This paper examines the effect of pile diameter on the unit shaft friction that can develop on a pile in sand. The study is based on a series of tension tests conducted on centrifuge model piles with a range of pile diameters and average initial stress levels. The inferred significant increases in lateral effective stresses on the shafts of these piles at peak capacity are shown to be consistent with the normal displacement (dilation)-stiffness relationship measured in appropriate constant normal stiffness (CNS) interface tests. The determination of the lateral stress increases (and hence shaft capacity) also requires measurement or prediction of the non-linear cavity expansion stiffness of the sand surrounding the pile shaft. Predictions obtained for this stiffness using a numerical technique indicate that the operational stiffness surrounding a model pile is well below that assuming the very small strain (elastic) stiffness, and that the degree of normal displacement (and hence the lateral stress increase) depends significantly on the sand's non-linear stiffness characteristics. A predictive approach, which combines the CNS interface data with cavity expansion stiffness, is shown to perform well against an independent test series of model pile tests and to be potentially suitable for the evaluation of lateral stress changes that take place during loading of full-scale piles.