本研究以Duncan and Chang (1970) 之雙曲線土壤強度理論作為求解邊坡滑動變位的土壤強度模型。本文蒐集11個不同尺寸與土樣種類之直接剪力試驗，根據雙曲線理論建立土壤剪應力-剪動位移之模型。以回歸分析求其雙曲線之應力-變位模型之控制參數K、n與Rf 。 回歸分析結果顯示 : 土壤初始勁度參數 (K) 在一般室內(小型)直剪試驗得到K之值約為640~1200，大型直剪之K值則介於50與870之間。K值受直剪盒尺寸之影響很大，直剪盒尺寸越小K值越大；而土壤初始勁度與圍壓之影響參數 (n) 較不受直剪盒尺寸與土壤種類的影響，其值大部分介於0.1與1.75之間；破壞比 (Rf) 亦不受直剪盒尺寸與土壤種類的影響，其值約介於0.7與0.9之間。低塑性黏土(CL)在大型直剪中的應力-變位參數(K=80~290, n=0.15~0.61,Rf =0.74~0.87)較接近Duncan-Chang (1980)的建議值(K=60~150, n=0.45, Rf =0.7)。
為了求解邊坡穩定之滑動變位問題，採用新電腦分析程式: SLICE DISP。此一電腦程式為Huang(2012)在Visual Basic Express (2010)平台撰寫而成之改良變位分析切片法，乃是以傳統二度空間(2-D) 之Janbu，Bishop及Fellenius切片分析法為基礎，導入位移相容性以及剪應力-剪動位移雙曲線模型，擴充成能計算滑動變位的邊坡穩定分析法。
收集兩個有實際監測變位紀錄的案例進行驗證分析，檢驗改良-切片法的可用性。分析結果顯示: 輸入適當的土壤凝聚力c、土壤摩擦角 、雙曲線模擬參數K、n、Rf等五個分析主控變數可有效計算邊坡在地下水位上升之影響下邊坡之滑動位移。本分析法對追蹤長期邊坡在地下水位影響下之滑動歷程亦有相當良好的結果。本方法之另一特點為可以求得沿滑動面之局部安全係數, 比以往之邊坡穩定分析中之單一安全係數更具實用之價值及在工程應用上之潛力。

To calculate the displacement of slopes induced by heavy rainfall, a hyperbolic shear stress vs. shear displacement model is developed here. This hyperbolic model is based on that proposed by Duncan and Chang (1970) which was for the shear vs. strain relationship of soils. A total of eleven test results including standard (small scale) and large-scale direct shear tests were studied. Results of curve-fitting showed that the initial stiffness parameter (K) are in the range of 640-1200 (from small-scale tests) or in the range of 50-870 (from large-scale test). Values of K can be significantly influenced by the size of direct shear boxs. Parametes, n (material constant for pressure-dependent initial stiffness) and Rf (failure ratio) are rather independent of the shear box sizes. It was found that material constants (K=80-290, n=0.15-0.61, Rf=0.74-0.87) obtained from large-scale tests on the low-plasticity clay (CL) are close the those (K=60~150, n=0.45, Rf =0.7) suggested by Duncan-Chang (1970).
To validate the hyperbolic model, three displacement-based slice methods are used to calculate the slope displacement of two well-monitored slopes. These displacement-based slice methods were extensions from the conventional Janbu’s, Bishop’s and Fellenius’ methods, and were formulated and coded by Huang (2012).
Results of preliminary analyses show good agreements between the calculated and the observed slope displacement induced by an elevated groundwater table during a heavy rainfall. Advantages of the proposed slice method with input parameters represented by a hyperbolic shear stress-shear displacement model were highlighted. However, more accurate analyses based on the results of on-site large-scale direct shear tests should be performed in the future to validate the proposed model for practical applications.

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