Earthquake Shaking Force, 3D vector sum of ground accelerations

Earthquake Shaking Force, 3D vector sum of ground accelerations

The formula for calculating the Earthquake force of the local ground motion is:

EqSF = 9.81{[Cahx^2+ Cahy^2 + (Cav/2)^2](t/20)^2}^0.2 Equation 1

where,

Cahx, Cahy and Cav are the corresponding horizontal and vertical accelerations (g) in x, y and z directions that provide the maximum vector sum,

Cav/2 is the correction accounting for a relatively reduced impact of the vertical acceleration,

t is the duration of strong ground motions in seconds,

t/20 is a correction for the strong motion duration,

^0.2 is the scaling correction for the 3D vector value (in lieu of ^0.5),

9.81 is the acceleration of gravity in m/sec/sec

m is the mass, taken as 1, which therefore does not appear in the equation.

All accelerations are taken from the three seismograms (two horizontals and one vertical) recorded at a ground station for a particular event. The time interval considering simultaneous action of the corresponding accelerations in three perpendicular directions is taken as 1.5 seconds. The duration of strong motion is the modified “bracketed duration” for the time interval between the first and last acceleration peaks greater than 0.1g. For the strong motion duration an upper limit of 75 seconds is used. An exception is made for seismograms with acceleration peaks smaller than 0.1 g that should result in t = 0 and EqSF = 0. The EqSF value for such earthquake readings is calculated with duration (t) equal to 0.5 seconds in order to allow comparing their ground shaking force with the forces at other locations. The original “bracketed duration”, proposed by Page et al. and Bolt accounts for the intervals between 0.05 g peaks.

When accelerations are given in cm/sec/sec, the EqSF values may be calculated directly from:

EqSF = 0.6237{[Cahx^2+ Cahy^2 + (Cav/2)^2](t/20)^2}^0.2 Equation 2

The correction for vertical acceleration is introduced to account for its relatively smaller influence on structural damage. Reduction factors from 1 to 3 produce small differential results less than 7 percent; therefore the final selected reduction factor is 2.

The t/20 is introduced to account for the influence of ground motion duration on structural damage. Twenty (20) seconds were selected as basic duration based on the analysis of more than 100 earthquake records. The scaling correction (^0.2 in lieu of ^0.5) is to reduce the sharp increase in calculated degrees between smaller and greater acceleration values, and to scale the values closer to the traditionally used values in earthquake scales.