Modeling of the angle of shearing resistance of soils using soft computing systems
Introduction
A primary requirement for more reliable design of geotechnical structures is to accurately determine the ϕ′ value. ϕ′ known as the interlocking among the soil particles is used for the computation of bearing capacity of foundations, lateral pressure acting on earth retaining walls, stability analyses of slopes against slope failures and landslides. The soil type, soil plasticity, and soil density are the main factors affecting it. The soils having high plasticity like clayey soils exhibit lower ϕ′. On the other hand, as the soil grain size increases, the ϕ′ value increases. Triaxial and direct shear tests of which testing procedures have been standardized by (ASTM WK3821, xxxx, ASTM-6528, xxxx), respectively, are commonly used for experimental determination of the ϕ′ value in laboratory. However they are the laborious, time consuming and costly methods. Although triaxial test is more complicated and difficult to be conducted, it gives more reliable results and has a loading condition closer to those of actual soil conditions. This test which is more suitable for clayey soils requires long time to be conducted for the clayey soils. For the sandy soils, direct shear test is prevalently used and requires simpler test procedure than the triaxial test. In order to obtain the ϕ′ value of soils by more effortless and economic way, the empirical equations based on the basic soil parameters which are determined by simpler laboratory tests can be often preferred. However most of them are based on limited experimental data and do not provide stable and accurate predictions. The other drawback of these equations is that they generally use the one soil parameter to estimate the ϕ′ value (Bowles, 1992, Korayem et al., 1996, Panwar and Seimens, 1972, Terzaghi et al., 1996). Whereas the soils have fairly complex structures, imprecise physical properties and spatial variability (i.e., heterogeneities) associated with the formation of them. Therefore their mechanical characteristics show the uncertain behavior in contrasts to most of the other engineering materials (Jaksa, 1995). The alternative approaches such as GEP, ANNs and ANFIS which enable to model spatially the complex systems have been recently used (Baykasoglu et al., 2008, Kayadelen, 2008, Shahin et al., 2003, Tutmez and Tercan, 2007). They are also becoming increasingly important in all engineering areas as a result of rapid development of information and computers technology. These methods enable the pattern recognition, classification, speech recognition, design of structures, automatic control, manufacturing process control, and modeling of material behavior (Adam, 2003, Najjar and Basheer, 1996).
In the content of this paper, new approaches based on GEP, ANN and ANFIS were presented for the prediction of ϕ′ value of soils. The data sets for training and testing were obtained from different geotechnical applications in Turkey and literature and experimental study performed herein. Four basic soil properties, the percentage of fine grained (FG), the percentage of coarse grained (CG), liquid limit (LL) and bulk density (BD) were presented to the GEP, ANN and ANFIS models as input parameters.
Section snippets
Definition of the angle of shearing resistance
The angle of shearing resistance is known as a component of the shear strength of the soils which is basically frictional material and composed of individual particles. The shear strength is described by Mohr–Coulomb failure criterion adopted as widely accepted approach among the geotechnical engineers. According to this theory, the shear strength of soils consists of two components. The first component is the cohesion (c). The second component is the friction between the soil particles defined
Overview of GEP
GEP introduced first by Ferreira (2001) is an algorithm based on genetic algorithms (GA) and genetic programming (GP). It mimics to biological evolution to evolve a computer program encoded in linear chromosomes of fixed-length. The main purpose of GEP is to find a mathematical function that fits a set of data presented to GEP model. For that purpose it performs the symbolic regression using the most of the genetic operators of GA. GA represents the individuals as symbolic strings of
GEP elements
The chromosomes and the expression trees are the main elements in GEP. Any information in each chromosome composed of one or more genes is translated to the expression trees using two bilingual and conclusive languages called Karva Language; the language of the genes and the language of the expression trees (ET). This beneficial feature allows inferring precisely the genotype. GEP genes consist of two parts called the head and the tail. The head of a gene used for encoding of a function for the
Overview of ANN
The main purpose of ANN of which working principle is inspired by the way biological nervous systems such as the human brain process information is similar to that of polynomial regression. However its methodology for the mathematical process is different from the classical regression analyses. In order to obtain the optimal multidimensional surface for the prediction of a dependent variable, any composite functions is fitted to the data presented to the ANN model modifying the parameters of
