Identification of Expansive Soils and Assessment of Expansion Potential by Fuzzy Approach

Transcription

1 Identification of Expansive Soils and Assessment of Expansion Potential by Fuzzy Approach P. Venkata Subba Reddy Department of Computer Science and Engineering, Sri Venkateswara University, Tirupati, India K. Mallikarjuna Rao Department of Civil Engineering Sri Venkateswara University, Tirupati, India Ch. Sudha Rani Department of Civil Engineering, Sri Venkateswara University, Tirupati, India ABSTRACT Expansive clayey soils are highly moisture sensitive with respect to stress, deformation and strength. These soils exhibit extreme variation in deformation such as heaving, loss of shear strength under certain Moisture Content and settlement and shrinkage as the Moisture Content alters. Swelling is the process of increase in volume of soil that occurs during its interaction with water. Expansive soils are classified based on Expansion Potential. Estimation of Expansion Potential serves as a guide for safe analysis and design of structures resting on expansive soils. Expansion potential is dependant on mineralogical composition of soil which influences the index properties of soil. Several investigators proposed criteria for qualitative assessment of Expansion Potential making use of index properties of soil.uncertainties arise in making use of these criteria, since the soil properties cannot be used separately but collectively to assess Expansion Potential. These soil properties are fuzzy rather than Crisp. This paper presents a Fuzzy Rule Based Approach using fuzzy IF-THEN rules to quantify the Expansion Potential in qualitative terms considering the index properties of expansive soils and expanding clay minerals. Fine Fraction, Liquid, Shrinkage limit, Plasticity Index and Free Swell Index are used as Linguistic and numeric input variables. The output is Expansion Potential in quantitative terms determined from the fuzzy output membership function using Mandani Fuzzy Inference. INTRODUCTION Engineering classification of soils is generally based on simple to determine field and laboratory identification and classification tests. Composition and environmental conditions of soil deposits are known to have influence on both identification and classification properties, as well as engineering properties. Hence, it is possible to extrapolate qualitatively engineering properties and engineering use of soils based on identification and classification. Several

2 Vol. 14 [2009], Bund. L 2 investigators in the past reported methods for identification and classification of soils as well as interpretation of classification in terms of probable range of engineering properties and engineering use of soils. Most commonly used engineering classification systems namely Indian Standard Classification System (ISC), Unified Soil Classification System (USC), American Association of State Highway Transportation Officials (AASHTO) American Society of Testing Materials (ASTM), and British Standard Classification System (BSC). None of the above engineering classification systems are found to be suitable for identification of expansive soils or for prediction of swelling characteristics or Expansion Potential. The methods developed by different investigators (Altmeyer 1953, Holtz 1959, Chen 1975, IS: , USBR: 1973, Snethen 1979) serve this purpose using Fuzzy / Linguistic Variables like High, Very High etcetera making them not suitable for development of develop software. Here a novel technique known as Fuzzy Approach System is adopted to overcome this problem. The objective of this paper is to develop an fuzzy approach system using the already available information for identifying and assessment of Expansion Potential of expansive soils. IDENTIFICATION OF EXPANSIVE SOILS-SIMPLE LABORATORY TESTS The behavior of the soil and rock at the location of any structure and the interactions of the earth materials during and after construction has major influence on the success, economy and safety of the structure. In Expansive soils, major problem is large ground deformations in and around the structures due to swelling and shrinking of soil on wetting and drying. These excessive movements can damage structures and utilities also. The problems may be large ones or small ones and these have tremendous negative impact on the structure performance in terms of time and cost. A knowledge and understanding of geology of earth materials is necessary while dealing with expansive soils. Three groups of methods are proposed in literature for recognizing expansive soils in practice namely (i) Mineralogical Identification, (ii) Direct measurement, and (iii) Indirect methods. Mineralogical identification is important for exploring the basic properties of clays, but it is impractical and uneconomical for practicing engineers. The second one being the direct measurement is most useful but time consuming and laborious, involving the use of costly and elaborate testing equipment and trained personnel to conduct the experiments. Soil type and mineral type can be inferred by simple laboratory tests and field observations. The third group of methods falls under this category. Recognition of soil type, mineral type or composition provides a guide to the expected properties of that soil and selection of appropriate methods for improving behaviour of soil. A knowledge base concerning simple laboratory tests and field tests as well as field observations for identification of expansive soils is collected and presented in the following sections. Expansive soils are classified basing on the term called potential expansion, also termed as potential swell or degree of expansion. Conventionally, Expansion Potential is expressed in terms of Fuzzy linguistic variables like critical/marginal/non critical or Very High / High / Medium / Low degree of expansiveness. In other words, the methods falling under first two groups may not be possible always in time and economy aspects. Criteria were developed by several investigators (Altmeyer 1955, Holtz & Gibbs 1956, Williams et.al. 1958, Holtz 1959, Chen 1975, Snethen 1979, Holtz and Kovacs 1981, Meehan & Karp 1994, Uniform building Code 1997 and IS 2

