Effect of Soil Spatial Variability on the Structural Reliability of a Statically Indeterminate Frame
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 1
Abstract
This paper presents a probabilistic procedure for assessing the structural responses of a statically indeterminate frame caused by soil spatial variability. Neglecting the soil spatial variability can underestimate the probability of structural failure, and lead to an unsafe structural design. The soil spatial variability is simulated by the random field theory implemented with Monte Carlo simulation. The diagrams of bending moment, shear force, and axial force induced by the differential settlement between the two footings of this indeterminate frame are solved by using the force method. The differential settlement, angular distortion, and frame internal forces are analyzed statistically. The probability of failure for three major structural failure modes, i.e., strength failure, in-plane buckling failure, and out-of-plane buckling failure, was rigorously assessed, revealing the dominant failure mode. It was demonstrated that there is a critical scale of fluctuation of soil property in the structural analysis. This study developed an innovative procedure for researchers and practitioners to assess the superstructure performance subjected to uncertain subsurface conditions.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Ahmed, A., and A.-H. Soubra. 2014. “Probabilistic analysis at the serviceability limit state of two neighboring strip footings resting on a spatially random soil.” Struct. Saf. 49 (Jul): 2–9. https://doi.org/10.1016/j.strusafe.2013.08.001.
Akbas, S. O., and F. H. Kulhawy. 2009. “Reliability-based design approach for differential settlement of footings on cohesionless soils.” J. Geotech. Geoenviron. 135 (12): 1779–1788. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000127.
Akbas, S. O., and F. H. Kulhawy. 2010. “Characterization and estimation of geotechnical variability in Ankara clay: A case history.” Geotech. Geol. Eng. 28 (5): 619–631. https://doi.org/10.1007/s10706-010-9320-x.
Al-Bittar, T., A.-H. Soubra, and J. Thajeel. 2018. “Kriging-based reliability analysis of strip footings resting on spatially varying soils.” J. Geotech. Geoenviron. Eng. 144 (10): 04018071. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001958.
Alonso, E. E., and R. J. Krizek. 1975. “Stochastic formulation of soil properties.” In Vol. 2 of Proc., 2nd Int. Conf. on Applications of Statistics and Probability in Soil and Structural Engineering, 9–32. Evanston, IL: Northwestern Univ.
Arapakou, A. E., and V. P. Papadopoulos. 2012. “Factors affecting differential settlements of framed structures.” Geotech. Geol. Eng. 30 (6): 1323–1333. https://doi.org/10.1007/s10706-012-9546-x.
Bjerrum, L. 1963. “Allowable settlement of structures.” In Proc., European Conf. on Soil Mechanics and Foundation Engineering, London: International Society for Soil Mechanics and Geotechnical Engineering.
Breysse, D. 2011. “Influence of soil variability on differential settlements of buildings.” Revue Française de Génie Civil 6 (3): 409–419. https://doi.org/10.1080/12795119.2002.9692376.
Breysse, D., P. Kouassi, and D. Poulain. 1999. “Influence of the spatial variability of compacted soils on slope stability of embankments.” In Vol. 1 of Proc., Int. Conf. on the Application of Statistics and Probability, ICASP 8, edited by R. E. Melchers and M. G. Stewart, 367–373. Rotterdam, Netherlands: A.A. Balkema.
Budhu, M. 2015. Soil mechanics fundamentals. New York: Wiley.
Burland, J. B., and M. C. Burbidge. 1985. “Settlement of foundations on sand and gravel.” Proc. Inst. Civ. Eng. 78 (6): 1325–1381. https://doi.org/10.1680/iicep.1985.1058.
Chen, F., L. Wang, and W. Zhang. 2019. “Reliability assessment on stability of tunnelling perpendicularly beneath an existing tunnel considering spatial variabilities of rock mass properties.” Tunnelling Underground Space Technol. 88 (Jun): 276–289. https://doi.org/10.1016/j.tust.2019.03.013.
El Haj, A.-K., A.-H. Soubra, and T. Al-Bittar. 2019. “Probabilistic analysis of strip footings based on enhanced Kriging metamodeling.” Int. J. Numer. Anal. Methods Geomech. 43 (17): 2667–2686. https://doi.org/10.1002/nag.2995.
Fenton, G. A. 1997. “Data analysis/geostatistics.” In Proc., ASCE GeoLogan'97 Conf.: Probabilistic Methods in Geotechnical Engineering, edited by G. A. Fenton, 51–73. Reston, VA: ASCE.
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.
Fenton, G. A., and D. V. Griffiths. 2008. Risk assessment in geotechnical engineering. Hoboken, NJ: Wiley.
Fenton, G. A., D. V. Griffiths, and M. B. Williams. 2005. “Reliability of traditional retaining wall design.” Géotechnique 55 (1): 55–62. https://doi.org/10.1680/geot.2005.55.1.55.
Frantziskonis, G., and D. Breysse. 2003. “Influence of soil variability on differential settlements of structures.” Comput. Geotech. 30 (3): 217–230. https://doi.org/10.1016/S0266-352X(02)00062-9.
Goh, A. T. C., W. Zhang, and K. S. Wong. 2019. “Deterministic and reliability analysis of basal heave stability for excavation in spatial variable soils.” Comput. Geotech. 108 (Apr): 152–160. https://doi.org/10.1016/j.compgeo.2018.12.015.
