Flow rule in a high-cycle accumulation model backed by cyclic test data of 22 sands

The flow rule used in the high-cycle accumulation (HCA) model proposed by Niemunis et al. (Comput Geotech 32: 245, 2005 ) is examined on the basis of the data from approximately 350 drained long-term cyclic triaxial tests ( N = 10 5 cycles) performed on 22 different grain-size distribution curves of a clean quartz sand. In accordance with (Wichtmann et al. in Acta Geotechnica 1: 59, 2006 ), for all tested materials, the “high-cyclic flow rule (HCFR)”, i.e., the ratio of the volumetric and deviatoric strain accumulation rates ε ˙ v acc / ε ˙ q acc , was found dependent primarily on the average stress ratio η av = q av / p av and independent of amplitude, soil density and average mean pressure. The experimental HCFR can be fairly well approximated by the flow rule of the modified Cam-clay (MCC) model. Instead of the critical friction angle φ c which enters the flow rule for monotonic loading, the HCA model uses the MCC flow rule expression with a slightly different parameter φ cc . It should be determined from cyclic tests. φ cc and φ c are of similar magnitude but not always identical, because they are calibrated from different types of tests. For a simplified calibration in the absence of cyclic test data, φ cc may be estimated from the angle of repose φ r determined from a pluviated cone of sand (Wichtmann et al. in Acta Geotechnica 1: 59, 2006 ). However, the paper demonstrates that the MCC flow rule with φ r does not fit well the experimentally observed HCFR in the case of coarse or well-graded sands. For an improved simplified calibration procedure, correlations between φ cc and parameters of the grain-size distribution curve ( d 50 , C u ) have been developed on the basis of the present data set. The approximation of the experimental HCFR by the generalized flow rule equations proposed in (Wichtmann et al. in J Geotech Geoenviron Eng ASCE 136: 728, 2010 ), considering anisotropy, is also discussed in the paper.