Uncertainty quantification of stability and damage detection parameters of coupled hydrodynamic-ground motion in concrete gravity dams
Nazim Abdul NARIMAN, Tom LAHMER, Peyman KARAMPOUR
Uncertainty quantification of stability and damage detection parameters of coupled hydrodynamic-ground motion in concrete gravity dams
In this paper, models of the global system of the Koyna dam have been created using ABAQUS software considering the dam-reservoir-foundation interaction. Non coupled models and the coupled models were compared regarding the horizontal displacement of the dam crest and the differential settlement of the dam base in clay foundation. Meta models were constructed and uncertainty quantification process was adopted by the support of Sobol’s sensitivity indices considering five uncertain parameters by exploiting Box-Behnken experimental method. The non coupled models results determined overestimated predicted stability and damage detection in the dam. The rational effects of the reservoir height were very sensitive in the variation of the horizontal displacement of the dam crest with a small interaction effect with the beta viscous damping coefficient of the clay foundation. The modulus of elasticity of the clay foundation was the decisive parameter regarding the variation of the differential settlement of the dam base. The XFEM approach has been used for damage detection in relation with both minimum and maximum values of each uncertain parameter. Finally the effects of clay and rock foundations were determined regarding the resistance against the propagation of cracks in the dam, where the rock foundation was the best.
massed foundation / hydrodynamic pressure / Box-Behnken method / meta model / Sobol’s sensitivity indices
[1] |
Ilinca C, Varvorea R, Popovici A. Influence of dynamic analysis methods on seismic response of a buttress dam. Mathematical Modelling in Civil Engineering, 2014, 10(3): 1–15
CrossRef
Google scholar
|
[2] |
Mohsin A Z, Omran HA, Al-Shukur A H K. Dynamic response of concrete gravity dam on random soil. International Journal of Civil Engineering and Technology, 2015, 6(11): 21–31
|
[3] |
Mehdipour B. Effect of foundation on seismic behavior of concrete dam considering the interaction of dam- Reservoir. Journal of Basic and Applied Scientific Research, 2013, 3(5): 13–20
|
[4] |
Wang G, Wang Y, Lu W, Zhou C, Chen M, Yan P. XFEM based seismic potential failure mode analysis of concrete gravity dam–water–foundation systems through incremental dynamic analysis. Engineering Structures, 2015, 98: 81–94
CrossRef
Google scholar
|
[5] |
Lu L, Li X, Zhou J, Chen G, Yun D. Numerical simulation of shock response and dynamic fracture of a concrete dam subjected to impact load. Earth Sciences Research Journal, 2016, 20(1): 1–6
CrossRef
Google scholar
|
[6] |
Huang J. Seismic Response Evaluation of Concrete Gravity Dams Subjected to Spatially Varying Earthquake Ground Motions. Dissertation for PhD degree. Drexel University, Philadelphia, USA, 2011
|
[7] |
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
|
[8] |
Ghasemi H, Brighenti R, Zhuang X, Muthu J, Rabczuk T. Optimum fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach. Structural and Multidisciplinary Optimization, 2015, 51(1): 99–112
CrossRef
Google scholar
|
[9] |
Zhang C, Nanthakumar S S, Lahmer T, Rabczuk T. Multiple cracks identification for piezoelectric structures. International Journal of Fracture, 2017, 206(2): 151–169
CrossRef
Google scholar
|
[10] |
Nanthakumar S, Zhuang X, Park H, Rabczuk T. Topology optimization of flexoelectric structures. Journal of the Mechanics and Physics of Solids, 2017, 105: 217–234
CrossRef
Google scholar
|
[11] |
Nanthakumar S, Lahmer T, Zhuang X, Park H S, Rabczuk T. Topology optimization of piezoelectric nanostructures. Journal of the Mechanics and Physics of Solids, 2016, 94: 316–335
CrossRef
Google scholar
|
[12] |
