摘 要
國內都會區捷運系統及下水道工程興建時，為減少對地面交通的衝擊，常採用隧道工法施工。然而在都會區進行隧道施工，周圍地盤往往有許多鄰近結構及地下維生管線。因此如何預測隧道開挖引致的地盤沉陷，評估其對鄰近結構物及地下維生管線之影響，就成為工程師關心的主要課題。另外，由於都市路權取得困難，上下行隧道通常併行而且相當靠近；因此兩隧道之互制行為及雙隧道開挖對周圍地盤之影響，值得進一步研究。
本研究在平面應變條件下分別以離心模型試驗和有限差分程式FLAC進行隧道開挖解壓變形之模擬，在隧道內施加支撐氣壓以維持隧道初始的穩定，然後逐步解除支撐氣壓來模擬開挖的過程。分別針對單隧道及左右併行雙隧道進行模型試驗及數值分析，藉由改變隧道的埋置深度和兩隧道的中心距離，探討單隧道及雙隧道的破壞機制，以及隧道開挖對周圍地盤變位、土壤應力及孔隙水壓之影響。另外，以15組國內外潛盾施工監測資料進行案例分析，驗證模型試驗和數值分析之預測成效。
根據試驗結果，考慮隧道埋置深度，建立土壤漏失量和地表沉陷之關係；若已知單隧道施工的土壤漏失量，便可由所建議的方法預測單隧道和雙隧道開挖所引致的地表沉陷。至於地下沉陷槽，考慮隧道所在深度，提出地下沉陷槽寬度參數隨著所在深度而遞減的關係式。統計經驗法之應用方面，以常態機率曲線迴歸單隧道地表沉陷槽求得沉陷槽寬度參數，將此沉陷槽寬度參數乘上0.85配合單隧道最大地表沉陷量，以兩個單隧道沉陷槽曲線疊加，可合理預測距徑比為1.5至2之雙隧道地表沉陷槽；對於距徑比大於2之雙隧道，建議直接以單隧道沉陷槽寬度參數配合最大沉陷量疊加。此外，以彈性理論分析隧道周圍地盤之應力變化，由塑性力學之上限理論推導單隧道和雙隧道之地盤破壞機制，和試驗量得之地盤位移方向相符。經過15組國內外潛盾施工監測資料之案例分析，由試驗結果所預測之地表沉陷和監測資料頗為接近，驗證了本研究所提出建議公式之預測成效。
數值分析部份，以FLAC程式建立和離心模型相同邊界條件與材料參數的數值模型，分析單隧道和雙隧道開挖引致的地盤沉陷及土壤應力變化。在隧道破壞前，數值分析所得橫斷面地表沉陷槽分佈型態和試驗量測結果大致接近。根據試驗量測之孔隙水壓反應和數值分析所得之地盤應力變化，繪製地拱效應的作用範圍，並以此解釋隧道周圍地盤應力的轉移機制及兩隧道的互制行為；若是在此作用範圍內有地下結構物，則必須考慮隧道開挖對地下結構物應力增量之影響。由試驗量測、數值分析及塑性理論求得超載係數之下限值與上限值，可用來評估隧道之穩定性。綜合離心模型試驗與數值分析成果，經過與現場監測資料相互驗證之後，提出預測單隧道和雙隧道施工引致地盤沉陷之方法，提供工程應用之參考。

Abstract
In order to reduce the interference with the surface traffic, tunnelling methods have been widely used in the construction of metro and sewage systems in Taipei. However, these tunnels were driven through the ground where structures and lifelines already existed. Therefore, it is very important for engineers to evaluate the impacts of tunnelling on the environment, i.e. the effect of surface settlement on adjacent buildings and the influence of subsurface ground movements on underground pipelines. Besides, because the tunnels in cities are usually driven in limited areas, the down track tunnel and up track tunnel are parallel and very close to each other. Hence, it is necessary to evaluate the settlements induced by parallel tunnelling and the interaction between two tunnels.
