Recent Improvements in MOC for Earthquake Response

The Method of Characteristics was introduced by Streeter, Wylie, and Richart (1974) over thirty years ago. The method demonstrated the ability to faithfully reproduce 1-dimensional, horizontally polarized, vertically propagating shear waves through soil. Since then, many adjustments and improvements have been introduced. This paper summarizes some of those improvements and presents further refinements to the approach. Such features as independent energy balance evaluation, interpolation along time (as opposed to space) lines, stress-reversal checking, and non-linear stress-strain table look-up are also included. These improvements have eliminated past problems with numerical damping and accuracy of stress-strain hysteresis. The newer version, WinMOC, employs a more user-friendly interface with a multitude of soil stress-strain models, full graphing capabilities, response spectra generation, and evaluation of many ground motion parameters. The Method of Characteristics is compared to an equivalent linear frequency domain method. Results generally show more accurate representation of strong motion with the same ease of use. This is especially demonstrated at sites with deep (> 150 ft) soil layers. A computational example is presented so that reader may judge the efficacy of the method.