REGRESSION ANALYSIS OF SHORT TERM TIME-SETTLEMENT RESPONSE OF SOFT CLAYEY SOIL AT CONSTANT LOADING CONDITION

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 9, Issue 10, October 2018, pp , Article ID: IJCIET_09_10_182 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed REGRESSION ANALYSIS OF SHORT TERM TIME-SETTLEMENT RESPONSE OF SOFT CLAYEY SOIL AT CONSTANT LOADING CONDITION Parbin Sultana Assistant Professor, Department of Civil Engineering, National Institute of Technology Silchar, Assam, India Ashim Kanti Dey Professor, Department of Civil Engineering, National Institute of Technology Silchar, Assam, India ABSTRACT The short term or immediate settlement of a foundation on soft clayey soil can be evaluated from the plate load tests (PLTs). The PLT conducted on a clayey soil is a lengthy process in comparison to that on a sandy soil. This is because of the longer time consumed by the clay to arrive at a steady amount of settlement. Hence, an attempt is made in this paper to fit the time-settlement response to a standard curve, so that the settlement corresponding to a longer elapsed time can be estimated from a short duration data. This study analyses the time-settlement responses of soft clays from PLT data by using non linear regression technique. The data consists of 5 timesettlement curves for various load intensities within the range of 0.8kPa 55. kpa. It is found that the logarithmic model fits well with the collected data. The model parameters, root mean squared error (RMSE), co-efficient of determination (R²) and adjusted co-efficient of determination (R adj ²) are presented. The variation of model parameters with respect to the load intensity is checked. Keywords: Plate load test, logarithmic model, soft clay, time-settlement response Cite this Article: Parbin Sultana and Ashim Kanti Dey, Regression Analysis of Short Term Time-Settlement Response of Soft Clayey Soil at Constant Loading Condition, International Journal of Civil Engineering and Technology, 9(10), 2018, pp editor@iaeme.com

2 Parbin Sultana and Ashim Kanti Dey 1. INTRODUCTION The estimation of total settlement is a major part of the foundation design process. The total settlement comprises of three types of settlements namely, the immediate settlement, the primary consolidation settlement and the secondary consolidation settlement. The short term settlement or immediate settlement is considered to be predominant in granular soil only and hence often neglected in cohesive soils. Therefore, the expected settlement of a foundation is determined from the consolidation settlement evaluated from an odometer test using Terzaghi s one-dimensional consolidation theory. But this method does not provide a very accurate measure of total settlement. Even for long term settlement prediction, this method has been criticized by some researchers [1-]. Stamatopoulos and Kotzias [4] have recommended the use of field permeability tests or test fills over the odometer test. In case of cohesive soils, the short term or immediate settlement is also significant, particularly in highly plastic or organic soils [5]. This type of settlement occurs due to the distortion of the clay in undrained condition. Hence, the evaluation of short term settlement is important for accuracy of total settlement prediction. The conventional theories of short term settlement assume a linear elastic soil model [6, 7]. These theories are recommended by various authors for calculation of immediate settlement on clay [8, 9]. The linear elastic model presents only a reasonably accurate result as the actual behaviour of soil is essentially non linear. Several non linear constitutive models have also been proposed by various researchers [5, 10-12]. Apart from all these theoretical approaches based on small scale laboratory test results, another simple approach to obtain short term settlement is by field Plate Load Tests (PLTs). In a PLT, the plate acts as a model footing and it considers all the uncertainties involved in the field condition. Hence the final settlement observed in a PLT at any constant loading condition makes a close estimate of the nonlinear, inelastic, short term settlement of the foundation at the same loading condition [1, 14]. The PLT is a large scaled, long and costly test in comparison to the other laboratory tests such as Unconfined Compressive Tests or Triaxial Tests. When a load increment is applied, the settlement is recorded at certain time intervals until the rate of settlement is reduced to a value of 0.02 mm/min or the time-settlement curve indicates the achievement of 70 to 80% of probable final settlement or 24 hours, whichever is earlier [15]. In case of cohesive soils, it takes a longer time to satisfy this criterion, and hence the test becomes costlier. In the present study, an attempt has been made to standardize the time-settlement curve, so that an extrapolation of small duration data can be used to estimate the final settlement. A set of 5 time-settlement datasets at different load levels were used for regression analysis. After checking with a number of regression models, it was found that a logarithmic model represents the time-settlement response very well. The statistical parameters of regression such as root mean squared error (RMSE), co-efficient of determination (R²) and adjusted coefficient of determination (R adj ²) showed a good fit of the model with the experimental data. The model co-efficient were also checked for their variation with the load intensity. 2. DATA COLLECTION The data used in this study were collected from six numbers of PLTs conducted by the authors on a soft clayey soil. The index properties of the soil are given in Table 1. The PLTs were performed on plates of different sizes e.g. 10 cm, 20 cm, 0 cm, 45 cm square and 10 cm and 20 cm diameter circular. The 0 cm and 45 cm plates were tested in a test pit of 18 editor@iaeme.com

Regression Analysis of Short Term Time-Settlement Response of Soft Clayey Soil at Constant Loading Condition dimension m x 2 m x m (depth) (Figure 1(a)) and the rest of the plates were tested in a

The settlement was measured by two LVDTs placed at the opposite corners of the plate and the average of the two outputs was considered as the settlement.

