## 1 Introduction  
Spudcan foundations are widely used to support jack-up barges, which are widely used for offshore construction. For the design and operation of jack-up barges, the estimation of the peak bearing capacity (\(q_{punk}\)) during spudcan installation is essential. A major concern is the installation into sand overlying clayey soil, which may produce large differential settlements and potentially lead to a punch through failure. Because of the evident similarities between a spudcan and a shallow foundation, bearing capacity equations developed for shallow foundations have been used by SNAME [1]. One of the earliest models to estimate the bearing capacity of shallow foundation in sand over clay profile was proposed by [PERSON] [2] and [PERSON] [3]. The procedure, termed as the punching shear method, assumes that a sand block with vertical failure surfaces is pushed into the clay layer. Modifications were proposed to the punching shear method to improve the prediction accuracy. In the projection method, the failure surface is assumed to be inclined at an angle of \(\beta\)[4; 5; 6]. A range of values have been used for \(\beta\). [PERSON] et al. [7; 8] performed the centrifuge experiments to measure the bearing capacity of shallow foundations on dense sand overlying clay. Based on the model test measurements, a limit equilibrium-based model that combines the concepts of the punching shear and projection models was presented. [PERSON] and [PERSON] [9] proposed a new model for bucket foundations on sand over clays profiles based on the outputs of non-linear finite element analyses. Although there are similarities between two types of foundation, the clear difference is that whereas the shallow foundation can be considered to be wished-into place, the spudcan is pushed into the ground from the surface. Centrifuge model tests have been extensively performed to investigate the peak penetration resistance (\(q_{peak}\)) of spudcan foundations. [PERSON] et al. [10] performed centrifuge model experiments to examine the failure mechanism of spudcan foundations at \(q_{peak}\) in sand overlying normally consolidated (NC) clay using the particle image velocimetry technique. It was revealed that at \(q_{peak}\), a sand wedge forms between the base of the spudcan and sand-clay interface. The results of the centrifuge model tests were utilized to develop predictive models for \(q_{peak}\). [PERSON] et al. [11] presented a stress dependent model based on the observations of [PERSON] et al. [10]. The model was calibrated against experimental data for limited dense sand overlying clay profiles. [PERSON] et al. [12] modified the model of [PERSON] et al. [11] to account for the embedment depth. The model was validated against centrifuge model tests. Alternatively, advanced numerical modelling techniques capable of simulating large-deformation penetration have been used to calculate the penetration resistance of spudcan foundations. [PERSON] et al. [13] utilized the coupled Eulerian-Lagrangian (CEL) approach to simulate the penetration of spudcan for both homogenous and layered soil profiles. The parameters which influence the results of penetration resistance of spudcan were identified. [PERSON] and [PERSON] [14] performed finite element (FE) analyses using the CEL approach on loose sand overlying soft clay. The influences of sand thickness and bottom clay strength on the bearing capacity of spudcan foundations were evaluated. [PERSON] and [PERSON] [15] conducted the CEL analyses using the hypo-plastic model for sand and a visco-plastic model for clay. An equation for \(q_{peak}\) was not presented. [PERSON] et al. [16] performed FE analyses using the CEL approach to simulate penetration of a spudcan into medium dense sand over NC clay. \(q_{peak}\) results from the numerical simulations were compared with the simplified model proposed by [PERSON] et al. [12]. [PERSON] et al. [17] further extended the CEL approach accounting for the strain-softening behavior of dense sand. The simplified model of [PERSON] et al.