Buildings on debris-flow fans are struck not by one idealized event but by sequences and overlapping groups of surges, and by hazard chains in which debris flows combine with floods, rockfall, or slope slides. Luo, Zhang, Wang and He (2020) proposed a physics-based fragility framework with Monte Carlo simulation for a reinforced-concrete frame impacted by multiple debris-flow surges: cumulative damage from sequentially arriving surges was formulated by tracking the damage state left by each surge, but the amplified damage effect of concurrently arriving surges proved case-specific, and they posed as open problems the general superposition law for interacting surges, element-level fragility under impact, impulse loading from bouldery fronts, validation against multi-hazard field damage data, and extension to longer and mixed hazard chains. Later literature (2022–2026) treats individual chains and single hazards but still states that the effect of simultaneous hazards on building vulnerability remains inadequately addressed. The open problem is a general, predictive, mechanics-based composition law for building vulnerability under interacting debris-flow surges and their multi-hazard extensions, validated against documented field damage.

Background

A debris flow is a rapidly moving, sediment-laden surge of water and debris that descends steep channels and spreads onto alluvial fans where settlements are located; it typically arrives as a train of discrete surges whose fronts are enriched in large boulders. In landslide risk analysis, the vulnerability of an element at risk is the expected degree of loss given a hazard intensity, and for buildings it is commonly expressed through fragility curves — functions giving the probability that a structure reaches or exceeds a damage state as a function of a hazard intensity measure (flow depth, velocity, or impact pressure). A standard engineering approximation for impact loading is the hydrodynamic pressure model p=αρv2p=\alpha\rho v^{2}, where ρ\rho is the flow density, vv the front velocity, and α\alpha a dynamic impact coefficient; it represents sustained fluid loading but not the sharp impulses produced when bouldery fronts strike a structure. Structural response is often estimated by pushover analysis, a nonlinear static finite-element procedure in which lateral loads representative of the debris thrust are applied in increasing magnitude while global frame displacement is monitored; the chosen response quantity is called an engineering demand parameter (EDP). Because both hazard intensity and structural resistance are uncertain, vulnerability is computed probabilistically, for example by Monte Carlo simulation — repeated random sampling of flow scenarios and building properties to estimate failure probability. Multi-hazard risk arises when several hazardous processes affect the same structure, either sequentially (a hazard chain, such as an earthquake that weakens a building that is then struck by a debris flow) or concurrently (overlapping surges or simultaneous processes). The prevailing simplification treats the events as independent, so that the vulnerability to several events is composed by elementary probability rules from the single-event vulnerabilities. Luo, Zhang, Wang and He (2020), building on their physics-based vulnerability studies for single flows and their reliability-based formulation of building vulnerability to debris-flow impact, showed with a fragility framework for a reinforced-concrete frame that this composition is physically wrong in general: damage from an earlier surge degrades the structure that later surges strike, so sequential surges demand a cumulative-damage formulation, and concurrently acting surges amplify loads in ways that proved case-specific rather than predictable by any general superposition law. Their own state-of-the-art review in 2023 concluded that vulnerability assessments in risk analysis rarely consider the effects of hazard interactions, and subsequent field-based studies of hazard cascades have confirmed that the vulnerability of buildings to cumulative impacts differs from the sum or sequence of single-hazard vulnerabilities.

Problem Statement

Establish a general, predictive, physics-based multi-vulnerability model for buildings subjected to multiple interacting debris-flow surges and, beyond them, to interacting landslide-hazard sequences — a composition law that replaces both the prevailing treatment of repeated or coupled events as independent (with vulnerabilities combined by elementary probability rules) and the current case-specific treatment of concurrently acting surges. All four of the following results are required to achieve this single objective: (1) formulate the load-overlap and interaction mechanics when two or more surges act on a structure concurrently — flow merging, particle and boulder interactions, dynamic amplification — so that the combined load on the structure can be predicted for specified flow scenarios rather than fitted per case; (2) represent damage accumulation at the element level, with engineering demand parameters and fragilities that capture progressive and local failure modes under debris-flow impact, including the sharp impulse loads of bouldery fronts that the sustained-pressure model p=αρv2p=\alpha\rho v^{2} does not represent, rather than only global frame displacement; (3) produce probabilistic vulnerability outputs with quantified uncertainty for at least one interacting sequence of three or more events and for at least two distinct mixed chains drawn from debris flow combined with flood, debris flow combined with rockfall, debris flow combined with slope slide, and dependent triggering, at a computational cost demonstrated not to grow combinatorially with the number of interacting events; and (4) validate the composition law against documented field damage from multiple interacting landslide processes, using existing damage databases and event reconstructions as the evidence base. The proposed law must explicitly represent the interaction mechanics rather than absorb them into fitted constants, and its predictive skill consists in reproducing documented field damage the law was not fitted to, over at least two distinct hazard combinations and at least one interacting sequence of three or more events and across cases rather than within a single documented case. That out-of-sample agreement with documented field damage, rather than an imposed numeric tolerance, defines predictive skill; the objective extends to no hazard combinations or event sequences beyond those set out in items (3) and (4), and whether independence-based composition is systematically deficient is a hypothesis for the law to decide rather than a prescribed conclusion.

References

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