Reliability Analysis and Design of Vertically Loaded Piles in Spatially Variable Soils
Publication: International Journal of Geomechanics
Volume 23, Issue 10
Abstract
At present, the reliability analysis and design method of vertically loaded piles embedded in spatially variable soils is difficult to be applied in practical engineering due to the huge computation effort required. To improve computational efficiency, this paper proposes a new method called the FORM–KL–LTM, which integrates the advantages of the first-order reliability method (FORM), the Karhunen–Loève (KL) expansion method, and the load transfer method (LTM). The main framework of the FORM–KL–LTM is the FORM, which is used to perform reliability analysis for the pile. The KL expansion method is adopted to carry out random discretization to generate the discrete soil parameters required by each iterative computation of the reliability index using the FORM, and the LTM is employed to evaluate the nonlinear load–settlement behavior of the pile head and to compute the values of limit state functions required by the FORM. The proposed method is computationally efficient because the number of random variables is controlled by the limit number of KL expansion terms. Based on the FORM–KL–LTM, a reliability sensitivity analysis method is proposed, which can compute the sensitivity index for measuring the relative sensitivity of the reliability index with respect to soil properties. Furthermore, a procedure for the reliability-based design (RBD) of piles embedded in spatially variable soils is established for the design of pile geometry, and a design ratio is defined to select the controlling limit state in the RBD of pile for both the ultimate limit state and the serviceable limit state. The procedure, accuracy, and efficiency of the proposed methods are demonstrated by providing an example of the reliability analysis and design of a vertically load pile in spatially variable soils.
Practical Applications
The spatial variability of soil has been recognized as an important source of uncertainty of the bearing performance of the pile, and therefore, it should be considered in the reliability analysis and design of a pile foundation. However, the methods used in the current literature, such as the discretization of a random field, the calculation of load–displacement curves, and the reliability analysis of a pile foundation, require a huge computation effort. Low computational efficiency is highly disadvantageous to designers, which makes the reliability analysis and design method by considering a soil’s spatial variability difficult to be widely applied to practical engineering. Therefore, this study proposes a new method called the FORM–KL–LTM to perform the reliability analysis and design of vertically loaded piles in spatially variable soils. This method greatly reduces the number of random variables and simulations of the performance function, thus improving the computational efficiency. Based on the FORM–KL–LTM, a reliability sensitivity analysis method is proposed to carry out a sensitivity analysis of soil parameters on the reliability of a pile foundation. Moreover, this paper defines the design ratios for discussing which limit state mainly controls the failure state of the pile foundation under different soil properties and pile geometry.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data used during the study are available from the corresponding author by request.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 41972278 and 42030710).
References
AASHTO. 2010. AASHTO LRFD bridge design specifications. Washington, DC: AASHTO.
Adam, K. 2012. “Proposal for calculating the bearing capacity of screw displacement piles in non-cohesive soils based on CPT results.” Stud. Geotech. Mech. 34 (4): 41–51. https://doi.org/10.2478/sgm041204.
Castelli, F., and M. Maugeri. 2002. “Simplified nonlinear analysis for settlement prediction of pile groups.” J. Geotech. Geoenviron. Eng. 128 (1): 76–84. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:1(76).
Chen, X., D. Li, X. Tang, and Y. Liu. 2021. “A three-dimensional large-deformation random finite-element study of landslide runout considering spatially varying soil.” Landslides 18 (9): 3149–3162. https://doi.org/10.1007/s10346-021-01699-1.
Cheon, J. Y., and R. B. Gilbert. 2014. “Modeling spatial variability in offshore geotechnical properties for reliability-based foundation design.” Struct. Saf. 49: 18–26. https://doi.org/10.1016/j.strusafe.2013.07.008.
Cho, S. E. 2007. “Effects of spatial variability of soil properties on slope stability.” Eng. Geol. 92 (3–4): 97–109. https://doi.org/10.1016/j.enggeo.2007.03.006.
Clough, G. W., and J. M. Duncan. 1971. “Finite element analyses of retaining wall behavior.” J. Soil Mech. Found. Div. 97 (12): 1657–1673. https://doi.org/10.1061/JSFEAQ.0001870.
