Theme T 15 Geotechnical Education and Professional Practice

Transcription

1 Theme T 15 Geotechnical Education and Professional Practice

2 Indian Geotechnical Conference 2010, GEOtrendz December 16 18, 2010 IGS Mumbai Chapter & IIT Bombay Development of Spreadsheet for Correlation of Soil Properties Shah, S.J. Abdurahiman, P. Shah, S.H. 1 Assistant Professor Lecturer Prof. and Head syedjshah@gmail.com abdupulikka@gmail.com shah@consultant.com IES College of Engineering, Chittilappilly, Thrissur 1 Department of Civil Engg., KMEA College of Engineering, Edathala, Aluva ABSTRACT Evolving a practical and economical solution to geotechnical problems requires a thorough understanding of soil behaviour. This paper presents an excel sheet providing a collection of correlations of different soil properties so that practicing engineers can get immediate insight into the empirical and engineering behaviour of soils. Correlations of the index and engineering soil properties have been collected and entered as formulae into the spread sheet so that upon entering test result data, possible behaviour of soil will be output. The spread sheet is organized in three parts, first sheet for entering test results of empirical properties, second sheet for entering test results of engineering properties, the third for field and laboratory tests. The result sheets indicate the possible behaviour of a soil with the entered properties. The spreadsheet presented here will reduce time and effort required in searching and accessing references containing the correlations and interpretations of soil properties. 1. INTRODUCTION To estimate the possible behavior of foundations of structures under loading, a geotechnical engineer needs the results of a large number of tests conducted in the field and laboratory. Detailed testing is expensive, time consuming and not always possible. Over the years, a large number of correlations have been developed by various researchers giving correlations of various index and engineering properties. However one needs to refer many books to access these correlations, which is a time consuming task. To make this exercise easy and speedy, a spreadsheet has been developed in excel, which is presented here. 2. UTILISATION OF MICROSOFT EXCEL FOR DEVELOPING CORRELATION SPREAD SHEETS Microsoft Excel is an application that helps us to create intricate and dynamic spreadsheets. This robust application can be used to enter numerical values or data into the rows or columns of a spreadsheet, and to use these numerical entries for such things as calculations, graphs, and statistical analysis. Microsoft Excel has the basic features of all spreadsheets, using a grid of cells arranged in numbered rows and letter-named columns to organize data manipulations like arithmetic operations. It has a number of supplied functions to answer statistical, engineering and financial needs. It has a variety of interactive features allowing user interfaces that can completely hide the spreadsheet from the user, so the spreadsheet presents itself as a so-called application, or decision support system (DSS), via a custom-designed user interface. Like some other spreadsheet applications, Microsoft Excel supports charts, graphs or histograms generated from specified groups of cells. The generated graphic component either can be embedded within the current sheet, or added as a separate object. Curve fitting is the process of constructing a curve, or mathematical function that has the best fit to a series of data points, possibly subject to constraints. Excel will allow us to find the equation for a curve that fits our data. The curve may be a line, quadratic, polynomial or several other types of functions. 3. ORGANISATION OF THE SPREAD SHEETS The excel sheet has been developed to facilitate easy calculations of the correlated values between various soil properties. There are four input sheets for entering the values which are known from experimental results. The first input sheet INPUTSHEET1 is for entering the test results of index properties of the soil. The second input sheet INPUTSHEET2 is prepared for entering the engineering properties of the soil. The third input sheet INPUTSHEET3 is meant for field test results. The fourth sheet INPUTSHEET4 is designed for input of results

