Abstract

Bedrock fracture is a key element of rock erosion and subsequent surface processes. Here, we test the hypothesis that rock’s susceptibility to subcritical cracking, a specific type of fracturing, significantly drives and limits rock erosion. We measured 10Be-derived erosion rates, compressive strength, and crack characteristics on 20 outcrops of different rock units (quartzite, granite, and two metasandstones) in the northern Blue Ridge Mountains of Virginia (USA). We also measured the subcritical cracking index (n), Charles’s law velocity constant (A), and fracture toughness (KIC) of samples from four of the same outcrops, representative of each rock type. Erosion rates range from 1.16 ± 0.67 to 32.3 ± 7.8 m/m.y. We find strong correlations—across the four rock units—between average erosion rates and the three subcritical cracking parameters (R2 > 0.85, p < 0.05), but not compressive strength (R2 = 0.6; p > 0.1). We also find a correlative relationship between n and outcrop fracture length (R2 = 0.91; p < 0.05). The latter correlation is consistent with that of published model predictions, further indicating a mechanistic link between subcritical cracking and rock erosion. We infer that subcritical cracking parameters closely tie to erosion rates, because subcritical cracking is the dominant process of mechanical weathering, leading to positive feedbacks relating subcritical cracking rates, crack length, porosity, and water accessibility. These data are the first that directly test and support the hypothesis that subcritical cracking can set the pace of long-term rock erosion.

INTRODUCTION

Rock erosion impacts a host of Earth system cycles (e.g., Chappell et al., 2016). Although measurements of erosion rates are proliferating, there has been no corresponding advance in identifying factors that predict those rates (e.g., Perron, 2017). Here, we begin to test a new hypothesis that subcritical cracking governs mechanical damage accumulation in rock, which in turn can set the pace of rock erosion. To our knowledge, there are no published studies of subcritical cracking parameters in the context of quantified rock exposure or erosion history over geologic time (>∼102 yr). We therefore examine the relationship between subcritical cracking and 10Be-derived erosion rates measured in the same locations. We isolate subcritical cracking as a variable by sampling natural rock outcrops with different lithologies but uniform geomorphic, climatic, and tectonic characteristics. We then identify a statistically significant correlation between subcritical cracking parameters, erosion rates, and crack characteristics measured for the outcrops, supporting the hypothesis that subcritical cracking is a rate-limiting process for rock erosion.

BACKGROUND

Rock Erosion and Subcritical Cracking

Mechanical bedrock erosion is predicated on the detachment of transportable particles from rock, which requires that cracks grow and coalesce. Thus, crack spacing, or density, commonly correlates with rates of erosion processes like cliff retreat (Benumof and Griggs, 1999), river incision (e.g., Shobe et al., 2017), and glacial scour (e.g., Krabbendam and Glasser, 2011). Here, we employ the generic term “crack” to include all planar voids at or near the surface (within ∼100 m). Because all cracks, regardless of initial origin, contribute to erosion as they propagate, we do not distinguish between large-scale tectonic joints, microfractures formed during lithification or metamorphism, and any other cracks subsequently propagated due to environmental or topographic stresses. Furthermore, it has been proposed that in the near surface, and over geologic time, all such cracks continue to grow primarily via subcritical cracking (Eppes and Keanini, 2017), a process driven by a magnitude of stress loading lower than a rock’s critical strength (e.g., tensile strength, compressive strength). Thus, we hypothesize that the mechanical parameters regulating rates of subcritical cracking correlate with rock erosion rates, particularly in locations where erosion style (e.g., fluvial, gravitational) and other climate and stress-loading factors are similar.

Subcritical Cracking Rates and Parameters

Existing cracks or other flaws, like pores or grain boundaries, mechanically concentrate external stresses; therefore, the concept of stress intensity is employed to determine whether a crack will propagate critically or subcritically (e.g., Atkinson, 1987; Anderson, 2005). For mode I tensile loading, the stress intensity factor (KI, hereafter termed stress intensity) is commonly given as graphic where σ is the stress induced by the external load and a is one-half of the crack length.