Duncan, J. M. 2000. “Factors of safety and reliability in geotechnical engineering.” J. Geotech. Geoenviron. Eng. 126 (4): 307–316. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307).
Dong, X., X. Tan, X. Lin, X. Zhang, X. Hou, and D. Wu. 2022. “Reliability analysis of piles based on proof vertical static load test.” Geomech. Eng. 29 (5): 487–496. https://doi.org/10.12989/gae.2022.29.5.487.
El-Ramly, H., N. R. Morgenstern, and D. M. Cruden. 2003. “Probabilistic stability analysis of a tailings dyke on presheared clay-shale.” Can. Geotech. J. 40 (1): 192–208. https://doi.org/10.1139/T02-095.
Fan, H., Q. Huang, and R. Liang. 2014. “Reliability analysis of piles in spatially varying soils considering multiple failure modes.” Comput. Geotech. 57: 97–104. https://doi.org/10.1016/j.compgeo.2014.01.009.
Fan, H., and R. Liang. 2013. “Reliability-based design of axially loaded drilled shafts using Monte Carlo method.” Int. J. Numer. Anal. Methods Geomech. 37 (14): 2223–2238. https://doi.org/10.1002/nag.2131.
Fan, H., and R. Liang. 2015. “Importance sampling based algorithm for efficient reliability analysis of axially loaded piles.” Comput. Geotech. 65: 278–284. https://doi.org/10.1016/j.compgeo.2015.01.005.
Fei, S., X. Tan, W. Gong, X. Dong, F. Zha, and L. Xu. 2021. “Reliability analysis of strip footing under rainfall using KL-FORM.” Geomech. Eng. 24 (2): 167–178. https://doi.org/10.12989/gae.2021.24.2.167.
Fenton, G. A., and D. V. Griffiths. 2005. “Three-dimensional probabilistic foundation settlement.” J. Geotech. Geoenviron. Eng. 131 (2): 232–239. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:2(232).
Haldar, S., and G. L. S. Babu. 2008. “Reliability measures for pile foundations based on cone penetration test data.” Can. Geotech. J. 45 (12): 1699–1714. https://doi.org/10.1139/T08-082.
Hirayama, H. 1990. “Load–settlement analysis for bored piles using hyperbolic transfer functions.” Soils Found. 30: 55–64. https://doi.org/10.3208/sandf1972.30.55.
Huffman, J. C., A. W. Strahler, and A. W. Stuedlein. 2015. “Reliability-based serviceability limit state design for immediate settlement of spread footings on clay.” Soils Found. 55 (4): 798–812. https://doi.org/10.1016/j.sandf.2015.06.012.
Janbu, N. 1976. “Static bearing capacity of friction piles.” Sechste Eur. Konf. Fuer Bodenmech. Grundbau 1 (2): 479–482.
Ji, J., and J. K. Kodikara. 2015. “Efficient reliability method for implicit limit state surface with correlated non-Gaussian variables: HL-RF variant FORM for implicit LSS involving correlated non-normals.” Int. J. Numer. Anal. Methods Geomech. 39 (17): 1898–1911. https://doi.org/10.1002/nag.2380.
Ji, J., C. Zhang, Y. Gao, and J. Kodikara. 2018. “Effect of 2D spatial variability on slope reliability: A simplified FORM analysis.” Geosci. Front. 9 (6): 1631–1638. https://doi.org/10.1016/j.gsf.2017.08.004.
Jiang, S., D. Li, Z. Cao, C. Zhou, and K. K. Phoon. 2015. “Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation.” J. Geotech. Geoenviron. Eng. 141 (2): 04014096. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001227.
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., and M. Momeni. 2015. “Stochastic analysis of ground response using non-recursive algorithm.” Soil Dyn. Earthquake Eng. 69: 57–82. https://doi.org/10.1016/j.soildyn.2014.10.025.
Johari, A., and A. Talebi. 2021. “Stochastic analysis of piled-raft foundations using the random finite-element method.” Int. J. Geomech. 21 (4): 04021020. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001966.