In this study, both centrifuge model tests and a finite difference program (FLAC) have been taken in plane strain conditions to investigate the tunnel stability and soil movements for both the single tunnel and parallel tunnels. A series of model tests was performed in centrifugal acceleration of 100g, including the single tunnel with various cover-to-diameter ratio (C/D) and the parallel tunnels with various C/D and distance-to-diameter ratio (d/D). The supporting air pressure was applied inside the tunnels to keep the tunnels in equilibrium during the accelerating stage, and then the supporting pressure was reduced gradually to simulate the process of excavation. From centrifuge modelling and numerical modelling, the ground movements and the changes of soil stresses and pore water pressures could be studied. Besides, 15 field cases of measured surface settlements due to shield tunnelling in Taipei were used to verify the predictions from centrifuge modelling and numerical modelling.
From test results, the relationships of both the volume of ground loss versus the maximum settlement and the burial depth of tunnels versus the width parameter of the settlement trough have been proposed. Since the volume of ground loss could be evaluated prior to tunnel construction and the burial depth was determined in the preliminary design stage, the settlement troughs induced by single tunnelling and parallel tunnelling could be predicted. Using empirical methods, the settlement troughs can be reasonably fit by a Normal Distribution Curve suggested by Peck (1969). By superimposing two curves with a factor of 0.85 times the width parameter fit from the single tunnel, the settlement trough due to parallel tunnelling with d/D less than 2 may be estimated. For the parallel tunnels with d/D greater than 2, the simple superposition of two settlement curves from single tunnel is suggested. Besides, the collapse mechanisms of both single tunnel and parallel tunnels derived from upper bound theorem compared well with the observed ground movements. From 15 case studies in field, the predicted settlements show reasonable agreement with the field data. Hence, the prediction from proposed formula is verified.
In addition, the program FLAC was carried out to solve the whole problem in the same material and boundary conditions as those in centrifuge tests. The surface settlement troughs computed from FLAC show reasonable agreement with results measured from model tests. According the pore water pressures measured from model tests and the soil stresses computed from numerical analysis, the extent of soil arching for single tunnel and parallel tunnels could be defined. It may be adopted to explain the transferring mechanism of soil stresses around tunnels and the interaction between parallel tunnels. If the underground facilities existed within the extent of soil arching, the influence of tunnelling to those structures should be taken into account. Based on test results, numerical modelling and theoretical solutions, the lower bound and upper bound of overload factors are determined for evaluation of tunnel stability. From test results verified by numerical modelling and field measurement, this study may provide reliable predictions of ground movements induced by single tunnelling and parallel tunnelling.