Using this stress intensity concept, subcritical cracking rates are described by Charles’s law for static loads: 
graphic
where da/dt (m/sec) is the crack tip propagation velocity; KI (MPa m1/2) is the stress intensity imposed on a crack of a given length by external stress loading; KIC (MPa m1/2) is the critical stress intensity, or fracture toughness; A (m/s) is a proportionality velocity constant representing cracking velocity when stresses are critical (i.e., when KI /KIC = 1); and n is the unitless subcritical cracking index, whose large magnitudes in most rocks (20–200) strongly influence subcritical cracking rates and styles (e.g., Atkinson, 1987).

As long as KI < KIC, all rock types crack subcritically (see the review in Atkinson, 1987). We emphasize that the combined parameters in Equation 1 describe rock damage that is different from that characterized by rock strength. Rock strength is described by parameters like tensile, shear, or compressive strength, and is the type of metric that has been classically employed in geomorphology studies to quantify resistance to erosion (e.g., Sklar and Dietrich, 2001).

Measured for a relatively homogeneous rock unit at constant conditions, Equation 1 parameters are constants, ranging within ∼2%–10% (e.g., Chandler et al., 2016), but can vary by ∼25%–50% within a generic rock type like granite (e.g., Atkinson, 1987). Across different rock types, the parameters may vary by >200%. They are also sensitive to changes in environment (e.g., Brantut et al., 2013).

METHODS

Field Area

In 10 locations in the northern Blue Ridge Mountains of Virginia (USA), we sampled 20 natural ridgeline (∼1000 m above sea level [masl]) outcrops for which erosion appears to occur primarily via gravitational loss of centimeter-scale grains or chips (Fig. 1; Fig. DR1, Table DR1, and methods in the GSA Data Repository1). Mean annual precipitation is 1.30 m and annual mean high and low temperatures are 13 °C and 3 °C, respectively (U.S. Southeast Regional Climate Center, Big Meadows, Virginia, station; http://www.sercc.com/cgi-bin/sercc/cliMAIN.pl?va0720). Vegetation consists of mixed deciduous and conifer forest. Sampled outcrops consist of four Mesoproterozoic (Y) to Cambrian (C) rock units (Southworth et al., 2009): Old Rag Granite coarse-grained metagranite (unit Yos, nine samples); Weverton Formation pebbly metasandstone (unit Ccw, two samples); Harpers Formation metasandstone (unit Cch, three samples); and Antietam Formation quartzite (unit Cca, six samples).

Bare-Rock Erosion Rates

We chiseled 10Be samples from the upper 5–10 cm of outcrop surfaces. Samples were processed following the methods of Kohl and Nishiizumi (1992) and von Blanckenburg et al. (1996). 10Be/9Be ratios were measured by accelerator mass spectrometry at the Purdue Rare Isotope Measurement Laboratory (PRIME) (Purdue University, Indiana, USA) in 2008–2009, and ratios determined using an ICN-revised (ICN Biomedical, Inc.) 10Be standard (07KNSTD; Nishiizumi et al., 2007). The CRONUS-Earth online calculator (version 2.3; https://hess.ess.washington.edu) was used to estimate erosion rates from 10Be concentrations (Table DR2), accounting for topographic shielding (Balco et al., 2008) and using the constant production rate model and scaling scheme of Lal (1991) and Stone (2000).

Subcritical Cracking Parameters

So as not to induce fractures through chiseling, fracture testing samples consisted of single, >20 cm, intact boulders collected at the base of, and distinctly originating from, one 10Be-sampled outcrop for each rock unit (Fig. DR2). No rocks of significant size were found at unit Yos outcrops, so we sampled talus ∼275 m downslope of a 10Be sampling location.

The four rock samples were sliced into plates (7.5 × 3.2 × 0.2 cm) that were smoothed and grooved along the central axis (Figs. DR3–DR6). Based on the numbers of plates successfully processed, varying numbers of tests per parameter per rock type were performed (Table DR3). Importantly, based on published rock physics studies examining similar properties (e.g., Heap et al., 2009; Chen et al., 2017; Nara et al., 2017), we note that four rock samples, with three to nine duplicates per parameter, represents a characteristic—and robust—number of both samples and measurements.

