| 摘要: | 岩坡穩定性受岩體不連續面位態及工程配置角顯著影響，其中坡面傾向（??s）與不連續面傾向（????）之交角，又稱斜交角（|???? ? ??s|, oblique angle）為控制岩坡穩定性與破壞模式轉換之關鍵參數。本文採用PFC3D（Particle Flow Code in Three Dimensions）離散元素法（Discrete Element Method, DEM），建立含單一不連續面之合成岩坡模型，模擬不同斜交角（|???? ? ??s|）與岩坡條件下的崩塌行為，並以崩塌能量為量化指標，探討摩擦角（?j）、坡角（βs）、坡高（H）及不連續面傾角（βj）對崩塌能量與臨界斜交角的影響。模型涵蓋順向坡至逆向坡之完整斜交角範圍，並輔以極限平衡法 RocTopple 進行比對分析，以驗證破壞趨勢之合理性。
研究結果顯示：（1）本文依據 PFC3D 模擬結果，建立平面破壞崩塌能量與臨界斜交角之連續函數，得以評估破壞模態轉換與崩塌能量。（2）平面破壞不利因子包含低斜交角、高坡角、高坡高、中等不連續面傾角及低摩擦角；傾覆破壞則以高斜交角、高坡角、高坡高、高不連續面傾角及低摩擦角為主要不利因子，當多項不利因子同時存在時，傾覆破壞崩塌能量將顯著上升，其潛在崩塌規模不亞於平面破壞。（3）在一般岩坡條件下，平面破壞臨界斜交角（γ_(cr,p)）約為 20?，與工程實務經驗及《水土保持技術規範》之順向坡定義相符；當岩坡處於多重不利條件時，臨界斜交角可能提升至約 40?。（4）本文依據 PFC3D 模擬結果，提出傾覆破壞臨界斜交角（γ_(cr,t)）判別式，並驗證其可視為既有現地調查經驗式形式。
整體而言，本文之模擬結果顯示斜交角對崩塌能量與破壞模式具有關鍵控制作用，其趨勢與 SMR 位態評分調整一致，並進一步指出既有岩坡分類系統未充分納入摩擦角與坡高等影響因子之侷限性，顯示數值模擬方法於岩坡穩定性評估與工程應用上具有重要價值。
關鍵字：離散元素法、異向性岩體、崩塌能量、臨界斜交角、連續函數
;Rock slope stability is strongly influenced by the orientation of rock mass discontinuities and engineering configuration angles. Among these factors, the angle between the slope face dip direction (??s) and the discontinuity dip direction (????), referred to as the oblique angle (|???? ? ??s|), is a key parameter governing slope stability and the transition of failure modes. In this study, the discrete element method (DEM) implemented in PFC3D (Particle Flow Code in Three Dimensions) is employed to construct three-dimensional synthetic rock slope models containing a single discontinuity. Slope failure behaviors under different oblique angles and slope conditions are simulated, and collapse energy is adopted as a quantitative indicator to investigate the effects of discontinuity friction angle (??), slope angle (β?), slope height (H), and discontinuity dip angle (β?) on collapse energy and critical oblique angles. The models cover the full range of oblique angles from dip slopes to anti-dip slopes, and limit equilibrium analyses using RocTopple are conducted for comparison to verify the rationality of the observed failure trends.
The results indicate that: (1) based on PFC3D simulation outcomes, continuous functions describing collapse energy and critical oblique angles for plane failure are established, enabling the evaluation of failure mode transitions and collapse energy levels; (2) unfavorable factors for plane failure include low oblique angles, high slope angles, large slope heights, intermediate discontinuity dip angles, and low friction angles, whereas toppling failure is primarily associated with high oblique angles, high slope angles, large slope heights, steep discontinuity dip angles, and low friction angles. When multiple unfavorable factors coexist, the collapse energy associated with toppling failure increases significantly, and the potential collapse scale is comparable to that of plane failure; (3) under general slope conditions, the critical oblique angle for plane failure (γ_(cr,p)) is approximately 20?, which is consistent with engineering practice and the definition of dip slopes in the Soil and Water Conservation Technical Regulations. When multiple adverse conditions are present, the critical oblique angle may increase to approximately 40?; (4) using PFC3D simulation results, a discriminant equation for the critical oblique angle of toppling failure (γ_(cr,t)) is proposed and verified to be a generalized form of existing empirical relationships derived from field investigations.
Overall, the simulation results demonstrate that the oblique angle plays a critical controlling role in collapse energy and failure mode development. The observed trends are consistent with the orientation adjustment logic adopted in the Slope Mass Rating (SMR) system. Furthermore, this study highlights the limitations of existing rock slope classification systems, which do not explicitly incorporate friction angles and slope height, and underscores the importance of numerical simulation as a complementary tool for rock slope stability assessment and engineering applications.
Keywords: discrete element method; anisotropic rock mass; collapse energy; critical oblique angle; continuous equation. |
