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Mathematical Problems in Engineering
Volume 2017, Article ID 7901918, 14 pages
Research Article

Maximum Likelihood Estimation of Model Uncertainty in Predicting Soil Nail Loads Using Default and Modified FHWA Simplified Methods

1School of Earth Science and Engineering, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China
2Provincial Key Laboratory of Mineral Resources and Geological Processes Guangzhou, Guangdong 510275, China
3Department of Civil Engineering, Ryerson University, Toronto, ON, Canada M5B 2K3

Correspondence should be addressed to Liansheng Tang; nc.ude.usys.liam@sltsee

Received 16 July 2017; Revised 5 November 2017; Accepted 15 November 2017; Published 19 December 2017

Academic Editor: Xiao-Qiao He

Copyright © 2017 Huifen Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Accuracy evaluation of the default Federal Highway Administration (FHWA) simplified equation for prediction of maximum soil nail loads under working conditions is presented in this study using the maximum likelihood method and a large amount of measured lower and upper bound nail load data reported in the literature. Accuracy was quantitatively expressed as model bias where model bias is defined as the ratio of measured to predicted nail load. The maximum likelihood estimation was carried out assuming normal and lognormal distributions of bias. Analysis outcomes showed that, based on the collected data, the default FHWA simplified nail load equation is satisfactorily accurate on average and the spread in prediction accuracy expressed as the coefficient of variation of bias is about 30%, regardless of the distribution type. Empirical calibrations were proposed to the default FHWA simplified nail load equation for accuracy improvement. The Bayesian Information Criterion was adopted to perform a comparison of suitability between the competing normal and lognormal statistical models that were intended for description of model bias. Example of reliability-based design of soil nail walls against internal pullout limit state of nails is provided in the end to demonstrate the benefit of performing model calibration and using calibrated model for design of soil nails.