16-Civ-A4 Geotechnical Materials and Analysis · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Examinations (Engineers Canada / PEO), 98-Civ-A4 Geotechnical Materials and Analysis, December 2014. Closed book, 3 hours, 100 marks. Six questions — answer all. Charts and equations supplied at the back of the paper.
Reference texts: Das & Sobhan, Principles of Geotechnical Engineering (9th ed.), Cengage; Holtz, Kovacs & Sheahan, An Introduction to Geotechnical Engineering (2nd ed.), Pearson; Craig’s Soil Mechanics (Knappett & Craig, 8th ed.), CRC Press.
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.
Given. Effective strength parameters (unique to the soil) $c' = 10$ kPa, $\phi' = 28^\circ$. CU stage: total confining stress $\sigma_3 = 100$ kPa; pore-water pressure at failure $u_w = 40$ kPa.
| Quantity | Symbol | Value |
|---|---|---|
| Effective cohesion | $c'$ | 10 kPa |
| Effective friction angle | $\phi'$ | $28^\circ$ |
| Total confining stress | $\sigma_3$ | 100 kPa |
| Pore-water pressure at failure | $u_w$ | 40 kPa |
Find. The total vertical stress $\sigma_1$ at failure in the CU test.
Approach. The effective-stress failure envelope $\tau_f = c' + \sigma'\tan\phi'$ is a property of the soil and is the same whether the test is CD or CU. Work in effective stresses (subtract $u_w$), apply the Mohr–Coulomb principal-stress relation to get $\sigma'_1$, then add $u_w$ back to recover the total stress.
| Quantity | Value |
|---|---|
| $\sigma'_3 = \sigma_3 - u_w$ | 60 kPa |
| $N_\phi = \tan^2(59^\circ)$ | 2.770 |
| $\sigma'_1$ (effective) | 199.5 kPa |
| $\sigma_1$ (total, applied) | 239.5 kPa |
(i) What the CU test with pore-pressure measurement gives the senior engineer. A consolidated-undrained test in which $u_w$ is measured yields both strength frameworks from one relatively quick test. Plotting total-stress circles gives the undrained (total-stress) parameters $c_{cu},\ \phi_{cu}$ (and, at a single confining pressure, the undrained shear strength $s_u$), which govern end-of-construction / rapid-loading stability. Simultaneously, subtracting the measured $u_w$ gives the effective-stress circles and hence $c',\ \phi'$ — the fundamental long-term parameters — without waiting weeks for a fully drained test. The pore-pressure record also yields Skempton’s pore-pressure parameter $A_f$, which characterises whether the clay is contractive (normally consolidated, positive $u_w$) or dilative (over-consolidated, negative $u_w$) and lets the engineer predict field pore pressures under undrained loading.
(ii) When to run CD versus CU. Use a CD (consolidated-drained) test when the field problem is governed by long-term, drained conditions in which excess pore pressures have fully dissipated — for example the long-term stability of a cut slope or an earth-dam slope in clay years after construction, where $c',\ \phi'$ apply directly. Use a CU (consolidated-undrained with $u_w$) test when loading is rapid relative to drainage, or when both short- and long-term parameters are needed quickly — for example staged embankment construction on a soft clay foundation, or the rapid-drawdown case on the upstream fill zone of a dam, where the CU test supplies the undrained strength for the critical short-term condition and, via $u_w$, the effective parameters for the drained checks. In short: CD for slow permeable/long-term behaviour; CU for fast loading of low-permeability clays and for getting effective parameters economically.
