Work Description

Date: 1 July, 2020

Dataset Title: Quantifying near-surface rock strength on a regional scale from hillslope stability models [Data set]

Dataset Creators: K.F. Townsend, S.F. Gallen, & M.K. Clark

Dataset Contact: Kirk Townsend kirkft@umich.edu

Funding: EAR-1528576 (NSF), Department of Earth and Environmental Sciences (University of Michigan), Rackham Graduate School (University of Michigan)

Key Points:
- We quantify hillslope-scale, near-surface rock strength on a regional scale using the Culmann and Newmark hillslope-stability models.
- Strength estimates are generally low, with cohesion model predictions less than 60 kPa for friction angle predictions of 24 to 44 degrees.
- The cohesion of young sedimentary rocks in the shallow subsurface increases with increasing maximum burial depth.

Research Overview:
Rock strength is a fundamental property of earth materials that influences the morphology of landscapes and modulates feedbacks between surface processes, tectonics, and climate. However, rock strength remains challenging to quantify over the broad spatial scales necessary for geomorphic investigations. Consequently, the factors that control rock strength in the near-surface environment (i.e. the “critical zone”) remain poorly understood. Here we quantify near-surface rock strength on a regional scale by exploiting two hillslope-stability models, which explicitly relate the balance of forces within a hillslope to Mohr-Coulomb strength parameters. We first use the Culmann finite-slope stability model (Culmann, 1875; Schmidt & Montgomery, 1995) to back-calculate static rock strength with high-density measurements of ridge-to-channel hillslope height and gradient. Second, we invert the Newmark infinite-slope stability model for strength using an earthquake peak ground acceleration model and coseismic landslide inventory (Gallen et al., 2015). We apply these two model approaches to a recently inverted sedimentary basin in the eastern Topatopa Mountains of southern California, USA, where a tectonic gradient has exposed stratigraphic units with variable burial histories. Results show similar trends in strength with respect to stratigraphic position and have comparable strength estimates to the lowest values of published direct-shear test data. Cohesion estimates are low, with Culmann results ranging from 3 to 60 kPa and Newmark results from 6 to 30 kPa, while friction angle estimates range from 24 to 44 degrees from the Culmann model. We find that maximum burial depth exerts the strongest control on the strength of these young sedimentary rocks, likely through diagenetic changes in porosity, cementation, and ultimately, lithification.

Methodology:
The data are apatite (U-Th)/He low-temperature thermochronometry sample analyses, and direct-shear test results for rock strength.

Bedrock samples for (U-Th)/He low-temperature thermochronometry were collected in April 2016 to infer magnitudes of exhumation. Samples were crushed, sieved, and separated using standard methods to isolate apatite by exploiting differences in density and magnetic susceptibility. Individual mineral grains were hand-selected under a high-powered binocular microscope to screen for clarity, crystal morphology, and minimal inclusions of other potentially radiogenic minerals. Grains selected for analysis were measured along major and minor axes, photographed, packaged into individual Pt tubes, and analyzed for 4He content using an Australian Scientific Instruments Helium Instrument (Alphachron) at the University of Michigan Thermochronology Laboratory. Grains were heated for 5 minutes at 900°C, released 4He was spiked with 3He, and the 4He /3He ratio was measured on a Pfeiffer quadrupole mass spectrometer to determine the quantity of 4He. Following this initial 4He measurement, these analytical procedures were repeated to check for any additional extraction of 4He that might be indicative of micro-inclusions of high-temperature radiogenic minerals that were not observed optically during grain selection. The Durango apatite age standard was also analyzed with our samples to ensure accuracy of measurements of unknown age. After measurement of 4He, grains were dissolved and analyzed for U, Th and Sm concentrations following standard procedures (Reiners and Nicolescu, 2006) using a Thermo Scientific Elements 2 ICP-MS at the University of Arizona Radiogenic Helium Dating Laboratory.

Individual grain dates were solved for numerically in Matlab using parent and daughter nuclide concentrations and the age equation. Analytical uncertainties were propagated through the age equation using Monte Carlo methods. Grains with low uranium concentrations are particularly susceptible to age biases that result from uranium-implantation from surrounding U-rich phases. Grains with uranium concentrations under 5 ppm are reported but excluded from calculation of mean values. Outliers were identified following the Dean-Dixon (1951) method based on the 90 percent confidence interval at two significant digits. We applied this outlier test only to bedrock samples with a 2-sigma standard error greater than 15 percent of the mean age. Using the remaining grain ages, we calculated a mean apatite (U-Th)/He age for each sample. Because the observed variability in our (U-Th)/He ages for individual bedrock samples is larger than the analytical error for single grains, we report mean ages for bedrock samples with uncertainty as the standard error of the mean for the multiple grains analyzed. We consider bedrock samples that have a one-sigma standard deviation greater than 45 percent of the mean age to have low reproducibility, and we do not report a mean age for 16-PC-1 for this reason. Each replicate age of 16-PC-3 is as older or older than the middle- to late-Miocene depositional age of the Monterey Formation, indicating that the ages are inherited and do not reflect cooling of the sample. We therefore do not report a mean age here.

Instrument and/or Software specifications: NA

Files contained here:
One spreadsheet containing thermochronometry sample information, and one spreadsheet containing direct-shear test results on rocks collected from each formation (three formations total).

- Thermochronometry.xlsx: contains thermochronometry sample information for three samples. Tab 1 contains general location and age information, and Tab 2 contains raw elemental concentrations for each grain analysis.

- DS_Saugus.xlsx: contains direct-shear strength test results for all rock samples from the Saugus Formation.

- DS_Pico.xlsx: contains direct-shear strength test results for all rock samples from the Pico Formation.

- DS_Monterey.xlsx: contains direct-shear strength test results for all rock samples from the Monterey Formation.

Related publication(s):
Townsend, K.F., Gallen, S.F., & Clark, M.K. 2020. Quantifying near-surface rock strength on a regional scale from hillslope stability models. Journal of Geophysical Research Earth Surface, https://doi.org/10.1029/2020JF005665.

References:
- Culmann, C. (1875). Die Graphische Statik. Zurich: Meyer and Zeller.

- Dean, R. B., & Dixon, W. J. (1951). Simplified statistics for small numbers of observations. Analytical chemistry, 23(4), 636-638.

- Gallen, S. F., Clark, M. K., & Godt, J. W. (2015). Coseismic landslides reveal near-surface rock strength in a high relief, tectonically active setting. Geology, 43(1), 11–14. https://doi.org/10.1130/G36080.1

- Reiners, P. W., & Nicolescu, S. (2006). Measurement of parent nuclides for (U-Th)/He chronometry by solution sector ICP-Ms. ARDHL Report 1, (December 2006), 1–33. Retrieved from http://www.geo.arizona.edu/~reiners/arhdl/arhdl.html

- Schmidt, K. M., & Montgomery, D. R. (1995). Limits to Relief. Science, 270(5236), 617–620.

Use and Access:
This data set is made available under an Attribution Non-Commercial 4.0 International License (CC BY-NC 4.0).

To Cite Data:
Townsend, K.F., Gallen, S.F., & Clark, M.K. (2020). Quantifying near-surface rock strength on a regional scale from hillslope stability models [Data set]. University of Michigan - Deep Blue. https://doi.org/10.7302/9bj1-q884