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Interpretation of a Progressive Slope Movement Using Balanced Cross Sections and Numerical Integration

机译：用平衡截面和数值积分解释边坡的渐进运动

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摘要

Gaussian quadrature, a numerical integration technique through fixed points, is applied to improve accuracy and efficiency in the cross-section balance modeling of a slope subjected to progressive displacements. This integration is employed to compute geometrical areas of individual stratigraphic units that have participated in the deformation. Given the initial and final states of a natural slope in which progressive failure has been carefully monitored for 7 years, the internal geometry of four stratigraphic layers that were displaced in a manner that characterizes the displacement kinematics of the entire slope has been analyzed. The area differences between the initial and final sections for three of the layers are zero. A fourth, basal, layer shows a unit area reduction of 13 percent, which can be accounted for by toe erosion. This implies that the total internal geometric area is found to be preserved during the course of the progressive deformation, a fact that is evident in repeated ground surveys conducted during the 7-year history of displacement. Also, factors of safety computed for the basal surface of slip at the initial and final stages of displacement monitoring demonstrate that the slope became less stable over a period of 7 years as a result of the progressive failure. Such a reduction in stability would be difficult to quantify without the application of numerical integration that allows the accurate construction of area-balanced geometrical models in a digital format amenable to validation and stability analysis.
机译：高斯求积法是通过 不动点的数值积分技术，用于在受 >渐进位移。该积分用于计算已参与变形的各个地层单元的 几何面积。给定自然坡度的初始和最终 状态，在该状态中已对连续破坏进行了 的监测，为期7年，四个地层的内部几何形状分析了以表征整个坡度的位移运动特征的方式进行了位移。 初始截面和最终截面之间的面积差 其中三层为零。第四层基础层显示 单位面积减少了13％，这可以由脚趾侵蚀来解释 。这意味着发现在进行性 变形的过程中保留了整个内部几何 区域，这一事实在重复的地面调查 在流离失所的7年历史中进行。另外，在位移监测的初始 和最终阶段为滑移基面计算的安全系数 表明， 在整个滑坡中，坡度变得不太稳定。由于 进行性失败而导致的7年期限。如果不应用数值 积分（该数值积分可以在区域中精确构造面积平衡的 几何模型），则很难量化这种稳定性的降低。适用于验证 和稳定性分析的数字格式。

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  • 来源
    《Environmental and Engineering Geoscience》 |2008年第2期|121-131|共11页
  • 作者

    RENNIE B. KAUNDA; RONALD B. CHASE; ALAN E. KEHEW; KARLIS KAUGARS; JAMES P. SELEGEAN;

  • 作者单位

    Department of Geosciences, Western Michigan University, Kalamazoo, MI 49008;

    Department of Geosciences, Western Michigan University, Kalamazoo, MI 49008;

    Department of Geosciences, Western Michigan University, Kalamazoo, MI 49008;

    Department of Computer Science, Western Michigan University, Kalamazoo, MI 49008-5466;

    Great Lakes Hydraulics and Hydrology Office, U.S. Army Corps of Engineers, Detroit District, 477 Michigan Ave., Detroit, MI 48226;

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