3.9. Cumulative Absolute Velocity

imcalculator.get_cav()

Computes the Cumulative Absolute Velocity (CAV).

CAV is defined as:

CAV = integral( abs(a(t)) dt )

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

Parameters:

None

Returns:

cav – Cumulative Absolute Velocity (m/s).

Return type:

float

Theoretical Background

Cumulative Absolute Velocity (CAV) is the integral of the absolute value of ground acceleration over the record duration (Kempton & Stewart, 2006). It captures both the amplitude and duration of shaking.

Definition

\[\text{CAV} = \int_0^{T_d} \bigl|\ddot{u}_g(t)\bigr| \, dt\]

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

Discrete approximation

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

\[\text{CAV} \approx \sum_{n=1}^{N} \bigl|\ddot{u}_g(n\,\Delta t)\bigr| \Delta t\]

The result is expressed in m/s.

Significance

CAV is closely related to the potential for structural damage and liquefaction. Unlike peak ground motion parameters, CAV accounts for the duration of shaking, making it a more informative measure for cumulative damage assessment.

Example

import numpy as np
from openquake.vmtk.imcalculator import imcalculator

acc = np.loadtxt("openquake/vmtk/tests/test_data/acceleration.txt")
im = imcalculator(acc, dt=0.005)

cav = im.get_cav()
print(f"CAV = {cav:.3f} m/s")