The Markovian Approach for Probabilistic Life-Cycle Assessment of Existing Structures

ABSTRACT

The reliability of structural systems, lying in aggressive environments, changes over time. Proper maintenance is usually required to achieve a suitable performance level of life-cycle. The damage process affecting the systems often suffers from uncertainty due to the randomness involved in each environmental attack. Therefore, basing on suitable damage modeling as well as on probabilistic analysis, the main features of time-variant deterioration process are modeled and then the life-cycle is assessed. On the basis of Markov renewal theory (MRT), this paper proposes a combined approach using an appropriate time dependent damage model and probabilistic analysis. Since repairing deteriorated structures requires the arrangement of maintenance strategies, possible selective maintenance scenarios have to be considered. Referring to the relationship between MRT and an appropriate condition index, some repair strategies have been proposed and compared with each other. Those strategies are applied just to seriously deteriorated members. Furthermore selective maintenance benefits are economically investigated.

Cite this paper

E. Garavaglia, N. Basso and L. Sgambi, "The Markovian Approach for Probabilistic Life-Cycle Assessment of Existing Structures,"*Applied Mathematics*, Vol. 3 No. 12, 2012, pp. 2080-2088. doi: 10.4236/am.2012.312A287.

E. Garavaglia, N. Basso and L. Sgambi, "The Markovian Approach for Probabilistic Life-Cycle Assessment of Existing Structures,"

References

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[2] L. Sgambi, F. Bontempi and E. Garavaglia, “Structural Response Evaluation of Two-Blade Bridge Piers Subjected to a Localized Deterioration,” Proceedings of the 3rd International Conference on Bridge Maintenance, Safety and Management, Porto, 16-19 July 2006, pp. 153-154.

[3] F. Biondini, F. Bontempi, D. M. Frangopol and P. G. Malerba, “Probabilistic Service Life Assessment and Maintenance Planning of Concrete Structures,” Structural Engineering, Vol. 132, No. 5, 2006, pp. 810-825. doi:10.1061/(ASCE)0733-9445(2006)132:5(810)

[4] F. Biondini and D. M. Frangopol, “Long-Term Performance of Structural Systems,” Structure and Infrastructure Engineering, Vol. 4, No. 2, 2008, p. 75.

[5] F. Biondini and E. Garavaglia, “Probabilistic Service Life Prediction and Maintenance Planning of Deteriorating Structures,” Proceedings of International Conference on Structural Safety and Reliability, Rome, 19-22 June 2005, pp. 495-501.

[6] R. A. Howard, “Dynamic Probabilistic Systems,” John Wiley and Sons, New York, 1971.

[7] N. Limnios and G. Oprisan, “Semi-Markov Processes and Reliability,” Birkhauser, Boston, 2001. doi:10.1007/978-1-4612-0161-8

[8] E. Alvarez, “Estimation in Stationary Markov Renewal Processes, with Application to Earthquake Forecasting in Turkey,” Methodology and Computing in Applied Probability, Vol. 7, No. 1, 2005, pp. 119-130. doi:10.1007/s11009-005-6658-2

[9] I. Votsi, N. Limnios, G. Tsaklidis and E. Papadimitriou, “Estimation of the Expected Number of Earthquake Occurrences Based on Semi-Markov Models,” Methodology and Computing in Applied Probability, Vol. 14, No. 3, 2012, pp. 685-703.

[10] G. Masala, “Hurricane Lifespan Modeling through a Semi-Markov Parametric Approach,” Journal of Forecasting, Online, 2012.

[11] G. Masala, “Earthquakes Occurrences Estimation through a Parametric Semi-Markov Approach,” Applied Statistics, Vol. 39, No. 1, 2011, pp. 81-96.

[12] E. Garavaglia and R. Pavani, “About Earthquake Forecasting by Markov Renewal Processes,” Methodology and Computing in Applied Probability, Vol. 13, No. 1, 2011, pp. 155-169. doi:10.1007/s11009-009-9137-3

[13] E. Garavaglia, E. Guagenti, R. Pavani and L. Petrini, “Renewal Models for Earthquake Predictability,” Journal of Seismology, Vol. 14, No. 1, 2010, pp. 79-93. doi:10.1007/s10950-008-9147-6

[14] E. Garavaglia, A. Gianni and C. Molina, “Reliability of Porous Materials: Two Stochastic Approaches,” Journal of Materials, Vol. 16, No. 5, 2004, pp. 419-426. doi:10.1061/(ASCE)0899-1561(2004)16:5(419)

[15] E. Garavaglia, A. Anzani, L. Binda and G. Cardani, “Fragility Curve Probabilistic Model Applied to Durability and Long Term Mechanical Damages of Masonry,” Materials and Structures, Vol. 41, No. 4, 2008, pp. 733-749. doi:10.1617/s11527-007-9277-2

