Eppes, et al., 2018, Rates of subcritical cracking and long-term rock erosion: Geology,

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1 GSA Data Repository Eppes, et al., 2018, Rates of subcritical cracking and long-term rock erosion: Geology, SUPPLEMENTARY METHODS Sampling Strategy We collected data for 20 naturally occurring outcrops within Blue Ridge physiographic province within of Shenandoah National Park (SNP) (Fig. S1). We focus on natural bedrock outcrops as the simplest, and therefore most testable, component of the erosion system. These outcrops have similar climate, tectonics and geomorphic history, thus we avoid the complex influence that these variables may have on erosion rates overall (West et al., 2005) or the subcritical cracking-rates themselves (Eppes and Keanini, 2017). Basinaveraged erosion rates average across different rock types and microclimates, in contrast, would require numerous inferences and assumptions regarding subcritical cracking data. For example, a major assumption that would need to be made if one were going to test the idea for basin-average erosion rates would be that erosion is proceeding at the same rate in the location where the bedrock was sampled for subcritical cracking as the erosion rate that is measured from 10Be in sediment in streams. In the case of the outcrops, both the erosion rates and the subcritical parameters are measured in virtually the same square meter of rock. Another assumption necessary to complete the work for basin-averaged erosion rates would be that the environmental variables (moisture and temperature at the bedrock surface) are held constant throughout the basin obviously not true. So, in that case, the subcritical cracking parameters would have to be measured or adjusted to fit these different conditions since subcritical cracking itself is dependent on climate (see Eppes and Keanini, 2017). All of the outcrops were located on main ridgelines or spur ridges following Portenga et al. (2013). Sampling was completed on outcrops and tors located within four major quartzbearing lithologic units in the SNP: quartzite from the Antietam Formation (Cca, n=6); quartzite and metasandstone from the Harpers Formation (Cch, n=3); metaconglomerates of the Weverton Formation (Ccw, n=2); and coarse-grained metagranites of the Old Rag Granite (Yos, n=9) (Southworth et al., 2009). We collected samples from additional outcrops for 10Be (n=4) as well as crack data (n=2) for a second member of the Old Rag Granite (Yor), but do not discuss in the text, as we did not collect any subcritical cracking data for this rock type. Sampled outcrops and tors ranged from ~0.5 m to ~3 m in height above the surrounding soil-mantled or talus-mantled surface, and with near-horizontal upper surfaces exceeding ~0.5 m in the shortest horizontal dimension. Outcrop heights >0.5 m were chosen to minimize the possibility that the outcrops were intermittently soilmantled in the recent past. Outcrop widths >0.5 m in the shortest horizontal dimension were chosen to minimize the potential influence of outcrop edges on both the cosmogenic and rock property measurements. At each sampled location, we determined the outcrop elevation and location using a Trimble GeoXT GPS collector with a Trimble Hurricane external antenna and post-processing using differential correction using CORS stations. 10Be Methods We measured bare-bedrock erosion rates from rock samples from outcrops and tors (Table S1). At each location, we collected samples on near-horizontal bare-bedrock surfaces and

