邊坡破壞所引發的土石災害時常危及人身及財產安全，而降雨又為引發邊坡破壞的重要原因。因此為能準確預測降雨所導致的邊坡變位，本研究以改良切片變位法為分析方法，並加入了土壤剪應力-變位曲線尖峰後應力軟化的概念(後尖峰分析)進行計算。改良切片變位法是以極限平衡之切片法為基礎，代入土壤材料之剪應力-變位雙曲線模式(雙曲線分析)，且在符合切片變位相容的原則下計算邊坡之變位。為驗證本法在實務上之可用性，對兩個具有長期監測變位紀錄的案例進行變位分析，結果顯示在有效的參數範圍內分析之變位能符合現地的量測值。為表現邊坡變位符合變位場及變位相容原理，以邊坡實際監測變位為基準決定適合案例的剪脹角(ψ)，使滑動土體中不同位置之變位差異可以適切地表現於變位分析之計算結果。
案例分析結果顯示，單純以雙曲線模擬之變位與加入土壤剪應力-變位尖峰後應力軟化曲線之模擬變位有所不同，因考慮到土壤變位在超過尖峰剪應力後的殘餘狀態，變位也隨之增加。此外，由於自然界的邊坡破壞面岩土分界並不明顯，除了以莫爾庫倫破壞準則為土體破壞之依據，另比較Hoek & Brown破壞準則對土體變位之影響。分析結果顯示，本研究所建議之分析方法對於上述兩種破壞準則，都可以得到良好的邊坡變位分析結果。

Rainfall-induced slope failures often causes debris hazards that will endanger lives and properties. To predict rainfall-induced slope displacements, the present study uses modified method of slices along with the concept of “post-peak stress softening of soil” (post-peak analysis). Modified method of slices is based on conventional limit equilibrium slice methods, with additional criteria regarding slice displacement compatibility and non-linear stress-displacement relationships represented by a hyperbolic soil model (hyperbolic analysis). Case studies on two well-monitored slopes were performed to validate practical engineering applications of the proposed method, the results shows the observed slope displacement induced by a ground table rise during a rainstorm event can be well simulated with properly defined parameters. Based on the displacement compatibility of slices, it is possible to determine the dilatancy angle(ψ) for the sliding mass using measured slope displacements at more than two locations pf the slope.
By taking into account the residual state in the post-peak analysis, the simulated displacements of slopes were higher than those using hyperbolic stress-displacement relationships for which no post-peak softening is considered. Another feature of the present study is that two failure criteria, namely the Mohr-Coulomb and the Hoek and Brown failure criteria, were used to verify the analytical procedure proposed here.

1. Atkinson, J. H. (1981) “Foundations and Slopes: An introduction to Applications of Critical State Soil Mechanics”, McGraw-Hill, London, pp. 109-145.
2. Abramson, L. W. (1996) “Slope stability and stabliztion methods”, John-Wiley and Sons, New York, pp. 339-343.
3. Culmann, K. (1866) “Die graphische Statik”, ETH-Bibliothek Zürich, pp. 547-562.
4. Chowdhury, R. N. (1978) “Slope analysis: Developments in geotechnical engineering”, Elsevier Scientific Pub Co., pp. 21-45.
5. Drucker, D. C., and Prager, W. (1952) “Soil Mechanics and plastic analysis for limit design”, Quarterly of Applied Mathematics, Vol. 10, No. 2, pp. 157-165
6. Dingwell J. C., Scrivner, F. H., Boyer, W. C., and Abrams, J. I. (1954) “Application of the elastic theory to highway embankments by use of difference equations”, Highway Research Board Proceedings, Vol. 33, pp. 474-482.
7. Duncan, J. M. and Chang, C.-Y. (1970) “Nonlinear analysis of stress and strain in soils” Journal of Soil Mechanics and Foundation Division, Proc. ASCE, Vol. 96, No. SM5, pp. 1629-1653.