3 Vol. 14 [2009], Bund. L :1970) for classifying the expansive soils to ascertain the Expansion Potentiality using some of factors such as Clay Content, Liquid (W L ) Plasticity Index (I P ) Shrinkage (W S ) and Free Swell Index (FSI).. The range of each property for different degrees of expansion vary from one investigator to another and also does not have sharply defined boundaries, leaving ambiguity and vagueness in deciding upon the probable degree of expansion of a given soil. This is also a stumbling block for development of expert systems for identification and classification of expansive soils. Inabilities to correctly identify the Expansion Potential, especially in transition zones, and the absence of a quantifiable parameter for Expansion Potential are obvious shortcomings of the available methods. Fuzzy methodology is investigated to meet this need and to help users to correctly interpret Expansion Potential using simple laboratory test results. A FUZZY APPROACH FOR PREDICTION OF EXPANSION POTENTIAL In this investigation, an attempt has been made to identify simple soil properties for identification of expansive soils and to assess the potential degree of expansion of any soil using these simple properties by expressing them as linguistic variables, in addition to numerical variables. The relationship between these variables is characterized by conditional Fuzzy statements. This facilitates the decision-making regarding the potential expansiveness nearer heuristic than mechanistic thereby facilitating adoption for development of expert systems for identification and classification of expansive soils. Parameters for Assessment of Expansion Potential According to opinion of domain experts and references on expansive soil characteristics (Grim 1968, Chen 1975, Mitchell 1993) clay mineralogy has significant influence on volume change behavior of expansive soils. Kaolinite, Montmorillonite and Illite are identified as commonly occurring clay minerals in soils. The soils containing Montmorillonite group of clay minerals are generally expansive in nature. Typical clay minerals and their characteristics as reported in literature (Mitchell, 1993; Koenner, 1985) are presented in Table 1. From Table 1 it can be seen that the readily expansive clay minerals like Montmorillonite are characterized by high Liquid, high Plasticity Index, low Shrinkage and less particle size compared to medium and less expansive clay minerals like Illite and Kaolinite. This fact can be efficiently utilized to identify expansive soils based on results of simple tests like grain size distribution and Atterberg s. Fuzzy Description of Expansion Potential of a Soil The process of estimation of Expansion Potential of a soil begins with search for presence of expanding clay minerals in the soil indirectly from the soil properties and parameters namely percentage passing 75µ sieve, Liquid, Plasticity Index and Free Swell Index. The Liquid, Plasticity Index, Shrinkage and Free Swell Index of expanding clay minerals significantly differ from those of non-expanding clay minerals. Based on this several investigators developed criteria for classification of expansive soils and their potential for expansion making use of two or more of these properties. The Expansion Potential is qualitatively expressed by descriptor terms like Very High, High, Marginal, Critical and so on. For each 3

4 Vol. 14 [2009], Bund. L 4 descriptor of Expansion Potential, the probable range of Liquid, Plasticity Index etcetera are suggested based on their experience and perception keeping in view the characteristics of expanding clay minerals. Table 1: Typical Values of Consistency s for Various Cohesive Soils (After Koenner, 1985) Mineral Exchangeable Ion Liquid Plastic Plasticity Index Shrinkage Na K Montmorillonite Ca Mg Fe Fe Na K Illite Ca Mg Fe Fe Na K Kaolinite Ca Mg Fe Fe Among the several parameters used for identification of expansive soils by different investigators, percentage passing 75µ sieve, Liquid, Plasticity Index, Shrinkage and Free Swell Index tests are easy to determine and are routinely determined in any laboratory. Hence these properties are used in this investigation for estimating the probable degree of expansion. Since the natural soil may contain both expanding clay minerals and non-expanding clay minerals along with silt and coarse fraction, their property may fall in between those of expanding clay minerals and non-expanding clay minerals leading to some uncertainty and 4

