Time Domain

For a time domain analysis, the options are:

• Step Control
  • Fixed
    • Number of Sub-Increments
  • Flexible (recommended)
    • Maximum Strain Increment

The accuracy of the time domain solution depends on the time step selected. There are two options in choosing the time step (Hashash and Park, 2001).

Fixed Step

Each time-step is divided into N equal sub-increments throughout the time series.

To choose this option:

1. Select Step Control = Fixed
2. The Number of sub-increments option is enabled.
3. Type the desired integer value of sub-increments into the text box or use the arrows buttons to increase or decrease the value.

Flexible Step

A time increment is subdivided only if computed strains in the soil exceed a specified maximum strain increment.

The procedure is the same as that for the Fixed Step, except the Flexible option is chosen. Enter the desired Maximum Strain Increment (%). The default and recommended value is 0.005 (%).

Integration Scheme

There are two available time integration methods:

• Implicit: Newmark β method (recommended)
• Explicit: Heun’s Method

Time-history Interpolation Method

This option is only available when the flexible step is selected. When subdividing a time step, accelerations must be computed at intermediate points. RSSeismic implements two subdivision strategies:

1. Linear time-domain interpolation
2. Zero-padded frequency-domain interpolation.

Linear in Time Domain

Linear (time-domain) interpolation is the classical approach in which the change in acceleration is simply divided into equal increments. This method has been shown to fundamentally alter the motion by adding energy to the signal at frequencies above the Nyquest frequency of the original signal. This can potentially add high frequency noise to the output signal.

Zero Padded in Frequency Domain

Zero-padded frequency-domain interpolation is often referred to as “perfect interpolation” because it allows for increased resolution (reduced time step) without adding energy above the Nyquist frequency of the original signal. This means that the intermediate points are added to the signal in a manner that is consistent with the actual behavior of the propagating wave. However, they are not reported in the output and hence can cause a distortion in the output motion. Results from this method should always be compared to the linear interpolation results.