參 考 文 獻
方永壽、陳秋宗，「潛盾隧道施工盾尾孔隙所引致之地盤沉陷」，榮工技術叢書，第151-163頁 (1988)。
王獻增，「台北盆地黏土土壤不排水剪力強度之研究」，碩士論文，國立中央大學土木工程研究所 (2000)。
吳偉特，「台北盆地土壤之工程特性」，中國土木水利工程學刊，第五卷，第四期，第53-64頁 (1979)。
吳國安、莊復盛、王復國，「粘土層潛盾施工引致之地表沉陷」，第七屆大地工程學術研究討論會論文集，第1025-1032頁 (1997)。
宋佳霖，「台北捷運新店線CH221標潛盾隧道施工引致之地盤變位」，碩士論文，國立交通大學土木工程研究所 (1995)。
李文瑄，「以經驗法評估潛盾隧道施工引致之地表沉陷」，碩士論文，國立交通大學土木工程研究所 (1999)。
李崇正、林志棟、林俊雄，「大地工程研究者之新工具：離心模型試驗」，’94岩盤工程研討會論文集，第649-669頁 (1994)。
沈智剛，「離心模型試驗」，地工技術雜誌，第二十三期，第84-93頁 (1988)。
林志忠，「潛盾機盾尾間隙閉合引致之土壓力轉移及襯砌應力之變化」，碩士論文，國立中央大學土木工程研究所 (1998)。
林俊雄，「離心模型黏土試體之準備與強度標定」，碩士論文，國立中央大學土木工程研究所 (1995)。
林建良，「潛盾隧道周圍之土壓力分布」，碩士論文，國立中央大學土木工程研究所 (1999)。
林照順，「以Peck–Fujita經驗方法估算潛盾隧道施工所引致之地表沉陷」，碩士論文，國立交通大學土木工程研究所 (1992)。
邱顯堯，「並行雙隧道變形之互制行為」，碩士論文，國立中央大學土木工程研究所 (1997)。
張吉佐、王建智、陳秋宗、吳東錦，「潛盾隧道施工之地盤變形資料蒐集分析」，中興工程顧問社 (1997)。
莊孟翰，「未襯砌隧道壁變形引致地盤下陷分布形態分析」，碩士論文，國立中央大學土木工程研究所 (1996)。
陳卓然、趙基盛、陳福勝，「台北盆地潛盾法施工引起之地表沉陷估算」，中華技術，第二十期，第3-10頁 (1993)。
陳思宏，「黏土層中未襯砌隧道之破壞機制」，碩士論文，國立中央大學土木工程研究所 (1996)。
陳秋宗，「台北市潛盾隧道施工對地盤沉陷之影響」，碩士論文，國立交通大學土木工程研究所 (1988)。
陳勝峰，「潛盾隧道施工所引致之地表及深層沉陷」，碩士論文，國立交通大學土木工程研究所 (1994)。
陳堯中、賴建宏、黃南輝、林國楨，「潛盾施工引致孔隙水壓變化之量測與分析」，地工技術，第六十期，第97-106頁 (1997)。
彭德俊，「黏土層中併行潛盾隧道互制現象之有限元素分析」，碩士論文，國立中央大學土木工程研究所 (2000)。
程日晟，「潛盾工程之有限元素法分析的合理化探討」，碩士論文，國立台灣工業技術學院工程技術研究所營建工程技術學程 (1991)。
黃南輝、黃奕洋、黃姿連、楊鵬飛，「潛盾隧道施工所導致之沉陷槽分析」，捷運施工及托底工程研討會，財團法人地工技術研究發展基金會，高雄，第37-48頁 (1997)。
蔡榮禎，「地下水平並列隧道力學行為之探討」，中華技術，第三十三期，第87-95頁 (1997)。
鄭建志，「軟地通遂引致地盤沉陷之有限元素分析」，碩士論文，國立中央大學土木工程研究所 (1999)。
冀樹勇、林金成、陳錦清，「間隙參數模式在潛盾隧道引致地盤位移之最佳化回饋分析」，中國土木水利工程學刊，第十二卷，第四期，第735-746頁 (2000b)。
冀樹勇、林金成、陳錦清，「間隙參數模式在潛盾隧道地盤位移之應用—I：最佳化回饋分析」，中興工程，第六十六期，第5-26頁 (2000a)。
賴韋中，「潛盾雙隧道引致之地盤沉陷」，碩士論文，國立台灣工業技術學院營建工程技術研究所 (1995)。
賴慶和、廖學良、余明山、鍾毓東，「平行雙潛盾雙隧道沉陷特性之研究」，第五屆大地工程學術研究討論會，第655-662頁 (1993)。
鄺寶山、王文禮，「FLAC程式於隧道工程之實例 分析」，地工技術雜誌，第四十一期，第50-61頁 (1993)。
鵜戶口英善，「2圓孔平面應力利用問題(1)」，應用數學力學，Vol. 1, No. 1, pp. 14-28 (1947).
鵜戶口英善，「2圓孔平面應力利用問題(2)」，應用數學力學，Vol. 1, No. 2, pp. 61-81 (1947).
蘇啟鑫，「台北市捷運系統潛盾隧道施工造成之地盤沉陷」，碩士論文，國立交通大學土木工程研究所 (1991)。
Akagi, H., and Komiya, K.,“Finite element analysis of the interaction of a pair of shield tunnels,”Proceedings, 14th International Conference on Soil Mechanics and Foundation Engineering, Hamburg, Vol. 2, pp. 1449-1452 (1997).
Atkinson, J.H. and Potts, D.M.,“Subsidence above shallow tunnels in soft ground,”Journal of Geotechnical Engineering, ASCE, Vol. 103, No. 4, pp. 307-325 (1977).
Attewell, P.B. and Woodman, J.P.,“Predicting the dynamics of ground settlement and its derivatives caused by tunnelling in soil,”Ground Engineering, pp. 13-20, November (1982).