2 away from the soil-mantled or steep outcrop edges. We collected slabs of rock from the top of the outcrop with measured thicknesses <10 cm. Using a Brunton compass, we measured the dip of sampled surfaces and the azimuth and altitude above the horizon for all major horizon breaks around each sample site. With this data, we calculated the horizon shielding using the CRONUS-Earth calculator version 1.1 to obtain topographic shielding (Balco et al., 2008). Rock samples were crushed in a jaw crusher and a disk pulverizer to reduce the most of the sample to <500 microns. Samples were dry sieved to retain the 250 um to 500 um fraction followed by hand removal of obvious non-quartz minerals. The sample was then treated following the procedure of Kohl and Nishiizumi (1992) to obtain pure quartz, including an initial 24-hour heated bath of 1:1 hydrochloric acid for removal of iron oxides and carbonates, followed by four 12-hour baths of 1% hydrofluoric acid/1% nitric acid at ~90 C in an ultrasonic tank to remove silicates (Kohl and Nishiizumi, 1992). Extraction and isolation of beryllium from the purified quartz was done following procedures modified from Von Blanckenburg et al. (1996). The 10Be/9Be ratios in the samples were measured by accelerator mass spectrometry by the PRIME Lab at Purdue University in 2008 to The ratios were determined using an ICN revised 10Be standard (07KNSTD, Nishiizumi et al., 2007). We ran a process blank in parallel with each group of seven samples, and we subtract the blank concentration from each group before calculations. We use the CRONUS-Earth online calculator (version 2.3, Balco et al., 2008) to estimate erosion rates and exposure ages using from the 10Be concentrations. We report erosion rate and exposure age calculations based on the constant production rate model and scaling scheme of Lal (1991) and Stone (2000). We note that comparison with other schemes provided in the online calculator yielded minor differences from the constant rate model (~+/-6%). Variables needed for the online calculator are provided in Table S1. For each of the four rock units, we calculate a mean erosion rate using all individual outcrops from that rock unit (Fig. 2 using data from Table S2). We then used a standard propagation of error method to calculate an associated uncertainty for each mean (Error Bars in Fig. 2) using the uncertainties from each individual outcrop (Table S2). These individual uncertainties were derived from CHRONOS. The CHRONOS uncertainty calculations incorporate several components of uncertainty within the 10Be methods generally that are described in full in Balco et al. (2008). Subcritical Cracking Analysis We were unable to extract sufficiently in-tact pieces of these resistant, quartz-rich outcrops for testing. Instead, we collected a single large boulders, >20 cm diameter from each of the four units as described in the text. The Ccw, Cch and Cca boulders were collected immediately at the base of their respective outcrops, and clearly originated from the outcrop that had been sampled. There were not boulders at the base of Yos outcrops, so the boulder was collected from a talus field ~275 m down slope from the sampled outcrop. Ccw, Cch and Cca boulders exhibited similar weathering characteristics to the outcrops from which they were derived. The Yos sample appeared more weathered (more oxidation,

3 rougher surface) than the nearest 10Be-sampled outcrops, but otherwise exhibited no evidence that it had been impacted by its transport down the slope. Although our search was not exhaustive, we found no study of subcritical cracking parameters where samples were collected in this way. Most studies measure blocks cut from quarries or cores. However, there is no reason to believe that the blocks would mechanically significantly different from their adjacent outcrops with respect to the subcritical cracking measurements. The benefit of subcritical measurements over other types of rock testing, is that the former measures the characteristics of deformation in a very small (<mm) region of the rock that is likely representative of such deformation at all crack tips throughout the rock, as evidenced by the relatively consistent values measured in replicates. This is not true of parameters like compressive strength or even KIC, that influenced by fracture interaction and thus weaken notably with increases in the size of the sample being analyzed as more flaws are incorporated (Weibull affect). In particular, values of n are closely tied to the rate of bond breaking processes at crack tips in regions of the rock mass where no damage has previously occurred (e.g. Brantut et al., 2013). The following analyses were completed on those boulders. Double Torsion Tests The double torsion technique is well established and suitable for investigating subcritical fracture behavior of rocks, metals, concrete, cements, polymers, and ceramics (Williams and Evans, 1973; Fuller, 1979; Pletka et al., 1979; Atkinson, 1984; Shyam and Lara-Curzio, 2006). In the double torsion setting, the mode I stress intensity factor KI is proportional to the applied load (Williams and Evans, 1973): 1/2 3(1 + νν) KK II = PPWW mm WWdd 3 dd nn ψψ where P is the load, Wm is bending moment arm, W is specimen width, d is specimen thickness, dn is specimen thickness at the groove (Fig. S6), is Poisson s ratio, and is the geometric correction factor associated with the specimen thickness/width ratio (Fuller, 1979): (SS1) ψψ = ττ + 1.2ττ exp ππ ττ (SS2) in which =2d/W is the reduced thickness/width ratio. Fracture toughness can be calculated using Eq. 1 by replacing P with Pmax, the peak load at critical failure under fast displacement rates of more than a few mm/min (Meredith and Atkinson, 1985; Selçuk and Atkinson, 2000; Nara et al., 2012). Using the load-relaxation technique (Williams and Evans, 1973), fracture velocity can be acquired from the load relaxation data by V = ϕ P 0a 0 dp P 2 dt (S3)

