Question 6 of 7: Compaction — Proctor Density, Borrow-Pit Volume, and the Moisture–Density Curve Family

Question 6: Compaction — Proctor Density, Borrow-Pit Volume, and the Moisture–Density Curve Family (20 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.

a) What "95% Proctor density" means. The standard (or modified) Proctor test finds, for a given compactive effort, the maximum dry density a soil can be compacted to and the moisture content (the optimum moisture content, OMC) at which that maximum occurs. "95% Proctor density" is a field-compaction specification requiring that the dry density actually achieved on site reach at least 95% of that laboratory-determined maximum dry density, $\rho_{d,\text{field}} \ge 0.95\,\rho_{d,\max,\text{lab}}$, verified by a field density test (nuclear gauge or sand-cone) after each compacted lift.

b) Can field density exceed 100% of the lab Proctor maximum? Yes. 100% Proctor density is not a physical ceiling on how dense the soil can ever be packed; it is simply the maximum achieved under one specific, standardised compactive effort (a fixed hammer weight, drop height and number of blows per layer, for the standard test). Field equipment — heavier rollers, vibratory compactors on granular soils, more passes, or compaction using the modified-Proctor effort (heavier hammer/more blows) — can deliver more compactive energy than the standard laboratory test used, and will drive the dry density above the standard-Proctor maximum, giving a reported percentage over 100%. This is common and unremarkable in practice; it simply means the reference test used for the percentage was the standard (not modified) Proctor.

Approach (c). The mass (and hence volume) of solids is conserved between the borrow pit and the compacted fill — only the void volume changes. Back out the solids volume from the required fill volume and its void ratio, then re-expand that same solids volume at the borrow pit's (looser) void ratio.

1. Solids volume needed. Since $V = V_s(1+e)$, $$V_s = \frac{V_{fill}}{1+e_{fill}} = \frac{500}{1.35} = \boxed{370.4\ \text{m}^3}$$
2. Borrow-pit volume to excavate. The same solids, at the borrow pit's void ratio, $$V_{borrow} = V_s(1+e_{borrow}) = 370.4(1.60) = \boxed{592.6\ \text{m}^3}$$

d, e) The moisture–density curve family. For a fixed compactive effort, dry density rises with added moisture up to an optimum moisture content (OMC) — water lubricates the particles enough to let them pack tighter under the same energy — then falls again beyond OMC, because further water occupies pore space that compaction energy can no longer expel, and the curve is bounded above by the zero-air-voids (ZAV) line, $\gamma_{zav} = G_s\gamma_w/(1+wG_s)$, the theoretical density at 100% saturation that no real compaction curve can cross. Increasing the compactive effort (e.g. modified vs. standard Proctor) raises the peak dry density and shifts the optimum to a lower moisture content, because more mechanical energy can do the particle-rearrangement job that water lubrication would otherwise be needed for; decreasing the effort does the opposite — a lower, flatter peak shifted to a higher OMC. All three curves in the figure share the same ZAV envelope, since G_s is a property of the soil, not of the compaction effort applied to it.

f) Achieving the required compaction in construction. Condition the borrow material's moisture content toward the target OMC before placement (aerate/dry if too wet, add water and mix if too dry) since compaction efficiency depends strongly on moisture; select compaction equipment matched to the soil type (sheepsfoot or padfoot rollers for cohesive fill, smooth-drum vibratory rollers for granular fill); place and compact in thin, controlled lifts (typically 150–300 mm loose) rather than one thick lift, since compactive energy does not penetrate deep uniformly; apply enough passes per lift, verified by trial compaction on a test strip; and confirm the specification is actually met with in-place field density testing (nuclear density gauge or sand-cone) on every lift, correcting the process (more passes, adjusted moisture) if a test fails before covering that lift with the next one.