Attewell, P.B.,“Engineering contract, site investigation and surface movements in tunneling works,”Soft Ground Tunneling: Failures and Displacements, Balkema, Rotterdam, pp. 5-12 (1981).
Bernat, S. and Cambou, B.,“Soil-structure interaction in shield tunnelling in soft soil,”Computers and Geotechnics, Vol. 22, No. 3/4, pp. 221-242 (1998).
Bernat, S., Cambou, B., and Dubois, P.,“Assessing a soft soil tunnelling numerical model using field data,”Geotechnique, Vol. 49, No. 4, pp. 427-452 (1999).
Calvello, M. and Taylor, R.N.,“Centrifuge modelling of a spile-reinforced tunnel heading,”Proceedings, International Symposium on Geotechnical Aspects of Underground Construction in Soft Ground, Balkema, Rotterdam, pp. 373-378 (2000).
Casarin, C., and Mair, R.J.“The assessment of tunnel stability in clay by model tests,”In Soft-Ground Tunneling, Balkema, Rotterdam, pp. 33-44 (1981).
Chambon, P. and Corté, J.F.,“Shallow tunnels in cohesionless soil: stability of tunnel face,”Journal of Geotechnical Engineering, ASCE, Vol. 120, No. 7, pp. 1148-1165 (1994).
Chambon, P., Corté, J.F., and Garnier,J.,“Face stability of shallow tunnels in granular soils,”Proceedings, International Conference Centrifuge 91, Boulder, Colorado, pp. 99-105 (1991).
Clough, G.W. and Schmidt, B.,“Design and performance of excavation and tunnels in soft clay,”In Soft Clay Engineering, pp. 600-634 (1981).
Clough, G.W., Shirasuna,T., and Finno, R.J.,“Finite element analysis of advanced shield tunneling in soils,”Proceedings, the Fifth International Conference on Numerical Methods in Geomechanics, Nagoya, pp. 1167-1174 (1985).
Cooper, M.A.R. and Robson, S.,“Theory of close range photogrammetry ,”In Close Range Photogrammetry and Machine Vision, Whittles, Caithness, Scotland, pp. 9-51 (1996).
Cording, E.J. and Hansmire W.H.,“Displacements around soft ground tunnels,”Proceedings, the 5th Pan-American Conference on Soil Mechanics and Foundation Engineering, Buenos Aires, pp. 571-633 (1975).
Corté J.F.,“General report / discussion session 11 : model testing – geotechnical model tests,”Proceedings, the 12th International Conference on Soil Mechanics and Foundation Engineering, pp. 2553-2571 (1989).
Das, B. M., Principles of Geotechnical Engineering, PWS-KENT, Boston, pp. 328-330 (1990).
Davis, E.H., Gunn, M.J., Mair, R.J., and Seneviratne, H.N.,“The stability of shallow tunnels and underground openings in cohesive material,”Geotechnique, Vol. 30, No. 4, pp. 397-416 (1980).
El-Nahhas, F.M., Ahmed, A.A., and Esmail, K.A.,“Prediction of ground subsidence above tunnels in Cairo,”Proceedings, the 14th International Conference on Soil Mechanics and Foundation Engineering, Hamburg, Vol. 2, pp. 1453-1456 (1997).
Ezzeldine, O.Y.,“Estimation of the surface displacement field due to construction of Cairo metro line Rl Khalafawy–St. Therese,”Tunnelling and Underground Space Technology, Vol. 14, No. 3, pp. 267-279 (1999).
FLAC User’s Manual, Version 3.3, ITASCA Consulting Group, Inc., U.S.A. (1996).
Fang, Y.S., Lin, J.S., and Su, C.S.,“An estimation of ground settlement due to shield tunnelling by the Peck-Fujita method,”Canadian Geotechnical Journal, Vol. 31, pp. 431-443 (1994).
Finno, R.J. and Clough, G.W.,“Evaluation of soil response to EPB shield tunneling,”Journal of Geotechnical Engineering, ASCE, Vol. 111, No. 2, pp. 155-173 (1985).
