Determination of the relative density of soils is a fundamental geotechnical testing procedure used to evaluate the compactness of cohesionless, free-draining soils such as sands and gravels. By comparing the in-situ void ratio of a soil with its maximum and minimum achievable density states, engineers can quantify compaction quality, assess liquefaction susceptibility, and verify compliance with earthwork specifications. This article explains the testing principle, applicable soil types, standard test methods, typical applications, and frequently asked questions related to soil relative density determination.
Technical Overview
Relative density, also known as the density index (Dr), is a dimensionless parameter that expresses the degree of compactness of a cohesionless soil relative to its loosest and densest possible states. Unlike cohesive soils, which are typically evaluated through Proctor-based compaction tests, clean granular soils cannot be meaningfully compacted by impact compaction molds alone and must instead be characterized through vibratory and loose-pouring techniques.
The relative density is calculated from the maximum, minimum, and in-situ void ratios of the soil using the following relationship:
Dr = (emax − e) / (emax − emin) × 100%, where e is the in-situ void ratio, emax is the void ratio at the minimum index density (loosest state), and emin is the void ratio at the maximum index density (densest state).
An equivalent expression in terms of dry densities is frequently used in practice: Dr = [(ρd − ρdmin) × ρdmax] / [(ρdmax − ρdmin) × ρd] × 100%. A relative density of 0% corresponds to the loosest possible state, while 100% corresponds to the densest achievable state under standardized vibration and surcharge loading. Soils are commonly classified as very loose (Dr < 15%), loose (15–35%), medium dense (35–65%), dense (65–85%), and very dense (Dr > 85%).
The principal international and national standards governing this test include ASTM D4253 (Standard Test Methods for Maximum Index Density and Unit Weight of Soils Using a Vibratory Table), ASTM D4254 (Standard Test Methods for Minimum Index Density and Unit Weight of Soils and Calculation of Relative Density), and the Chinese geotechnical testing standard GB/T 50123 (Standard for Geotechnical Testing Method). Related procedures for in-situ density determination, such as ASTM D1556 (sand cone), ASTM D2167 (rubber balloon), and ASTM D6938 (nuclear gauge), are often performed in conjunction with index density testing to complete the relative density calculation.
Testing Samples
Clean Sands
Uniform and well-graded sands classified as SP or SW under the Unified Soil Classification System (USCS) are the primary materials evaluated by relative density testing. These free-draining soils respond strongly to vibration, making vibratory table methods appropriate for establishing maximum index density.
Gravels and Sandy Gravels
Coarse-grained soils classified as GP or GW, including crushed rock aggregates and gravely sands, may be tested using large-diameter molds to accommodate particle sizes up to approximately 50 mm. Oversized particles are typically corrected or scalped according to the applicable standard.
Low-Plasticity Fine-Grained Fraction Soils
Soils containing a limited quantity of non-plastic fines may be accepted for relative density testing, provided the fines content does not exceed the threshold specified by the governing standard, typically around 12% by mass. Soils with plastic fines should instead be evaluated by Proctor compaction and relative compaction methods.
Sample Requirements
Testing is normally performed on disturbed, representative bulk samples collected from borrow pits, stockpiles, or compacted fill layers. Sufficient material should be supplied to permit multiple determinations of both maximum and minimum index density, as well as moisture content and gradation verification. Typical sample quantities range from 25 kg for fine sands to 100 kg or more for gravels, depending on the maximum particle size.
Testing Items
A complete relative density determination typically involves the following measured and derived parameters:
- Maximum index dry density (ρdmax) and corresponding minimum void ratio (emin)
- Minimum index dry density (ρdmin) and corresponding maximum void ratio (emax)
- In-situ or field dry density (ρd) and natural void ratio (e)
- Relative density or density index (Dr), expressed as a percentage
- Soil specific gravity (Gs), required for void ratio conversion
- Particle size distribution and fines content, to confirm test applicability
- Moisture content of the as-received or in-situ material
- Relative compaction (degree of compaction), when Proctor-based evaluation is required in parallel
Testing Methods
Maximum Index Density — Vibratory Table Method (ASTM D4253)
Oven-dried soil is placed in a rigid steel mold mounted on a vertically oscillating electromagnetic vibratory table. A calibrated surcharge weight is applied to the soil surface, and the assembly is vibrated for a standardized duration, typically 8 minutes plus additional seating time. The vibration rearranges particles into their densest packing configuration. The final mass and volume of the soil are measured to compute the maximum index dry density. GB/T 50123 specifies a comparable vibratory procedure for Chinese practice.
