Technical Papers
Jan 22, 2019

Interrelationship between Elastic Deformation and Soil-Water Characteristic Curve of Expansive Soils

Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 145, Issue 4

Abstract

Compacted and undisturbed expansive soils have widely been modeled as dual-porosity materials with two levels of pore systems: micropores and macropores. The micropores accommodate the soil activity of swelling and shrinkage behavior. However, the macropores experience a volume change mainly resulting from the structural rearrangement. Due to the deformation of the macropores, a plastic volumetric strain takes place. However, after several wetting–drying cycles, an equilibrium state is reached. Beyond the equilibrium, the volume change becomes elastic and mainly is led by the micropores. This study investigated the volume change characteristics of expansive soils from the viewpoint of the soil shrinkage curve. The slope of the normal shrinkage curve at equilibrium was found to be parallel to the saturation line. Based on these observations and laboratory test results, a conceptual framework for the interrelationship between the virgin line of the soil-water characteristic curve and the reversible volume change of the micropores is presented. Experimental data demonstrated the applicability of the presented framework to slurry and compacted soils.

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Acknowledgments

The authors thank the anonymous reviewers for their valuable comments and suggestions that improved the quality of this manuscript.

References

Airò Farulla, C., A. Ferrari, and E. Romero. 2010. “Volume change behaviour of a compacted scaly clay during cyclic suction changes.” Can. Geotech. J. 47 (6): 688–703. https://doi.org/10.1139/T09-138.
Al-Dakheeli, H. A. 2016. “Hydro-mechanical analysis of shrinkage and shrinkage cracking due to environmental loads on saturated to unsaturated expansive soils.” M.S. thesis, School of Civil and Environmental Engineering, Oklahoma State Univ.
Al-Homoud, A. S., A. A. Basma, A. I. Husein Malkawi, and M. A. Al Bashabsheh. 1995. “Cyclic swelling behavior of clays.” J. Geotech. Eng. 121 (7): 562–565. https://doi.org/10.1061/(ASCE)0733-9410(1995)121:7(562).
Alonso, E. E., A. Gens, and A. Josa. 1990. “A constitutive model for partially saturated soils.” Géotechnique 40 (3): 405–430. https://doi.org/10.1680/geot.1990.40.3.405.
Alonso, E. E., N. M. Pinyol, and A. Gens. 2013. “Compacted soil behaviour: Initial state, structure and constitutive modelling” Géotechnique 63 (6): 463. https://doi.org/10.1680/geot.11.P.134.
Alonso, E. E., E. Romero, C. Hoffmann, and E. García-Escudero. 2005. “Expansive bentonite–sand mixtures in cyclic controlled-suction drying and wetting.” Eng. Geol. 81 (3): 213–226. https://doi.org/10.1016/j.enggeo.2005.06.009.
Alonso, E. E., J. Vaunat, and A. Gens. 1999. “Modelling the mechanical behaviour of expansive clays.” Eng. Geol. 54 (1): 173–183. https://doi.org/10.1016/S0013-7952(99)00079-4.
ASTM. 2012. Standard test methods for laboratory compaction characteristics of soil using standard effort (12400  ft-lbf/ft3 (600  kN-m/m3)). ASTM D698. West Conshohocken, PA: ASTM.
Azam, S., M. Ito, and R. Chowdhury. 2013. “Engineering properties of an expansive soil.” In Proc., 18th Int. Conf. on Soil Mechanics and Geotechnical Engineering. Paris: Presses des Ponts.
Baker, R., and S. Frydman. 2009. “Unsaturated soil mechanics: Critical review of physical foundations.” Eng. Geol. 106 (1): 26–39. https://doi.org/10.1016/j.enggeo.2009.02.010.
