Stability analysis of slopes based on dynamic strength reduction- improved vector sum method
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摘要: 在边坡稳定性分析中，极限平衡法与矢量和法均假定边坡失稳是由剪切破坏造成的，因此难以正确求解坡体上部存在拉裂区这类复杂边坡的安全系数，应用整体强度折减法虽能求得前述复杂边坡的安全系数，却难以搜索得到包含坡体上部拉裂区的完整滑动面。针对上述问题，采用动态强度折减法来搜索边坡滑动面，并提出了可兼顾边坡张拉破坏与剪切破坏的改进矢量和法，从而可更好地求解边坡稳定性问题。算例表明，应用所提出的方法不仅能搜索得到完整的边坡滑动面，而且求得的安全系数与整体强度折减法基本相同。所提出的方法适用于土质、岩质以及土岩组合等各类型边坡的稳定性分析，且受主滑方向、网格尺寸、模型尺寸的影响较小，有助于推动边坡稳定性分析方法的进一步完善。Abstract: In the slope stability analysis, both the limit equilibrium method and the vector sum method assume that the slope instability is caused by shear failure, accordingly, it is difficult to correctly solve the safety factor of the complex slope with tensile failure at the upper part, while the global strength reduction method can obtain the safety factor, it is difficult to search for the complete sliding surface containing the tensile failure zone in the upper part of the slope. In view of the above problems, the dynamic strength reduction method is adopted to search for the sliding surface of slope, and an improved vector sum method which can take into account the tension failure and shear failure is proposed, so that the slope stability problem can be solved better. The results of three cases show that the dynamic strength reduction method can completely reflect the sliding surface of slopes, and the safety factor obtained by the improved vector sum method is basically the same as that by the global strength reduction method. The proposed method is applicable to the stability analysis of various types of slopes, such as soil, rock and soil-rock combinations, and is less affected by the main sliding direction, mesh size and model size, which helps to promote the further improvement of slope stability analysis methods.
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图 2 动态强度折减法搜索滑动面流程图
Figure 2. Flow chart of sliding surface search by dynamic strength reduction method
表 1 土质边坡土体物理力学指标的取值
Table 1 Physico-mechanical indices of soil slopes
土休 黏聚力/kPa 内摩擦角/(°) 重度/ (kN·m-3) 均质土坡 20.00 20.0 20.00 非均质土坡 #1土层 49.00 29.0 20.38 #2土层 0 30.0 17.64 #3土层 7.84 20.0 20.38 #4土层 0 30.0 17.64 
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表 2 土质边坡计算结果对比
Table 2 Comparison of calculated results of soil slopes
计算方法 均质土坡 非均质土坡 安全系数 相对误差/% 安全系数 相对误差/% 整体强度折减法 1.293 — 1.363 — Morgenstern-Price 1.271 -1.70 1.440 +5.65 本文方法(1) 1.277 -1.24 1.410 +3.45 本文方法(2) 1.275 -1.39 1.410 +3.45 本文方法(3) 1.278 -1.16 1.410 +3.45 传统矢量和法(1) 1.291 -0.15 1.234 -9.46 传统矢量和法(2) 1.284 -0.70 1.234 -9.46 传统矢量和法(3) 1.293 0 1.233 -9.54 应力代数和法 1.275 -1.39 1.412 +3.60 注：本表以整体强度折减法的计算结果为基准进行比较；(1)、(2)、(3)分别表示以极限抗滑力方向、滑动力方向、滑入点指向滑出点方向作为边坡的主滑方向(其中，均质土坡主滑方向与水平方向的夹角分别为28.21°，26.13°，29.25°；非均质土坡主滑方向与水平方向的夹角分别为24.98°，25.10°，21.41°)。
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表 3 岩质边坡岩土体物理力学指标
Table 3 Physico-mechanical indices of rock slope
介质 弹性模量/GPa 泊松比 黏聚力/MPa 内摩擦角/(°) 天然重度/(kN·m-3) 抗拉强度/MPa f231 2.0 0.28 0.9 22.8 25.8 0 卸荷裂隙 2.0 0.28 2.0 36.0 26.2 0 V2 2.0 0.27 1.8 21.8 22.1 0 V1 4.0 0.27 2.0 26.5 24.5 1.00 IV 6.0 0.26 7.0 38.6 25.8 3.35 III2 7.5 0.23 17.5 51.3 26.2 6.00 III1 8.0 0.24 15.0 50.2 26.2 5.50 III 9.0 0.22 20.0 52.5 26.5 7.00
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表 4 岩质边坡计算结果对比
Table 4 Comparison of calculated results of rock slopes
计算方法 岩质边坡 安全系数 相对误差/% 整体强度折减法 1.659 — Morgenstern-Price 12.800 +671.55 本文方法(1) 1.657 -0.12 本文方法(2) 1.660 +0.06 本文方法(3) 1.652 -0.42 传统矢量和法(1) 1.854 +11.75 传统矢量和法(2) 1.841 +10.97 传统矢量和法(3) 1.773 +6.87 应力代数和法 1.980 +19.35 注：(1)、(2)、(3)对应的边坡主滑方向与水平方向的夹角分别为34.09°，36.96°，51.08°。
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