Nanthakumar S, Lahmer T, Zhuang X, Zi G, Rabczuk T. Detection of material interfaces using a regularized level set method in piezoelectric structures. Inverse Problems in Science and Engineering, 2016, 24(1): 153–176
CrossRef
Google scholar
|
[13] |
Nanthakumar S, Valizadeh N, Park H, Rabczuk T. Surface effects on shape and topology optimization of nanostructures. Computational Mechanics, 2015, 56(1): 97–112
CrossRef
Google scholar
|
[14] |
Nanthakumar S S, Lahmer T, Rabczuk T. Detection of flaws in piezoelectric structures using extended FEM. International Journal for Numerical Methods in Engineering, 2013, 96(6): 373–389
CrossRef
Google scholar
|
[15] |
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
CrossRef
Google scholar
|
[16] |
Vu-Bac N, Silani M, Lahmer T, Zhuang X, Rabczuk T. A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites. Computational Materials Science, 2015, 96: 520–535
CrossRef
Google scholar
|
[17] |
Vu-Bac N, Rafiee R, Zhuang X, Lahmer T, Rabczuk T. Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters. Composites. Part B, Engineering, 2015, 68: 446–464
CrossRef
Google scholar
|
[18] |
Rabczuk T, Akkermann J, Eibl J. A numerical model for reinforced concrete structures. International Journal of Solids and Structures, 2005, 42(5-6): 1327–1354
CrossRef
Google scholar
|
[19] |
Bažant Z P. Why continuum damage is nonlocal: micromechanics arguments. Journal of Engineering Mechanics, 1991, 117(5): 1070–1087
CrossRef
Google scholar
|
[20] |
Thai T Q, Rabczuk T, Bazilevs Y, Meschke G. A higher-order stress-based gradient-enhanced damage model based on isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, 2016, 304: 584–604
CrossRef
Google scholar
|
[21] |
Fleck N A, Hutchinson J W. A phenomenological theory for strain gradient effects in plasticity. Journal of the Mechanics and Physics of Solids, 1993, 41(12): 1825–1857
CrossRef
Google scholar
|
[22] |
Rabczuk T, Eibl J. Simulation of high velocity concrete fragmentation using SPH/MLSPH. International Journal for Numerical Methods in Engineering, 2003, 56(10): 1421–1444
CrossRef
Google scholar
|
[23] |
Rabczuk T, Eibl J, Stempniewski L. Numerical analysis of high speed concrete fragmentation using a meshfree Lagrangian method. Engineering Fracture Mechanics, 2004, 71(4–6): 547–556
CrossRef
Google scholar
|
[24] |
Rabczuk T, Xiao S P, Sauer M. Coupling of meshfree methods with nite elements: basic concepts and test results. Communications in Numerical Methods in Engineering, 2006, 22(10): 1031–1065
CrossRef
Google scholar
|
[25] |
Rabczuk T, Eibl J. Modelling dynamic failure of concrete with meshfree particle methods. International Journal of Impact Engineering, 2006, 32(11): 1878–1897
CrossRef
Google scholar
|
[26] |
Etse G, Willam K. Failure analysis of elastoviscoplastic material models. Journal of Engineering Mechanics, 1999, 125(1): 60–69
CrossRef
Google scholar
|
[27] |
Miehe C, Hofacker M, Welschinger F. A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering, 2010, 199(45–48): 2765–2778
CrossRef
Google scholar
|
[28] |
Amiri F, Millan D, Arroyo M, Silani M, Rabczuk T. Fourth order phase-field model for local max-ent approximants applied to crack propagation. Computer Methods in Applied Mechanics and Engineering, 2016, 312(C): 254–275
CrossRef
Google scholar
|
[29] |
Areias P, Rabczuk T, Msekh M. Phase-field analysis of finite-strain plates and shells including element subdivision. Computer Methods in Applied Mechanics and Engineering, 2016, 312(C): 322–350
CrossRef
Google scholar
|
[30] |
Msekh M A, Silani M, Jamshidian M, Areias P, Zhuang X, Zi G, He P, Rabczuk T. Predictions of J integral and tensile strength of clay/epoxy nanocomposites material using phase-eld model. Composites. Part B, Engineering, 2016, 93: 97–114
CrossRef
Google scholar
|
[31] |
Hamdia K, Msekh M A, Silani M, Vu-Bac N, Zhuang X, Nguyen-Thoi T, Rabczuk T. Uncertainty quantication of the fracture properties of polymeric nanocomposites based on phase field modeling. Composite Structures, 2015, 133: 1177–1190
CrossRef
Google scholar
|
[32] |
