3.8. Arias Intensity

imcalculator.get_arias_intensity()[source]

Computes the Arias Intensity of the ground-motion record.

Arias Intensity is defined as:

AI = (pi / 2g) * integral(a(t)^2 dt)

where a(t) is the ground acceleration in m/s².

Parameters:: None
Returns:: ai – Arias Intensity (m/s).
Return type:: float

Theoretical Background

Arias Intensity (\(I_A\)) measures the total energy of a ground-motion record per unit weight (Arias, 1970). It is proportional to the integral of the squared ground acceleration over the record duration.

Definition

\[I_A = \frac{\pi}{2g} \int_0^{T_d} \bigl[\ddot{u}_g(t)\bigr]^2 \, dt\]

where \(\ddot{u}_g(t)\) is the ground acceleration (m/s²), \(g\) is the gravitational acceleration (9.81 m/s²), and \(T_d\) is the total record duration.

Discrete approximation

For a digitised record with time step \(\Delta t\) and \(N\) samples:

\[I_A \approx \frac{\pi}{2g} \sum_{n=1}^{N} \bigl[\ddot{u}_g(n\,\Delta t)\bigr]^2 \Delta t\]

The result is expressed in m/s.

Significance

\(I_A\) is related to the cumulative damage potential of a record and is commonly used to define the start and end of the strong-motion phase (e.g. the 5%–95% significant duration).