3 Regression Analysis of Short Term Time-Settlement Response of Soft Clayey Soil at Constant Loading Condition dimension m x 2 m x m (depth) (Figure 1(a)) and the rest of the plates were tested in a test tank of dimension 1 m x 1 m x 1 m (Figure 1(b)). The load was measured by a load cell and the load intensity was calculated by dividing the load with the plate area. The settlement was measured by two LVDTs placed at the opposite corners of the plate and the average of the two outputs was considered as the settlement. Total 5 sets of time-settlement data for loading intensities in the range of 0.8kPa 55. kpa were collected. The time-settlement curves for all the data are presented in Figure 2. Table 1 Index properties of the soil Property Specific gravity Liquid limit (%) Plastic limit (%) Plasticity index (%) Fraction of fine particles (< 75 μ size) (%) Unified soil classification Value CH (a) In the test pit (b) In the test tank Figure 1 The PLTs performed by the authors Figure 2 Time-settlement curves for the 5 numbers of datasets. SELECTION OF MODEL Regression analysis is an essential tool to construct mathematical models out of any set of experimental data. If some data appears to be non-linearly correlated with one another, then non linear regression is done assuming some appropriate non linear function [16]. Later on, editor@iaeme.com

4 Parbin Sultana and Ashim Kanti Dey the suitability of the regression equation is checked with some statistical estimates as R 2 value, standard error etc. The time-settlement data shown in Figure 2 indicate a non linear relationship between time and settlement at constant loading condition. It is observed that settlement increases with time, but the rate of increase of settlement decreases with time. Hence some of the data were checked for exponential, logarithmic, polynomial and power functions with trend line in Microsoft Excel. In every case, the R 2 value of logarithmic curve showed the maximum value and hence the regression analysis was done to fit the data on logarithmic curve model. The equation of the model function is as follows: Where, ( ) s = Settlement in mm t = Time in minute a,b = Model co-efficients (1) 4. RESULTS AND DISCUSSIONS A MATLAB code was developed to perform the non linear regression. All the datasets were separately fitted to equation (1). The model parameters, their standard errors, R 2 values and 95% confidence limits were evaluated and are presented in Table 2. From Table 2 it is observed that when the time-settlement behaviour of soil at constant loading is fitted to the logarithmic curve as shown in equation (1), the parameter a lied within the range of and parameter b lied within the range of The maximum root mean squared error (RMSE) was and the value of R 2 and adjusted R 2 were within the range of 26 1 and 15 1 respectively. All these findings support the logarithmic model for the current data. But these are global model properties and hence cannot be used solely to ensure model adequacy [17]. Generally Residual Analysis is performed to check the goodness of a statistical model. A residual is the deviation between the data and the fit. A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, the regression model is appropriate for the data. Figures and 4 show the time-settlement curves with 95% confidence limits, 95% prediction limits and residual plots for two representative regressions. The confidence limits and prediction limits indicate the data to lie within the acceptable range. All the residual plots in the analysis showed randomness without making any particular pattern. Hence the logarithmic model can be considered to be acceptable for timesettlement curves. Load a b Inten sity (kpa) Table 2 Statistical parameters of logarithmic fit of time-settlement curve RM SE R² Adj Standard error R² a b 95% confidence limit of 'a' Minim um Maxim um 95% confidence limit of 'b' Minim um Maximu m editor@iaeme.com

5 Regression Analysis of Short Term Time-Settlement Response of Soft Clayey Soil at Constant Loading Condition editor@iaeme.com

6 Parbin Sultana and Ashim Kanti Dey (a) (b) editor@iaeme.com

7 Regression Analysis of Short Term Time-Settlement Response of Soft Clayey Soil at Constant Loading Condition (c) Figure Time-settlement curve with (a) 95% confidence limit (b) 95% prediction limit and (c) residual plot for load intensity 5.5 kpa (a) (b) (c) Figure4 Time-settlement curve with (a) 95% confidence limit (b) 95% prediction limit and (c) residual plot for load intensity 8.2 kpa It is obvious that the model parameters a and b will change with the change in the load intensity. A plot of a against load intensity (Figure 5) shows that the value of a increases with the increase of load intensity. The best fitted trend line between these two indicates an exponential relationship as given in equation (2). (2) editor@iaeme.com