Bani Hashem, E., and S. L. Houston. 2015. “Volume change consideration in determining unsaturated soil properties for geotechnical applications.” Int. J. Geomech. 16 (6): D4015003. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000586.
Basma, A. A., A. S. Al-Homoud, A. I. H. Malkawi, and M. A. Al-Bashabsheh. 1996. “Swelling-shrinkage behavior of natural expansive clays.” Appl. Clay Sci. 11 (2–4): 211–227. https://doi.org/10.1016/S0169-1317(96)00009-9.
Baumgartl, T., and B. Köck. 2004. “Modeling volume change and mechanical properties with hydraulic models.” Soil Sci. Soc. Am. J. 68 (1): 57–65. https://doi.org/10.2136/sssaj2004.5700.
Braudeau, E., R. H. Mohtar, and N. Chahinian. 2004. “Estimating soil shrinkage parameters.” In Vol. 30 of Development of pedotransfer functions in soil hydrology: Developments in soil science, edited by Y. Pachepsky and W. Rawls, 1st ed., 225–240. Amsterdam, Netherlands: Elsevier Science.
Bulut, R., and E. C. Leong. 2008. “Indirect measurement of suction.” Geotech. Geol. Eng. 26 (6): 633–644. https://doi.org/10.1007/s10706-008-9197-0.
Chen, F. H. 2012. Vol. 12 of Foundations on expansive soils. New York: Elsevier.
Chertkov, V. Y. 2008. “The physical effects of an intra-aggregate structure on soil shrinkage.” Geoderma 146 (1): 147–156. https://doi.org/10.1016/j.geoderma.2008.05.011.
Cornelis, W. M., J. Corluy, H. Medina, J. Diaz, R. Hartmann, M. Van Meirvenne, and M. E. Ruiz. 2006. “Measuring and modelling the soil shrinkage characteristic curve.” Geoderma 137 (1): 179–191. https://doi.org/10.1016/j.geoderma.2006.08.022.
Croney, D., and J. D. Coleman. 1953. “Soil moisture suction properties and their bearing on the moisture distribution on soils.” In Proc., 3rd Int. Conf. of Soil Mechanics and Foundation Engineering, 13–18. Zurich, Switzerland: Organizing Committee ICOSOMEF.
Day, R. W. 1994. “Swell-shrink behavior of compacted clay.” J. Geotech. Eng. 120 (3): 618–623. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:3(618).
Delage, P., and J. Graham. 1996. “Mechanical behaviour of unsaturated soils: Understanding the behaviour of unsaturated soils requires reliable conceptual models.” In Vol. 3 of Proc., 1st Int. Conf. on Unsaturated Soils, 1223–1256. Paris: Presses de l'Ecole Nationale des Ponts et Chaussées.
Della Vecchia, G., A. C. Dieudonné, C. Jommi, and R. Charlier. 2015. “Accounting for evolving pore size distribution in water retention models for compacted clays.” Int. J. Numer. Anal. Methods Geomech. 39 (7): 702–723. https://doi.org/10.1002/nag.2326.
Dieudonné, A. C., G. Della Vecchia, and R. Charlier. 2017. “Water retention model for compacted bentonites.” Can. Geotech. J. 54 (7): 915–925. https://doi.org/10.1139/cgj-2016-0297.
Dif, A., and W. Bluemel. 1991. “Expansive soils under cyclic drying and drying.” Geotech. Test. J. 14 (1): 96–102. https://doi.org/10.1520/GTJ10196J.
Estabragh, A. R., B. Parsaei, and A. A. Javadi. 2015. “Laboratory investigation of the effect of cyclic wetting and drying on the behaviour of an expansive soil.” Soils Found. 55 (2): 304–314. https://doi.org/10.1016/j.sandf.2015.02.007.
Fityus, S., and O. Buzzi. 2009. “The place of expansive clays in the framework of unsaturated soil mechanics.” Appl. Clay Sci. 43 (2): 150–155. https://doi.org/10.1016/j.clay.2008.08.005.
Fredlund, D. G., and S. L. Houston. 2013. “Interpretation of soil-water characteristic curves when volume change occurs as soil suction is changed.” In Proc., 1st Pan-American Conf. on Advances in Unsaturated Soils, 15–31. Boca Raton, FL: CRC Press.
