Cracking Patterns of Brittle Hemispherical Domes: an Experimental Study

Crack formation in hemispherical domes is a distinguished problem in structural mechanics. The safety of cracked domes has a long track record; the evolution of the cracking pattern received less attention. Here, we report displacement-controlled loading tests of brittle hemispherical dome specimens, including the evolution of the meridional cracking pattern. The 27 investigated specimens, 20 cm in diameter, were prepared in 3D printed molds, and their material is one of the three mixtures of gypsum and cement. We find that neither the (limited) tensile strength nor the exact value of the thickness significantly affects the statistical description of the cracking pattern, i.e., the cracking phenomenon is robust. The maximal number of the meridional cracks never exceeds seven before the fragments’ disintegration (collapse). We find that the size distribution of the fragments exhibits a lognormal distribution. The evolution is reflected in the load-displacement diagrams recorded in the test, too, as significant drops in the force are accompanied by an emergence of one or more new cracks, reflecting the brittle nature of the phenomenon. A simple, stochastic fragmentation model, in which a segment is fragmented at either in the middle or at the fourth point, fairly recovers the observed size distribution.

Structured coagulation-fragmentation equation in the space of radon measures: Unifying discrete and continuous models

We present a structured coagulation-fragmentation model which describes the population dynamics of oceanic phytoplankton. This model is formulated on the space of Radon measures equipped with the bounded Lipschitz norm and unifies the study of the discrete and continuous coagulation-fragmentation models. We prove that the model is well-posed and show it can reduce down to the classic discrete and continuous coagulation-fragmentation models. To understand the interplay between the physical processes of coagulation and fragmentation and the biological processes of growth, reproduction, and death, we establish a regularity result for the solutions and use it to show that stationary solutions are absolutely continuous under some conditions on model parameters. We develop a semi-discrete approximation scheme which conserves mass and prove its convergence to the unique weak solution. We then use the scheme to perform numerical simulations for the model.

Controls on the grain size distribution of landslides in Taiwan: the influence of drop height, scar depth and bedrock strength

The size of grains delivered to rivers by hillslope processes is thought to be a key factor controlling sediment transport, long-term erosion and the information recorded in sedimentary archives. Recently, models have been developed to estimate the grain size distribution produced in soil, but these models may not apply to active orogens where high erosion rates on hillslopes are driven by landsliding. To date, relatively few studies have focused on landslide grain size distributions. Here, we present grain size distributions (GSDs) obtained by grid-by-number sampling on 17 recent landslide deposits in Taiwan, and we compare these GSDs to the geometrical and physical properties of the landslides, such as their width, area, rock type, drop height and estimated scar depth. All slides occurred in slightly metamorphosed sedimentary units, except two, which occurred in younger unmetamorphosed shales, with a rock strength that is expected to be 3–10 times weaker than their metamorphosed counterparts. For 11 landslides, we did not observe substantial spatial variations in the GSD over the deposit. However, four landslides displayed a strong grain size segregation on their deposit, with the overall GSD of the downslope toe sectors being 3–10 times coarser than apex sectors. In three cases, we could also measure the GSD inside incised sectors of the landslides deposits, which presented percentiles that were 3–10 times finer than the surface of the deposit. Both observations could be due to either kinetic sieving or deposit reworking after the landslide failure, but we cannot explain why only some deposits had strong segregation. Averaging this spatial variability, we found the median grain size of the deposits to be strongly negatively correlated with drop height, scar width and depth. However, previous work suggests that regolith particles and bedrock blocks should coarsen with increasing depth, which is the inverse of our observations. Accounting for a model of regolith coarsening with depth, we found that the ratio of the estimated original bedrock block size to the deposit median grain size (D50) of the deposit was proportional to the potential energy of the landslide normalized to its bedrock strength. Thus, the studied landslides agree well with a published, simple fragmentation model, even if that model was calibrated on rock avalanches with larger volume and stronger bedrock than those featured in our dataset. Therefore, this scaling may serve for future modeling of grain size transfer from hillslopes to rivers, with the aim to better understanding landslide sediment evacuation and coupling to river erosional dynamics.

