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The compression index is one of the important geotechnical parameters, essential for the structural design. Since the determination of the compression index based on oedometer tests is relatively expensive and time-consuming, different authors have proposed for its estimation models using regression analysis and artificial neuron networks. However, they have ignored several parameters that could have increased the predictive capability of models. Other studies have concluded that genetic programming could have yielded better results. Unfortunately, no compression index models or effective comparisons of different methods have been published. The aim of this study is to propose a novel approach for estimating the compression index more accurately. To test the approach, a comparison study using K-fold cross-validation technique was conducted utilizing several models of multilayer neural networks, genetic programming, and multiple regression analysis. These models have been applied to 373 oedometer test samples to predict the compression index from soil physical parameters. The results indicate that the neural network with two hidden layers (7-14-4-1) provides the most appropriate prediction, compared with other models and the formulae suggested by previous studies. Based on these findings, this study‏ proposed a MATLAB script for efficiently estimating the compression index in the future studies.
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A new approach to predict the compression index using articial intelligence methods
Mohammed Amin Benbouras, Ratiba Kettab Mitiche, Hamma Zedira, Alexandru-Ionut Petrisor, Nourredine Mezouar, Fatiha
Debiche
Marine Georesources and Geotechnology, October 2018, Taylor & Francis
DOI: 10.1080/1064119x.2018.1484533
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A new approach to predict the
Compression Index using Articial
Intelligence Methods
What is it about?
The aim of this study is to propose a novel approach for estimating the compression
index more accurately. In order to test the approach, a comparison study between AI
methods has been made (multilayer neural networks, genetic programming, and
multiple regression analysis). These models have been applied to samples consisting
of 373 oedometer tests to predict the compression index from physical soil
parameters. Based on the tangible ndings, this study proposed a MATLAB program
script for eciently estimating the compression index in the future studies.
Why is it important?
the best-tted model proposed in these study can easily used in the future studies
for estimating the compression index of a new site based on physical soil
parameters, in order to help geotechnical engineers and researchers. Also, for
making the use of the proposed model more easier, we proposed an algorithm
programmed by MATLAB software.
Perspectives
BM
Benbouras Mohammed Amin (Author)
Ecole Nationale Polytechnique
Since the use of oedometer tests for estimating the compression index parameter is
considered relatively expensive and time-consuming, I really hope that this article
help engineers and researchers in the future studies.
The following have contributed to this page: HAmma Zedira, Alexandru-Ionut Petrisor, and Benbouras
Mohammed Amin
PDF generated on 30-Nov-2018
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... Utilizing an artificial neural network (ANN), a machine learning technique, researchers predicted the compression index using a dataset that included parameters like w, LL, PI, and G s [27]. Benbouras et al. [36] used ANN models, genetic programming, and multiple regression analysis to estimate the compression index on a dataset that contained LL, w, FCs (fine contents), P h (wet density), PI, e 0 , and soil types. In addition, Tsang et al. [37] employed machine learning techniques like extreme gradient boosting and random forest models on a dataset comprising e 0 , w, LL, PI, and G s to predict the compression index. ...
... Park and Lee [27] used artificial neural networks (ANNs) and achieved an R 2 value of 0.885. Benbouras et al. [36] obtained R 2 values of 0.562 with artificial neural networks, 0.360 with genetic programming, and 0.409 with multiple regression analysis. Tsang et al. [37] achieved R 2 values of 0.833 with extreme gradient boosting and 0.818 with random forest methods. ...
... Comparison of the results of the testing R 2 between this study and previous studies.Park and Lee[27] Artificial Neural Network [w, e 0 , LL, PI, G s , W sand, silt, clay ] 0.885Benbouras et al.[36] ...
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Soil consolidation, particularly in fine-grained soils like clay, is crucial in predicting settlement and ensuring the stability of structures. Additionally, the compressibility of fine-grained soils is of critical importance not only in civil engineering but also in various other fields of study. The compression index (Cc), derived from soil properties such as the liquid limit (LL), plastic limit (PL), plasticity index (PI), water content (w), initial void ratio (e0), and specific gravity (Gs), plays a vital role in understanding soil behavior. This study employs machine learning algorithms—the random forest regressor (RFR), gradient boosting regressor (GBR), and AdaBoost regressor (ABR)—to predict the Cc values based on a dataset comprising 915 samples. The dataset includes LL, PL, W, PI, Gs, and e0 as the inputs, with Cc as the output parameter. The algorithms are trained and evaluated using metrics such as the coefficient of determination (R2), mean absolute error (MAE), mean squared error (MSE), and root mean squared error (RMSE). Hyperparameter optimization is performed to enhance the model performance. The best-performing model, the GBR model, achieves a training R2 of 0.925 and a testing R2 of 0.930 with the input combination [w, PL, LL, PI, e0, Gs]. The RFR model follows closely, with a training R2 of 0.970 and a testing R2 of 0.926 using the same input combination. The ABR model records a training R2 of 0.847 and a testing R2 of 0.921 under similar conditions. These results indicate superior predictive accuracy compared to previous studies using traditional statistical and machine learning methods. Machine learning algorithms, specifically the gradient boosting regressor and random forest regressor, demonstrate substantial potential in predicting the Cc value for fine-grained soils based on multiple soil parameters. This study involves leveraging the efficiency and effectiveness of these algorithms in geotechnical engineering applications, offering a promising alternative to traditional oedometer testing methods. Accurately predicting the compression index can significantly aid in the assessment of soil settlement and the design of stable foundations, thereby reducing the time and costs associated with laboratory testing.
