Developing Site-specific Small-strain Shear Modulus Correlations from SCPT Data

Why Small-strain Shear Modulus Matters

The small-strain shear modulus (G₀) describes how stiff soil is before strain-related degradation occurs. During strong earthquakes, soils experience moderate to large strains that reduce stiffness. The extent of this degradation depends on soil type, density, plasticity, and whether liquefaction occurs.

In practice, G₀ is estimated using its fundamental relationship:

where ρ is soil density and Vₛ is shear wave velocity. A degradation curve is then applied, chosen to suit the soil’s properties. The seismic cone penetration test (SCPT) is an ideal tool because it provides both shear wave velocity profiles and indirect correlations for soil density.

Research has shown strong links between void ratio and G₀, but empirical equations vary widely. This article outlines a practical method for deriving a site-specific G₀ correlation directly from SCPT data. The adopted form of the empirical G₀ equation is:

When to Apply This Method

• Inorganic soils only (exclude organics, peats, and fills).

• Fully saturated zones below the groundwater table (confirm with u₂ readings, dissipation tests, or equivalent).

• Assume typical quartz–sand mineralogy (Gs ≈ 2.65).

Step-by-Step Workflow

Step 1 – Estimate bulk unit weight, γ from CPT

Use Robertson’s (2010) correlation:

where:

• γw = unit weight of water

• Rf = CPT friction ratio (%)

• qt = corrected cone resistance

• pa = atmospheric pressure

This gives soil density with depth.

Step 2 – Calculate small-strain shear modulus, G₀ from Vs measurements

Using r estimates from Step 1 and measured Vs, G₀ can be determined for each depth interval using G₀ = ρV_s².

Step 3 – Determine effective overburden pressure, s‘v

Estimate from total overburden minus pore water pressure.

Step 4 – Compute void ratio, e

For saturated sands:

Step 5 – Calculate the stress-normalised void ratio parameter, SNVR:

Note: The exponent m is adjusted to maximise correlation strength.

Step 6 – Plot G₀ versus the stress-normalised void ratio parameter

The site-specific G₀ correlation can be established by plotting the G₀ values against SNVR, varying the m-parameter until the strongest possible correlation is established. An example of this is shown below.

In this case, the strongest possible correlation was produced with m = 0.36. The resulting empirical parameters were A = 100.51 and x = 2.27. The simplified version of the site-specific G₀ correlation is therefore:

Note: n = m*x = 0.36*2.27 = 0.82

Summary

With a single SCPT and a straightforward workflow, engineers can generate site-specific G₀ correlations that:

• Provide more reliable estimates than generic published equations.

• Allow extension to CPTu-only sites using derived void ratio and overburden profiles (provided soil conditions are sufficiently like the site where the correlation was derived).

• Better reflect local soil behaviour under seismic loading.

Workflow recap:

1. Estimate soil density (γ) from CPT.

2. Calculate G₀ = ρVₛ².

3. Determine σ′v.

4. Derive void ratio (e).

5. Compute SNVR.

6. Optimise m and establish the best G₀–SNVR relationship.

For further details, see Barounis & Philpot (2019), presented at the 7th ICEGE, Rome.