Question 4 of 6: Proctor Compaction — Watering and Haulage for a Borrow-Pit Fill
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
Paper format. 04-Agric-A2 Soil Physics & Mechanics,
National Exams May 2017 — a three-hour open-book examination;
any non-communicating calculator is permitted. The cover page states that five (5)
questions constitute a complete exam paper and that only the first five as they
appear in the answer book are marked, that each question is of equal value, and that
some questions require a written answer whose clarity and organization matter for
marks. All six printed questions are worked here, because the set is a study resource
rather than a timed attempt; on exam day a candidate submits only the first five, in
order.
Reference texts. B.M. Das, Principles of Geotechnical
Engineering, 9th ed. (weight-volume relationships, permeability, grain-size
analysis, USCS classification, compaction, slope stability, well hydraulics); R.F.
Craig, Craig's Soil Mechanics, 9th ed. (effective stress, seepage and flow
nets, shear strength); USDA NRCS National Engineering Handbook (compaction
and earthwork field practice).
Question 4: Proctor Compaction — Watering and Haulage for a Borrow-Pit Fill (20 marks)
Find. The additional water weight needed to bring the borrow soil
to optimum moisture (a), and the number of truckloads of borrow-pit soil required
(b).
Approach. Work from dry (solid-mass) unit weights throughout,
since it is the DRY mass that is conserved between the borrow pit and the compacted
fill — moisture is added on site, and the borrow soil's own void ratio changes
on compaction. Find the target dry unit weight of the compacted fill, then (a) compare
the water carried per cubic metre of fill at the borrow moisture vs. at optimum
moisture, and (b) equate total dry mass to find the in-situ borrow volume, hence the
truck count.
Target dry unit weight and borrow dry unit weight.
$$\gamma_{d,\text{target}}=0.95\,\gamma_{d,\max}=0.95(19)=18.05\ \text{kN/m}^3$$
$$\gamma_{d,\text{borrow}}=\frac{\gamma_{\text{bulk}}}{1+w_{\text{borrow}}}
=\frac{17.2}{1.082}=15.90\ \text{kN/m}^3$$
a) Additional water weight. Per cubic metre of COMPACTED fill,
the dry-soil weight present is γd,target; the water it already
carries (at the borrow moisture) and the water it needs (at optimum) both scale off
that same dry weight:
$$w_{\text{water, borrow}}=w_{\text{borrow}}\,\gamma_{d,\text{target}}=0.082(18.05)=1.480\ \text{kN/m}^3$$
$$w_{\text{water, opt}}=w_{\text{opt}}\,\gamma_{d,\text{target}}=0.115(18.05)=2.076\ \text{kN/m}^3$$
$$\Delta w=w_{\text{water, opt}}-w_{\text{water, borrow}}=0.596\ \text{kN per m}^3\text{ of fill}$$
$$W_{\text{extra}}=\Delta w\times V_{\text{fill}}=0.596(100{,}000)=\boxed{5.96\times10^4\ \text{kN}\ (\approx6070\ \text{m}^3\text{ of water})}$$
b) Truckloads of borrow soil. Total dry weight needed in the
fill, then the in-situ (borrow) volume that supplies it, using the BORROW dry unit
weight (not the fill's):
$$W_{d,\text{total}}=\gamma_{d,\text{target}}\,V_{\text{fill}}=18.05(100{,}000)=1{,}805{,}000\ \text{kN}$$
$$V_{\text{borrow}}=\frac{W_{d,\text{total}}}{\gamma_{d,\text{borrow}}}=\frac{1{,}805{,}000}{15.90}
=113{,}550\ \text{m}^3$$
$$N_{\text{trucks}}=\frac{V_{\text{borrow}}}{10}=11{,}355\ \text{trucks (rounded up)}
=\boxed{11{,}355\ \text{truckloads}}$$