Msekh M A, Sargado M, Jamshidian M, Areias P, Rabczuk T. ABAQUS implementation of phase-field model for brittle fracture. Computational Materials Science, 2015, 96: 472–484
CrossRef
Google scholar
|
[33] |
Amiri F, Millán D, Shen Y, Rabczuk T, Arroyo M. Phase-field modeling of fracture in linear thin shells. Theoretical and Applied Fracture Mechanics, 2014, 69: 102–109
CrossRef
Google scholar
|
[34] |
Hamdia K M, Zhuang X, He P, Rabczuk T. Fracture toughness of polymeric particle nanocomposites: evaluation of Models performance using Bayesian method. Composites Science and Technology, 2016, 126: 122–129
CrossRef
Google scholar
|
[35] |
Rabczuk T, Belytschko T, Xiao S P. Stable particle methods based on Lagrangian kernels. Computer Methods in Applied Mechanics and Engineering, 2004, 193(12–14): 1035–1063
CrossRef
Google scholar
|
[36] |
Rabczuk T, Belytschko T. Adaptivity for structured meshfree particle methods in 2D and 3D. International Journal for Numerical Methods in Engineering, 2005, 63(11): 1559–1582
CrossRef
Google scholar
|
[37] |
Nguyen V P, Rabczuk T, Bordas S, Duflot M. Meshless methods: a review and computer implementation aspects. Mathematics and Computers in Simulation, 2008, 79(3): 763–813
CrossRef
Google scholar
|
[38] |
Zhuang X, Cai Y, Augarde C. A meshless sub-region radial point interpolation method for accurate calculation of crack tip elds. Theoretical and Applied Fracture Mechanics, 2014, 69: 118–125
CrossRef
Google scholar
|
[39] |
Zhang X, Zhu H, Augarde C. An improved meshless Shepard and least square method possessing the delta property and requiring no singular weight function. Computational Mechanics, 2014, 53(2): 343–357
CrossRef
Google scholar
|
[40] |
Zhuang X, Augarde C, Mathisen K. Fracture modelling using meshless methods and level sets in 3D: framework and modelling. International Journal for Numerical Methods in Engineering, 2012, 92(11): 969–998
CrossRef
Google scholar
|
[41] |
Chen L, Rabczuk T, Bordas S, Liu G R, Zeng KY, Kerfriden P.Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth. Computer Methods in Applied Mechanics and Engineering, 2012, 209‒212: 250–265
|
[42] |
Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601–620
CrossRef
Google scholar
|
[43] |
Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 1999, 46(1): 131–150
CrossRef
Google scholar
|
[44] |
Vu-Bac N, Nguyen-Xuan H, Chen L, Lee C K, Zi G, Zhuang X, Liu G R, Rabczuk T. A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics. Journal of Applied Mathematics, 2013( 2013): 978026
CrossRef
Google scholar
|
[45] |
Bordas S P A, Natarajan S, Kerfriden P, Augarde C E, Mahapatra D R, Rabczuk T, Dal Pont S. On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM). International Journal for Numerical Methods in Engineering, 2011, 86(4–5): 637–666
CrossRef
Google scholar
|
[46] |
Bordas S P A, Rabczuk T, Hung N X, Nguyen V P, Natarajan S, Bog T, Quan D M, Hiep N V. Strain Smoothing in FEM and XFEM. Computers & Structures, 2010, 88(23–24): 1419–1443
CrossRef
Google scholar
|
[47] |
Rabczuk T, Zi G, Gerstenberger A, Wall W A. A new crack tip element for the phantom node method with arbitrary cohesive cracks. International Journal for Numerical Methods in Engineering, 2008, 75(5): 577–599
CrossRef
Google scholar
|
[48] |
Chau-Dinh T, Zi G, Lee P S, RabczukT, Song J H. Phantom-node method for shell models with arbitrary cracks. Computers & Structures, 2012, 92– 93: 242–256
CrossRef
Google scholar
|
[49] |
Song J H, Areias P M A, Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering, 2006, 67(6): 868–893
CrossRef
Google scholar
|
[50] |
Areias P M A, Song J H, Belytschko T. Analysis of fracture in thin shells by overlapping paired elements. Computer Methods in Applied Mechanics and Engineering, 2006, 195(41–43): 5343–5360
CrossRef
Google scholar
|
[51] |
Rabczuk T, Areias P M A. A meshfree thin shell for arbitrary evolving cracks based on an external enrichment. CMES-Computer Modeling in Engineering and Sciences, 2006, 16(2): 115–130