4 where ϕ is a geometric correction factor associated with the curved fracture front (Fig. S6), P0 and a0 are the load and fracture length at the beginning of the relaxation period, respectively, and dp/dt is the first order derivative of the load relaxation data. We chose ϕ =0.2 for our calculations (Williams and Evans, 1973; Atkinson, 1979). A constant fracture length of a0=1.3 cm was used to calculate fracture velocity to avoid the difficulty of directly measure fracture length (Chen et al., 2017). Once stress intensity and fracture velocity were calculated from the load-relaxation measurements, K-V curves can be constructed and subcritical index can be calculated through power-law approximations to the K-V curves by V = A 0 KK nn (S4) where the power-law exponent n is the subcritical index, and A0 (in m/s) is the fitting constant. Experimental Procedure The rock samples were first cut into thin plates of about 3 by 1.25 by The cut surfaces were then smoothed and fracture guiding grooves were cut along the central axis (Fig. S7). The groove depth was about half the specimen thickness. We performed tests on specimens both in ambient air at an ambient temperature of ~25 C. Initial fractures were first introduced by pre-cracking the intact specimens at the specified environments at a slow displacement rate of 0.45 µm/s followed by a relaxation period of about 15 min. For load relaxation measurements, four to six load relaxation measurements were then performed on these pre-cracked specimens at a displacement rate of 45 µm/s until complete failure (Fig. S8, Chen et al., 2017). For fracture toughness measurements, a faster displacement rate of 225 µm/s was applied to crack the specimens until critical failure. Due to the heterogeneity of the Cca, Cch and Yos rock samples, however, we only succeeded in measuring fracture toughness using this critical failure method for Cca (Table S3). For the other three rock samples, we therefore estimated fracture toughness values from the maximum stress intensity factor during individual load relaxation measurements, a commonly employed approach. In order to compare comparably collected data, we estimated fracture toughness for Cca in this way as well (Table S3) and found a <3% difference in the results. We therefore use the K-V-derived KIC values for all four rocks in Fig. 2 of the manuscript. Our double torsion testing apparatus is equipped with a Sensor Werks Model-113 load cell with maximum range of ~25 lbs and accuracy of 0.2% for load measurements, an Applied Motion step motor combined with an Applied Motion Si3540 programmable step motor driver for displacement control, and a Trans Tek linear variable displacement sensor at resolution of 0.2 m for displacement measurements. A National Instruments USB-6215 multifunction I/O device and Labview software were used for motor control and digital signal acquisition. We used a sampling frequency of 4 Hz.For each rock type, we calculate mean and standard deviation for the parameters (Figs. 2 & 3), using all available data.

