Application of a fuzzy rule-based method for the determination of clay dispersibility Ismail Zorluer a, ⁎, Yilmaz Icaga a , Saban Yurtcu a , Hasan Tosun b a Department of Construction Education, University of Afyon Kocatepe, ANS Campus, Afyonkarahisar, Turkey b Department of Civil Engineering, University of Osmangazi, Meselik Campus, Eskisehir, Turkey abstract article info Article history: Received 9 September 2009 Received in revised form 30 August 2010 Accepted 19 September 2010 Available online 16 October 2010 Keywords: Dispersive clay Double hydrometer Pinhole ESP–CEC Na(%)–TDS Fuzzy logic Some clay soils are highly susceptible to erosion and piping because of dispersion or deflocculation in pore water. These soils, called “dispersive clay soil” in geotechnical engineering, are structurally unstable, easily dispersive and, thus, highly erodible. There are many tests to determine dispersibility both physically and chemically. However, these tests can give different results for the same soil sample. Therefore, more than one test should be used to identify dispersive soils more accurately. In previous research, the discriminant method was used to combine these test results. In this study, a fuzzy logic approximation method was developed to combine the different results of the double hydrometer, pinhole, Na(%)–TDS and ESP–CEC methods into a single value. This new method was applied to the dispersibility test results of 29 samples, and it gave more reliable and objective results for identifying the dispersibility of the clay soil. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Some soils have a dispersive tendency when subjected to water. These soils are known as dispersive clay or dispersive soil. These soils are considered problematic with respect to erosion and piping because they are unstable, easily dispersive, and highly erodible. The dispersibility of clay depends on the clay's mineralogy, chemical texture, dissolved salt content, and quality of soil voids in the pore water (Zorluer, 2003). Dispersion occurs in cohesive soils when the repulsive forces among the clay particles exceed the attractive forces. In the presence of pore water, the particles repel each other to form a colloidal suspension (Bell and Bruyn, 1997; Bell and Walker, 2000). Clay particles in the suspension are removed by water, creating internal erosion (Tosun, 1994). The main difference between dispersive and nondispersive clays is the amount and type of cations. The lower the content of dissolved salts in the water, the greater the susceptibility of sodium saturated clays to dispersion. The presence of exchangeable sodium is an important chemical factor contributing toward disper- sive behavior in soil (Bell and Walker, 2000). Another property that enhances the susceptibility of clay soils to dispersion is total dissolved salts (TDS) in the pore water. In other words, sodium saturated clays are more susceptible to dispersion as the dissolved salt concentration in the pore water decreases (Bell and Bruyn, 1997). If dispersive clay soils are used in earthfill dams or road embankments, they should be accurately identified. Otherwise, serious engineering problems may occur, leading to dam failure (Tosun, 1997). Dispersive clay soils cannot be identified with ordinary soil mechanics tests. The most commonly used dispersibility deter- mination tests consist of chemical and physical measurement techniques, including the pinhole test, the double hydrometer test and the crumb test. Chemical data, which are obtained from standard chemical tests, are used directly or indirectly through their relations with each other to determine dispersibility. Examples include the values of sodium (Na), potassium (K), calcium (Ca), magnesium (Mg) and cation exchange capacity (CEC), electrical conductivity (EC), and pH as well as exchangeable sodium percentage (ESP), total dissolved salts (TDS) and sodium percentage (Na%) (Zorluer, 2003). The results of dispersibility tests may show differences for the same soil sample. For this reason, the results of several tests are usually evaluated together. Craft (1986) and Bell and Walker (2000) applied discriminant analysis to dispersion test results to make the dispersibility evaluations more efficient. Craft (1986) used 28 soil samples from Oklahoma for dispersion tests. A discriminant function derived from discriminant analysis was applied to the data of these samples. Similarly, Bell and Walker (2000) used 94 samples from Natal in Southern Africa. After a series of physical and chemical tests to assess dispersibility, they made a discriminate analysis to ensure the reliability of the test results. Fuzzy logic can be viewed as a language that allows one to translate sophisticated statements from natural language into a mathematical formalism (McNeil and Thro, 1994). In most applications, fuzzy logic can deal with highly variable, linguistic, vague, and uncertain data or information to allow for logical, reliable and transparent information (Adriaenssens et al., 2004). Fernández et al. (2009) worked with fuzzy rules based on classification systems using a preprocessing step to deal with class imbalance. Their aim was to analyze the behavior of fuzzy Geoderma 160 (2010) 189–196 ⁎ Corresponding author. Tel.: + 90 272 2281311/339; fax: + 90 272 2281319. E-mail addresses: izorluer@aku.edu.tr (I. Zorluer), yicaga@aku.edu.tr (Y. Icaga), syurtcu@aku.edu.tr (S. Yurtcu), htosun@ogu.edu.tr (H. Tosun). 0016-7061/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.geoderma.2010.09.017 Contents lists available at ScienceDirect Geoderma journal homepage: www.elsevier.com/locate/geoderma