Fuglsang, L.D. and Ovesen, N.K.,“The application of the theory of modelling to centrifuge studies,”In Centrifuges in Soil Mechanics, pp.119-138, Balkema, Rotterdam (1988).
Fujita, K.,“Prediction of surface settlements caused by shield tunnelling,”Proceedings, International Conference on Soil Mechanics, Mexico City, Vol. 1, pp. 239-246 (1982).
Grant, R.J., and Taylor, R.N.,“Tunnelling-induced ground movements in clay,”Proceedings, Institution of Civil Engineers, Geotechnical Engineering, Vol. 143, Issue 1, pp. 43-55 (2000a).
Grant, R.J. and Taylor, R.N. “Evaluating plasticity solutions for the response of clay around tunnels,”Proceedings, International Symposium on Geotechnical Aspects of Underground Construction in Soft Ground, Balkema, Rotterdam, pp. 373-378 (2000b).
Hagiwara, T., Grant, R.J., Calvello, M., and Taylor, R.N.,“The effect of overlying strata on the distribution of ground movements induced by tunnelling in clay,”Soils and Foundations, Vol. 39, No. 3, pp. 63-73 (1999).
Hanya, T., “Ground movements due to construction of shield-driven tunnel,”Proceedings, the 9th International Conference on Soil Mechanics and Foundation Engineering, Tokyo, Case History Volume, pp. 759-790 (1977).
Hashimoto, T., Nagaya, J., and Konda, T.,“Prediction of ground deformation due to shield excavation in clayey soils,”Soils and Foundations, Vol. 39, No. 3, pp. 53-61 (1999).
Henkel, D.J.,“The shear strength of saturated remoulded clays,”Proceedings, Research Conference on Shear Strength of Cohesive Soils, Boulder, Colorado, pp. 533-560 (1960).
Hisatake, M. and Ito, T.,“Prediction of surface settlements due to parallel shield tunnels,”Proceedings, the 8th Asian Conference on Soil Mechanics and Foundation Engineering, Vol. 1, pp. 293-296 (1987).
Hoyaux, B. and Ladadyi, B.,“Gravitational stress field around a tunnel in soft ground,”Canadian Geotechnical Journal. Vol. 7, pp. 54-61 (1970).
Hwang, R. N., Fan, C. B., and Yang, G. R.,“Consolidation Settlements due to Tunneling,”Proc., South East Asian Symposium on Tunnelling and Underground Space Development, Japan Tunnelling Association, Bangkok, pp. 79-86 (1995).
Jeffery, G.B.,“Plane stress and plane strain in bipolar coordinates,”Transactions of the Royal Society, London, England, Series A, Vol. 221, pp. 265-293 (1920).
Kim, S.H., Burd, H.J., and Milligan, W.E.,“Model testing of closely spaced tunnels in clay,”Geotechnique, Vol. 48, No. 3, pp. 375-388 (1998).
Kimura T. and Mair, R.J.,“Centrifuge testing of model tunnels in soft clay,”Proceedings, the 10th International Conference on Soil Mechanics and Foundation Engineering, Stockholm, Vol. 1, pp. 319-322 (1981).
König, D., Jessberger, H.L., Bolton, M., Phillips, R., Bagge, G., Renzi ,R., and Garnier, J.,“Pore pressure measurement during centrifuge model tests: experience of five laboratories,”Proceedings, International Conference Centrifuge 94, Singapore, pp. 101-108 (1994).
König, D., Güttler, U., , and Jessberger, H.,“Stress redistributions during tunnel and shaft constructions,”Proceedings, International Conference Centrifuge 91, Boulder, Colorado, pp. 129-135 (1991).
Ko, H.Y.,“Summary of the state-of-the-art in centrifuge model testing,”In Centrifuge in Soil Mechanics, pp.11-18, Balkema, Rotterdam (1988).
Kuwahara, H., and Yamazaki, T.,“Ground deformation mechanism of shield tunneling due to tail void formation in soft clay,”Proceedings, the 14th International Conference on Soil Mechanics and Foundation Engineering, Hamburg, Vol. 2, pp. 1457-1460 (1997).
