An approximate analytic relationship is developed between the maximum radial stress on the shaft of a displacement pile in sand and the base resistance of the pile. Using the cavity expansion analogy, together with a confined failure mechanism, the ratio between the two quantities, defined as a factor S t, is established as a function of the friction angle, shear stiffness, compressibility and mean effective stress of the sand near the pile tip. It is shown that, given otherwise identical input parameters, the value of S t will decrease with increasing friction angle, and with decreasing mean stress level. It also tends to decrease with an increase in relative density. It is predicted that S t has typical values between 0.03 and 0.05, in broad agreement with the range of empirically derived values in the literature. The relationship also predicts that S t may take much higher values (~0.1) for piles installed in dense sand or in highly compressible sand. Because of the analytical nature, the established relationship provides useful insights into the mechanisms involved and important implications for design practice.
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