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Environmental and Engineering Geoscience

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

¹ Department of Geosciences, Western Michigan University, Kalamazoo, MI 49008
² Department of Computer Science, Western Michigan University, Kalamazoo, MI 49008-5466
³ Great Lakes Hydraulics and Hydrology Office, U.S. Army Corps of Engineers, Detroit District, 477 Michigan Ave., Detroit, MI 48226

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.

Key Words: Geotechnical • Gaussian Quadrature • Structure • Landslides • Modeling • Soil Mechanics