... While statistical models based on geotechnical variables like natural water content (w), liquid limit (LL), plasticity index (PI), and initial void ratio (e 0 ) have been proposed [12][13][14][15], they often lack generalizability across diverse datasets. Recent studies have shifted towards machine learning models [16][17][18], particularly ensemble learning approaches, to overcome these limitations and improve predictive accuracy. For example, Zhang et al. [19] implemented Random Forest (RF), a classic ensemble learning technique, utilizing a dataset of 311 samples with three factors: LL, PI, and e 0 . ...
... A comprehensive global dataset of clay soil parameters was compiled from peerreviewed studies, representing 1080 samples from diverse geographical regions such as Algeria, Spain, Nigeria, Iran, India, Germany, Ireland, and Bangladesh, among others [18,23,[27][28][29][30][31][32][33][34] This dataset was selected to reduce regional bias and improve the generalizability of the model across a wide range of soil conditions. It encompasses four independent variables (i.e., the input features)-LL, PI (with 169 missing values), e 0 , and w-which are used to establish a relationship with the output feature, the compression index. ...
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Accurate prediction of the compression index (𝑐𝑐 ) is essential for geotechnical infrastructure design, especially in clay-rich coastal regions. Traditional methods for determining 𝑐𝑐 are often time-consuming and inconsistent due to regional variability. This study presents an explainable ensemble learning framework for predicting the 𝑐𝑐 of clays. Using a comprehensive dataset of 1080 global samples, four key geotechnical input variables—liquid limit (LL), plasticity index (PI), initial void ratio (e0), and natural water content w—were leveraged for accurate 𝑐𝑐 prediction. Missing data were addressed with K-Nearest Neighbors (KNN) imputation, effectively filling data gaps while preserving the dataset’s distribution characteristics. Ensemble learning techniques, including Random Forest (RF), Gradient Boosting Decision Trees (GBDT), Extreme Gradient Boosting (XGBoost), and a Stacking model, were applied. Among these, the Stacking model demonstrated the highest predictive performance with a Root Mean Squared Error (RMSE) of 0.061, a Mean Absolute Error (MAE) of 0.043, and a Coefficient of Determination (𝑅2) value of 0.848 on the test set. Model interpretability was ensured through SHapley Additive exPlanations (SHAP), with 𝑒0 identified as the most influential predictor. The proposed framework significantly improves both prediction accuracy and interpretability, offering a valuable tool to enhance geotechnical design efficiency in coastal and clay-rich environments.
... The compression index, which may be calculated from the slope of the e -log p curve using the oedometer consolidation test, is one of the parameters needed to calculate the settlement of fine-grained soil. In addition to being difficult, time-consuming, and arduous, estimating the compression index from the oedometer test also requires personal experience because it uses the graphical technique of calculation [2,20]. As a result, the idea of calculating the compression index from several factors using empirical correlations was developed. ...
... Nodes stand in for purposes when connections are employed to categorize. Each tree is made up of branches and nodes, where each branch represents a subset of the node's possible values and each node contains features in a category that needs to be classified [2,6,18]. Decision trees have a wide range of application domains and are used for a variety of tasks, including pattern recognition, image processing, and machine learning because of their straightforward analysis and accuracy on various data types [24]. ...
Chapter
The compression index is an important consideration when figuring out how fine-grained soil settles. The compression index is determined from the oedometer consolidation test which is tedious and time-consuming. As a result, numerous correlations between the compression index and the index properties were developed. As soil is a very unpredictable substance, those correlations do not hold for all types of soil. This opens the door for the development of machine learning methods to forecast compression index. In this study, the compression index of soil is predicted using a decision tree, random forest, and multiple linear regression. Index properties, like liquid limit, natural moisture content, initial void ratio, and plasticity index are used as input variables in the machine learning models that are created to forecast the output variable compression index. The dataset used contains 359 data from diverse soil types and was gathered from several published articles (CH soil—62, CI soil—186, and CL soil—111). Since the machine learning models are trained using the training dataset before being evaluated using the testing dataset, the data has been divided into a training dataset and a testing dataset. In this paper, the impact of data splitting is also examined because it affects model performance. Mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient (R2) are used to assess the performance of the models. The results show that when training, decision trees perform well, whereas the testing dataset favors multiple linear regression for prediction. The data partitioning that results in the optimum performance for each model is different.
