本文主要目的在建立一套三維數值模擬程序以便分析預組式垂直排水帶(PVD)改良地盤之改良效果。在實際情況中PVD改良地盤之壓密行為應屬於三維(3-D)的問題,但為了簡化計算,通常以二維(2-D)的方式來進行分析。以二維代替三維之簡易分析方法是否適宜仍值得商榷。因此在三維模擬中，各種影響排水帶行為的因素值得進一步探討。

本研究首先對PVD改良之圓形土柱單元 (unit cell) 進行三維壓密分析,分析結果顯示數值解與數學解析解(Zeng,1988)相當吻合，因此可確認程式模擬之適當性。接著,以一實際案例-曼谷第二國際機場(SBIA)軟弱黏土層之PVD改良工程及其相關文獻求得所需之輸入參數,進行模擬分析。在三維模擬分析中同時將PVD之施工塗抹效應(smear effect)和井孔阻抗(well resistance)納入考慮。最後再將其數值分析值與現場觀測值進行比較,以評估所採用三維模擬程序在實際工程應用之有效性。由分析結果得知本研究所建立之現場三維模擬程序可有效計算現地觀測所得如沉陷率、地表沉陷量、側向位移及孔隙水壓。此外,在模擬分析過程中發現以固定之滲透係數進行現場模擬將導致沉陷量被高估,其中在壓密過程中排水帶之排水容量qw(discharge capacity)將隨著時間遞減，同時qw為PVD改良地盤壓密行為之重要影響因素。

A three-dimensional (3-D) Finite Difference Method (FDM) simulation with a simulation scheme for smear effect and well resistance in Prefabricated Vertical Drain (PVD) improved ground was proposed. The FDM computer program, FLAC3D, is employed through this study. Prefabricated vertical drain improved ground has often been analyzed by two-dimensional model due to the simplicity in computation. However, whether such an approach is adequate remains questionable. Therefore, it is desirable to investigate the effects of variable for parameters of PVD which using 3-D numerical techniques. The proposed matching schemes were incorporated into three-dimensional (3-D) Finite Difference Method (FDM) was performed on PVD unit cell. It was found that the numerical result appears good agreement with the theoretical solution and implies that the proposed matching schemes are appropriate for 3-D numerical simulation. Then, the testing embankment on prefabricated vertical drain improved ground at Second Bangkok International Airport (SBIA) was analyzed by the proposed method. The numerical predictions indicate that the proposed matching schemes are capable of applying in engineering practice. In addition, it was found that the constant permeability used in analysis may leads to overestimation of consolidation rate and the discharge capacity of PVD for the elapsed time interval is one of the influential factors on the consolidation behavior of PVD improved ground.

[1] AIT, 1995, The Full Scale Field Test of Prefabricated Vertical Drains for the Second Bangkok International Airport: Final Report-Agreement No. 24/2537, Vol. 1, Vol.2, Asian Institute of Technology, Bangkok, Thailand.

[2] Asaoka, A., Nakano, M. G. S. K. Fernando and Nozu, M., Mass permeability Concept in the Analysis of Treated Ground with Sand Drains., 1995. Soils and Foundations Vol. 35, No. 3, pp 43-53.

[3] Atkinson, M. S. and Eldred, P. J. L. Consolidation of Soil using Vertical Drains.

[4] Barron, R. A., 1948. Consolidation of Fine Grained Soils by Vertical Drains Wells, Transaction, American Society of Civil Engineers, Vol. 124.

[5] Bergado, D. T., Chai, J. C., Alfaro, M. C., and Balasubramaniam, A. S., 1992. Improvement Techniques of Soft Ground in Subsiding and Lowland Environment, Asian Institute of Technology, Bangkok, Thailand.

[6] Bergado, D.T., Mukherjee, K., Alfaro, M. C., and Balasubraniam, A.S. 1993. Perdition of Vertical-Band-Drain Performance by Finite Element Method. Geotextiles and Geomembranes 12.

[7] Bergado, D.T., and Long, P.V., 1993. Numerical Analysis of Embankment on Subsiding Ground Improved by Vertical Drains. Geotechnical Engineering Bulletin, Vol. 2, No. 3, pp. 177-188.

[8] Bergado, D. T., Alfaro, M.C., and Balasubramaniam, A. S., 1993. Improvement of Soft Bangkok Clay using Vertical Drains, Geotextiles and Geomembranes 12.

[9] Bergado, D. T., 1997. Monitoring and Evaluation of Vacuum Consolidation with PVD for the Second Bangkok International Airport at Nong Ngu Hao, Final Report, Submitted to Geotechnics Company Limited, Bangkok, Thailand.

