Predicting the Limit Void Ratios of Coarse-Grained Soils Using Articial Neural Networks

25 In this study, the prediction performance of the artificial neural network (ANN) and multiple regression 26 (MR) models in predicting the limit void ratios of coarse-grained soils was investigated and compared. The data 27 available in the literature were collected and used to construct both two distinct ANN-1 and ANN-2 models and 28 two distinct MR-1 and MR-2 models: ANN-1 and MR-1 for the prediction of minimum void ratio (e min ) and 29 ANN-2 and MR-2 for the prediction of maximum void ratio (e max ) of coarse-grained soils. Two basic soil 30 graining properties such as coefficient of uniformity ( C u ) and mean grain size ( D 50 ) are utilized in the simulation 31 of the feed forward ANN models with back propagation algorithm and the MR models.The e max and e min values 32 predicted from both ANN and MR models were compared with the experimental values taken from the literature. 33 Moreover, five performance indices i.e. the determination coefficient, variance account for, mean absolute error, 34 root mean square error, and the scaled percent error were calculated to examine the prediction capacity of the 35 ANN and MR models developed in this study. The performance indices calculated indicated that both ANN 36 models showed better performance than both MR models. It has been demonstrated that both ANN models can 37 be used satisfactorily to predict limit void ratio values of coarse-grained soils as a rapid inexpensive substitute 38 for laboratory techniques. 39


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The characteristics and properties of granular materials is mostly connected with the relative density 57 (Dr) (Lade et al., 1988). Dr is commonly used in geotechnical engineering to indicate the in-situ denseness or 58 looseness of granular soils (Das, 2010; Sulewska, 2010).) The liquefaction resistance of soil is also controlled by 59 the Dr value of soil (Polito and Martin, 2001). The lower the Dr value of the soil, the higher the liquefaction 60 potential of the soil (Seed 1979;Seed 1983

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In this study, the data available in the literature were collected and used to develop both two distinct artificial 79 neural network models (ANN-1 and ANN-2) and two distinct multiple regression models (MR-1 and MR-2):

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ANN-1 and MR-1 for the prediction of the emin values of coarse-grained soils and ANN-2 and MR-2 for the 81 prediction of the emax values of coarse-grained soils. The results predicted from the ANN and MR models were 82 compared with the experimental results taken from the literature (Polito, 1999 94 Erzin et al. 2016) to form a wider database were used to establish a predictive relationship between the limit void 95 ratios (emax and emin ) of coarse-grained soils and their two graining parameters, namely, mean particle size (D50) 96 and uniformity coefficient (Cu). The descriptive statistics of the data containing the graining parameters and limit 97 void ratios of different 181 soils are given in Table 1. To visualize the distribution of the samples, the data are 98 presented by frequency histograms (Fig. 1). As it can be observed from the figure, the distributions of the 99 predictor variables are not uniform.

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The relationship between the soil graining parameters (Cu and D50) and limit void ratios (emin and emax) 102 are shown in Fig. 2. Correlation analysis were carried out the strength of the relationship between these two soil 103 graining parameters and limit void ratios and the Pearson correlation coefficient (r) values are given in Table 2.

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It can be noted from Table 2 that there is no significant relation between the soil gaining parameters and limit 105 void ratios, as the determined r values are very low.

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In order to examine the relationship between emin and emax for the data utilized in this study, the emin 108 values were plotted against the emax values, as shown in Fig. 3. It can be seen from the figure that a strong linear          Fig. 11 for all samples taken from the literature. Figures 10 and 11 show that 228 there is not a good agreement between the predicted and experimental (emax and emin) values.

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variance account for (VAF), given by Eq. (7), mean absolute error (MAE), given by Eq. (8), and root mean 231 square error (RMSE), given by Eq. (9) were calculated for comparing and evaluating the prediction performance 232 of the ANN and MR models developed in this paper. The computed indices are listed in Table 3.
where var denotes the variance, y is the measured value, ŷ is the predicted value.

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In addition to the four performance indices computed, in order to gain an insight into the prediction 239 capabilities of the proposed ANN and MR models, a graph between the scaled percent error (SPE), as given by