This work is licensed under the Creative Commons Attribution 4.0 International License.
Au SK, Beck L. Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Engineering Mechanics; 2001; 16:263–277.AuSKBeckLEstimation of small failure probabilities in high dimensions by subset simulation20011626327710.1016/S0266-8920(01)00019-4Search in Google Scholar
Bagińska I, Kawa M, Janecki W. Estimation of spatial variability of lignite mine dumping ground soil properties using CPTu results. Studia Geotechnica et Mechanica; 2016; 38(1), 3–13.BagińskaIKawaMJaneckiWEstimation of spatial variability of lignite mine dumping ground soil properties using CPTu results201638131310.1515/sgem-2016-0001Search in Google Scholar
Bagińska I, Kawa M, Łydżba D, Identification of soil types and their arrangement in overburden heaps using the deconvolution approach and CPTu test results. Engineering Geology 276, 105759BagińskaIKawaMŁydżbaDIdentification of soil types and their arrangement in overburden heaps using the deconvolution approach and CPTu test results27610575910.1016/j.enggeo.2020.105759Search in Google Scholar
Ching J, Wu TJ, Stuedlein AW, Bong T. Estimating horizontal scale of fluctuation with limited CPT soundings. Geoscience Frontiers; 2018; Vol. 9, 6, 1597–1608. https://doi.org/10.1016/j.gsf.2017.11.008ChingJWuTJStuedleinAWBongTEstimating horizontal scale of fluctuation with limited CPT soundings20189615971608https://doi.org/10.1016/j.gsf.2017.11.00810.1016/j.gsf.2017.11.008Search in Google Scholar
Chwała M. (2019). Undrained bearing capacity of spatially random soil for rectangular footings. Soils and Foundations, Volume 59, Issue 5, 1508–1521. https://doi.org/10.1016/j.sandf.2019.07.005ChwałaM.2019Undrained bearing capacity of spatially random soil for rectangular footings59515081521https://doi.org/10.1016/j.sandf.2019.07.00510.1016/j.sandf.2019.07.005Search in Google Scholar
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. https://doi.org/10.1371/journal.pone.0231992ChwałaMPułaW2020Evaluation of shallow foundation bearing capacity in the case of a two-layered soil and spatial variability in soil strength parameters154e0231992https://doi.org/10.1371/journal.pone.023199210.1371/journal.pone.0231992719014832348332Search in Google Scholar
Chwała M., (2020). On determining the undrained bearing capacity coefficients of variation for foundations embedded on spatially variable soil. Studia Geotechnica et Mechanica, 2020, 42(2); 125–136. 10.2478/sgem-2019-0037ChwałaM.2020On determining the undrained bearing capacity coefficients of variation for foundations embedded on spatially variable soil202042212513610.2478/sgem-2019-0037Open DOISearch in Google Scholar
Chwała M., (2020). Soil sounding location optimisation for spatially variable soil. Geotechnique Letters 10, 1–10. https://doi.org/10.1680/jgele.20.00012ChwałaM.2020Soil sounding location optimisation for spatially variable soil10110https://doi.org/10.1680/jgele.20.0001210.1680/jgele.20.00012Search in Google Scholar
Chwała M., (2021). Optimal placement of two soil soundings for rectangular footings. Journal of Rock Mechanics and Geotechnical Engineering, Volume 13, Issue 3, 603–611 https://doi.org/10.1016/j.jrmge.2021.01.007ChwałaM.2021Optimal placement of two soil soundings for rectangular footings133603611https://doi.org/10.1016/j.jrmge.2021.01.00710.1016/j.jrmge.2021.01.007Search in Google Scholar
