Technical Papers
Feb 2, 2022

Failure Probability of an Optimally Designed Gravity Retaining Wall

Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 8, Issue 2

Abstract

The paper presents an optimal design for a gravity retaining wall based on a mixed-integer constrained optimization. To solve this optimization problem, a real coded genetic algorithm was applied. The gravity retaining wall optimization model (OPT-GRW) includes a cost function of the wall, which is limited by design and resistance constraints. The deterministic optimization model, based on partial safety factors, was extended by an optimization approach in which the cost objective function was constrained by a defined target probability of failure. The paper presents an example for determining the most cost-effective gravity retaining wall for given design parameters. The presented case study shows the optimization process based on Eurocode 7, which takes into account part of the uncertainty of the soil parameters. As the study progresses, the need for optimization based on the probability of failure becomes crucial, as several designs exist with the same probability of failure, but only one is optimal.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All data, models, and code generated or used during the study appear in the published article.

Acknowledgments

The authors acknowledge financial support from the Slovenian Research Agency, research core funding No. P2-0268.

References

Basha, B. M., and G. L. S. Babu. 2007. “Reliability based design optimization of gravity retaining walls.” Geotech. Spec. Publ. 3 (170): 1–10. https://doi.org/10.1061/40914%28233%293.
Bathurst, R. J., S. Javankhoshdel, and T. M. Allen. 2017. “LRFD calibration of simple soil-structure limit states considering method bias and design parameter variability.” J. Geotech. Geoenviron. Eng. 143 (9): 04017053. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001735.
Bond, A., and A. Harris. 2008. Decoding Eurocode 7. London: CRC Press.
BSI (British Standard Institution). 2004. Eurocode 7: Geotechnical design, Part 1. EN 1997-1. London: BSI.
Camp, C. V., and A. Akin. 2012. “Design of retaining walls using big bang-big crunch optimization.” J. Struct. Eng. 138 (3): 438–448. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000461.
Ching, J., J.-R. Chen, J.-Y. Yeh, and K.-K. Phoon. 2011. “Updating uncertainties in friction angles of clean sands.” J. Geotech. Geoenviron. Eng. 138 (2): 217–229. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000573.
Deep, K., K. P. Singh, M. L. Kansal, and C. Mohan. 2009. “A real coded genetic algorithm for solving integer and mixed integer optimization problems.” Appl. Math. Comput. 212 (2): 505–518. https://doi.org/10.1016/j.amc.2009.02.044.
Fenton, G. A., D. V. Griffiths, and F. Naghibi. 2017. “Future directions in reliability-based geotechnical design.” In Geo-risk 2017, 69–97. Reston, VA: ASCE.
Fenton, G. A., F. Naghibi, and D. V. Griffiths. 2016. “On a unified theory for reliability-based geotechnical design.” Comput. Geotech. 78 (Sep): 110–122. https://doi.org/10.1016/j.compgeo.2016.04.013.
Gandomi, A. H., A. R. Kashani, D. A. Roke, and M. Mousavi. 2015. “Optimization of retaining wall design using recent swarm intelligence techniques.” Eng. Struct. 103 (Nov): 72–84. https://doi.org/10.1016/j.engstruct.2015.08.034.
Gao, G.-H., D.-Q. Li, Z.-J. Cao, Y. Wang, and L. Zhang. 2019. “Full probabilistic design of earth retaining structures using generalized subset simulation.” Comput. Geotech. 112 (Aug): 159–172. https://doi.org/10.1016/j.compgeo.2019.04.020.
ISO. 2015. General principles on reliability for structures. ISO 2394. Geneva: ISO.
Juang, C. H., and L. Wang. 2013. “Reliability-based robust geotechnical design of spread foundations using multi-objective genetic algorithm.” Comput. Geotech. 48 (Mar): 96–106. https://doi.org/10.1016/j.compgeo.2012.10.003.
Kaveh, A., and A. F. Behnam. 2013. “Charged system search algorithm for the optimum cost design of reinforced concrete cantilever retaining walls.” Arab. J. Sci. Eng. 38 (3): 563–570. https://doi.org/10.1007/s13369-012-0332-0.
Kaveh, A., K. Biabani Hamedani, and T. Bakhshpoori. 2020. “Optimal design of reinforced concrete cantilever retaining walls utilizing eleven meta-heuristic algorithms: A comparative study.” Period. Polytech. Civ. Eng. 64 (Jan): 156–168.
