24-Bld-A6 Geotechnical Materials and Analysis · December 2018
Question 2 of 7
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
07-BLD-A6 Geotechnical Materials and Analysis — National Examinations, December 2018. 3 hours, closed book, 100 marks. Section A (Q1–Q3) is compulsory; Section B directs "answer any three of Q4–Q7," but for completeness this solution answers all four.
Reference texts: B.M. Das, Principles of Geotechnical Engineering, 9th ed.; B.M. Das, Principles of Foundation Engineering, 9th ed.
Given. Compacted fill volume needed $V_f=9000\text{ m}^3$ at void ratio $e_f=0.72$.
Borrow-pit data
Borrow Pit
Void ratio, e
$G_s$
Unit cost ($/m³)
A
0.82
2.67
9
B
0.93
2.70
7
Find. Which pit supplies the required fill at lower total cost.
Approach. The volume of solid particles is conserved between the borrow pit and the compacted fill (excavation and compaction change only the void space, never the particles themselves), so convert the target compacted volume to a solids volume once, then re-expand it at each pit's own (higher) void ratio to find how much must actually be excavated from that pit.
Volume of solids required. $V_s=\dfrac{V_f}{1+e_f}=\dfrac{9000}{1.72}=5232.6\text{ m}^3$ — this quantity is the same no matter which pit supplies it.
Borrow volume from Pit A. $V_A=V_s(1+e_A)=5232.6\times1.82=9523.3\text{ m}^3$. Cost$_A=9523.3\times\$9=\boxed{\$85{,}709}$.
Borrow volume from Pit B. $V_B=V_s(1+e_B)=5232.6\times1.93=10098.8\text{ m}^3$. Cost$_B=10098.8\times\$7=\boxed{\$70{,}692}$.
Pit B needs a larger volume in place (its soil is looser), but its lower haul cost per cubic metre more than compensates — Pit B is about $15{,}017 cheaper overall. Note that $G_s$ cancelled out of this comparison entirely: it converts volume to mass, which is irrelevant here since cost is charged per cubic metre moved, not per tonne — a reminder that a real spec sheet often carries more properties than any one calculation needs.
