Scour induces the loss of soil support around the pile foundations for the offshore and coastal structures, and thus increases their bending moments and lateral deflections, which may change the vertical loads effect on the lateral response of piles applied in such cases. In this paper, the stress changes of the remaining soils at the corresponding pile location due to the three-dimensional scour-hole formation are first determined based on the Mindlin's elastic solutions. Then, the calculated new soil stresses are adopted to re-examine the Young's modulus of the remaining soils undergoing a stress history due to scour. With this key soil parameter that have been modified appropriately to reasonably reflect the effects of three-dimensional scour-hole geometry and the stress history of the soils simultaneously, an analytical model based on the principle of minimum potential energy is further developed to investigate the influence of vertical loads on the lateral responses of offshore piles in marine clay under scour conditions. The influence of related parameters including the lateral displacement level and the vertical load level with different scour-hole dimensions (i.e., scour depth, scour width and scour-hole slope angle), considering or ignoring stress history effect, have also been analyzed based on a case study. The results show that scour depth plays the most important role among the various scour-hole dimensions in influencing the responses of scoured piles under combined vertical and lateral loading. Although still possessing some limitations (e.g., the simplistic assumption of linear-elastic behavior for the soil and the approximate allowance made to account for the gapping effect), the simplicity and relative ease of utilization offered by this proposed analytical model make it a good alternative approach for estimating the deflection and moment responses of the scoured pile foundations subjected to combined lateral and vertical loading.
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