Technical Papers
Apr 11, 2023

Probabilistic Stability Design Charts for Shallow Passive Trapdoors in Spatially Variable Clays

Publication: International Journal of Geomechanics
Volume 23, Issue 6

Abstract

Geotechnical engineers are faced with great uncertainty with regard to the stability design of soil structures such as retaining walls, foundations, and slope stability. Instead of using a deterministic approach by replacing the design parameter with a single mean number, Monte Carlo simulations could be used to provide better decisions by considering all possible outcomes under parametric uncertainty. This paper studies probabilistic failures of classical passive trapdoors in shallow depths with spatially random soils. The effects of soil strength variability are investigated for various spatial correlation lengths and trapdoor depths using the latest adaptive finite-element upper-bound limit analysis with second-order cone programming. In addition, probabilistic stability results are compared with those published in renowned literature, and a comprehensive probability of design failure (PF) charts is developed for a practical range of deterministic factors of safety. The extensive results reported in this paper would be of great interest to engineering practitioners because better decisions can be made in the design process and design confidence improved.

Get full access to this article

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

Acknowledgments

This work was supported by the Thailand Science Research and Innovation Fundamental Fund fiscal year 2023. We would like to thank Dr. Thanh Son Nguyen at the Mientrung University of Civil Engineering for his valuable discussions and assistance throughout this research journey.

