Analytical System Reliability Analysis of a Geotextile-Reinforced Retaining Wall
Publication: International Journal of Geomechanics
Volume 24, Issue 10
Abstract
A geotextile-reinforced retaining wall is a geotechnical structure with many design parameters. Hence, the uncertainty of the input parameters considerably affects the design of these structures. On the other hand, when the number of uncertain parameters increases, the time of this analysis increases drastically. Accordingly, the current study used an analytical method, namely, jointly distributed random variables (JDRV) method, that requires less running time than the simulation methods for stochastic analysis. For this purpose, stochastic analysis of the geotextile-reinforced retaining wall was carried out based on the limit equilibrium method (LEM), with soil parameters considered as uncertain variables. To verify the results, the probability density functions (PDFs) of the wall safety factors were compared with the Monte Carlo simulation (MCS). Next, to assess the effect of the external and internal stability modes on system reliability, the system reliability index was determined using the sequential compounding method (SCM). The results of the system reliability analysis revealed that, among the reliability indices of the components, the minimum values are attributed to the bearing capacity. The correlation between the rupture and pullout safety factors exhibited the maximum correlation, indicating that they are more dependent components than others. Based on the stochastic sensitivity analysis, the internal friction angle emerged as the most influential in the external and internal safety factors.
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Data Availability Statement
Some or all data, models, or codes generated or used during the study are available from the corresponding author by request including input and output data and detailed design plans.
References
Ambartzumian, R., A. Der Kiureghian, V. Ohaniana, and H. Sukiasiana. 1998. “Multinormal probability by sequential conditioned importance sampling: Theory and application.” Probab. Eng. Mech. 13 (4): 299–308. https://doi.org/10.1016/S0266-8920(98)00003-4.
Ang, A. H.-S., and W. H. Tang. 1984. “Probability concepts in engineering planning and design.” In Vol. 2 of Decision, risk, and reliability, edited by E. Hua-Sing Ang and W. H. Tang, 608. New York: Wiley.
Ardah, A., M. Abu-Farsakh, and G. Voyiadjis. 2021. “Numerical parametric study of geosynthetic reinforced soil integrated bridge system (GRS-IBS).” Geotext. Geomembr. 49 (1): 289–303. https://doi.org/10.1016/j.geotexmem.2020.10.005.
Baecher, G. B., and J. T. Christian. 2005. Reliability and statistics in geotechnical engineering. London, UK: Wiley.
Bathurst, R. J., and F. M. Naftchali. 2021. “Geosynthetic reinforcement stiffness for analytical and numerical modelling of reinforced soil structures.” Geotext. Geomembr. 49 (4): 921–940. https://doi.org/10.1016/j.geotexmem.2021.01.003.
Bathurst, R. J., and F. M. Naftchali. 2022. “Influence of uncertainty in geosynthetic stiffness on deterministic and probabilistic analyses using analytical solutions for three reinforced soil problems.” Geotext. Geomembr. 51 (1): 117–130.
Berg, R. R., N. C. Samtani, and B. R. Christopher. 2009. Design of mechanically stabilized earth walls and reinforced soil slopes—Volume II. Washington, DC: DOT, Federal Highway Administration.
Cardile, G., D. Gioffrè, N. Moraci, and L. S. Calvarano. 2017. “Modelling interference between the geogrid bearing members under pullout loading conditions.” Geotext. Geomembr. 45 (3): 169–177. https://doi.org/10.1016/j.geotexmem.2017.01.008.
Chehade, H. A., D. Dias, M. Sadek, O. Jenck, and F. H. Chehade. 2022. “Seismic internal stability of saturated reinforced soil retaining walls using the upper bound theorem of limit analysis.” Soil Dyn. Earthquake Eng. 155: 107180. https://doi.org/10.1016/j.soildyn.2022.107180.
Chen, R.-H., C.-P. Wu, F.-C. Huang, and C.-W. Shen. 2013. “Numerical analysis of geocell-reinforced retaining structures.” Geotext. Geomembr. 39: 51–62. https://doi.org/10.1016/j.geotexmem.2013.07.003.
Das, B. M. 2010. Principles of foundation engineering. SI ed. Boston, MA: Cengage Learning.
Djabri, M., and S. Benmebarek. 2016. “FEM analysis of back-to-back geosynthetic-reinforced soil retaining walls.” Int. J. Geosynth. Ground Eng. 2 (3): 1–8. https://doi.org/10.1007/s40891-016-0067-1.
Elias, V., B. R. Christopher, R. R. Berg, and R. R. Berg. 2001. Mechanically stabilized earth walls and reinforced soil slopes: Design and construction guidelines (updated version). Washington, DC: Federal Highway Administration.