Overview of ANFIS
Unlike classical set theory which has a crisp definition as to whether a variable belongs to a set or not, the fuzzy theory introduced by (Lotfi Zadeh in 1965) does not give a sharp answer to questions. In this approach, the belongings of a variable to different sets are defined partially by continuous membership functions that vary between 0 and 1 (Dubois and Prade, 1980, Topçu and Sarıdemir, 2008). Mamdani and Tagagi–Sugeno (TS) models are two types of fuzzy approach commonly used (Takagi &
Experimental study and test results
A series of triaxial tests were performed to determine the effective angle of shearing resistance (ϕ′) of 10 different undisturbed soil samples taken from Adana province in Turkey. The undisturbed samples were taken from drilling boreholes with Shelby tube (thin-walled metal) in accordance with (ASTM-1587). The soils taken at the depth ranging from 15 m to 3 m were homogeneous and contain no gravel or larger particles. The triaxial tests were conducted under consolidated-drained condition (CID)
Data collection
In addition to data obtained from the present experimental work, further data were collected from various projects applied in different region in Turkey and literature. Kayadelen (2008) reported the data that are collected by him from literature. The references of these data used for this study are given in Kayadelen (2008 and references therein). Table 2 shows the geotechnical properties used as input parameters and target parameter for the training and testing of the models. Fig. 6 indicates
GEP model development
The fundamental aim of development of GEP models was to generate the mathematical functions for the prediction of ϕ′. For that purpose, two GEP models (GEP Model I and GEP Model II) were developed. While the GEP Model I has four input parameters (FG, CG, LL, BD), the GEP Model II has three input parameters (FG, CG, BD). LL was excluded from the inputs in the GEP Model II. So two mathematical functions were generated in the form of y = f (FG, CG, LL, BD) and y = f (FG, CG, BD) for ϕ′. In both models
ANN model development
Two ANN models (ANN Model I and ANN Model II) were developed for prediction of ϕ′. The input parameters of the ANN models are the same as those of GEP models. The ANN toolbox of MATLAB computer-aided Software (Demuth & Beale, 2001) was used to perform the necessary computations. The numbers of neurons in the hidden layer were adopted as the main parameter to obtain the most appropriate ANN architecture, and a number of multi layer networks with different transfer function were tried to predict ϕ
ANFIS model development
Two ANFIS models (ANFIS Model I and ANFIS Model II) were developed using identical inputs for as in GEP and ANN models. For generation of the membership functions associated with each input variable, the grid partition and subtractive clustering methods were employed for ANFIS Model I and ANFIS Model II, respectively. In both models the Gaussian membership function was assigned. The hybrid learning algorithm for both models was used for optimizing the parameters allows a fast identification of
Results and discussion
In this study, it was basically aimed to explore the applicability of the GEP, ANN and ANFIS for prediction of the ϕ′ value of soils that have great significance for soil mechanics and foundation engineering. This section comparatively presents the analyses results obtained from these approaches and quantitative assessments of the model’s predictive abilities. Of the 122 data sets, 90 were used for training the models and 32 which are not used in training stage were presented for testing of the
Sensitivity analysis
The explanatory knowledge about the degree of effects of each independent input variable on the behavior of models was examined performing a series of sensitivity analyses. Some researchers have reported several algorithms for sensitivity analysis to extract how the input parameters individually influence to the model behavior (Scardi Kose, 2007, Scardi and Harding, 1999). In this work, the sensitivity analysis described by Kose (2007) was executed. This analysis is done after the training
Conclusion
The main objective of this study was to explore the capability of Genetic Expression Programming (GEP), Artificial Neural Network (ANN) and Adaptive Neuro Fuzzy (ANFIS) in prediction of ϕ′. Data for development of the models were obtained from the different project in Turkey and literature and experimental study performed herein.
The results obtained from all models developed herein are in satisfactory agreement with the experimental results. The comparison between soft computing systems
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2022, Measurement: Journal of the International Measurement ConfederationCitation Excerpt :The encoded function is indicated by constants, functions, and variables; while the non-encoded function is only represented by constants and variables. The constants and variables in the genes tail are often used as supplementary terminal symbols, in case the terminal symbols in the head are not sufficient to encode a function [61]. The functions in the head can be basic arithmetic (+, /, >, etc.), trigonometric (tan, cos, etc.), or any other mathematical operators (such as ^, exp, etc.), for the development of a mathematical expression.