Kaveh, A., and N. Soleimani. 2015. “CBO and DPSO for optimum design of reinforced concrete cantilever retaining walls.” Asian J. Civ. Eng. 16 (6): 751–774.
Khajehzadeh, M., M. R. Taha, A. El-Shafie, and M. Eslami. 2010. “Economic design of retaining wall using particle swarm optimization with passive congregation.” Aust. J. Basic Appl. Sci. 4 (11): 5500–5507.
Kulhawy, F. H. 2017. “Foundation engineering, geotechnical uncertainty, and reliability-based design.” Geotech. Spec. Publ. 174–184. https://doi.org/10.1061/9780784480731.015.
Li, D.-Q., Z.-Y. Yang, Z.-J. Cao, S.-K. Au, and K.-K. Phoon. 2017. “System reliability analysis of slope stability using generalized subset simulation.” Appl. Math. Modell. 46 (Jun): 650–664. https://doi.org/10.1016/j.apm.2017.01.047.
Liu, L., D. Y. Yang, and D. M. Frangopol. 2021. “Determining target reliability index of structures based on cost optimization and acceptance criteria for fatality risk.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 7 (2): 04021013. https://doi.org/10.1061/AJRUA6.0001127.
Low, B. K., and K.-K. Phoon. 2015. “Reliability-based design and its complementary role to Eurocode 7 design approach.” Comput. Geotech. 65 (Apr): 30–44. https://doi.org/10.1016/j.compgeo.2014.11.011.
Phoon, K. K., and F. H. Kulhawy. 1999a. “Characterization of geotechnical variability.” Can. Geotech. J. 36 (4): 612–624. https://doi.org/10.1139/t99-038.
Phoon, K. K., and F. H. Kulhawy. 1999b. “Evaluation of geotechnical property variability.” Can. Geotech. J. 36 (4): 625–639. https://doi.org/10.1139/t99-039.
Phoon, K.-K., and J. V. Retief. 2016. Reliability of geotechnical structures in ISO2394. Boca Raton, FL: CRC Press.
Rackwitz, R. 2000. “Reviewing probabilistic soils modelling.” Comput. Geotech. 26 (3): 199–223. https://doi.org/10.1016/S0266-352X(99)00039-7.
Sadoglu, E. 2014. “Design optimization for symmetrical gravity retaining walls.” Acta Geotech. Slov. 11 (2): 71–79.
Saribas, A., and F. Erbatur. 1996. “Optimization and sensitivity of retaining structures.” J. Geotech. Eng. 122 (8): 649–656. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:8(649).
Talatahari, S., R. Sheikholeslami, M. Shadfaran, and M. Pourbaba. 2012. “Optimum design of gravity retaining walls using charged system search algorithm.” Math. Probl. Eng. 2012 (Jan): 1–10.
Tomlinson, M. J., and R. Boorman. 1995. Foundation design and construction. New York: Wiley.
Wang, Y. 2011. “Reliability-based design of spread foundations by Monte Carlo simulations.” Géotechnique 61 (8): 677–685. https://doi.org/10.1680/geot.10.P.016.
Wang, Y. 2022. “Bayesian equivalent sample toolkit (BEST).” Accessed December 26, 2021. https://sites.google.com/site/yuwangcityu/software-download/bayesian-equivalent-sample-toolkit-best.
Wang, Y., O. V. Akeju, and Z. Cao. 2016a. “Bayesian equivalent sample toolkit (BEST): An Excel VBA program for probabilistic characterisation of geotechnical properties from limited observation data.” Georisk 10 (4): 251–268. https://doi.org/10.1080/17499518.2016.1180399.
Wang, Y., T. Schweckendiek, W. Gong, T. Zhao, and K.-K. Phoon. 2016b. “Direct probability-based design methods.” In Reliability of geotechnical structures in ISO2394. Boca Raton, FL: CRC Press.

Information & Authors

Information

Published In

Go to ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 8Issue 2June 2022

History

Received: Apr 14, 2021
Accepted: Dec 13, 2021
Published online: Feb 2, 2022
Published in print: Jun 1, 2022
Discussion open until: Jul 2, 2022

Permissions

Request permissions for this article.

Authors

Affiliations

Ph.D. Student, Faculty of Civil Engineering, Transportation Engineering and Architecture, Univ. of Maribor, Smetanova 17, Maribor 2000, Slovenia. ORCID: https://orcid.org/0000-0002-3473-2029. Email: [email protected]
Primož Jelušič [email protected]
Associate Professor, Faculty of Civil Engineering, Transportation Engineering and Architecture, Univ. of Maribor, Smetanova 17, Maribor 2000, Slovenia (corresponding author). Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

  • Influence of Modeling Approaches on the Response of a Retaining Wall, Advanced Engineering Forum, 10.4028/p-7wfmni, 49, (103-112), (2023).

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share