Fredlund, D. G., and N. R. Morgenstern. 1977. “Stress state variables for unsaturated soils.” J. Geotech. Geoenviron. Eng. Div. 103 (5): 447–466.
Fredlund, D. G., H. Rahardjo, and M. D. Fredlund. 2012. Unsaturated soil mechanics in engineering practice. New York: Wiley.
Fredlund, D. G., and A. Xing. 1994. “Equations for the soil-water characteristic curve.” Can. Geotech. J. 31 (4): 521–532. https://doi.org/10.1139/t94-061.
Fredlund, D. G., A. Xing, and S. Huang. 1994. “Predicting the permeability function for unsaturated soils using the soil-water characteristic curve.” Can. Geotech. J. 31 (4): 533–546. https://doi.org/10.1139/t94-062.
Fredlund, D. G., and F. Zhang. 2013. “Combination of shrinkage curve and soil-water characteristic curves for soils that undergo volume change as soil suction is increased.” In Proc., 18th Int. Conf. on Soil Mechanics and Geotechnical Engineering. Paris: Presses des Ponts.
Fredlund, M. D., G. W. Wilson, and D. G. Fredlund. 2002. “Representation and estimation of the shrinkage curve.” In Proc., 3rd Int. Conf. on Unsaturated Soils (UNSAT 2002), 145–149. Leiden, Netherlands: A.A. Balkema.
Frydman, S., and R. Baker. 2009. “Theoretical soil-water characteristic curves based on adsorption, cavitation, and a double porosity model.” Int. J. Geomech. 9 (6): 250–257. https://doi.org/10.1061/(ASCE)1532-3641(2009)9:6(250).
Gallipoli, D. B. 2012. “A hysteretic soil-water retention model accounting for cyclic variations of suction and void ratio.” Geotechnique 62 (7): 605–616. https://doi.org/10.1680/geot.11.P.007.
Gallipoli, D. B., and A. W. Bruno. 2017. “A bounding surface compression model with a unified virgin line for saturated and unsaturated soils.” Géotechnique 67 (8): 703–712. https://doi.org/10.1680/jgeot.16.P.145.
Gens, A., and E. E. Alonso. 1992. “A framework for the behaviour of unsaturated expansive clays.” Can. Geotech. J. 29 (6): 1013–1032. https://doi.org/10.1139/t92-120.
Gerke, H. H. 2006. “Preferential flow descriptions for structured soils.” J. Plant Nutr. Soil Sci. 169 (3): 382–400. https://doi.org/10.1002/jpln.200521955.
Gerke, H. H., and M. T. van Genuchten. 1996. “Macroscopic representation of structural geometry for simulating water and solute movement in dual-porosity media.” Adv. Water Resour. 19 (6): 343–357. https://doi.org/10.1016/0309-1708(96)00012-7.
Guney, Y., D. Sari, M. Cetin, and M. Tuncan. 2007. “Impact of cyclic wetting–drying on swelling behavior of lime-stabilized soil.” Build. Environ. 42 (2): 681–688. https://doi.org/10.1016/j.buildenv.2005.10.035.
Jiang, Y., W. Chen, G. Wang, G. Sun, and F. Zhang. 2017. “Influence of initial dry density and water content on the soil–water characteristic curve and suction stress of a reconstituted loess soil.” Bull. Eng. Geol. Environ. 76 (3): 1085–1095. https://doi.org/10.1007/s10064-016-0899-x.
Johnston, J. R., and H. O. Hill. 1945. “A study of the shrinking and swelling properties of Rendzina soils.” Soil Sci. Soc. Am. J. 9: 24–29. https://doi.org/10.2136/sssaj1945.036159950009000C0004x.
Kalkan, E. 2011. “Impact of wetting–drying cycles on swelling behavior of clayey soils modified by silica fume.” Appl. Clay Sci. 52 (4): 345–352. https://doi.org/10.1016/j.clay.2011.03.014.
Koliji, A., L. Vulliet, and L. Laloui. 2010. “Structural characterization of unsaturated aggregated soil.” Can. Geotech. J. 47 (3): 297–311. https://doi.org/10.1139/T09-089.
Larsbo, M., S. Roulier, F. Stenemo, R. Kasteel, and N. Jarvis. 2005. “An improved dual-permeability model of water flow and solute transport in the vadose zone.” Vadose Zone J. 4 (2): 398–406. https://doi.org/10.2136/vzj2004.0137.
