The estimation of the wave-induced instantaneous liquefaction is particularly important for the design of foundations of offshore structures. Regarding the occurrence of liquefaction in a non-cohesive seabed, most existing studies using constant permeability were found to cause fallacious tensile stresses in the liquefied zone and further pollute the overall pore pressure distribution. A dynamic permeability model was previously presented to mitigate the shortcoming but posed difficulties in the nonlinear convergence. To overcome the shortcoming of the previous studies, this study proposes the concept of modelling the liquefaction-involved wave-seabed interactions as a nonlinear complementarity problem, wherein a Karush–Kuhn–Tucker condition is constructed, based on revisiting the liquefaction criterion most widely applied in ocean engineering. The Lagrange multiplier method and the primal–dual active set strategy are employed to numerically deal with the nonlinear complementarity problem. The performance of the chosen multiplier space is investigated by theoretical analyzing and numerical modelling. Compared with the previous dynamic permeability model, the present model is totally free of extra parameters and precisely fulfills the no-tension requirement. Moreover, the difficulties of dynamic permeability in the nonlinear convergence are overcome and no divergence is observed in the numerical tests.

波浪引起的瞬时液化的估计对于海上结构的基础设计尤为重要。关于非粘性海床液化的发生，现有的大多数使用恒定渗透率的研究被发现会在液化区引起错误的拉应力，并进一步污染整体孔隙压力分布。先前提出了动态渗透率模型以减轻缺点，但在非线性收敛方面造成困难。为克服以往研究的不足，本研究提出了将涉及液化的波浪-海底相互作用建模为非线性互补问题的概念，其中基于重新审视应用最广泛的液化准则，构建了 Karush-Kuhn-Tucker 条件。在海洋工程。采用拉格朗日乘子法和原始-对偶活动集策略在数值上处理非线性互补问题。通过理论分析和数值建模来研究所选乘数空间的性能。与之前的动态渗透率模型相比，本模型完全没有额外的参数，准确地满足了无张力要求。此外，克服了非线性收敛中动态渗透率的困难，在数值试验中没有观察到发散。与之前的动态渗透率模型相比，本模型完全没有额外的参数，准确地满足了无张力要求。此外，克服了非线性收敛中动态渗透率的困难，在数值试验中没有观察到发散。与之前的动态渗透率模型相比，本模型完全没有额外的参数，准确地满足了无张力要求。此外，克服了非线性收敛中动态渗透率的困难，在数值试验中没有观察到发散。