Pure appl. geophys. 157 (2000) 989–1007 0033 – 4553/00/080989–19 $ 1.50 +0.20/0 A Two-dimensional Boundary Element Method for Calculating Elastic Gravitational Stresses in Slopes STEPHEN J. MARTEL 1 and JORDAN R. MULLER 1 Abstract — Elastic stresses arising from gravitational loads in a two-dimensional slope of arbitrary shape are calculated easily using a displacement-discontinuity boundary element method (BEM). A long stress-free crack simulates the topographic surface. Gravity-induced stresses (i.e., body forces) in a laterally confined body are simulated by vertical and horizontal ‘‘far-field’’ stresses equal to rgy and [n /(1 -n )]rgy, respectively. Here r is material density, n is Poisson’s ratio, g is gravitational acceleration, and y is elevation, with y =0 along the surface far from a ridge top or valley floor. BEM stress solutions compare well with analytical solutions for symmetric topography based on conformal mapping. Our analyses indicate that slope failures are likely to initiate near the bases of bedrock ridges and to be widespread along the slopes of gentle valleys cut in bedrock. The BEM method can be applied to the slopes of arbitrary shape and steepness, and it is well suited for evaluating the near-surface propagation of fractures or fracture-like structures, such as dikes and landslide failure surfaces. Our analysis also highlights the critical importance of properly accounting for the boundary conditions in a boundary value problem. Key words: Boundary element, continuum mechanics, slope stability, stress analysis, topography. Introduction Gravitational stresses affect geologic processes and engineering operations in slopes, and also how we explore the subsurface. Gravity induces a shear stress on planes parallel to the ground surface that acts to drive landslides. Where the slope is long and planar, this shear stress scales with the vertical distance from the ground surface to the slide plane and the sine of the slope angle (LAMBE and WHITMAN, 1969). Gravity-induced stresses also affect the stability of volcanoes (BORGIA 1994) and influence how dikes propagate to the surface (FISKE and JACKSON, 1972). These stresses play a role in the formation of near-surface fractures and conse- quently how streams erode the landscape (MILLER and DUNNE, 1996). Gravita- tional stresses associated with topography have long been suspected to influence the formation of exfoliation joints (GILBERT, 1904). Effects of topographic relief also complicate efforts to stabilize oil wells and safely construct underground excava- 1 Department of Geology and Geophysics, 2525 Correa Road, University of Hawaii, Honolulu, HI 96822. E-mail: [email protected]
A Twodimensional Boundary Element Method for Calculating Elastic Gravitational Stresses in Slopes
Jun 14, 2023
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