Fragmentation model for tensile behavior of intermingled hybrid composites and optimal mixing ratio

A numerical fragmentation model is proposed to predict the mechanical response of intermingled, unidirectional hybrid composites under tensile loads. The model is based on a previously developed for unidirectional composites considering the critical number of fiber breaks and the correction of the fiber-matrix interfacial strength. Hybrids comprising two reinforcements are considered, and the energetic contribution of reinforcements is evaluated during the damage process. Additionally, the pseudo-ductile strain, yield strength, and the level of degradation of each reinforcement are estimated. The present model is compared with a progressive failure model and micromechanical finite element simulations, obtaining some similarities in the stress-strain behavior. Results show that both low elongation and high elongation fiber sub-composite experience a linear tensile response where fibers remain intact (IF), and fragmentation (FM) where breaking appears. The sliding/separation phenomenon (SS) occurs in one of the sub-composites when crack saturation is obtained, and failure occurs when the other one undergoes the crack saturation. Results also show that the IF, FM, and SS phenomena are conditioned by the fiber mixing ratio, α. The model allows estimating the optimal value of α for which the highest pseudo-ductile strain and hybrid effect are reached.

A finite volume scheme for the solution of a mixed discrete-continuous fragmentation model

This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the equations. The approximate solutions provided by this scheme are first shown to display conservation of mass and preservation of nonnegativity. Then, by utilising a Dunford-Pettis style argument, the sequence of approximate solutions generated is shown, under given restrictions on the model and the mesh, to converge (weakly) in an appropriate L1 space to a weak solution to the problem. By applying the methods and theory of operator semigroups, we are able to show that these weak solutions are unique and necessarily classical (differentiable) solutions, a degree of regularity not generally established when finite volume schemes are applied to such problems. Furthermore, this approach enabled us to derive a bound for the error induced by the truncation of the mass domain, and also establish the convergence of the truncated solutions as the truncation point is increased without bound. Finally, numerical simulations are performed to investigate the performance of the scheme and assess its rate of convergence as the mesh is refined, whilst also verifying the bound on the truncation error.

Controls on the grain size distribution of landslides in Taiwan: the influence of drop height, scar depth and bedrock strength

The size of grains delivered to river by hillslopes processes is thought to be a key factor to better understand sediment transport, long-term erosion as well as sedimentary archives. Recently, models have been developed for the grain size distribution produced in soil, but they may not apply to active orogens where high erosion rates on hillslopes are driven by landsliding. Until now relatively few studies have focused on landslide grain size distributions. Here we present grain size distribution 5 (GSD) obtained by the grid-by-number sampling on 17 recent landslide deposits in Taiwan, and we compare it to the geometrical and physical properties of the landslides, such as their width, area, rock-type, drop height and estimated depth. All slides occurred in slightly metamorphosed sedimentary units, except two, which occurred in younger unmetamorphosed shales, with rock strength expected to be 3 to 10 times weaker from their metamorphosed counterparts. We found that 4 deposits displayed a strong grain-size segregation on their deposit with downslope toe deposits 3 to 10 times coarser than apex 10 deposits. In 3 cases, we could also measure the GSD inside the landslides that presented percentiles 3 to 10 times finer than the surface of the deposit. Both observations could be due to either kinetic sieving or deposit reworking after the landslide failure but we cannot explain why only some deposits had a strong segregation. Averaging this spatial variability we found the median grainsize of the deposits to be strongly negatively correlated to drop height, scar width and depth. However, previous work suggest that regolith particles and bedrock blocks should coarsen with increasing depth, opposite to our observation. 15 Accounting for a model of regolith coarsening with depth, we found that the ratio of the original bedrock block size and the D50 was proportional the potential energy of the landslide normalized to its bedrock strength. Thus the studied landslides agree well with a published, simple fragmentation model, even if that model was calibrated on much larger and much stronger rock avalanches than those featured in our dataset. This scaling may thus serve for future model of grain size transfer from hillslopes to river, trying to better understand landslide sediment evacuation and coupling to river erosional dynamics.