[10] Bergado, D. T., Chatchai Eurfur, 2000., Investigations on Factors Affecting Prefabricated Vertical Drain Behaviour Including Discharge Capacity and Filter Characteristic, M.Eng. Thesie, Asian Institute of Technology, Bangkok, Thailand.

[11] Biot, M. A., 1941. General Theory of Three Dimensional Consolidation, Journal of Applied Physics, Vol. 12, pp. 155~164.

[12] Britto,A.M., and M.J.Gunn., 1987. Critical State Soil Mechanics via Finite Elements. Chichester U.K.: Elllis Horwood Ltd.

[13] Carillo, N., 1942. Simple Two Dimensional and Three Dimensional Cases in the Theory of Consolidation of Soils, Journal of Math. Phys. Vol 21, No. 1, pp. 1-5

[14] Chai, J. C., And Bergado, D. T., 1993. Some Techniques for Finite Element Analysis of Embankments on Soft Ground, Canadian Geotechnical Journal, Vol. 30, pp. 710-719.

[15] Chai, J. C., Miura, N., Sakajo, S., and Bergado, D. T., 1995. Behavior of Vertical Drain Improved Subsoil Under Embankment Loading, Soils and Foundations, Vol. 35, No. 4, pp. 49-61

[16] Chai, J.C., Bergado, D.T., Miura,N., and Sakajo, S., 1996. Back calculated field effect of vertical drain. Proc. Second Int. Conf. On Soft Soil Eng., Vol. 1, pp. 270-275, Nanjing, China.

[17] Chai, J.C.and Miura, N. 1997a. Methods for Modelling Vertical Drain improve Subsoil. Proc. China-Japan Joint Synposium on Recent Development of Theory and Practice in Geotechnology, pp. 1-8, Shanghai, China.

[18] Chai, J.C. and Miura, N. 1997b. Investigation on Some Factors affecting Vertical Drain behavior. Submitted to The Journal of Geotechnical and Environmental Engineering, ASCE.

[19] Chai, J.C., and Miura, N., 1999. Investigate of Factors Affecting Vertical Drain Behavior, Journal of Geotechnical and Geoenvironmental Engineering/ March 1999, pp.216-226

[20] Chai, J. C., Miura, N., and Bergado, D. T. Modelling Vertical Drain Improved Subsoil in 2-D Condition and Parameter Determination. Department of Civil Engineering, Saga, Japan.

[21] Cheung, Y. K., Lee, P. K. K., And Xie, K. H., 1991. Some Remarks on Two And Three Dimensional Consolidation Analysis of Sand-Drained Ground. Computers and Geotechnics, Vol. 12, pp. 73-87

[22] Federal Highway Administration 1986, Prefabricated Vertical Drains. Vol.1 Engineering Guidelines. Report No. FHWA/ RD-86/168

[23] Goughnour, R.R. 1994. Finite Strain Consolidation for Vertical Drains, Vertical and Horizontal Deformations of foundations and Embankments, Yeung, A.T. and Felio, G.Y., EDS., Geotech. Special Publ. NO. 40, ASCE, NEW York,N.Y.,1.

[24] Hansbo, S., 1960. Consolidation of Clay with Special Reference to Influence of Vertical Sand Drain, Proc Swedish Geotech. Inst., NO. 18, pp. 41-61

[25] Hansbo, S., 1979. Consolidation of Clay by Band-Shaped Prefabricated Drains. Ground Eng’g., Vol. 12, No. 5, pp. 16-25

[26] Hansbo, S., 1981. Consolidation of Fine Grained Soil by Prefabricated Drains. Proceedings of the 10th International Conference on Soil Mechanics and Foundation Engineering, Stockholm, Vol. 3, pp. 677-682

[27] Hansbo, S., 1983, How to evaluate the properties of Prefabricated drains. Ground Engrg., London, 12(5), 16-25.

[28] Hansbo, S., 1987, Design Aspects of Vertical Drains and Lime Column Installations, Proc. 9th Southeast Asian Geotech. Conf. Bankkok, Thailand, Vol. 2, pp. 8-12

[29] Hird, C. C., Pyrah, I. C., And Russel, D., 1992. Finite Element Modeling of Vertical Drains Beneath Embankments on Soft Ground. Geotechniques, Vol. 42, pp. 499-511.

