To control serviceability problems arising from excessive settlement of shallow footings, geotechnical design codes generally include specifications regarding maximum settlement, which often govern the footing design. Once the footing has been designed and constructed, the actual settlement it experiences on a real three-dimensional soil mass can be quite different than expected, due to the soil's spatial variability. Because of this generally large variability (compared to other engineering materials, such as concrete and steel) and because this particular serviceability limit state often governs the design, it makes sense to consider a reliability-based approach to settlement design. This paper looks in some detail at a load and resistance factor design (LRFD) approach to limiting footing settlement. In particular, the resistance factors required to achieve a certain level of settlement reliability as a function of soil variability and site investigation intensity are determined analytically using random field theory. Simplified approximate relationships are proposed and tested using simulation via the random finite element method. It is found that the simplified relationships are validated both by theory and simulation and so can be used to augment the calibration of geotechnical LRFD code provisions with respect to shallow foundation settlement. Key words: reliability-based design, settlement, geotechnical, shallow foundation, random field, probability.
Thermal critical behavior and universality aspects of the three-dimensional random-field Ising model