5 Data Analysis Load relaxation data was first used to derive the stress intensity factor KI (Eq. S1) and fracture velocity V (Eq. S3), then the K-V curves were constructed. K-V curves deviating from the power-law relation by more than 50% away from the main population were thought as bad tests and were removed. The screened K-V curves for the four rock types were shown in Fig. S9. An exponential fitting to the K-V curves yielded subcritical index n and the fitting constant A0 (Eq. S4). A0 was then converted to A (Eq. 1 of the text) by A=A0KK IIII nn. Mean and 1σ standard derivation values were then calculated from the raw data (Table S3) and used to construct Fig. 2. Fracture toughness KIC were calculated using the peak load during critical failure for Cca, and were also estimated from the maximum stress intensity factor during individual load relaxation measurements (Table S3). For the Cca sample, KIC value derived from peak load at critical failure is 2.7% larger than that estimated from the maximum stress intensity factor during load-relax measurements, indicating that the later approach is reasonable for KIC measurement. Outcrop Properties We collected compressive strength, crack density and crack length data for the same outcrops from which 10Be data were collected. In order to determine the locations of the boxes in which data would be collected, we first measured the length, width and height of the outcrop (if the outcrop was taller than we could reach, we used the accessible portion). We then established a transect down the middle line of the side for which we were making measurements, and divided the transect into equal intervals. At the dividing point between each interval, we centered a box. The size of the box depended on the overall crack density of the rock type. For rocks with lower crack density, we employed larger boxes in order to adequately characterize the outcrop s cracking. Overall, boxes ranged from ~ cm 2. Due to outcrop shape, size and access (some were dangerously exposed), the numbers of boxes for which data were collected varied by outcrop. Because the distribution of both datasets was characterized by a long tail in high values, we log-transformed the data in order to calculated the averages presented in Table S4. Compressive Strength Measurements We used a Proceq brand Type N SilverSchmidt hammer (Schmidt hammer) to measure the uniaxial compressive strength of the bedrock surfaces sampled for CRN-derived erosion rates. The Schmidt hammer measures uniaxial compressive rock strength by recording the rebound velocity of a plunger that strikes the rock surface. Lower rebound velocity indicates lower compressive rock strength, while higher rebound velocity indicates higher compressive strength. The Schmidt hammer uses a proxy of compressive strength, Q, which is interpreted to be the percentage of the rebound velocity relative to the impact velocity, with a low detection limit of 10 and a maximum value of ~100 (Proceq, SilverSchmidt user manual). For a given rock type, we assume that a lower Q value, and hence a lower compressive strength, implies greater erodibility related to primary rock properties and/or greater rock weathering (e.g. Goudie, 2006). We do not convert Q to compressive strength, as published conversion equations do not span the entire range of our measurements. Hence, we report Q when providing numerical values, but refer to compressive strength when discussing the implications of the measurements.

6 Though the Schmidt hammer is susceptible to error from surface roughness, distance from fractures, and moisture (e.g. Hoek and Brown, 1997), it has been shown to be an effective tool for exploring the extent of surface weathering for geomorphic purposes (e.g. Goudie, 2006; Sumner and Nel, 2002). Two possible sources of error that are difficult to account for are fractures beneath the rock surface and lichen growing on the rock surface that may dampen the Schmidt hammer impact. Here, however, the possible presence of subsurface fractures is not a critical uncertainty because small fractures in the subsurface may be caused or enlarged by weathering, so we assume that fracturing at this scale is expression of weathering that is recorded by the Schmidt hammer. We avoided taking measurements of lichen-covered rock. The suggested minimum sample size for Schmidt hammer datasets is 15 to 30 measurements on a single bedrock surface (e.g. Niedzielski et al., 2009). At each sample location, we placed a sampling grid (a 35 cm x 35 m sampling grid with 100 ~2.5 cm x ~2.5 cm square cells) on at least two adjacent, near-horizontal, intact rock surfaces on sampled bedrock outcrops, and collected 25 Schmidt hammer measurements within each grid at randomly chosen points. At each bedrock outcrop, a total of at least 50 Schmidt hammer measurements were collected (Table S3). When collecting data, we avoided locations where the rock was visibly wet, as wet rock has been found to reduce Schmidt hammer rebound values compared to the same rock when dry (Sumner and Nel, 2002). Although the sampled surfaces were not smooth, we made sure that the Schmidt hammer plunger tip was striking a flat surface. All Schmidt hammer measurements were taken at least 15 cm from any significant joint (>5 mm width). Following each field day, we tested the Schmidt hammer by collecting 25 measurements from a certified calibration anvil and calculated the average Q and standard deviation for the test. Crack Measurements For each outcrop, we measured cracking characteristics within 2-6 boxes, depending on the size of the outcrop. Within each box, we took measurements for all cracks any linear void longer than it was wide that crossed through or occurred entirely within the box boundary that were >2 cm in length. Crack length was measured as its entire exposed distance both in and out of the box - along the surface of the rock using a flexible seamstress tape, in lieu of a point to-point caliper type of measurement. Eppes has found this to be a more reproducible metric. This crack surface exposure length also is more relevant to rock erosion as it describes the total amount of rock surface that the crack intersects. We also noted the length of the portion of the crack found within the box. To arrive at crack density, we summed the lengths of all of the in box portions of all cracks that crossed through or occurred entirely in the box and divided by box area. As such, our crack length measurements describe the characteristic length of individual cracks; whereas the crack density describes the spacing between the cracks in any given area on the outcrop. Regressions For each rock unit we present the mean and standard deviation of measured subcritical parameters, as well as the mean and propagated uncertainty of the measured erosion rates