[16] A. Anzani, E. Garavaglia and L. Binda, “Long-Term Damage of Historic Masonry: A Probabilistic Model,” Construction and Building Materials, Vol. 23, No. 2, 2009, pp. 713-724. doi:10.1016/j.conbuildmat.2008.02.010

[17] F. Biondini, D. M. Frangopol and E. Garavaglia, “LifeCycle Reliability Analysis and Selective Maintenance of Deteriorating Structures,” Proceedings of 1st International Symposium on Life-Cycle Civil Engineering, Varenna, 10-14 June 2008, CRC Press, Taylor & Francis Group, London, 2008, pp. 483-488.

[18] J. S. Kong and D. M. Frangopol, “Life-Cycle Reliability-Based Maintenance Cost Optimization of Deteriorating Structures with Emphasis on Bridges,” Structural Engineering, Vol. 129, No. 6, 2003, pp. 818-824. doi:10.1061/(ASCE)0733-9445(2003)129:6(818)

[19] D. R. Cox, “Renewal Theory,” Methuen Ltd., London, 1962.

[20] D. Vere-Jones, D. Harte and M. Kosuch, “Operational Requirements for an Earthquake Forecasting Programme in New Zealand,” Bulletin of the New Zealand National Society for Earthquake Engineering, Vol. 31, 1998, pp. 194-205.

[21] G. Grandori, E. Guagenti and A. Tagliani, “A Proposal for Comparing the Reliabilities of Alternative Seismic Hazard Models,” Journal of Seismology, Vol. 2, No. 1, 1998, pp. 27-35. doi:10.1023/A:1009779806984

[22] G. Grandori, E. Guagenti and A. Tagliani, “Magnitude Distribution versus Local Seismic Hazard, BSSA,” Bulletin of Seismological Society of America, Vol. 93, No. 3, 2003, pp. 1091-1098.

[23] E. Garavaglia, “The Credibility Measure of Probabilistic Approaches in Life-Cycle Assessment of Complex Systems: A Discussion,” Materials with Complex Behaviour II, Ochsner, et al., Eds., Springer-Verlag, Berlin, 2012, pp. 619-636. doi:10.1007/978-3-642-22700-4_38

[24] M. Ciampoli, “A Probabilistic Methodology to Assess the Reliability of Deteriorating Structural Elements,” Computer Methods in Applied Mechanics and Engineering, Vol. 168, No. 1-4, 1999, pp. 207-220. doi:10.1016/S0045-7825(98)00141-8

[25] A. Gupta and C. Lawsirirat, “Strategically Optimum Maintenance of Monitoring Enabled Multi-Component Systems Using Continuous-Time Jump Deterioration Models,” International Conference on Simulation and Modeling, Bankgok, 17-19 January 2005, pp. 306-329.

[1] P. G. Malerba, L. Sgambi, D. Ielmini and G. Gotti, “Influence of Corrosive Phenomena on the Mechanical behaviour of R. C. Elements,” Proceedings of 2011 World Congress on Advances in Structural Engineering and Mechanics, Seoul, 18-22 September 2011, pp. 1269-1288.

[2] L. Sgambi, F. Bontempi and E. Garavaglia, “Structural Response Evaluation of Two-Blade Bridge Piers Subjected to a Localized Deterioration,” Proceedings of the 3rd International Conference on Bridge Maintenance, Safety and Management, Porto, 16-19 July 2006, pp. 153-154.

[3] F. Biondini, F. Bontempi, D. M. Frangopol and P. G. Malerba, “Probabilistic Service Life Assessment and Maintenance Planning of Concrete Structures,” Structural Engineering, Vol. 132, No. 5, 2006, pp. 810-825. doi:10.1061/(ASCE)0733-9445(2006)132:5(810)

[4] F. Biondini and D. M. Frangopol, “Long-Term Performance of Structural Systems,” Structure and Infrastructure Engineering, Vol. 4, No. 2, 2008, p. 75.

[5] F. Biondini and E. Garavaglia, “Probabilistic Service Life Prediction and Maintenance Planning of Deteriorating Structures,” Proceedings of International Conference on Structural Safety and Reliability, Rome, 19-22 June 2005, pp. 495-501.

[6] R. A. Howard, “Dynamic Probabilistic Systems,” John Wiley and Sons, New York, 1971.

