Estimating the Void Ratio of Saturated Sands from CPT

Why Void Ratio Matters 

Soil is a three-phase material made up of solids, water, and air. In sands and gravels, how tightly the grains are packed, expressed by the void ratio (e = Vv/Vs), strongly influences stiffness, strength, drainage, and liquefaction potential.

• Dense sands → low void ratio, high stiffness/strength, less liquefaction risk.

• Loose sands → high void ratio, lower stiffness/strength, highly susceptible to liquefaction.

Mapping this “state” across the site and with depth is a core geotechnical task. Traditional options to achieve this include:

• Judgement/experience: lowest cost, lowest confidence (screening only).

• In situ testing (SPT, CPT): moderate cost, variable confidence.

• High-quality sampling and lab testing: most reliable but costly and impractical in clean sands.

This article highlights a simple CPT-based method to estimate void ratio in saturated sands, following the Barounis & Philpot (2017) approach.

When to Apply this Method

• Inorganic sands only (exclude organics, peats, fill).

• Fully saturated zones below the groundwater level, confirm with u₂ readings, dissipation tests, or other.

• Assume typical sand mineralogy: Gs ≈ 2.65.

Step-by-Step Method

Step 1 – Estimate bulk unit weight (γ) from CPT

Use Robertson’s (2010) correlation:

where:

• γ = bulk unit weight

• γw = unit weight of water

• Rf = CPT friction ratio (%)

• qt = corrected cone resistance

• pa = atmospheric pressure

Step 2 – Compute void ratio

For saturated sands, combining phase relationships gives:

Below the water table, this yields a continuous depth profile of void ratio from a CPT.

Example Results

The results below are from a Christchurch site where both CPT data and machine boreholes with soil samples and water content measurements were obtained. Water content was estimated from the void ratio using the relationship w = e/Gs. Comparisons between estimated and measured water contents show good agreement for this site. However, care should always be taken to cross-check estimated values against any available laboratory measurements of water content or soil density to confirm reliability.

How Engineers Use Void Ratio

• Foundation design: check φ′, settlement, and density consistency.

• Ground improvement: map high-void zones for densification or grouting; track pre- and post-treatment.

• Hydraulic design: link void ratio trends to permeability, drainage, and dewatering performance.

• Seismic response modelling: initialise state parameters in FLAC, PLAXIS, OpenSees.

Summary

With just one CPT and a short physics-based workflow, you can estimate continuous void ratio profiles in saturated sands:

1. Use Robertson’s correlation to estimate the unit weight.

2. Assume Gs = 2.65 for sands.

3. Apply the saturation relationship to estimate the void ratio.

   
   

Provided the soils are within scope, estimated values tend to align well with laboratory results. This makes void ratio a practical, reliable input for analysis, design, and ground improvement quality control.

For further details, see Barounis & Philpot (2017), published for the 2017 NZGS Symposium.