Modelling the wave-induced instantaneous liquefaction in a non-cohesive seabed as a nonlinear complementarity problem

A non-Darcy flow model for a non-cohesive seabed involving wave-induced instantaneous liquefaction

“…To address this issue, Zhou et al (2021) modeled the instantaneous liquefaction problem in physics as a nonlinear complementarity problem (NCP) in mathematics. The improvements over the dynamic permeability model (Zhou et al, 2020b) are apparent.…”

“…The improvements over the dynamic permeability model (Zhou et al, 2020b) are apparent. Within the NCP treatment (Zhou et al, 2021), a Karush-Kuhn-Tucker (KKT) condition is constructed specified for instantaneous liquefaction. It is treated by the Lagrange multiplier method and the primal-dual active set strategy (PDASS) (Kunisch and RöSch, 2002).…”

“…To minimize the implementation effort and at the same time obtain numerical performances close to the NCP treatment (Zhou et al, 2021), this study establishes a non-Darcy flow model specified for instantaneous liquefaction, on the basis of physical evidences (e.g., micro mechanisms, laboratory experiments and field trials). In order to avoid any unnecessary misleading of the existing non-Darcy models determining the limits of Darcy's law validity by means of Reynolds number (e.g.…”

“…It was previously applied to model multi-body contact behavior (Wriggers, 2006;Popp et al, 2013;Zhou et al, 2018), multiple cracks (Zheng et al, 2015) and the non-associative plasticity with non-smooth yield surfaces (Zheng et al, 2020) etc. Motivated by these works, Zhou et al (2021) presented a KKT condition for instantaneous liquefaction and treated the KKT condition by constrained variational principle. In this work, we construct a new type of KKT condition that is different from the KKT condition presented in Zhou et al (2021).…”

“…Motivated by these works, Zhou et al (2021) presented a KKT condition for instantaneous liquefaction and treated the KKT condition by constrained variational principle. In this work, we construct a new type of KKT condition that is different from the KKT condition presented in Zhou et al (2021). Furthermore, by means of the penalty method and variational equivalence, the KKT condition constructed here turns out to be clear in physics as a concise non-Darcy formulation, which can be conveniently treated by the standard Newton-Raphson method.…”