Mesh-free shakedown analysis of cohesive-frictional pavement under moving traffic loads: deterministic and probabilistic frameworks

References

• Ali, A., Lyamin, A. V., Huang, J., Li, J. H., Cassidy, M. J., & Sloan, S. W. (2016). Probabilistic stability assessment using adaptive limit analysis and random fields. Acta Geotechnic, 12(a), 937–948.
   Google Scholar
• Ali, A., Lyamin, A. V., Huang, J., Sloan, S. W., & Cassidy, M. J. (2017). Undrained stability of a single circular tunnel in spatially variable soil subjected to surcharge loading. Computers and Geotechnics, 84, 16–27. doi: 10.1016/j.compgeo.2016.11.013
   Web of Science ®Google Scholar
• Allahverdizadeh Sheykhloo, P. (2015). Risk assessment and spatial variability in geotechnical stability problems, Doctoral dissertation, Colorado School of Mines, Colorado.
   Google Scholar
• Binesh, S. M., & Gholampour, A. (2015). Mesh-free lower bound limit analysis. International Journal of Computational Methods, 12(01), 1350105. doi: 10.1142/S0219876213501053
   Google Scholar
• Binesh, S. M., Hataf, N., & Ghahramani, A. (2010). Elasto-plastic analysis of reinforced soils using mesh-free method. Applied Mathematics and Computation, 215(12), 4406–4421. doi: 10.1016/j.amc.2010.01.004
   Web of Science ®Google Scholar
• Charlton, T. S., & Rouainia, M. (2017). A probabilistic approach to the ultimate capacity of skirted foundations in spatially variable clay. Structural Safety, 65, 126–136. doi: 10.1016/j.strusafe.2016.05.002
   Web of Science ®Google Scholar
• Chen, S. S., Liu, Y. H., & Cen, Z. Z. (2008a). Lower bound shakedown analysis by using the element free Galerkin method and non-linear programming. Computer Methods in Applied Mechanics and Engineering, 197, 3911–3921. doi: 10.1016/j.cma.2008.03.009
   Web of Science ®Google Scholar
• Chen, S. S., Liu, Y. H., & Cen, Z. Z. (2008b). Lower-bound limit analysis by using the EFG method and non-linear programming. International Journal for Numerical Methods in Engineering, 74(3), 391–415. doi: 10.1002/nme.2177
   Web of Science ®Google Scholar
• Chen, J. S., Wu, C. T., Yoon, S., & You, Y. (2001). A stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering, 50(2), 435–466. doi: 10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A
   Web of Science ®Google Scholar
• Cherubini, C. (2000). Reliability evaluation of shallow foundation bearing capacity on c' ϕ' soils. Canadian Geotechnical Journal, 37(1), 264–269.
   Web of Science ®Google Scholar
• Collins, I. F., & Cliffe, P. F. (1987). Shakedown in frictional materials under moving surface loads. International Journal for Numerical and Analytical Methods in Geomechanics, 11(4), 409–420. doi: 10.1002/nag.1610110408
   Web of Science ®Google Scholar
• Dilip, D. M., & Sivakumar Babu, G. L. (2013). Influence of spatial variability on pavement responses using latin hypercube sampling on two-dimensional random fields. Journal of Materials in Civil Engineering, 26(11), 04014083. doi: 10.1061/(ASCE)MT.1943-5533.0000994
   Web of Science ®Google Scholar
• El-Ramly, H., Morgenstern, N. R., & Cruden, D. M. (2003). Probabilistic stability analysis of a tailings dyke on presheared clay shale. Canadian Geotechnical Journal, 40(1), 192–208. doi: 10.1139/t02-095
   Web of Science ®Google Scholar
• Fenton, G. A., & Griffiths, D. V. (2008). Risk assessment in geotechnical engineering. Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• Gordon, W. J., & Wixom, J. A. (1978). Shepard’s method of “metric interpolation” to bivariate and multivariate interpolation. Mathematics of Computation, 32(141), 253–264.
   Web of Science ®Google Scholar
• 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. doi: 10.1144/qjegh.35.1.41
   Google Scholar
• Huang, J., Lyamin, A. V., Griffiths, D. V., Krabbenhøft, K., & Sloan, S. W. (2013). Quantitative risk assessment of landslide by limit analysis and random fields. Computers and Geotechnics, 53, 60–67. doi: 10.1016/j.compgeo.2013.04.009
   Web of Science ®Google Scholar
• Jamshidi Chenari, R., & Alaie, R. (2015). Effects of anisotropy in correlation structure on the stability of an undrained clay slope. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 9(2), 109–123.
   Web of Science ®Google Scholar
• Jamshidi Chenari, R., & Oloomi Dodaran, R. (2010). New method for estimation of the scale of fluctuation of geotechnical properties in natural deposits. Computational Methods in Civil Engineering, 1(1), 55–64.
   Google Scholar
• Johnson, K. L. (1985). Contact mechanics. Cambridge: Cambridge University Press.
