The high-cyclic model for sand tested beyond the usual ranges of application

Abstract

The high-cycle accumulation (HCA) model proposed by Niemunis et al. (Comput Geotech 32(4):245–263, 2005) predicts permanent deformations due cyclic loading with many small cycles (i.e. N≥104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N \\ge 10^4$$\\end{document} cycles of strain amplitudes εampl≤10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varepsilon }^{{\\rm ampl}}\\le 10^{-3}$$\\end{document}). In the presented tests, the pressure range pav\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p^{{\\rm av}}$$\\end{document} is extended from 3 to 9 bar; the influence of the void ratio e∈(0.72,0.95)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e \\in (0.72, 0.95)$$\\end{document} and amplitudes of strains εampl∈(0.1%,1%)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon ^{{\\rm ampl}} \\in (0.1{\\%}, 1{\\%})$$\\end{document} is tested in the extended range. Some empirical HCA functions could be confirmed and some require modifications. An interesting qualitative controversy pertains to the direction of circulation in the P–Q-plane for a validation of the polarization function fπ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_\\pi $$\\end{document}, which does influence the rate of accumulation contrarily to the HCA assumption. The previous assumption that ε˙acc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\dot{\\varepsilon }^{{{\\rm acc}}}$$\\end{document} remains constant above a certain pressure level, i.e. is independent of pav\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p^{{{\\rm av}}}$$\\end{document}, was experimentally refuted. Investigations on the cyclic preloading (f˙N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\dot{f}_N$$\\end{document}) using 21 cyclic triaxial tests with varried monotonic strain paths between the cycle packages found a relationship of the direction of the monotonic strain path and the capacity to reduce cyclic preloading. This study’s findings deepen the understanding of how cyclic preloading is reduced, but the tests also highlight the need for future research in the area.