Elsevier

Engineering Geology

Volume 276, October 2020, 105758
Engineering Geology

High performance prediction of soil compaction parameters using multi expression programming

https://doi.org/10.1016/j.enggeo.2020.105758Get rights and content

Highlights

  • A new prediction model for the soil compaction parameters is developed using MEP for large number of soils with high accuracy.

  • The monotonicity analysis with each input parameter verifies the correctness and the validity of proposed model.

  • The plastic limit and the fines content have more significant influences on the prediction results.

Abstract

Previous prediction models for soil compaction parameters were developed using limited data of specific soils and their accuracy also needs to be improved. This study presents the development of a new prediction model for the soil compaction parameters (i.e. optimum water content and maximum dry density) using the multi expression programming (MEP). Numerous soil compaction tests with a wide range of soil classifications and compaction energies are first collected to form a large database. Then, the optimal setting of the MEP code parameters is investigated and determined. The explicit formulations for the two key compaction parameters are finally proposed. The validity and the sensitivity analysis of the model are conducted. The results show that the proposed model enables to predict the soil compaction parameters for all kinds of soils in the database with high accuracy. The monotonicity analysis of the predicted compaction parameters with each input property (four physical properties of soil and one compaction energy) verifies the correctness and the validity of proposed model, showing consistency with the monotonicity concerning the actual data in the database. From the sensitivity analysis about the relevance of each input property on the predicted compaction parameters, it is indicated that the plastic limit and the fines content have more significant influences on the prediction results, while the effect of the liquid limit is the least pronounced.

Introduction

Soil compaction is the process of compacting the soil particles more closely together, by reducing the air void but maintaining the water content between the soil particles (Verma and Kumar, 2019). Through soil compaction, the mechanical behaviors can be improved variously. Proctor (1933) recommended to compact the soil at a desired compaction energy with various water contents in the laboratory. In this way, the optimum water content and the maximum dry density can be obtained from the compaction curve. For the geotechnical practice, these two compaction parameters are widely used to maintain the long-term performance of numerous geotechnical structures, such as railway track-beds (Zhao et al., 2017; Chen et al., 2018; Wang et al., 2018a, Wang et al., 2018b, Wang et al., 2018c; Chen et al., 2019; Wang and Chen, 2019; Wang et al., 2019a, Wang et al., 2019b; Zhao et al., 2019; Chen et al., 2020), highway embankments (Lim and Miller, 2004; Kim et al., 2005; Rahman et al., 2008), earth dams (Di Matteo et al., 2009; Ardakani and Kordnaeij, 2019), nuclear waste disposal (Delage et al., 2006; Sun et al., 2009), etc. Therefore, understanding and predicting the compaction parameters of different soils is of paramount importance for the construction and the maintenance of the geotechnical structures.

To date, the soil compaction parameters, i.e. optimum water content and maximum dry density, can be determined by both laboratory tests and analytical methods. As suggested by the widely accepted standards of ASTM D698 (ASTM, 2012a, standard Proctor compaction) and ASTM D1557 (ASTM, 2012b, modified Proctor compaction), the soil compaction curve can be obtained through the testing procedures of sample preparation, compaction with specified energy, measurement and calculation. In general, at least six tests need to be appropriately performed to identify the compaction curve with reasonable accuracy. Thus, the laboratory test for soil compaction is still time- and labor-consuming. To determine the soil compaction parameters more efficiently, several prediction models were proposed. Most of these models were built based on the regression analysis using limited data of specific soils (Blotz et al., 1998; Omar et al., 2003; Gurtug and Sridharan, 2004; Sridharan and Nagaraj, 2005; Di Matteo et al., 2009; Günaydın, 2009; Mujtaba et al., 2013; Khuntia et al., 2015; Farooq et al., 2016). The prediction accuracies were scattered using these models, with the coefficients of determination ranging from 0.64 to 0.98. In addition, the prediction accuracy using these models appeared to decrease for a larger database (the number of samples for the regression analysis was smaller than 126 for these models, Verma and Kumar, 2019).

To address the issue with a larger database and a higher accuracy, some machine learning techniques were applied to predict the compaction parameters. By the methods of artificial neural network (ANN, Sinha and Wang, 2008) and evolutionary polynomial regression (EPR, Ahangar-Asr et al., 2011), the compaction parameters of 55 soil samples under standard Proctor compaction conditions were predicted. Ardakani and Kordnaeij (2019) used the group method of data handling (GMDH) type neural network to establish a more complex model to predict the compaction parameters for 212 samples. Based on 451 soil samples, Kurnaz and Kaya (2020) predicted the soil compaction parameters using GMDH–type neural network, support vector machine (SVM), Bayesian regularization neural network (BRNN), and extreme learning machine (ELM), while no explicit expressions were provided. On the whole, these prediction models show relatively higher coefficients of determination (from 0.90 to 0.98) than those using the regression analysis. However, in these studies, the soil type was limited. For example, in some studies, the soft clay with high plasticity was not considered, and in some others either the fine-grained soil or the coarse-grained soil could not be related. Furthermore, the influencing factors for the compaction parameters were not completely integrated in these models. Although the prediction accuracy can be guaranteed for a specific soil range in the previous studies, the issue about the limited soil type and the deficient consideration of the influencing factors might lead to predicting errors for the soils with different properties. Hence, for more convenient engineering application, a comprehensive model with explicit formulations to predict the soil compaction parameters needs to be developed, considering the overall range of soil types and influencing factors.

