Prediction of Compression Index of Saturated Clays Using Robust Optimization Model

Document Type : Regular Article


1 Professor, Department of Civil Engineering, Faculty of Engineering, Manisa Celal Bayar University, Manisa, Turkey

2 Assistant Professor, Department of Civil Engineering, Gonbad Kavous University, Gonbad, Iran

3 Department of Civil Engineering, Imam Khomeini International University, Iran

4 Instructor, Department of Physics, Faculty of Science, Dokuz Eylul University, Izmir, Turkey


Compression index (Cc) of normally consolidated (NC) clays determined by the oedometer experiments is utilized for calculating the consolidation settlement of shallow foundations. The determination of the Cc from the tests takes much more time and so empirical correlations based on clay properties can be a suitable alternative for the prediction of settlement. However, uncertainty in the measurements of input parameters has always been a major concern. Robust optimization is very popular due to its computational tractability for many classes of uncertainty sets and problem types. Therefore, in this research, an innovative method based on robust optimization has been used to investigate the effect of such uncertainties. To achieve these, the results of 433 oedometer tests taken from geotechnical investigation locations in Mazandaran province of Iran have been used. Based on Frobenius norm of the data points, uncertainty definition is presented and examined against the correlation coefficients for several empirical models for predicting Cc value and thus optimum values are determined. The results in compare with previous models indicate the robust method is a better pattern recognition tool for datasets with degrees of uncertainty. The variation of the Cc values with soil properties, namely, water content (ωn), initial void ratio (eo), and liquid limit (LL), by considering different value of uncertainties (0, 5 and 10%) was considered and indicated that the effect of eo is more than other two physical parameters (ωn and LL). The best model performance during in deterministic valuation and considering uncertainty is further shown.


