The offshore wind industry faces new challenges as cost-efficiency is a key issue for its further development. Steps towards feasible offshore wind energy are taken by building wind farms farther into the sea. This strategy, however, raises many economic and technical concerns. Wind turbine foundations is one of them.

Suction bucket technology is an option that carries great potential in terms of reducing the overall price of offshore wind turbine installation process. Multi-footed jacket structures mounted on buckets represent a solution for supporting high capacity wind turbines in transitional water depths. In this set-up the buckets are mainly subjected to axial loading. Knowledge about their performance is scarce, so readily-available methods to predict their behaviour are yet to be established.

This study is concerned with the formulation of $t-z$ curves for suction buckets installed in sand using numerical modelling. Finite element analysis software PLAXIS 2D and PYTHON programming language are used to create 100 axisymmetric models. Prescribed vertical displacements in both directions are applied considering drained and partially drained conditions. The simulated buckets have diameters from 10 to 20 m and an embedment ratio of 1. Cohesionless soil is assumed as Frederikshavn sand and is defined with the Hardening Soil small strain model. Compaction states ranging from loose to very dense are taken into account.

The shear stresses in skirt interfaces are plotted against bucket displacements and the resulting curves are normalized with respect to peak shear stress and peak displacement. The formulation of these two quantities is based on regression analysis of data related to each set numerical models that comprises a given combination of loading direction and drainage condition. Based on normalized curves and studies of fitting parameters, a mathematical model is created for each of the four sets.

Applying the Winkler method of idealizing soil reaction with springs, the $t-z$ formulations are employed to calculate the total frictional response of suction buckets. The spring properties are dependent on vertical stress, bucket diameter, skirt length and friction angle, all of which are basic parameters in geotechnical design.

The verification of mathematical models highlights some of their limitations and concludes on the better performance of drained formulations. Suggestions for improvements of $t-z$ expressions and further research on the topic are presented.