Efficient and conservative estimation reliability analysis of strip footing on spatially variable c - ϕ soil using random finite element limit analysis

[1] Ali, A., Lyamin, A. V., Huang, J., Li, J. H., Cassidy, M. J., & Sloan, S. W. (2017). Probabilistic stability assessment using adaptive limit analysis and random fields. Acta Geotechnica, 12(4), 937–948. https://doi.org/10.1007/s11440-016-0505-1 AliA. LyaminA. V. HuangJ. LiJ. H. CassidyM. J. SloanS. W. 2017 Probabilistic stability assessment using adaptive limit analysis and random fields Acta Geotechnica 12 4 937 948 https://doi.org/10.1007/s11440-016-0505-1 Search in Google Scholar

[2] Ali, A., Lyamin, A. V., Huang, J., Sloan, S. W., & Cassidy, M. (2016). Effect of Spatial Correlation Length on the Bearing Capacity of an Eccentrically Loaded Strip Footing. In H. W. Huang, J. Li, J. Zhang, & Chen J.B. (Eds.), APSSRA. AliA. LyaminA. V. HuangJ. SloanS. W. CassidyM. 2016 Effect of Spatial Correlation Length on the Bearing Capacity of an Eccentrically Loaded Strip Footing In HuangH. W. LiJ. ZhangJ. ChenJ.B. (Eds.), APSSRA Search in Google Scholar

[3] Au, S.-K., & Beck, J. L. (2001). Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Engineering Mechanics, 16(4), 263–277. https://doi.org/10.1016/S0266-8920(01)00019-4 AuS.-K. BeckJ. L. 2001 Estimation of small failure probabilities in high dimensions by subset simulation Probabilistic Engineering Mechanics 16 4 263 277 https://doi.org/10.1016/S0266-8920(01)00019-4 Search in Google Scholar

[4] Chen, X.-J., Fu, Y., & Liu, Y. (2022). Random finite element analysis on uplift bearing capacity and failure mechanisms of square plate anchors in spatially variable clay. Engineering Geology, 304, 106677. https://doi.org/10.1016/j.enggeo.2022.106677 ChenX.-J. FuY. LiuY. 2022 Random finite element analysis on uplift bearing capacity and failure mechanisms of square plate anchors in spatially variable clay Engineering Geology 304 106677 https://doi.org/10.1016/j.enggeo.2022.106677 Search in Google Scholar

[5] Cheng, P., Guo, J., Yao, K., & Chen, X. (2023). Numerical investigation on pullout capacity of helical piles under combined loading in spatially random clay. Marine Georesources & Geotechnology, 41(10), 1118–1131. https://doi.org/10.1080/1064119X.2022.2120843 ChengP. GuoJ. YaoK. ChenX. 2023 Numerical investigation on pullout capacity of helical piles under combined loading in spatially random clay Marine Georesources & Geotechnology 41 10 1118 1131 https://doi.org/10.1080/1064119X.2022.2120843 Search in Google Scholar

[6] Ching, J., Wu, T. J., Stuedlein, A. W., & Bong, T. (2018). Estimating horizontal scale of fluctuation with limited CPT soundings. Geoscience Frontiers, 9(6), 1597–1608. https://doi.org/10.1016/j.gsf.2017.11.008 ChingJ. WuT. J. StuedleinA. W. BongT. 2018 Estimating horizontal scale of fluctuation with limited CPT soundings Geoscience Frontiers 9 6 1597 1608 https://doi.org/10.1016/j.gsf.2017.11.008 Search in Google Scholar

[7] Chwała, M., Komatsu, G., & Haruyama, J. (2024). Structural stability of lunar lava tubes with consideration of variable cross-section geometry. Icarus, 411. https://doi.org/10.1016/j.icarus.2023.115928 ChwałaM. KomatsuG. HaruyamaJ. 2024 Structural stability of lunar lava tubes with consideration of variable cross-section geometry Icarus 411 https://doi.org/10.1016/j.icarus.2023.115928 Search in Google Scholar

