Tectonic and gravitational stress in long symmetric ridges and valleys

Abstract

We present an exact elastic solution for the effects of topography on the near-surface stresses caused by a uniform, uniaxial tectonic compression or tension acting normal to the axial planes of isolated symmetric ridges and valleys of realistic shape. The solution, obtained by the Kolosov-Muskhelishvili method of complex potentials, gives stresses in the vicinity of these topographic features that, with the exception of the vertical component, are of the order of the regional tectonic stress. The effect of topography is to reduce a regional tectonic compression near the crest of a ridge and, if the ridge is sufficiently steep, to cause a stress reversal resulting in a small tension. Valleys, on the other hand, concentrate the far-field tectonic stress. When a previously derived exact solution for the topographic effect on the gravity-induced stress field is combined with the present solution for the topographic modification of a regional compressive tectonic stress, we find a slight increase in the lateral components of the gravity-induced compressive stress at the ridge crest and, under the valley bottoms, a decrease in the gravity-induced tensile stresses. The opposite effects occur when a far-field tension is superposed on the gravity-induced stress field.

Quantifying the controls on potential soil production rates: a case study of the San Gabriel Mountains, California

“…Savage and Swolfs (1986) studied the role of topography in modifying local stresses in a model ridge-and-valley geometry that uses a conformal transformation that includes length scales b and a that define the vertical and horizontal extents of the ridge, respectively. Because the data from Heimsath et al (2012) are acquired from locations at or near ridgetops, I focused only on the portion of the Savage and Swolfs (1986) Savage and Swolfs (1986) and the average slope S av ) using Eqs. (34) and (35) of Savage and Swolfs (1986).…”

“…Because the data from Heimsath et al (2012) are acquired from locations at or near ridgetops, I focused only on the portion of the Savage and Swolfs (1986) Savage and Swolfs (1986) and the average slope S av ) using Eqs. (34) and (35) of Savage and Swolfs (1986). The hillslopes are plotted with no vertical exaggeration.…”

“…Given the pervasively fractured nature of bedrock in the SGM (e.g., Dibiase et al, 2015), I assume that changes in the stress state of bedrock or intact regolith near ridgetops lead to the opening of preexisting fractures (i.e., an increase in the bulk porosity of bedrock or intact regolith) rather than the fracturing of intact rock. I adopt the analytic solutions of Savage and Swolfs (1986), who solved for the topographic modification of regional compressive stresses beneath ridges and valleys oriented perpendicular to the most compressive-stress direction. Savage and Swolfs (1986) demonstrated that the horizontal stress (σ xx ) in bedrock or intact regolith becomes less compressive near ridgetops as the average slope (measured over a spatial scale that includes ridgetops and side slopes) increases (Fig.…”

“…I adopt the analytic solutions of Savage and Swolfs (1986), who solved for the topographic modification of regional compressive stresses beneath ridges and valleys oriented perpendicular to the most compressive-stress direction. Savage and Swolfs (1986) demonstrated that the horizontal stress (σ xx ) in bedrock or intact regolith becomes less compressive near ridgetops as the average slope (measured over a spatial scale that includes ridgetops and side slopes) increases (Fig. 3).…”

Effects of crustal stresses on fluid transport in fractured rock: case studies from northeastern and southwestern USA

“…7) reveal stress-induced breakouts (e.g., Bell and Gough 1979) that have undergone a 90°shift in orientation with depth, a polarity change that implies an exchange of the maximum, S H , and minimum, S h , horizontal principal stress directions. Savage and Morin (2002) explain this 90°shift in S H and S h with depth by using an analytical model (Savage and Swolfs 1986) for gravity-and tectonically-induced stresses beneath an idealized symmetric and isolated valley. Physical coordinates of the model are aligned with the valley configuration at Alpine and results represent stress conditions in the subsurface at this site.…”