A tool for the soil compaction test that controls how reliably embankments and pavements are compacted. Enter a single compaction-mould measurement (wet mass, volume, water content, specific gravity) and the dry density, zero-air-voids density, void ratio, degree of saturation and air-voids content update in real time, so you can grasp the Proctor compaction curve and optimum moisture content intuitively.
Parameters
Wet mass of compacted soil
g
Mass of soil compacted into the mould (moist state)
Mould volume
cm³
Internal volume of the compaction mould (standard is about 1000 cm³)
Water content w
%
Ratio of water mass to the dry mass of the soil
Specific gravity of solids Gs
Density of the soil particles divided by the density of water (dimensionless)
Results
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Bulk density (g/cm³)
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Dry density (g/cm³)
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Zero-air-voids density (g/cm³)
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Void ratio e
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Saturation S (%)
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Air-voids content (%)
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Compaction curve and phase diagram — animation
Shows the hump-shaped compaction curve, the zero-air-voids line above it, the peak (maximum dry density and optimum moisture) and a marker at the current water content. The phase diagram below shows the soil, water and air volume fractions.
Dry density ρ_d and zero-air-voids density ρ_zav. ρ_bulk: bulk density, w: water content (decimal), G_s: specific gravity of solids, ρ_w: density of water (1.0 g/cm³). The dry density can approach but never cross the zero-air-voids line, and the peak of the compaction curve defines the optimum moisture content.
Void ratio e (volume of voids divided by volume of solids) and degree of saturation S (fraction of the voids filled with water).
$$A_v=\frac{e\,(1-S)}{1+e}\times 100\ [\%]$$
Air-voids content A_v (fraction of the total volume that is air). S is used as a decimal here.
What is the compaction test?
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The "soil compaction test" just packs soil down tight, right? Why bother doing it in a lab? It feels like you could just roll it down on site.
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Good question. Compaction is the process of mechanically pressing the air out of a soil so the particles pack closer together. A well-compacted fill is stronger, stiffer, less permeable and less prone to later settlement than a loose one. It is one of the most important operations in all of earthwork. But to decide on site "how compact is good enough", you need a target value for that particular soil — and the Proctor compaction test produces that target ahead of time in the lab. It is the standard control test for compaction, established by Ralph Proctor in the 1930s.
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I see. But what does the "amount of water" have to do with packing soil? I would have thought drier soil packs harder.
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This is the most interesting part of the test. You compact the soil with a fixed compaction effort, vary only the water content a little at a time, measure the dry density and plot it. The plot is not a straight line — it is a distinct hump. With little water the soil is stiff and the particles resist rearrangement, so the dry density is low. Add water and it lubricates the particles so they slide into a denser packing, and the density rises. But past a certain point the extra water occupies space soil grains could have filled, and the dry density falls again. Move the water-content slider on the left and watch the hump on the chart above.
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So the very top of the hump, where the density is highest — is that the point that matters?
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Yes — that peak defines two design values: the maximum dry density and the optimum moisture content at which it is reached. On site, compaction is specified as "achieve such-and-such percent of the laboratory maximum dry density". For a road embankment body that might be 90%, for the subgrade or the foundation of an important structure 95% or more. So the maximum dry density and optimum moisture content are, in effect, the pass line for fill quality control.
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There is a second curve in the upper right of the chart. What is that sloping line?
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That is the zero-air-voids line, also called the saturation line. It is the theoretical dry density of a soil with no air at all — fully saturated — plotted against water content. The compaction curve can approach it but can never cross it, because some air can never quite be driven out. The gap between the compaction curve and the zero-air-voids line represents the air still left in the soil. If a plotted test point breaks through the line, that is a sign of a measurement error in the water content or the specific gravity.
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Is compacting exactly at the optimum moisture content always best?
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That actually depends on the goal. For the foundation of a structure that needs maximum strength and stiffness, slightly dry of optimum — the dry side — is favorable. But for a dam core where you want low permeability, or where you must not let the soil swell or collapse on wetting, the wet side is standard. At the same dry density, the dry side and the wet side produce different soil microstructure, so strength, permeability and shrinkage behavior change. That is why the compaction test is not "find the peak and done" — reading the whole curve matters.
Frequently Asked Questions
The Proctor compaction test measures how a soil's dry density responds to its water content under a fixed compaction effort. A rammer of fixed weight is dropped a fixed number of times in fixed layers, the dry density is found for several specimens at different water contents, and the dry density is plotted against water content as a single curve. That curve is a distinct hump, and its peak gives the maximum dry density and the optimum moisture content. This tool computes the dry density and other density and phase relations from a single compaction-mould measurement.
First divide the wet (moist) mass of compacted soil by the mould volume to get the bulk density ρ_bulk. The dry density is the density with the water removed: ρ_d = ρ_bulk / (1 + w), where w is the water content as a decimal. For a bulk density of 1.850 g/cm³ and a water content of 14%, ρ_d = 1.850/1.14 ≈ 1.623 g/cm³. Compaction quality is always judged from the dry density, never from the bulk density, because the bulk density is inflated by the water and does not reflect how tightly the soil grains themselves are packed.
The zero-air-voids line (saturation line) is the theoretical dry density of a soil that contains no air at all (degree of saturation 100%), plotted against water content. Its formula is ρ_zav = G_s·ρ_w / (1 + G_s·w), where G_s is the specific gravity of the soil particles and ρ_w is the density of water. It is the theoretical upper limit of dry density at each water content: the real compaction curve can approach this line but can never cross it. How close the compaction curve sits to the zero-air-voids line tells the engineer how much air still remains in the soil.