Chwała M, Kawa M, (2021). Random failure mechanism method for working platform bearing capacity assessment with a linear trend in undrained shear strength. Journal of Rock Mechanics and Geotechnical Engineering. https://doi.org/10.1016/j.jrmge.2021.06.004ChwałaMKawaM2021Random failure mechanism method for working platform bearing capacity assessment with a linear trend in undrained shear strengthhttps://doi.org/10.1016/j.jrmge.2021.06.00410.1016/j.jrmge.2021.06.004Search in Google Scholar
Fenton GA, Griffiths DV, (2003). Bearing-capacity prediction of spatially random c ϕ soils. Canadian geotechnical journal, 40(1), 54–65. https://doi.org/10.1139/t02-086FentonGAGriffithsDV2003Bearing-capacity prediction of spatially random c ϕ soils4015465https://doi.org/10.1139/t02-08610.1139/t02-086Search in Google Scholar
Fenton GA, Griffiths DV. Risk assessment in geotechnical engineering. Wiley; 2008.FentonGAGriffithsDVWiley200810.1002/9780470284704Search in Google Scholar
Huang J, Lyamin AV, Griffiths DV, Sloan SW, Krabbenhoft K, Fenton GA. (2013). Undrained bearing capacity of spatially random clays by finite elements and limit analysis. Proceedings of the 18th ICSMGE; Paris 2013;731–734.HuangJLyaminAVGriffithsDVSloanSWKrabbenhoftKFentonGA2013Proceedings of the 18th ICSMGEParis2013731734Search in Google Scholar
Ferreira V, Panagopulos T, Andrade R, Guerrero C, Loures L. (2015). Spatial variability of soil properties and soil erodibility in the Alqueva reservoir watershed. Soild Earth, 6, 383–392.FerreiraVPanagopulosTAndradeRGuerreroCLouresL2015Spatial variability of soil properties and soil erodibility in the Alqueva reservoir watershed638339210.5194/se-6-383-2015Search in Google Scholar
Ghanem R, Brzakała W, (1996). Stochastic Finite-Element Analysis of Soil Layers with Random Interface. Journal of Engineering Mechanics, Vol. 122, Issue 4 (April 1996), https://doi.org/10.1061/(ASCE)0733-9399(1996)122:4(361)GhanemRBrzakałaW1996Stochastic Finite-Element Analysis of Soil Layers with Random Interface1224April1996https://doi.org/10.1061/(ASCE)0733-9399(1996)122:4(361)10.1061/(ASCE)0733-9399(1996)122:4(361)Search in Google Scholar
Griffiths DV, Fenton GA, Manoharan N, (2002). Bearing Capacity of Rough Rigid Strip Footing on Cohesive Soil: Probabilistic Study. Journal of Geotechnical and Geoenvironmental Engineering, 2002, 128(9): 743–755. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:9(743)GriffithsDVFentonGAManoharanN2002Bearing Capacity of Rough Rigid Strip Footing on Cohesive Soil: Probabilistic Study20021289743755https://doi.org/10.1061/(ASCE)1090-0241(2002)128:9(743)10.1061/(ASCE)1090-0241(2002)128:9(743)Search in Google Scholar
Griffiths DV, Fenton GA, (2004). Probabilistic slope stability analysis by finite elements Journal of Geotechnical and Geoenvironmental Engineering, 130 (5) (2004), pp. 507–518, 10.1061/(ASCE)1090-0241(2004)130:5(507)GriffithsDVFentonGA2004Probabilistic slope stability analysis by finite elements1305200450751810.1061/(ASCE)1090-0241(2004)130:5(507)Open DOISearch in Google Scholar
Halder K, Chakraborty D, (2019). Probabilistic bearing capacity of strip footing on reinforced soil slope. Computers and Geotechnics, 2019, 116: 103213. https://doi.org/10.1016/j.compgeo.2019.103213HalderKChakrabortyD2019Probabilistic bearing capacity of strip footing on reinforced soil slope2019116103213. https://doi.org/10.1016/j.compgeo.2019.10321310.1016/j.compgeo.2019.103213Search in Google Scholar
Halder K, Chakraborty D, (2020). Influence of soil spatial variability on the response of strip footing on geocell-reinforced slope. Computers and Geotechnics, Volume 122, 2020, 103533, https://doi.org/10.1016/j.compgeo.2020.103533.HalderKChakrabortyD2020Influence of soil spatial variability on the response of strip footing on geocell-reinforced slope1222020103533, https://doi.org/10.1016/j.compgeo.2020.103533.10.1016/j.compgeo.2020.103533Search in Google Scholar
