Research paperGenetic programming for soil-fiber composite assessment
Introduction
Soil reinforcement is essential to improve engineering properties (such as shear strength, compressibility, hydraulic conductivity); thereby increasing the bearing capacity, ductility and decreasing the soil settlement [1]. A large array of synthetic tensile inclusions ranging from high tensile strength metallic sheets to low-modulus polymeric materials has been integrated into soil reinforcement applications [2]. Additionally, unconventional and eco-friendly reinforcing measures have also been investigated in the recent past [3], [4], [5], [6], [7]. In the past, researchers have used natural and synthetic fibers for reinforcing soil in geotechnical applications [8], [9], [10], [11]. These soil reinforcement measures using fibers have in general been discussed as randomly distributed fiber reinforced soil (RDFS). RDFS has gained traction as it enhances soil performance which includes improvement in soil ductility, increase in shear strength and reduction of the drop in post-peak strength [12]. Figure 1(a-e) showcase the various mechanisms involved in fiber reinforcement by an individual fiber. The inclusion of these fibers in soil enhances the load-deformation response of the soil-fiber composite by interacting with the soil particles mechanically via surface friction and interlocking. The interlock leads to a stress transfer mechanism, whereby the stresses induced in the soil on loading are transmitted to the discrete fibers by mobilizing the tensile strength of the fiber. It is evident that this surface friction and interlocking forces developed on an individual fiber will be highly dependent on the surface roughness of the fiber, soil type, soil-fiber composite density and also the moisture content in the soil [5], [12], [13]. Among the synthetic fibers, polypropylene fiber (PP) is one of the most popular fibers used in soil reinforcement due to high tensile strength and resistance to biodegradation [12], [13], [14]. Unconfined compressive strength (UCS) is a quick and reliable mechanical parameter that is used to judge the representative strength of soil for the initial design and analysis of various geotechnical infrastructures [15], [16], [17]. UCS of reinforced soil is known to be influenced by fiber content, fiber type as well as soil parameters such as soil moisture content and soil density [8], [9], [10], [13], [15], [16], [17], [18], [19]. Variations in UCS due to change in these parameters influence the stability of various field applications [20]. Hence, it is imperative to know the variability expected in strength improvement by the inclusion of fibers considering other parameters mentioned previously.
The use of soft computing approaches to formulating models for estimation, prediction and assessment of soil properties is gaining popularity owing to its robustness [21], [22], [23], [24], [25], [26], [27]. Numerous models have been developed to estimate soil strength with and without fiber [28], [29], [30], [31], [32]. However, these models rarely capture the coupled effect of soil parameters (soil moisture content, soil density) as well as fiber content (%). These effects can be studied by the development of a holistic model for a dimensionless factor (which can represent the improvement in strength) based on the three inputs (fiber content, soil density, moisture content) parameters. Statistical methods such as Taguchi design and response surface methodology can also be applied in modeling of soil strength based on input parameters. However, these methods are based on the statistical assumptions, such as pre-definition of the structure of the model, non-correlated residuals and are generally built on the entire database without considering testing of the method on the test data samples [33]. Alternate approaches of modeling approaches includeArtificial Neural Network (ANN), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC). [34], [35], [36], [37]. Evolutionary approaches such as genetic programming (GP) are well known for evolving the functional expression (explicit models) based on only the given data [38], [39], [40]. GP is chosen as it is widely suited to mimic geotechnical properties such as unconfined compressive strength, hydraulic conductivity, volumetric water content [39], [40], [41]. Moreover, as compared to conventional ANN approaches in geotechnical engineering, GP approach was found to be more reliable based on model's prediction statistics [7]. This evolutionary approach has many variants such as Multi gene genetic programming (MGGP) which combined GP approach and least square analysis (Searson-GPTIPS2). GP could outperform other conventional soft computing methodologies such as artificial neural network (ANN), support vector regression (SVR) [7], [40]. Its formulation not being based on statistical assumptions (assumption of model structure and non-correlated residuals) offers a robust methodology. It has been successfully applied to different engineering problems [42], [43].
