STRESS MODIFICATIONS PRODUCED BY A CRACK CROSSING THE INTERFACE BETWEEN TWO
ELASTIC MEDIA
M. Bonafede and E. Rivalta
Dipartimento di Fisica, Viale Berti-Pichat 8, I-40127 Bologna
ABSTRACT.
Magma ascent through a mid-oceanic ridge can be modeled as a tensile
crack within which the overpressure is determined by magma buoyancy. In spite
of the large heterogeneity present in the crust, most crack models have been
developed so far in homogeneous media. In this paper the most simple elastic
medium is considered, made up of two welded half spaces characterized by
different elastic parameters. The elementary dislocation problem is solved
first, in which a constant Burgers vector is assigned along a rectilinear
dislocation line parallel to the plane separating the two half-spaces; the
dislocation surface is a half-plane orthogonal to the interface and bounded
by the dislocation line. Explicit analytic solutions are provided for the
displacement and stress fields which are found to reproduce the results
obtained for a tensile dislocation in a half-space with free surface if the
rigidity of the upper half-space vanishes. The problem for a crack entirely
embedded in one of the two media is then considered. The singular Cauchy
integral equation is solved employing a truncated expansion in Chebyshev
polynomials and semi-analytical solutions are given for the displacement and
stress fields provided by a constant overpressure within the crack. Finally
the problem of a crack cutting across the boundary between the two media is
considered. In this case a further singularity appears in the kernel of the
integral equation, which is connected with the presence of the boundary
surface. The problem can be solved by splitting the crack into two interacting
open cracks. The application of a constant overpressure within the crack is
found to produce drastically different stress regimes in neighbouring regions
located on opposite sides of the interface plane; this feature may provide a
straightforward explanation for the episodic reversal (from sinistral to
dextral) of strike-slip mechanisms observed in the South-Iceland seismic zone.