Controls on the grain size distribution of landslides in Taiwan: the influence of drop height, scar depth and bedrock strength

<div>The size of grains delivered to rivers by hillslopes processes is thought to be a key factor to better understand sediment transport, long-term erosion as well as sedimentary archives. Recently, models have been developed for the grain size distribution produced in soils, but they may be irrelevant to active orogens where high erosion rates on hillslopes are driven by landsliding. Still, until now relatively few studies have focused on measuring and explaining the variability of landslide grain size distributions.</div><div>Here we present grain size distribution obtained by the grid-by-number method on 17 recent landslide deposits in Taiwan, and we compare it to the geometrical and physical properties of the landslides, such as their width, area, rock-type and strength, drop height and estimated depth. All landslides occurred in slightly metamorphosed sedimentary units, except two which occurred in younger unmetamorphosed shales, with rock strength expected to be 3 to 10 times weaker from their metamorphosed counterparts. We found that 4 deposits displayed a strong grain size segregation on their deposit with grains at the toe (downslope) of the deposit 3 to 10 times coarser than the one at the apex. In 3 cases, we could also measure the grain size distribution inside the landslides that presented percentiles 3 to 10 times finer than the surface of their deposits. Both observations could be due to either kinetic sieving or deposit reworking after the landslide failure but we could not explain why only some deposits had a strong segregation.</div><div>Averaging this spatial variability we found the median grain size (D50) of the deposits to be strongly negatively correlated to drop height, scar width and depth. However, previous work suggests that regolith particlesvand bedrock blocks should become coarser with increasing depth (Cohen et al., 2010; Clarke and Burbank, 2011), opposite to our observation. Accounting for a model of regolith coarsening with depth, we found that the ratio of the original bedrock blocksize and the D50 was proportional to the potential energy of the landslide normalized to its bedrock strength. Thus the studied landslides agree well with the simple fragmentation model from Locat et al. (2006), even if it was calibrated on much larger and much stronger rock avalanches. This scaling may thus serve for future model of grain size transfer from hillslopes to river, trying to better understand landslide sediment evacuation and the coupling between hillslopes and river erosional dynamic.</div><div> </div><div>References:</div><div> <div> <div>Clarke, B. A. and Burbank, D. W.: Quantifying bedrock-fracture patterns within the shallow subsurface: Implications for rock mass strength, bedrock landslides, and erodibility, Journal of Geophysical Research: Earth Surface, 116(F4), F04009, , 2011.</div> <div>Cohen, S., Willgoose, G. and Hancock, G.: The mARM3D spatially distributed soil evolution model: Three-dimensional model framework and analysis of hillslope and landform responses, Journal of Geophysical Research: Earth Surface, 115(F4), , 2010.</div> <div>Locat, P., Couture, R., Leroueil, S., Locat, J. and Jaboyedoff, M.: Fragmentation energy in rock avalanches, Canadian Geotechnical Journal, 43(8), 830–851, , 2006.</div> </div> </div><div> </div>

Modelling size distributions of marine plastics under the influence of continuous cascading fragmentation

<p>Field studies have shown that plastic fragments make up the majority of plastic pollution in the oceans in terms of abundance. How quickly environmental plastics fragment is not well understood, however. Here, we study this process by considering a model which captures continuous fragmentation of particles over time in a cascading fashion. With this cascading fragmentation model, we simulate particle size distributions (PSDs), specifying the abundance or mass of particles for different size classes.</p><p> </p><p>The fragmentation model is coupled to an environmental box model, simulating the distributions of plastic particles in the ocean, coastal waters, and on the beach. Transport in the box model is based on a previous study regarding a previous study regarding sources and sinks of marine plastics in the Mediterranean Sea. We compare the modelled PSDs to available observations, and use the results to illustrate the effect of size-selective processes such as vertical mixing in the water column and resuspension of particles from the beach into coastal waters.</p><p> </p><p>Using the coupled fragmentation and environmental box model, we quantify the role of fragmentation on the marine plastic mass budget. While fragmentation is a major source of (secondary) plastic particles in terms of abundance, it seems to have a minor effect on the total mass of particles larger than 0.1 mm. Future comparison to observed PSD data should allow us to understand size-selective plastic transport in the environment, and potentially inform us on plastic longevity.</p>