[30] Hird, C. C., Pyrah, I. C., Russel, D., and Cinicioglu, F., 1995. Modeling the Effect of Vertical Drains in Two-Dimensional Finite Element Analyses of Embankments on Soft Ground. Canadian Geotechnical Journal, Vol. 32, pp. 795-807

[31] Holtz, R. D., Janiolkowski, M. B. Lancellotta, R. and Perdroni, R. 1993. Prefabricated vertical Drains: Design and Performance. Ground Engineering Report: Ground Improvement, CIRIA, pp. 1-127.

[32] Indraratna, B and Bamunawita, C. Laboratory Modeling of Prefabricated Vertical Drain Behaviour, Geotech-Year 2000, Bnakkok, Thailand, pp. 645-653.

[33] Kim, Y. T., and Lee, S. R., 1997. An Equivalent Model and Back-Analysis Technique For Modelling In Situ Consolidation Behavior of Drainage-Installed Soft Deposits, Computers and Geotechnics, Vol. 20, No. 2, pp. 125-142

[34] Kjellman, W., 1952. Consolidation of Clay Soil by means of Atmospheric Pressure, Proc. of the Conference on Soil Stabilization, Massachussetts Institute of Technology, pp. 258~263

[35] Kumamoto, N., Sumioka, N., Moriwaki, T., Yoshikuni, H. 1988. Settlement behavior of Improved Ground with Vertical Drain System, Japanese Society of Soil Mechanics and Foundation Engineering 28.

[36] Jamiolkowski, m., Lancellotta, R., and Wolski, W., 1983, Precompression and Speeding Up Consolidation, General Report, Special Session 6, Proc. 8th Europe Conf. Soil Mech. and Found. Eng’g., Helsinki, Vol. 3, pp. 1201-1226

[37] Long, R.P. and Covo, A., 1994, Equivalent Diameter of Vertical Drains with an Oblond Cross Section, J. Geotech. Eng’g. Div., ASCE, Vol. 117, No. 9, pp. 1625-1630

[38] Mesri, G. and Lo, D.O.K., 1991, Field Performance of Prefabricated Vertical Drains, Proc. Int. Conf. On Geotech. Eng’g. for Coastal Development - Theory to Practice, Yokohama, Vol. 1, pp. 231-236

[39] Mikasa, M., 1965, The Consolidation of Soft Clay, Civil Engineering in Japan, Japan Society of Civil Engineers, pp. 21-26.

[40] Onoue, A., 1988. Consolidation of Multilayered Anisotropic Soils by Vertical Drains with Well Resistance, Soils and Foundations, Vol. 28, No. 3, pp. 75-90

[41] Onoue, A., 1988. Consolidation by Vertical Drains taking Well Resistance and Smear into Consideration, Soils and Foundations, Vol. 28, No. 4, pp. 165-174

[42] Paskkaran, K., 1997, Analysis of Test Embankments with Vertical Drains, M. Eng. Thesis, Asian Institute of Technology, Bangkok, Thailand.

[43] Saha, J., 1996, Comparison of Three Test Embankments with PVD on soft Bangkok Clay, M. Eng. Thesis, Asian Institute of Technology, Bangkok, Thailand.

[44] Sekiguchi, H., Shibata, T., Fujimoto, A., And Yamaguchi, H., 1986. A Macro Element Approach to Analyzing the Plain Strain Behavior of Soft Foundation With Vertical Drain, Proc. 31st Symp. on Soil Engineering, Japanese Society of Soil Mechanics and Foundation Engineering, pp. 111-116.

[45] Terzaghi, K. and R. B. Peck. (1967), Soil Mechanics in Engineering Practice, 2nd ed., Wiley, New York.

[46] Yoshikuni, H., and Nakanodo, H., 1974. Consolidation of Soil by Vertical Drain Wells with Finite Permeability. Soils and Foundations, Vol. 14, No. 2, pp. 35-46

[47] Yoshikuni, H. and Nakanodo, H. (1975), Consolidation of a clay cylinder with external radial drainage. Soils and Foundations (Journal of the Japanese Society of Soil Mechanics and Foundation Engineering), Vol. 15, No. 1, pp. 17-27.

[48] Yoshikuni, H. (1979), Design and Control of Construction in the Vertical Drain Method. Gihoudou Publishing Co. Ltd., 208 pp.

[49] Zeng, G. X., Xie, K.H., and Shi, Z. Y., 1987. Consolidation Analysis of Sand Drained Ground by FEM. Proceedings of the 8th Asian Regional Conference on Soil Mechanics and Foundation Engineering, Kyoto, Vol. 3, pp. 139-142.

[50] Zeng, G. X., and Xie, K. H., 1989. New Development of the Vertical Drain Theories, Proc. 12th International Conference on Soil Mechanics and Foundation, Rio De Janeiro, Vol. 2, pp. 1435~1438.