Probabilistic Analysis of Immediate Settlement of Sandy Soil for Strip Foundation using MATLAB

Abstract

This study examines the immediate settlement of a strip foundation on sandy soil subjected to a 100 kPa load across three boreholes (BH 1, BH 2, and BH 3). The goal is to compare deterministic and probabilistic methods to improve design reliability and assess risks due to parameter uncertainty. The objectives include: (i) determining settlement through deterministic analysis, (ii) estimating the statistical distribution of settlement using Monte Carlo simulation, (iii) developing a MATLAB-based probabilistic model that accounts for variability in soil parameters, and (iv) comparing the results from both probabilistic and deterministic approaches. The deterministic analysis employed Schleicher’s elastic theory with fixed parameters (Young’s modulus E = 12,000 kPa, Poisson’s ratio = 0.3, applied load q = 100 kPa, and foundation width B ranging from 1.0 to 5.0 m). The settlement results were below the allowable limits for strip foundations on sand (25 mm) and the serviceability limit (30 mm). A MATLAB model with 10,000 iterations using the Monte Carlo simulation method, which included random inputs (E: lognormal, COV = 25%; nu: normal, COV = 17%; q: normal, COV = 10%; B: normal, COV = 10%) for the three boreholes, yielded a right-skewed (skewness = 0.861) and heavy-tailed (kurtosis = 1.498) settlement distribution with a mean of 18.003 mm, a median of 17.310 mm, a standard deviation of 5.215 mm, and a range of 4.636 – 53.811 mm. The 95th percentile exceeded the critical threshold, and outliers surpassed the serviceability limit, indicating a moderate to high risk. Visual representations (box plot and CDF plot with mean, median, and exceedance lines for 25 mm and 30 mm) illustrate how the deterministic approach underestimates variability and tail risks, as the 95th percentile and outliers significantly exceed the predictions from the deterministic analysis. This study, conducted to address uncertainties in soil parameters and enhance design robustness, underscores the importance of probabilistic analysis in identifying risks that deterministic methods overlook, thereby guiding safer foundation design.