Question 1 of 6: True / False with Justification

Question 1: True / False with Justification (10 marks)

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 ten statements in the exam’s True/False table are answered below. Each verdict carries the one-line justification the exam demands — a bare T/F earns no marks.

1. 1 — The zero-air-voids line (ZAVL) always plots above the compaction curve and is roughly parallel to the wet-of-optimum branch. TRUE. The ZAVL is the locus for full saturation ($S=100\%$); a compacted soil always retains some air ($S\lt100\%$), so its dry density at any water content is lower and the field curve lies below the ZAVL. Beyond optimum the compaction curve tracks nearly parallel to the ZAVL because the wet-side density is saturation-controlled.
2. 2 — Effective cohesion $c'$ is typically larger in over-consolidated than in normally consolidated clay. TRUE. A truly normally consolidated clay has an effective failure envelope through the origin ($c'\approx0$). Over-consolidation leaves the soil denser than its current stress warrants, producing a curved/offset envelope with a positive $c'$ intercept over the working stress range.
3. 3 — Soil B (LL = 50%) has a lower compression index than Soil A (LL = 60%). TRUE. With Skempton’s correlation $C_c \approx 0.009(LL-10)$, $C_{c,A}=0.009(50)=0.45$ and $C_{c,B}=0.009(40)=0.36$. Compressibility scales with liquid limit, not with the (here equal) plasticity index, so the lower-$LL$ Soil B is less compressible.
4. 4 — A saturated specimen sheared CD undergoes more volume change than one sheared CU. TRUE. In a consolidated-undrained test drainage is closed, so a saturated specimen shears at essentially constant volume ($\Delta V \approx 0$) and the tendency to change volume shows up as pore pressure instead. In a consolidated-drained test drainage is open, so the volumetric strain is free to develop — hence CD shows the larger volume change.
5. 5 — If 30% consolidation takes 3 months under 100 kPa, then 90% takes 9 months under 300 kPa. FALSE. Time to a given degree of consolidation depends on the time factor $T_v = c_v t/d^2$, which is independent of the load magnitude. For the same soil, $t_{90}=t_{30}\,(T_{v,90}/T_{v,30})=3\times(0.848/0.0707)\approx \boxed{36\ \text{months}}$, not 9 — and tripling the stress does not change it.
6. 6 — Boussinesq’s point-load equation is not valid at zero depth. TRUE. $\sigma_z = \dfrac{3Q}{2\pi z^2}\Big[1+(r/z)^2\Big]^{-5/2}$ is singular at $z=0$ (division by zero, giving an unbounded stress at the load point), so it cannot be evaluated at the surface directly beneath the load.
7. 7 — Knowledge of $C_c$ is required to determine the settlement of sand. FALSE. The compression index describes one-dimensional consolidation of clay. Sand settles essentially immediately (elastic/distortion settlement) and is analysed with an elastic modulus or SPT/CPT-based methods — $C_c$ plays no role.
8. 8 — The stress–strain behaviour of NC clay resembles that of loose sand. TRUE. Both are contractive on shearing and give a ductile, strain-hardening response that climbs to an ultimate strength with no distinct peak — unlike the strain-softening peak of OC clay or dense sand.
9. 9 — The plasticity index of low-compressibility silt (ML) is typically lower than that of high-compressibility clay (CH). TRUE. On the Casagrande chart ML plots low and below the A-line while CH plots high above it; the more plastic, more compressible clay carries the larger $I_p$.
10. 10 — The amount of volume change under load depends on the permeability $k$. FALSE. The magnitude of consolidation settlement is fixed by compressibility ($m_v$ or $C_c$) and the stress increment. Permeability governs the rate at which that settlement occurs (through $c_v = k/(m_v\gamma_w)$), not its final amount.