... They considered as input variables, w, LL, PI, e 0 , specific gravity of soil particles (G s ), and weight percentage of sand, silt and clay. Benbouras et al. (2019) developed an ANN model with 373 oedometer test samples to correlate c c with wet density, w, e 0 , fine content, LL, PI, and soil type. The dataset utilized in this research comprised samples gathered from various projects executed in the city of Algiers (Algeria). ...
... The collection of the dataset is the first step in the building of a machine learning model. In the present work, the experimental database of c c (1008 samples) comprised 913 samples from research papers (Alhaji et al., 2017;Benbouras et al., 2019;Kalantary and Kordnaeij, 2012;LCPC, 1973;McCabe et al., 2014;Mitachi and Ono, 1985;Widodo and Ibrahim, 2012), and 95 samples from authors' own data. This database has samples of different countries as Nigeria, Ireland, Spain, Iran, Indonesia, France, Algeria, Bangladesh, among others. ...
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Settlement of structures is determined by the stiffness of the soil where they are built. Compression index ( ) quantifies the compressibility of the soil and is a key parameter in the design of geotechnical structures. To predict the value of in clay soils, a global database of more than 1000 data points was collected and analysed. Liquid limit, plasticity index, natural water content, and initial void ratio were considered as predictor variables. A super-learner machine learning model was developed to predict from these variables. The model demonstrated a reasonable predictive performance and was subsequently integrated into an online tool. Additionally, four symbolic regression expressions were obtained to relate with some of the input variables when not all data are available, providing simple and practical alternatives for , estimation. This study provided two major contributions: (1) the non-local nature of the data expands the scope and generalizability of the findings, and (2) the availability of the proposed algorithm through an online application ensures its accessibility for geotechnical engineers, enhancing the work's practical applicability and intrinsic value.
... Using the above settings, the models were developed and, their effectiveness and generalizability were assessed using different performance indices. The results of the performance indexes stated above (MAE, RMSE, R 2 , NSE, VAF, PI, WI, and MBE) were used to assess the predictive capability of the proposed models, as shown in Tables 3 and 4 [33][34][35][36][37][38][39][40]. The scatter plots for the models CNN, DNN, and RNN were illustrated in figure 3a-c for training datasets, and in Figure 4a, b, and c for testing datasets. ...
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... Soil settlement is a key consideration in finegrained soils, and it is determined by calculating the compression index (Cc), which can be obtained from the e -log p curve of the oedometer consolidation test. The consolidation test is frequently time consuming and tiresome, since the result is read graphically [1,2]. Therefore various researches IOP Publishing doi: 10.1088/1755-1315/1326/1/012121 2 have been carried out to correlate the compression index with other soil parameters [3][4][5][6][7][8][9][10][11]. ...
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... They used 41 test results with inputs fines content (FC), LL, PI, maximum dry density (MDD), and optimum water content (OWC). Lastly, Benbouras et al. (2019) tried to propose a novel approach for an accurate estimation of Cc. To test the approach, they adopted a Kfold cross-validation technique based on several multilayer neural network models, genetic programming and multiple regression analysis. ...
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Book
This book presents a one-stop reference to the empirical correlations used extensively in geotechnical engineering. Empirical correlations play a key role in geotechnical engineering designs and analysis. Laboratory and in situ testing of soils can add significant cost to a civil engineering project. By using appropriate empirical correlations, it is possible to derive many design parameters, thus limiting our reliance on these soil tests. The authors have decades of experience in geotechnical engineering, as professional engineers or researchers. The objective of this book is to present a critical evaluation of a wide range of empirical correlations reported in the literature, along with typical values of soil parameters, in the light of their experience and knowledge. This book will be a one-stop-shop for the practising professionals, geotechnical researchers and academics looking for specific correlations for estimating certain geotechnical parameters. The empirical correlations in the forms of equations and charts and typical values are collated from extensive literature review, and from the authors' database.
Chapter
Over the last decade or so, artificial intelligence (AI) has proved to provide a high level of competency in solving many geotechnical engineering problems that are beyond the computational capability of classical mathematics and traditional procedures. This chapter presents one of the most interesting AI techniques, i.e. genetic programming (GP), and its applications in geotechnical engineering. In the last few years, GP, which is inspired by natural evolution of the human being, has proved to be successful in modelling several geotechnical engineering problems and has demonstrated superior predictive ability compared to traditional methods. In this chapter, the modelling aspects and formulation of GP are described and explained in some detail and an overview of most successful GP applications in geotechnical engineering are presented and discussed.