24-Bld-A6 Geotechnical Materials and Analysis · May 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, May 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.

Question 2 (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.

Figure 1 (reproduced): standard Proctor compaction curve. γd rises from w₁ (dry of optimum) to a peak at w_f, then falls toward w₂ (wet of optimum); the zero-air-voids (ZAV) line bounds all physically possible states from above.

At water contents below $w_f$ (the dry side of optimum), the compaction energy is largely spent overcoming inter-particle friction and the stiffness of thin water films around clay particles. Adding water at this stage lubricates the particle contacts, letting them slide into a denser, more efficient packing arrangement for the same compactive effort — so $\gamma_d$ rises as $w$ increases toward $w_f$. Each added increment of water is doing useful work: it is *displacing air* from the voids, and because water is a much better lubricant than air-dry friction, dry unit weight climbs steeply on this branch.

At $w=w_f$ the soil has reached the densest arrangement the compactive effort can achieve — essentially all the air that can be squeezed out by that effort has been squeezed out, and the soil sits near (though still below) the zero-air-voids line. Beyond $w_f$, additional water no longer helps rearrange particles: the compaction energy cannot expel water (unlike air, water is essentially incompressible and cannot be forced from the voids in the short compaction timescale), so the extra water simply occupies void space that would otherwise have been filled with more closely-packed soil solids. Because dry unit weight is defined as $\gamma_d=W_s/V_{total}$ (solids weight over *total* volume), and the total volume must expand to accommodate the extra incompressible water without a compensating increase in solids, $\gamma_d$ falls on the wet side of optimum even though the *total* (bulk) unit weight may still be rising. This is why the curve peaks at $w_f$ and descends thereafter, always remaining below (never crossing) the ZAV line, which represents the theoretical 100%-saturation boundary.

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