3 1114 S.J. Shah, P. Abdurahiman and S.H. Shah from empirical laboratory tests. All the INPUT SHEETS contain ranges and units of all properties which are to be entered. The next part FITTING OF EQNS is the sheet where curve fitting has been done. To find the equations for correlations of properties from various graphs and tables, curves are plotted. Then using add trend lines option in EXCEL, best fitting curve is drawn and its equation is obtained. In each case, curves have been developed such that correlations can be obtained either way. This has been done so that one can check for any contradiction between results of different interrelated properties. All available correlations for each property have been fitted. These equations which relate properties of soil are used for correlation of the input values with other properties. In the next sheet named CALCULATION SHEET, calculations are done using the input values entered in the different input sheets. Using the equations developed in FITTING OF EQNS, properties related to these input values are obtained in this sheet using arithmetical functions of EXCEL. In the next sheet named CORRELATIONS, the entered properties and calculated properties are correlated using logical functions and the equations which have been developed as mentioned earlier. Cells containing the entered values in the input sheets and calculated values in the calculation sheet are linked to different cells in this sheet. The results displayed in this sheet give all the possible correlations for the entered properties. 4. CORRELATION OF INDEX PROPERTIES WITH OTHER PROPERTIES Index properties are the observable physical characteristics with significant influence on a soil s behaviour. They are Grain Size, Bulk Density(γ), Saturated Density(γ sat ), Soil Consistency, Relative Density D r (Density Index), Moisture Content(w), Specific Gravity(G), Porosity(n), Void Ratio(e). Table 1 shows INPUT sheet. Index properties are used for soil classification, estimation of other properties etc. Some examples are given here. Automatic Classification of Soil Based on Plasticity Chart The plasticity chart gives classification of clay and silt provided plasticity index and liquid limit are known. Once the Atterberg limits are entered in the INPUTSHEET1 of developed spreadsheet, the plasticity index is calculated in CALCULATION sheet and compared with the value obtained from A-line. Again based on the liquid limit value, and using IF, AND condition statement in recursive manner, it checks whether the liquid of the given soil is less than 35 (meaning low compressible), or between 35 and 50 (medium compressible) or greater than 50 (highly compressible). Then, if PI value of the soil is greater than A line value, then it is decided whether it is inorganic or organic clay or whether it is silt. Then, the CORRELATIONS sheet combines the two results and directly gives the type of soil as for example, organic clay of high plasticity. Correlation of Liquid Limit (LL) with Coefficient of Consolidation (Cv) Using the relation between LL and Cv values given by Gulhati & Datta (2005), a plot was made (Fig. 1). Using regression analysis, a power equation was fitted so as to obtain a best fit curve with regression coefficient 0.99 (Fig. 3). Using this fitted equation, the CALCULATION sheet computes Cv using the input value of LL, and the CORRELATIONS sheet gives Cv value to the user. Using the arithmetic-logic functions available in EXCEL, other correlations such as between plasticity index and angle of internal friction (Coduto & Donald 2006), unit weight and angle of internal friction (Venkatramaiah 2006), Consistency index and unconfined compressive strength (Arora 2008) etc. were fitted. The CORRELATIONS sheet gives the values corresponding to the input values using the fitted equations and arithmetic-logical conditions. For the computed condition, the values from equations or the appropriate stored result key words are printed. Fig. 1: Actual Relation and Fitted Equation Between Cv and Liquid Limit Table 1: Sheet1 for Entering Index Properties of Soil Properties LL PL SL Grain Size G γ γ sat D r e n S w units mm (kn/m 3 ) 0-25 (kn/m 3 ) <=1

4 Development of Spreadsheet for Correlation of Soil Properties 1115 Table 2: Sheet 2 for Entering Engg. Properties of Soil Properties c φ Cv Cc k Es G υ Capillary Rise Units (mm) 0-90 (m 2 /day) 1x (mm/s) (KN/m 2 ) 9->70 (KN/m 3 ) (m) 5. CORRELATION OF ENGINEERING PROPERTIES WITH OTHER PROPERTIES Engineering properties determines engineering behaviour of soil. Engineering properties of soil depend on a number of factors and it is not possible to characterize them by two or three parameters. Elaborate testing is required to determine the characteristics of the soil before design can be done. They are Cohesion(c), Friction(f), Coefficient of Permeability(k), Capillarity, Coefficient of Consolidation (Cv), Compression Index (Cc), Compressibility, Modulus of Elasticity(E s ), Shear Modulus(G), Poisson s ratio(u). sheet for engineering properties is shown in Table 2. Modulus of Elasticity (E S ) and type of soil Table 3 indicates corresponding E S values for clays of various consistencies and for sands of different relative densities (adopted from Bowles, 1997). On entering the E S value (say 3000), the CORRELATIONS sheet gives all the possible types of soil (very soft/soft clay or silty/dense sand) with its state (consistency or D r ) as in the table 3. Table 3: Range of Values of Elastic Modulus (E s ) for Selected Soils IF Clay is THEN E s (kn/m 2 ) Very soft 2000 to Soft 5000 to Medium to Hard to IF Sand is THEN E s Silty 5000 to Loose to Dense 5000 to Consistency of Clay Based on Cohesion Value Knowing the characteristics of clay is necessary for the designer to get a physical feeling of the strength. To convenience this, the spreadsheet checks the input value of cohesion using IF statement and whichever range it falls in, the corresponding consistency and physical characteristic gets printed in the output sheet. Table 4 gives the condition relation between cohesion value, consistency and characteristics of the soil which will be printed in the CORRELATIONS Sheet. Data from Arora (2008) has been adapted for developing the relations. Correlation equations between Permeability constant and soil type, unit weight, suitable method of compaction, suitability as embankment material and degree of permeability based on Jha & Sinha (2001) and Arora (2008) are built-in. Other relations such as between φ and plasticity index (Coduto & Donald 2006), angle of internal friction and unit weight (Venkatramaiah 2006), etc. are also developed. On entering a particular value of capillary rise in the INPUT SHEET2, one can also obtain the appropriate type of soil which will give that value of rise. This will be useful in choosing soil type for providing drainage cutoff layers. Table 4: Cohesion, Consistency and Clay Characteristics Cohesion c THEN (kn/m 3 ) Consistency Characteristics of soil IF c<12 Very soft Fist can be pressed into soil IF c>12 Thumb can be pressed into Soft AND<=25 soil IF c>25 AND<=50 Medium (firm) Thumb can be pressed with pressure IF c>50 Thumb can be pressed with AND Stiff great difficulty c<=100 IF c>100 AND <=200 IF c>200 Very stiff Hard 6. CORRELATION OF FIELD AND LABORATORY TESTS The soil can be readily intended with thumb nail The soil can be intended with difficulty by thumb nail Empirical tests like Dynamic Cone Penetration Test (DCPT), Standard Penetration Test (SPT), California Bearing Ratio (CBR), Modulus of Subgrade reaction (K) etc are very common in Geotechnical Engineering practice. Their widespread use has led to the development of various correlations which allow one to estimate the engineering properties of the tested soil. sheet for the above is illustrated in Table 5.

