Shear Wave Velocity Calculator

Shear Wave Velocity

Shear wave velocity $V_s$ is the speed at which shear (S) waves propagate through a solid. Seismologists and geotechnical engineers use $V_s$ to classify soil stiffness, estimate earthquake site response, and evaluate foundation bearing capacity.

Formula

$$V_s = \sqrt{\frac{G}{\rho}}$$

$G$ is the shear modulus in pascals and $\rho$ is mass density in kg/m³. For steel with $G = 80$ GPa and $\rho = 7850$ kg/m³, $V_s \approx 3192$ m/s.

Relationship to Elastic Moduli

Shear modulus links to Young's modulus $E$ and Poisson's ratio $\nu$ by $G = E / (2(1+\nu))$. Knowing $V_s$ and density, you can back-calculate $G$ and infer material stiffness in the field.

Related tools: Shear Modulus Calculator and Earthquake Calculator.

Frequently Asked Questions

What is a typical shear wave velocity for soil?

Soft clay may have $V_s$ below 180 m/s. Dense sand and stiff clay range from 180 to 360 m/s. Rock and hard soil often exceed 760 m/s.

How is shear wave velocity measured?

Common methods include cross-hole seismic tests, surface wave (MASW/ReMi) surveys, and down-hole geophone arrays that record S-wave arrival times.

Why use GPa for shear modulus in the calculator?

Engineering tables often list $G$ in gigapascals. The tool converts GPa to pascals internally before applying the square root formula.

Does this formula apply to fluids?

No. Shear waves do not propagate in fluids because fluids cannot sustain shear stress. This formula applies to solids and stiff soils.

How does $V_s$ differ from P-wave velocity?

P-waves (compression) travel faster than S-waves in solids. $V_s$ depends only on shear modulus and density, while P-wave velocity also involves bulk modulus.

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Shear Wave Velocity Calculator