Design of foundations against differential settlement

The serviceability limit state (SLS) design of foundations typically proceeds by limiting the total settlement of individual foundations and thereby attempting to restrict the differential settlement between pairs of foundations. Due to the uncertain nature of the supporting ground, the magnitude of settlement and differential settlement are random. As it is often the differential settlement that governs serviceability, it is desirable to provide design requirements that suitably restrict differential settlements. This paper investigates, by Monte Carlo simulation, the distribution of the maximum differential settlement between pairs of foundations as a function of the spacing between foundations and the number of foundations — groups of four, nine, or 16 foundations, arranged on a grid — are considered. The effects of the correlations between the equivalent stiffness of the ground under each foundation, as well as between the loads applied to the foundations, on the distribution of the maximum differential settlements and angular distortions are investigated. Ratios of resistance factor to resistance bias factor are presented that can be used to calibrate design requirements on the total settlement of individual foundations that also simultaneously achieve acceptable performance with respect to angular distortion.