Kuwano J., Honda, T., Takahashi, A., and Miki, K.,“Centrifuge investigation on deformations around tunnels in nailed clay,” Proceedings, International Symposium on Geotechnical Aspects of Underground Construction in Soft Ground, Balkema, Rotterdam, pp. 245-250 (2000).
Ladanyi, B.,“Expansion of a cavity in a saturated clay medium,”Journal of Soil Mechanics and Foundations, ASCE, Vol. 90, No. 4, pp. 127-161 (1963).
Leca, E. and Dormieux, L.,“Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material,”Geotechnique, Vol. 40, No. 4, pp. 581-606 (1990).
Lee, C.J., Wu, B.R., and Chiou, S.Y., “Soil Movements around a Tunnel in Soft Soils,” Proceedings of the National Science Council, Part A: Physical Science and Engineering, Vol. 23, No. 2, pp. 235-247 (1999).
Lee, K.M. and Rowe, R.K.,“An analysis of three-dimensional ground movements: the Thunder Bay tunnel,”Canadian Geotechnical Journal, Vol. 28, pp. 25-41 (1991).
Lee, K.M. and Rowe, R.K.,“Deformations caused by surface loading and tunnelling: the role of elastic anisotropy,”Geotechnique, Vol. 39, No. 1, pp. 125-140 (1989a).
Lee, K.M. and Rowe, R.K.,“Effect of undrained strength anisotropy on surface subsidences induced by the construction of shallow tunnels,”Canadian Geotechnical Journal, Vol. 26, 279-291 (1989b).
Lee, K.M. and Rowe, R.K.,“Finite element modelling of the three-dimensional ground deformations due to tunnelling in soft cohesive soils, part I – method of analysis,”Computers and Geotechnics, Vol. 10, No. 2, 87-110 (1990a).
Lee, K.M. and Rowe,R.K.,“Finite element modelling of the three-dimensional ground deformations due to tunnelling in soft cohesive soils, part II – results,”Computers and Geotechnics, Vol. 10, No. 2, 111-138 (1990b).
Lee, K.M., Keery, R., and Lo, K.Y.,“Subsidence owing to tunnelling. I. estimating the gap parameter,”Canadian Geotechnical Journal, Vol. 29, pp. 929-940 (1992).
Lee, K.M.,“Prediction of subsidence above shallow tunnels in soft clay,”Proceedings, the Eleventh Southeast Asian Geotechnical Conference, Singapore, pp. 745-749 (1993).
Ling, C.B.,“On the stresses in a plate containing two circular holes,”Journal of Applied Physics, Vol. 19, pp. 77-82 (1948).
Loganathan, N., and Poulos, H.G.,“Analytical prediction for tunneling-induced ground movements in clay,”Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 124, No. 9, pp. 846-856 (1998).
Longanathan, N., Poulos H.G., and Stewart, D.P.,“Centrifuge model testing of tunnelling-induced ground and pile deformations,”Geotechnique, Vol. 50, No. 3, pp. 283-294 (2000).
Mair, R.J. and Taylor, R.N.,“Prediction of clay behavior around tunnels using plasticity solutions,”Proceedings, Wroth Memorial Symposium, Oxford, pp. 449-463 (1993).
Mair, R.J., Gunn M.J., and O''Reilly, M.P.,“Ground movements around shallow tunnels in soft clay,”Proceedings, the 10th International Conference on Soil Mechanics and Foundation Engineering, Stockholm, Vol. 1, pp. 323-328 (1981).
Mair, R.J., Taylor, R.N., and Bracegirdle, A.,“Subsurface settlement profiles above tunnels in clays,”Geotechnique, Vol. 43, No. 2, pp. 315-320 (1993).
Mair, R.J., Phillips, R., Schofield, A.N., and Taylor, R.N.,“Application of centrifuge modelling to the design of tunnels and excavations in soft clay,”Proceedings, Symposium on the Application of Centrifuge Modelling to Geotechnical Design, Manchester, pp. 356-379 (1984).
Mair, R.J.,“Centrifugal modelling of tunnel construction in soft clay,”Ph.D. Thesis, London, University of Cambridge (1979).