Therefore, the objective of the present study is to demonstrate the evolutionary approach of genetic programming in the formulation of the functional relationships between the strength improvement factor (SIF) and the three inputs of a soil reinforced with polypropylene fiber (PP). The performance of these models is being evaluated based on statistical metrics and hypothesis tests to determine the best model. On the best model, sensitivity and parametric analysis are then performed to unveil the hidden relationships between the SIF and the three inputs. The robustness of the model is further validated by comparing the results obtained from the GP analysis with the physics related to the soil fiber composite. Coupled effects of soil parameters (soil moisture, soil density) and fiber content have been studied using parametric analysis. The parametric analysis is represented by smooth 3D surfaces [40], [44] which are generated by the association of input parameters value with each set of points, arbitrarily positioned in the output parameter plane. These smooth 3D surface graphs help us finding the optimum values of input parameters for field application.
Section snippets
Experimental study on effects of density, soil moisture and fiber content on UCS of soil-PP fiber composite
To examine the UCS of soil (both reinforced and unreinforced), a series (108) of laboratory tests (as per ASTM-d-2166, 2013, [45]) were conducted. Details related to soil parameters, fiber properties, testing program, and procedures as well as results are provided as follows.
Genetic programming
The GP algorithm is based on the Darwinian principle of “Survival of the fittest” [51]. In GP, genes are evolved, and every gene is considered as a model. The step by step mechanism of GP is shown in Fig. 3. For conducting GP modeling on a problem, several settings are to be chosen. Initially, the elements of functional and terminal set are to be selected based on the problem. Both arithmetic operators (+, -, /, × ) and non-linear functions (sin, cos, tan, exp, tanh, plog) are considered for
Statistical metrics for the evaluation of performance of GP model
The GP model (equation 3) was formulated for understanding the effect of three set of input parameters (soil moisture (%), soil density (g/cc) and fiber content (%)) on the SIF of the reinforced soil. Five statistical metrics (the coefficient of determination (R2), the mean absolute percentage error (MAPE), the root mean square error (RMSE), the relative error (%) and the multi-objective error (MO) [52] are chosen to evaluate the performance of the GP model and is given by
Summary, conclusions, and future scope
In this study, a model for the strength improvement factor (SIF) as a function of three input parameters (soil moisture, density, and fiber content) was developed for soil-PP fiber composite using an evolutionary GP algorithm. To make the model, measured data was generated in the laboratory based on 108 UCS tests in three different testing parameter conditions. The formulated GP model (Equation 3 in Section 3) can be used to predict the SIF, i.e. the strength improvement expected for various
References (55)
- et al.
Improving and correcting unsaturated soil hydraulic properties with plant parameters for agriculture and bioengineered slopes
Rhizosphere
(2016) - et al.
Effects of plant roots on soil-water retention and induced suction in vegetated soil
Eng Geol
(2015) - et al.
Study on the efficacy of harmful weed species Eicchornia crassipes for soil reinforcement
Ecol Eng
(2015) - et al.
Performance evaluation of silty sand subgrade reinforced with fly ash and fibre
Geotext Geomembr
(2008) - et al.
Interfacial shear strength of fiber reinforced soil
Geotext Geomembr
(2010) - et al.
Strength and mechanical behavior of short polypropylene fiber reinforced and cement stabilized clayey soil
Geotext Geomembr
(2007) - et al.
A simple review of soil reinforcement by using natural and synthetic fibers
Constr Building Mater
(2012) - et al.
Effect of polypropylene fibre and lime admixture on engineering properties of clayey soil
Eng Geol
(2006) - et al.
Compressive strength of fiber reinforced highly compressible clay
Constr Build Mater
(2006) - et al.