|
[52] |
Zi G, Rabczuk T, Wall W A. Extended meshfree methods without branch enrichment for cohesive cracks. Computational Mechanics, 2007, 40(2): 367–382
CrossRef
Google scholar
|
[53] |
Rabczuk T, Bordas S, Zi G. A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Computational Mechanics, 2007, 40(3): 473–495
CrossRef
Google scholar
|
[54] |
Rabczuk T, Zi G. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760
CrossRef
Google scholar
|
[55] |
Rabczuk T, Areias P M A, Belytschko T. A meshfree thin shell method for nonlinear dynamic fracture. International Journal for Numerical Methods in Engineering, 2007, 72(5): 524–548
CrossRef
Google scholar
|
[56] |
Bordas S, Rabczuk T,Zi G. Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by extrinsic discontinuous enrichment of meshfree methods without asymptotic enrichment. Engineering Fracture Mechanics, 2008, 75(5): 943–960
CrossRef
Google scholar
|
[57] |
Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A geometrically non-linear three dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758
CrossRef
Google scholar
|
[58] |
Rabczuk T, Gracie R, Song J H, Belytschko T. Immersed particle method for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 2010, 81(1): 48–71
|
[59] |
Rabczuk T, Bordas S, Zi G. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 2010, 88(23–24): 1391–1411
CrossRef
Google scholar
|
[60] |
Amiri F, Anitescu C, Arroyo M, Bordas S, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57
CrossRef
Google scholar
|
[61] |
Talebi H, Samaniego C, Samaniego E, Rabczuk T. On the numerical stability and mass- lumping schemes for explicit enriched meshfree methods. International Journal for Numerical Methods in Engineering, 2012, 89(8): 1009–1027
CrossRef
Google scholar
|
[62] |
Nguyen-Thanh N, Zhou K, Zhuang X, Areias P, Nguyen-Xuan H, Bazilevs Y, Rabczuk T. Isogeometric analysis of large-deformation thin shells using RHTsplines for multiple-patch coupling. Computer Methods in Applied Mechanics and Engineering, 2017, 316: 1157–1178
CrossRef
Google scholar
|
[63] |
Nguyen-Thanh N, Valizadeh N, Nguyen M N, Nguyen-Xuan H, Zhuang X, Areias P, Zi G, Bazilevs Y, De Lorenzis L, Rabczuk T. An extended isogeometric thin shell analysis based on Kirchho-Love theory. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 265–291
CrossRef
Google scholar
|
[64] |
Jia Y, Anitescu C, Ghorashi S, Rabczuk T. Extended isogeometric analysis for material interface problems. IMA Journal of Applied Mathematics, 2015, 80(3): 608–633
CrossRef
Google scholar
|
[65] |
Ghorashi S, Valizadeh N, Mohammadi S, Rabczuk T. T-spline based XIGA for fracture analysis of orthotropic media. Computers & Structures, 2015, 147: 138–146
CrossRef
Google scholar
|
[66] |
Rabczuk T, Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343
CrossRef
Google scholar
|
[67] |
Rabczuk T, Areias P M A. A new approach for modelling slip lines in geological materials with cohesive models. International Journal for Numerical and Analytical Methods in Geomechanics, 2006, 30(11): 1159–1172
CrossRef
Google scholar
|
[68] |
Rabczuk T, Belytschko T. Application of particle methods to static fracture of reinforced concrete structures. International Journal of Fracture, 2006, 137(1–4): 19–49
CrossRef
Google scholar
|
[69] |
Rabczuk T, Belytschko T. A three dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799
CrossRef
Google scholar
|
[70] |
Rabczuk T, Areias P M A, Belytschko T. A simplied meshfree method for shear bands with cohesive surfaces. International Journal for Numerical Methods in Engineering, 2007, 69(5): 993–1021
CrossRef
Google scholar
|
[71] |
Rabczuk T, Samaniego E. Discontinuous modelling of shear bands using adaptive meshfree methods. Computer Methods in Applied Mechanics and Engineering, 2008, 197(6–8): 641–658
CrossRef
Google scholar
|
[72] |
Rabczuk T, Song J H, Belytschko T. Simulations of instability in dynamic fracture by the cracking particles method. Engineering Fracture Mechanics, 2009, 76(6): 730–741