   Google Scholar
• Kasama, K., & Whittle, A. J. (2011). Bearing capacity of spatially random cohesive soil using numerical limit analyses. Journal of Geotechnical and Geo-Environmental Engineering, 137(11), 989–996. doi: 10.1061/(ASCE)GT.1943-5606.0000531
   Web of Science ®Google Scholar
• Kasama, K., & Whittle, A. J. (2016). Effect of spatial variability on the slope stability using random field numerical limit analyses. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 10(1), 42–54.
   Web of Science ®Google Scholar
• Kim, J. M., & Sitar, N. (2013). Reliability approach to slope stability analysis with spatially correlated soil properties. Soils and Foundations, 53(1), 1–10. doi: 10.1016/j.sandf.2012.12.001
   Web of Science ®Google Scholar
• Koiter, W. T. (1960). General theorems for elastic-plastic solids. In I. N. A. H. R. Sneddon (Ed.), Progress in solid mechanics (pp. 165–221). North-Holland, Amsterdam.
   Google Scholar
• Krabbenhøft, K., Lyamin, A. V., & Sloan, S. W. (2007). Shakedown of a cohesive-frictional half-space subjected to rolling and sliding contact. International Journal of Solids and Structures, 44(11), 3998–4008. doi: 10.1016/j.ijsolstr.2006.11.001
   Web of Science ®Google Scholar
• Lea, J. D., & Harvey, J. T. (2015). A spatial analysis of pavement variability. International Journal of Pavement Engineering, 16(3), 256–267. doi: 10.1080/10298436.2014.942857
   Web of Science ®Google Scholar
• Li, H. X. (2010). Kinematic shakedown analysis under a general yield condition with non -associated plastic flow. International Journal of Mechanical Sciences, 52, 1–12. doi: 10.1016/j.ijmecsci.2009.09.040
   Web of Science ®Google Scholar
• Li, J. H., Cassidy, M. J., Tian, Y., Huang, J., Lyamin, A. V., & Uzielli, M. (2016). Buried footings in random soils: Comparison of limit analysis and finite element analysis. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 10(1), 55–65.
   Web of Science ®Google Scholar
• Li, H. X., & Yu, H. S. (2005). Kinematic limit analysis of frictional materials using nonlinear programming. International Journal of Solids and Structures, 42, 4058–4076. doi: 10.1016/j.ijsolstr.2004.11.023
   Web of Science ®Google Scholar
• Li, H. X., & Yu, H. S. (2006). A nonlinear programming approach to kinematic shakedown analysis of frictional materials. International Journal of Solids and Structures, 43, 6594–6614. doi: 10.1016/j.ijsolstr.2006.01.009
   Web of Science ®Google Scholar
• Liu, G. R. (2002). Mesh free methods: Moving beyond the finite element method. Washington, DC: CRC Press.
   Google Scholar
• Liu, S., Wang, J., Yu, H. S., & Wanatowski, D. (2014). Shakedown of layered pavements under repeated moving loads. In Pavement Materials, Structures, and Performance (pp. 179–188).
   Google Scholar
• Lumb, P. (1970). Safety factors and the probability distribution of soil strength. Canadian Geotechnical Journal, 7, 225–242. doi: 10.1139/t70-032
   Google Scholar
• Melan, E. (1938). Zur plastizitat des raumlichen kontinuums. Ingenieur-Archiv, 9, 116–126. doi: 10.1007/BF02084409
   Google Scholar
• Qian, J., Lin, H., Gu, X., & Xue, J. (2018). Dynamic shakedown limits for flexible pavement with cross-anisotropic materials. Road Materials and Pavement Design. Advance online publication. doi: 10.1080/14680629.2018.1491881
   Web of Science ®Google Scholar
• Qian, J., Wang, Y., Wang, J., & Huang, M. (2017). The influence of traffic moving speed on shakedown limits of flexible pavements. International Journal of Pavement Engineering, 106, 1–12. doi: 10.1080/10298436.2017.1293259
   Google Scholar
• Raad, L., Najm, W., Weichert, D., & Gross-Weege, J. (1989). Application of shakedown theory in soil mechanics. Zeitschrift fur Angewandte Mathematik und Mechanik, 69, 482–483.
   Web of Science ®Google Scholar
• Raad, L., Weichert, D., & Haidar, A. (1989). Analysis of full-depth asphalt concrete pavements using shakedown theory. Transportation Research Record, 1227, 53–65.
   Google Scholar
• Raad, L., Weichert, D., & Najm, W. (1988). Stability of multilayer systems under repeated loads. Transportation Research Record, 1207, 159–172.