Mair, R.J.,“Centrifuge model testing of tunnel construction in soft clay,”Seminar on Tunnels and Underground Structure Technology, Taipei (1978).
Matsumoto, Y. and Nishioka, T., Theoretical tunnel mechanics, University of Tokyo Press (1991).
Mindlin, R.D.,“Stress distribution around a tunnel,”Transactions, ASCE, Vol. 105, pp.1117-1140 (1940).
Muir Wood, A.M. ,“The circular tunnel in elastic ground,”Geotechnique, Vol. 25, No. 1, pp. 115-127 (1975).
Ng, M.C., Lo, K.Y., and Rowe, R.K.,“Analysis of field performance—the Thunder Bay tunnel,”Canadian Geotechnical Journal, Vol. 23, pp. 30-50 (1986).
Nomoto, T., Mito, K., Imamura, S., Uemo, K., and Kusakabe, O.,“A miniature shield tunneling machine for a centrifuge,”Proceedings, International Conference Centrifuge 94, Singapore, pp. 699-704 (1994).
Nomoto, T., Imamura, S., Hagiwara, T., Kusakabe, O., and Fujii, N.,“Shield tunnel construction in centrifuge,”Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 125, No. 4, pp. 289-300 (1999).
O’Reilly, M.P. and New, B.M.,“Settlements above tunnels in the United Kingdom – their magnitude and prediction ,”Tunnelling’82, pp. 173-240 (1982).
Ohta, H., Kitamura, H., Itoh, M., and Katsumata, M.,“Ground movement due to advance of two shield tunnels parallel in vertical plane,”Proceedings, the Fifth International Conference on Numerical Methods in Geomechanics, Nagoya, pp. 1161-1166 (1985).
Ou, C.Y. and Cherng, J.C.,“Effect of tail void closure on ground movement during shield tunnelling in sandy soil,”Geotechnical Engineering, Vol. 26, No. 1, pp. 17-32 (1995).
Outzka, M.T., Yamazaki, T., Hashimoto, T., and Oumoto, T. ,“Ground movement around tunnelling,”Tsuchi-to-Kiso (in Japanese), Vol. 43, No. 9, pp. 67-73 (1995).
Ovesen, N. K. ,“The scaling law relationship – Pannel Discussion,”Proceedings, 7th European Conference on Soil Mechanics and Foundation Engineering, Brighton, No. 4, pp. 319-323 (1979)
Parreira, A.B. and Azevedo, R.F.,“Prediction of displacements in soft-ground tunnelling,”In Numerical Models in Geomechanics, Balkema, Rotterdam, pp. 675-683 (1992).
Peck, R.B.,“Deep excavations and tunneling in soft ground,”Proceedings, the 7th International Conference on Soil Mechanics and Foundation Engineering, Mexico City, State-of-the-Art Volume, pp. 225-290 (1969).
Prevost, J.H.,“Constitutive theory for soil,”Proceedings, Workshop on Limit Equilibrium, Plasticity, and Generalized Stress-Strain in Geotechnical Engineering, pp. 745-814 (1980).
Reséndiz, D. and Romo, M.P.,“Settlements upon soft-ground tunneling: theoretical solution,”In Soft Ground Tunneling: Failures and Displacements, Balkema, Rotterdam, pp. 65-74 (1981).
Rowe, R.K. and Kack, G.J.,“A theoretical examination of the settlements induced by tunnelling: four case histories,”Canadian Geotechnical Journal, Vol. 20, pp. 299-314 (1983).
Rowe, R.K. and Lee, K.M.,“An evaluation of simplified techniques for estimating three-dimensional undrained ground movements due to tunnelling in soft soils,”Canadian Geotechnical Journal, Vol. 29, pp. 39-52 (1992a).
Rowe, R.K. and Lee, K.M.,“Subsidence owing to tunnelling. II. evaluation of a prediction technique,”Canadian Geotechnical Journal, Vol. 29, pp. 941-954 (1992b).
Rowe, R.K. and Lo, K.Y.,“A method of estimating surface settlement above tunnels constructed in soft ground,”Canadian Geotechnical Journal, Vol. 20, pp. 11-22 (1983).
