Measurement of stress dependent permeability of unsaturated clay
Introduction
Unsaturated permeability is one of the essential input functions, which is often used in interpretation of behavior of crop water consumption, suction distribution in landfill covers and slopes [1], [2], [3], [4]. It is well known to depend on the degree of saturation as well as void ratio [5]. In addition to this, stress, which is one of two constitutive variables that governs unsaturated soil behavior [6] could also influence permeability [7] by altering soil fabric (macropores, minipores and micropores) [8]. The influence of stress on the permeability is widely studied by various researchers [7], [9], [10], [11], [12]. Any influence of net stress on permeability is important for analyzing slope stability [7].
Different methods (Fig. 1) are available in literature for the indirect estimation of permeability. In most of cases, permeability is usually determined from soil water characteristic curve based on analytical approaches proposed by Genuchten [13] and Fredlund and Xing [14]. Alternatively, permeability can be also estimated from soil properties, which are commonly known as Pedotransfer functions [15], and are mainly utilized in agricultural and environmental science [16]. Besides these, soft computing methods (artificial neural network (ANN) and support vector regression (SVR)) were also used to develop models for predicting the permeability for various types of soil [17], [18], [19], [20], [21], [22], [23], [24], [25]. However, the models developed do not take into account any influence of stress on permeability of soil [26], [27], [28]. Therefore, considering the importance of stress effect on permeability and its influence on seepage modeling, there is a need to develop models which explains the phenomenon effect of permeability on soil particles. Also, the methods such as ANN and SVR do known for achieving good generalization but it is difficult to extract functional relationships between parameters [29], [30].
Over the years, the evolutionary based optimization framework of Genetic programming (GP) has been applied extensively in modeling of the complex non-linear systems [31], [32], [33], [34]. The advantages of using an optimization framework of GP is that it only needs experimentally collected data and settings of its parameters to formulate the model for the given system [35], [36]. It is not based on statistical assumptions such as traditional regression methods nor it needs any human expertise to select the optimum settings [37], [38]. Therefore, the present work will introduce an application of GP in deriving the relationship of the permeability and the two input parameters (suction and net stress) for Firouzkouh clay. Firouzkouh clay is a low plasticity clay mainly present in Firouzkouh (northern part in Iran). The models are evaluated statistically based on the root mean square error, coefficient of determination and mean absolute percentage error. 2-D analysis is then performed to find the main effects of suction and net stress on the permeability of the clay.
Section snippets
Experimental study to investigate effect of net stress on unsaturated permeability
Study of investigating the effect of net stress on the permeability under varying conditions of suction on residual soil is referred from Mirzaii and Yasrobi [7]. Soil investigated was Firouzkouh clay, which is clay of low plasticity. Liquid limit and plastic limit are 30% and 9% respectively. Unsaturated permeability for this clay was measured at three different suction values (at 30 kPa, 100 kPa and 180 kPa) and under three different applied net stress i.e., 20 kPa, 150 kPa and 300 kPa.
Proposed optimization framework
In this study, the optimization framework based on Genetic programming (GP) is proposed to evaluate the effect of the stress and suction inputs on the permeability of the soil. The framework is based on same mechanism of genetic algorithms but the former one is used for structural optimization [41]. GP had been applied extensively in the past to model the complex systems when there is uncertainty about behavior of the system [42], [43], [44].
The implementation of GP (Fig. 3) is based on the
Statistical validation of proposed framework against the experimental data
The metrics such as the coefficient of determination (R2), the mean absolute percentage error (MAPE), RMSE, the relative error (%) and the multiobjective error (MO) [48]) are used to evaluate the performance of the GP based permeability model. Their mathematical representations are given by Eqs. (1), (2), (3), (4), (5) in Appendix A. Table 2 clearly indicates that the GP based permeability model has learned effectively from the set of chosen training samples and is able to generalized well on
2-D analysis for the permeability of the clay with respect to stress and suction
The main effects of each of the two inputs on the permeability of the clay can be studied by performing the parametric and sensitivity analysis. The assumption behind this analysis is that for each of the effect, the other inputs are kept at their mean level. There may exists interaction (slight) between the two inputs. The complete procedure of performing the analysis is discussed in the study conducted by Gandomi et al. [49]. Parametric analysis (Fig. 4) shows that the permeability of the
Conclusions
The present work introduced an application of optimization framework of GP and discusses its performance in prediction of permeability of the clay based on the two inputs (net stress and suction). The novelty of the work lies in the development of explicit stress dependent permeability model. The results and analysis suggests that the GP based permeability model is able to accurately generalize the permeability values based on the net stress and the suction. The model developed can be useful in
Acknowledgement
This study was supported by Shantou University Scientific Research Funded Project.
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