Larsson, M. H., and N. J. Jarvis. 1999. “Evaluation of a dual-porosity model to predict field-scale solute transport in a macroporous soil.” J. Hydrol. 215 (1): 153–171. https://doi.org/10.1016/S0022-1694(98)00267-4.
Li, X., and L. M. Zhang. 2009. “Characterization of dual-structure pore-size distribution of soil.” Can. Geotech. J. 46 (2): 129–141. https://doi.org/10.1139/T08-110.
Li, X., L. M. Zhang, and L. Z. Wu. 2014. “A framework for unifying soil fabric, suction, void ratio, and water content during the dehydration process.” Soil Sci. Soc. Am. J. 78 (2): 387–399. https://doi.org/10.2136/sssaj2013.08.0362.
Likos, W. J. 2004. “Measurement of crystalline swelling in expansive clay.” Geotech. Test. J. 27 (6): 540–546. https://doi.org/10.1520/GTJ11857.
Lloret Morancho, A., M. V. Villar, M. Sanchez, A. Gens Solé, X. Pintado Llurba, and E Alonso Pérez de Agreda. 2003. “Mechanical behaviour of heavily compacted bentonite under high suction changes.” Géotechnique 53 (1): 27–40. https://doi.org/10.1680/geot.2003.53.1.27.
Lu, N., J. W. Godt, and D. T. Wu. 2010. “A closed-form equation for effective stress in unsaturated soil.” Water Resour. Res. 46 (5): 1–14. https://doi.org/10.1029/2009WR008646.
Lytton, R. L. 1977. “Foundations in expansive soils.” In Numerical methods in geotechnical engineering, edited by C. S. Desai and J. T. Christian, 427–457. New York: McGraw Hill.
Lytton, R. L. 1994. “Prediction of movement in expansive clays.” In Vol. 2 of Proc., Vertical and Horizontal Deformations of Foundations and Embankments, Geotechnical Special Publication No. 40, edited by A. T. Yeung and G. Y. Felio, 1827–1845. New York: ASCE.
Lytton, R. L., C. Aubeny, and R. Bulut. 2005. Vol. 1 of Design procedure for pavements on expansive soils. San Antonio: Texas Transportation Institute.
Mašín, D. 2010. “Predicting the dependency of a degree of saturation on void ratio and suction using effective stress principle for unsaturated soils.” Int. J. Numer. Anal. Methods Geomech. 34 (1): 73–90. https://doi.org/10.1002/nag.808.
Mašín, D. 2013. “Double structure hydromechanical coupling formalism and a model for unsaturated expansive clays.” Eng. Geol. 165 (Oct): 73–88. https://doi.org/10.1016/j.enggeo.2013.05.026.
McKeen, R. G. 1992. “A model for predicting expansive soil behavior.” In Proc., 7th Int. Conf. on Expansive Soils, 1–6. Lubbock, TX: Texas Tech University Press.
Mitchell, J. K., and K. Soga. 2005. Fundamentals of soil behavior. Hoboken, NJ: Wiley.
Musso, G., E. Romero, and G. Della Vecchia. 2013. “Double-structure effects on the chemo-hydro-mechanical behaviour of a compacted active clay.” Geotechnique 63 (3): 206–220. https://doi.org/10.1680/geot.SIP13.P.011.
Nowamooz, H., and F. Masrouri. 2008. “Hydromechanical behaviour of an expansive bentonite/silt mixture in cyclic suction-controlled drying and wetting tests.” Eng. Geol. 101 (3): 154–164. https://doi.org/10.1016/j.enggeo.2008.04.011.
Nowamooz, H., and F. Masrouri. 2010. “Mechanical behaviour of expansive soils after several drying and wetting cycles.” Geomech. Geoeng.: Int. J. 5 (4): 213–221. https://doi.org/10.1080/17486025.2010.521588.
Osipov, V. I., N. N. Bik, and N. A. Rumjantseva. 1987. “Cyclic swelling of clays.” Appl. Clay Sci. 2 (4): 363–374. https://doi.org/10.1016/0169-1317(87)90042-1.
Pedrotti, M., and A. Tarantino. 2014. “Microstructural interpretation of compression behaviour of compacted kaolin clay.” In Unsaturated soils, 739–745. Leiden, Netherlands: CRC Press.