[7] N. Limnios and G. Oprisan, “Semi-Markov Processes and Reliability,” Birkhauser, Boston, 2001. doi:10.1007/978-1-4612-0161-8

[8] E. Alvarez, “Estimation in Stationary Markov Renewal Processes, with Application to Earthquake Forecasting in Turkey,” Methodology and Computing in Applied Probability, Vol. 7, No. 1, 2005, pp. 119-130. doi:10.1007/s11009-005-6658-2

[9] I. Votsi, N. Limnios, G. Tsaklidis and E. Papadimitriou, “Estimation of the Expected Number of Earthquake Occurrences Based on Semi-Markov Models,” Methodology and Computing in Applied Probability, Vol. 14, No. 3, 2012, pp. 685-703.

[10] G. Masala, “Hurricane Lifespan Modeling through a Semi-Markov Parametric Approach,” Journal of Forecasting, Online, 2012.

[11] G. Masala, “Earthquakes Occurrences Estimation through a Parametric Semi-Markov Approach,” Applied Statistics, Vol. 39, No. 1, 2011, pp. 81-96.

[12] E. Garavaglia and R. Pavani, “About Earthquake Forecasting by Markov Renewal Processes,” Methodology and Computing in Applied Probability, Vol. 13, No. 1, 2011, pp. 155-169. doi:10.1007/s11009-009-9137-3

[13] E. Garavaglia, E. Guagenti, R. Pavani and L. Petrini, “Renewal Models for Earthquake Predictability,” Journal of Seismology, Vol. 14, No. 1, 2010, pp. 79-93. doi:10.1007/s10950-008-9147-6

[14] E. Garavaglia, A. Gianni and C. Molina, “Reliability of Porous Materials: Two Stochastic Approaches,” Journal of Materials, Vol. 16, No. 5, 2004, pp. 419-426. doi:10.1061/(ASCE)0899-1561(2004)16:5(419)

[15] E. Garavaglia, A. Anzani, L. Binda and G. Cardani, “Fragility Curve Probabilistic Model Applied to Durability and Long Term Mechanical Damages of Masonry,” Materials and Structures, Vol. 41, No. 4, 2008, pp. 733-749. doi:10.1617/s11527-007-9277-2

[16] A. Anzani, E. Garavaglia and L. Binda, “Long-Term Damage of Historic Masonry: A Probabilistic Model,” Construction and Building Materials, Vol. 23, No. 2, 2009, pp. 713-724. doi:10.1016/j.conbuildmat.2008.02.010

[17] F. Biondini, D. M. Frangopol and E. Garavaglia, “LifeCycle Reliability Analysis and Selective Maintenance of Deteriorating Structures,” Proceedings of 1st International Symposium on Life-Cycle Civil Engineering, Varenna, 10-14 June 2008, CRC Press, Taylor & Francis Group, London, 2008, pp. 483-488.

[18] J. S. Kong and D. M. Frangopol, “Life-Cycle Reliability-Based Maintenance Cost Optimization of Deteriorating Structures with Emphasis on Bridges,” Structural Engineering, Vol. 129, No. 6, 2003, pp. 818-824. doi:10.1061/(ASCE)0733-9445(2003)129:6(818)

[19] D. R. Cox, “Renewal Theory,” Methuen Ltd., London, 1962.

[20] D. Vere-Jones, D. Harte and M. Kosuch, “Operational Requirements for an Earthquake Forecasting Programme in New Zealand,” Bulletin of the New Zealand National Society for Earthquake Engineering, Vol. 31, 1998, pp. 194-205.

[21] G. Grandori, E. Guagenti and A. Tagliani, “A Proposal for Comparing the Reliabilities of Alternative Seismic Hazard Models,” Journal of Seismology, Vol. 2, No. 1, 1998, pp. 27-35. doi:10.1023/A:1009779806984

[22] G. Grandori, E. Guagenti and A. Tagliani, “Magnitude Distribution versus Local Seismic Hazard, BSSA,” Bulletin of Seismological Society of America, Vol. 93, No. 3, 2003, pp. 1091-1098.

[23] E. Garavaglia, “The Credibility Measure of Probabilistic Approaches in Life-Cycle Assessment of Complex Systems: A Discussion,” Materials with Complex Behaviour II, Ochsner, et al., Eds., Springer-Verlag, Berlin, 2012, pp. 619-636. doi:10.1007/978-3-642-22700-4_38

[24] M. Ciampoli, “A Probabilistic Methodology to Assess the Reliability of Deteriorating Structural Elements,” Computer Methods in Applied Mechanics and Engineering, Vol. 168, No. 1-4, 1999, pp. 207-220. doi:10.1016/S0045-7825(98)00141-8

[25] A. Gupta and C. Lawsirirat, “Strategically Optimum Maintenance of Monitoring Enabled Multi-Component Systems Using Continuous-Time Jump Deterioration Models,” International Conference on Simulation and Modeling, Bankgok, 17-19 January 2005, pp. 306-329.