Other
Scientific paper
Dec 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011agufm.p34a..07c&link_type=abstract
American Geophysical Union, Fall Meeting 2011, abstract #P34A-07
Other
[5417] Planetary Sciences: Solid Surface Planets / Gravitational Fields, [5420] Planetary Sciences: Solid Surface Planets / Impact Phenomena, Cratering
Scientific paper
The most characteristic geophysical signature of an impact crater is a circular negative gravity anomaly, centered over the crater. The cause of the gravity low is dilatancy: fracturing and brecciation, induced by the passage of the shock wave and comminution during crater formation, creates pore space between fragments and fractures, reducing the bulk density of the sub-crater material. Calculation of damage accumulation is routine in modern numerical impact simulations; accounting for dilatancy is not. As a result, most impact simulations do not correctly predict density changes beneath an impact crater, which limits the scope for comparison of model results with geophysical data. A simple approach to account for dilation during shear failure in impact simulations is to supplement the pressure computed by the equation of state with a "dilatancy pressure," representing the outward force of grains moving passed one another, in cells where shear failure has occurred (Johnson and Holmquist, 1994; doi:10.1063/1.46199). This additional pressure effectively shifts the pressure-density relationship for the dilatant material up (to a higher pressure) so that when the material unloads to atmospheric pressure the density drops to a (dilated) bulk density that is below the reference density of the pristine material. A limitation of this approach is that the bulk modulus of the dilated material is the same as that of the pristine material and, consequently, that an unrealistically large dilatancy pressure is required to achieve typical bulk densities of fractured rock. Here we propose an improvement to this approach where both the distension (porosity) and the pressure are modified during shear failure, which allows for the correct reduction in bulk modulus with increasing dilation. In our approach, shear failure leads to a prescribed decrease in the reference density of the dilatant material. The ratio of this reference density to the current density is used to compute a distension (porosity), which through the ɛ-α porosity model acts to increase the pressure by the amount required to shift the material from its current equation of state surface to that of the more distended, dilatant material. We show that simulations of crater formation using our dilatancy model are in good agreement with observed density and porosity variations beneath terrestrial simple craters and make predictions about the role of dilatancy in the formation of larger, complex craters. Our new dilatancy model will allow future numerical impact simulations to be directly compared with geophysical observations, such as gravity and seismic velocity anomalies, providing much greater observational constraint on simulation results. This is of particular significance for models of terrestrial craters where the surface expression has been removed by erosion and the geophysical signature is the only vestige of impact. Moreover, numerical simulations of cratering with dilatancy will aid in the interpretation of high-resolution gravity data soon to be collected over lunar craters by GRAIL.
Collins Gary S.
Melosh Henry Jay
Wilson Richard C.
Wuennemann K.
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