Griffiths, D. V., and G. A. Fenton. 1993. “Seepage beneath water retaining structures founded on spatially random soil.” Géotechnique 43 (4): 577–587. https://doi.org/10.1680/geot.1993.43.4.577.
Griffiths, D. V., and G. A. Fenton. 2004. “Probabilistic slope stability analysis by finite elements.” J. Geotech. Geoenviron. 130 (5): 507–518. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507).
Halder, K., and D. Chakraborty. 2020. “Influence of soil spatial variability on the response of strip footing on geocell-reinforced slope.” Comput. Geotech. 122 (Jun): 103533. https://doi.org/10.1016/j.compgeo.2020.103533.
Hamrouni, A., D. Dias, and B. Sbartai. 2020. “Soil spatial variability impact on the behavior of a reinforced earth wall.” Front. Struct. Civ. Eng. 14 (2): 518–531. https://doi.org/10.1007/s11709-020-0611-x.
Jaksa, M. B., P. I. Brooker, and W. S. Kaggwa. 1997. “Modelling the spatial variability of the undrained shear strength of clay soils using geostatistics.” In Vol. 2 of Geostatistics Wollongong ’96, edited by E. Y. Baafi and N. A. Schofield, 1284–1295. Alphen aan den Rijn, Netherlands: Kluwer Publisher.
Jaksa, M. B., W. S. Kaggwa, and P. I. Brooker. 1993. “Geostatistical modelling of the spatial variation of the shear strength of a stiff, overconsolidated clay.” In Probabilistic methods in geotechnical engineering, edited by K. S. Li and S.-C. R. Lo. Rotterdam, Netherlands: A.A. Balkema.
Kassimali, A. 2005. Structural analysis. 3rd ed. Toronto: Thompson.
Lü, Q., Z. Xiao, J. Zheng, and Y. Shang. 2018. “Probabilistic assessment of tunnel convergence considering spatial variability in rock mass properties using interpolated autocorrelation and response surface method.” Geosci. Front. 9 (6): 1619–1629. https://doi.org/10.1016/j.gsf.2017.08.007.
Lumb, P. 1975. “Spatial variability of soil properties.” In Vol. 2 of Proc., 2nd Int. Conf. on Application of Statistics and Probability to Soil and Structural Engineering, 397–421. Aachen, Germany: German Society for Earthworks and Foundation Engineering.
Luo, N., R. J. Bathurst, and S. Javankhoshdel. 2016a. “Probabilistic stability analysis of simple reinforced slopes by finite element method.” Comput. Geotech. 77 (Jul): 45–55. https://doi.org/10.1016/j.compgeo.2016.04.001.
Luo, Z., S. Atamturktur, C. H. Juang, H. Huang, and P. S. Lin. 2011. “Probability of serviceability failure in a braced excavation in a spatially random field: Fuzzy finite element approach.” Comput. Geotech. 38 (8): 1031–1040. https://doi.org/10.1016/j.compgeo.2011.07.009.
Luo, Z., and B. Hu. 2019. “Probabilistic design model for energy piles considering soil spatial variability.” Comput. Geotech. 108 (Apr): 308–318. https://doi.org/10.1016/j.compgeo.2019.01.003.
Luo, Z., Y. Li, S. Zhou, and H. Di. 2018. “Effect of vertical spatial variability on supported excavations in sands considering multiple geotechnical and structural failure modes.” Comput. Geotech. 95 (Mar): 16–29. https://doi.org/10.1016/j.compgeo.2017.11.017.
Luo, Z., J. R. Martin, L. Wang, W. Gong, and C. H. Juang. 2016b. “Bayesian updating of spatially varied soil property for ultimate limit state design of drilled shafts.” In Geo-Chicago 2016: Sustainable Materials and Resource Conservation, Geotechnical Special Publication 272, edited by K. R. Reddy, N. Yesiller, D. Zekkos, A. Farid and A. De, 631–640. Reston, VA: ASCE.
Roberts, C., and G. Casella. 1999. Monte Carlo statistical methods. New York: Springer.
Skempton, A. W., and D. M. McDonald. 1956. “The allowable settlement of buildings.” Proc. Inst. Civ. Eng. 5 (3): 727–768. https://doi.org/10.1680/ipeds.1956.12202.
Vanmarcke, E. H. 1977. “Probabilistic modelling of soil profiles.” J. Geotech. Eng. Div. 103 (11): 1227–1246.
Vanmarcke, E. H. 1983. Random fields: Analysis and synthesis. Cambridge, MA: MIT Press.
Wu, Z., and Z. Luo. 2020. “Life-cycle system reliability-based approach for bridge pile foundations under scour conditions.” KSCE J. Civ. Eng. 24 (2): 412–423. https://doi.org/10.1007/s12205-020-0916-2.
Zhang, L., and J. J. Chen. 2012. “Effect of spatial correlation of standard penetration test (SPT) data on bearing capacity of driven piles in sand.” Can. Geotech. J. 49 (4): 394–402. https://doi.org/10.1139/t2012-005.
Zhang, W., L. Han, X. Gu, L. Wang, F. Chen, and H. Liu. 2020. “Tunneling and deep excavations in spatially variable soil and rock masses: A short review.” Underground Space https://doi.org/10.1016/j.undsp.2020.03.003.
Information & Authors
Information
Published In
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Apr 13, 2020
Accepted: Jul 31, 2020
Published online: Oct 29, 2020
Published in print: Mar 1, 2021
Discussion open until: Mar 29, 2021
Authors
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.