Sagaseta, C.,“Analysis of undrained soil deformation due to ground loss,”Geotechnique, Vol. 37, No. 3, pp. 301-320 (1987).
Samarasekera, L. and Eisenstein, Z.,“Pore pressure around tunnels in clay,”Canadian Geotechnical, Journal, Vol. 29, pp. 819-831 (1992).
Schofield, A.N.,“Cambridge geotechnical centrifuge operations,”Geotechnique, Vol.30, No. 3, pp. 227-268 (1980).
Seneviratne, H.N. and Gunn, M.J.,“Prediction and observed time-dependent deformations around shallow model tunnels in soft clay,”Proceedings, the Fifth International Conference on Numerical Methods in Geomechanics, Nagoya, pp. 1135-1140 (1985).
Szechy, D., The Art of Tunnelling (Translated from the Hungarian), Budapest, Akademiai Kiado, pp. 869-877 (1966).
Takemura, J., Kimura, T., and Wong, S.F.,“Undrained stability of two-dimensional unlined tunnels in soft soil,”Proceedings, JSCE, No. 418/III-12 (Geotechnical Eng.), pp. 267-277 (1990).
Taylor, R.N., Geotechnical Centrifuge Technology, Chapman & Hall (1995).
Taylor, R.N., Robson, S., , Grant, R.J., and Kuwano, J.,“An image analysis system for determining plane and 3-d displacements in centrifuge models,”Proceedings, International Conference Centrifuge 98, Tokyo, pp. 73-78 (1998).
Taylor, R.N.,“Tunnelling in soft ground in the UK,”Proceedings, International Symposium on Underground Construction in Soft Ground, Balkema, Rotterdam, pp. 123-126 (1995).
Terzaghi. K., Theoretical Soil Mechanics, New York, Wiley, pp. 66-76 (1943).
Terzaghi, K. and Richart, F.E.,“Stresses in rock about cavities,”Geotechnique, Vol. 3, pp. 57-90 (1952).
Verruijt, A. and Booker, J.R.,“Surface settlements due to deformation of a tunnel in an elastic half plane,”Geotechnique, Vol. 46, No. 4, pp. 753-756 (1996).
Vesić, A.S.,“Expansion of cavities in infinite soil mass,”Journal of Soil Mechanics and Foundations, ASCE, Vol. 98, No. 3, pp. 265-290 (1972).
Wang, J.J. and Chang, C.T.,“Numerical method in analysis of stacked tunnels,”In Towards New Worlds in Tunnelling, pp. 197-202 (1992).
Wang, J.J. and Chang, C.T.,“Subsurface subsidence due to tunnelling by EPB shield,”Proceedings, South East Asian Symposium on Tunnelling and Underground Space Development, Japan Tunnelling Association, Bangkok, pp. 217-222 (1995).
Wanninger, R.,“New Austrian tunnelling method and finite elements,”Proceedings, the third international conference on numerical methods in geomechanics, Aachen, pp. 587-597 (1979).
Wroth, C.P. and Houlsby, G.T.,“A critical state model of predicting the behavior of clays,”proceedings, Workshop on Limit Equilibrium, Plasticity, and Generalized Stress-Strain in Geotechnical Engineering, pp. 592-627 (1980).
Wu, B. R., S. Y. Chiou, C. J. Lee, and H. T. Chen, “Soil Movements around Parallel Tunnels in Soft Ground,” Proc., Centrifuge’98, Tokyo, Japan, pp. 739-744 (1998).
Yamaguchi, I., Yamazaki, I., and Kiritani, Y.,“Study of ground-tunnel interactions of four shield tunnels driven in close proximity, in relation to design and construction of parallel shield tunnels,”Tunnelling and Underground Space Technology, Vol. 13, No. 3, pp. 289-304 (1998).
Yamaguti, N.,“On the stresses around a horizontal circular hole in gravitating elastic soild,”Journal of the Civil Engineering Society of Japan (土木學會誌), Vol. 15, No. 4, pp. 291-304 (1929).
Yi, X., R. Rowe, K., and Lee, K.M.,“Observed and calculated pore pressures and deformations induced by an earth balance shield,”Canadian Geotechnical Journal, Vol. 30, pp. 476-490 (1993).