Residual and Fully Softened Strength Evaluation of Soils using Artificial Neural Networks

Abstract

A backpropagation artificial neural network (ANN) model is developed to predict the secant friction angle of residual and fully softened soils, using data reported by Stark et al. (J Geotech Geoenviron Eng ASCE 131:575–588, 2005). In the ANN model, index properties such as liquid limit, plastic limit, activity, clay fraction and effective normal stress are used as input variables while secant residual friction angle is used as output variable. The model is verified using data that were not used for model training and testing. The results also indicate that the secant residual friction angle of cohesive soils can be predicted quite accurately using liquid limit, clay fraction and effective normal stress as input variables with R ² = 0.93. The sensitivity analysis results indicate that plastic limit and activity have no appreciable effect on ANN predicted secant friction angles. The secant friction angle predictions of the ANN model were also compared with those of Stark’s et al. (2005) curves and the empirical formulas suggested for the same data sets by Wright (Evaluation of soil shear strengths for slope and retaining wall stability with emphasis on high plasticity clays, 2005). The comparison shows that the ANN model predictions are very close to those suggested by the Stark et al. (2005) curves but much better than the prediction of Wright’s (2005) empirical equations. The results also show that ANN is an alternative powerful tool to predict the secant friction angle of soils.

Appendix A: Definition of Statistical Parameters

The following error measuring parameters were used in evaluating the performance of the developed ANN model:

$$ {\text{RMSE}} = \frac{1}{n}\sum\limits_{i = 1}^n {y_i - x_i^2 } $$

(A1)

$$ {\text{RMSPE}} = \frac{{\frac{1}{n}\sum\limits_{i = 1}^n {y_i - x_i^2 } }}{y} $$

(A2)

$$ {\text{MAPE}} = \frac{1}{n}\sum\limits_{i = 1}^n {\frac{{y_i - x_i }}{{x_i }}} $$

(A3)

In the above equation, RMSE is Root Mean Square Error, RMSPE is Root Mean Square Percentage Error, and MAPE is Mean Absolute Percentage Error. The parameters in the error functions, x _i is measured data, y _i is ANN model prediction, n is number of data points, x is mean value of measured data, and y is the mean valued of ANN model prediction.