07-Str-A3 · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. Engineers Canada / PEO National Examinations, May 2015 — 07-Str-A3 Geotechnical Materials and Analysis. Closed book, three hours, 100 marks, approved Casio or Sharp calculator, drawing instruments required. All six questions are compulsory and are weighted 20 / 10 / 10 / 20 / 20 / 20. The paper supplies its own appendix: a formula sheet, the rectangular-loading m–n influence chart and a Newmark influence chart with influence value $I_N = 0.005$ (200 elements). Values quoted from those sheets are used here.
Reference texts.
Check — two printing slips in the source, carried as printed. (1) Question 1 is headed “(4 x 5 = 20 marks)” but prints five lettered parts (i)–(v). All five are answered below and the header total of 20 marks is kept; read the header as five parts at four marks each. (2) In Question 5 the surcharge and the two cohesion intercepts are printed with the units $\text{kN/m}^{3}$ — dimensionally these are stresses and must be read as $\text{kPa}$ ($\text{kN/m}^{2}$); the unit weights carry the $\text{kN/m}^{3}$ correctly. The solution states each value in the unit its symbol requires.
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 test programme follows from the drainage condition that governs, and this tank has three distinct ones. Construction and the very first filling apply the load far faster than a saturated clay can drain, so that stage is undrained and is analysed in total stress with the undrained shear strength $c_u$ and $\phi = 0$. Once the tank has stood, the excess pore pressures dissipate and the clay consolidates under the tank dead load and the average product weight; the clay gains strength and the long-term case is drained, analysed in effective stress with $c'$ and $\phi'$. Between the two lies the condition the question is really pointing at: after the clay has consolidated, the tank is filled and emptied rapidly and repeatedly, which is a fast load applied to an already-consolidated soil — that is precisely the consolidated–undrained condition. A programme that covers only the first or only the last of these will miss the governing case.
The primary test is the consolidated undrained (CU) triaxial test with pore-water pressure measurement, run on specimens consolidated isotropically (better, anisotropically, to $K_0$ conditions) to cell pressures that bracket the in-situ effective stress plus the stress increase under the tank. It is the right test for three reasons. It reproduces the field sequence exactly — consolidate first, then shear fast. It yields the undrained strength appropriate to the consolidated state, which is what the rapid-filling case needs. And because the pore pressure is measured, the same specimens also deliver the effective-stress parameters $c'$ and $\phi'$ for the long-term analysis, along with Skempton’s pore-pressure coefficient $A_f$, which quantifies how much excess pore pressure each rapid filling will generate. One test therefore serves two design cases, which is why the CU test with pore-pressure measurement is the workhorse of tank and embankment design.
It is supported rather than replaced by the others. Unconsolidated undrained (UU) triaxial tests, and unconfined compression tests, give $c_u$ in the present in-situ state and cover end-of-construction and first filling; they are quick and cheap and give the strength profile with depth. Consolidated drained (CD) triaxial tests, run slowly enough that no excess pore pressure develops, give $c'$ and $\phi'$ directly and are worth running on two or three specimens as an independent check on the effective-stress envelope inferred from the CU tests, although on a clay they are slow. In-situ field vane shear tests should be run in the same boreholes: they give an undisturbed profile of $c_u$, together with the remoulded strength and hence the sensitivity, and they provide the cross-check that shows whether the laboratory specimens have been damaged in sampling. The vane strength must be corrected by Bjerrum’s plasticity factor $\mu$ before use in design. If the filling and emptying cycles are frequent enough to accumulate over the design life, cyclic triaxial tests should be added to check strength degradation and accumulated strain. Oedometer (consolidation) tests are also required, not for strength but for the settlement and rate-of-settlement analysis and to establish the preconsolidation pressure that tells you whether the deposit is normally or over consolidated.
All of the strength tests above must be run on high-quality undisturbed samples. In a soft to firm saturated clay that means thin-walled Shelby tubes pushed in one continuous stroke, never driven, with an area ratio below about ten per cent, a small inside clearance ratio and a sharp cutting edge; in soft or sensitive clay a stationary-piston sampler, and for the highest quality a Laval or Sherbrooke block sample. Samples must be sealed at both ends with wax immediately, transported upright with minimal vibration, and stored in a humid room so that no water is lost before testing.
The reason is that the shear strength of a clay is a property of its fabric, water content and stress history together, not of its grain assemblage alone. Remoulding destroys the inter-particle bonding built up over geological time, and in a sensitive Canadian marine clay the remoulded strength can be a small fraction of the intact value. Sample disturbance also flattens the $e - \log \sigma'$ curve, which masks the preconsolidation pressure, and it drives measured undrained strengths downward, giving an apparently conservative but in fact simply unreliable design value. A CU or CD test only means anything if the specimen still carries its in-situ structure.
Disturbed samples still have a role, but a limited one. Split-spoon (SPT) and auger samples are collected for classification — water content, Atterberg limits, grain-size distribution, unit weight — and for correlating strength with index properties between the undisturbed sampling depths. Sampling should extend over the full depth of significant stress increase, conventionally to about twice the tank diameter below foundation level, with undisturbed samples at close vertical spacing through the soft strata. This sampling-class hierarchy is the one set out in the Canadian Foundation Engineering Manual.