5 Vol. 14 [2009], Bund. L 5 ambiguity in assessing the Expansion Potential of a soil, by comparing its properties with those of clay minerals. However, high Liquid, high Fine Fraction, low Shrinkage, high Plasticity Index and high Free Swell Index in contrast to non-expansive soils characterize potentially expansive soils. The exact numeric range of each of the soil properties namely Liquid, Plasticity Index, Shrinkage, Fine Fraction and Free Swell Index for each descriptor namely Very High (VH) High (H) Medium (M) and Low (L) are not explicitly known and are generally left to the perception of the expert. Further, the degree of expansion itself is described qualitatively in terms of very high, high, medium and low. The theory of Fuzzy sets is a mathematically intuitive method of quantifying imprecision and uncertainty by grouping individuals into classes that do not have sharply defined boundaries. Hence the theory of Fuzzy sets can very well be applied to the problem of qualitative estimation of Expansion Potential from index properties of soils. Fuzzy Sets And Relations Fuzzy sets are useful for describing the ambiguity and vagueness in conceptual or mathematical models of empirical phenomena (Gupta & Yamakawa, 1988). A brief introduction to the Fuzzy set theory is presented as follows. According to Zadeh (1965) The Fuzzy set A of X is defined by its membership function µ A and take the values in the unit interval l [0, 1] µ A : X [0, 1], where X is finite set. For example, consider the proposition x is tall and is defined as µtall (x) [0, 1], x Є X Tall= µtall(x1)/0.6+µtal l (x 2 )/ µ tall (x n)/0.67 Fuzzy logic is defined as combination of Fuzzy sets using logical operators. Some of the logical operations are given bellows Suppose A, B, C are Fuzzy sets AVB=max {µa(x) µb(x)} AΛB=min {µa(x) µb(x)} A =1-µA(x) disjunction negation conjunction If A then B= min(1, µa(x) +µb(x)} implication According to Mandani Fuzzy Inference, If A1, A2,, An then B B=min( A1, A2,, An) 5

6 Vol. 14 [2009], Bund. L 6 as The Fuzzy propositions may contain quantifiers. These Fuzzy quantifiers may be eliminated µ very (x) =µ A (x) ² µ more or less (x) = µ A (x) ½. Fuzzy Approach System In this study, Fuzzy theory is adopted to assess the Expansion Potential of a soil using five index properties namely percentage passing 75µ sieve i.e. Fine Fraction, Liquid, Plasticity Index, Shrinkage and Free Swell Index. The problem of qualitative assessment of degree of Expansion Potential can be approached using combination of degree of match and the Fuzzy rule based system. In a Fuzzy rule based system, the knowledge concerning the classification of the object (potential expansion) is represented in the form of rules. Each rule has a set of antecedent propositions comprising attribute names namely percentage passing 75µ sieve i.e. Fine Fraction, Liquid, Plasticity Index, Shrinkage and Free Swell Index and linguistic description of attributes like very high, high etcetera. These linguistic variables are invariably imprecise, keeping in view the inadequate information on influence of each attribute on the object (that is Expansion Potential) and the integrated effect of all the attributes in the potential expansion (object). The set of rules formed are based on the criteria developed for Expansion Potential by Altmeyer 1955, Holtz 1959, Chen 1975, IS: , Snethen 1979 and the properties of expanding clay mineral presented Table 1. The rules framed for use in this investigation are shown in Table 1. The degree of match of each classification rule indicates the certainty value of classification. The greater the degree of match, the greater is the possibility that the object (Expansion Potential) is classified in that class. Table 2: Rules Framed in Fuzzy Inference System LL PL PI SL Montmorillonite Rule 1: IF VH VH VH L Illite Rule 2: IF VH H H L Kaolinite Rule 3: IF VH H H M Fuzzy inference process consists of five steps: 1. Fuzzification of the input variables 2. Application of the Fuzzy operator (AND or OR) in the antecedent 3. Implication from the antecedent to the consequent 4. Aggregation of the consequents across the rules 5. Defuzzification. 6