Fathipour, H., M. Payan, and R. J. Chenari. 2021. “Limit analysis of lateral earth pressure on geosynthetic-reinforced retaining structures using finite element and second-order cone programming.” Comput. Geotech. 134: 104119. https://doi.org/10.1016/j.compgeo.2021.104119.
Fenton, G. A., and D. V. Griffiths. 2003. “Bearing-capacity prediction of spatially random c φ soils.” Can. Geotech. J. 40 (1): 54–65. https://doi.org/10.1139/t02-086.
Forrest, W. S., and T. L. Orr. 2010. “Reliability of shallow foundations designed to Eurocode 7.” Georisk 4 (4): 186–207.
Gholampour, A., and A. Johari. 2019. “Reliability-based analysis of braced excavation in unsaturated soils considering conditional spatial variability.” Comput. Geotech. 115: 103163. https://doi.org/10.1016/j.compgeo.2019.103163.
Goswami, A., S. Deka, and A. Chakraborty. 2022. “Deterministic and probabilistic analysis of effects of fibre reinforcement on strength and deformation of soil—A state-of-the-art review.” Adv. Geosci. Geostruct. 154: 163–170. https://doi.org/10.1007/978-981-16-1993-9_17.
Griffiths, D. V., and G. A. Fenton. 2007. Vol. 491 of Probabilistic methods in geotechnical engineering. CISM, Udine (Italy): Springer Science & Business Media.
Hatami, K., and A. F. Witthoeft. 2008. “A numerical study on the use of geofoam to increase the external stability of reinforced soil walls.” Geosynth. Int. 15 (6): 452–470. https://doi.org/10.1680/gein.2008.15.6.452.
Hoel, P. G. 1971. “Introduction to statistical theory.” In The Houghton‒Mifflin series in statistics, edited by P. G. Hoel, S. C. Port, and C. J. Stone. Boston, MA: Houghton–Mifflin.
Hoel, P. G., S. C. Port, and C. J. Stone. 1971. Introduction to probability theory. Boston, MA: Houghton Mifflin.
Hohenbichler, M., and R. Rackwitz. 1982. “First-order concepts in system reliability.” Struct. Saf. 1 (3): 177–188. https://doi.org/10.1016/0167-4730(82)90024-8.
Javankhoshdel, S., and R. J. Bathurst. 2017. “Deterministic and probabilistic failure analysis of simple geosynthetic reinforced soil slopes.” Geosynth. Int. 24 (1): 14–29. https://doi.org/10.1680/jgein.16.00012.
Johari, A., A. K. Hajivand, and S. M. Binesh. 2020. “System reliability analysis of soil nail wall using random finite element method.” Bull. Eng. Geol. Environ. 79 (6): 2777–2798. https://doi.org/10.1007/s10064-020-01740-y.
Johari, A., and A. R. Khodaparast. 2013. “Modelling of probability liquefaction based on standard penetration tests using the jointly distributed random variables method.” Eng. Geol. 158: 1–14. https://doi.org/10.1016/j.enggeo.2013.02.007.
Johari, A., and A. R. Khodaparast. 2015. “Analytical stochastic analysis of seismic stability of infinite slope.” Soil Dyn. Earthquake Eng. 79: 17–21. https://doi.org/10.1016/j.soildyn.2015.08.012.
Johari, A., and A. M. Lari. 2016. “System reliability analysis of rock wedge stability considering correlated failure modes using sequential compounding method.” Int. J. Rock Mech. Min. Sci. 82: 61–70. https://doi.org/10.1016/j.ijrmms.2015.12.002.
Johari, A., M. Momeni, and A. A. Javadi. 2015. “An analytical solution for reliability assessment of pseudo-static stability of rock slopes using jointly distributed random variables method.” Iran. J. Sci. Technol.-Trans. Civ. Eng. 39 (C2): 351–363.
Johari, A., and S. Mousavi. 2019. “An analytical probabilistic analysis of slopes based on limit equilibrium methods.” Bull. Eng. Geol. Environ. 78 (6): 4333–4347. https://doi.org/10.1007/s10064-018-1408-1.
Kang, W.-H., and J. Song. 2010. “Evaluation of multivariate normal integrals for general systems by sequential compounding.” Struct. Saf. 32 (1): 35–41. https://doi.org/10.1016/j.strusafe.2009.06.001.
Keykhosropur, L., A. Soroush, and R. Imam. 2012. “3D numerical analyses of geosynthetic encased stone columns.” Geotext. Geomembr. 35: 61–68. https://doi.org/10.1016/j.geotexmem.2012.07.005.
Khorsandiardebili, N., and M. Ghazavi. 2022. “Internal stability analysis of geocell-reinforced slopes subjected to seismic loading based on pseudo-static approach.” Geotext. Geomembr. 50 (3): 393–407. https://doi.org/10.1016/j.geotexmem.2021.12.001.
