The effect of micro-structural uncertainties of recycled aggregate concrete on its global stochastic properties via finite pixel-element Monte Carlo simulation

Abstract

In this paper, the effect of micro-structural uncertainties of recycled aggregate concrete (RAC) on its global stochastic elastic properties is investigated via finite pixel-element Monte Carlo simulation. Representative RAC models are randomly generated with various distribution of aggregates. Based on homogenization theory, effects of recycled aggregate replacement rate, aggregate volume fraction, the unevenness of old mortar, proportion of old mortar, aggregate size and elastic modulus of aggregates on overall variability of equivalent elastic properties are investigated. Results are in a good agreement with experimental data in literature and finite pixel-element method saves the computation cost. It is indicated that the effect of mesoscopic randomness on global variability of elastic properties is considerable.

Keywords

RAC / Monte Carlo analysis / stochastic / finite pixel-element method / homogenization / coefficient of variation

References

[1] Li W, Xiao J, Sun Z, Kawashima S, Shah S P. Interfacial transition zones in recycled aggregate concrete with different mixing approaches. Construction & Building Materials, 2012, 35: 1045–1055

[2] Xiao J, Sun Y, Falkner H. Seismic performance of frame structures with recycled aggregate concrete. Engineering Structures, 2006, 28(1): 1–8

[3] Xiao J, Li J, Sun Z. Study on compressive strength of recycled aggregate concrete. Journal of Tongji University, 2004, 12: 001

[4] Xiao J, Li J, Zhang C. Mechanical properties of recycled aggregate concrete under uniaxial loading. Cement and Concrete Research, 2005, 35(6): 1187–1194

[5] Xiao J, Xie H, Yang Z. Shear transfer across a crack in recycled aggregate concrete. Cement and Concrete Research, 2012, 42(5): 700–709

[6] Xiao J, Ying J, Shen L. FEM simulation of chloride diffusion in modeled recycled aggregate concrete. Construction & Building Materials, 2012, 29: 12–23

[7] Xiao J, Li W, Corr D J, Shah S P. Simulation study on the stress distribution in modeled recycled aggregate concrete under uniaxial compression. Journal of Materials in Civil Engineering, 2012, 25(4): 504–518

[8] Xiao J, Li W, Liu Q. Mesoscopic numerical simulation of uniaxial compressive behavior of model recycled aggregate concrete. Journal of Tongji University (Natural Science), 2011, 39(6): 791–797

[9] Zhou F P, Lydon F D, Barr B I G. Effect of coarse aggregate on elastic modulus and compressive strength of high performance concrete. Cement and Concrete Research, 1995, 25(1): 177–186

[10] Stock A F, Hannantt D J, Williams R I T. The effect of aggregate concentration upon the strength and modulus of elasticity of concrete. Magazine of Concrete Research, 1979, 31(109): 225–234

[11] Stefanou G. The stochastic finite method: Past, present and future. Computer Methods in Applied Mechanics and Engineering, 2009, 198(9): 1031–1051

[12] Wall F J, Deodatis G. Variability response functions of stochastic plane stress/strain problems. Journal of Engineering Mechanics, 1994, 120(9): 1963–1982

[13] Argyris J, Papadrakakis M, Stefanou G. Stochastic finite element analysis of shells. Computer Methods in Applied Mechanics and Engineering, 2002, 191(41): 4781–4804

[14] Craham L, Deodatis G. Response and eigenvalue analysis of stochastic finite element systems with multiple correlated material and geometric properties. Probabilistic Engineering Mechanics, 2001, 16(1): 11–29

[15] Noh H C. A formulation for stochastic finite element analysis of plate structures with uncertain Poisson’s ratio. Computer Methods in Applied Mechanics and Engineering, 2004, 193(45): 4857–4873

[16] Stefanou G, Papadrakakis M. Stochastic finite element analysis of shells with combined random material and geometric properties. Computer Methods in Applied Mechanics and Engineering, 2004, 193(1): 139–160

