https://doi.org/10.1130/G47089.1
Manuscript received 9 October 2019 Revised manuscript received 24 December 2019 Manuscript accepted 23 January 2020
© 2020 Geological Society of America. For permission to copy, contact [email protected]. Published online 18 March 2020
Experimental quantification of bedrock abrasion under oscillatory flow James F. Bramante1,2, J. Taylor Perron2, Andrew D. Ashton1 and Jeffrey P. Donnelly1 1Department of Geology & Geophysics, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USA 2Department of Earth, Atmospheric & Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
ABSTRACT geometry, bedrock strength, and sediment char- Although wave-driven abrasion of submarine bedrock affects the evolution of rocky coasts acteristics (Sklar and Dietrich, 2006; Turowski and reefs globally, the dependence of the abrasion rate on wave forcing and sediment avail- et al., 2007; Lamb et al., 2008). ability remains poorly quantified. We performed experiments in which an artificial substrate The unsteadiness of flow and sediment mo- was abraded by varying amounts of coarse-grained sediment subjected to oscillatory flows. In tion under waves may cause rate laws for wave- these experiments, the bedrock incision rate scaled by the square of bedrock tensile strength (I, driven abrasion to deviate from those derived –1 2 –1 m yr MPa ) varied with mean root-mean-square (rms) velocity (
1GSA Data Repository item 2020154, Figures DR1–DR4, Videos DR1–DR5 of bed forms, and Tables DR1 and DR2 (summarizing the videos and all experiments), is available online at http://www.geosociety.org/datarepository/2020/, or on request from [email protected].
CITATION: Bramante, J.F., Perron, J.T., Ashton, A.D., and Donnelly, J.P., 2020, Experimental quantification of bedrock abrasion under oscillatory flow: Geology, v. 48, p. 541–545, https://doi.org/10.1130/G47089.1
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Downloaded from http://pubs.geoscienceworld.org/gsa/geology/article-pdf/48/6/541/5051203/541.pdf by MBL WHOI Library user on 01 December 2020 2 square of the substrate tensile strength (σT ; Sk- A lar and Dietrich, 2001; Scheingross et al., 2014). (In situations where sediment instead slides on top of exposed bedrock, shear strength may be a more appropriate quantity for scaling abrasion rates.) The abrasion medium, subrounded silici-
clastic gravel with sieve diameter D50 = 6.1 mm, was scattered uniformly across the duct floor and foam before initiation of each experiment. We re- fer to the average volume of gravel per unit area of the duct floor as sediment load,S (cm3 cm–2). Upon initiation of oscillatory flow in each ex- periment, most of the sediment rapidly self-or- ganized into one or more bedforms, leaving most of the duct floor covered only by scattered sedi- ment grains. The morphology of the bedforms varied with S. At low S (0.0075–0.015 cm3 cm–2), the bedforms consisted of mobile bands 1–2 grain diameters thick and 10–30 grain diameters wide that migrated over distances much greater than B their width (Fig. 1B; Videos DR1 and DR2). In experiments with high S (≥0.12 cm3 cm–2), the bedforms consisted of mounds several grain di- ameters high with appearance similar to rolling- grain ripples (Fig. 1B; Videos DR3 and DR4; Pedocchi and Garcia, 2009). Motion of these mounds differed between low (<0.75 m s–1) and –1 high (≥0.75 m s ) urms. In low-urms/moderate-S
and high-urms/high-S experiments, the mounds had a stationary core, and sediment saltated from the stoss face of a mound, over the mound crest, to the bare substrate on the lee side every half- oscillation (Fig. 1B; Videos DR3 and DR4). In
high-urms/moderate-S experiments, the mounds migrated back and forth in their entirety, pri- marily through saltation (Fig. 1B; Video DR5). The isolated bedforms in our experiments with high-S resembled isolated ripples of sand- sized sediment observed in the field. For ex- ample, on the Ningaloo Australia fringing reef, large wave events expose bare substrate that is covered by coarse sand ripples (Rosenberger et al., 2019). On mixed sand-gravel beaches, iso- lated ripples form on otherwise immobile beds Figure 1. Experimental design and influence of bedforms. (A) Schematic drawing of the oscil- when flows are insufficiently strong to mobilize latory flow tunnel. PVC—polyvinyl chloride. (B) Video stills from two experiments illustrating gravel (Hay et al., 2014). a fully mobile sediment band (left column) and a partially static isolated ripple (right column). Blue boxes indicate two layers of sediment grains that remain stationary during the entire The number and spacing of bedforms in our wave period and cover the bed. Sediment had median (95% confidence interval) sieve diameter experiments tended to increase with increasing –3 of D50 = 6.1 (4.2–7.6) mm and density ρs = 2570 (2300–2840) kg m ;
ing scaled with do (range: 0.6do−1do) and was maintained sinusoidal water-level fluctuations which varied between experiments due to differ- consistent with field observations of orbital rip- in the vertical reservoirs. When the POUT was ences between foam batches from the manufactur- ple spacing in coarse sediment beds (Fig. DR3; filled, the water in the horizontal duct oscil- er, to simulate reef or bedrock substrate (Schein- Pedocchi and Garcia, 2009). Because these bed-
lated with a natural period of Ts ≈ 4.75 s and gross et al., 2014). The erosion rate was measured forms produced spatial variability in the abra-
with root-mean-square (rms) velocity (urms, m by weighing the foam and was normalized by sion rate, the foam was cut to the length of one –1 –1 s ) of up to 1 m s . Given a particular urms and the foam surface area and density to produce the full bed-form spacing (0.8do). Because only one