References

Ali, A., J. Huang, A. V. Lyamin, S. W. Sloan, D. V. Griffiths, M. J. Cassidy, and J. H. Li. 2014. “Simplified quantitative risk assessment of rainfall-induced landslides modelled by infinite slopes.” Eng. Geol. 179: 102–116. https://doi.org/10.1016/j.enggeo.2014.06.024.
Ali, A., A. V. Lyamin, J. Huang, J. H. Li, M. J. Cassidy, and S. W. Sloan. 2017a. “Probabilistic stability assessment using adaptive limit analysis and random fields.” Acta Geotech. 12 (4): 937–948. https://doi.org/10.1007/s11440-016-0505-1.
Ali, A., A. V. Lyamin, J. Huang, S. W. Sloan, and M. J. Cassidy. 2017b. “Undrained stability of a single circular tunnel in spatially variable soil subjected to surcharge loading.” Comput. Geotech. 84: 16–27. https://doi.org/10.1016/j.compgeo.2016.11.013.
Ali, A., A. V. Lyamin, J. Huang, S. W. Sloan, and M. J. Cassidy. 2017c. “Undrained stability of an unlined square tunnel in spatially random soil.” In Geo-Risk 2017: Impact of Spatial Variability, Probabilistic Site Characterization, and Geohazards, Geotechnical Special Publication 284, edited by J. Huang, G. A. Fenton, L. Zhang, and D. V. Griffiths, 507–517. Reston, VA: ASCE.
Brahmi, N., M. Y. Ouahab, A. Mabrouki, D. Benmeddour, and M. Mellas. 2021. “Probabilistic analysis of the bearing capacity of inclined loaded strip footings near cohesive slopes.” Int. J. Geotech. Eng. 15 (6): 732–739. https://doi.org/10.1080/19386362.2018.1496005.
Davis, E. H. 1968. “Theories of plasticity and the failure of soil masses.” In Soil mechanics: Selected topics, edited by I. K. Lee, 341–380. London: Butterworths.
Fenton, G. A., and E. H. Vanmarcke. 1990. “Simulation of random fields via local average subdivision.” J. Eng. Mech. 116 (8): 1733–1749.
Griffiths, D. V., and G. A. Fenton. 2001. “Bearing capacity of spatially random soil: The undrained clay Prandtl problem revisited.” Géotechnique 51 (4): 351–359. https://doi.org/10.1680/geot.2001.51.4.351.
Griffiths, D. V., and G. A. Fenton. 2004. “Probabilistic slope stability analysis by finite elements.” J. Geotech. Geoenviron. Eng. 130 (5): 507–518. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507).
Griffiths, D. V., G. A. Fenton, and N. Manoharan. 2002. “Bearing capacity of rough rigid strip footing on cohesive soil: Probabilistic study.” J. Geotech. Eng. 128 (9): 743–755. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:9(743).
Griffiths, D. V., J. Huang, and G. A. Fenton. 2009. “Influence of spatial variability on slope reliability using 2-D random fields.” J. Geotech. Geoenviron. Eng. 135 (10): 1367–1378. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000099.
Guan, Z., Y. Wang, Z. Cao, and Y. Hong. 2020. “Smart sampling strategy for investigating spatial distribution of subsurface shallow gas pressure in Hangzhou Bay area of China.” Eng. Geol. 274: 105711. https://doi.org/10.1016/j.enggeo.2020.105711.
Gunn, M. J. 1980. “Limit analysis of undrained stability problems using a very small computer.” In Proc., Symp. on Computer Applications in Geotechnical Problems in Highway Engineering. Washington, DC: The National Academies of Sciences, Engineering, and Medicine.
Huang, J., A. V. Lyamin, D. V. Griffiths, K. Krabbenhøft, and S. W. Sloan. 2013a. “Quantitative risk assessment of landslide by limit analysis and random fields.” Comput. Geotech. 53: 60–67. https://doi.org/10.1016/j.compgeo.2013.04.009.
Huang, J., A. V. Lyamin, D. V. Griffiths, S. W. Sloan, K. Krabbenhøft, and G. A. Fenton. 2013b. “Undrained bearing capacity of spatially random clays by finite elements and limit analysis.” In Proc., 18th Int. Conf. on Soil Mechanics and Geotechnical Engineering, edited by P. Delage, J. Desrues, R. Frank, A. Puech, and F.Schlosser. Paris: Presses des Ponts.
Jiang, S. H., I. Papaioannou, and D. Straub. 2018. “Bayesian updating of slope reliability in spatially variable soils with in-situ measurements.” Eng. Geol. 239: 310–320. https://doi.org/10.1016/J.ENGGEO.2018.03.021.
Kasama, K., and A. Whittle. 2011. “Bearing capacity of spatially random cohesive soil using numerical limit analyses.” J. Geotech. Geoenviron. Eng. 137 (11): 989–996. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000531.
Kasama, K., and K. Zen. 2010. “The reliability assessment for slope stability considering the spatial variability of soil strength using random field numerical limit analyses.” J. Soc. Mater. Sci. J. 59 (5): 336–341. https://doi.org/10.2472/jsms.59.336.
Keawsawasvong, S., and V. Q. Lai. 2021. “End bearing capacity factor for annular foundations embedded in clay considering the effect of the adhesion factor.” Int. J. Geosynth. Ground Eng. 7: 15. https://doi.org/10.1007/s40891-021-00261-2.
Keawsawasvong, S., and J. Shiau. 2022a. “Stability of active trapdoors in axisymmetry.” Underground Space 7 (1): 50–57. https://doi.org/10.1016/j.undsp.2021.05.001.
Keawsawasvong, S., and J. Shiau. 2022b. “Stability of spherical cavity in Hoek–Brown rock mass.” Rock Mech. Rock Eng. 55: 5285–5296.
Keawsawasvong, S., and J. Shiau. 2022c. “Instability of boreholes with slurry.” Int. J. Geosynth. Ground Eng. 7 (81): 1–11.
