Application of Mapping and Superimposing Rule for Solution of Parabolic PDE in Porous Medium under Cyclic Loading
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Application of Mapping and Superimposing Rule for Solution of Parabolic PDE in Porous Medium under Cyclic Loading

Authors: Mohammad M. Toufigh, Ahad Ouria


This paper presents an analytical method to solve governing consolidation parabolic partial differential equation (PDE) for inelastic porous Medium (soil) with consideration of variation of equation coefficient under cyclic loading. Since under cyclic loads, soil skeleton parameters change, this would introduce variable coefficient of parabolic PDE. Classical theory would not rationalize consolidation phenomenon in such condition. In this research, a method based on time space mapping to a virtual time space along with superimposing rule is employed to solve consolidation of inelastic soils in cyclic condition. Changes of consolidation coefficient applied in solution by modification of loading and unloading duration by introducing virtual time. Mapping function is calculated based on consolidation partial differential equation results. Based on superimposing rule a set of continuous static loads in specified times used instead of cyclic load. A set of laboratory consolidation tests under cyclic load along with numerical calculations were performed in order to verify the presented method. Numerical solution and laboratory tests results showed accuracy of presented method.

Keywords: Mapping, Consolidation, Inelastic porous medium, Cyclic loading, Superimposing rule.

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[1] Wilson N. E, Elgohary M. M, "Consolidation of soils under cyclic loading," Canadian Geotechnical Journal. 1974:11(3): 420-433.
[2] Baligh M. M, Levadoux J "Consolidation theory for cyclic loading," Journal of the Geotechnical Engineering Division, ASCE. 1978:104(4): 415-431.
[3] Rahal M. A, Vueza A. R, "Analysis of settlement and pore pressure induced by cyclic loading of silo," Journal of Geotechnical and Geoenvironmental Engineering, December 1998: 1208-1210.
[4] Vueza A. R, Rahal M. A, "Cyclic loading for the measuring of soil consolidation parameters," In: Proceedings of Settlement. ASCE, Reston, 1994: 1: 760-774.
[5] Favaretti M, Mazzucato A, "Settlements of a silo subjected to cyclic loading," In: Proceedings of Settlement. ASCE, Reston, 1994: 1: 775- 785.
[6] Favaretti M, Soranzo M, "A simplified consolidation theory in cyclic loading condition," Int: Symposium on Compression and Solidation of Clayey Soils, A. A. Balkema, Rotterdam, The Netherlands, 1995: 405- 409.
[7] Zhuang Ying-chun, Xie Kange-he, "Study on one-dimensional consolidation of soils under cyclic loading with varied compressibility," Journal of Zhejiang University Science 2005; (6A):141-147.
[8] Toufigh M. M, Ouria A, "Nonlinear consolidation of inelastic soils under rapidly cyclic loading," Proceeding of Iranian NCCE1, Iran, (Persian) 2004: 174-182.
[9] Toufigh M. M, Shafiei B, "Finite element consolidation model for subsidence problem based on Biot's three dimensional theory," Indian Geotechnical Journal, 1996: 26(3):286-296.
[10] Toufigh, M.M, Ouria A, "Laboratory investigation of land subsidence under cyclic loading in Kerman province, Iran," Proc of Seventh International Symposium on Land Subsidence, China, 2005:(1): 335- 343.
[11] Toufigh M. M, Shafiei B, "Prediction of future land subsidence in Kerman, Iran, due to groundwater withdrawal," International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1996: 33(8): A344.