Abstract
The purpose of the present study was to develop a fuzzy finite element method, for uncertainty quantification of saturated soil properties on dynamic response of porous media, and also to discrete the coupled dynamic equations known as u-p hydro-mechanical equations. Input parameters included fuzzy numbers of Poisson’s ratio, Young’s modulus, and permeability coefficient as uncertain material of soil properties. Triangular membership functions were applied to obtain the intervals of input parameters in five membership grades, followed up by a minute examination of the effects of input parameters uncertainty on dynamic behavior of porous media. Calculations were for the optimized combinations of upper and lower bounds of input parameters to reveal soil response including displacement and pore water pressure via fuzzy numbers. Fuzzy analysis procedure was verified, and several numerical examples were analyzed by the developed method, including a dynamic analysis of elastic soil column and elastic foundation under ramp loading. Results indicated that the range of calculated displacements and pore pressure were dependent upon the number of fuzzy parameters and uncertainty of parameters within equations. Moreover, it was revealed that for the input variations looser sands were more sensitive than dense ones.
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Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100:19–31
Hamdia K M, Silani M, Zhuang X, He P, Rabczuk T. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, 206(2):215–227
Hamdia K M, Ghasemi H, Zhuang X, Alajlan N, Rabczuk T. Sensitivity and uncertainty analysis for flexoelectric nanostructures. Computer Methods in Applied Mechanics and Engineering, 2018, 337:95–109
Rao S S, Berke L. Analysis of uncertain structural systems using interval analysis. AIAA Journal, 1997, 35(4):727–735
Rao S S, Chen L, Mulkay E. Unifed finite element method for engineering systems with hybrid uncertainties. AIAA Journal, 1998, 36(7):1291–1299
Muhanna R L, Mullen R L, Rao M V R. Nonlinear interval finite elements for beams. Vulnerability, Uncertainty, and Risk ASCE, 2014: 2227–2236
Sofi A, Muscolino G. Static analysis of Euler—Bernoulli beams with interval Young’s modulus. Computers & Structures, 2015, 156:72–82
Cheng Y, Zhang L L, Li J H, Zhang L M, Wang J H, Wang D Y. Consolidation in spatially random unsaturated soils based on coupled flow-deformation simulation. International Journal for Numerical and Analytical Methods in Geomechanics, 2017, 41(5):682–706
Papadopoulos M, Francois S, Degrande G, Lombaert G. Analysis of stochastic dynamic soil-structure interaction problems by means of coupled finite lements perfectly matched layers. In: VII European Congress on Computational Methods in Applied Sciences and Engineering. Crete Island: ECCOMAS Congress, 2016, 5–10
Effati Daryani M, Bahadori H, Effati Daryani K. Soil probabilistic slope stability analysis using stochastic finite difference method. Modern Applied Science, 2017, 11(4):23–29
Jiang S H, Li D Q, Zhang L M, Zhou C B. Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method. Engineering Geology, 2014, 168:120–128
Fujita K, Kojima K, Takewaki I. Prediction of worst combination of variable soil properties in seismic pile response. Soil Dynamics and Earthquake Engineering, 2015, 77:369–372
Behera D, Chakraverty S, Huang H Z. Non-probabilistic uncertain static responses of imprecisely defined structures with fuzzy parameters. Journal of Intelligent & Fuzzy Systems, 2016, 30(6):3177–3189
Luo Z, Atamturktur S, Juang C H, Huang H, Lin P S. Probability of serviceability failure in a braced excavation in a spatially random field: Fuzzy finite element approach. Computers and Geotechnics, 2011, 38(8):1031–1040
Qiu Z, Muller P C, Frommer A. An approximate method for the standard interval eigenvalue problem of real non-symmetric interval matrices. Communications in Numerical Methods in Engineering Banner, 2001, 17(4):239–251
Valliappan S, Pham T D. Fuzzy finite element analysis of a foundation on an elastic soil medium. International Journal for Numerical and Analytical Methods in Geomechanics, 1993, 17(11):771–789
