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基于有限元極限平衡法的三維邊坡穩定性

Three-dimensional slope stability based on the finite element limit equilibrium method

  • 摘要: 提出了一種基于有限元彈塑性應力場和極限平衡狀態的三維邊坡穩定分析方法——三維有限元極限平衡法。首先,考慮三維空間中滑動方向,提出滑動面上一點在滑動方向上的極限平衡條件,并證明滑動面上土體整體達到極限平衡狀態與滑動面上土體各處在滑動方向上處于極限平衡狀態等價。再通過剛體極限平衡假定計算主滑方向和滑動面上各點滑動方向。最后,定義局部安全系數為抗剪強度與滑動方向上剪應力投影的比值,基于三維邊坡整體極限平衡條件將局部安全系數通過積分中值定理轉變為整體安全系數。該方法計算簡單,消除了剪應力比形式定義安全系數滑動面形狀限制,具備合理性與有效性。算例驗證結果表明,該方法滑動方向假設合理,安全系數與嚴格三維極限平衡法結果一致。

     

    Abstract: A finite element limit equilibrium method was proposed based on finite element stress analysis combined with a limit equilibrium condition to analyze the slope stability. The local safety factor defined in the form of shear strength and shear stress ratio in a three-dimensional (3D) space does not consider the sliding direction influence on the calculation results. In this paper, a 3D finite element limit equilibrium method that considers the sliding direction was proposed. This method was different from the limit equilibrium and strength reduction methods and analyzed slope stability through the “true” stress state without reducing the material strength parameters. First, considering the sliding direction in the 3D space, the limit equilibrium condition of a point was proposed on the slip surface in the sliding direction. An equivalent relationship was proved of the slip surface was in the limit equilibrium state, and each point of the slip surface was in the limit equilibrium state in the sliding direction. Then, the main sliding direction and the sliding direction of each point on the slip surface were calculated assuming the rigid body limit equilibrium. Finally, the local safety factor was defined as the ratio of the shear strength to the shear stress projection in the sliding direction. Based on the equivalent relationship of the limit equilibrium state of the 3D slope, the local safety factor was transformed into a global safety factor by applying the integral median theorem. The method is simple to calculate, eliminates the limitation of the slip surface shape of the safety factor defined by the shear stress ratio form, and is reasonable and effective. The verification result of the calculation example shows that the sliding direction assumption of the method is reasonable, and the safety factor is consistent with the result of the strict 3D limit equilibrium method.

     

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