7 (see above). Because erosion rate uncertainty (or standard deviations) varied, we employed weighted least squares regressions to assess the given relationships (Figs. 2 and 3). Supplementary References Cited Balco, G., Stone, J. O., Lifton, N. A., and Dunai, T. J., 2008, A complete and easily accessible means of calculating surface exposure ages or erosion rates from 10Be and 26Al measurements: Quaternary geochronology, v. 3, no. 3, p Goudie, A. S., 2006, The Schmidt Hammer in geomorphological research: Progress in Physical Geography, v. 30, no. 6, p Hoek, E., and E. T. Brown Practical estimates of rock mass strength. International Journal of Rock Mechanics and Mining Sciences 34(8): Kohl, C., and Nishiizumi, K., 1992, Chemical isolation of quartz for measurement of in-situproduced cosmogenic nuclides: Geochimica et Cosmochimica Acta, v. 56, no. 9, p Niedzielski, T., Migoń, P., and Placek, A., 2009, A minimum sample size required from Schmidt hammer measurements: Earth Surface Processes and Landforms, v. 34, no. 13, p Nishiizumi, K., Imamura, M., Caffee, M. W., Southon, J. R., Finkel, R. C., and McAninch, J., 2007, Absolute calibration of 10Be AMS standards: Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, v. 258, no. 2, p Portenga, E. W., Bierman, P. R., Rizzo, D. M., and Rood, D. H., 2013, Low rates of bedrock outcrop erosion in the central Appalachian Mountains inferred from in situ 10Be: Geological Society of America Bulletin, v. 125, no. 1-2, p Southworth, S., Aleinikoff, J. N., Bailey, C. M., Burton, W. C., Crider, E., Hackley, P. C., Smoot, J. P., and Tollo, R. P., 2009, Geologic map of the Shenandoah National Park region, Virginia: US Geological Survey, Stone, J. O., 2000, Air pressure and cosmogenic isotope production: Journal of Geophysical Research: Solid Earth, v. 105, no. B10, p Sumner, P., and Nel, W., 2002, The effect of rock moisture on Schmidt hammer rebound: tests on rock samples from Marion Island and South Africa: Earth Surface Processes and Landforms, v. 27, no. 10, p Von Blanckenburg, F., Belshaw, N., and O'Nions, R., 1996, Separation of 9Be and cosmogenic 10Be from environmental materials and SIMS isotope dilution analysis: Chemical Geology, v. 129, no. 1-2, p West, A. J., Galy, A., and Bickle, M., 2005, Tectonic and climatic controls on silicate weathering: Earth and Planetary Science Letters, v. 235, no. 1, p

8 Sample Sample Location Latitude Longitude Elevation (m) Thickness (cm) Density (g/cm3) Slab width (cm) Horizon Concentration Blockage (Atoms 10 Be/g) Uncertainty (Atoms 10 Be/g) Outcrop Sites Cca-01 Turk Mt E E+04 Cca-02 Turk Mt E E+04 Cca-03 Rocky Mt E E+04 Cca-04 Rocky Mt E E+04 Cca-05 Rocky Mt E E+04 Cca-06 Calvary Rocks E E+04 Cch-01 Blackrock E E+04 Cch-02 Blackrock E E+04 Cch-03 Blackrock E E+04 Ccw-01 Knob Mt E E+04 Ccw-02 Knob Mt E E+04 Yos-01 Hogback E E+04 Yos-02 Hogback E E+04 Yos-03 Mary's Rock > E E+04 Yos-04 Mary's Rock > E E+04 Yos-05 Mary's Rock > E E+04 Yos-06 Mary's Rock > E E+04 Yos-07 Pinnacle E E+04 Yos-08 Pinnacle > E E+04 Yos-09 Pinnacle > E E+04 Table S1. Outcrop Location Data and Raw 10 Be Data

