  A geometric model of a physical network affected by a disaster is proposed
and analyzed using integral geometry (geometric probability). This analysis
provides a theoretical method of evaluating performance metrics, such as the
probability of maintaining connectivity, and a network design rule that can
make the network robust against disasters.
  The proposed model is of when the disaster area is much larger than the part
of the network in which we are interested. Performance metrics, such as the
probability of maintaining connectivity, are explicitly given by linear
functions of the perimeter length of convex hulls determined by physical
routes. The derived network design rule includes the following. (1) Reducing
the convex hull of the physical route reduces the expected number of nodes that
cannot connect to the destination. (2) The probability of maintaining the
connectivity of two nodes on a loop cannot be changed by changing the physical
route of that loop. (3) The effect of introducing a loop is identical to that
of a single physical route implemented by the straight-line route.