7 Vol. 14 [2009], Bund. L 7 Fuzzification of the Input Variables The parameter used as input for assessing the Expansion Potential varies from one method to another. Different methods have different criteria s for obtaining the degree of expansion (Altmeyer, 1955; Holtz, 1959; Chen, 1975; IS 1498:1970; and Snethen, 1979). Altmeyer (1955) has considered Shrinkage and Linear Shrinkage for obtaining the degree of expansion of soil. IS classification method has used Liquid, Plasticity Index, Shrinkage Index, Free Swell Index as the criteria for obtaining degree of expansion. Though each of the input parameters possess certain crisp values, it may not be always possible to expect all the input parameters to fall in any one output descriptor using certain method. Even though when single parameter criteria is considered instead of combination of different parameters, the parameter with certain value may fall in one output descriptor as per one method and another output descriptor as per another method. In such situations ambiguity arises in assigning the degree of expansion. For example, for a soil with Liquid value of 65%, Plasticity Index of 35% and Shrinkage of 12%, the degree of expansion predicted by different methods considering each parameter separately is given in the following Table 3. Table 3: Degree of Expansion by different methods for a given input Method Holtz/USBR (Table 2.3) IS Classification (Table 2.5) Snethen/UASEWES (Table 2.11) Input Parameter Plasticity Index Shrinkage Liquid Shrinkage Index Liquid Plasticity Index Degree of Expansion (Output in terms of descriptor) Very High/ High High/Medium High Medium High Medium Chen (Table 2.4) Liquid Very High Note: Parameters are w L = 65%, I P = 35% and w S = 12% From Table 3 it is clear that for same input, predicted Expansion Potential varies not only from one method to another method but also from one parameter to another parameter in any given method. That is, according to Holtz/USBR method for soil of 65% Liquid, the Expansion Potential is very high to medium where as it is high to medium for Plasticity Index of 36%. This gives raise to ambiguity in assessing Expansion Potential even by any one given method also. Such situations can efficiently be handled in Fuzzy-Logic method by fuzzify the input variables. Fuzzification is the process of making a crisp quantity fuzzy. In this investigation the input parameters to the system are percentage passing 75µ sieve that is Fine Fraction, Liquid, Plasticity Index, Shrinkage and Free Swell Index. Ambiguity or vagueness exists in all these parameters as their relation to degree of expansion or Expansion Potential is not crisp. In Fuzzy approach system the parameters representing inputs and outputs are represented in the form of Fuzzy sets. A Fuzzy set represents the set of values that a parameter can take. The Fuzzy 7

8 Vol. 14 [2009], Bund. L 8 sets can be represented by a function whether continuous or discontinuous, symmetrical or asymmetrical in shape. All the information contained in a Fuzzy set is described by its membership function. All of these Fuzzy sets or membership functions are characterized by core, support and boundaries. The core of a membership function for a Fuzzy set A is defined as the region of the universe that is characterized by complete and full membership in the set A. That is, the core comprises those elements x of the universe such that μ A (x) = 1. The support of a membership function for a Fuzzy set A is defined as the region of the universe that is characterized by nonzero membership in the set A. That is, the support comprises those elements x of the universe such that μ A (x) > 0. The boundary comprises of a membership function for a Fuzzy set A and is defined as the region of the universe containing elements that have a nonzero membership but not complete membership. That is, the boundaries comprise those elements of x the universe such that 0 < =μ A (x)<=1 For example, the Rule 1 presented in Table 2 has five antecedents namely FF(VH) W L (VH) I P (VH) W s (L) and FSI (VH). For any given set of input variables, the membership values for Fuzzy descriptors that is L, M, H and VH can be obtained based on Fuzzy Membership Function. Different parts of these antecedent can be clubbed by either AND or OR operators in order to represent only one result of the antecedent rule. The same is explained through the following numerical example. By the observation, the Fuzziness for parameters are as given below for a certain soil. Mineral Exchangeable Ion Liquid Plastic Plasticity Index Shrinkage Na 0.85/ /54 0.9/ /9.9 K 0.8/ /98 0.8/ /9.3 Montmorillonite Ca 0.75/ /81 0.7/ /10.5 Mg 0.7/ /60 0.6/ /14.7 Fe 0.65/ / /10.3 Fe++ 0.6/ /73 0.2/67 0.8/10.0 The Low. High and Medium are computed as Low(X) = min(x) High(X)=Max(X) Medium(X)=(Low(X) + High(X))/2 Very High(X)= ( High ) 2 Where X is Liquid, Plastic, Plasticity and Shrinkage 8