Keawsawasvong, S., J. Shiau, K. Limpanawannakul, and S. Panomchaivath. 2022a. “Stability charts for closely spaced strip footings on Hoek–Brown rock mass.” Geotech. Geol. Eng. 40: 3051–3066.
Keawsawasvong, S., J. Shiau, C. Ngamkhanong, V. Q. Lai, and C. Thongchom. 2022b. “Undrained stability of ring foundations: Axisymmetry, anisotropy, and non-homogeneity.” Int. J. Geomech. 22 (1): 04021253. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002229.
Koutsabeloulis, N. C., and D. V. Griffiths. 1989. “Numerical modelling of the trap door problem.” Géotechnique 39 (1): 77–89. https://doi.org/10.1680/geot.1989.39.1.77.
Krabbenhoft, K., A. V. Lyamin, and S. W. Sloan. 2007. “Formulation and solution of some plasticity problems as conic programs.” Int. J. Solids Struct. 44 (5): 1533–1549. https://doi.org/10.1016/j.ijsolstr.2006.06.036.
Lai, V. Q., J. Shiau, S. Keawsawasvong, and D. T. Tran. 2022. “Bearing capacity of ring foundations on anisotropic and heterogenous clays: FEA, NGI-ADP, and MARS.” Geotech. Geol. Eng. 40: 3913–3928.
Li, C., F. Lai, J. Shiau, S. Keawsawasvong, and H. Huang. 2022. “Passive earth pressure in narrow cohesive-frictional backfills.” Int. J. Geomech. 23 (1): 04022262.
Li, X., L. Zhang, L. Gao, and H. Zhu. 2017. “Simplified slope reliability analysis considering spatial soil variability.” Eng. Geol. 216: 90–97. https://doi.org/10.1016/j.enggeo.2016.11.013.
Liu, L., Z.-P. Deng, S.-H. Zhang, and Y.-M. Cheng. 2018. “Simplified framework for system reliability analysis of slopes in spatially variable soils.” Eng. Geol. 239: 330–343. https://doi.org/10.1016/j.enggeo.2018.04.009.
Liu, X., D. Li, Z. Cao, and Y. Wang. 2019. “Adaptive Monte Carlo simulation method for system reliability analysis of slope stability based on limit equilibrium methods.” Eng. Geol. 264: 105384. https://doi.org/10.1016/j.enggeo.2019.105384.
Lyamin, A. V., and S. W. Sloan. 2002a. “Lower bound limit analysis using non-linear programming.” Int. J. Numer. Methods Eng. 55 (5): 573–611. https://doi.org/10.1002/nme.511.
Lyamin, A. V., and S. W. Sloan. 2002b. “Upper bound limit analysis using linear finite elements and non-linear programming.” Int. J. Numer. Anal. Methods Geomech. 26 (2): 181–216. https://doi.org/10.1002/nag.198.
Lyamin, A. V., S. W. Sloan, K. Krabbenhøft, and M. Hjiaj. 2005. “Lower bound limit analysis with adaptive remeshing.” Int. J. Numer. Methods Eng. 63 (14): 1961–1974. https://doi.org/10.1002/nme.1352.
Martin, C. M. 2009. “Undrained collapse of a shallow plane-strain trapdoor.” Géotechnique 59 (10): 855–863. https://doi.org/10.1680/geot.8.T.023.
Nguyen, T. S., and S. Likitlersuang. 2019. “Reliability analysis of unsaturated soil slope stability under infiltration considering hydraulic and shear strength parameters.” Bull. Eng. Geol. Environ. 78 (8): 5727–5743. https://doi.org/10.1007/s10064-019-01513-2.
Nguyen, T. S., and S. Likitlersuang. 2021. “Influence of the spatial variability of soil shear strength on deep excavation: A case study of a Bangkok underground MRT station.” Int. J. Geomech. 21 (2): 04020248. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001914.
Nguyen, T. S., T. N. Phan, S. Likitlersuang, and D. T. Bergado. 2022. “Characterization of stationary and nonstationary random fields with different copulas on undrained shear strength of soils: Probabilistic analysis of embankment stability on soft ground.” Int. J. Geomech. 22 (7): 04022109. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002444.
OptumCE. 2020. OptumG2. Copenhagen, Denmark: Optum Computational Engineering.
Phoon, K.-K., and F. H. Kulhawy. 1999. “Characterization of geotechnical variability.” Can. Geotech. J. 36 (4): 612–624. https://doi.org/10.1139/t99-038.
Shiau, J., and F. Al-Asadi. 2020a. “Three-dimensional heading stability of twin circular tunnels.” Geotech. Geol. Eng. 38 (3): 2973–2988. https://doi.org/10.1007/s10706-020-01201-z.
Shiau, J., and F. Al-Asadi. 2020b. “Stability analysis of twin circular tunnels using shear strength reduction method.” Geotech. Lett. 10 (2): 1–9. https://doi.org/10.1680/jgele.19.00003.
Shiau, J., and F. Al-Asadi. 2020c. “Three-dimensional analysis of circular tunnel headings using Broms and Bennermarks’ original stability number.” Int. J. Geomech. 20 (7): 06020015. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001734.
Shiau, J., and F. Al-Asadi. 2021. “Revisiting circular tunnel stability using Broms and Bennermarks’ original stability number.” Int. J. Geomech. 21 (5): 06021009. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001996.
Shiau, J., and F. Al-Asadi. 2022. “Stability factors Fc, Fs, and Fγ for twin tunnels in three dimensions.” Int. J. Geomech. 22 (3): 04021290. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002264.
Shiau, J., B. Chudal, and S. Keawsawasvong. 2022a. “Three-dimensional sinkhole stability of spherical cavity.” Acta Geotech. 17: 3947–3958.
Shiau, J., and M. M. Hassan. 2020. “Undrained stability of active and passive trapdoors.” Geotech. Res. 7 (1): 40–48. https://doi.org/10.1680/jgere.19.00033.