Popescu, M. 1980. “Behaviour of expansive soils with a crumb structure.” In Vol. 1 of Proc., 4th Int. Conf. on Expansive Soils, 158–171. Reston, VA: ASCE.
Rao, P. S. C., D. E. Rolston, R. E. Jessup, and J. M. Davidson. 1980. “Solute transport in aggregated porous media: Theoretical and experimental evaluation.” Soil Sci. Soc. Am. J. 44 (6): 1139–1146. https://doi.org/10.2136/sssaj1980.03615995004400060003x.
Rao, S. M., and K. Revanasiddappa. 2006. “Influence of cyclic wetting drying on collapse behaviour of compacted residual soil.” Geotech. Geol. Eng. 24 (3): 725–734. https://doi.org/10.1007/s10706-004-5077-4.
Romero, E., A. Gens, and A. Lloret. 1999. “Water permeability, water retention and microstructure of unsaturated compacted Boom clay.” Eng. Geol. 54 (1–2): 117–127. https://doi.org/10.1016/S0013-7952(99)00067-8.
Rosenbalm, D., and C. E. Zapata. 2016. “Effect of wetting and drying cycles on the behavior of compacted expansive soils.” J. Mater. Civ. Eng. 29 (1): 04016191. https://doi.org/10.1061/(ASCE)MT.1943-5533.0001689.
Salager, S., M. S. El Youssoufi, and C. Saix. 2010. “Definition and experimental determination of a soil-water retention surface.” Can. Geotech. J. 47 (6): 609–622. https://doi.org/10.1139/T09-123.
Salager, S., M. Nuth, A. Ferrari, and L. Laloui. 2013. “Investigation into water retention behaviour of deformable soils” Can. Geotech. J. 50 (2): 200–208. https://doi.org/10.1139/cgj-2011-0409.
Sánchez, M., A. Gens, L. do Nascimento Guimarães, and S. Olivella. 2005. “A double structure generalized plasticity model for expansive materials.” Int. J. Numer. Anal. Methods Geomech. 29 (8): 751–787. https://doi.org/10.1002/nag.434.
Seiphoori, A., A. Ferrari, and L. Laloui. 2014. “Water retention behaviour and microstructural evolution of MX-80 bentonite during wetting and drying cycles.” Géotechnique 64 (9): 721–734. https://doi.org/10.1680/geot.14.P.017.
Sheng, D., S. Zhang, and Z. Yu. 2013. “Unanswered questions in unsaturated soil mechanics.” Sci. China Technol. Sci. 56 (5): 1257–1272. https://doi.org/10.1007/s11431-013-5202-9.
Sitharam, T. G., P. V. Sivapulloiah, and K. S. Subba Rao. 1995. “Shrinkage behaviour of compacted unsaturated soil.” In Proc., 1st Int. Conf. on Unsaturated Soil, 195–200. Paris: Presses de l'Ecole Nationale des Ponts et Chaussées.
Snethen, D. R., and G. Huang. 1992. “Evaluation of soil suction-heave prediction methods.” In Proc., 7th Int. Conf. on Expansive Soils, 12–17. Lubbock, TX: Texas Tech University Press.
Subba Rao, K. S., and G. G. Satyadas. 1987. “Swelling potential with cycles of swelling and partial shrinkage.” In Vol. 1 of Proc., 6th Int. Conf. on Expansive Soils, 137–142. New Delhi, India: Central Board of Irrigation and Power.
Sun, D. A., D. Sheng, L. Xiang, and S. W. Sloan. 2008. “Elastoplastic prediction of hydro-mechanical behaviour of unsaturated soils under undrained conditions” Comput. Geotech. 35 (6): 845–852. https://doi.org/10.1016/j.compgeo.2008.08.002.
Tarantino, A., and E. De Col. 2008. “Compaction behaviour of clay.” Géotechnique 58 (3): 199–213. https://doi.org/10.1680/geot.2008.58.3.199.
Thom, R., R. Sivakumar, V. Sivakumar, E. Murray, and P. A. MacKinnon. 2007. “Pore size distribution of unsaturated compacted kaolin: The initial states and final states following saturation.” Geotechnique 57 (5): 469–474. https://doi.org/10.1680/geot.2007.57.5.469.
Thyagaraj, T., S. R. Thomas, and A. P. Das. 2016. “Physico-chemical effects on shrinkage behavior of compacted expansive clay.” Int. J. Geomech. 17 (2): 06016013. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000698.
