The PVD-Accelerated Soil Deposit Consolidation Based on Elliptic Cylindrical Model

Yulvi Zaika, Gilang R. Kololikiye, . Harimurti


One method to deal with the problem of soft soil is to accelerate consolidation by preloading and prefabricating a vertical drain (PVD). Consolidation analysis was based on a one-dimensional theory that required PVD as an equivalent circular well. Further studies on a simple approximate for consolidated soil were represented by equivalent permeability coefficients, kve. The equivalent conductivity coefficient is influenced by the soil and PVD permeability coefficients. The formulation of kve based on the influence area in cylindrical has been applied to a lot of construction projects. According to the comparative analysis of the classical consolidation theory, it is considered that the diameter of the circle is less representative. This study proposed a simple formulation of kve based on the elliptical assumption of influence area. The kvewas derived based on an equal average degree of consolidation in one dimension, which applied the elliptical coordinate for degree of consolidation in the radial direction. The formulation is based on an elliptical cross-section and a cylindrical coordinate formulation. The validation of this formula is conducted with numerical calculations using 2D FEM. The results show that the consolidation time in the elliptical discharge area is shorter than that in the circular discharge area.


Doi: 10.28991/CEJ-2023-09-07-08

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Vertical Permeability Equivalence; Consolidation; Influence Area; Radial; Ellipse.


Lu, M., Li, D., Jing, H., & Deng, Y. (2019). Analytical Solution for Consolidation of Band-Shaped Drain Based on an Equivalent Annular Drain. International Journal of Geomechanics, 19(6). doi:10.1061/(asce)gm.1943-5622.0001423.

Abuel-Naga, H., & Bouazza, A. (2009). Equivalent diameter of a prefabricated vertical drain. Geotextiles and Geomembranes, 27(3), 227–231. doi:10.1016/j.geotexmem.2008.11.006.

Lorenzo, G. A., Bergado, D. T., Bunthai, W., Hormdee, D., & Phothiraksanon, P. (2004). Innovations and performances of PVD and dual function geosynthetic applications. Geotextiles and Geomembranes, 22(1–2), 75–99. doi:10.1016/S0266-1144(03)00053-0.

Rowe, R. K., & Li, A. L. (2005). Geosynthetic-reinforced embankments over soft foundations. Geosynthetics International, 12(1), 50–85. doi:10.1680/gein.

Shen, S. L., Chai, J. C., Hong, Z. S., & Cai, F. X. (2005). Analysis of field performance of embankments on soft clay deposit with and without PVD-improvement. Geotextiles and Geomembranes, 23(6), 463–485. doi:10.1016/j.geotexmem.2005.05.002.

Li, A. L., & Rowe, R. K. (2001). Combined effects of reinforcement and prefabricated vertical drains on embankment performance. Canadian Geotechnical Journal, 38(6), 1266–1282. doi:10.1139/t01-059.

Arivalagan, J., Indraratna, B., Rujikiatkamjorn, C., & Warwick, A. (2022). Effectiveness of a Geocomposite-PVD system in preventing subgrade instability and fluidisation under cyclic loading. Geotextiles and Geomembranes, 50(4), 607-617. doi:10.1016/j.geotexmem.2022.03.001.

Rowe, R. K., & Taechakumthorn, C. (2008). Combined effect of PVDs and reinforcement on embankments over rate-sensitive soils. Geotextiles and Geomembranes, 26(3), 239–249. doi:10.1016/j.geotexmem.2007.10.001.

Hansbo, S. (1979). Consolidation of Clay by Band-Shaped Prefabricated Drains. Ground Engineering, 12(5), 16–18, 21. doi:10.1016/0148-9062(80)90141-2.

Long, R. P., & Covo, A. (1994). Equivalent diameter of vertical drains with an oblong cross section. Journal of Geotechnical Engineering, 120(9), 1625–1630. doi:10.1061/(ASCE)0733-9410(1994)120:9(1625).

Welker, A. L., & Herdin, K. M. (2003). Evaluation of four equivalent diameter formulations for prefabricated vertical drains using flow rates. Geosynthetics International, 10(3), 103–109. doi:10.1680/gein.2003.10.3.103.

Chai, J.-C., Shen, S.-L., Miura, N., & Bergado, D. T. (2001). Simple Method of Modeling PVD-Improved Subsoil. Journal of Geotechnical and Geoenvironmental Engineering, 127(11), 965–972. doi:10.1061/(asce)1090-0241(2001)127:11(965).

Karstunen, M., & Yildiz, A. (2008). Three-dimensional analyses of PVD-improved soft soils. Geotechnics of Soft Soils: Focus on Ground Improvement, 197–203. doi:10.1201/9780203883334.ch23.

Huang, C., Deng, Y., & Chen, F. (2016). Consolidation theory for prefabricated vertical drains with elliptic cylindrical assumption. Computers and Geotechnics, 77, 156–166. doi:10.1016/j.compgeo.2016.04.015.

Tian, Y., Wu, W., Jiang, G., Hesham El Naggar, M., Mei, G., & Ni, P. (2019). Analytical solutions for vacuum preloading consolidation with prefabricated vertical drain based on elliptical cylinder model. Computers and Geotechnics, 116, 103202. doi:10.1016/j.compgeo.2019.103202.

Barron, R. A. (1948). Consolidation of fine-grained soils by drain wells by drain wells. Transactions of the American Society of Civil Engineers, 113(1), 718-742. doi:10.1061/TACEAT.0006098.

Carrillo, N. (1942). Simple two and three dimensional case in the theory of consolidation of soils. Journal of Mathematics and Physics, 21(1-4), 1-5. doi:10.1002/sapm19422111.

Atkinson, M. S., & Eldred, P. J. L. (1981). Consolidation of soil using vertical drains. Geotechnique, 31(1), 33–43. doi:10.1680/geot.1981.31.1.33.

Fellenius, B. H., & Castonguay, N. G. (1985). The efficiency of band shaped drains: a full scale laboratory study. Report to National Research Council and the Industrial Research Assistance Programme, 1(2), 27-35.

Zaika, Y., Rachmansyah, A., & Harimurti. (2019). Geotechnical behaviour of soft soil in East Java, Indonesia. IOP Conference Series: Materials Science and Engineering, 615(1), 12043. doi:10.1088/1757-899X/615/1/012043.

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DOI: 10.28991/CEJ-2023-09-07-08


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