16-Civ-A4 Geotechnical Materials and Analysis · May 2018
Question 3 of 6: Test Selection from the Consolidation Analogy
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
Paper format: National Examinations — 16-Civ-A4 Geotechnical Materials and Analysis, May 2018.
Closed book, 3 hours, 100 marks. Answer all six questions. All required charts (rectangular-area influence chart, Newmark chart) and a formula sheet are provided at the back of the exam.
Reference texts: R.F. Craig & J. Knappett, Craig’s Soil Mechanics (8th ed.); B.M. Das, Principles of Geotechnical Engineering; R.D. Holtz, W.D. Kovacs & T.C. Sheahan, An Introduction to Geotechnical Engineering (2nd ed.); M. Budhu, Soil Mechanics and Foundations. Take $\gamma_w = 9.81\ \text{kN/m}^3$ throughout.
Question 3: Test Selection from the Consolidation Analogy (15 marks)
The spring–piston–valve model is Terzaghi’s analogy for consolidation: the spring is the soil skeleton (carries effective stress) and the water beneath the piston is the pore fluid (carries excess pore pressure until the valve lets it escape). The state of the valve at the moment of loading therefore dictates whether the soil is sheared drained or undrained — and that, in turn, fixes which laboratory test reproduces the field condition. Diagrams (a) and (c) are reference states — (a) the unloaded soil with the valve open and (c) the fully consolidated soil after drainage — and carry no shear-strength test of their own; the question concerns only the two loading events, (b) and (d).
Typical shear-strength envelopes: horizontal total-stress (undrained, φᵘ = 0) envelope for the closed-valve loading (b); effective-stress envelope through the origin (NC clay, c' ≈ 0) for the open-valve loading (d).
Loading (b) — valve closed (undrained). With the valve shut, no water can leave when the piston is loaded, so the increment is carried entirely by the pore water as excess pore pressure and the effective stress on the spring does not change at the instant of loading. This is the undrained field case — a load applied faster than the clay can drain.
Recommended test: an unconsolidated–undrained (UU) triaxial test (drainage valves closed throughout), or for a quick index the unconfined-compression or field/lab vane test.
Equipment: triaxial cell with the sample sealed in a rubber membrane and both drainage lines closed; undisturbed (Shelby-tube) samples; a load frame giving a fast strain rate.
Parameter obtained: the undrained shear strength $c_u=s_u$ with $\phi_u=0$ — a horizontal (total-stress) envelope.
Practical example: short-term (end-of-construction) stability of an embankment or footing placed rapidly on a soft saturated clay — bearing capacity and slope stability immediately after loading, before any consolidation.
Loading (d) — valve open (drained). With the valve open the water escapes as the piston is loaded, the excess pore pressure stays at zero, and the full increment transfers to the spring as effective stress. This is the drained field case — loading slow enough that no excess pore pressure builds up.
Recommended test: a consolidated–drained (CD) triaxial test — the sample is first consolidated under the cell pressure, then sheared slowly with drainage open so that pore pressure never accumulates.
Equipment: triaxial cell with open drainage and pore-pressure/volume-change measurement, run at a strain rate slow enough for full dissipation (or a drained direct-shear box).
Parameter obtained: the effective-stress parameters $c'$ and $\phi'$; for the NC clay assumed here the envelope passes through the origin ($c'\approx0$), with slope $\phi'$.
Practical example: long-term stability of a natural or cut slope, or of an earth dam under steady seepage, where pore pressures have fully equalised; long-term settlement and bearing analyses.