8. Davoudi, M. H. (2011) “Influence of Willow Root Density on Shear Resistance Parameters in Fine Grain Soils using in situ Direct Shear Tests”, Research Journal of Environment Sciences, Vol. 5. No. 2, pp. 157-170.
9. Hoek, E., and Bray, J. (1981) “Rock Slope Engineering Shear Strength of Rock”, London: Institution of Mining and Metallergy, 3rd ed., pp.83-125.
10. Huang, C.-C. (2013) “Developing a new slice method for slope displacement analyses”, Engineering Geology, Vol.157, pp. 39-47.
11. Huang, C.-C., and Yeh, S.-W. (2015) “Predicting periodic rainfall-induced slope displacements using force-equalibrium-based finite displacement method”, Journal of GeoEngineering, Vol. 10, No. 3, pp. 83-89.
12. Huang, C.-C. (2016) “Back-calculating strength parameters and predicting displacements of deep-seated sliding surface comprising weathered rocks”, International Journal of Rock Mechanics & Mining Sciences, Vol. 88, pp. 98-104.
13. Janbu, N. (1973) “Slope stability computations, Embankment-Dam Engineering”, Casagrande Volume, John-Wiley and Sons, pp. 47-86.
14. Pao, M. L. (1986) “An Empirical Examination of Lotka’s Law”, Journal of the American Society For Information Science, Vol. 37, No.1, pp. 26-33.
15. Qiu, J.-Y., Tatsuoka, F., and Uchimura, T. (2000) “Constant Pressure and Constant Volume Direct Shear Tests on Reinforced Sand”, Soils and Foundations, Vol. 40, No. 4, pp. 1-17.
16. Ziaie Moayed, R., Alibolandi M., and Alizadeh A. (2017) “Specimen size effects on direct shear test of silty sands”, International Journal of Geotechnical Engineering, Vol. 11, No. 2, pp. 198-205.
17. Taylor, D. W. (1948) “Fundamentals of Soil Mechanics”, John-Wiley and Sons, New York, pp.67-73.
18. Terzaghi, K. (1950) “Mechanisms of Landslides” Geotechnical Society of America,
pp. 83-125.
19. Tatsuoka F., Siddiquee, M. S. A., Park, C.-C., Sakamoto, M., and Abe, F. (1993) “Modelling stress-strain relations of sand” Soil and Foundation, Vol. 33, No. 2, pp.
60-81.
20. 吳偉特 (1980)，「邊坡穩定之分析方法與應用」，兆林出版社。
21. 褚炳麟、黃承郎及鄭順義 (1989)，「台地礫石堆積層與頭嵙山礫岩層之現地直接剪力試驗研究」，第三屆大地工程學術研討會，第695-706頁。
22. 許琦 (2006)，「剪力盒間隙對礫石剪力強度之影響」，岩盤工程研討會論文集，台南，第31-40頁。
23. 蔡宗成 (2006)，「台19線五彎仔地滑研究」，國立成功大學土木工程研究所碩士論文。
24. 行政院農業委員會水土保持局第三工程所、黎明工程顧問有限公司 (2006)，「台14線88K至91K地滑地治理調查規劃工程」。
25. 行政院農業委員會水土保持局第三工程所、黎明工程顧問有限公司 (2007)，「廬山地滑監測及後續治理規劃」。
26. 徐薇 (2009)，「以三為個別原素法模擬卵礫石層的物理特性」，朝陽科技大學營建工程系碩士論文。
27. 吳國維 (2011)，「應用真直接剪力試驗結果至路提共構穩定分析」，逢甲大學土木工程學系碩士論文。
28. 謝弘毅 (2012)，「土壤應力-變位模式之建立與邊坡變位分析之應用」，國立成功大學土木工程研究所碩士論文。
29. 葉憲文 (2015)，「雙曲剪力變位模式之建立與應用」，國立成功大學土木工程研究所碩士論文。
30. 徐浩怡 (2017)，「土壤之反覆直接剪力行為與模式化」，國立成功大學土木工程研究所碩士論文。