[8] Chwała, M., & Puła, W. (2020). Evaluation of shallow foundation bearing capacity in the case of a two-layered soil and spatial variability in soil strength parameters. PLoS One, 15(4), e0231992. ChwałaM. PułaW. 2020 Evaluation of shallow foundation bearing capacity in the case of a two-layered soil and spatial variability in soil strength parameters PLoS One 15 4 e0231992 Search in Google Scholar

[9] Cho, S. E., & Park, H. C. (2010). Effect of spatial variability of cross-correlated soil properties on bearing capacity of strip footing. International Journal for Numerical and Analytical Methods in Geomechanics, 34(1), 1–26. ChoS. E. ParkH. C. 2010 Effect of spatial variability of cross-correlated soil properties on bearing capacity of strip footing International Journal for Numerical and Analytical Methods in Geomechanics 34 1 1 26 Search in Google Scholar

[10] Ciria Suárez, H. (2004). Computation of Upper and Lower Bounds in Limit Analysis using Second-order Cone Programming and Mesh Adaptivity [Master of Science]. Massachusetts Institute of Technology. Ciria SuárezH. 2004 Computation of Upper and Lower Bounds in Limit Analysis using Second-order Cone Programming and Mesh Adaptivity [Master of Science]. Massachusetts Institute of Technology Search in Google Scholar

[11] Dobrzanski, J., & Kawa, M. (2021). Bearing capacity of eccentrically loaded strip footing on spatially variable cohesive soil. Studia Geotechnica et Mechanica, 43(4), 425–437. https://doi.org/10.2478/sgem-2021-0035 DobrzanskiJ. KawaM. 2021 Bearing capacity of eccentrically loaded strip footing on spatially variable cohesive soil Studia Geotechnica et Mechanica 43 4 425 437 https://doi.org/10.2478/sgem-2021-0035 Search in Google Scholar

[12] EN-1990, Basis of Structural Design. (2002). EN-1990, Basis of Structural Design 2002 Search in Google Scholar

[13] Engwirda, D. (2014). Locally Optimal Delaunay-refinement and Optimisation-based Mesh Generation. EngwirdaD. 2014 Locally Optimal Delaunay-refinement and Optimisation-based Mesh Generation Search in Google Scholar

[14] Fenton, G. A., & Griffiths, D. V. (2008). Risk assessment in geotechnical engineering. John Wiley & Sons. FentonG. A. GriffithsD. V. 2008 Risk assessment in geotechnical engineering John Wiley & Sons Search in Google Scholar

[15] Griffiths, D. V., & Fenton, G. A. (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 GriffithsD. V. FentonG. A. 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 Search in Google Scholar

[16] Griffiths, D. V., & Fenton, G. A. (2004). Probabilistic Slope Stability Analysis by Finite Elements. Journal of Geotechnical and Geoenvironmental Engineering, 130(5), 507–518. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507) GriffithsD. V. FentonG. A. 2004 Probabilistic Slope Stability Analysis by Finite Elements Journal of Geotechnical and Geoenvironmental Engineering 130 5 507 518 https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507) Search in Google Scholar

[17] Griffiths, D. V., Huang, J., & Fenton, G. A. (2009). Influence of Spatial Variability on Slope Reliability Using 2-D Random Fields. Journal of Geotechnical and Geoenvironmental Engineering, 135(10), 1367–1378. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000099 GriffithsD. V. HuangJ. FentonG. A. 2009 Influence of Spatial Variability on Slope Reliability Using 2-D Random Fields Journal of Geotechnical and Geoenvironmental Engineering 135 10 1367 1378 https://doi.org/10.1061/(ASCE)GT.1943-5606.0000099 Search in Google Scholar

[18] Hicks, M. A., & Samy, K. (2002). Influence of heterogeneity on undrained clay slope stability. Quarterly Journal of Engineering Geology and Hydrogeology, 35(1), 41–49. https://doi.org/10.1144/qjegh.35.1.41 HicksM. A. SamyK. 2002 Influence of heterogeneity on undrained clay slope stability Quarterly Journal of Engineering Geology and Hydrogeology 35 1 41 49 https://doi.org/10.1144/qjegh.35.1.41 Search in Google Scholar

