## 1 Introduction
Meanwhile, the traditional design practice aims to prevent gapping (uplift) under operational loads [23], which is achieved by restricting the width of the gapping area to 25% of the base width, or 50% depending on the chosen standards or design guidelines. [PERSON] and [PERSON] [1] used a Wrinkler model to simulate uplift in a WT foundation, and concluded that considering the uplift in modeling is necessary to correctly evaluate the seismic response. [PERSON] and [PERSON] [24] summarized the available knowledge on Winkler models and their usage for modeling rocking shallow foundations. Based on their literature review, they concluded that moment capacity of rocking foundations is reliable, and their seismic settlement is tolerable. [PERSON] et al. [25] used uniaxial hysteretic springs to model rocking shallow foundations and showed the excellent self-centering behavior of such foundations. [PERSON] et al. [26] used particle image velocimetry to evaluate soil deformation mechanisms of rocking foundations on sand, and observed that multiple soil deformation mechanisms including wedge deformation and scoop deformation happened under rocking foundations. [PERSON] et al. [27] conducted a review of modeling techniques and performance of rocking shallow foundations. They reported that rocking foundations have better performance compared to conventional foundations due to their dissipation of seismic energy, and provide a low-cost base isolation mechanism. [PERSON] et al. [28] developed a numerical model of rocking foundations for the OpenSees software, and investigated the effects of several properties like column height and foundation size on moment and settlement responses of the foundation. [PERSON] [29] evaluated the effects of shallow foundation properties on moment-rotation response of wind towers using a Winkler model. They concluded that response was affected by modulus of Winkler model, ultimate stress, axial load, and flexibility of the foundation. [PERSON] and [PERSON] [2] conducted experimental results of small-scale WT foundation modelson non-cohesive soils and observed that accumulation of rotations under cyclic loads does not depend on uplift. Therefore, they concluded that prevention of uplift under operational loads as required by design codes seems unnecessary for the case of non-cohesive soils. [PERSON] and [PERSON] [3] presented a method of numerical modeling of shallow WT foundations on dry sand. They demonstrated that the uplift restrictions in design codes are overly conservative and concluded that relaxing such criteria can safely allow repurposing existing foundations of out-of-service WTs for installing larger WTs. However, research on the dynamic behavior of rocking wind turbine foundations is still lacking. To evaluate the consequences of the rocking of a wind turbine foundation on undrained clay is undertaken herein as a part of a series of studies by the authors on shallow wind turbine foundations rocking on different types of soils. To model the rocking of a foundation on clay under undrained conditions such as seismic events or dynamic aerodynamic loads, a suitable constitutive model should be used in the numerical model. Several constitutive models have been developed and tested in the literature for undrained clay. [PERSON] [30] developed a constitutive model with multiple von Mises yield surfaces and both isotropic and kinematic hardenings. [PERSON] and [PERSON] [31] used Cam clay and modified Cam clay models to model compression tests of soil samples and showed that the original Cam clay model performed better than the modified version. [PERSON] and [PERSON] [32] developed an effective stress model for clay with the coupling of volumetric and shear behavior. [PERSON] [33] presented the hypoplastic model for clay, which incorporated aspects of the modified Cam clay model and the Matsuoka-Nakai failure surface with the hypoplastic formulation of the non-linear behavior of the soil. [PERSON] et al. [34] used a von Mises model with kinematic hardening to model rocking foundations on clay.