Shear Wave Velocity Calculator

Estimate Vs from SPT N-values using empirical correlations. Essential for site response, liquefaction analysis, and dynamic soil properties.

General Correlation: Vs = a · (N60)b (m/s — output in m/s)

Where a and b depend on soil type (see table below). N60 is the SPT blow count corrected to 60% energy.

Corrected blow count (N60). Typical range 0–100. For N=0, Vs ≈ 0 (very soft).
Select soil type to apply appropriate coefficients.
Used for profile visualization (optional).
Calculating...

Understanding Shear Wave Velocity

What is Vs?

Shear wave velocity (Vs) is the speed at which shear (S) waves propagate through soil. It is a direct measure of soil stiffness at small strains and is expressed as:

Gmax = ρ · Vs2

where Gmax is the small-strain shear modulus and ρ is the soil density. Vs is independent of frequency and is a fundamental property used in dynamic analyses.

Why is it important?

  • Site classification: Vs30 (average Vs over 30 m depth) defines NEHRP site classes (A–F).
  • Liquefaction assessment: Vs-based triggering correlations (Andrus & Stokoe, 2000).
  • Ground response analysis: Vs profiles control amplification of seismic waves.
  • Foundation design: Dynamic stiffness for machine foundations.

How to measure Vs?

In-situ geophysical methods:

  • Down-hole / Cross-hole: Direct measurement in boreholes.
  • MASW (Multichannel Analysis of Surface Waves): Non-invasive, uses surface waves.
  • ReMi (Refraction Microtremor): Passive-source method.
  • PS Logging: Suspension logging in boreholes.

Empirical correlations (like this calculator) are used when direct measurements are not available, but they should be calibrated locally.

Applications in Design

  • Earthquake engineering: Site-specific response spectra.
  • Liquefaction potential: Vs-based screening (e.g., Idriss & Boulanger, 2008).
  • Pile dynamics: Soil-pile interaction during earthquakes.
  • Stiffness degradation curves: Normalized modulus reduction (G/Gmax vs. shear strain).

Typical Vs Values (for N60 = 20, based on selected correlations)

Soil Type Formula Vs at N=20 (m/s) Reference
Sand Vs = 100·N0.33 271 Imai & Tonouchi (1982)
Clay Vs = 150·N0.30 347 Ohta & Goto (1978)
Silt Vs = 120·N0.31 282 Mayne (2001)
Gravel Vs = 80·N0.35 235 Rollins et al. (1998)
All soils Vs = 97·N0.30 224 Japan Road Association

Factors Affecting Vs

1

Effective confining stress (σ'v): Vs increases with depth approximately as σ'0.25.

2

Soil density and aging: Denser, older soils (with cementation) exhibit higher Vs.

3

Soil type and plasticity: Fines content and plasticity index influence Vs; clay typically has higher Vs than sand at the same N-value due to cohesive bonding.

Note on N60: The correlations provided assume the SPT N-value has been corrected to 60% energy efficiency (N60). If your N-value is from a different energy ratio, apply correction: N60 = Nfield · (ER/60). Hammer efficiency (ER) typically ranges from 30% to 100%.

References for further reading:

Andrus, R.D., & Stokoe, K.H. (2000). Liquefaction resistance based on shear wave velocity. Journal of Geotechnical and Geoenvironmental Engineering.

Mayne, P.W. (2001). Stress-strain-strength-flow parameters from enhanced in-situ tests. International Conference on In-Situ Measurement of Soil Properties.

Wair, B.R., DeJong, J.T., & Shantz, T. (2012). Guidelines for Estimation of Shear Wave Velocity Profiles. PEER Report 2012/08.

Frequently Asked Questions

Vs30 is the time-averaged shear wave velocity to a depth of 30 meters. It is the primary parameter for seismic site classification in codes like IBC, NEHRP, and Eurocode 8. Sites with lower Vs30 (softer soils) amplify ground motions more, requiring different design spectra.

Empirical correlations typically have a coefficient of variation of 20–30%. They are suitable for preliminary screening but not for final design in critical projects. Direct measurement (geophysical methods) is always preferred for final design.

Yes, you can calculate Vs for each layer individually using the appropriate N60 and soil type. To obtain an overall Vs profile, you can then compute the travel-time average for the desired depth range (e.g., Vs30).