Variational approach for settlement analysis of circular plate on multilayered soil. (English) Zbl 1462.74114
Summary: A continuum-based analysis method is developed to analyze a uniformly-loaded circular plate founded on a multilayered soil deposit. The multilayered soil deposit forms a semi-infinite half space, and the behavior of each soil layer is assumed to be linear elastic. The plate is considered to be isotropic, homogeneous, and linear elastic. We apply variational principles to obtain the governing differential equations of the plate-layered soil system and solve them semi-analytically. We then compare results from the present analyses with those from finite element analysis. Using the proposed analysis method we perform a parametric study, results from which provide important insights into the effects of soil layering – such as the thicknesses and stiffness ratios of multiple soil layers – on the flexural behavior of the circular plate. Analyses for wide ranges of plate-to-soil stiffness ratios provide further insights on plate-soil interactions.
MSC:
| 74L10 | Soil and rock mechanics |
| 74K20 | Plates |
| 74G65 | Energy minimization in equilibrium problems in solid mechanics |
References:
| [1] | Borowicka, H., Influence of rigidity of a circular foundation slab on the distribution of pressure over the contact surface, (Proceedings of First International Conference on Soil Mechanics Foundation Engineering, 2 (1936)), 144-149 |
| [2] | Cheung, Y. K.; Zienkiewicz, O. C., Plates and tanks on elastic foundations-an application of finite element method, Int. J. Solid Struct., 1, 451-461 (1965) |
| [3] | Selvadurai, A. P.S., The interaction between a uniformly loaded circular plate and an isotropic elastic halfspace, J. Struct. Mech., 7, 231-246 (1979) |
| [4] | Smith, I. M., A finite element approach to elastic soil-structure interaction, Canad. Geotechn. J., 7, 95-105 (1970) |
| [5] | Chakravorty, A. K.; Ghosh, A., Finite difference solution for circular plates on elastic foundations, Int. J. Numer. Method Eng., 9, 73-84 (1975) · Zbl 0298.73078 |
| [6] | Mahmood, I. U., Finite element analysis of cylindrical tank foundation resting on isotropic soil medium including soil-structure interaction (1984), University of Oklahoma: University of Oklahoma Norman, M.S. Thesis |
| [7] | Issa, A.; Zaman, M. M., A cylindrical tank-foundation-halfspace interaction using and energy approach, Comput. Methods Appl. Mech. Eng., 56, 47-60 (1986) · Zbl 0576.73116 |
| [8] | Melerski, E. S., Simple elastic analysis of axisymmetric cylindrical storage tanks, J. Struct. Eng., 117, 3239-3260 (1991) |
| [9] | Zmerli, M.; Plaut, R. H., Design of a circular plate on an elastic halfspace for minimum differential settlement, Struct. Optim., 6, 52-58 (1993) |
| [10] | Kukreti, A. R.; Siddiqi, Z. A., Analysis of fluid storage tanks including foundation-superstructure interaction using differential quadrature method, Appl. Math. Model., 21, 193-205 (1997) · Zbl 0875.73360 |
| [11] | Gunerathne, S.; Seo, H.; Lawson, W. D.; Jayawickrama, P. W., Analysis of edge-to-center settlement ratio for circular storage tank foundation on elastic soil, Comput. Geotechn., 102, 136-147 (2018) |
| [12] | Burmister, D. M., The general theory of stresses and displacements in layered soil systems, J. Appl. Phys., 16, 89-94 (1945), 126-27; 296-302 |
| [13] | Peattie, K. R., Stress and strain factors for three-layer elastic systems, Highway Res. Board Bull., 342, 215-253 (1962) |
| [14] | Chow, Y. K., Vertical deformation of rigid foundations of arbitrary shape on layered soil media, Int. J. Numer. Anal. Methods Geomech., 11, 1-15 (1987) · Zbl 0599.73103 |
| [15] | Yue, Z. Q., Indentation of a rigid plate on a multilayered solid, WIT Trans. Eng. Sci., 7, 8, 91-98 (1995) |
