Open AccessAn elliptical asperity in shear: fracture process and seismic radiation
Author(s) -
Das S.,
Kostrov B. V.
Publication year - 1985
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1985.tb05121.x
Subject(s) - asperity (geotechnical engineering) , geology , fracture (geology) , ellipse , shear (geology) , slip (aerodynamics) , geometry , materials science , mechanics , geotechnical engineering , physics , mathematics , petrology , thermodynamics
Summary. The fracture of a single, elliptical asperity of uniform strength and having aspect ratios (major: minor axes) of 3:1 and 5:1 on an infinite fault plane is studied. The initial stress distribution is obtained from a solution of the static problem of a pre‐existing unbroken elliptical region on a plane of contact. The initial traction on the asperity is parallel to the direction of the applied shift at infinity only if this shift is along the major or minor axis of the ellipse; otherwise it is at some small angle to the applied shift direction. The initial stress concentration is always larger at the end of the major axis than at the end of the minor axis. The fact that a material cannot support a stress concentration higher than its yield strength, together with the fact that long, thin asperities are more effective stress concentrators suggests that there may be a bias in asperity population away from long, thin asperities. The dynamic fracture problem is studied for the cases when the applied shift is parallel to the major axis, parallel to the minor axis and at 45° to the axes. It is found that dynamic fracture can be initiated only by relaxing a point within the highly stressed areas at the ends of the major axis. The fracture processes obtained for the different asperities depend on the yield strength required for fracture and on the direction in which the remote shift is applied. In some cases, the fracture front sweeps across the asperity from one end to the other as a nearly straight line at a nearly constant speed. In other cases, only the highly stressed regions at the two ends of the asperity break leaving the remaining asperity unbroken. In other cases, it was found that the fracture at first only broke the highly stressed region near one end of the major axis but when the P ‐ or S ‐wave (depending on the particular case) from the first few broken points reached the other end, fracture was spontaneously initiated there and the highly stressed region at this end was broken. Thus the configuration of the asperity in the stress field together with its material strength completely controls the fracture process. The radiated displacement pulse shapes for some of the cases studied are shown.