Research paper
Genetic programming for soil-fiber composite assessment

https://doi.org/10.1016/j.advengsoft.2018.04.004Get rights and content

Highlights

  • Problem of Assessment of soil-fiber composite is undertaken in this work.

  • The effect of fiber content, moisture content and soil density on composite is studied.

  • Genetic programming with variable subtrees and depth is proposed to solve problem.

  • Parametric-Sensitivity analysis reveals complex relationships among the variables.

  • GP is able to estimate the mechanical factor of soil-fiber composite accurately.

Abstract

Unconfined compressive strength (UCS) of soil is one of the basic index parameters for representing the compressive bearing strength of soil. Fiber reinforced soil is one of the most popular and practical ground improvement approaches used in geotechnical infrastructures. Analytical models for estimating UCS of soil-fiber composites have been developed in the literature. However, these models rarely incorporate the combined effects of dynamic field parameters such as fiber content, soil moisture, and density. These effects can be studied by the development of a holistic model based on a dimensionless strength improvement factor (SIF), which is defined as the ratio of UCS of reinforced soil to the unreinforced UCS. The current model estimating SIF indicates the improvement expected in UCS of soil-PP fiber composite based on the three design conditions such as fiber content, soil density, and moisture content. For this purpose, a series of 108 laboratory tests were first conducted to measure UCS of both fiber-reinforced soil and unreinforced soil under different fiber contents, soil density, and soil moisture content. Clayey silt soil and commercially used polypropylene (PP) fibers were selected in this study as soil and fiber material respectively. Genetic programming (GP) approach was then used to formulate models based on the measured data. The hidden non-linear relationships between SIF and the three inputs were determined by sensitivity and parametric analysis of the GP model. It was found that the moisture content in the soil has the highest influence on the strength factor that accounts for the change in strength. Coupled effects of soil parameters (soil moisture, soil density) and fiber content have been studied using parametric analysis which includes different possible field conditions (parameters). The results have been discussed along with the reinforcement mechanism of PP fiber for different soil conditions. It is believed that the robust GP model developed will be useful to determine optimum input values for designing safe bearing foundation soils which are reinforced with PP fibers.

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 byR2=(i=1n(AiAi¯)(MiMi

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

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