16-Civ-A4 Geotechnical Materials and Analysis · May 2018
Question 1 of 6: True / False with Justification
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 1: True / False with Justification (10 marks)
The ten statements to be judged (taken from the exam’s True/False table) are answered below. Each verdict is followed by the reasoning the exam requires — a bare T/F earns no marks.
1 — OC clay (A) settles less than NC clay (B) under the same footing load. TRUE.
Both clays start at the same void ratio, but the over-consolidated clay carries the applied stress increment on its recompression line (slope $C_s$), while the normally consolidated clay compresses on its much steeper virgin line (slope $C_c \gg C_s$). Since $s_c = \dfrac{C\,H}{1+e_0}\log\dfrac{\sigma_1'}{\sigma_0'}$, the smaller index for A gives the smaller settlement.
2 — Pore pressures in NC clay in a triaxial test can sometimes be negative. FALSE.
A normally consolidated clay is contractive: during shear it tends to reduce in volume, so in an undrained test it generates positive excess pore pressure (Skempton $A_f$ typically $0.5$–$1.0$). Negative excess pore pressure is the signature of a dense sand or a heavily over-consolidated clay that dilates on shearing, not of an NC clay.
3 — Soil D has the higher compression index $C_c$. FALSE.
Using $C_c \approx 0.009(LL-10)$: Soil C ($LL=60\%$) gives $C_c \approx 0.009(60-10)=0.45$, whereas Soil D ($LL=50\%$) gives $C_c \approx 0.009(50-10)=0.36$. Compressibility tracks the liquid limit, so Soil C — not D — is the more compressible soil.
4 — Significant volume change occurs in a saturated clay when total stress is increased rapidly. FALSE.
When the load is applied faster than water can drain, the saturated clay responds undrained: pore water (essentially incompressible) carries the increment as excess pore pressure and there is almost no immediate volume change. Volume change — consolidation — develops only slowly, as that excess pore pressure dissipates and effective stress rises.
5 — 90% consolidation under 300 kN/m² would occur in 9 months. FALSE.
The degree of consolidation depends on the time factor $T_v$, not on the magnitude of the load. From the same specimen, $t \propto T_v$. With $T_v(30\%)=\tfrac{\pi}{4}(0.30)^2 = 0.0707$ and $T_v(90\%)=-0.933\log(1-0.9)-0.085 = 0.848$, the time for 90% is $t_{90}=3\times\dfrac{0.848}{0.0707}\approx \boxed{36\ \text{months}}$, not 9. The higher load raises the amount of settlement but leaves the rate unchanged.
6 — $c'$ can never be negative for any clay. TRUE.
The effective cohesion is the shear strength the soil skeleton carries at zero effective normal stress. For a normally consolidated clay the effective envelope passes through the origin, so $c'=0$; for an over-consolidated clay the stress history (and any bonding) gives a small positive intercept, $c'>0$. A negative $c'$ would mean the soil fails in shear at zero normal stress with less than no strength, which is physically impossible. If a straight-line regression through a limited set of test points returns a slightly negative intercept, that is a fitting artefact and $c'$ is taken as zero in design.
7 — $C_c$ for an NC clay is not a function of effective stress. TRUE.
On the $e$–$\log\sigma'$ plot the virgin compression line of a normally consolidated clay is essentially straight, so its slope $C_c$ is a constant for the soil and does not vary with the current effective stress level.
8 — The stress–strain behaviour of OC clay resembles that of dense sand. TRUE.
Both are dense/stiff structures that dilate on shearing: they show a stiff initial response, a pronounced peak strength, then strain-softening toward a lower residual/critical-state value, and both develop negative excess pore pressure under undrained shear.
9 — Settlement of saturated clay is mainly compression of the pore water. FALSE.
Both the water and the solid grains are effectively incompressible. Consolidation settlement is the expulsion of pore water and the resulting reduction of void volume (grain rearrangement into a denser packing), not compression of the water itself.
10 — The amount of volume change depends on the permeability $k$. FALSE.
The magnitude of the ultimate volume change is governed by compressibility ($m_v$ or $C_c$). Permeability controls only the rate (time) at which that change is reached, through the coefficient of consolidation $c_v = k/(m_v\gamma_w)$ — a low-$k$ soil takes longer but reaches the same final settlement.