We measured fracture mechanical parameters on each plate using a standard double torsion method (Fig. DR7; e.g., Shyam and Lara-Curzio, 2006). Pre-cracking introduced initial fractures at a displacement rate of 0.45 μm/s (Fig. DR8). Load relaxation measurements were made at a displacement rate of 45 μm/s, and parameters were derived from the resulting data (Figs. DR8 and DR9). Tests were performed using a Sensor-Werks Model 113 load cell and a Trans Tek 0241–0000 linear variable displacement sensor. Displacement control was established using an Applied Motion 5017–009 step motor combined with an Applied Motion Si3540 programmable step motor drive. A National Instruments USB-6215 multifunction input-output device and LabVIEW software (http://www.ni.com/en-us/shop/labview.html) were used for motor control and digital signal acquisition.

Outcrop Field Properties

Numerical fracture propagation models (e.g., Olson, 2004), though limited in number, predict relationships between crack length and density and n. Thus, if subcritical cracking is driving and limiting cracking on our outcrops, these models provide a secondary test of our central hypothesis. We therefore collected crack data (length and density of all natural cracks >2 cm) at the same 20 outcrops sampled for 10Be concentration (Table DR4).

Finally, in order to place our results in the context of a commonly measured critical cracking parameter, we measured in situ rock compressive strength (reported in unitless Q) with a SilverSchmidt type N hammer for all 20 outcrops (after Shobe et al., 2017; Table DR4).

RESULTS AND DISCUSSION

Subcritical Cracking and Erosion Rates

Lower values of n and KIC and higher values of A—all leading to faster subcritical cracking via Equation 1—correlate with higher erosion rates (Figs. 2A–2C; R2 > 0.85; p < 0.05). Schmidt hammer Q values, as a proxy for compressive strength, do not relate strongly to erosion rates (R2 = 0.6; p > 0.1; Fig. 2D). We infer that the subcritical cracking parameter, n, best correlates with erosion rates, as values of n are closely tied to the rate of bond-breaking processes directly at crack tips (e.g., Brantut et al., 2013), where prior rock damage, like that caused by weathering, is minimal. In contrast, compressive strength, KIC, and A are all predicated, in part, on crack interactions throughout the tested rock mass. (e.g., Anderson, 2005) and thus are potentially more influenced by the unique characteristics of individual samples. Consequently, measured values of n may be more representative of all past cracking—and thus erosion—than the other metrics, which change with exposure history.

Nevertheless, we submit that subcritical cracking parameters together correlate with rock erosion rates largely because the majority of stresses that lead to rock fracture in this and other settings are very low in magnitude (e.g., Leith et al., 2014; Lamp et al., 2017). In other words, most stresses at Earth’s surface can frequently exceed the threshold for subcritical cracking (≤∼10% KIC; e.g., Atkinson, 1987; Eppes and Keanini, 2017) but rarely exceed critical thresholds (Collins et al., 2018). When external stress loading, climate, and erosion styles are similar (as in our outcrops), subcritical cracking parameters themselves predict erosion rates because they predict subcritical cracking rates (Equation 1). Although a rock’s critical strength—as measured through properties like Q—may well forecast the potential for catastrophic failure, it may not necessarily reflect the long-term subcritical crack growth that any given rock experienced during most of its near-surface history, which drives long-term erosion.

We propose that feedbacks strengthen the subcritical cracking–erosion relationship. Namely, as cracks subcritically propagate, their increased length accelerates cracking due to the concurrent increase in stress intensity (KI in Equation 1). Because KIC also incorporates crack length, it may predict erosion rates better than compressive strength (Fig. 2). In addition, accelerated cracking should result in faster growth in porosity, providing more access for moisture at crack tips. Moisture hastens cracking through its influence both on water-dependent stress loading processes like freezing as well as on the subcritical cracking bond-breaking processes themselves (e.g., reviewed in Eppes and Keanini, 2017). These feedbacks may be evident, for example, in observations that rocks undergoing abundant microcracking have deeper weathering profiles than those without, despite the former being more chemically resistant to weathering (Bazilevskaya et al., 2013).