[17] Kamiński M, Świta P. Structural stability and reliability of the underground steel tanks with the stochastic finite element method. Archives of Civil and Mechanical Engineering, 2015, 15(2): 593–602

[18] Xia B, Yu D, Liu J. Transformed perturbation stochastic finite element method for static response analysis of stochastic structures. Finite Elements in Analysis and Design, 2014, 79: 9–21

[19] Fink S, Nackenhorst U. Simulation of uncertain inelastic material behaviour using the stochastic finite mlement Method. Proceedings in Applied Mathematics and Mechanics, 2014, 14(1): 265–266

[20] Gunzburger M D, Webster C G, Zhang G. Stochastic finite element methods for partial differential equations with random input data. Acta Numerica, 2014, 23: 521–650

[21] Stefanou G, Savvas D, Papadrakakis M. Stochastic finite element analysis of composite structures based on material microstructure. Composite Structures, 2015, 132: 384–392

[22] Xu X F, Graham-Brady L. A stochastic computational method for evaluation of global and local behavior of random elastic media. Computer Methods in Applied Mechanics and Engineering, 2005, 194(42): 4362–4385

[23] Xu X F. A multiscale stochastic finite element method on elliptic problems involving uncertainties. Computer Methods in Applied Mechanics and Engineering, 2007, 196(25): 2723–2736

[24] Xu X F. Generalized variational principles for uncertainty quantification of boundary value problems of random heterogeneous materials. Journal of Engineering Mechanics, 2009, 135(10): 1180–1188

[25] Kamiński M. Stochastic boundary element method analysis of the interface defects in composite materials. Composite Structures, 2012, 94(2): 394–402

[26] Kamiński M. On semi–analytical probabilistic finite element method for homogenization of the periodic fiber–reinforced composites. International Journal for Numerical Methods in Engineering, 2011, 86(9): 1144–1162

[27] Ma X, Zabaras N. A stochastic mixed finite element heterogeneous multiscale method for flow in porous media. Journal of Computational Physics, 2011, 230(12): 4696–4722

[28] Sakata S, Ashida F, Zako M. Kriging-based approximate stochastic homogenization analysis for composite materials. Computer Methods in Applied Mechanics and Engineering, 2008, 197(21): 1953–1964

[29] Sakata S, Ashida F, Kojima T, Zako M. Three-dimensional stochastic analysis using a perturbation-based homogenization method for elastic properties of composite material considering microscopic uncertainty. International Journal of Solids and Structures, 2008, 45(3): 894–907

[30] Sakata S, Ashida F, Kojima T. Stochastic homogenization analysis on elastic properties of fiber reinforced composites using the equivalent inclusion method and perturbation method. International Journal of Solids and Structures, 2008, 45(25): 6553–6565

[31] Ma X, Zabaras N. An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations. Journal of Computational Physics, 2009, 228(8): 3084–3113

[32] Ma X, Zabaras N. An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations. Journal of Computational Physics, 2010, 229(10): 3884–3915

[33] Hou T Y, Liu P. A heterogeneous stochastic FEM framework for elliptic PDEs. Journal of Computational Physics, 2015, 281: 942–969

[34] 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

[35] Miehe C, Koch A. Computational micro-to-macro transitions of discretized microstructures undergoing small strains. Archive of Applied Mechanics, 2002, 72(4): 300–317

[36] Vu-Bac N, Lahmer T, Zhang Y, Zhuang X, Rabczuk T. Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs). Composites. Part B, Engineering, 2014, 59: 80–95

[37] Vu-Bac N, Lahmer T, Keitel H, Zhao J, Zhuang X, Rabczuk T. Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations. Mechanics of Materials, 2014, 68: 70–84

[38] 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

[39] 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

Acknowledgement

This work is sponsored by the National Natural Science Foundation of China (Grant Nos. 10972162 and 51325802). This support is gratefully acknowledged.

RIGHTS & PERMISSIONS

2017 Higher Education Press and Springer-Verlag GmbH Germany