To fulfill this purpose, a genetic programming method namely multi expression programming (MEP) has proven to be an alternative and efficient approach to solve nonlinear and complex prediction problems. The MEP method was firstly proposed by Oltean and Dumitrescu (2002). Using this approach, the problem with multi computer programs can be encoded into a single chromosome. The best encoded prediction equations can be generated through the calculation process and be easily manipulated in practical cases. With the advantages of high efficiency, easy implementation and high predicting accuracy, the MEP approach has been developed rapidly in the field of geotechnical engineering for the last decade. Successful applications of this approach can be found in predicting compressive and tensile strengths (Baykasoğlu et al., 2008), peak ground acceleration (Cabalar and Cevik, 2009), soil classification (Alavi et al., 2010), secant and reloading soil deformation moduli (Alavi et al., 2012), etc. Thereby, the prediction about the soil compaction parameters using MEP is feasible, supported by previous relevant studies of this approach on the specific geotechnical problems.

In this study, the prediction model of soil compaction parameters, including the optimum water content and the maximum dry density, is developed using the approach of multi expression programming (MEP). A large database of soils encompassing various classifications (gravel, sand, silt, clay) are collected from the literature. The soils with the odd line number in the database are selected as the training data to generate the optimal formulations, which are then validated using the testing soils with the even line number in the database. Furthermore, the validity of the prediction model is evaluated by the analysis of monotonicity and sensitivity.

Section snippets

Multi expression programming (MEP)

Genetic algorithms (GA) is a stochastic method to search and to optimize the solution of a problem based on the principles of genetics and natural selection (Goldberg, 1989). Through conventional optimization techniques, GA produces a series of binary strings to represent the solution. By evolving the string expression into the computer programs such as tree structures or functional programming language, the genetic programming (GP) was introduced as an extension of GA (Koza, 1992). GP can be

Geological database

To develop a prediction model of the soil compaction parameters for a wide range of soil classifications with high precision, 226 soil compaction tests were collected from the literature (Al-Khafaji, 1993; Daniel and Wu, 1993; Othman and Benson, 1993; Shelley and Daniel, 1993; Delage et al., 1996; Miller et al., 2002; Fleureau et al., 2003; Inci et al., 2003; Lim and Miller, 2004; Clariá and Rinaldi, 2007; Vassallo et al., 2007; Ito and Komine, 2008; Shafiee, 2008; Taïbi et al., 2008; Günaydın,

Model validity

The soils with the even line number in the database are used as the testing data to evaluate the validity of the developed model. The comparisons between the predicted and the reference soil compaction parameters are presented in Fig. 8, also listing the values of MAE, RMSE and R2. The indicators showing high accuracy can be observed for both the optimum water content and the maximum dry density, with the R2 values as 0.923 and 0.858, respectively. This suggests that the prediction of both

Conclusions

In this study, the prediction model of soil compaction parameters, i.e. the optimum water content and the maximum dry density, was developed using a method of genetic programming, namely multi expression programming (MEP). A large database of soils covering a wide range of classifications was formed by collecting data of published works.

The optimal parameter setting in the MEP source code was first investigated. The prediction accuracy of both soil compaction parameters increases with the

Notations

    A1, A2, A3

    Parameters for predicting optimum water content

    B1, B2, B3, B4, B5, B6

    Parameters for predicting maximum dry density

    CF

    Fines content

    CG

    Gravel content

    CS

    Sand content

    E

    Compaction energy

    F

    Function set

    hi

    Actual output variable

    hi¯

    Average value of actual outputs

    LL

    Liquid limit

    mi

    Input variable

    MAE

    Mean absolute error

    n

    Number of outputs

    N

    Number of soil compaction tests in the database

    PL

    Plastic limit

    PI

    Plasticity index

    R2

    Coefficient of determination

    Rsen

    Sensitivity

    RMSE

    Root mean squared error

    ti

    Predicted output

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The financial supports provided by the RIF Project (Grant No. R5037-18F) from Research Grants Council (RGC) of Hong Kong are gratefully acknowledged.

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