Reliability-based analysis of settlements of shallow foundations on cohesionless soils
Authors:   , Al-Sumaiday Hashim Ghalib 
Published: August 2021

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI-COLUMBIA AT REQUEST OF AUTHOR.] Although settlements of foundations on cohesionless soils usually are small, it is important to be able to predict them because the primary issue in the design of shallow foundations on sand is the settlement requirement. Many methods for estimation of settlements in cohesionless soils have been published and evaluated. The majority of these methods rely on an empirical or semiempirical correlation with in-situ tests due to the difficulty and expense of obtaining undisturbed samples of cohesionless soils. The empiricism, in addition to the natural inherent soil variability, bring significant uncertainties into evaluation of design soil properties, and consequently to the settlement estimations. Traditional settlement analysis methodologies do not incorporate a consistent approach to account for the uncertainties and can lead to either costly design by overestimation of the settlement or a risky design by underestimation of the settlement. In contrast, a reliability-based methodology allows engineers to produce designs with a consistent level of safety that separately accounts for variability and uncertainty. The published works have extended the reliability-based methodology to settlement prediction. However, in the previous works, the uncertainties have been considered as one lumped factor and footing size has never been considered as an input variable. The research aims to extend the reliability-based methodology to settlement of shallow foundations on cohesionless soils considering the footing size and the main sources of uncertainties. It is hypothesized that incorporating the footing size in addition to the main sources of uncertainties in the reliability-based methodology will improve the reliability estimation of the settlement prediction; and consequently, improve the designs of shallow foundations on cohesionless soils. In the research described herein, six settlement prediction methods were evaluated using a database of 361 settlement case histories in terms of reliability, "the percentage of cases which the predicted settlement is equal or larger than measured settlement", and accuracy, "the ratio of the average of predicted settlement to the average of measured settlement". Sources of uncertainties associated with settlement prediction were investigated. The sources included inherent soil variability (from the natural formation of the soil), measurement uncertainty (from equipment, procedural, and random errors of the in-situ testing), transformation uncertainty (from empirical models to transform field or laboratory measurements into a design soil property), and the applied stress variability. Three probabilistic approaches were used to estimate: (i) probability of failure "the probability that the actual settlement exceeds a tolerable settlement", and (ii) settlement factors "multipliers are used in the design equations to target one of several acceptable probabilities of failure for serviceability limit state". The first approach was performed to estimate the probability of failure and the settlement factors probabilistically based on the total uncertainties of each settlement prediction method. The total uncertainties were characterized as one lumped factor by the statistics of the predicted to the measured settlements ratios. The second approach considered the main sources of uncertainty separately. A second-moment probabilistic technique was used to estimate the upper bound of the transformation uncertainty based on best- and worst- case scenarios of other uncertainty components. The estimated upper bound of the transformation uncertainty for each settlement prediction method was used in the probabilistic analysis herein. In the third approach, a framework was developed to estimate the realistic transformation uncertainty of each settlement prediction method to be used in the probabilistic analysis. A new approach to estimate the settlement is presented. The method has better accuracy and lower dispersion of the predicted to the measured settlement ratio than existing methods. The influence of soil type, size of footing, embedment depth, elevation of groundwater, and length to width ratio on both reliability and accuracy of the settlement prediction methods were examined. The width of the footing was found to be the most influential factor on the reliability and accuracy of the settlement prediction. The results support the hypothesis and show that the same amount of predicted settlement might indicate a different reliability according to the footing size. The results can be used to determine the reliability of settlement prediction in terms of probability of failure at different ranges of footing size, inherent soil variability and measurement uncertainty. The findings of this study can be used as a guide for geotechnical engineers to avoid over- or under- estimation of settlement. The results of the research described herein allow geotechnical engineers to achieve a better design of shallow foundations on cohesionless soils with a consistent level of safety that accounts for variability and uncertainty.