Although this study does not consider sufficient data to directly test these complex feedbacks, field data do provide some evidence that observed outcrop cracks grew subcritically. Specifically, numerical modeling of fracture growth (e.g., Renshaw and Pollard, 1994; Olson, 2004) predicts that when cracks grow subcritically, their spacing and length are strongly influenced by n. Values of n of ∼20 are predicted to lead to the lowest crack density and largest crack lengths, and high n values (∼80) to notably shorter crack lengths and widely spaced, but dense, crack clusters (e.g., Olson, 2004). Values of n in this study (∼40 to ∼80) exhibit the predicted positive correlations (Fig. 3), supporting the idea that their growth occurred subcritically. Although few other field tests of such relationships exist (Olson et al., 2001), our observed correlations comprise an independent data set that is at least consistent with a causal link between subcritical cracking and rock erosion.

Applicability, Limitations, and Conclusions

Although ridgeline outcrops represent a relatively simple eroding system that may well be composed of more-resistant rock than the surrounding subsurface rock (Portenga et al., 2013), we believe that the potential for rocks to subcritically crack may set a baseline for erosion rates in a wide variety of surface and subsurface environments. The brittle-elastic subcritical cracking parameters presented herein are comparable to those measured globally (e.g., Brantut et al., 2013). Also, a growing body of literature implicates subcritical cracking as a key component of weathering and erosion processes (Eppes and Keanini, 2017), including rock fall and exfoliation (Collins et al., 2018), boulder breakdown (Eppes et al., 2016), glacier dynamics (Weiss, 2004), and bedrock channel incision (Shobe et al., 2017). Thus, where erosion or regolith production is predicated on the detachment of particles from bedrock, subcritical cracking likely plays a key role. One implication of this conclusion is that frequently recurring, low-magnitude stresses may play an equal or greater role in preparing rock for erosion than infrequent high-magnitude ones.

Undoubtedly, when stress loading, climate, and erosion styles vary, the link between subcritical cracking parameters and erosion or regolith production rates becomes complex. This complexity arises, in part, because both the magnitude of stress intensity as well as the subcritical cracking parameters vary with environment and with progressive chemical weathering. Feedbacks between chemical weathering and fracture are also likely strong, but are not widely documented or understood (e.g., Brantley et al., 2017). Further, moisture not only affects chemical reaction rates, but also can accelerate subcritical cracking even when stress loading is constant (Eppes and Keanini, 2017). Finally, stress loading at Earth’s surface varies significantly in both time and space (e.g., Draebing et al., 2017), with factors like soil depth adding to the complexity of rock response (e.g., Heimsath et al., 2012). Thus, exploring links and feedbacks between subcritical cracking, weathering, and erosion for settings beyond outcrops will require a strong understanding of not only low-magnitude stress loading, but also how subcritical cracking parameters themselves vary under different environmental conditions for rocks with different exposure histories.

We acknowledge that this data set is only a beginning. However, our findings support the novel hypothesis that subcritical cracking is a foundational process in rock mechanical weathering and erosion. These data therefore illustrate a new avenue of exploration that may help to better quantify the age-old question of how and why rock type matters.

ACKNOWLEDGMENTS

This research was funded in part by the U.S. Geological Survey, the University of North Carolina at Charlotte, and the College of William and Mary (Virginia). We thank Shenandoah National Park and Peter Eichhubl at the University of Texas at Austin. Dewers gratefully acknowledges funding from the U.S. Department of Energy (contract DE-SC0006883) at Sandia National Laboratories (New Mexico, USA), a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525, U.S. Department of Energy grant DE-FE0023316.

1GSA Data Repository item 2018364, details regarding all methods described in the manuscript, and supplemental tables and figures, is available online at http://www.geosociety.org/datarepository/2018/ or on request from editing@geosociety.org.