Optimization of the Ultimate Bearing Capacity of Reinforced Soft Soils through the Concept of the Critical Length of Stone Columns
Vol. 7 No. 9 (2021): September
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The objective of this paper is to develop an analytical equation based on the concept of the critical-length of columns in order to optimize the ultimate bearing-capacity of soft soils, supporting a strip footing and reinforced by a group of floating stone columns. Optimization procedure was performed on three-dimensional numerical models simulated on the Flac3D computer code, for various soft-soils with different undrained-cohesions (Cu=15–35kPa), reinforced by columns of varying lengths (L) and area replacement ratio (As=10-40%), considering different footing widths B. Obtained results indicate that the optimal bearing-capacity ratio (Ultimate bearing-capacity of reinforced soil/unreinforced soil) is reached for the column critical-length ratio (Lc/B) and increase with increase of the later ratio, depending on As and Cu. Analysis of results also showed that the optimal values of the bearing-capacity ratio in the reinforced soils remain bounded between the lower and higher values (1.28-2.32), respectively for minimal and maximal values of the critical-length ratio (1.1) and (4.4). Based on these results, a useful analytical equation is proposed by the authors, for the expression of the critical-length; thus ensuring an optimal pre-dimensioning of the stone columns. The proposed equation was compared with the data available in the literature and showed good agreement.
Doi: 10.28991/cej-2021-03091737
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Boumekik, N. E. I., Labed, M., Mellas, M., & Mabrouki, A. (2021). Optimization of the Ultimate Bearing Capacity of Reinforced Soft Soils through the Concept of the Critical Length of Stone Columns. Civil Engineering Journal, 7(9), 1472–1487. https://doi.org/10.28991/cej-2021-03091737
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[22] Fattah, Mohammed Y., Mohammed A. Al-Neami, and Ahmed Shamel Al-Suhaily. "Estimation of Bearing Capacity of Floating Group of Stone Columns.” Engineering Science and Technology, an International Journal 20, no. 3 (June 2017): 1166–1172. doi:10.1016/j.jestch.2017.03.005.
[23] Najjar, Shadi S., Salah Sadek, and Tarek Maakaroun. "Effect of Sand Columns on the Undrained Load Response of Soft Clays.” Journal of Geotechnical and Geoenvironmental Engineering 136, no. 9 (September 2010): 1263–1277. doi:10.1061/(asce)gt.1943-5606.0000328.
[24] McKelvey, D., V. Sivakumar, A. Bell, and J. Graham. "Modelling Vibrated Stone Columns in Soft Clay.” Geotechnical Engineering 157, no. 3 (July 2004): 137–149. doi:10.1680/geng.157.3.137.42416.
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[27] Castro, Jorge. "Numerical Modelling of Stone Columns Beneath a Rigid Footing.” Computers and Geotechnics 60 (July 2014): 77–87. doi:10.1016/j.compgeo.2014.03.016.
[28] FLAC3D, Itasca. "Fast Lagrangian Analysis of Continua in 3 D.” Itasca Consulting Group, Ver. 3.10. Inc., (2006).
[29] Ambily, A. P., and Shailesh R. Gandhi. "Behavior of Stone Columns Based on Experimental and FEM Analysis.” Journal of Geotechnical and Geoenvironmental Engineering 133, no. 4 (April 2007): 405–415. doi:10.1061/(asce)1090-0241(2007)133:4(405).
[30] Khalifa, M., M. Etezad, A. Hanna, and M. Sabry. "Bearing Capacity of Strip Foundation on Soft Soil Reinforced with Stone Columns Using Method of Slices.” Sustainable Civil Infrastructures (July 12, 2017): 79–91. doi:10.1007/978-3-319-61902-6_8.
[31] Das, Manita, and Ashim Kanti Dey. "State of Art on Load-Carrying Capacity and Settlements of Stone Columns.” Lecture Notes in Civil Engineering (July 3, 2020): 101–124. doi:10.1007/978-981-15-4577-1_9.
[32] Ladd, Charles C. "Stress-Strain Modulus of Clay in Undrained Shear.” Journal of the Soil Mechanics and Foundations Division 90, no. 5 (September 1964): 103–132. doi:10.1061/jsfeaq.0000647.
[33] Dheerendra Babu, M. R., Sitaram Nayak, and R. Shivashankar. "A Critical Review of Construction, Analysis and Behaviour of Stone Columns.” Geotechnical and Geological Engineering 31, no. 1 (September 13, 2012): 1–22. doi:10.1007/s10706-012-9555-9.
[34] Etezad, M., A. M. Hanna, and M. Khalifa. "Bearing Capacity of a Group of Stone Columns in Soft Soil Subjected to Local or Punching Shear Failures.” International Journal of Geomechanics 18, no. 12 (December 2018): 04018169. doi:10.1061/(asce)gm.1943-5622.0001300.