[19] Huang, L., Cheng, Y. M., Li, L., & Yu, S. (2021). Reliability and failure mechanism of a slope with non-stationarity and rotated transverse anisotropy in undrained soil strength. Computers and Geotechnics, 132. https://doi.org/10.1016/j.compgeo.2020.103970 HuangL. ChengY. M. LiL. YuS. 2021 Reliability and failure mechanism of a slope with non-stationarity and rotated transverse anisotropy in undrained soil strength Computers and Geotechnics 132 https://doi.org/10.1016/j.compgeo.2020.103970 Search in Google Scholar

[20] ISO 2394:2015, General principles on reliability for structures. (2015). ISO 2394:2015 General principles on reliability for structures 2015 Search in Google Scholar

[21] J. L. Doob. (1990). Stochastic processes. Wiley-Interscience. DoobJ. L. 1990 Stochastic processes Wiley-Interscience Search in Google Scholar

[22] Jerez D. J. & Chwała M. & Jensen H. A. & Beer M. (2024). Optimal borehole placement for the design of rectangular shallow foundation systems under undrained soil conditions: A stochastic framework. Reliability Engineering & System Safety. doi.org/10.1016/j.ress.2023.109771. JerezD. J. ChwałaM. JensenH. A. BeerM. 2024 Optimal borehole placement for the design of rectangular shallow foundation systems under undrained soil conditions: A stochastic framework Reliability Engineering & System Safety doi.org/10.1016/j.ress.2023.109771. Search in Google Scholar

[23] Jha, S. K., & Ching, J. (2013). Simulating Spatial Averages of Stationary Random Field Using the Fourier Series Method. Journal of Engineering Mechanics, 139(5), 594–605. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000517 JhaS. K. ChingJ. 2013 Simulating Spatial Averages of Stationary Random Field Using the Fourier Series Method Journal of Engineering Mechanics 139 5 594 605 https://doi.org/10.1061/(ASCE)EM.1943-7889.0000517 Search in Google Scholar

[24] Kawa, M. (2023). Zastosowania pól losowych do opisu anizotropowych ośrodków gruntowych w wybranych zagadnieniach geoinżynierii. Oficyna Wydawnicza Politechniki Wrocławskiej (in Polish). KawaM. 2023 Zastosowania pól losowych do opisu anizotropowych ośrodków gruntowych w wybranych zagadnieniach geoinżynierii Oficyna Wydawnicza Politechniki Wrocławskiej (in Polish) Search in Google Scholar

[25] Kawa, M., Baginska, I., & Wyjadlowski, M. (2019). Reliability analysis of sheet pile wall in spatially variable soil including CPTu test results. Archives of civil and mechanical engineering, 19, 598–613. KawaM. BaginskaI. WyjadlowskiM. 2019 Reliability analysis of sheet pile wall in spatially variable soil including CPTu test results Archives of civil and mechanical engineering 19 598 613 Search in Google Scholar

[26] Kawa, M., & Puła, W. (2020). 3D bearing capacity probabilistic analyses of footings on spatially variable c–φ soil. Acta Geotechnica, 15(6), 1453–1466. https://doi.org/10.1007/s11440-019-00853-3 KawaM. PułaW. 2020 3D bearing capacity probabilistic analyses of footings on spatially variable c–φ soil Acta Geotechnica 15 6 1453 1466 https://doi.org/10.1007/s11440-019-00853-3 Search in Google Scholar

[27] Kawa, M., Puła, W., & Truty, A. (2021). Probabilistic analysis of the diaphragm wall using the hardening soil-small (HSs) model. Engineering Structures, 232. https://doi.org/10.1016/j.engstruct.2021.111869 KawaM. PułaW. TrutyA. 2021 Probabilistic analysis of the diaphragm wall using the hardening soil-small (HSs) model Engineering Structures 232 https://doi.org/10.1016/j.engstruct.2021.111869 Search in Google Scholar

[28] Krabbenhoft, K., Lyamin, A. V., Hjiaj, M., & Sloan, S. W. (2005). A new discontinuous upper bound limit analysis formulation. International Journal for Numerical Methods in Engineering, 63(7), 1069–1088. https://doi.org/10.1002/nme.1314 KrabbenhoftK. LyaminA. V. HjiajM. SloanS. W. 2005 A new discontinuous upper bound limit analysis formulation International Journal for Numerical Methods in Engineering 63 7 1069 1088 https://doi.org/10.1002/nme.1314 Search in Google Scholar