Zadeh L A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1978, 1(1):3–28
Valliappan S, Pham T D. Elasto-plastic finite element analysis with fuzzy parameters. International Journal for Numerical Methods in Engineering, 1995, 38(4):531–548
Cherki A, Plessis G, Lallemand B, Tison T, Level P. Fuzzy behavior of mechanical systems with uncertain boundary conditions. Computer Methods in Applied Mechanics and Engineering, 2000, 189(3):863–873
Möller B, Graf W, Beer M. Fuzzy structural analysis using α-level optimization. Computational Mechanics, 2000, 26(6):547–565
Hanss M. Applied Fuzzy Arithmetic: An Introduction with Engineering Applications. Berlin: Springer-Verlag, 2005
Liu Y, Duan Z D. Fuzzy finite element model updating of bridges by considering the uncertainty of the measured modal parameters. Science China. Technological Sciences, 2012, 55(11):3109–3117
Behera D, Chakraverty S. Fuzzy finite element analysis of imprecisely definedstructures with fuzzy nodal force. Engineering Applications of Artificial Intelligence, 2013, 26(10):2458–2466
Yang L, Li G. Fuzzy stochastic variable and variational principle. Applied Mathematics and Mechanics, 1999, 20(7):795–800
Huang H, Li H. Perturbation finite element method of structural analysis under fuzzy environments. Engineering Applications of Artificial Intelligence, 2005, 18(1):83–91
Abbasbandy S, Jafarian A, Ezzati R. Conjugate gradient method for fuzzy symmetric positive definite system of linear equations. Applied Mathematics and Computation, 2005, 171(2):1184–1191
Skalna I, Rama Rao M V, Pownuk A. Systems of fuzzy equations in structural mechanics. Journal of Computational and Applied Mathematics, 2008, 218(1):149–156
Mikaeilvand N, Allahviranloo T. Solutions of the fully fuzzy linear system. In: The 39th Annual Iranian Mathematics Conference. Kerman: Shahid Bahonar University of Kerman, 2009
Mikaeilvand N, Allahviranloo T. Non zero solutions of the fully fuzzy linear systems. Applied and Computational Mathematics, 2011, 10(2):271–282
Verhaeghe W, Munck M D, Desmet W, Vandepitte D, Moens D. A fuzzy finite element analysis technique for structural static analysis based on interval fields. In: The 4th International Workshop on Reliable Engeering Compuataions, 2010, 117–128
Kumar A, Bansal A. A method for solving fully fuzzy linear system with trapezoidal fuzzy numbers. Iranian Journal of Optimization, 2010, 2:359–374
Senthilkumar P, Rajendran G. New approach to solve symmetric fully fuzzy linear systems. Sadhana, 2011, 36(6):933–940
Farkas L, Moens D, Vandepitte D, Desmet W. Fuzzy finite element analysis based on reanalysis technique. Structural Safety, 2010, 32(6):442–448
Balu A S, Rao B N. High dimensional model representation based formulations for fuzzy finite element analysis of structures. Finite Elements in Analysis and Design, 2012, 50:217–230
Babbar N, Kumar A, Bansal A. Solving fully fuzzy linear system with arbitrary triangular fuzzy numbers (m, α, β). Soft Computing, 2013, 17(4):691–702
Biot M A. Theory of propagation of elastic waves in a fluid-saturated porous solid. Journal of the Acoustical Society of America, 1956, 28(2):168–178
Zienkiewicz O C, Shiomi T. Dynamic behavior of saturated porous media; the generalized Biot formulation and its numerical solution. International Journal for Numerical and Analytical Methods in Geomechanics, 1984, 8(1):71–96
Ghasemi H, Park H S, Rabczuk T. A multi-material level set-based topology optimization of flexoelectric composites. Computer Methods in Applied Mechanics and Engineering, 2018, 332:47–62
Badnava H, Msekh M A, Etemadi E, Rabczuk T. An h-adaptive thermo-mechanical phase field model for fracture. Finite Elements in Analysis and Design, 2018, 138:31–47
Ghasemi H, Park H S, Rabczuk T. A level-set based IGA formulation for topology optimization of flexoelectric materials. Computer Methods in Applied Mechanics and Engineering, 2017, 313:239–258
Zhuang X, Huang R, Liang C, Rabczuk T. A coupled thermo-hydromechanical model of jointed hard rock for compressed air energy storage. Mathematical Problems in Engineering, 2014, 2014:179169
