Published

2018-10-01

A mathematical approach for assessing landslide vulnerability

Un modelo matemático para la evaluación de la vulnerabilidad por deslizamientos

DOI:

https://doi.org/10.15446/esrj.v22n4.68553

Keywords:

Landslide vulnerability, quantitative vulnerability, vulnerability assessment, landslide risk analysis, vulnerability T-Model (en)
Vulnerabilidad por deslizamientos, cuantificaciòn de la vulnerabilidad, model T de vulnerabilidad (es)

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Authors

  • Hernan Eduardo Martinez-Carvajal University of Brasilia/Universidad Nacional de Colombia https://orcid.org/0000-0001-7966-1466
  • Maria Tamara de Moraes Guimaraes Silva Goiás Federal Institute
  • Edwin Fabian Garcia-Aristizabal University of Antioquia
  • Edier Vicente Aristizabal-Giraldo Universidad Nacional de Colombia
  • Mayra Alejandra Larios-Benavides Universidad Nacional de Colombia

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.

Un fenómeno natural (peligro) puede caracterizarse en términos de probabilidades temporales, espaciales y de magnitud. Los efectos de la interacción entre el peligro y el elemento expuesto dependen de la intensidad del peligro y de la resistencia, a veces llamada susceptibilidad, del elemento en riesgo, que describe la propensión de un edificio u otra infraestructura a sufrir daños de un peligro especìfico. En consecuencia, un concepto moderno de vulnerabilidad debe considerar la intensidad del peligro así como la resistencia estructural de la infraestructura expuesta. Este concepto se conoce como vulnerabilidad física, y la definición más aceptada es una representación del grado de pérdida esperado cuantificado en una escala de 0 (sin daño) a 1 (destrucción total). Por lo tanto, este trabajo presenta un modelo matemático para la evaluación de la vulnerabilidad física por deslizamientos, aquí denominado el modelo T, basado en el "Principio de proporcionalidad natural" y calibrado con observaciones de campo del evento de deslizamientos provocado por la lluvis intensa que tuvo lugar en Nova Friburgo, Brasil en noviembre de 2011. El modelo también fue calibrado para un movimiento de flujo a partir de observaciones de campo de la falla de una presa de relaves que afectó al distrito de Bento Rodrigues, Brasil en noviembre de 2015. Los resultados mostraron un buen ajuste entre las predicciones y el nivel observado de daños. Por lo tanto, es posible concluir que desde un punto de vista matemático, el modelo puede calificarse como universal. Se reconoce que un modelo objetivo universal real para la vulnerabilidad a los deslizamientos de tierra no es práctico en la actualidad. Más importante que el modelo en sí es la metodología que se presenta aquí, que conduce al usuario a tomar información de daños cualitativos del campo y desarrollarla en un marco matemático cuantitativo. Los usuarios potenciales del modelo T deben ser cautelosos con respecto a los valores de los parámetros que se presentan en este documento. El modelo T es solo una propuesta modesta que requiere una mayor calibración y profundas críticas de expertos.

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How to Cite

APA

Martinez-Carvajal, H. E., de Moraes Guimaraes Silva, M. T., Garcia-Aristizabal, E. F., Aristizabal-Giraldo, E. V. and Larios-Benavides, M. A. (2018). A mathematical approach for assessing landslide vulnerability. Earth Sciences Research Journal, 22(4), 251–273. https://doi.org/10.15446/esrj.v22n4.68553

ACM

[1]
Martinez-Carvajal, H.E., de Moraes Guimaraes Silva, M.T., Garcia-Aristizabal, E.F., Aristizabal-Giraldo, E.V. and Larios-Benavides, M.A. 2018. A mathematical approach for assessing landslide vulnerability. Earth Sciences Research Journal. 22, 4 (Oct. 2018), 251–273. DOI:https://doi.org/10.15446/esrj.v22n4.68553.

ACS

(1)
Martinez-Carvajal, H. E.; de Moraes Guimaraes Silva, M. T.; Garcia-Aristizabal, E. F.; Aristizabal-Giraldo, E. V.; Larios-Benavides, M. A. A mathematical approach for assessing landslide vulnerability. Earth sci. res. j. 2018, 22, 251-273.

ABNT

MARTINEZ-CARVAJAL, H. E.; DE MORAES GUIMARAES SILVA, M. T.; GARCIA-ARISTIZABAL, E. F.; ARISTIZABAL-GIRALDO, E. V.; LARIOS-BENAVIDES, M. A. A mathematical approach for assessing landslide vulnerability. Earth Sciences Research Journal, [S. l.], v. 22, n. 4, p. 251–273, 2018. DOI: 10.15446/esrj.v22n4.68553. Disponível em: https://revistas.unal.edu.co/index.php/esrj/article/view/68553. Acesso em: 22 apr. 2025.

Chicago

Martinez-Carvajal, Hernan Eduardo, Maria Tamara de Moraes Guimaraes Silva, Edwin Fabian Garcia-Aristizabal, Edier Vicente Aristizabal-Giraldo, and Mayra Alejandra Larios-Benavides. 2018. “A mathematical approach for assessing landslide vulnerability”. Earth Sciences Research Journal 22 (4):251-73. https://doi.org/10.15446/esrj.v22n4.68553.

Harvard

Martinez-Carvajal, H. E., de Moraes Guimaraes Silva, M. T., Garcia-Aristizabal, E. F., Aristizabal-Giraldo, E. V. and Larios-Benavides, M. A. (2018) “A mathematical approach for assessing landslide vulnerability”, Earth Sciences Research Journal, 22(4), pp. 251–273. doi: 10.15446/esrj.v22n4.68553.

IEEE

[1]
H. E. Martinez-Carvajal, M. T. de Moraes Guimaraes Silva, E. F. Garcia-Aristizabal, E. V. Aristizabal-Giraldo, and M. A. Larios-Benavides, “A mathematical approach for assessing landslide vulnerability”, Earth sci. res. j., vol. 22, no. 4, pp. 251–273, Oct. 2018.

MLA

Martinez-Carvajal, H. E., M. T. de Moraes Guimaraes Silva, E. F. Garcia-Aristizabal, E. V. Aristizabal-Giraldo, and M. A. Larios-Benavides. “A mathematical approach for assessing landslide vulnerability”. Earth Sciences Research Journal, vol. 22, no. 4, Oct. 2018, pp. 251-73, doi:10.15446/esrj.v22n4.68553.

Turabian

Martinez-Carvajal, Hernan Eduardo, Maria Tamara de Moraes Guimaraes Silva, Edwin Fabian Garcia-Aristizabal, Edier Vicente Aristizabal-Giraldo, and Mayra Alejandra Larios-Benavides. “A mathematical approach for assessing landslide vulnerability”. Earth Sciences Research Journal 22, no. 4 (October 1, 2018): 251–273. Accessed April 22, 2025. https://revistas.unal.edu.co/index.php/esrj/article/view/68553.

Vancouver

1.
Martinez-Carvajal HE, de Moraes Guimaraes Silva MT, Garcia-Aristizabal EF, Aristizabal-Giraldo EV, Larios-Benavides MA. A mathematical approach for assessing landslide vulnerability. Earth sci. res. j. [Internet]. 2018 Oct. 1 [cited 2025 Apr. 22];22(4):251-73. Available from: https://revistas.unal.edu.co/index.php/esrj/article/view/68553

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