## 4 Conclusions  
This study systematically revealed the penetration mechanisms and stability laws of spudcans for WTIVs in complex seabeds through CEL numerical simulations, entire four-legged platform centrifuge model tests at 150\(\times\)\(g\), and full-scale case validations. A comprehensive methodology for the evaluation of jack-up stability was proposed. The key findings are as follows:  
1. The penetration behavior of the spudcan exhibited fundamental differences between clay and sand. In clay, penetration evolved through three distinct phases: shallow penetration (\(\leq\)4 m) triggered general shear failure, forming near-vertical cavities; intermediate depths (\(\approx\)8 m) transitioned to localized shear, with a 38% increase in surface heave; and deep penetration (\(\geq\)12 m) shifted to plastic flow dominated by soil backfilling, stabilizing at the remolded strength. Conversely, sand displayed nonlinear resistance growth, surging sharply beyond a critical depth (0.8 m) to reach the design limit (4400 t) at 1.9 m. Sand's failure zone was 42% smaller than that of clay, and early cavity collapse (diameter \(\approx\) 1.2 \(L\)) confirmed particle rearrangement as the primary energy dissipation mechanism. 2. Platform stability was critically influenced by soil type. For sliding resistance, clay showed linear improvement with penetration depth, with early peak resistance that remained stable, while sand delivered 2-5 times higher peak resistance but exhibited delayed attenuation. Overturning analysis revealed that although the horizontal loads in clay were 50% of those in sand, the tilt angles at equal sliding distances were 8-10 times greater due to the significant settlement of compression legs in low-strength clay, triggering chain-overturning effects. This highlights the necessity of an integrated assessment combining horizontal loads and seabed bearing capacity. 3. A comprehensive framework for WTIVs' operational stability integrates sea conditions, geological parameter inputs, and penetration analysis as the basis for anti-overturning/sliding and punch-through assessments. Loads must encompass platform gravity, environmental forces (including DAF), crane operational load, and P-\(\Delta\) effects. For multi-layered soils, CEL simulations outperformed traditional methods in accuracy (with an error of \(<\)5% at a mesh size of \(\leq\)0.03 \(L\) and a penetration rate of 0.2 m/s), capturing soil plug dynamics and interlayer interactions. The case validation using the 'Haidian Yunwei 801' platform at Guangdong Lemen Wind Farm confirmed a controllable punch-through risk (365 kPa equivalent pressure \(<\) 412 kPa ultimate bearing capacity), with the preload (4707.5 t) outside the critical zone (7300-8400 t) and the sliding resistance (2407 t) exceeding the environmental loads by 185%. Crane operation during installation (safety factor \(\gamma\) = 2.437) posed a higher overturning risk than storm scenarios (\(\gamma\) =2.441), underscoring the dominance of operational load combinations. Despite analyzing the global anti-overturning and anti-sliding stability through scaled full-model tests, this study encountered two primary limitations: (i) The entire four-legged platform centrifuge test at 150\(\times\)\(g\) failed to capture microscopic images of soil deformation evolution during spudcan penetration and sliding, due to funding and equipment limitations. (ii) The synchronous implementation of CEL numerical analysis was precluded by insufficient computational resources. Furthermore, as WTIVs continue expanding into new operational waters, the following areas require further investigation: the penetration mechanisms of spudcans in hetero neous complex strata; anti-overturning/sliding behaviors under multi-layer geological conditions; and punch-through risk assessment methodologies for non-uniform seabels. M.X. : conceptualization, data curation, formal analysis, investigation, methodology, validation, writing--original draft, and writing--review and editing. Z.W.