CrossRef
Google scholar
|
[73] |
Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455
CrossRef
Google scholar
|
[74] |
Cai Y,Zhuang X Y, Zhu H. A generalized and ecient method for nite cover generation in the numerical manifold method. International Journal of Computational Methods, 2013, 10(5): 1350028
CrossRef
Google scholar
|
[75] |
Liu G, Zhuang X, Cui Z. Three-dimensional slope stability analysis using independent cover based numerical manifold and vector method. Engineering Geology, 2017, 225: 83–95
CrossRef
Google scholar
|
[76] |
Nguyen H B, Zhuang X, Wriggers P, Rabczuk T, Mears M E, Tran H D. 3D Isogeometric symmetric Galerkin boundary element methods. Computer Methods in Applied Mechanics and Engineering, 2017, 323: 132–150
CrossRef
Google scholar
|
[77] |
Nguyen B H, Tran H D, Anitescu C, Zhuang X, Rabczuk T. An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems. Computer Methods in Applied Mechanics and Engineering, 2016, 306: 252–275
CrossRef
Google scholar
|
[78] |
Zhu H, Wu W, Chen J, Ma G, Liu X, Zhuang X. Integration of three dimensional discontinuous deformation analysis (DDA) with binocular photogrammetry for stability analysis of tunnels in blocky rock mass. Tunnelling and Underground Space Technology, 2016, 51: 30–40
CrossRef
Google scholar
|
[79] |
Wu W, Zhu H, Zhuang X, Ma G, Cai Y. A multi-shell cover algorithm for contact detection in the three dimensional discontinuous deformation analysis. Theoretical and Applied Fracture Mechanics, 2014, 72: 136–149
CrossRef
Google scholar
|
[80] |
Cai Y, Zhu H, Zhuang X. A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modelling. Frontiers of Structural and Civil Engineering, 2013, 7(4): 369–378
CrossRef
Google scholar
|
[81] |
Nguyen-Xuan H, Liu G R, Bordas S, Natarajan S, Rabczuk T. An adaptive singular ES-FEM for mechanics problems with singular eld of arbitrary order. Computer Methods in Applied Mechanics and Engineering, 2013, 253: 252–273
CrossRef
Google scholar
|
[82] |
Areias P, Rabczuk T. Steiner-point free edge cutting of tetrahedral meshes with applications in fracture. Finite Elements in Analysis and Design, 2017, 132: 27–41
CrossRef
Google scholar
|
[83] |
Areias P, Reinoso J, Camanho P, Rabczuk T. A constitutive-based element-by-element crack propagation algorithm with local mesh refinement. Computational Mechanics, 2015, 56(2): 291–315
CrossRef
Google scholar
|
[84] |
Areias P M A, Rabczuk T, Camanho P P. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63
CrossRef
Google scholar
|
[85] |
Areias P, Rabczuk T, Dias-da-Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 110: 113–137
CrossRef
Google scholar
|
[86] |
Areias P, Rabczuk T, Camanho P P. Initially rigid cohesive laws and fracture based on edge rotations. Computational Mechanics, 2013, 52(4): 931–947
CrossRef
Google scholar
|
[87] |
Areias P, Rabczuk T. Finite strain fracture of plates and shells with congurational forces and edge rotation. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122
CrossRef
Google scholar
|
[88] |
Silani M, Talebi H, Hamouda A S, Rabczuk T. Nonlocal damage modeling in clay/epoxy nanocomposites using a multiscale approach. Journal of Computational Science, 2016, 15: 18–23
CrossRef
Google scholar
|
[89] |
Talebi H, Silani M, Rabczuk T. Concurrent multiscale modelling of three dimensional crack and dislocation propagation. Advances in Engineering Software, 2015, 80: 82–92
CrossRef
Google scholar
|
[90] |
Silani M, Talebi H, Ziaei-Rad S, Hamouda A M S, Zi G, Rabczuk T. A three dimensional extended Arlequin method for dynamic fracture. Computational Materials Science, 2015, 96: 425–431
CrossRef
Google scholar
|
[91] |
Silani M, Ziaei-Rad S, Talebi H, Rabczuk T. A semi-concurrent multiscale approach for modeling damage in nanocomposites. Theoretical and Applied Fracture Mechanics, 2014, 74: 30–38
CrossRef
Google scholar
|
[92] |