   Google Scholar
• Radovsky, B. S., & Murashina, N. V. (1996). Shakedown of subgrade soil under repeated loading. Transportation Research Record: Journal of the Transportation Research Board, 1547(1), 82–88. doi: 10.1177/0361198196154700112
   Google Scholar
• Reale, C., Xue, J., & Gavin, K. (2016). System reliability of slopes using multimodal optimisation. Géotechnique, 66(5), 413–423. doi: 10.1680/jgeot.15.P.142
   Web of Science ®Google Scholar
• Sharp, R. W., & Booker, J. R. (1984). Shakedown of pavements under moving surface loads. Journal of Transportation Engineering, 110(1), 1–14. doi: 10.1061/(ASCE)0733-947X(1984)110:1(1)
   Web of Science ®Google Scholar
• Shepard, D. (1968). A two-dimensional interpolation function for irregularly-spaced data. Proceedings -ACM national conference.
   Google Scholar
• Shiau, S. H. (2001). Numerical methods for shakedown analysis of pavements. Ph.D. Thesis, the University of Newcastle, Australia.
   Google Scholar
• Shiau, S. H., & Yu, H. S. (2000a). Load and displacement prediction for shakedown analysis of layered pavements. Transportation Research Record: Journal of the Transportation Research Board, 1730, 117–124. doi: 10.3141/1730-14
   Google Scholar
• Shiau, S. H., & Yu, H. S. (2000b). Shakedown analysis of flexible pavements. In D. W. Smith, & J. P. Carter (Eds.), Proceedings of the John Booker memorial symposium (pp. 643–653). Sydney: University of Sydney.
   Google Scholar
• Simoes, J. T., Neves, L. C., Antao, 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(02), 1342008. doi: 10.1142/S0219876213420085
   Google Scholar
• Sloan, S. W. (1988). Lower bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics, 12, 61–77. doi: 10.1002/nag.1610120105
   Web of Science ®Google Scholar
• Vanmarcke, E. H. (1977). Probabilistic modelling of soil profiles. Journal of the Geotechnical Engineering Division, ASCE, 103(11), 1227–1246.
   Google Scholar
• Vanmarcke, E. H. (1984). Random fields, analysis and synthesis. Cambridge, MA: MIT Press.
   Google Scholar
• Wang, J. (2011). Shakedown Analysis and design of flexible road pavements under moving surface loads. Ph.D. thesis, The University of Nottingham, Nottingham, UK.
   Google Scholar
• Wang, B., Hicks, M. A., & Vardon, P. J. (2016). Slope failure analysis using the random material point method. Géotechnique Letters, 6(2), 113–118. doi: 10.1680/jgele.16.00019
   Web of Science ®Google Scholar
• Wang, J., Liu, S., & Yang, W. (2018). Dynamics shakedown analysis of slab track substructures with reference to critical speed. Soil Dynamics and Earthquake Engineering, 106, 1–13. doi: 10.1016/j.soildyn.2017.12.004
   Web of Science ®Google Scholar
• Wang, J., & Yu, H. S. (2013a). Residual stresses and shakedown in cohesive-frictional half-space under moving surface loads. Geo-mechanics and Geoengineering: an International Journal, 8(1), 1–14. doi: 10.1080/17486025.2012.759281
   Google Scholar
• Wang, J., & Yu, H. S. (2013b). Shakedown analysis for design of flexible pavements under moving loads. Road Materials and Pavement Design, 14(3), 703–722. doi: 10.1080/14680629.2013.814318
   Web of Science ®Google Scholar
• Yu, H. S. (2005). Three-dimensional analytical solutions for shakedown of cohesive-frictional materials under moving surface loads. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461(2059), 1951–1964. doi: 10.1098/rspa.2005.1445
   Web of Science ®Google Scholar
• Yu, H. S. (2007). Plasticity and geotechnics. New York: Springer Science & Business Media.
   Google Scholar
• Yu, H. S., & Hossain, M. Z. (1998). Lower bound shakedown analysis of layered pavements using discontinuous stress fields. Computer Methods in Applied Mechanics and Engineering, 167, 209–222. doi: 10.1016/S0045-7825(98)00120-0
   Web of Science ®Google Scholar
• Yu, H. S., & Wang, J. (2012). Three-dimensional shakedown solutions for cohesive-frictional materials under moving surface loads. International Journal of Solids and Structures, 49(26), 3797–3807. doi: 10.1016/j.ijsolstr.2012.08.011
   Web of Science ®Google Scholar
• Yucemen, M. S., Tang, W. H., & Ang A. H. S. (1973). A probabilistic study of safety and design of earth slopes. Civil engineering studies, structural research series, vol. 402. University of Illinois, Urbana.
   Google Scholar
• Zhao, J. D., Sloan, S. W., Lyamin, A. V., & Krabbenhøft, K. (2008). Bounds for shakedown of cohesive-frictional materials under moving surface loads. International Journal of Solids and Structures, 45(11), 3290–3312. doi: 10.1016/j.ijsolstr.2008.01.030
   Web of Science ®Google Scholar
• Zhuang, Y., & Wang, K. (2018). Shakedown solutions for pavement structures with von Mises criterion subjected to Hertz loads. Road Materials and Pavement Design, 19(3), 710–726. doi: 10.1080/14680629.2017.1301265
   Web of Science ®Google Scholar