Toll, D. G. 1995. “A conceptual model for the drying and wetting of soil.” In Vol. 2 of Proc., 1st Int. Conf. on Unsaturated Soils. Paris: Presses de l'Ecole Nationale des Ponts et Chaussées.
Tripathy, S., and K. S. S. Rao. 2009. “Cyclic swell–shrink behaviour of a compacted expansive soil.” Geotech. Geol. Eng. 27 (1): 89–103. https://doi.org/10.1007/s10706-008-9214-3.
Tripathy, S., K. S. S. Rao, and D. G. Fredlund. 2002. “Water content - void ratio swell-shrink paths of compacted expansive soils.” Can. Geotech. J. 39 (4): 938–959. https://doi.org/10.1139/t02-022.
Umezaki, T., and T. Kawamura. 2013. “Shrinkage and desaturation properties during desiccation of reconstituted cohesive soil.” Soils Found. 53 (1): 47–63. https://doi.org/10.1016/j.sandf.2012.12.003.
Vanapalli, S. K., D. G. Fredlund, and D. E. Pufahl. 1996. “The relationship between the soil water characteristic curve and the unsaturated shear strength of a compacted glacial till.” Geotech. Test. J. 19 (3): 259–268. https://doi.org/10.1520/GTJ10351J.
Van Genuchten, M. T. 1980. “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J. 44 (5): 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x.
Van Genuchten, M. T., and P. J. Wierenga. 1976. “Mass transfer studies in sorbing porous media I. Analytical solutions.” Soil Sci. Soc. Am. J. 40 (4): 473–480. https://doi.org/10.2136/sssaj1976.03615995004000040011x.
Wang, G., and X. Wei. 2014. “Modeling swelling–shrinkage behavior of compacted expansive soils during wetting–drying cycles.” Can. Geotech. J. 52 (6): 783–794. https://doi.org/10.1139/cgj-2014-0059.
Wheeler, S. J., R. S. Sharma, and M. S. R. Buisson. 2003. “Coupling of hydraulic hysteresis and stress–strain behaviour in unsaturated soils.” Géotechnique 53 (1): 41–54. https://doi.org/10.1680/geot.2003.53.1.41.
Wijaya, M., and E. C. Leong. 2017. “Modelling the effect of density on the unimodal soil-water characteristic curve.” Géotechnique 67 (7): 637–645. https://doi.org/10.1680/jgeot.15.P.270.
Wijaya, M., E. C. Leong, and H. Rahardjo. 2015. “Effect of shrinkage on air-entry value of soils.” Soils Found. 55 (1): 166–180. https://doi.org/10.1016/j.sandf.2014.12.013.
Zapata, C. E., W. N. Houston, S. L. Houston, and K. D. Walsh. 2000. “Soil-water characteristic curve variability.” In Proc., Geo-Denver 2000, Advances in Unsaturated Geotechnics, 84–124. Reston, VA: ASCE.
Zemenu, G., A. Martine, and C. Roger. 2009. “Analysis of the behaviour of a natural expansive soil under cyclic drying and wetting.” Bull. Eng. Geol. Environ. 68 (3): 421–436.
Zhou, A. N., D. Sheng, and J. P. Carter. 2012. “Modelling the effect of initial density on soil-water characteristic curves.” Géotechnique 62 (8): 669–680. https://doi.org/10.1680/geot.10.P.120.

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Journal of Geotechnical and Geoenvironmental Engineering
Volume 145Issue 4April 2019

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Received: Oct 23, 2017
Accepted: Sep 10, 2018
Published online: Jan 22, 2019
Published in print: Apr 1, 2019
Discussion open until: Jun 22, 2019

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Hussein Al-Dakheeli, S.M.ASCE [email protected]
Ph.D. Student, School of Civil and Environmental Engineering, Oklahoma State Univ., Stillwater, OK 74078. Email: [email protected]
Rifat Bulut, M.ASCE [email protected]
Professor, School of Civil and Environmental Engineering, Oklahoma State Univ., Stillwater, OK 74078 (corresponding author). Email: [email protected]

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