16-Civ-A4 Geotechnical Materials and Analysis · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Examinations (PEO/Engineers Canada) — 16-Civ-A4 Geotechnical Materials and Analysis, December 2019. Six questions, 100 marks, closed book, 3 hours; all questions are to be answered. A formula sheet, an m–n influence chart and a Newmark chart are provided at the back of the paper.
Reference texts: Das & Sobhan, Principles of Geotechnical Engineering, 9th ed. (Cengage); Craig’s Soil Mechanics (Knappett & Craig), 8th ed.; Holtz, Kovacs & Sheahan, An Introduction to Geotechnical Engineering, 2nd ed.
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.
(a) The spring analogy and effective stress. In Terzaghi’s piston-and-spring model the spring represents the soil skeleton, the water filling the cylinder represents the pore water, and the valve represents the soil’s drainage capacity (permeability). Any applied load is shared according to the effective-stress principle, $\Delta\sigma = \Delta\sigma' + \Delta u$, where $\Delta\sigma'$ is carried by the spring and $\Delta u$ by the water.
In panel (a) the valve is closed and no new load acts, so the system is in equilibrium; the spring carries the seating stress and the excess pore pressure is zero. When the load is suddenly applied with the valve closed (panel b), the water — being far stiffer than the skeleton and unable to escape — carries essentially the entire increment: $\Delta u = \Delta\sigma$, the spring is unchanged, $\Delta\sigma'=0$, and there is no settlement yet. This is the undrained instant $t=0$.
Once the valve is opened (panels c–d), water bleeds out at a rate set by the permeability; as it does, load transfers from the water to the spring, the excess pore pressure dissipates ($\Delta u \to 0$) and the effective stress grows ($\Delta\sigma' \to \Delta\sigma$). The piston descends — this gradual, time-dependent settlement is consolidation. At the end (panel d) the excess pore pressure has fully dissipated, the spring carries the whole load ($\Delta\sigma'=\Delta\sigma$), and primary consolidation is complete. The essential lesson is that settlement is governed by the transfer of load from pore water to skeleton, i.e. by the growth of effective stress.
(b) Tests and equipment for the loading in Figure 3(b). Panel (b) is the undrained condition — valve closed, load carried entirely by pore water — on a normally consolidated saturated clay. The relevant strength for that instant is the undrained shear strength $s_u$. It is measured with an unconsolidated-undrained (UU) triaxial test in a triaxial cell (a saturated, undisturbed Shelby-tube specimen sheared with no drainage), supplemented in the field by a vane shear test or, in the laboratory, an unconfined compression test ($s_u = q_u/2$). Because the specimen is saturated and sheared undrained, the total-stress strength envelope is horizontal — a $\phi_u = 0$ analysis, with $\tau_f = s_u = c_u$ independent of total confining stress.
By contrast, the drained end-state of panel (d) — valve open, excess pore pressure fully dissipated — would be characterised by the effective-stress parameters $c',\phi'$ from a consolidated-drained (CD) test (or a CU test with pore-pressure measurement), which is why the question distinguishes (b) from (d): the immediate (undrained) and long-term (drained) shear strengths are governed by different envelopes.
