Geodesic Location–Allocation for Liquefaction Investigation Coverage in Uttarakhand, India

MOHIT SHEODE 

Site-scale liquefaction investigations in Uttarakhand are concentrated in the Roorkee–Haridwar and Rudrapur–Khatima corridors. This article asks a narrower, operational question: where should a limited reconnaissance programme investigate next to reduce geographic gaps in that evidence? Fifteen settlement-centred nodes were represented as a complete weighted graph, with four literature-supported investigation centres fixed as anchors. Exact enumeration evaluated one to five additions using p-median, p-center and equally weighted, within-budget normalised objectives. Existing anchors produced a mean nearest-centre distance of 27.15 km and a maximum of 69.29 km. For two additions, Dehradun–Kashipur and Vikasnagar–Kashipur were exactly co-optimal under the balanced and p-median objectives, reducing the mean to 15.61 km and the maximum to 41.04 km; all nodes then lay within an illustrative 50 km planning radius. A WGS 84 ellipsoidal ablation preserved all principal selections and changed the two-site balanced mean by only −0.003 km. In 2,000 seeded coordinate-perturbation trials, a western node was effectively invariant, while Kashipur and Bazpur divided most central-eastern selections. The result is a reproducible coverage design, not a liquefaction-hazard map. Complete tie reporting, coordinate provenance, deterministic rules, pinned software versions, convergence checks and file hashes make the analysis independently auditable.