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Technical paper: Prediction of footing settlements on sand

By M Arnold, University of Adelaide

This paper was first published in GE’s March 1980 issue


The field of settlement predictions for footings resting on sand is one of the last strongholds of empiricism ‘in the whole range of soil mechanics. Terzaghi and Peck (1967) state categorically that, in practice, the magnitude of the settlement of footings on sand cannot be pred’icted on the basis of the results of laboratory tests on soil specimens. A direct correlation has generally been made between settlement and relative density of the soil mass as determined from a Standard Penetration Test (SPT) or a cone penetrometer test, either static or dynamic. More recent correlations have been made between penetration test results and soil parameters such as the modulus of compressibility, with these parameters then being used in analytical methods based on elasticity theory (Schultze & Menzenbach, 1961; Thomas, 1968). Louw (1971) used elasticity theory with portable dynamic penetrometer data to predict settlements. This method, however, predicts a linear relationship between settlement and footing pressure. A similar defect is evident in the method of Schultze & Sherif (1973) as well as in the earlier method of Alpan (1964). A significant advance was the method of Schmertmann (1970) in which an assumed (simplified) distribution of vertical strain below the centre of a footing is used in conjunction with an empirical correlation between static cone penetration resistance and equivalent Young’s modulus in compression. The approach made here is to establish the relative density of a sand deposit empirically from the results of a standard penetration test using a previously pub- I’ished relationship. Then, using empirical stress-strain relationships for sands of varying densities, the strains below the centre of a footing are predicted and integrated to give the total settlement of a footing. This approach is similar to that of Alpan but the stress-strain relationships used are continuous functions and not restricted to the quasi-linear range only. No allowance is made for long-term creep. This can be incorporated in the analysis by means of an additional factor. 

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