“…These include the analytical and semi-analytical solutions proposed by Marshall (1968), Dagan and Tulin (1969), Collins (1972Collins ( , 1978, Karafiath and Nowatzki (1978), Petryk (1983), Tordesillas and Shi (2000), and Hambleton and Drescher (2009a), as well as the numerical models developed using either finite element or discrete element methods by Yong et al (1978), Liu and Wong (1996), Fervers (2004), Chiroux et al (2005), Shoop et al (2006a,b), Asaf et al (2006), Hambleton and Drescher (2009a,b), Modenese (2013), Johnson et al (2015), Xiao and Zhang (2016), Ozaki and Kondo (2016), and Nishiyama et al (2016) among others. Alternative mathematical models, developed ad hoc from theoretical considerations or experimental evidence (e.g., Higa et al, 2015) or based on simplifying physical assumptions (e.g., Gray et al 2016), can also be found in the literature.…”