“…Traditionally, the macro-element model is usually used to model the non-linear load-deflection response of a foundation under threedimensional loads (Ibsen et al, 2014;Villalobos Jara, 2006;Byrne, 2000;Pisanò et al, 2016;Skau et al, 2018a;Yin et al, 2020). For example, Houlsby and Cassidy (2002), Zhang et al (2014) and Wang et al (2021) proposed macro-element models of spudcan for integrated dynamic analysis of the jack-up system; Salciarini and Tamagnini (2009) and Jin et al (2019) proposed macro-element models for shallow foundations, and Li et al (2016) proposed macro-element model for piles. For the suction caisson in undrained clay, Cassidy et al (2006) Taiebat and Carter (2000) Clay 𝑓 = ( ; 𝜆 is the function of the shape of failure envelope; 𝛼, 𝛽 are the fitting parameters of the embedment ratio; 𝑛 1 , 𝑛 2 , 𝑛 3 are the coefficients with respect to the embedment ratio et al (2018b) and Yin et al (2020) also developed different macroelement models based on the traditional plasticity theory, hypoplastic theory or the multi-surface concept.…”