  The propagation of elastic waves in a fractured rock is investigated, both
theoretically and numerically. Outside the fractures, the propagation of
compressional waves is described in the simple framework of one-dimensional
linear elastodynamics. The focus here is on the interactions between the waves
and fractures: for this purpose, the mechanical behavior of the fractures is
modeled using nonlinear jump conditions deduced from the Bandis-Barton model
classicaly used in geomechanics. Well-posedness of the initial-boundary value
problem thus obtained is proved. Numerical modeling is performed by coupling a
time-domain finite-difference scheme with an interface method accounting for
the jump conditions. The numerical experiments show the effects of contact
nonlinearities. The harmonics generated may provide a non-destructive means of
evaluating the mechanical properties of fractures.