Shiau, J., and M. M. Hassan. 2021. “Numerical investigation of undrained trapdoors in three dimensions.” Int. J. Geosynth. Ground Eng. 7: 30.
Shiau, J., and S. Keawsawasvong. 2022c. “Producing undrained stability factors for various tunnel shapes.” Int. J. Geomech. 22 (8): 06022017. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002487.
Shiau, J., S. Keawsawasvong, B. Chudal, K. Mahalingasivam, and S. Seehavong. 2021a. “Sinkhole stability in elliptical cavity under collapse and blowout conditions.” Geosciences 11 (10): 421. https://doi.org/10.3390/geosciences11100421.
Shiau, J., S. Keawsawasvong, and J. S. Lee. 2022b. “Three-dimensional stability investigation of trapdoors in collapse and blowout conditions.” Int. J. Geomech. 22 (4): 04022007. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002339.
Shiau, J., J.-S. Lee, and F. Al-Asadi. 2021b. “Three-dimensional stability analysis of active and passive trapdoors.” Tunnelling Underground Space Technol. 107: 103635. https://doi.org/10.1016/j.tust.2020.103635.
Shiau, J., A. V. Lyamin, and S. W. Sloan. 2006a. “Application of pseudo-static limit analysis in geotechnical earthquake design.” In Proc., 6th European Conf. on Numerical Methods in Geotechnical Engineering, 249–255. London: Taylor & Francis.
Shiau, J., S. Pather, and R. Ayers. 2006b. “Developing physical models for geotechnical teaching and research.” In Proc., 6th Physical Modelling in Geotechnics, 157–162. Boca Raton, FL: CRC Press.
Shiau, J., and H. Yu. 2000. “Shakedown analysis of flexible pavements.” In Proc., John Booker Memorial Symposium, edited by D. W. Smith and J. P. Carter, 643–653. Rotterdam, The Netherlands: A.A. Balkema.
Sloan, S. W. 1988. “Lower bound limit analysis using finite elements and linear programming.” Int. J. Numer. Anal. Methods Geomech. 12 (1): 61–77. https://doi.org/10.1002/nag.1610120105.
Sloan, S. W. 1989. “Upper bound limit analysis using finite elements and linear programming.” Int. J. Numer. Anal. Methods Geomech. 13 (3): 263–282. https://doi.org/10.1002/nag.1610130304.
Sloan, S. W. 2013. “Geotechnical stability analysis.” Geotechnique 63 (7): 531–537. https://doi.org/10.1680/geot.12.RL.001.
Sloan, S. W., A. Assadi, and N. Purushothaman. 1990. “Undrained stability of a trapdoor.” Geotechnique 40 (1): 45–62. https://doi.org/10.1680/geot.1990.40.1.45.
Terzaghi, K. 1936. “Stress distribution in dry and saturated sand above a yielding trapdoor.” In Proc, 1st Int. Conf. on Soil Mechanics and Foundation Engineering, 307–311. Cambridge, MA: Harvard Univ.
Terzaghi, K. 1943. Theoretical soil mechanics. New York: Wiley.
Vanmarcke, E. H. 1984. Random fields: Analysis and synthesis. Cambridge, MA: MIT Press.
Wang, L., B. Leshchinsky, T. M. Evans, and Y. Xie. 2017a. “Active and passive arching stress in c′-Ф′ soils: A sensitivity study using computational limit analysis.” Comput. Geotech. 84: 47–55. https://doi.org/10.1016/j.compgeo.2016.11.016.
Wang, Y., O. V. Akeju, and T. Zhao. 2017b. “Interpolation of spatially varying but sparsely measured geo-data: A comparative study.” Eng. Geol. 231: 200–217. https://doi.org/10.1016/j.enggeo.2017.10.019.
Wang, Z., and S. Goh. 2021. “Novel approach to efficient slope reliability analysis in spatially variable soils.” Eng. Geol. 281: 105989. https://doi.org/10.1016/j.enggeo.2020.105989.
Wu, G., H. Zhao, and M. Zhao. 2021a. “Undrained stability analysis of strip footings lying on circular voids with spatially random soil.” Comput. Geotech. 133: 104072. https://doi.org/10.1016/j.compgeo.2021.104072.
Wu, G., H. Zhao, M. Zhao, and Z. Zhu. 2021b. “Stochastic analysis of dual tunnels in spatially random soil.” Comput. Geotech. 129: 103861. https://doi.org/10.1016/j.compgeo.2020.103861.
Yodsomjai, W., S. Keawsawasvong, and V. Q. Lai. 2021. “Limit analysis solutions for bearing capacity of ring foundations on rocks using Hoek-Brown failure criterion.” Int. J. Geosynth. Ground Eng. 7: 29. https://doi.org/10.1007/s40891-021-00281-y.
Zhu, D., D. V. Griffiths, J. Huang, Y. Gao, and G. A. Fenton. 2019. “Probabilistic analysis of shallow passive trapdoor in cohesive soil.” J. Geotech. Geoenviron. Eng. 145 (6): 06019003. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002051.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 23Issue 6June 2023

History

Received: Apr 6, 2022
Accepted: Jan 3, 2023
Published online: Apr 11, 2023
Published in print: Jun 1, 2023
Discussion open until: Sep 11, 2023

Permissions

Request permissions for this article.

ASCE Technical Topics:

Authors

Affiliations

Associate Professor, School of Civil Engineering and Surveying, Univ. of Southern Queensland, Toowoomba, QLD 4350, Australia. ORCID: https://orcid.org/0000-0002-9220-3184. Email: [email protected]
Assistant Professor, Research Unit in Sciences and Innovative Technologies for Civil Engineering Infrastructures, Dept. of Civil Engineering, Thammasat School of Engineering, Thammasat Univ., Pathumthani 12120, Thailand (corresponding author). ORCID: https://orcid.org/0000-0002-1760-9838. 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.

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