Topographic stress and rock fracture: a two-dimensional numerical model for arbitrary topography and preliminary comparison with borehole observations
Theoretical calculations indicate that elastic stresses induced by surface topography may be large enough in some landscapes to fracture rocks, which in turn could influence slope stability, erosion rates, and bedrock hydrologic properties. These calculations typically have involved idealized topogr...
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| Format: | Article |
| Language: | en_US |
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Wiley Blackwell
2015
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| Online Access: | http://hdl.handle.net/1721.1/97898 https://orcid.org/0000-0002-0404-8701 https://orcid.org/0000-0002-2646-7384 |
| _version_ | 1811097708950192128 |
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| author | Perron, J. Taylor Martel, Stephen J. Singha, Kamini Slim, Mirna I. |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Perron, J. Taylor Martel, Stephen J. Singha, Kamini Slim, Mirna I. |
| author_sort | Perron, J. Taylor |
| collection | MIT |
| description | Theoretical calculations indicate that elastic stresses induced by surface topography may be large enough in some landscapes to fracture rocks, which in turn could influence slope stability, erosion rates, and bedrock hydrologic properties. These calculations typically have involved idealized topographic profiles, with few direct comparisons of predicted topographic stresses and observed fractures at specific field sites. We use a numerical model to calculate the stresses induced by measured topographic profiles and compare the calculated stress field with fractures observed in shallow boreholes. The model uses a boundary element method to calculate the stress distribution beneath an arbitrary topographic profile in the presence of ambient tectonic stress. When applied to a topographic profile across the Susquehanna Shale Hills Critical Zone Observatory in central Pennsylvania, the model predicts where shear fractures would occur based on a Mohr–Coulomb criterion, with considerable differences in profiles of stresses with depth beneath ridgetops and valley floors. We calculate the minimum cohesion required to prevent shear failure, C[subscript min], as a proxy for the potential for fracturing or reactivation of existing fractures. We compare depth profiles of C[subscript min] with structural analyses of image logs from four boreholes located on the valley floor, and find that fracture abundance declines sharply with depth in the uppermost 15 m of the bedrock, consistent with the modeled profile of C[subscript min]. In contrast, C[subscript min] increases with depth at comparable depths below ridgetops, suggesting that ridgetop fracture abundance patterns may differ if topographic stresses are indeed important. Thus, the present results are consistent with the hypothesis that topography can influence subsurface rock fracture patterns and provide a basis for further observational tests. |
| first_indexed | 2024-09-23T17:03:39Z |
| format | Article |
| id | mit-1721.1/97898 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T17:03:39Z |
| publishDate | 2015 |
| publisher | Wiley Blackwell |
| record_format | dspace |
| spelling | mit-1721.1/978982022-09-29T23:22:29Z Topographic stress and rock fracture: a two-dimensional numerical model for arbitrary topography and preliminary comparison with borehole observations Perron, J. Taylor Martel, Stephen J. Singha, Kamini Slim, Mirna I. Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Slim, Mirna I. Perron, J. Taylor Theoretical calculations indicate that elastic stresses induced by surface topography may be large enough in some landscapes to fracture rocks, which in turn could influence slope stability, erosion rates, and bedrock hydrologic properties. These calculations typically have involved idealized topographic profiles, with few direct comparisons of predicted topographic stresses and observed fractures at specific field sites. We use a numerical model to calculate the stresses induced by measured topographic profiles and compare the calculated stress field with fractures observed in shallow boreholes. The model uses a boundary element method to calculate the stress distribution beneath an arbitrary topographic profile in the presence of ambient tectonic stress. When applied to a topographic profile across the Susquehanna Shale Hills Critical Zone Observatory in central Pennsylvania, the model predicts where shear fractures would occur based on a Mohr–Coulomb criterion, with considerable differences in profiles of stresses with depth beneath ridgetops and valley floors. We calculate the minimum cohesion required to prevent shear failure, C[subscript min], as a proxy for the potential for fracturing or reactivation of existing fractures. We compare depth profiles of C[subscript min] with structural analyses of image logs from four boreholes located on the valley floor, and find that fracture abundance declines sharply with depth in the uppermost 15 m of the bedrock, consistent with the modeled profile of C[subscript min]. In contrast, C[subscript min] increases with depth at comparable depths below ridgetops, suggesting that ridgetop fracture abundance patterns may differ if topographic stresses are indeed important. Thus, the present results are consistent with the hypothesis that topography can influence subsurface rock fracture patterns and provide a basis for further observational tests. United States. Army Research Office (Award W911NF-14-1-0037) United States. Dept. of Energy (Award DE-FG01-97ER14760) 2015-07-28T14:02:47Z 2015-07-28T14:02:47Z 2014-09 2014-07 Article http://purl.org/eprint/type/JournalArticle 01979337 1096-9837 http://hdl.handle.net/1721.1/97898 Slim, Mirna, J. Taylor Perron, Stephen J. Martel, and Kamini Singha. “Topographic Stress and Rock Fracture: a Two-Dimensional Numerical Model for Arbitrary Topography and Preliminary Comparison with Borehole Observations.” Earth Surface Processes and Landforms 40, no. 4 (September 18, 2014): 512–529. https://orcid.org/0000-0002-0404-8701 https://orcid.org/0000-0002-2646-7384 en_US http://dx.doi.org/10.1002/esp.3646 Earth Surface Processes and Landforms Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Wiley Blackwell MIT web domain |
| spellingShingle | Perron, J. Taylor Martel, Stephen J. Singha, Kamini Slim, Mirna I. Topographic stress and rock fracture: a two-dimensional numerical model for arbitrary topography and preliminary comparison with borehole observations |
| title | Topographic stress and rock fracture: a two-dimensional numerical model for arbitrary topography and preliminary comparison with borehole observations |
| title_full | Topographic stress and rock fracture: a two-dimensional numerical model for arbitrary topography and preliminary comparison with borehole observations |
| title_fullStr | Topographic stress and rock fracture: a two-dimensional numerical model for arbitrary topography and preliminary comparison with borehole observations |
| title_full_unstemmed | Topographic stress and rock fracture: a two-dimensional numerical model for arbitrary topography and preliminary comparison with borehole observations |
| title_short | Topographic stress and rock fracture: a two-dimensional numerical model for arbitrary topography and preliminary comparison with borehole observations |
| title_sort | topographic stress and rock fracture a two dimensional numerical model for arbitrary topography and preliminary comparison with borehole observations |
| url | http://hdl.handle.net/1721.1/97898 https://orcid.org/0000-0002-0404-8701 https://orcid.org/0000-0002-2646-7384 |
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