Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams — December 2014 — 04-Env-A3 / Geotechnical & Hydrogeological Engineering. 3 hours duration; open book exam, any non-communicating calculator permitted. The first five questions as they appear in the answer book are marked (20 marks each, 100 marks total); all six are solved below for completeness.
Reference texts. Braja M. Das, Principles of Geotechnical Engineering (9th ed.) — weight–volume relations, compaction, seepage/flow nets, effective stress and shear strength chapters; Craig & Knappett, Craig's Soil Mechanics (8th ed.) — cross-reference for flow nets, method of fragments and shear strength; Freeze & Cherry, Groundwater (1979) — Darcy's law and the Dupuit–Thiem equation for unconfined radial flow to a well.
Find. (a) volume of soil to excavate from the borrow site; (b) number of trucks required.
Approach. Track the dry-solids mass balance from the borrow pit (in-situ) through to the compacted fill, since the solids mass is conserved while only water content and packing change; bulk the excavated (bank) volume by the bulking factor to get the loose (hauled) volume, then size the truck fleet from the cycle time and shift schedule.
Dry unit weights. Borrow soil (in-situ): $\gamma_{d,borrow}=\gamma_{bulk}/(1+w)=16/1.05=15.24\ \text{kN/m}^3$. Target compacted fill (95% Proctor, dry basis): $\gamma_{d,fill}=0.95\times19.5=18.525\ \text{kN/m}^3$.
Part (a) — volume to excavate. Equal dry-solids weight links the two states: $V_{insitu}\,\gamma_{d,borrow}=V_{fill}\,\gamma_{d,fill}$, so
$$V_{insitu}=\frac{V_{fill}\,\gamma_{d,fill}}{\gamma_{d,borrow}}=\frac{10{,}000\times18.525}{15.24}=\boxed{12{,}157\ \text{m}^3}.$$
Part (b) — bulked (hauled) volume. Excavated soil swells by the bulking factor before it re-compacts:
$$V_{loose}=V_{insitu}(1+0.30)=12{,}157\times1.30=\boxed{15{,}804\ \text{m}^3}.$$
Truck fleet sizing. Total working time $=2\times2\times8=32\ \text{h}$. Loads per truck $=32\times60/15=128$, so each truck moves $128\times25=3{,}200\ \text{m}^3$ over the job. The fleet size is
$$n_{trucks}=\frac{V_{loose}}{3{,}200}=\frac{15{,}804}{3{,}200}=4.94\ \Rightarrow\ \boxed{5\ \text{trucks}}$$
(rounded UP, since a fractional truck cannot be fielded and the job must finish within the fixed two-day window).
Check: assumes the fill is compacted at (or trucked/placed to allow adjustment toward) the Proctor optimum water content, so the dry-unit-weight mass balance is the correct basis for comparing borrow soil to finished fill — the moist bulk unit weights of the two states are not directly comparable because their water contents differ.
