Date: 11 October 2006 To: FLAC Users From: Peter Cundall Re: A note concerning hysteretic damping in FLAC Ref: 2001-06

There have been several changes to the hysteretic damping (HD) logic in FLAC recently that may have led to confusion and in some cases to different results when running different sub-versions of the code with the same data file. This note is intended to clarify the situation.

Sub-versions of FLAC prior to 360 (see FLAC 5.0 Revision History1 on the Itasca web site) contained a bug that caused some hysteresis loops to be incomplete: i.e., these loops did not exhibit the correct modulus reduction; rather, their loading and unloading modulus was non-hysteretic, and equal to the initial, small-strain modulus. Unfortunately, some simulations that previously appeared to give reasonable results now exhibited large strains, using the corrected code (subversions 360 through 363). The large strains are almost invariably associated with a large amount of plastic flow that occurs in these simulations.

It is believed that the implementation of HD is now correct (following subversion 360) in its representation of hysteretic loops, given a particular level of cyclic strain. However, it is believed that HD is inappropriately applied if it takes over the function of a plastic constitutive model. In extreme cases, strains may be so large in some regions of a model that the tangent modulus (as calculated by HD) reduces to zero. Thus, HD is causing zones in these regions to act as if their strengths are very low, leading to excessive displacements and strains. One remedy is to exclude HD from regions that are known to exhibit large-scale plastic flow (using, for example, the INITIAL dy_damp hyst off .. command to turn off HD in particular ranges of zones). By using such exclusion, the plastic model (e.g., Mohr Coulomb) is able to reproduce plastic yielding in a realistic manner, without being overridden by spurious HD yield. The consequent lack of added damping in these regions is probably unimportant, given that plastic flow already provides considerable energy dissipation.

The exclusion of HD from regions of strong plastic flow was necessary (prior to subversion 364) because HD was formulated in terms of total shear strains. Since these include plastic strains, the HD scheme overestimates the level of cyclic strain. In the latest subversion (364), the accumulation of HD shear strains is automatically suppressed during episodes of plastic flow. (This is similar to the manual exclusion described above, but now performed automatically). Using this subversion, simulations involving large plastic strains now show reasonable response without the need to exclude HD manually.

1 http://www.itascacg.com/flac_download.html#notes

A note concerning hysteretic damping in FLAC Page 2

Users of FLAC are recommended to use subversion 364 (and upward) of FLAC when both hysteretic damping and plastic flow are present in a dynamic simulation. Even with the exclusion of plastic strains in the HD scheme, there may still be large modulus reduction due to large cyclic (non-plastic) strains. Hysteretic damping is intended to provide damping, not to serve as a substitute for a plastic constitutive model. Thus, if moduli calculated by HD are seen to reduce to near zero for more than a small proportion of dynamic time, the simulation should be regarded as suspect, and changes made (to models, properties or excitations). In order to track modulus reductions, histories may be made of selected zones (using HISTORY hyst modfac ..).

In some simulations, large modulus reductions have been seen in areas remote from regions of plastic flow: e.g., near the base of the model. It appears that the use of a single degradation curve is unrealistic in these cases. There is evidence (e.g., see Darendeli, 2001) that degradation curves depend on the mean stress level: for example, at depth (high mean stress) there is less damping and modulus reduction. By making the HD depth-dependent the simulation should be more realistic.

In general, it should be noted that the hysteretic damping approach in FLAC is still relatively new, and some teething problems (some numerical, some physical) might be expected before the scheme is fully proven and accepted for routine dynamic simulations. Indeed, the state of the art in seismic design is itself changing, from equivalent-linear analyses to time-domain, nonlinear simulations. We need to accumulate more experience with using HD in nonlinear simulations before we can formulate design approaches that are generally accepted by the community.

Reference

DARENDELI, MEHMET BARIS . DEVELOPMENT OF A NEW FAMILY OF NORMALIZED MODULUS REDUCTION AND MATERIAL DAMPING CURVES Ph.D. dissertation, presented to the Faculty of the Graduate School of The University of Texas at Austin, August, 2001

Ref:2001-06