8 Parbin Sultana and Ashim Kanti Dey Where q is the load intensity in kpa. Again Figure 6 shows the variation of parameter b with load intensity. The value of b also increases with load intensity following a 2 nd order polynomial trend line given by equation (). () Figure 5 Variation of parameter a with load intensity Figure 6 Variation of parameter b with load intensity 5. CONCLUSION In this paper, the short term time-settlement response of soft clay is studied with the help of PLT data. It covers load intensity in the range of 0.8kPa 55. kpa. From the regression analysis, it can be concluded that at constant loading condition, the settlement varies logarithmically with time. The statistical parameters and residual plots supported the logarithmic model for the present data. When variation of model parameters with load intensity were checked, it was found that parameter a increases exponentially with the increase of load intensity and parameter b increases as second order polynomial with the increase of load intensity. These findings can be used to predict the settlement after a longer elapsed time (say 24 hours) from the available short duration data for any load level within the studied range editor@iaeme.com

9 Regression Analysis of Short Term Time-Settlement Response of Soft Clayey Soil at Constant Loading Condition REFERENCES [1] Asaoka, A. Observational procedure of settlement prediction, Soils and Foundations, 18(4), 1978, pp [2] Tan, S. A. Validation of Hyperbolic Method for Settlement in Clays With Vertical Drains, Soils and Foundations, 5(1), 1995, pp [] Li, C. A Simplified Method for Prediction of Embankment Settlement in Clays, Journal of Rock Mechanics and Geotechnical Engineering, 6, 2014, pp [4] Stamatopoulos, A. C. and Kotzias, P. C. Settlement-Time Predictions in Preloading, Journal of Geotechnical Engineering, 109(6), 198, pp [5] Foye, K. C., Basu, P. and Prezzi, M. Immediate Settlement of Shallow Foundations Bearing on Clay, International Journal of Geomechanics, 8(5), 2008, pp [6] Terzaghi, K. Theoretical Soil Mechanics, John Wiley & Sons, 194. [7] Christian, J. T., and Carrier, W. D. Janbu, Bjerrum and Kjaernsli schart reinterpreted, Canadian Geotechnical Journal, 15, 1978, pp [8] Murthy, V. N. S. Advanced Foundation Engineering, First Edition, CBS Publishers and Distributors Pvt. Ltd. 2007, pp [9] Venkatramaiah, C. Geotechnical Engineering, Sixth Edition, New Age International Publishers, 2018, pp [10] Kondner, R. L. Hyperbolic stress-strain response: Cohesive soils, Journal of Soil Mechanics and Foundation Division, 89(1), 196, pp [11] D Appolonia, D. J., and Lambe, T. W. Method for Predicting Initial Settlement, Journal of Soil Mechanics and Foundation Division, 96(2), 1970, pp [12] Simon, R. M., Christian, J. T., and Ladd, C. C. Analysis of Undrained Behavior of Loads on Clay, Soils and Foundations: Analysis and Design in Geotechnical Engineering, Austin, Tex., ASCE, New York, 1974, pp [1] Huffman, J. C., Strahler, A. W. and Stuedlein, A. W. Reliability-Based Serviceability Limit State Design for Immediate Settlement of Spread Footings on Clay, Soils and Foundations, 55, 2015, pp [14] Sultana, P. and Dey, A. K. Estimation of Ultimate Bearing Capacity of Footings on Soft Clay from Plate Load Test Data Considering Variability, Indian Geotechnical Journal, DOI: /s [15] IS: (Reaffirmed 2002), Indian Standard Method of Load Test on Soils, Bureau of Indian Standards, New Delhi. [16] The KaleidaGraph Guide to Curve Fitting, [17] Montgomery, D. C., Peck, E. A. and Vining, G. G. Introduction to Linear Regression Analysis, Third Edition, Wiley, editor@iaeme.com

DERIVATIVE OF STRESS STRAIN, DEVIATORIC STRESS AND UNDRAINED COHESION MODELS BASED ON SOIL MODULUS OF COHESIVE SOILS

DERIVATIVE OF STRESS STRAIN, DEVIATORIC STRESS AND UNDRAINED COHESION MODELS BASED ON SOIL MODULUS OF COHESIVE SOILS International Journal of Civil Engineering and Technology (IJCIET) Volume 6, Issue 7, Jul 2015, pp. 34-43, Article ID: IJCIET_06_07_005 Available online at http://www.iaeme.com/ijciet/issues.asp?jtypeijciet&vtype=6&itype=7