Horn RA, Johnson CR. Matrix Analysis. Cambridge University Press 1985.HornRAJohnsonCRCambridge University Press198510.1017/CBO9780511810817Search in Google Scholar
Juan C. Viviescas, Álvaro J. Mattos & Juan P. Osorio (2020) Uncertainty quantification in the bearing capacity estimation for shallow foundations in sandy soils, Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, DOI: 10.1080/17499518.2020.1753782ViviescasJuan C.MattosÁlvaro J.OsorioJuan P.2020Uncertainty quantification in the bearing capacity estimation for shallow foundations in sandy soils10.1080/17499518.2020.1753782Open DOISearch in Google Scholar
Kasama K, Whittle AJ, (2011). Bearing Capacity of Spatially Random Cohesive Soil Using Numerical Limit Analyses. Journal of Geotechnical and Geoenvironmental Engineering, 2011, 137(11): 989–996. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000531KasamaKWhittleAJ2011Bearing Capacity of Spatially Random Cohesive Soil Using Numerical Limit Analyses201113711989996https://doi.org/10.1061/(ASCE)GT.1943-5606.000053110.1061/(ASCE)GT.1943-5606.0000531Search in Google Scholar
Kawa M, Bagińska I, Wyjadłowski M. Reliability analysis of sheet pile wall in spatially variable soil including CPTu test results. Archives of Civil and Mechanical Engineering; 2019; 19(2):598–613.KawaMBagińskaIWyjadłowskiMReliability analysis of sheet pile wall in spatially variable soil including CPTu test results201919259861310.1016/j.acme.2018.10.007Search in Google Scholar
Kawa M, Puła W. (2020). 3D bearing capacity probabilistic analyses of footings on spatially variable c–ϕ soil. Acta Geotechnica (2020) 15:1453–1466. https://doi.org/10.1007/s11440-019-00853-3KawaMPułaW20203D bearing capacity probabilistic analyses of footings on spatially variable c–ϕ soil20201514531466https://doi.org/10.1007/s11440-019-00853-310.1007/s11440-019-00853-3Search in Google Scholar
Kirkpatrick S, Gelatt CD, Vecchi MP. Optimization by Simulated Annealing. Science; 1983; 220, 671–680.KirkpatrickSGelattCDVecchiMPOptimization by Simulated Annealing198322067168010.1126/science.220.4598.671Search in Google Scholar
Kirkpatrick S. Optimization by Simulated Annealing: Quantitative Studies. Journal of Statistical Physics; 1984; Vol. 34, Nos. 5/6.KirkpatrickSOptimization by Simulated Annealing: Quantitative Studies1984345/610.1007/BF01009452Search in Google Scholar
Li Y, Fenton GA, Hicks MA, Xu N, (2021). Probabilistic Bearing Capacity Prediction of Square Footings on 3D Spatially Varying Cohesive Soils. Journal of Geotechnical and Geoenvironmental Engineering 147 (6), 04021035LiYFentonGAHicksMAXuN2021Probabilistic Bearing Capacity Prediction of Square Footings on 3D Spatially Varying Cohesive Soils14760402103510.1061/(ASCE)GT.1943-5606.0002538Search in Google Scholar
Li J, Wu C, Luo W, Sun L, White DJ, (2021). An extended Prandtl solution for analytical modelling of the bearing capacity of a shallow foundation on a spatially variable undrained clay. Géotechnique, https://doi.org/10.1680/jgeot.20.P.118LiJWuCLuoWSunLWhiteDJ2021An extended Prandtl solution for analytical modelling of the bearing capacity of a shallow foundation on a spatially variable undrained clayhttps://doi.org/10.1680/jgeot.20.P.11810.1680/jgeot.20.P.118Search in Google Scholar
Phoon KK, Kulhawy FH, (1999). Characterization of geotechnical variability. Canadian Geotechnical Journal, 36(4), 612–624. https://doi.org/10.1139/t99-038PhoonKKKulhawyFH1999Characterization of geotechnical variability364612624https://doi.org/10.1139/t99-03810.1139/t99-038Search in Google Scholar
