Evaluation and calibration of ultimate bond strength models for soil nails using maximum likelihood method

Statistical evaluation of the accuracy of effective stress method (ESM) equations for prediction of the ultimate bond strength of soil nails was performed using the maximum likelihood method. Over 500 pullout tests were examined for soil nails installed in two different Hong Kong soils. The data were parsed into tests that reached pullout failure before reaching 90% of the nail tendon yield strength (uncensored data) and tests terminated at the 90% yield strength criterion (censored data). A log-likelihood function was constructed to include both types of bias data, where bias is the ratio of measured to predicted ultimate nail bond strength. The accuracy of two ESM equations previously reported in the literature was evaluated using both uncensored data alone and then combined censored and uncensored data. A revised ESM equation with two empirical coefficients is calibrated using the larger combined data sets, and its accuracy is compared to the two earlier formulations using the same expanded database. The revised formulation has the advantage that mean of bias values is 1 for both soil types and there are no bias dependencies with magnitude of predicted pullout capacity or overburden pressure. However, for one soil type the COV of bias values is less using the larger database and for the other soil type the value is greater. A practical lesson for calibration of equations of the type investigated here is that including censored data for calibration is of great importance to reach a better and more thorough understanding of the performance of the model.