Probabilistic analysis at the serviceability limit state of two neighboring strip footings resting on a spatially random soil

• Tow neighboring strip footings resting on a spatially varying soil were studied.
• The probability Pe of exceeding tolerable differential settlement was calculated.
• An improved subset simulation (iSS) approach was proposed to calculate Pe.
• A relatively small number of realizations was needed when using the iSS.

The computation of the failure probability of geotechnical structures considering the soil spatial variability is generally performed using Monte Carlo Simulation (MCS) methodology. This method is very time-consuming especially when computing a small failure probability. As an alternative, Subset Simulation (SS) approach was proposed by Au and Beck [3] to efficiently calculate the small failure probability. In the present paper, a more efficient approach called “improved Subset Simulation (iSS)” approach is employed. In this method, the first step of the SS approach is replaced by a conditional simulation in which the samples are generated outside a hypersphere of a given radius. The efficiency of the iSS approach is illustrated here through the probabilistic analysis at the serviceability limit state (SLS) of two neighboring strip footings resting on a soil with 2D spatially varying Young’s modulus. The system response is the differential settlement between the two footings. The probabilistic results have shown that the probability Pe of exceeding a tolerable differential settlement computed by the iSS approach is very close to that calculated by the MCS methodology applied on the original deterministic model. The results have also shown that the use of the iSS approach has reduced the number of calls of the deterministic model by about 50% with respect to the SS approach.