运用拓扑学原理研究汶川与唐山地区公路网络的稳定性

Study on the Stability of Road Networks in Wenchuan and Tangshan Region Using Topology Theory

摘要:

汶川地震与唐山地震几乎将当地生命线系统完全损毁。以评价在近场地震作用下的城镇生命线系统的"稳健性"为研究目标,采用地震灾害比较学中拓扑学原理,计算两地公路网络相关评价参数并进行分析。参数包括拓扑指数(TI(G))、拓扑逆指数(TII(G))和节点孤立指数(NSI)等。研究得出公路网络"稳健性"唐山震后(2008年)最优,汶川(2007年)次之,唐山震前(1975年)最低的结论。从纯数学角度引入最优化理论,认为在复建原有公路前提下加修北川到安县等五条公路,区域分散性最高,且节点孤立指数最小,这时的公路网络易损性最低。

Abstract:

In Wenchuan earthquake and Tangshan earthquake the local lifeline systems were almost totally damaged.To evaluate the ＂stability＂ of the local lifeline systems under the condition of near field earthquake,the evaluation parameters of the two road nets are calculated and analyzed based on the theory of earthquake disaster comparatology.Those parameters are Topological Index（TI（G））,Topological Inverse Index（TII（G）） and Node Solitude Index（NSI） etc.The result shows that the ＂Stabilities＂ from low to high are Tangshan Before-earthquake （1975）, Wenchuan Before-earthquake （2007）, Tangshan After-earthquake （2008）. It is concluded that five additional roads, Beichuan to Anxian and so on, should be built in case of rehabilitation the existing roads before Wenchuan earthquake with the optimization theory from a purely mathematical point of view, in which the local road nets would be the highest regional dispersion, the smallest node isolation index, and would be most stability.