High performance prediction of soil compaction parameters using multi expression programming
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
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.
References (84)
- et al.
Modeling of permeability and compaction characteristics of soils using evolutionary polynomial regression
Comput. Geosci.
(2011) - et al.
Prediction of compressive and tensile strength of limestone via genetic programming
Expert Syst. Appl.
(2008) - et al.
Genetic programming-based attenuation relationship: an application of recent earthquakes in Turkey
Comput. Geosci.
(2009) - et al.
Genetic programming model for estimating soil suction in shallow soil layers in the vicinity of a tree
Eng. Geol.
(2020) - et al.
Investigating the mud pumping and interlayer creation phenomena in railway sub-structure
Eng. Geol.
(2014) - et al.
Generalised effective stress analysis of strength and small strains behaviour of a silty sand, from dry to saturated state
Soils Found.
(2003) - et al.
Compaction behaviour and prediction of its characteristics of fine grained soils with particular reference to compaction energy
Soils Found.
(2004) - et al.
Dynamic compaction properties of bentonite-based materials
Eng. Geol.
(2008) - et al.
A single-objective EPR based model for creep index of soft clays considering L2 regularization
Eng. Geol.
(2019) - et al.
Microstructure, geotechnical and mechanical characteristics of quicklime-lateritic gravels mixtures used in road construction
Constr. Build. Mat.
(2012)
Prediction of pile bearing capacity using a hybrid genetic algorithm-based ANN
Measurement
Correlation of compaction characteristics of natural aoils with modified plastic limit
Transpor. Geotech.
Permeability of compacted granule–clay mixtures
Eng. Geol.
Numerical modeling of stress–strain behavior of sand under cyclic loading
Eng. Geol.
Swelling of compacted sand–bentonite mixtures
Appl. Clay Sci.
Investigation on the mechanical behavior of track-bed materials at various contents of coarse grains
Constr. Build. Mat.
Investigation on geogrid reinforcement and pile efficacy in geosynthetic-reinforced pile-supported track-bed
Geotext. Geomembr.
Real-time analysis and regulation of EPB shield steering using Random Forest
Automat. Constr.
Mechanical properties and behaviour of a partially saturated lime-treated, high plasticity clay
Eng. Geol.
A simplified axisymmetric model for column supported embankment systems
Comput. Geotech.
A novel hybrid surrogate intelligent model for creep index prediction based on particle swarm optimization and random forest
Eng. Geol.
A closed-form solution for column-supported embankments with geosynthetic reinforcement
Geotext. Geomembr.
Measurements of suction versus water content for bentonite–sand mixtures
Can. Geotech. J.
Effect of wetting–drying cycles on swelling behavior of lime stabilized sand–bentonite mixtures
Environ. Earth Sci.
A robust data mining approach for formulation of geotechnical engineering systems
Eng. Comput.
Multi expression programming: a new approach to formulation of soil classification
Eng. Comput.
Formulation of secant and reloading soil deformation moduli using multi expression programming
Eng. Comput.
Design equations for prediction of pressuremeter soil deformation moduli utilizing expression programming systems
Neural. Comput. Appl.
Volume Change Behaviour of Some Geomaterials Under Combined Influence of Freeze-thaw and Wet-dry Cycles: An Experimental Investigation
Estimation of soil compaction parameters by means of Atterberg limits
Q. J. Eng. Geol. Hydrog.
Soil compaction parameters prediction using GMDH-type neural network and genetic algorithm
Eur. J. Environ. Civil Eng.
Standard Test Method for Laboratory Compaction Characteristics of Soil Using Standard Effort. ASTM D698
Standard Test Method for Laboratory Compaction Characteristics of Soil Using Modified Effort. ASTM D1557
Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System)
Estimating optimum water content and maximum dry unit weight for compacted clays
J. Geotech. Geoenviron. Eng.
Bimodal pore size distribution of a high-plasticity compacted clay
Géotech. Lett.
Effects of degree of compaction and fines content of the subgrade bottom layer on moisture migration in the substructure of high-speed railways
P. I. Mech. Eng. F-J. Rail Rapid Transit.
Microstructure and hydraulic properties of coarse-grained subgrade soil used in high-speed railway at various compaction degrees
J. Mater. Civil Eng.
Performance of geosynthetic-reinforced pile-supported embankment on soft marine deposit
P. I. Civil Eng.-Geotech. Eng.
Shear wave velocity of a compacted clayey silt
Geotech. Test. J.
Compacted clay liners and covers for arid sites
J. Geotech. Eng.
Microstructure of a compacted silt
Can. Geotech. J.
Cited by (82)
Predictive modeling for depth of wear of concrete modified with fly ash: A comparative analysis of genetic programming-based algorithms
2024, Case Studies in Construction MaterialsMulti-expression programming based prediction of the seismic capacity of reinforced concrete rectangular columns
2024, Engineering Applications of Artificial IntelligenceEnhancing clay content estimation through hybrid CatBoost-GP with model class selection
2024, Transportation GeotechnicsComparing the efficacy of GEP and MEP algorithms in predicting concrete strength incorporating waste eggshell and waste glass powder
2024, Developments in the Built Environment