  This paper proposes a method to quickly and efficiently compute the voltage
and current along a transmission line which can be "damaged"; that is its
electrical properties can be unevenly distributed. The method approximates a
transmission line by a self-similar circuit network and leverages our previous
work regarding the frequency response for that class of networks. The main
motivation arises from the research for railway track circuit systems where
transmission line models are often employed. However, in contrast to real
transmission lines, railway track circuits are more likely to be damaged due to
its scale and environmental uncertainties; furthermore, changes in circuit
properties due to a train occupying a segment of the track also is of great
interest as a means to ensure safety. As a result, an accurate and quick
simulation of damaged track circuits is necessary and can contribute to the
corresponding health monitoring research area in the future.