Lin, P., and J. Liu. 2017. “Analysis of resistance factors for LFRD of soil nail walls against external stability failures.” Acta Geotech. 12 (1): 157–169. https://doi.org/10.1007/s11440-016-0443-y.
Lumb, P. 1970. “Safety factors and the probability distribution of soil strength.” Can. Geotech. J. 7 (3): 225–242. https://doi.org/10.1139/t70-032.
Luo, N., R. J. Bathurst, and S. Javankhoshdel. 2016. “Probabilistic stability analysis of simple reinforced slopes by finite element method.” Comput. Geotech. 77: 45–55. https://doi.org/10.1016/j.compgeo.2016.04.001.
Madhavi Latha, G., and K. Rajagopal. 2007. “Parametric finite element analyses of geocell-supported embankments.” Can. Geotech. J. 44 (8): 917–927. https://doi.org/10.1139/T07-039.
Metropolis, N., and S. Ulam. 1949. “The Monte Carlo method.” J. Am. Stat. Assoc. 44 (247): 335–341. https://doi.org/10.1080/01621459.1949.10483310.
Meyerhof, G. G. 1963. “Some recent research on the bearing capacity of foundations.” Can. Geotech. J. 1 (1): 16–26. https://doi.org/10.1139/t63-003.
Nadim, F. 2007. “Tools and strategies for dealing with uncertainty in geotechnics.” In Probabilistic methods in geotechnical engineering, edited by D. V. Griffiths and G. A. Fenton, 71–95. Berlin, Germany: Springer.
Nunes, G. B., F. H. M. Portelinha, M. M. Futai, and C. Yoo. 2022. “Numerical study of the impact of climate conditions on stability of geocomposite and geogrid reinforced soil walls.” Geotext. Geomembr. 50 (4): 807–824.
Pandey, M. D., and A. Sarkar. 2002. “Comparison of a simple approximation for multinormal integration with an importance sampling-based simulation method.” Probab. Eng. Mech. 17 (2): 215–218. https://doi.org/10.1016/S0266-8920(02)00003-6.
Peng, M., R. Sun, J.-F. Chen, S. Rajesh, L.-M. Zhang, and S.-B. Yu. 2020. “System reliability analysis of geosynthetic reinforced soil slope considering local reinforcement failure.” Comput. Geotech. 123: 103563. https://doi.org/10.1016/j.compgeo.2020.103563.
Peng, M., R. Sun, J.-F. Chen, L.-M. Zhang, and S.-B. Yu. 2021. “Stochastic seismic analysis of geosynthetic-reinforced soil slopes using the probability density evolution method.” Comput. Geotech. 140: 104485. https://doi.org/10.1016/j.compgeo.2021.104485.
Portelinha, F. H. M., and J. G. Zornberg. 2017. “Effect of infiltration on the performance of an unsaturated geotextile-reinforced soil wall.” Geotext. Geomembr. 45 (3): 211–226. https://doi.org/10.1016/j.geotexmem.2017.02.002.
Rosenblueth, E. 1975. “Point estimates for probability moments.” Proc. Natl. Acad. Sci. U. S. A. 72 (10): 3812–3814. https://doi.org/10.1073/pnas.72.10.3812.
USACE. 1995. Engineering and design introduction to probability and reliability methods for use in geotechnical engineering. Engineering Technology Letter No. 1110-2-547. Washington, DC: Dept. of the Army.
Vibhoosha, M. P., A. Bhasi, and S. Nayak. 2021. “A review on the design, applications and numerical modeling of geocell reinforced soil.” Geotech. Geol. Eng. 39 (6): 4035–4057. https://doi.org/10.1007/s10706-021-01774-3.
Wu, X. Z. 2013. “Trivariate analysis of soil ranking-correlated characteristics and its application to probabilistic stability assessments in geotechnical engineering problems.” Soils Found. 53 (4): 540–556. https://doi.org/10.1016/j.sandf.2013.06.006.
Zevgolis, I. E., and P. L. Bourdeau. 2006. “System reliability of cantilever retaining walls with correlated failure modes.” In Proc., GeoCongress 2006: Geotechnical Engineering in the Information Technology Age, D. J. DeGroot, J. T. DeJong, D. Frost, and L. G. Baise, 1–6. Reston, VA: ASCE.
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Published In
International Journal of Geomechanics
Volume 24 • Issue 10 • October 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Aug 22, 2023
Accepted: Feb 13, 2024
Published online: Aug 8, 2024
Published in print: Oct 1, 2024
Discussion open until: Jan 8, 2025
ASCE Technical Topics:
- Analysis (by type)
- Engineering fundamentals
- Engineering materials (by type)
- Geomaterials
- Geosynthetics
- Geotechnical engineering
- Materials engineering
- Mathematics
- Parameters (statistics)
- Probability
- Retaining structures
- Statistics
- Stochastic processes
- System analysis
- System reliability
- Systems engineering
- Systems management
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