Pieczyńska-Kozłowska JM, Puła W, Vessia G. A collection of fluctuation scale values and autocorrelation functions of fine deposits in Emilia Romagna plain (Italy) Geo-Risk 2017 in ASCE Geotechnical Special Publication, 284 (2017), pp. 290–299Pieczyńska-KozłowskaJMPułaWVessiaGA collection of fluctuation scale values and autocorrelation functions of fine deposits in Emilia Romagna plain (Italy) Geo-Risk 2017in284201729029910.1061/9780784480717.027Search in Google Scholar
Pieczyńska-Kozłowska JM, Puła W, Chwała M. Search for the worst-case correlation length in the bearing capacity probability of failure analyses. Geo-Risk 2017 in ASCE Geotechnical Special Publication, GSP 283, 534–544.Pieczyńska-KozłowskaJMPułaWChwałaMSearch for the worst-case correlation length in the bearing capacity probability of failure analyses283534544Search in Google Scholar
Pramanik, R., Baidya, D.K. & Dhang, N, (2020). Reliability analysis for bearing capacity of surface strip footing using fuzzy finite element method. Geomechanics and Geoengineering: An International Journal, 2020, 15(1): 29–41. https://doi.org/10.1080/17486025.2019.1601268PramanikR.BaidyaD.K.DhangN2020Reliability analysis for bearing capacity of surface strip footing using fuzzy finite element method20201512941https://doi.org/10.1080/17486025.2019.160126810.1080/17486025.2019.1601268Search in Google Scholar
Pramanik, R., Baidya, D.K. & Dhang, N, (2021). Reliability assessment of three-dimensional bearing capacity of shallow foundation using fuzzy set theory. Front. Struct. Civ. Eng. (2021). https://doi.org/10.1007/s11709-021-0698-8PramanikR.BaidyaD.K.DhangN2021Reliability assessment of three-dimensional bearing capacity of shallow foundation using fuzzy set theory2021https://doi.org/10.1007/s11709-021-0698-810.1007/s11709-021-0698-8Search in Google Scholar
Puła W. Applications of structural reliability theory to foundations safety evaluation. Wrocław 2004; Wroclaw University of Technology Press [in Polish].PułaWWrocław2004Wroclaw University of Technology Press[in Polish].Search in Google Scholar
Puła W. On some aspects of reliability computations in bearing capacity of shallow foundations. In: Griffiths DV, Fenton Gordon A, editors. Puła in: probabilistic methods in geotechnical engineering. CISM courses and lectures, Wien, New York: Springer; 2007; No. 491, 127–45.PułaWOn some aspects of reliability computations in bearing capacity of shallow foundationsIn:GriffithsDVFentonGordon Aeditors.CISM courses and lectures, Wien, New YorkSpringer20074911274510.1007/978-3-211-73366-0_5Search in Google Scholar
Puła W, Chwała M, On spatial averaging along random slip lines in the reliability computations of shallow strip foundations. Computers and Geotechnics; 2015; 68, 128–136.PułaWChwałaMOn spatial averaging along random slip lines in the reliability computations of shallow strip foundations20156812813610.1016/j.compgeo.2015.04.001Search in Google Scholar
Puła W, Chwała M. Random bearing capacity evaluation of shallow foundations for asymmetrical failure mechanisms with spatial averaging and inclusion of soil self-weight. Computers and Geotechnics; 2018; 101, 176–195.PułaWChwałaMRandom bearing capacity evaluation of shallow foundations for asymmetrical failure mechanisms with spatial averaging and inclusion of soil self-weight201810117619510.1016/j.compgeo.2018.05.002Search in Google Scholar
