Earthquake physical damage and functional serviceability of lifeline network models

The connectivity of lifeline systems is studied in this paper in terms of two ratios: ‘damage ratio’, which is the degree of physical damage to the system, and is defined as the expected number of failures per unit length or per link; and ‘service ratio’, which is a measurement of system operation. First, the relationship between the two ratios in a historic event is examined. Second, a method is developed for determining this relationship in simple network systems immediately following an earthquake. Density function, expected value and covariance of service ratio are calculated as functions of the damage ratio. Even in a simple checkerboard-type network, the density function of the service ratio has two peaks. Third, the variation in reliability of the network is examined with respect to difference in scale and configuration of the network, which may accompany growth of the community. When the damage ratio is small, the service ratio of a complex network is as large as, or larger, than that of a simple network. This pattern is, however, reversed for larger damage ratios. Finally, the relationship prior to operation restoration is examined. During the initial stages of restoration, the service ratio increases steeply, almost linearly, with decrease in the damage ratio. The increase then slows in the last stages of restoration.