Khoei A R, Azami S M, Haeri S M. Implementation of plasticity based models in dynamic analysis of earth and rockfill dams: A comparison of Pastor-Zienkiewicz and cap models. Computers and Geotechnics, 2004, 31(5):384–410
Grabe J, Hamann T, Chmelnizkij A. Numerical simulation of wave propagation in fully saturated soil modeled as a two-phase medium. In: Proceedings of the 9th International Conference on Structural Dynamics. EURODYN, 2014, 631–637
Ye J, Jeng D, Wang R, Zhu C. Validation of a 2-D semi-coupled numerical model for fluid-structure-seabed interaction. Journal of Fluids and Structures, 2013, 42:333–357
Fattah M Y, Abbas S F, Karim H H. A model for coupled dynamic elasto-plastic analysis of soils. Journal of GeoEngineering, 2012, 7(3):89–96
Rahmani A, Ghasemi Fare O, Pak A. Investigation of the influence of permeability coefficient on thenumerical modeling of the liquefaction phenomenon. Scientia Iranica, 2012, 19(2):179–187
Khoei A R, Haghighat E. Extended finite element modeling of deformable porous media with arbitrary interfaces. Applied Mathematical Modelling, 2011, 35(11):5426–5441
Muhanna R L, Mullen R L. Formulation of fuzzy finite-element methods for solid mechanics problems. Computer-Aided Civil and Infrastructure Engineering, 1999, 14(2):107–117
Hanss M, Willner K. A fuzzy arithmetical approach to the solution of finite element problems with uncertain parameters. Mechanics Research Communications, 2000, 27(3):257–272
Bárdossy A, Bronstert A, Merz B. 1-, 2- and 3-dimensional modeling of water movement in the unsaturated soil matrix using a fuzzy approach. Advances in Water Resources, 1995, 18(4):237–251
Arman A, Samtani N, Castelli R, Munfakh G. Geotechnical and Foundation Engineering Module1-Subsurface Investigations. Report No. FHWA-HI-97-021. 1997
Das Braja M. Advanced Soil Mechanics. 3rd ed. London: Taylor & Francis, 2008
Khoei A R, Gharehbaghi S A, Tabarraie A R, Riahi A. Error estimation, adaptivity and data transfer in enriched plasticity continua to analysis of shear band localization. Applied Mathematical Modelling, 2007, 31(6):983–1000
Zhou S, Zhuang X, Zhu H, Rabczuk T. Phase field modelling of crack propagation, branching and coalescence in rocks. Theoretical and Applied Fracture Mechanics, 2018, 96:174–192
Zhou S, Zhuang X, Rabczuk T. A phase-field modeling approach of fracture propagation in poroelastic media. Engineering Geology, 2018, 240:189–203
Zhou S, Rabczuk T, Zhuang X. Phase field modeling of quasi-static and dynamic crack propagation: COMSOL implementation and case studies. Advances in Engineering Software, 2018, 122:31–49
Zhou S W, Xia C C. Propagation and coalescence of quasi-static cracks in Brazilian disks: An insight from a phase field model. Acta Geotechnica, 2018, 14(4):1–20
Fu Z, Chen W, Wen P, Zhang C. Singular boundary method for wave propagation analysis in periodic structures. Journal of Sound and Vibration, 2018, 425:170–188
Fu Z, Xi Q, Chen W, Cheng A H D. A boundary-type meshless solver for transient heat conduction analysis of slender functionally graded materials with exponential variations. Computers & Mathematics with Applications (Oxford, England), 2018, 76(4):760–773
Katona M G, Zienkiewicz O C. A unified set of single step algorithms. Part 3: the beta-m method, a generalisation of the newmark scheme. International Journal for Numerical Methods in Engineering, 1985, 21(7):1345–1359
Huang M, Zienkiewicz O C. New unconditionally stable staggered solution procedures for coupled soil-pore fluid dynamic problems. International Journal for Numerical Methods in Engineering, 1998, 43(6):1029–1052
Chan A H C. A unified finite element solution to static and dynamic problems of geomechanics. Dissertation for the Doctoral Degree. Swansea: University of Wales, 1988
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Kalateh, F., Hosseinejad, F. Uncertainty assessment in hydro-mechanical-coupled analysis of saturated porous medium applying fuzzy finite element method. Front. Struct. Civ. Eng. 14, 387–410 (2020). https://doi.org/10.1007/s11709-019-0601-z
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DOI: https://doi.org/10.1007/s11709-019-0601-z