Laloy, E., B. Rogiers, J. A. Vrugt, D. Mallants, and D. Jacques. 2013. “Efficient posterior exploration of a high-dimensional groundwater model from two-stage Markov chain Monte Carlo simulation and polynomial chaos expansion.” Water Resour. Res. 49 (5): 2664–2682. https://doi.org/10.1002/wrcr.20226.
Lee, K. M., and Z. R. Xiao. 2001. “A simplified nonlinear approach for pile group settlement analysis in multilayered soils.” Can. Geotech. J. 38 (5): 1063–1080. https://doi.org/10.1139/t01-034.
Leung, Y. F., and M. K. Lo. 2018. “Probabilistic assessment of pile group response considering superstructure stiffness and three-dimensional soil spatial variability.” Comput. Geotech. 103: 193–200. https://doi.org/10.1016/j.compgeo.2018.07.010.
Li, D., S. Jiang, Z. Cao, W. Zhou, C. Zhou, and L. Zhang. 2015. “A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties.” Eng. Geol. 187: 60–72. https://doi.org/10.1016/j.enggeo.2014.12.003.
Li, L., and W. Gong. 2019. “Prediction of nonlinear vertical settlement of a pile group consisting of new and existing displacement piles in clay strata.” Soils Found. 59 (5): 1336–1348. https://doi.org/10.1016/j.sandf.2019.06.001.
Lin, X., X. Tan, Y. Yao, X. Dong, S. Fei, and L. Ma. 2022. “Realization of multi-dimensional random field based on Jacobi–Lagrange–Galerkin method in geotechnical engineering.” Comput. Geotech. 144: 104533. https://doi.org/10.1016/j.compgeo.2021.104533.
Misra, A., and L. A. Roberts. 2006. “Probabilistic analysis of drilled shaft service limit state using the ‘t–z’ method.” Can. Geotech. J. 43 (12): 1324–1332. https://doi.org/10.1139/t06-074.
Misra, A., and L. A. Roberts. 2009. “Service limit state resistance factors for drilled shafts.” Géotechnique 59 (1): 53–61. https://doi.org/10.1680/geot.2008.3605.
O’Neill, M. W., R. A. Hawkins, and L. J. Mahar. 1982. “Load transfer mechanisms in piles and pile groups.” J. Geotech. Eng. Div. 108 (12): 1605–1623. https://doi.org/http://dx.doi.org/10.1061/(ASCE)0733-9410(1983)109:10(1361).
O’Neil, M. W., and L. C. Reese. 1990. “Drilled shafts: Construction procedures and design methods.” Tunnelling Underground Space Technol. 5 (1): 156–157. https://doi.org/10.1016/0886-7798(90)90101-O.
Phoon, K. K., S. P. Huang, and S. T. Quek. 2002. “Implementation of Karhunen–Loeve expansion for simulation using a wavelet-Galerkin scheme.” Probab. Eng. Mech. 17: 293–303. https://doi.org/10.1016/S0266-8920(02)00013-9.
Phoon, K.-K., and F. H. Kulhawy. 1999. “Characterization of geotechnical variability.” Can. Geotech. J. 36 (4): 612–624. https://doi.org/10.1139/cgj-36-4-612.
Randolph, M. F. 2003. “Science and empiricism in pile foundation design.” Geotechnique 53 (10): 847–876. https://doi.org/10.1680%2fgeot.53.10.847.37518.
Randolph, M. F., and C. P. Wroth. 1979. “An analysis of the vertical deformation of pile groups.” Géotechnique 29 (4): 423–439. https://doi.org/10.1680/geot.1979.29.4.423.
Roberts, L. A., and A. Misra. 2009. “Reliability-based design of deep foundations based on differential settlement criterion.” Can. Geotech. J. 46 (2): 168–176. https://doi.org/10.1139/T08-117.
Roberts, L. A., and A. Misra. 2010. “Performance-based design of deep foundation systems in load and resistance factor design framework.” Transp. Res. Rec. 2186 (1): 29–37. https://doi.org/10.3141/2186-04.
Roberts, L., A. Misra, and S. Levorson. 2008. “Practical method for load and resistance factor design (LRFD) of deep foundations at the strength and service limit states.” Int. J. Geotech. Eng. 2 (4): 355–368. https://doi.org/10.3328/IJGE.2008.02.04.355-368.