Google Scholar


Main Subjects

[1]     MolaAbasi H, Shooshpasha I, Ebrahimi A. Prediction of Compression Index of Saturated Clays (Cc) Using polynomial models. Sci Iran 2016;23:500–7. doi:10.24200/sci.2016.2134.
[2]     Al-Taie AJ, Al-Bayati AF, Taki ZNM. Compression index and compression ratio prediction by artificial neural networks. J Eng 2017;23:96–106.
[3]     Dagdeviren U, Demir AS, Kurnaz TF. Evaluation of the Compressibility Parameters of Soils Using Soft Computing Methods. Soil Mech Found Eng 2018;55:173–80. doi:10.1007/s11204-018-9522-4.
[4]     Mohammadzadeh S D, Bolouri Bazaz J, Vafaee Jani Yazd SH, Alavi AH. Deriving an intelligent model for soil compression index utilizing multi-gene genetic programming. Environ Earth Sci 2016;75:262. doi:10.1007/s12665-015-4889-2.
[5]     Kumar R, Jain PK, Dwivedi P. Prediction of compression index (Cc) of fine grained remolded soils from basic soil properties. Int J Appl Eng Res 2016;11:592–8.
[6]     Polidori E. On the intrinsic compressibility of common clayey soils. Eur J Environ Civ Eng 2015;19:27–47. doi:10.1080/19648189.2014.926295.
[7]     Nesamatha R, Arumairaj PD. Numerical modeling for prediction of compression index from soil index properties. Electron J Geotech Eng 2015;20:4369–78.
[8]     Kurnaz TF, Dagdeviren U, Yildiz M, Ozkan O. Prediction of compressibility parameters of the soils using artificial neural network. Springerplus 2016;5:1801. doi:10.1186/s40064-016-3494-5.
[9]     Habibbeygi F. Determination of The Compression Index of Reconstituted Clays Using Intrinsic Concept And Normalized Void Ratio. Int J GEOMATE 2017;13. doi:10.21660/2017.39.98271.
[10]    Buchheim C, Kurtz J. Min-max-min robustness: a new approach to combinatorial optimization under uncertainty based on multiple solutions. Electron Notes Discret Math 2016;52:45–52. doi:10.1016/j.endm.2016.03.007.
[11]    Gorissen BL, Yanıkoğlu İ, den Hertog D. A practical guide to robust optimization. Omega 2015;53:124–37. doi:10.1016/
[12]    Yanıkoğlu İ, Gorissen BL, den Hertog D. A survey of adjustable robust optimization. Eur J Oper Res 2019;277:799–813. doi:10.1016/j.ejor.2018.08.031.
[13]    Alizadeh F, Goldfarb D. Second-order cone programming. Math Program 2003;95:3–51.
[14]    Kalantary F, MolaAbasi H, Salahi M, Veiskarami M. Prediction of liquefaction induced lateral displacements using robust optimization model. Sci Iran 2013;20:242–50.
[15]    MolaAbasi H, Kalantary F, Salahi M. Uncertainty in Shear Wave Velocity Based on Standard Penetration Test by Using Error Least Square Model. J Eng Geol 2013;6:1559–76.
[16]    Azzouz AS, Krizek RJ, Corotis RB. Regression Analysis of Soil Compressibility. Soils Found 1976;16:19–29. doi:10.3208/sandf1972.16.2_19.
[17]    Koppula S. Statistical Estimation of Compression Index. Geotech Test J 1981;4:68. doi:10.1520/GTJ10768J.
[18]    Rendon‐Herrero O. Closure to “ Universal Compression Index Equation ” by Oswald Rendon‐Herrero (November, 1980). J Geotech Eng 1983;109:755–61. doi:10.1061/(ASCE)0733-9410(1983)109:5(755).
[19]    Park H Il, Lee SR. Evaluation of the compression index of soils using an artificial neural network. Comput Geotech 2011;38:472–81. doi:10.1016/j.compgeo.2011.02.011.
[20]    Ahadiyan J, Ebne JR, Bajestan MS. Prediction determination of soil compression index, Cc. Ahwaz Reg (In Persian) J Fac Eng 2008;35:75–80.
[21]    Gunduz Z, Arman H. Possible relationships between compression and recompression indices of a low-plasticity clayey soil. Arab J Sci Eng 2007;32:179.
[22]    Farzi M. Suggesting a Formula to Calculate the Compression Index in Ahvaz. Indian J Sci Technol 2017;10:1–8. doi:10.17485/ijst/2017/v10i32/106232.
[23]    Mayne PW. Cam-Clay Predications of Undrained Strength. J Geotech Eng Div 1980;106:1219–42.
[24]    Terzaghi K, Peck RB, Mesri G. Soil Mechanics in Engineering Practice. Wiley; 1996.
[25]    Jain VK, Dixit M, Chitra R. Correlation of plasticity index and compression index of soil. Int J Innov Eng Technol 2015;5:263–70.
[26]    Al‐Khafaji AWN, Andersland OB. Equations for Compression Index Approximation. J Geotech Eng 1992;118:148–53. doi:10.1061/(ASCE)0733-9410(1992)118:1(148).
[27]    Yoon GL, Kim BT. Regression analysis of compression index for Kwangyang marine clay. KSCE J Civ Eng 2006;10:415–8. doi:10.1007/BF02823980.
[28]    Ozer M, Isik NS, Orhan M. Statistical and neural network assessment of the compression index of clay-bearing soils. Bull Eng Geol Environ 2008;67:537–45. doi:10.1007/s10064-008-0168-8.
[29]    Sturm JF. Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones. Optim Methods Softw 1999;11:625–53. doi:10.1080/10556789908805766.
[30]    Wang B. Implementation of interior point methods for second order conic optimization, MSc thesis, MacMaster University 2003.
[31]    Liu S, Cai G, Puppala AJ, Tu Q. Prediction of embankment settlements over marine clay using piezocone penetration tests. Bull Eng Geol Environ 2011;70:401–9. doi:10.1007/s10064-010-0329-4.
[32]    Dutta RK, Rani R, Rao TG. Prediction of ultimate bearing capacity of skirted footing resting on sand using artificial neural networks. J Soft Comput Civ Eng 2018;2:34–46.
[33]    Salahudeen AB, Ijimdiya TS, Eberemu AO, Osinubi KJ. Artificial neural networks prediction of compaction characteristics of black cotton soil stabilized with cement kiln dust. Soft Comput Civ Eng 2018;2:50–71. doi:10.22115/SCCE.2018.128634.1059.
[34]    Srikanth S, Mehar A. Development of MLR, ANN and ANFIS Models for estimation of PCUs at different levels of service. J Soft Comput Civ Eng 2018;2:18–35. doi:10.22115/SCCE.2018.50036.