###### Abstract  
A numerical model with a Coupled Eulerian-Lagrangian (CEL) approach is proposed for spudcan penetration into sand overlying clay. Both stress-dependence and strain-softening effects are incorporated into the M-C model to describe the sand, whereas the Tresca model with softening effect is used to describe the clay. Effects of the critical state strain threshold in the strain-softening model of sand and the clay sensitivity in the strain-softening model for clay are investigated. The model is verified against different soil conditions: uniform sand, loose sand overlying clay, and dense sand overlying clay. It is found that the stress-dependence effect dominates shallow penetration, whereas the strain-softening effect dominates deep penetration. The assumption of a constant peak friction angle for the accumulated deviatoric plastic strain less than the threshold of peak friction angle leads to an overestimation of the resistance in loose sand. Furthermore, the fit parameter obtained from triaxial tests tends to underestimate the peak resistance in dense sand. The proposed model should provide a valuable tool for geotechnical engineering analysis in sand. foundation on dense sand overlying clay was discussed. [PERSON] et al. [10] performed more tests of spudcan penetration in dense sand overlying clay and proposed a simplified conceptual model for the bearing capacity on dense sand overlying clay. [PERSON] et al. [12] performed more tests of spudcan penetration in medium-loose sand overlying clay and extended the model proposed by [PERSON] et al. [13] to medium-loose sand overlying clay. [PERSON] et al. conducted field tests of spudcan penetration in sand overlying clay [14], providing valuable references for future study. These tests are inadequate to cover all the spudcan foundations and the soil properties of the seabed. Therefore, tremendous numerical analyses were conducted to further study the problem and to propose prediction methods [1; 15; 16; 17]. Many researchers tried to propose an accurate numerical model for the problem [18; 19; 20; 21; 22]. The numerical approaches used in these papers are RITSS and CEL. As reviewed by [PERSON] et al. [23], RITSS and CEL agree well for quasi-static problems, so the main difference between these numerical models is the constitutive model of the soil, especially the sand. The constitutive models and the simulation performance models are compared in Table 1 and Figure 1, respectively. Both [PERSON] et al. [18] and [PERSON] et al. [19] used the M-C model for sand and the Tresca model for clay and obtained a similar prediction of the resistance profile in loose sand overlying clay. [PERSON] et al. [21] used the M-C model for sand and incorporated the softening effect into the Tresca model of clay, with which the peak resistance is well captured; however, the post-peak resistance is overestimated. [PERSON] and [PERSON] [20] used the hypoplastic model for sand and gave an accurate prediction of the peak resistance. However, the post-peak resistance is also significantly overestimated. To improve the prediction of post-peak resistance, [PERSON] and [PERSON] [24] employ the vischypoplastic model for clay. It predicts smaller resistance for the post-peak stage than [PERSON] and [PERSON] [20], but it is still much larger than the test. [PERSON] et al. (2019) [22] subsequently tried some other constitutive models for the sand and clay material, as summarized in Table 1.  
This paper takes into account the strain effect for both loose and dense sand and proposes a numerical model for spudcan penetration, which can capture both the peak bearing resistance and the post-peak behavior. In Section 2, the numerical methodology is proposed based on the CEL approach. The CEL model is implemented with a new constitutive model of sand, taking into account both the stress-dependence and strain softening. In Section 3, sensitivity analysis is conducted.