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This paper proposes a method to 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 research for railway track circuit systems where transmission line models are often employed. Determining deviations from baseline properties of the railway circuit is important for health monitoring of the system and 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. Thus, in addition to monitoring the integrity of the railway circuit, our approach also could provide a means for safe operation in that it can be used to detect segments of the rail system that are occupied by trains.