Probabilistic Dynamic Analysis of Circular Foundation Embedded in Loose Sand Under Vertical Machine Vibration Considering Soil Spatial Variability

The present study investigates the impact of soil spatial variability on the dynamic settling of an embedded circular foundation in loose sand at its resonance frequency under variable‐amplitude vertical harmonic machine vibration, utilizing the random finite difference method (RFDM). The resonant frequency was chosen to study the foundation at its worst within the soil spatial variability framework. Both deterministic and probabilistic analyses are executed using FLAC 3D software. The probabilistic analysis assumes a lognormally distributed random field for the elastic modulus ( E ) of loose sand. The mean dynamic settlement ( µ δ ) and exceedance probability ( p e ) of allowable settlement at different depths of the soil model are evaluated considering different spatially variable parameters (e.g., horizontal scale of fluctuation, L x = L y ; vertical scale of fluctuation, L z ; coefficient of variation of elastic modulus, COV E ) under the Monte Carlo simulation (MCS) framework. The probability density function ( PDF ) plots of the probabilistic dynamic settlement are also produced for a more accurate representation of the exceedance probability. The findings indicate that the probabilistic dynamic settlement values of the system exceed the deterministic values. However, the probabilistic values approach the deterministic result for the lower values of COV E , L x = L y , and higher values of L z , assuming the other statistical parameters remain constant.