Equal Area, Unequal Connectivity: A Random-Field Framework for Liquefaction Hazard Organization

Abstract. Scalar liquefaction hazard descriptors quantify the amount of potentially unstable ground, but they do not describe how susceptible or low-resistance zones are spatially organized. As a result, equal weak-zone area may correspond to fragmented, clustered, or domain-scale connected configurations with different field-scale implications.

This study develops a connectivity-based random-field framework to distinguish weak-zone extent from weak-zone organization in spatially variable liquefaction susceptibility fields. Dataset-informed synthetic Gaussian Random Field realizations were generated from cleaned SPT_N160 statistics and investigation-domain geometry. The fields were converted into binary low-resistance weak-zone domains through lower-tail equal-area thresholding and quantified using graph-based connectivity descriptors.

Across a dense Pf−θ parameter space, where Pf is the prescribed weak-zone area fraction and θ is the spatial correlation length, the results reveal a systematic transition from fragmented to clustered and spanning regimes. Low-Pf fields remain fragmented across the explored range, whereas higher-Pf​ fields progressively develop larger connected components and domain-scale continuity. The clearest transition occurs around Pf=0.50, where spanning probability exceeds 0.50 once θ reaches approximately 200 m.

A random-allocation null model shows that spatially correlated fields produce fewer connected components, lower fragmentation, larger dominant components, and stronger top-cluster concentration than random fields with the same weak-zone area fraction. The 2011 Christchurch manifestation field further indicates that observed liquefaction patterns also contain non-random spatial organization beyond affected-area fraction. By separating hazard extent from spatial organization, the framework provides a topology-aware basis for interpreting field-scale liquefaction hazard and for identifying whether susceptible zones imply local, cluster-scale, or system-scale mitigation relevance.