Uncertainty assessment in hydro-mechanical-coupled analysis of saturated porous medium applying fuzzy finite element method
Farhoud KALATEH, Farideh HOSSEINEJAD
Uncertainty assessment in hydro-mechanical-coupled analysis of saturated porous medium applying fuzzy finite element method
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.
fuzzy finite element method / saturated soil / hydro-mechanical coupled equations / coupled analysis / uncertainty analysis
[1] |
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
|
[2] |
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
CrossRef
Google scholar
|
[3] |
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
CrossRef
Google scholar
|
[4] |
Rao S S, Berke L. Analysis of uncertain structural systems using interval analysis. AIAA Journal, 1997, 35(4): 727–735
CrossRef
Google scholar
|
[5] |
Rao S S, Chen L, Mulkay E. Unifed finite element method for engineering systems with hybrid uncertainties. AIAA Journal, 1998, 36(7): 1291–1299
CrossRef
Google scholar
|
[6] |
Muhanna R L, Mullen R L, Rao M V R. Nonlinear interval finite elements for beams. Vulnerability, Uncertainty, and Risk ASCE, 2014: 2227–2236
|
[7] |
Sofi A, Muscolino G. Static analysis of Euler–Bernoulli beams with interval Young’s modulus. Computers & Structures, 2015, 156: 72–82
CrossRef
Google scholar
|
[8] |
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
|
[9] |
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
|
[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
CrossRef
Google scholar
|
[11] |
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
CrossRef
Google scholar
|
[12] |
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
CrossRef
Google scholar
|
[13] |
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
CrossRef
Google scholar
|
[14] |
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
CrossRef
Google scholar
|
[15] |
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
|
[16] |
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
CrossRef
Google scholar
|
[17] |
Zadeh L A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1978, 1(1): 3–28
CrossRef
Google scholar
|
[18] |
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
CrossRef
Google scholar
|
[19] |
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
CrossRef
Google scholar
|
[20] |
Möller B, Graf W, Beer M. Fuzzy structural analysis using α-level optimization. Computational Mechanics, 2000, 26(6): 547–565
CrossRef
Google scholar
|
[21] |
Hanss M. Applied Fuzzy Arithmetic: An Introduction with Engineering Applications. Berlin: Springer-Verlag, 2005
|
[22] |
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
CrossRef
Google scholar
|
[23] |
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
CrossRef
Google scholar
|
[24] |
Yang L, Li G. Fuzzy stochastic variable and variational principle. Applied Mathematics and Mechanics, 1999, 20(7): 795–800
CrossRef
Google scholar
|
[25] |
Huang H, Li H. Perturbation finite element method of structural analysis under fuzzy environments. Engineering Applications of Artificial Intelligence, 2005, 18(1): 83–91
CrossRef
Google scholar
|
[26] |
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
CrossRef
Google scholar
|
[27] |
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
CrossRef
Google scholar
|
[28] |
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
|
[29] |
Mikaeilvand N, Allahviranloo T. Non zero solutions of the fully fuzzy linear systems. Applied and Computational Mathematics, 2011, 10(2): 271–282
|
[30] |
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
|
[31] |
Kumar A, Bansal A. A method for solving fully fuzzy linear system with trapezoidal fuzzy numbers. Iranian Journal of Optimization, 2010, 2: 359–374
|
[32] |
Senthilkumar P, Rajendran G. New approach to solve symmetric fully fuzzy linear systems. Sadhana, 2011, 36(6): 933–940
CrossRef
Google scholar
|
[33] |
Farkas L, Moens D, Vandepitte D, Desmet W. Fuzzy finite element analysis based on reanalysis technique. Structural Safety, 2010, 32(6): 442–448
CrossRef
Google scholar
|
[34] |
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
CrossRef
Google scholar
|
[35] |
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
CrossRef
Google scholar
|
[36] |
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
CrossRef
Google scholar
|
[37] |
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
CrossRef
Google scholar
|
[38] |
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
CrossRef
Google scholar
|
[39] |
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
CrossRef
Google scholar
|
[40] |
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
CrossRef
Google scholar
|
[41] |
Zhuang X, Huang R, Liang C, Rabczuk T. A coupled thermo-hydro-mechanical model of jointed hard rock for compressed air energy storage. Mathematical Problems in Engineering, 2014, 2014: 179169
CrossRef
Google scholar
|
[42] |
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
CrossRef
Google scholar
|
[43] |
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
|
[44] |
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
CrossRef
Google scholar
|
[45] |
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
|
[46] |
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
|
[47] |
Khoei A R, Haghighat E. Extended finite element modeling of deformable porous media with arbitrary interfaces. Applied Mathematical Modelling, 2011, 35(11): 5426–5441
CrossRef
Google scholar
|
[48] |
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
CrossRef
Google scholar
|
[49] |
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
CrossRef
Google scholar
|
[50] |
Bárdossy A, Bronstert A, Merz B. l-, 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
CrossRef
Google scholar
|
[51] |
Arman A, Samtani N, Castelli R, Munfakh G. Geotechnical and Foundation Engineering Module1-Subsurface Investigations. Report No. FHWA-HI-97–021. 1997
|
[52] |
Das Braja M. Advanced Soil Mechanics. 3rd ed. London: Taylor & Francis, 2008
|
[53] |
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
CrossRef
Google scholar
|
[54] |
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
CrossRef
Google scholar
|
[55] |
Zhou S, Zhuang X, Rabczuk T. A phase-field modeling approach of fracture propagation in poroelastic media. Engineering Geology, 2018, 240: 189–203
CrossRef
Google scholar
|
[56] |
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
CrossRef
Google scholar
|
[57] |
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
|
[58] |
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
CrossRef
Google scholar
|
[59] |
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
CrossRef
Google scholar
|
[60] |
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
CrossRef
Google scholar
|
[61] |
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
CrossRef
Google scholar
|
[62] |
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
|
/
〈 | 〉 |