Research ArticleGEOPHYSICS

Universal characteristics of particle shape evolution by bed-load chipping

See allHide authors and affiliations

Science Advances  28 Mar 2018:
Vol. 4, no. 3, eaao4946
DOI: 10.1126/sciadv.aao4946
  • Fig. 1 Expected evolution of the roundness R plotted as a function of the relative mass loss μ.

    Properties of R(μ) in decreasing order of their universality: (i) vertical tangent at μ = 0; (ii) horizontal tangent at μ = 1; (iii) monotonic increase of R(μ); (iv) R(1) = 1; and (v) monotonic decrease of dR/dμ (convexity).

  • Fig. 2 Environments and sediments examined in this study.

    Field data were collected from different environments: (A) gravel-bed river in Puerto Rico, (B) gypsum dune field in New Mexico, (C) pebble beach in Marina di Pisa, and (D) experiment in a rotating drum. All illustrated environments select for the conditions of bed-load transport (right side) where impacts from saltation drive chipping.

  • Fig. 3 Evolution of circularity.

    Field, experimental, and model data showing the evolution of circularity with (A) transport distance from source and (B) mass loss. Data points represent the median value of R. Note in (A) that axes have been linearly rescaled so that curves fall on each other; the curves of circularity naturally collapse when replotted against mass loss (B). Note that model results do not appear in (A) because transport distance is not relevant, whereas wave results are absent because initial conditions (at x = μ = 0) and transport distance are not known. Initial measurements (at t = 0) for wave data in (B) are projected onto the curve because these particles were already partially rounded; changes in roundness following recovery of tracers, however, are consistent with other data.

  • Fig. 4 Field data from Marina di Pisa of wave-transported pebbles.

    Red and blue show initially angular and rounded pebbles, respectively. (A) Change in R and (B) mass loss (μ) for the individual pebbles. The legend in (B) applies to both panels. (C) Examples of an initially angular (top) and initially rounded (bottom) pebble before (left) and after (right) the experiment.

  • Fig. 5 Evolution of the number of particles during the rotating drum experiment on limestone fragments.

    The initial increase is evidence of fragmentation occurring in the beginning of the experiment.

  • Fig. 6 Numerical chipping model with the addition of moderate fragmentation compared to available data.

    Shape data examined are (A) roundness, (B) axis ratio, (C) number of stable points, and (D) number of unstable points; the latter two were not available for White Sands data. Data points represent average values.

  • Fig. 7 Phase space for attrition: Effect of relative size, normalized collision energy, and normalized grain size on attrition mode.

    The zone corresponding to chipping and self-dual collisions is highlighted in gray; this is the region associated with bed-load transport.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/3/eaao4946/DC1

    Model results without fragmentation

    Evolution of equilibrium points for the wave data

    Effect of fragmentation on axis ratio and circularity

    Estimating transport distance for the beach data

    fig. S1. Numerical chipping model without fragmentation compared to available data.

    fig. S2. Field data from Marina di Pisa showing change in the number of equilibrium points.

    fig. S3. β, γ, and β/γ.

    fig. S4. Transport and mass loss of wave-driven pebbles at Marina di Pisa.

  • Supplementary Materials

    This PDF file includes:

    • Model results without fragmentation
    • Evolution of equilibrium points for the wave data
    • Effect of fragmentation on axis ratio and circularity
    • Estimating transport distance for the beach data
    • fig. S1. Numerical chipping model without fragmentation compared to available data.
    • fig. S2. Field data from Marina di Pisa showing change in the number of equilibrium points.
    • fig. S3. β, γ, and β/γ.
    • fig. S4. Transport and mass loss of wave-driven pebbles at Marina di Pisa.

    Download PDF

    Files in this Data Supplement:

Stay Connected to Science Advances


Editor's Blog

Navigate This Article