An iterative algorithm for random upper bound kinematical analysis

• Autorzy: Chwała Marcin

Identyfikatory

DOI

10.2478/sgem-2021-0027

• Języki publikacji: EN

Abstrakty

EN

A new approach for stochastic upper bound kinematical analyses is described. The study proposes an iterative algorithm that uses the Vanmarcke spatial averaging and kinematical failure mechanisms. The iterative procedure ensures the consistency between failure geometry and covariance matrix, which influences the quality of the results. The proposed algorithm can be applied to bearing capacity evaluation or slope stability problems. The iterative algorithm is used in the study to analyse the three-dimensional undrained bearing capacity of shallow foundations and the bearing capacity of the foundation for two-layered soil, in both cases, the soil strength spatial variability is included. Moreover, the obtained results are compared with those provided by the algorithm, based on the constant covariance matrix. The study shows that both approaches provide similar results for a variety of foundation shapes and scale of fluctuation values. Therefore, the simplified algorithm can be used for purposes that require high computational efficiency and for practical applications. The achieved efficiency using a constant covariance matrix for one realisation of a three-dimensional bearing capacity problem that includes the soil strength spatial variability results in about 0.5 seconds for a standard notebook. The numerical example presented in the study indicates the importance of the iterative algorithm for further development of the failure mechanism application in probabilistic analyses. Moreover, because the iterative algorithm is based on the upper bound theorem, it could be utilised as a reference for other methods for spatially variable soil.

Słowa kluczowe

EN

random bearing capacity; shallow foundation; scale of fluctuation; iterative algorithm; upper bound; spatial variability

• Wydawca: De Gruyter
• Czasopismo: Studia Geotechnica et Mechanica
• Rocznik: 2022
• Tom: Vol. 44, nr 1
• Strony: 13--25
• Opis fizyczny: Bibliogr. 49 poz., rys.

Twórcy

autor

Chwała Marcin

• Wroclaw University of Science and Technology, Department of Geotechnics and Hydrotechnics, Faculty of Civil Engineering, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

• [1] Au SK, Beck L. Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Engineering Mechanics; 2001; 16:263–277.
• [2] 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.
• [3] 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, 105759
• [4] 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.2017.11.008
• [5] 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.2019.07.005
• [6] 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.0231992
• [7] 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-2019-0037
• [8] Chwała M., (2020). Soil sounding location optimisation for spatially variable soil. Geotechnique Letters 10, 1–10. https://doi.org/10.1680/jgele.20.00012
• [9] 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.2021.01.007
• [10] 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.2021.06.004
• [11] 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/t02-086
• [12] Fenton GA, Griffiths DV. Risk assessment in geotechnical engineering. Wiley; 2008.
• [13] 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.
• [14] 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.
• [15] 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)
• [16] 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)
• [17] 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)
• [18] 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.2019.103213
• [19] 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.
• [20] Horn RA, Johnson CR. Matrix Analysis. Cambridge University Press 1985.
• [21] 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: 10.1080/17499518.2020.1753782
• [22] 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.1943-5606.0000531
• [23] 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.
• [24] 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/s11440-019-00853-3
• [25] Kirkpatrick S, Gelatt CD, Vecchi MP. Optimization by Simulated Annealing. Science; 1983; 220, 671–680.
• [26] Kirkpatrick S. Optimization by Simulated Annealing: Quantitative Studies. Journal of Statistical Physics; 1984; Vol. 34, Nos. 5/6.
• [27] 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), 04021035
• [28] 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.118
• [29] Phoon KK, Kulhawy FH, (1999). Characterization of geotechnical variability. Canadian Geotechnical Journal, 36(4), 612–624. https://doi.org/10.1139/t99-038
• [30] 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. 290–299
• [31] 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.
• [32] 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/10.1080/17486025.2019.1601268
• [33] 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/s11709-021-0698-8
• [34] Puła W. Applications of structural reliability theory to foundations safety evaluation. Wrocław 2004; Wroclaw University of Technology Press [in Polish].
• [35] 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.
• [36] 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.
• [37] 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.
• [38] 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.
• [39] 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.
• [40] Shield RT, Drucker DC. The application of limit analysis to punch-indentation problems. Journal of Applied Mechanics; 1953; 20, 453–460.
• [41] 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.2009.11.006
• [42] 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.1943-5606.0000723
• [43] The MathWorks. MATLAB R2017b; 2017; Natick.
• [44] Vanmarcke E.H. Probabilistic modelling of soil profiles. Journal of the Geotechnical Engineering Division; 1977; Vol. 103, 11, 1227–46.
• [45] Vanmarcke EH. Reliability of earth slopes. Journal of the Geotechnical Engineering Division; 1977; Vol. 103, 11, 1247–65.
• [46] Vanmarcke E.H. Random fields – analysis and synthesis. Cambridge 1983: MIT Press.
• [47] 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/10.1080/19386362.2021.1888509
• [48] 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.223
• [49] 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/10.1063/5.0007811