[29] Kumar, V., Burman, A., Portelinha, F. H. M., Kumar, M., Burman, A., Portelinha, F. H. M., & Das, G. (2023). Influence of Variation of Soil Properties in Bearing Capacity and Settlement Analysis of a Strip Footing Using Random Finite Element Method. Civil Engineering Infrastructures Journal. https://doi.org/ DOI:10.22059/CEIJ.2023.360871.1930 KumarV. BurmanA. PortelinhaF. H. M. KumarM. BurmanA. PortelinhaF. H. M. DasG. 2023 Influence of Variation of Soil Properties in Bearing Capacity and Settlement Analysis of a Strip Footing Using Random Finite Element Method Civil Engineering Infrastructures Journal https://doi.org/ DOI:10.22059/CEIJ.2023.360871.1930 Search in Google Scholar

[30] Liu, Y., Chen, X., & Hu, M. (2022). Three-dimensional large deformation modeling of landslides in spatially variable and strain-softening soils subjected to seismic loads. Canadian Geotechnical Journal, 60(4), 426–437. LiuY. ChenX. HuM. 2022 Three-dimensional large deformation modeling of landslides in spatially variable and strain-softening soils subjected to seismic loads Canadian Geotechnical Journal 60 4 426 437 Search in Google Scholar

[31] Liu, X., Wang, Y., & Li, D. Q. (2019). Investigation of slope failure mode evolution during large deformation in spatially variable soils by random limit equilibrium and material point methods. Computers and Geotechnics, 111, 301–312. https://doi.org/10.1016/j.compgeo.2019.03.022 LiuX. WangY. LiD. Q. 2019 Investigation of slope failure mode evolution during large deformation in spatially variable soils by random limit equilibrium and material point methods Computers and Geotechnics 111 301 312 https://doi.org/10.1016/j.compgeo.2019.03.022 Search in Google Scholar

[32] Lyamin, A. V., & Sloan, S. W. (2002a). Lower bound limit analysis using non-linear programming. International Journal for Numerical Methods in Engineering, 55(5), 573–611. https://doi.org/10.1002/nme.511 LyaminA. V. SloanS. W. 2002a Lower bound limit analysis using non-linear programming International Journal for Numerical Methods in Engineering 55 5 573 611 https://doi.org/10.1002/nme.511 Search in Google Scholar

[33] Lyamin, A. V., & Sloan, S. W. (2002b). Upper bound limit analysis using linear finite elements and non-linear programming. International Journal for Numerical and Analytical Methods in Geomechanics, 26(2), 181–216. https://doi.org/10.1002/nag.198 LyaminA. V. SloanS. W. 2002b Upper bound limit analysis using linear finite elements and non-linear programming International Journal for Numerical and Analytical Methods in Geomechanics 26 2 181 216 https://doi.org/10.1002/nag.198 Search in Google Scholar

[34] Lyamin, A. V., & Sloan, S. W. (2003). Mesh generation for lower bound limit analysis. Advances in Engineering Software, 34(6), 321–338. https://doi.org/10.1016/S0965-9978(03)00032-2 LyaminA. V. SloanS. W. 2003 Mesh generation for lower bound limit analysis Advances in Engineering Software 34 6 321 338 https://doi.org/10.1016/S0965-9978(03)00032-2 Search in Google Scholar

[35] Makrodimopoulos, A., & Martin, C. M. (2008). Upper bound limit analysis using discontinuous quadratic displacement fields. Communications in Numerical Methods in Engineering, 24(11), 911–927. https://doi.org/10.1002/cnm.998 MakrodimopoulosA. MartinC. M. 2008 Upper bound limit analysis using discontinuous quadratic displacement fields Communications in Numerical Methods in Engineering 24 11 911 927 https://doi.org/10.1002/cnm.998 Search in Google Scholar