5 1116 S.J. Shah, P. Abdurahiman and S.H. Shah Table 5: Sheet 3 and 4 for Field and Laboratory Tests Properties DCPT N SPT N K CBR Units (kg/cm 3 ) Standard Penetration Test N value with φ, D r and γ The N value has correlations with φ, D r and γ for fine, medium and coarse sand (Table 6). The spread sheet checks an input N for its range with the values of the table and gives corresponding φ, γ, D r, with description of relative density condition for the three conditions of fine, medium and coarse sand. Data from Bowles (1997) has been utilized for developing the logical cum numerical equations. Table 6: SPT N Values for Fine, Medium and Coarse Sands Conditionally Related to φ, D r and γ Description Very loose Loose M e d i u m Dens e Very Dense IF N:fine IF N:medium >40 IF N:coarse >45 THEN φ : fine φ: medium <50 φ: coarse γ, kn/m Relative density D r On similar lines the spread sheet has been developed for giving c, γ, and consistency condition of clay from the N value. Safe Bearing Pressure is also obtained in the CORRELATIONS sheet using the formula 11N kn/m 2 for general preliminary design. Modulus of Subgrade Reaction (K) and CBR CBR is a very common and easy test, while determination of K is very expensive, time taking and requires a lot of effort. IRC 58:2001 gives a correlation of CBR and K(kg/ cm 3 ) value. This has been fitted into an equation Eq. (1) so as to obtain K value. On entering CBR value, the result sheet gives K values using this equation. It is also possible to find the CBR value if the K value is input in the spreadsheet using the equation Eq. (2) K= (CBR^2) (CBR) (1) CBR = (K 2 ) (K) (2) The correlations between Cone Penetration test and c values have also been implemented in the spreadsheet. Using the representative values of K for various types of soil reported by Bowles (1997), the output for an entered value of K also gives possible soil type and corresponding consistency or relative density. 7. CONCLUSIONS The correlations of various index and engineering soil properties as well as empirical tests reported by various researchers have been fitted into equations in a spreadsheet. Using arithmetic-logic functions in MICROSOFT EXCEL, conditional equations also have been framed so as to obtain correlated values of various soil properties corresponding to input values of properties. The spreadsheet will provide an effortless means for the practicing engineers to understand index and engineering properties of soils, their physical significance and help in a better understanding of soil behavior. REFERENCES Arora, K.R. (2008) Soil Mechanics and Foundation Engineering, Standard Publishers and Distributors, New Bowles, J.E. (1997) Foundation Analysis and Design, McGraw-Hill International editions, New York. Coduto, D.P. (2006) Geotechnical Engineering Principles and Practices, Prentice-Hall of India Pvt. Ltd., New Gulhati, S.K. and Datta, M. (2005) Geotechnical Engineering, The McGraw-Hill Companies Ltd., New IRC:58 (2002) Guidelines for the Design of Plain Jointed Rigid Pavements for Highways (Second Revision), Indian Roads Congress, New Jha. J. and Sinha, S. K. (2001) Construction and Foundation Engineering, Khanna Publishers, New Venkatramaiah, C. (2006) Geotechnical Engineering, New Age International Publishers, New