Talebi H, Silani M, Bordas S, Kerfriden P, Rabczuk T. A computational library for multiscale modelling of material failure. Computational Mechanics, 2014, 53(5): 1047–1071
CrossRef
Google scholar
|
[93] |
Talebi H, Silani M, Bordas S P A, Kerfriden P, Rabczuk T. Molecular dynamics/XFEM coupling by a three-dimensional extended bridging domain with applications to dynamic brittle fracture. International Journal for Multiscale Computational Engineering, 2013, 11(6): 527–541
CrossRef
Google scholar
|
[94] |
Yang S W, Budarapu P R, Mahapatra D R, Bordas S P A, Zi G, Rabczuk T. A meshless adaptive multiscale method for fracture. Computational Materials Science, 2015, 96: 382–395
CrossRef
Google scholar
|
[95] |
Budarapu P, Gracie R, Bordas S, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148
CrossRef
Google scholar
|
[96] |
Budarapu P, Gracie R, Yang S W, Zhuang X, Rabczuk T. Ecient coarse graining in multiscale modeling of fracture. Theoretical and Applied Fracture Mechanics, 2014, 69: 126–143
CrossRef
Google scholar
|
[97] |
Zhuang X, Wang Q, Zhu H. Multiscale modelling of hydro-mechanical couplings in quasi-brittle materials. International Journal of Fracture, 2017, 204(1): 1–27
CrossRef
Google scholar
|
[98] |
Zhu H, Wang Q, Zhuang X. A nonlinear semi-concurrent multiscale method for fractures. International Journal of Impact Engineering, 2016, 87: 65–82
CrossRef
Google scholar
|
[99] |
Zhuang X, Wang Q, Zhu H. A 3D computational homogenization model for porous material and parameters identication. Computational Materials Science, 2015, 96: 536–548
CrossRef
Google scholar
|
[100] |
Kouznetsova V, Geers M G D, Brekelmans W A M. Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme. International Journal for Numerical Methods in Engineering, 2002, 54(8): 1235–1260
CrossRef
Google scholar
|
[101] |
Rabczuk T, Ren H. Peridynamic formulation for the modelling of quasi-static fractures and contacts in brittle rocks. Engineering Geology, 2017, 225: 42–48
|
[102] |
Amani J, Oterkus E, Areias P M A, Zi G, Nguyen-Thoi T, Rabczuk T. A non-ordinary state-based peridynamics formulation for thermoplastic fracture. International Journal of Impact Engineering, 2016, 87: 83–94
CrossRef
Google scholar
|
[103] |
Ren H, Zhuang X, Rabczuk T. A new peridynamic formulation with shear deformation for elastic solid. Journal of Micromechanics and Molecular Physics, 2016, 1(2): 1650009
CrossRef
Google scholar
|
[104] |
Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476
CrossRef
Google scholar
|
[105] |
Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: a stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782
CrossRef
Google scholar
|
[106] |
Gaun F, Moore I D, Lin G. Seismic Analysis of Reservoir-Dam-Soil Systems in the Time Domain. The 8th international conference on Computer Methods and Advances in Geomechanics, Siriwardane & Zaman (Eds), 1994, 2: 917–922
|
[107] |
Zeidan B. State of Art in Design and Analysis of Concrete Gravity Dams. Tanta University, 2014, 1–56
|
[108] |
Wieland M, Ahlehagh S. Dynamic stability analysis of a gravity dam subject to the safety evaluation earthquake. 9th European club symposium IECS2013, Venice, Italy, 10–12 April, 2013
|
[109] |
Benerjee A, Paul D K, Dubey R N. Estimation of cumulative damage in concrete gravity dam considering foundatiom-reservoir interaction. Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering, Anchorage, Alaska, USA, 21–25 July, 2014
|
[110] |
Shariatmadar H, Mirhaj A. Modal Response of Dam-Reservoir-Foundation Interaction. 8th International Congress on Civil Engineering, Shiraz University, Shiraz, Iran, 11–13 May, 2009
|
[111] |
Berrabah A T, Belharizi M, Bekkouche A. Modal behavior of dam reservoir foundation system. Electronic Journal of Geotechnical Engineering, 2011, 16: 1593–1605
|
[112] |
Khosravi S, Heydari M. Modelling of concrete gravity dam including dam-water-foundation rock interaction. World Applied Sciences Journal, 2013, 22(4): 538–546
|
[113] |
Benerjee A, Paul D K, Dubey R N. Modelling issues in the seismic analysis of concrete gravity dams. Dam Engineering, 2014, 24(2): 18–38