9 Vol. 14 [2009], Bund. L 9 The Table given below summarizes the membership values for each of the input variable for all the four Fuzzy descriptors. Fuzzy Membership Values for the example considered. Fuzzy Descriptor Liquid Plastic Plasticity Index Shrinkage Low Medium High Very High All parts of the antecedent of rule 1 are clubbed by AND operator. For the above data, rule 1 appears as given below. Montmorillonite LL PL PI SL Rule 1 IF VH VH VH L IF ( LL is 0.72 ) AND ( PL is 0.81 ) AND ( PI is 0.81 ) AND ( SL is 0.7 ) The consequent / output for this antecedent is a single truth value obtained using the function min as given below RULE 1 : min (0.72, 0.81M 0.81, 0.71) = 0.7 Hence the truth value of Rule 1 is 0.7 In other words the consequent Expansion Potential of Rule 1 is 0.7 memberships.. The other Rules will be calculated similar lines. Montmorillonite LL PL PI SL IF VH VH VH L Expansion Potential THEN 0.7 Defuzzification of the Output Set The aggregate Fuzzy set is defuzzified in order to resolve a single output value from the set. The conversion of a Fuzzy set to single crisp value is called defuzzification. Five built-in methods are used to defuzzify the output set: centroid, bisector, middle of maximum, largest of maximum and the smallest of maximum. Here the smallest of maximum method is considered. According to Mandani method of fuzzy Inference, the Expansion Potential is 0.7 and is High. In the centroid method is used to deffuzzify the output. Initially, the centroids are computed for each 9

10 Vol. 14 [2009], Bund. L 10 competing membership functions. Then, the new output areas determined by shortening the height of the membership value on the Y-axis as dictated by the rule strength value. Finally, the Center of Gravity (CG) is computed using weighted average of the X-axis centroid points with the newly computed output areas The details of this method may be found in Timothy Ross (2004) or any other text book on Fuzzy Set Theory and Application. CONCLUSIONS A rule based Fuzzy Approach System has been developed for identification and estimation of potential degree of expansion of a soil basing on simple index properties of the soil. Methods of Fuzzy knowledge representation and fuzzy reasoning were employed to convert uncertain system inputs to Fuzzy linguistic information. The results from 3 different soils reported in literature indicate that the proposed system is effective in predicting potential degree of expansion. The proposed system can be effectively used as a subsystem for expert system dealing with prediction of engineering properties of soils using Index properties. REFERENCES 1. Altmeyer, W.T. (1955) Discussion of Engineering properties of expansive clays, Proc. ASCE, Vol.81, Separate No Bellman and Zadeh, L.A. (1970) Decision Making in Fuzzy Environment, Management Science 17, pp Chen, F.H. (1973) The Basic physical property of expansive soils, Proc. 3rd Int. Conf. On Expansive soils, Haifa, Israel, Vol.1. pp Gupta, M.M. and Yamakawa, T. (1988) Fuzzy Logic in Knowledge Based System, Decision and Control, North-Holland, New York. 5. Holtz, W.G. (1959) Expansive clays-properties and problems, Quarterly of the Colorado School of Mine, Vol.54, No.4. PP I.S.1498 (1970) Classification and Identification of soils for general Engineering purposes, First revision, Fourth Reprint November, Koenner, M (1985) Construction and Geotechnical Methods in Foundation Engineering, McGraw-Hill Book C0 Singapore. 8. Mallikarjuna Rao, K. (1988) A Proper parameter for correlation of swell potential and swell index for remoulded Expansive clays, M.Tech thesis submitted to Jawaharlal Nehru Technological University, Kakinada. 9. Meehan, R.L., and Karp, L.B. (1994) California Housing Damage Related to Expansive Soils, Journal of Performance and Construction Facilities, ASCE, Vol. 8, No. 2, pp Mitchell, K James (1993) Fundamentals of Soil Behaviour, John Wiley & Sons, New York. 11. Seed, H.B. et al. (1962) Prediction of Swelling Potential for compacted clays, Jrl. Of S.M and F. E. Divn. ASCE. Vol.88, No.Sm3, Part-1, Proc. Paper 3169, pp

11 Vol. 14 [2009], Bund. L Snethen, D.R. (1979) An evaluation of methodology for prediction and minimization of determental volume change of Expansive Soils in highway subgrades, Research report Vol.1, Federal Highway Administration, Washington, D.C. 13. Sudharani, Ch., etal (2004) Identification and assessment of Engineering properties of soil using a Knowledge Based System, International e-conference, Indian Institute of Technology, Chennai. 14. Uniform Building Code (1997) International Conference of Building Officials, Whittier, Calif. 15. Zadeh, L. A. (1964) Fuzzy Sets, Information and control, 8, pp Zimmerman, H.J. (1985) Fuzzy set Theory and its Applications, Kluwer Nijhoff, Boston ejge 11