Selig, E., and ISSMFE. 1985. “Axial pile loading test—Part 1: Static loading.” Geotech. Test. J. 8 (2): 79. https://doi.org/10.1520/GTJ10514J.
Shao, W., Y. Nie, D. Shi, and Y. Xu. 2020. “Probabilistic analysis of the behaviour of laterally loaded piles in chloride environments.” Ocean Eng. 217: 107872. https://doi.org/10.1016/j.oceaneng.2020.107872.
Su, Y., X. Li, and Z. Xie. 2011. “Probabilistic evaluation for the implicit limit-state function of stability of a highway tunnel in China.” Tunnelling Underground Space Technol. 26 (2): 422–434. https://doi.org/10.1016/j.tust.2010.11.009.
Suchomel, R., and D. Mašín. 2010. “Comparison of different probabilistic methods for predicting stability of a slope in spatially variable c–φ soil.” Comput. Geotech. 37 (1–2): 132–140. https://doi.org/10.1016/j.compgeo.2009.08.005.
Tan, X., P. Li, M. Shen, M. Hu, X. Hou, and H. Ma. 2020. “Evaluation of the spatial variability characteristics of the unsaturated clay in Hefei, China.” Soils Found. 60 (2): 454–465. https://doi.org/10.1016/j.sandf.2020.03.010.
Vanmarcke, E. 1983. Random fields: Analysis and synthesis. Cambridge, MA: MIT Press.
Wijerathna, M., and D. S. Liyanapathirana. 2019. “Significance of spatial variability of deep cement mixed columns on reliability of column-supported embankments.” Int. J. Geomech. 19 (8): 04019087. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001473.
Zhang, J., L. M. Zhang, and W. H. Tang. 2011. “Kriging numerical models for geotechnical reliability analysis.” Soils Found. 51 (6): 1169–1177. https://doi.org/10.3208/sandf.51.1169.
Zhang, Q., S. Li, F. Liang, M. Yang, and Q. Zhang. 2014. “Simplified method for settlement prediction of single pile and pile group using a hyperbolic model.” Int. J. Civ. Eng. 12 (2B): 179–192.
Zhang, Q., S. Liu, S. Zhang, J. Zhang, and K. Wang. 2016. “Simplified non-linear approaches for response of a single pile and pile groups considering progressive deformation of pile–soil system.” Soils Found. 56 (3): 473–484. https://doi.org/10.1016/j.sandf.2016.04.013.
Zhang, Q., Z. Zhang, and J. He. 2010. “A simplified approach for settlement analysis of single pile and pile groups considering interaction between identical piles in multilayered soils.” Comput. Geotech. 37 (7–8): 969–976. https://doi.org/10.1016/j.compgeo.2010.08.003.
Zhang, X., B. Jiao, Y. Han, S. Chen, and X. Li. 2021a. “Random field model of soil parameters and the application in reliability analysis of laterally loaded pile.” Soil Dyn. Earthquake Eng. 147: 106821. https://doi.org/10.1016/j.soildyn.2021.106821.
Zhang, X., B. Jiao, and B. Hou. 2021b. “Reliability analysis of horizontally loaded pile considering spatial variability of soil parameters.” Soil Dyn. Earthquake Eng. 143: 106648. https://doi.org/10.1016/j.soildyn.2021.106648.
Zhou, J., C. Zhou, Q. Feng, and T. Gao. 2020. “Analytical model for load-transfer mechanism of rock-socketed drilled piles: Considering bond strength of the concrete–rock interface.” Int. J. Geomech. 20 (6): 04020059. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001672.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 23 • Issue 10 • October 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Sep 20, 2022
Accepted: Apr 23, 2023
Published online: Jul 31, 2023
Published in print: Oct 1, 2023
Discussion open until: Dec 31, 2023
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.
Cited by
- Xiaohui Tan, Pengfei Zhang, Xiaole Dong, Xin Lin, Zhitang Lu, Reliability Analysis of Single Pile in Spatially Variable Soil Based on Variance Reduction Method, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 10.1061/AJRUA6.RUENG-1183, 10, 2, (2024).