9 Table S2. Erosion Rates Erosion rate Uncertainty Effective half- Sample (m/my) (m/my) life (105 yrs) Cca Cca Cca Cca Cca Cca Cch Cch Cch Ccw Ccw Yos Yos Yos Yos Yos Yos Yos Yos Yos Table S2. Outcrop Erosion Rates 1

10 Rock 1 Plate # Cca 2 KIC (MPa m 1/2 ) 3_n _n Cch - - Yos - - Ccw Format of plate # column: first number represents plate number, last number represent cycle of load relaxation. 2 K IC for Cca was calculated from peak load at critical failure under a fastest loading rate of 225 m/s. 3 K IC is derived from the maximum stress intensity factor for each load relax cycle. 4 da/dt represents crack velocity at K=0.999K IC. Table S3. Measured values for the indicated parameters for different plates cut from the rock samples indicated. 3 KIC 1 Plate # (MPa m 1/2 ) n A (m/s) 4 da/dt (m/s) 1_n E E-6 1_n E E-6 1_n E E-10 1_n E E-5 1_n E E-7 4_n E E-5 4_n E E-5 5_n E E-6 5_n E E-5 5_n E E-5 5_n E E-5 5_n E E-5 5_n E E-5 5_n E E-5 5_n E E-5 2_n E E-5 3_n E E-3 3_n E E-7 1_n _n E E-2 1_n E E-5 1_n E E-7 1_n E E-9 1b_n E E+6 1b_n E E-9 3_n _n

11 Sample Mean Compressive Strength (Q) n Mean Crack Density (1/m) n Mean Crack Length (mm) n Formation Cca 52 ± ± ± Ccw 41 ± ± ± 3 55 Cch 56 ± ± ± Yos 41 ± ± ± Table S4 Compressive Strength and Crack Data. Data are means of log transformed means and standard deviations for both density and length due to the long tails of their distributions. For Q, averages and standard deviations are of all Schmidt strikes from all outcrops of the indicated rock unit (ex: 180 strikes on Cca outcrops). For density, data are for all measured boxes (supplementary methods) on all outcrops of the indicated rock unit (ex: 46 boxes on Cca outcrops). For crack length, data are calculated from all measured cracks on all outcrops of the indicated rock unit (ex: 469 measured cracks on Cca outcrops).

12 Front Royal, VA 38 54'36.31 N 78 12'4.10 W Figure S1 Sampling locations by rock type in Shenandoah National Park (black outline). See Supplementary Methods for rock type descriptions. Inset photograph depicts a typical outcrop sampled in the study.

13 Ccw Cch ~10 cm Cca Yos Figure S2 The four boulders employed for all subcritical cracking measurements.

14 Figure S3 Photograph of examples of plates (~7.5 x 3.2 x 0.2 cm) that were cut and analyzed for subcritical cracking parameters for the Cca sample

15 Figure S4 Photograph of examples of plates (~7.5 x 3.2 x 0.2 cm) that were cut and analyzed for subcritical cracking parameters for the Cch sample

16 Figure S5 Photograph of (~7.5 x 3.2 x 0.2 cm) examples of plates that were cut and analyzed for subcritical cracking parameters for the Ccw sample

17 Figure S6 Photograph of plates (~7.5 x 3.2 x 0.2 cm) that were cut and analyzed for subcritical cracking parameters for the Yos sample

18 Figure S7 Loading configuration and specimen geometric parameters for the double torsion method. Two curved fracture tip lines are marked in the cross sectional view, indicating a predominant fracture propagation direction along the y axis with a small component along the z axis.

19 Figure S8 Loading history for the Cch wafer 5. At the loading stage, load was slowly applied at displacement rate of 0.45 mm/s until pre cracking was initiated. A total of 9 load relax cycles were applied until complete sample failure when the crack front approached the far end of the wafer. Inset shows the detail of loadrelax cycle 4, which was loaded at displacement rate of 45 mm/s and used to construct K V curve and subcritical crack growth parameters. specimen in ambient air. Inset: detailed view at peak load of N during critical failure.

20 Figure S9 K V curves for the four types of rocks measured in ambient air. Mean fracture toughness values were marked by dashed black lines. Examples of the power law fit to one K V curve for each rock are marked in red, where A 0 and n values were derived.