|
[114] |
Joghataie A, Dizaji M S, Dizaji F S. Neural Network Software for Dam-Reservoir-Foundation Interaction. International Conference on Intelligent Computational Systems (ICICS'2012), Dubai, UAE, 7–8 January, 2012
|
[115] |
Hung J, Zerva A. Nonlinear analysis of a dam-reservoir-foundation system under spatially variable seismic excitations. The 14th World Conference on Earthquake Engineering, Beijing, China, 12–17 October, 2008
|
[116] |
Heirany Z, Ghaemian M. The effect of foundation’s modulus of elasticity on concrete gravity dam’s behavior. Indian Journal of Science and Technology, 2012, 5(5): 2738–2740
|
[117] |
Berrabah A T. Dynamic Soil-Fluid –Structure Interaction Applied for Concrete Dam. Dissertation for PhD degree. Chetouane, Algeria, Aboubekr Belkaid University, 2012
|
[118] |
Zeidan B. Effect of foundation flexibility on dam-reservoir-foundation interaction. Eighteenth International Water Technology Conference (IWTC18), Sharm El-Sheikh, Egypt, 12–14 March, 2015
|
[119] |
Burman A, Maity D, Sreedeep S. Iterative analysis of concrete gravity dam-nonlinear foundation interaction. International Journal of Engineering Science and Technology, 2010, 2(4): 85–99
CrossRef
Google scholar
|
[120] |
Chopra A K. Hydrodynamic pressures on dams during earthquakes. Journal of Engineering Mechanics, ASCE, 1967, 93(6): 205–223
|
[121] |
Fereydooni M, Jahanbakhsh M. An analysis of the hydrodynamic pressure on concrete gravity dams under earthquake forces using ANSYS software. Indian Journal of Fundamental and Applied Life Sciences, 2015, 5(S4): 984–988
|
[122] |
Berrabah AT, Armouti N, Belharizi M, Bekkouche A. Dynamic soil structure interaction study. Jordan Journal of Civil Engineering, 2012, 6(2): 161–173
|
[123] |
Pekan O A, Cui Y Z. Failure analysis of fractured dams during earthquakes by DEM. Eng Struct, 2004, 26: 1483–1502.
|
[124] |
Patil S V, Awari U R. Effect of soil structure interaction on gravity dam. International Journal of Science, Engineering and Technology Research (IJSETR), 2015, 4(4): 1046– 4053
|
[125] |
Chopra A K, Chakrabarti P. The earthquake experience at Koyna dam and stress in concrete gravity dam. Earthquake Engineering and Structural Dynamic, 1972, 1(2): 151–164
|
[126] |
Pal W. Seismic cracking of concrete gravity dam. Journal of Structural Division, 1976, 102 (ST9): 1827–1844
|
[127] |
Pasma S A, Daik R, Maskat M Y, Hassan O. Application of box-behnken design in optimization of glucose production from oil palm empty fruit bunch cellulose. International Journal of Polymer Science, 2013, 2013: 104502
CrossRef
Google scholar
|
[128] |
Qiu P, Cui M, Kang K, Park B, Son Y, Khim E, Jang M, Khim J. Application of Box–Behnken design with response surface methodology for modeling and optimizing ultrasonic oxidation of arsenite with H2O2. Central European Journal of Chemistry, 2014, 12(2): 164–172
CrossRef
Google scholar
|
[129] |
Tekindal M A, Bayrak H, Ozkaya B, Genc Y. Box Behnken experimental design in factorial experiments: the importance of bread for nutrition and health. Turkish Journal of Field Crops, 2012, 17(2): 115–123
|
[130] |
Amenaghawon N A, Nwaru K I, Aisien F A, Ogbeide S E, Okieimen C O. Application of Box-Behnken design for the optimization of citric acid production from corn starch using aspergillus niger. British Biotechnology Journal, 2013, 3(3): 236–245
CrossRef
Google scholar
|
[131] |
Souza A S, dos Santos W N L, Ferreira S L C. Application of Box–Behnken design in the optimization of an on-line pre-concentration system using knotted reactor for cadmium determination by flame atomic absorption spectrometry. Spectrochimica Acta Part B: Atomic Spectroscopy, 2005, 60(5): 737–742
CrossRef
Google scholar
|
[132] |
Aslan N, Cebeci Y. Application of Box-Behnken design and response surface methodology for modeling of some Turkish coals. Fuel, 2007, 86(1–2): 90–97
CrossRef
Google scholar
|
/
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