[35] Zhang, Zhen, Jie Han, and Guanbao Ye. "Numerical Investigation on Factors for Deep-Seated Slope Stability of Stone Column-Supported Embankments over Soft Clay.” Engineering Geology 168 (January 2014): 104–113. doi:10.1016/j.enggeo.2013.11.004.
[2] Hanna, A. M., M. Etezad, and T. Ayadat. "Mode of Failure of a Group of Stone Columns in Soft Soil.” International Journal of Geomechanics 13, no. 1 (February 2013): 87–96. doi:10.1061/(asce)gm.1943-5622.0000175.
[3] Hu, W. E. T. "Physical Modelling of Group Behaviour of stone column foundations.” Doctoral dissertation, University of Glasgow (June 1995).
[4] Hughes, J.M.O., and N.J. Withers. "Reinforcing of Soft Cohesive Soils with Stone Columns.” International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 11, no. 11 (November 1974): A234. doi:10.1016/0148-9062(74)90643-3.
[5] Madhav, M. R., and P. P. Vitkar. "Strip Footing on Weak Clay Stabilized with a Granular Trench or Pile.” Canadian Geotechnical Journal 15, no. 4 (November 1, 1978): 605–609. doi:10.1139/t78-066.
[6] Aboshi, H., Ichimoto, E., Enoki, M., and Harada, K. "The composer ” a method to improve characteristics of soft clay by inclusion of large diameter sand columns.” In Proceedings of the International Conference on Soil Reinforcement: Reinforced Earth and other Techniques, Paris. Vol. 1. (1979): 211–216.
[7] Muir Wood, D., W. Hu, and D. F. T. Nash. "Group Effects in Stone Column Foundations: Model Tests.” Géotechnique 50, no. 6 (December 2000): 689–698. doi:10.1680/geot.2000.50.6.689.
[8] Balaam, N. P., and J. R. Booker. "Analysis of Rigid Rafts Supported by Granular Piles.” International Journal for Numerical and Analytical Methods in Geomechanics 5, no. 4 (October 1981): 379–403. doi:10.1002/nag.1610050405.
[9] Impe, W. Van. 1983. "Improvement of Settlement Behaviour of Soft Layers by Means of Stone Columns.” In Proceedings, 8th European Conference on Soil Mechanics and Foundation Engineering: Improvement of Ground, 1:309–12.
[10] Jellali, B., M. Bouassida, and P. de Buhan. "A Homogenization Method for Estimating the Bearing Capacity of Soils Reinforced by Columns.” International Journal for Numerical and Analytical Methods in Geomechanics 29, no. 10 (2005): 989–1004. doi:10.1002/nag.441.
[11] Etezad, M., A. M. Hanna, and T. Ayadat. "Bearing Capacity of a Group of Stone Columns in Soft Soil.” International Journal of Geomechanics 15, no. 2 (April 2015): 04014043. doi:10.1061/(asce)gm.1943-5622.0000393.
[12] Mitchell, James K., and Timothy R. Huber. "Performance of a Stone Column Foundation.” Journal of Geotechnical Engineering 111, no. 2 (February 1985): 205–223. doi:10.1061/(asce)0733-9410(1985)111:2(205).
[13] Elshazly, H. A., D. H. Hafez, and M. E. Mossaad. "Reliability of Conventional Settlement Evaluation for Circular Foundations on Stone Columns.” Geotechnical and Geological Engineering 26, no. 3 (January 26, 2008): 323–334. doi:10.1007/s10706-007-9169-9.
[14] Tan, Xin, Longjian Feng, Zhengbo Hu, and Minghua Zhao. "Failure Modes and Ultimate Bearing Capacity of the Isolated Stone Column in Soft Soil.” Bulletin of Engineering Geology and the Environment 80, no. 3 (January 11, 2021): 2629–2642. doi:10.1007/s10064-020-02066-5.
[15] Bouassida, Mounir, Belgacem Jellali, and Ali Porbaha. "Limit Analysis of Rigid Foundations on Floating Columns.” International Journal of Geomechanics 9, no. 3 (May 2009): 89–101. doi:10.1061/(asce)1532-3641(2009)9:3(89).
[16] Salam, Mahmood A., and Qiyao Wang. "Numerical Study on Bearing Capacity and Bulging of the Composite Stone Column.” The Open Civil Engineering Journal 15, no. 1 (March 17, 2021): 13–28. doi:10.2174/1874149502115010013.
[17] Zhou, Haizuo, Yu Diao, Gang Zheng, Jie Han, and Rui Jia. "Failure Modes and Bearing Capacity of Strip Footings on Soft Ground Reinforced by Floating Stone Columns.” Acta Geotechnica 12, no. 5 (April 4, 2017): 1089–1103. doi:10.1007/s11440-017-0535-3.
[18] Lee, J. S., and G. N. Pande. "Analysis of stone"column reinforced foundations." International Journal for Numerical and Analytical Methods in Geomechanics 22, no. 12 (1998): 1001-1020. doi:10.1002/(SICI)1096-9853(199812)22:12<1001::AID-NAG955>3.0.CO;2-I.
