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The model uncertainty in prediction of facing tensile forces using the default Federal Highway Administration (FHWA) simplified equation is assessed in this study based on the Bayesian inference method and a large number of measured lower and upper bound facing tensile force data collected from the literature. Model uncertainty was quantified by model bias which is the ratio of measured to nominal facing tensile force. The Bayesian assessment was carried out assuming normal and lognormal distributions of model bias. Based on the collected facing tensile force data, it is shown that both the on-average accuracy and the spread in prediction accuracy of the default FHWA simplified facing tensile force equation depend largely upon the distribution assumptions. Two regression approaches were used to calibrate the default FHWA simplified facing tensile force equation for accuracy improvement. The Bayesian Information Criterion was adopted to quantitatively compare the rationality between the competing normal and lognormal statistical models that were intended for description of model bias. A case study is provided in the end to demonstrate both the importance of model uncertainty and the influence of distribution assumptions on model bias in reliability-based design of soil nail walls against facing flexural limit state.

This paper presents the development of a simplified model for estimation of maximum nail loads during or at completion of construction of soil nail walls. The developed simplified nail load model consists of two multiplicative components: the theoretical nail load and the correction factor. The theoretical nail load is computed as the product of lateral active Earth pressure at nail depth and the nail tributary area. The correction factor is introduced to account for the difference between the theoretical and the measured nail loads. A total of 85 measured nail load data were collected from the literature; out of which, 74 were used to develop a simple formulation for the correction factor, whereas the remaining 11 were used for validation. After the validation, the model was updated using all 85 data. The updated simplified nail load model was demonstrated to be accurate on average (mean of model factor equal to 1), and the spread in prediction quantified as the coefficient of variation of the model factor was about 40%. Here, model factor is the ratio of measured to estimated nail load. The randomness of the model factor was also verified. Finally, the model factor was demonstrated to be a lognormal random variable. The proposed simplified nail load model is beneficial due to its simplicity and quantified model uncertainty; thus it is practically valuable to both direct reliability-based design and load and resistance factor design of soil nail wall internal limit states.

Due to the characteristics of dispersion of guided waves, the waveforms recorded in ultrasonic nondestructive testing (NDT) of rock bolts are complicated to interpret. With a goal to increase the inspection sensitivity and accuracy in NDT of rock bolts, an approach of waveform interpretation based on wave modes identification is developed. The numerical simulation of full rock bolt and rock bolts with grout defect by Finite Element Method (FEM) is applied to illustrate the approach; it is found that the sensitive and low attenuation wave modes exist. Laboratory tests on full rock bolt and rock bolt with grout loss using NDT are conducted to evaluate the efficacy of the approach of waveform interpretation. In addition to that, a parametric study was conducted on rock bolt models with different sectional defect size. Based on the waveform interpretation, the mode-based reflection coefficientRis proposed to evaluate the sensitivity of wave modes to the defect size of sectional area. It is found that the sensitivity of the wave mode does not change with the defect sectional area, and the amplitude depends on the size of the defect.

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.