[36] Pieczyńska-Kozłowska, J. M., Puła, W., Griffiths, D. V., & Fenton, G. A. (2015). Influence of embedment, self-weight and anisotropy on bearing capacity reliability using the random finite element method. Computers and Geotechnics, 67, 229–238. https://doi.org/10.1016/j.compgeo.2015.02.013 Pieczyńska-KozłowskaJ. M. PułaW. GriffithsD. V. FentonG. A. 2015 Influence of embedment, self-weight and anisotropy on bearing capacity reliability using the random finite element method Computers and Geotechnics 67 229 238 https://doi.org/10.1016/j.compgeo.2015.02.013 Search in Google Scholar

[37] Podlich, N. C. (2018). The Development of Efficient Algorithms for Large-Scale Finite Element Limit Analysis [Doctor of Philosophy]. University of Newcastle. PodlichN. C. 2018 The Development of Efficient Algorithms for Large-Scale Finite Element Limit Analysis [Doctor of Philosophy]. University of Newcastle Search in Google Scholar

[38] Podlich, N. C., Lyamin, A. V., & Sloan, S. W. (2014). A Comparison of Conic Programming Software for Finite Element Limit Analysis. Applied Mechanics and Materials, 553, 439–444. https://doi.org/10.4028/www.scientific.net/AMM.553.439 PodlichN. C. LyaminA. V. SloanS. W. 2014 A Comparison of Conic Programming Software for Finite Element Limit Analysis Applied Mechanics and Materials 553 439 444 https://doi.org/10.4028/www.scientific.net/AMM.553.439 Search in Google Scholar

[39] Puła, W., Szabowicz, H., & Kawa, M. (2022). Efficient and conservative estimation of failure probability of strip footing on spatially variable soil using random finite element limit analysis. In J. Huang, D. V., Griffiths, S.-H. Jiang, A. Giacomini, & R. Kelly (Eds.), 8th International Symposiumon Geotechnical Safety and Risk (ISGSR) (pp. 303–308). https://doi.org/10.3850/978-981-18-5182-7_04-007-cd PułaW. SzabowiczH. KawaM. 2022 Efficient and conservative estimation of failure probability of strip footing on spatially variable soil using random finite element limit analysis In HuangJ. GriffithsD. V. JiangS.-H. GiacominiA. KellyR. (Eds.), 8th International Symposiumon Geotechnical Safety and Risk (ISGSR) 303 308 https://doi.org/10.3850/978-981-18-5182-7_04-007-cd Search in Google Scholar

[40] Sert, S., Luo, Z., Xiao, J., Gong, W., & Juang, C. H. (2016). Probabilistic analysis of responses of cantilever wall-supported excavations in sands considering vertical spatial variability. Computers and Geotechnics, 75, 182–191. https://doi.org/10.1016/j.compgeo.2016.02.004 SertS. LuoZ. XiaoJ. GongW. JuangC. H. 2016 Probabilistic analysis of responses of cantilever wall-supported excavations in sands considering vertical spatial variability Computers and Geotechnics 75 182 191 https://doi.org/10.1016/j.compgeo.2016.02.004 Search in Google Scholar

[41] Simões, J. T., Neves, L. C., Antão, A. N., & Guerra, N. M. C. (2014). Probabilistic analysis of bearing capacity of shallow foundations using three-dimensional limit analyses. International Journal of Computational Methods, 11(2). https://doi.org/10.1142/S0219876213420085 SimõesJ. T. NevesL. C. AntãoA. N. GuerraN. M. C. 2014 Probabilistic analysis of bearing capacity of shallow foundations using three-dimensional limit analyses International Journal of Computational Methods 11 2 https://doi.org/10.1142/S0219876213420085 Search in Google Scholar

[42] Zaskórski, L., & Puła, W. (2016). Calibration of characteristic values of soil properties using the random finite element method. Archives of Civil and Mechanical Engineering, 16(1), 112–124. https://doi.org/10.1016/j.acme.2015.09.007 ZaskórskiL. PułaW. 2016 Calibration of characteristic values of soil properties using the random finite element method Archives of Civil and Mechanical Engineering 16 1 112 124 https://doi.org/10.1016/j.acme.2015.09.007 Search in Google Scholar