safety for short- and long-term analyses.
NOTE 1 — question numbering in the source. The printed paper labels the retaining-wall problem (Figure 4) and the drilled-pier problem (Figure 5) both as "Question 9", while the Section B heading reads "answer any THREE of the following FOUR questions". Section B therefore contains five printed problems under four numbers. They are set out below as Question 9 (retaining wall) and Question 10 (drilled pier) in printed order, so that each can be referred to unambiguously; the marks shown are those printed against each problem.
NOTE 2 — dimensions scaled from Figure 1. Figure 1 is a hand-drawn slope on a 1 m × 1 m grid with no written dimensions other than $R=10$ m. The geometry used in Question 6 was scaled from that grid: slope height 7 m over a 9 m horizontal run, a 3 m thick lower layer, and the centre of the trial circle 1.4 m horizontally beyond the toe and 8.0 m above it. Every one of these values reproduces the drawing to within about 0.2 m (one fifth of a grid square). Check against the original if the paper is used for marking rather than study.
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.
For an embankment built of clay, the end-of-construction condition is the critical one: pore pressures are at their maximum the moment the last lift is placed, and every subsequent day of consolidation increases effective stress and therefore strength. The soil is at its weakest exactly when the geometry first reaches full height. That alone justifies care, but the reasons for demanding a larger margin are about uncertainty rather than about the mean strength.
The strength parameter is the least reliable one available. An undrained analysis rests on $s_u$ (or on total-stress $c$ and $\phi$ for a partly saturated compacted fill). Undrained strength is not a material constant: it depends on sample disturbance, on the direction of the major principal stress relative to the deposit (anisotropy of 2:1 between triaxial compression and extension is common), on strain rate, and on whether the clay is fissured. A field vane result must be reduced by Bjerrum's plasticity correction before it can be used at all. The effective-stress parameters $c'$ and $\phi'$ that govern the long-term case are, by comparison, fundamental and repeatable; scatter in $\phi'$ of a few degrees is normal, scatter in $s_u$ of a factor of two is not unusual.
The construction pore pressures are predicted, not measured. The undrained strength mobilised in a compacted clay core depends on the pore pressure generated during placement, which depends on the placement water content relative to optimum, the air content of the compacted fill, and the rate at which the embankment is raised — none of which is known precisely at design stage. A design that is only just adequate is a design that assumes the contractor will place fill exactly at the specified water content.
The failure mode itself is unforgiving. An undrained failure in a compacted or sensitive clay is rapid and, where the clay is strain-softening, brittle: once the peak is passed on part of the surface, load sheds to the rest and the slide runs. There is no slow warning of the sort that a drained failure under steady seepage usually gives, and therefore no opportunity for the observational method — piezometer and inclinometer readings, a pause in construction, a berm — to intervene. Add to this that construction is the period when the dam is most likely to be surcharged by plant and haul traffic and least likely to have its instrumentation fully commissioned.
Check — which convention is being followed. Several widely used standards specify the opposite ranking of numerical factors: Duncan and Wright, and USACE EM 1110-2-1902, recommend a minimum $F$ of about 1.3 at end of construction against 1.5 for the long-term steady-seepage case, on the grounds that the short-term condition is temporary, monitored and has better-known loads. The answer above justifies the statement as the paper poses it, by reference to the uncertainty in undrained strength and construction pore pressures. In an examination it is worth stating explicitly which convention is being used and why; the Canadian Dam Association guidelines require the designer to state the strength model and the associated target factor together, precisely because the number is meaningless without it.
| Quantity | Symbol | Role in the analysis |
|---|---|---|
| Undrained shear strength of the compacted fill | $s_u$, or total-stress $c$ and $\phi$ | Shear resistance on the trial surface within the embankment; a $\phi=0$ analysis applies only if the fill is saturated |
| Undrained strength of the foundation clay | $s_u$ (with depth) | Governs any surface that passes below the embankment into soft foundation soil |
| Bulk (total) unit weight at placement | $\gamma$ | Slice weights and driving moment |
| Placement density and water content | $\gamma_d$, $w$ | Fix the strength and the pore pressure response; the specification is written in these terms |
| Construction pore pressure | $u$, or $r_u=u/\gamma h$ | Required if the check is run as an effective-stress analysis rather than a total-stress one |
| Pore pressure parameters | $A$, $B$ | Predict $u$ from the stress change imposed by each lift |
| Consolidation properties | $c_v$, $m_v$ | Needed only if strength gain during staged construction is to be credited |
| Classification and index properties | $w_L$, $I_p$, grading, $G_s$ | Vane correction, correlation checks, and identification of dispersive or sensitive materials |
The core test is the unconsolidated–undrained (UU or Q) triaxial test, run on specimens compacted in the laboratory to the design dry density and water content, at cell pressures spanning the range of confining stress in the dam. For a partly saturated compacted fill this returns a curved total-stress envelope that is normally linearised as $c$ and $\phi$ over the working stress range; for a saturated fill it collapses to the $\phi=0$ case with $s_u=q_u/2$. A consolidated–undrained (CU or R) triaxial test with pore-pressure measurement should be run alongside it: it gives $s_u$ after consolidation for staged-construction checks, and simultaneously gives the $c'$ and $\phi'$ needed for the long-term steady-seepage case, so it is efficient to run both series on the same borrow material.
For the foundation clay, the field vane test is the standard Canadian tool for a soft deposit, corrected by Bjerrum's $\mu$ factor as a function of plasticity index, supported by piezocone soundings for continuous profiling and by UU triaxial tests on high-quality thin-walled tube samples. The standard Proctor compaction test establishes the target density and optimum water content against which the fill is specified and against which the triaxial specimens are prepared. Atterberg limits, grain-size distribution and specific gravity support classification and the vane correction, and oedometer tests supply $c_v$ and $m_v$ where the rate of construction is to be controlled by pore-pressure dissipation. Unconfined compression tests are a useful rapid index but should not be the basis of design, since they impose zero confinement and are unreliable in fissured clay. Finally, the field programme should include piezometers and settlement plates installed as the fill rises: the design is only as good as its pore-pressure assumption, and the instrumentation is what converts that assumption into an observation.