| [16] | Sadecka, L., A finite/infinite element analysis of thick plate on a layered foundation, Comput. Struct., 76, 609-610 (2000) |
| [17] | Wang, Y.; Ni, J.; Cheung, Y. K., Plate on non-homogeneous elastic half-space analysed by FEA, Struct. Eng. Mech., 9, 127-139 (2000) |
| [18] | Fraser, R. A.; Wardle, L. J., Numerical analysis of rectangular raft on layered foundations, Geotechnique, 26, 613-630 (1976) |
| [19] | Tham, L. G.; Man, K. F.; Cheung, Y. K., Analysis of footing resting on non-homogeneous soil by double spline element, Comput. Geotechn., 5, 249-268 (1988) |
| [20] | Brooker, J. R.; Balaam, N. P.; Davis, E. H., The behavior of an elastic non-homogeneous half space, part II - circular and strip footings, Int. J. Numer. Anal. Methods Geomech., 9, 369-381 (1985) · Zbl 0569.73107 |
| [21] | Wang, Y. H.; Tham, L. G.; Tsui, Y.; Yue, Z. Q., Plate on layered foundation analyzed by a semi-analytical and semi-numerical method, Comput. Geotech., 30, 409-418 (2003) |
| [22] | Aizikovich, S. M.; Vasiliev, A. S.; Volkov, S. S.; Mitrin, B. I.; Sadyrin, E. V., An analytical solution to the problem of interaction of a circular plate with an inhomogeneous soft layer, (Shell Structures: Theory and Applications: Proceedings of the Tenth SSTA Conference, 3 (2014)), 45-48 |
| [23] | Aizikovich, S. M.; Volkvov, S. S.; Mitrin, B. I., The solution of a certain class of dual integral equations with the right-hand side in the form of a Fourier series and its application to the solution of contact problems for inhomogeneous media, J. Appl. Math. Mech., 81, 486-491 (2017) · Zbl 1440.74242 |
| [24] | Vlasov, V. Z.; Leont’ev, N. N., Beams, plates and shells on elastic foundations (1966), Israel Program for Scientific Translations Ltd: Israel Program for Scientific Translations Ltd Jerusalem, Israel · Zbl 0214.24203 |
| [25] | Vallabhan, C. V.G.; Das, Y. C., Parametric study of beams on elastic foundations, J. Eng. Mech., 114, 2072-2082 (1988) |
| [26] | Vallabhan, C. V.G.; Das, Y. C., Analysis of circular tank foundation, J. Eng. Mech., 117, 789-797 (1991) |
| [27] | Basu, D.; Prezzi, M.; Salgado, R., Settlement analysis of piles with rectangular cross sections in multi-layered soils, Comput. Geotech., 35, 563-575 (2008) |
| [28] | Seo, H.; Basu, D.; Prezzi, M.; Salgado, R., Load-settlement response of rectangular and circular piles in multilayer soil, J. Geotech. Geoenviron. Eng., 135, 420-430 (2009) |
| [29] | Salgado, R.; Seo, H.; Prezzi, M., Variational elastic solution for axially loaded piles in multilayered soil, Int. J. Numer. Anal. Methods Geomech., 37, 423-440 (2013) |
| [30] | Timoshenko, S. P.; Goodier, J. N., Theory of Elasticity (1970), McGraw-Hill: McGraw-Hill New York · Zbl 0266.73008 |
| [31] | Timoshenko, S.; Woinowsky-Krieger, S., Theory of Plates and Shells (1959), McGraw-Hill: McGraw-Hill New York · Zbl 0114.40801 |
| [32] | Jones, R.; Xenophontos, J., The Vlasov foundation model, Int. J. Mech. Sci., 19, 317-323 (1977) · Zbl 0374.73016 |
| [33] | PLAXIS 2D [Computer Software] (Plaxis, 2016).; PLAXIS 2D [Computer Software] (Plaxis, 2016). |
| [34] | Settlement Analysis (EM 1110-1-1904) (1990), Department of the Army: Department of the Army Washington, DC |
| [35] | M.S. Brannan, Design and construction of concrete tanks for refrigerated liquefied gas containment, part 2. ACI Spring convention 2012. https://www.concrete.org/Portals/0/Files/PDF/Webinars/Brannan.pdf; M.S. Brannan, Design and construction of concrete tanks for refrigerated liquefied gas containment, part 2. ACI Spring convention 2012. https://www.concrete.org/Portals/0/Files/PDF/Webinars/Brannan.pdf |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