[19] Kumar, G., and M. Samanta. "Experimental Evaluation of Stress Concentration Ratio of Soft Soil Reinforced with Stone Column.” Innovative Infrastructure Solutions 5, no. 1 (February 12, 2020). doi:10.1007/s41062-020-0264-6.
[20] Thakur, Ankit, Saurabh Rawat, and Ashok Kumar Gupta. "Experimental and Numerical Investigation of Load Carrying Capacity of Vertically and Horizontally Reinforced Floating Stone Column Group.” Geotechnical and Geological Engineering 39, no. 4 (January 2, 2021): 3003–3018. doi:10.1007/s10706-020-01674-y.
[21] Bora, Mukul. "Regression Model for Floating Stone Column Improved Soft,” Proceedings of Indian Geotechnical Conference IGC-2014 no (December 2014).
[22] Fattah, Mohammed Y., Mohammed A. Al-Neami, and Ahmed Shamel Al-Suhaily. "Estimation of Bearing Capacity of Floating Group of Stone Columns.” Engineering Science and Technology, an International Journal 20, no. 3 (June 2017): 1166–1172. doi:10.1016/j.jestch.2017.03.005.
[23] Najjar, Shadi S., Salah Sadek, and Tarek Maakaroun. "Effect of Sand Columns on the Undrained Load Response of Soft Clays.” Journal of Geotechnical and Geoenvironmental Engineering 136, no. 9 (September 2010): 1263–1277. doi:10.1061/(asce)gt.1943-5606.0000328.
[24] McKelvey, D., V. Sivakumar, A. Bell, and J. Graham. "Modelling Vibrated Stone Columns in Soft Clay.” Geotechnical Engineering 157, no. 3 (July 2004): 137–149. doi:10.1680/geng.157.3.137.42416.
[25] Black, J. A., V. Sivakumar, M. R. Madhav, and G. A. Hamill. "Reinforced Stone Columns in Weak Deposits: Laboratory Model Study.” Journal of Geotechnical and Geoenvironmental Engineering 133, no. 9 (September 2007): 1154–1161. doi:10.1061/(asce)1090-0241(2007)133:9(1154).
[26] Das, Braja M. "Bearing capacity of shallow foundation on granular column in weak clay." In Foundation Engineering: Current Principles and Practices, ASCE (1989): 1252-1263.
[27] Castro, Jorge. "Numerical Modelling of Stone Columns Beneath a Rigid Footing.” Computers and Geotechnics 60 (July 2014): 77–87. doi:10.1016/j.compgeo.2014.03.016.
[28] FLAC3D, Itasca. "Fast Lagrangian Analysis of Continua in 3 D.” Itasca Consulting Group, Ver. 3.10. Inc., (2006).
[29] Ambily, A. P., and Shailesh R. Gandhi. "Behavior of Stone Columns Based on Experimental and FEM Analysis.” Journal of Geotechnical and Geoenvironmental Engineering 133, no. 4 (April 2007): 405–415. doi:10.1061/(asce)1090-0241(2007)133:4(405).
[30] Khalifa, M., M. Etezad, A. Hanna, and M. Sabry. "Bearing Capacity of Strip Foundation on Soft Soil Reinforced with Stone Columns Using Method of Slices.” Sustainable Civil Infrastructures (July 12, 2017): 79–91. doi:10.1007/978-3-319-61902-6_8.
[31] Das, Manita, and Ashim Kanti Dey. "State of Art on Load-Carrying Capacity and Settlements of Stone Columns.” Lecture Notes in Civil Engineering (July 3, 2020): 101–124. doi:10.1007/978-981-15-4577-1_9.
[32] Ladd, Charles C. "Stress-Strain Modulus of Clay in Undrained Shear.” Journal of the Soil Mechanics and Foundations Division 90, no. 5 (September 1964): 103–132. doi:10.1061/jsfeaq.0000647.
[33] Dheerendra Babu, M. R., Sitaram Nayak, and R. Shivashankar. "A Critical Review of Construction, Analysis and Behaviour of Stone Columns.” Geotechnical and Geological Engineering 31, no. 1 (September 13, 2012): 1–22. doi:10.1007/s10706-012-9555-9.
[34] Etezad, M., A. M. Hanna, and M. Khalifa. "Bearing Capacity of a Group of Stone Columns in Soft Soil Subjected to Local or Punching Shear Failures.” International Journal of Geomechanics 18, no. 12 (December 2018): 04018169. doi:10.1061/(asce)gm.1943-5622.0001300.
[35] Zhang, Zhen, Jie Han, and Guanbao Ye. "Numerical Investigation on Factors for Deep-Seated Slope Stability of Stone Column-Supported Embankments over Soft Clay.” Engineering Geology 168 (January 2014): 104–113. doi:10.1016/j.enggeo.2013.11.004.
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