Two dimensional self-similar expanding crack problems in elastic half-space

• Exact response of P–SV wave effect has been evaluated using dynamic similarity.
• Transient response has been obtained via body force equivalent.
• Result is valid at least up to the time of arrival of diffracted waves.
• The expression of the surface displacement contains the head wave contribution.
• The spectral behavior of the source time function is moderate than Brune’s model.

The application of the property of dynamic similarity is useful to the solution which admits a self-similarity or homogeneous form. One independent variable has been dropped in the present equivalent set of the governing equations. The displacement discontinuity on the crack face and also the displacement field on the surface due to an in-plane shear model over an expanding zone of slippage of arbitrary dip have been obtained. The moving slip edge extends towards the surface with a constant velocity. Cagniard De-Hoop technique has been used here to obtain the two dimensional exact transient response due to the slip in the vertical mode via body force equivalent. The results of the present paper are valid at least up to the time when the diffracted waves from the crack edge have not reached the receiving station. The spectral behavior of the source time function has also been discussed.