It depends on the goal. For structural foundations where maximum strength and stiffness are wanted, compacting slightly dry of the optimum moisture content (the dry side) gives higher strength. For a dam core or anywhere low permeability is needed, or where swelling or collapse on wetting must be avoided, compacting slightly wet of optimum (the wet side) is the standard practice. At the same dry density, the dry side and wet side give different soil fabric (flocculated versus dispersed), so strength, permeability and shrinkage behavior differ. On site, the control target is usually within plus or minus 2 to 3 percent of the optimum moisture content.
Real-World Applications
Road and railway embankments and pavement layers: Road and railway embankments are built by spreading the soil layer by layer and compacting each layer with rollers. The contract documents specify a degree of compaction as "such-and-such percent of the laboratory Proctor maximum dry density" — typically about 90% for the embankment body and 95% or more for the subgrade and important upper layers. On site, the density is measured by the sand-replacement or nuclear-gauge method, the in-place dry density is computed with the same calculation as this tool, and it is compared with the laboratory maximum dry density to judge acceptance.
Earth-dam cores and embankments: In a fill dam built mainly of soil, compacting the impervious core is the most critical task. The core must keep low permeability and withstand the water pressure on filling and the deformation during earthquakes, so it is compacted carefully slightly wet of the optimum moisture content. The relationship between the compaction curve and the zero-air-voids line is used to control whether the target degree of saturation and air-voids content are met. River-levee fills use the same principle.
Land development and structural backfill: Compaction control is essential in development fills for housing, in the backfill behind retaining walls and over culverts, and in backfill around foundations. Poor compaction leads to differential settlement of buildings, cracking of pavements and sinkholes around buried structures. In tight spaces, a tamper or rammer is used with thin lift thicknesses, the water content is adjusted near the optimum value, and the specified degree of compaction is secured.
Fill quality troubleshooting: When a defect occurs — "part of the embankment has settled" or "the slope failed after rainfall" — the cause is often insufficient compaction, or compacting too far on the wet side. By coring out a sample, measuring the water content and density, and back-calculating the degree of saturation and air-voids content with this tool, the engineer can estimate how far the original construction was from the optimum moisture content. That becomes the basis for deciding the repair strategy and the extent of re-construction.
Common Misconceptions and Pitfalls
The biggest misconception is that "higher bulk density means better compaction". Compaction quality is always judged from the dry density. The bulk density is the density of soil particles and water together, so the higher the water content, the heavier it reads simply because of the water. Comparing two points with very different water contents by their bulk densities tells you nothing about which is better compacted. That is exactly why this tool computes the dry density ρ_d = ρ_bulk/(1+w). When you measure density on site, always measure the water content at the same time and convert to dry density.
Next, the assumption that "the maximum dry density and optimum moisture content are constants intrinsic to the soil". They are values "under a particular compaction effort", and they shift when the effort changes. Increasing the compaction effort raises the maximum dry density and moves the optimum moisture content to a smaller (drier) value. That is why standard Proctor and modified Proctor, whose specified efforts differ by about 4.5 times, produce two different compaction curves. If the site compaction machinery applies more energy than the lab test, the field can even reach a higher density. Always check which standard and which effort produced the laboratory value.
Finally, overlooking it when "the compaction curve crosses the zero-air-voids line, probably just chart error". The zero-air-voids line is the physical upper limit of degree of saturation 100%, and it is fundamentally impossible for real soil to exceed it. If a plotted point breaks through the line, that is not chart error but a clear warning sign of a measurement mistake in the water content, a wrong value of the specific gravity G_s, or an error in the mould volume. In this tool too, certain input combinations can give an unrealistic saturation above 100%. In that case, review the input values of mass, volume, specific gravity and water content.
How to Use
Enter the wet mass of compacted soil (in grams) extracted from the mould after the standard or modified Proctor hammer drop sequence
Input the mould volume (typically 944 cm³ for standard Proctor, 2124 cm³ for modified) and water content percentage by dry mass
Supply the specific gravity of soil solids (usually 2.65–2.80 for silts and clays) to calculate zero-air-voids density and saturation degree
Review output: bulk density, dry density, void ratio, air-voids content, and degree of saturation to confirm compliance with embankment or pavement specifications
Worked Example
A standard Proctor test on clay-silt fills: wet mass = 1840 g, mould volume = 944 cm³, water content = 12.5%, specific gravity = 2.72. Calculated bulk density = 1.95 g/cm³, dry density = 1.73 g/cm³, zero-air-voids density = 2.08 g/cm³, void ratio e = 0.575, degree of saturation S = 78%, air-voids content = 3.2%. The 3.2% air void indicates acceptable compaction for a road base course (target typically 2–5% depending on traffic class).
Practical Notes
Modified Proctor (25 blows, 4.5 kg hammer, 45 cm drop) produces dry density 5–10% higher than standard (10 blows, 2.5 kg, 30 cm); verify which test specification applies to your project (ASTM D698 vs. D1557)
Saturation above 95% and air voids below 1% indicate over-compaction; re-check water content and hammer energy to avoid rutting in asphalt pavements
For cohesive materials, remould two or three passes at different water contents (−2%, optimum, +2%) to define the complete compaction curve and peak dry density location