Minimum Index Density — Loose Pouring Method (ASTM D4254)
To establish the loosest achievable state, oven-dried soil is gently poured or funneled into a calibrated mold from a controlled height with minimal disturbance, or the soil is inverted carefully using a specialized pouring device. Any surface leveling is performed without vibration or compaction. The resulting mass and volume yield the minimum index dry density. Multiple trials are performed, and the lowest consistent value is adopted.
In-Situ Density Determination
The field dry density required in the relative density calculation is obtained by one of the following methods:
- Sand cone method (ASTM D1556): excavating a small test hole and replacing the soil with calibrated sand of known density
- Rubber balloon method (ASTM D2167): measuring the volume of an excavated hole with a water-filled balloon apparatus
- Nuclear density gauge (ASTM D6938): non-destructive measurement of wet density and moisture content by nuclear transmission or backscatter techniques
- Core cutter or water/oil replacement methods, applicable to certain coarse-grained fills
Relative Compaction — Proctor Reference (ASTM D698 / ASTM D1557)
For projects where specifications are written in terms of percent compaction rather than relative density, laboratory standard or modified Proctor tests establish the maximum dry density of the material, and field density results are expressed as a percentage of that reference value. The choice between relative density and relative compaction depends on soil gradation and project specifications.
Calculation and Reporting
Once the three density states are established, the relative density is computed and reported together with mold dimensions, vibration time, surcharge pressure, gradation data, and any corrections for oversized particles. Results are typically reported to the nearest 1%. Accredited third-party laboratories commonly issue test reports that are directly usable for earthwork acceptance documentation.
Applications
Relative density determination is widely applied across geotechnical and civil engineering practice:
- Quality control and acceptance of compacted granular fill beneath foundations, floor slabs, and pavement layers
- Embankment and earth dam construction, where dense placement of shell materials is essential for stability
- Backfill specification verification behind retaining walls, in trenches, and around buried pipelines
- Seismic liquefaction potential assessment, since liquefaction resistance correlates strongly with relative density
- Estimation of soil strength and compressibility parameters for foundation design of cohesionless strata
- Settlement evaluation of loose sand deposits and densification verification after ground improvement techniques such as vibro-compaction, dynamic compaction, and stone columns
- Quarry, mine, and reclamation fill certification where granular materials dominate
FAQ
What is the difference between relative density and relative compaction?
Relative density compares the in-situ void ratio of a cohesionless soil with its minimum and maximum index void ratios obtained by vibration and loose pouring, and is best suited to clean sands and gravels. Relative compaction compares field dry density with the maximum dry density from a Proctor impact test and is generally applied to cohesive or fine-grained soils. Both express compactness as a percentage but are defined by different reference states.
What types of soil are suitable for relative density testing?
The test is intended for free-draining, cohesionless soils, typically sands and gravels with fines content below about 12% and essentially non-plastic fines. If the fines are plastic or excessive, the soil will not respond properly to vibratory densification and Proctor-based methods should be used instead.
How is the in-situ density obtained for the calculation?
In-situ density is measured directly in the field using the sand cone method, rubber balloon method, or nuclear density gauge, and the dry density is then calculated from the measured moisture content. The field dry density is substituted into the relative density formula along with the laboratory-determined maximum and minimum index densities.
What relative density values are typically required by specifications?
Common earthwork specifications require a relative density of at least 70% to 75% for general granular fill, and 75% to 85% or higher for critical zones such as areas beneath foundations, within liquefiable strata, or under seismic loading conditions. The governing project specification should always be consulted for acceptance limits.
Why is vibration used instead of impact compaction for maximum index density?
Granular particles densify most effectively when subjected to vibration, which momentarily reduces interparticle friction and allows particles to rearrange into a denser packing. Impact compaction, as used in Proctor testing, is less effective for clean coarse-grained soils and is more appropriate for soils with cohesive fines where moisture-dependent compaction behavior governs.
How long does a relative density test take?
Laboratory index density testing, including sample preparation, gradation checks, and replicate determinations of maximum and minimum density, is typically completed within a few working days. When combined with in-situ field density testing, a full evaluation can usually be reported within one week, depending on sample logistics and the number of test locations.