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The assumption that distributions of mass versus size interval for fragmented materials fit the log normal distribution is empirically based and has historical roots in the late 19th century. Other often used distributions (e.g., Rosin‐Rammler, Weibull) are also empirical and have the general form for mass per size interval: n(l) = klα exp (−lβ), where n(l) represents the number of particles of diameter l, l is the normalized particle diameter, and k, α, and β are constants. We describe and extend the sequential fragmentation distribution to include transport effects upon observed volcanic ash size distributions. The sequential fragmentation/transport (SFT) distribution is also of the above mathematical form, but it has a physical basis rather than empirical. The SFT model applies to a particle‐mass distribution formed by a sequence of fragmentation (comminution) and transport (size sorting) events acting upon an initial mass m′: n(x, m) = C ∫∫ n(x′, m′)p(ξ)dx′ dm′, where x′ denotes spatial location along a linear axis, C is a constant, and integration is performed over distance from an origin to the sample location and mass limits from 0 to m. We show that the probability function that models the production of particles of different size from an initial mass and sorts that distribution, p(ξ), is related to mg, where g (noted as γ for fragmentation processes) is a free parameter that determines the location, breadth, and skewness of the distribution; g(γ) must be greater than −1, and it increases from that value as the distribution matures with greater number of sequential steps in the fragmentation or transport process; γ is expected to be near −1 for “sudden” fragmentation mechanisms such as single‐event explosions and transport mechanisms that are functionally dependent upon particle mass. This free parameter will be more positive for evolved fragmentation mechanisms such as ball milling and complex transport processes such as saltation. The SFT provides better fits to many types of volcanic ash samples than does the log normal curve. Modeling of the SFT shows its similarity to the log normal curve on size frequency histograms; it differs by its variable skewness controlled by γ. Skewed distributions are typical of many volcanic ash samples, and characterization of them by the SFT allows interpretation of eruptive and transport mechanisms.

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Geophysical mass flows-debris flows, volcanic avalanches, landslides-are often initiated by volcanic activity. These flows can contain O(10 6-10 7) m 3 or more of material, typically soil and rock fragments that might range from centimeters to meters in size, are typically O(10 m) deep, and can run out over distances of tens of kilometers. This vast range of scales, the rheology of the geological material under consideration, and the presence of interstitial fluid in the moving mass, all make for a complicated modeling and computing problem. Although we lack a full understanding of how mass flows are initiated, there is a growing body of computational and modeling research whose goal is to understand the flow processes, once the motion of a geologic mass of material is initiated. This paper describes one effort to develop a tool set for simulations of geophysical mass flows. We present a computing environment that incorporates topographical data in order to generate a numerical grid on which a parallel, adaptive mesh Godunov solver can simulate model systems of equations that contain no interstitial fluid. The computational solver is flexible, and can be changed to allow for more complex material models, as warranted.