An approach to estimate unsaturated shear strength using artificial neural network and hyperbolic formulation
Comput Geotech
(2003)
Application of genetic-based neural network to lateritic soil strength modeling
Constr Build Mater
Shape optimization of arch dams by metaheuristics and neural networks for frequency constraints
Scientia Iranica
Performance-based optimum seismic design of steel structures by a modified firefly algorithm and a new neural network
Adv Eng Softw
Modelling the mechanical behaviour of unsaturated soils using a genetic algorithm-based neural network
Comput Geotech
Prediction of shear strength parameters of soils using artificial neural networks and multivariate regression methods
Eng Geol
Ant colony optimization techniques for the vehicle routing problem
Adv Eng Inf
On the performance of artificial bee colony (ABC) algorithm
Appl Soft Comput
Improving environmental sustainability by formulation of generalized power consumption models using an ensemble based multi-gene genetic programming approach
J Cleaner Prod
Measurement of stress dependent permeability of unsaturated clay
Measurement
Study of the volumetric water content based on density, suction and initial water content
Measurement
Model development and surface analysis of a bio-chemical process
Chemo Intell Lab Syst
A hybrid computational approach to derive new ground-motion prediction equations
Eng Appl Artif Intell
Measurement of mechanical characteristics of fiber from a novel invasive weed: A comprehensive comparison with fibers from agricultural crops
Measurement
The principle of reinforced earth
Highway Res Rec.
Behavior of fabric-versus fiber-reinforced sand
J Geotech Eng
Potential of uncultivated, harmful and abundant weed as a natural geo-reinforcement material
Adv Civil Eng Mater
Compressive strength analysis of soil reinforced with fiber extracted from water hyacinth
Eng Comput
Cited by (24)
Estimation of unconfined compressive strength of marine clay modified with recycled tiles using hybridized extreme gradient boosting method
2023, Construction and Building MaterialsA high dimensional features-based cascaded forward neural network coupled with MVMD and Boruta-GBDT for multi-step ahead forecasting of surface soil moisture
2023, Engineering Applications of Artificial IntelligenceA novel integrated approach of ELM and modified equilibrium optimizer for predicting soil compression index of subgrade layer of Dedicated Freight Corridor
2022, Transportation GeotechnicsCitation Excerpt :In the parlance of geotechnical engineering, several ML models have been used to predict the Cc of soil, including the artificial neural network (ANN) [6,11,21,24,32-35], least square support vector machine (LSSVM) [23], relevance vector machine (RVM) [29], support vector machine (SVM) [25,31], support vector regression (SVR) [1], gene expression programming (GEP) [6,28], genetic programming (GP) [32], Gaussian process for regression analysis (GPRA) [1], minimax probability machine regression (MPMR) [27], extreme learning machine (ELM) [25,27], Bayesian regularization neural network (BRNN) [25], extra gradient boosting method (XGBoost) [1], and random forest (RF) [1], and attained significant accuracy with coefficient of determination (R2) ranging from 0.85 to 0.99 in many cases [1,6,21-23,25,27,29-31,34]. These ML models have also been successfully employed to solve problems in other engineering fields [36-44]. Despite the good performance of SVM, ANNs, BRNN, ANFIS, and many other traditional machine learning (TML) algorithms, they are considered black-box models [1,6,20,45,46], which may produce undesirable results [47,48].
A state-of-the-art review on modeling the biochar effect: Guidelines for beginners
2022, Science of the Total EnvironmentCitation Excerpt :Our understanding of the biochar modeling effect on agricultural soil properties is not complete enough to guide biochar application in the field over large-scale areas. Other topics include biochar effects on crop production (Archontoulis et al., 2016; Basche et al., 2016; Devereux et al., 2012; Jeffery et al., 2011; Yu et al., 2019), biochar-based carbon management networks (Aviso et al., 2018; Aviso et al., 2019; Belmonte et al., 2018, 2019; Tan, 2019), biochar stability assessment (Leng et al., 2019a,b; Liang et al., 2008), marginal biomass-derived biochar (Buss et al., 2016a,b; Melo et al., 2019; Schimmelpfennig and Glaser, 2012), and other programming, design, and optimization topics relevant to biochar (Akhtar and Saidina Amin, 2012; Kim et al., 2011; Kurugodu et al., 2018; H. Qiang et al., 2020; X. Qiang et al., 2020; Salehi et al., 2011; Song et al., 2020). These are all hot issues to advance the application of biochar modeling.
Effect of fiber dispersion, content and aspect ratio on tensile strength of PP fiber reinforced soil
2021, Journal of Materials Research and TechnologyCitation Excerpt :Artificial intelligence algorithms have been widely introduced into the field of civil engineering in recent years. And the genetic programming (GP) is a very popular and reliable approach on formulating models [20]. As a result, the study focuses on investigating tensile strength of fiber reinforced soil by conducting Brazilian split test [25].