Rainer J, Szabowicz H, (2020). Analysis of underground stratification based on CPTu profiles using high-pass spatial filter. Studia Geotechnica et Mechanica. 2020, s. 1–11.RainerJSzabowiczH2020Analysis of underground stratification based on CPTu profiles using high-pass spatial filter202011110.2478/sgem-2020-0002Search in Google Scholar
Simoes JT, Neves LC, Antao AN, Guerra NMC. Probabilistic analysis of bearing capacity of shallow foundations using three-dimensional limit analyses. International Journal of Computational Methods; 2014; Vol. 11, No. 02, 1342008-1-20.SimoesJTNevesLCAntaoANGuerraNMCProbabilistic analysis of bearing capacity of shallow foundations using three-dimensional limit analyses201411021342008-1-20.10.1142/S0219876213420085Search in Google Scholar
Shield RT, Drucker DC. The application of limit analysis to punch-indentation problems. Journal of Applied Mechanics; 1953; 20, 453–460.ShieldRTDruckerDCThe application of limit analysis to punch-indentation problems19532045346010.1115/1.4010747Search in Google Scholar
Srivastava AGL, Sivakumar BGL, Haldar S, (2010). Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis. Engineering Geology, 2010, 110(3–4): 93–101. https://doi.org/10.1016/j.enggeo.2009.11.006SrivastavaAGLSivakumarBGLHaldarS2010Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis20101103–493101https://doi.org/10.1016/j.enggeo.2009.11.00610.1016/j.enggeo.2009.11.006Search in Google Scholar
Stuedlein AW, Kramer SL, Arduino P, Holtz RD, (2012). Geotechnical Characterization and Random Field Modeling of Desiccated Clay. Journal of Geotechnical and Geoenvironmental Engineering, 138(11), 1301–1313. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000723StuedleinAWKramerSLArduinoPHoltzRD2012Geotechnical Characterization and Random Field Modeling of Desiccated Clay1381113011313https://doi.org/10.1061/(ASCE)GT.1943-5606.000072310.1061/(ASCE)GT.1943-5606.0000723Search in Google Scholar
Vanmarcke E.H. Probabilistic modelling of soil profiles. Journal of the Geotechnical Engineering Division; 1977; Vol. 103, 11, 1227–46.VanmarckeE.H.Probabilistic modelling of soil profiles19771031112274610.1061/AJGEB6.0000517Search in Google Scholar
Vanmarcke EH. Reliability of earth slopes. Journal of the Geotechnical Engineering Division; 1977; Vol. 103, 11, 1247–65.VanmarckeEHReliability of earth slopes19771031112476510.1061/AJGEB6.0000518Search in Google Scholar
Vanmarcke E.H. Random fields – analysis and synthesis. Cambridge 1983: MIT Press.VanmarckeE.H.Cambridge1983MIT PressSearch in Google Scholar
Viviescas J.C, Griffiths DV, Osorio JP, (2021). Geological influence on the spatial variability of soils. International Journal of Geotechnical Engineering, 00(00), 1–9. https://doi.org/10.1080/19386362.2021.1888509ViviescasJ.CGriffithsDVOsorioJP2021Geological influence on the spatial variability of soils000019https://doi.org/10.1080/19386362.2021.188850910.1080/19386362.2021.1888509Search in Google Scholar
Zhu D, Griffiths DV, Huang J, Fenton GA, (2017). Probabilistic stability analyses of undrained slopes with linearly increasing mean strength. Géotechnique, 2017, 67(8): 733–746. https://doi.org/10.1680/jgeot.16.P.223ZhuDGriffithsDVHuangJFentonGA2017Probabilistic stability analyses of undrained slopes with linearly increasing mean strength2017678733746https://doi.org/10.1680/jgeot.16.P.22310.1680/jgeot.16.P.223Search in Google Scholar
Żyliński K, Korzec A, Winkelmann K, Górski J., (2020). Random Field Model of Foundations at the Example of Continuous Footing. AIP Conf. Proc. 2239, 020052-1–020052-11; https://doi.org/10.1063/5.0007811ŻylińskiKKorzecAWinkelmannKGórskiJ2020AIP Conf. Proc. 2239020052-1020052-11https://doi.org/10.1063/5.000781110.1063/5.0007811Search in Google Scholar