Dynamic tensile strength of terrestrial rocks and application to impact cratering

Abstract

Dynamic tensile strengths and fracture strengths of 3 terrestrial rocks, San Marcos gabbro, Coconino sandstone, and Sesia eclogite were determined by carrying out flat-plate (PMMA and aluminum) impact experiments on disc-shaped samples in the 5 to 60 m/sec range. Tensile stresses of 125 to 300 MPa and 245 to 580 MPa were induced for gabbro and eclogite, respectively (with duration time of ~1 smicroseonds. For sandstone (porosity 25%), tensile stresses normal to bedding of ~13 to 55 MPa were induced (with duration times of 2.4 and ~1.4 microseconds). Tensile crack failure was detected by the onset of shock-induced (damage) P and S wave velocity reduction. The dynamic tensile strength of gabbro determined from P and S wave velocity deficits agrees closely with the value of previously determined values by post-impact microscopic examination (~150 MPa). Tensile strength of Coconino sandstone is 20 MPa for a 14 microseconds duration time and 17 MPa for a 2.4 microseconds duration time. For Sesia eclogite, the dynamic tensile strength is ~240 MPa. The fracture strength for gabbro is ~250 MPa, ~500 MPa for eclogite, and ~40 MPa for sandstone. Relative crack induced reduction of S wave velocities is less than that of post-impact P wave velocity reductions for both gabbro and eclogite, indicating that the cracks were predominantly spall cracks. Impacts upon planetary surfaces induce tensile failure within shock-processed rocks beneath the resulting craters. The depth of cracking beneath impact craters can be determined both by seismic refraction methods for rocks of varying water saturation and, for dry conditions (e.g., the Moon), from gravity anomalies. In principle, depth of cracking is related to the equations-of-state of projectile and target, projectile dimension, and impact velocity. We constructed a crack-depth model applicable to Meteor Crater. For the observed 850 m depth of cracking, our preferred strength scaling model yields an impact velocity of 33 km/s and impactor radius of 9 m for an iron projectile.