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## Earth Sciences Research Journal

*versão impressa* ISSN 1794-6190

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MARTINEZCARVAJAL, Hernán Eduardo et al. A mathematical approach for assessing landslide vulnerability.* Earth Sci. Res. J.* [online]. 2018, vol.22, n.4, pp.251-273.
ISSN 1794-6190. http://dx.doi.org/10.15446/esrj.v22n4.68553.

A natural phenomenon (hazard) may be characterized in terms of temporal, spatial and magnitude probabilities. The effects of the interaction between the hazard and the exposed element depend on the intensity of the hazard and on the resistance, sometimes called susceptibility, of the element at risk, which describes the propensity of a building or other infrastructure to suffer damage from a specific hazard impact. Consequently, a modern concept of vulnerability must consider the intensity of the hazard as well as the structural resistance of the exposed infrastructure. This concept is referred to as physical vulnerability, and the most accepted definition is a representation of the expected degree of loss quantified on a scale of 0 (no damage) to 1 (total destruction). Thus, this work presents a mathematical model for landslide physical vulnerability assessment, here named the T-Model, based on the “Principle of Natural Proportionality” and calibrated with field observations of the massive rainfall-triggered landslide event that occurred in Nova Friburgo, Brazil in November of 2011. The model was also calibrated for a flow-type movement that is based on field observations of the failure of a tailing dam that affected the district of Bento Rodrigues, Brazil in November of 2015. The results showed a good agreement between predictions and the observed level of damages. Thus, it is possible to conclude that from a mathematical point of view, the model may be qualified as universal. It is recognized that a real universal objective model for vulnerability to landslides is not practical at present. More important than the model itself is the methodology that is presented here, which leads the user to take qualitative damage information from the field and develop it into a quantitative mathematical framework. Potential users of the T-Model must be cautious regarding the values of parameters that are presented in this paper. The T-Model is just a modest proposal that requires further calibration and deep expert criticisms.

**Palavras-chave
:
**Landslide vulnerability; quantitative vulnerability; vulnerability assessment; landslide risk analysis; vulnerability T-Model.