Ts, the distance a water parcel travels during incision rate. Because bedrock subjected to the bedform would be located on the foam, we nor- half of an oscillation is the orbital diameter, low-velocity impacts of rolling or saltating sedi- malized S in each experiment by the number of
duor= 2/msTs π. ment fails in tension (Sklar and Dietrich, 2001), bedforms, which we will refer to as normalized To generate detectable erosion during short and following previous experiments investigat- sediment load (S*, cm3 cm–2). experiments, we used closed-cell urethane foam ing the volumetric erosion rate of rock, concrete, We performed two sets of experiments us-
with low tensile strength (σT = 0.34–0.71 MPa), and foam, we multiplied the incision rate by the ing the POUT (Table DR2). In the first set,
542 www.gsapubs.org | Volume 48 | Number 6 | GEOLOGY | Geological Society of America
Downloaded from http://pubs.geoscienceworld.org/gsa/geology/article-pdf/48/6/541/5051203/541.pdf by MBL WHOI Library user on 01 December 2020 3 –2 2 we held S constant at either 0.03 cm cm or where I is incision rate scaled by σT rate increased with increasing S* until reaching 3 –2 –1 2 7 –1 0.12 cm cm and varied urms in the range 0.4– (m yr MPa ); Ct = 3.15 × 10 s yr is a a maximum (tools effect) and then decreased –1 1.0 m s . In the second set, we held urms con- conversion factor for time; K is a constant with increasing S* (cover effect). The shape of stant at 0.5, 0.6, or 0.75 m s–1 and varied S over [s(n–1) m–(n–1) MPa2]; angle brackets (< >) indicate our inferred tools and cover effect was similar 0.0075–0.48 cm3 cm–2. time-averaging over an entire experiment; and n to that found in rotary mill experiments (Sklar is a dimensionless exponent. A nonlinear least- and Dietrich, 2001), but it had a slower decay CONTROLS ON BEDROCK INCISION squares fit provided estimates (95% confidence of incision rate, indicating a weaker cover ef-
Across all experiments, mean incision rate of interval) of n = 4.2 (3.6, 4.8) and CtK = 1.0 (0.7, fect. The tools and cover effects can be mod- 2 the bedrock simulant increased with urms (Fig. 2), 1.3), with R = 0.86. Thus, incision rate scales eled with a power function of sediment mass
which is described well by a power law of the with urms raised to a power of ∼4. (T17; Turowski and Hodge, 2017). Applied to
form: For a given urms, the relationship between the the abrasion mill experiments, T17 collapses to incision rate and S was characterized by tools a special case in which additional sediment falls n I =
) 95% confidence interval 2 σT = 0.71 MPa form motion (Fig. 4A), because the entire bed- of fit. Vertical error bars form was mobilized during each flow oscillation.
MPa represent ±1 standard -1 Total sediment load deviation in mean inci- However, for high S, a portion of the bedform (cm3cm-2) 10-1 sion rate as estimated remained immobile, and incision rates were low- S = 0.48 from Monte Carlo uncer- est under the center of the bedform and highest S = 0.24 tainty analysis in which at the bed-form edges, where sediment saltated S = 0.12 measurement uncertainty S = 0.09 and variability in material vigorously (Fig. 4A). For a constant, high S, a S = 0.06 properties (foam weight, large portion of the bed under the bedform was S = 0.03 foam density, and foam Incision rate, I (myr covered at low urms, whereas the same region S = 0.015 tensile strength) were experienced maximum incision rates at higher S = 0.0075 propagated through the u as the bedform was fully mobile (Fig. 4B). incision rate calculation rms 4.2 2 I = 1.0
was calculated as I = (mpre – mpost)/(Asub × ρsub × texp), where mpost is post-experimental weight rate under oscillatory flow increases exponentially after foam was dried in an oven at 100 °C for 8 h, mpre is pre-experiment weight, texp is experi- with orbital velocity and that S provides a sec- ment duration, Asub is the foam’s exposed surface area, and ρsub is foam density. ondary control through tools and cover effects. The transition of bedforms from fully mobile to partially static appears to mark the transition in Figure 3. Influence of Abrasion dominance from the tools to the cover effect. The POUT mill sediment availability on = 0.76 ± 0.015 m s-1 power-law dependence of abrasion rate on oscil- 0.5 rms bedrock incision rate. Ver- = 0.60 ± 0.015 m s-1 tical error bars represent lation velocity implies a strong feedback between
) rms 2 -1 ±1 standard deviation of water depth and abrasion rate, because the orbital
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Downloaded from http://pubs.geoscienceworld.org/gsa/geology/article-pdf/48/6/541/5051203/541.pdf by MBL WHOI Library user on 01 December 2020 A relationship between oscillation velocity and in- Figure 4. Variability in cision rate that predicts coastal bedrock abrasion abrasion rate with position rates from typical wave characteristics. relative to bedforms. Inci- sion rate was measured ACKNOWLEDGMENTS along the length of foam We thank the Massachusetts Institute of Technol- substrate demonstrating ogy (MIT) Makerworkshop for material assistance. the influence of bedforms This study was supported by the U.S. Department of in three experiments: (A) Defense Strategic Environmental Research and Devel- with mean oscillation opment Program through award SERDP RC-2336, velocity time-averaged by the Woods Hole Oceanographic Institution Ocean over an entire experiment Venture Fund, and by the MIT Department of Earth, = 0.75 m s–1, includ- rms Atmospheric and Planetary Sciences Student Research ing those in Figure 1B, Fund. We also thank Jens Turowski and an anony- and (B) with sediment B mous reviewer for their insightful comments on our load S* = 0.12 cm3 cm–2. manuscript. Incision rates were nor- malized by the maximum incision rate in each REFERENCES CITED profile. 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