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**Modelling the flow of self-compacting concrete.**
*(English)*
Zbl 1274.76282

Summary: A Lagrangian particle-based method, smooth particle hydrodynamics (SPH), is used in this paper to model the flow of self-compacting concretes (SCC) with or without short steel fibres. An incompressible SPH method is presented to simulate the flow of such non-Newtonian fluids whose behaviour is described by a Bingham-type model, in which the kink in the shear stress vs shear strain rate diagram is first appropriately smoothed out. The viscosity of the SCC is predicted from the measured viscosity of the paste using micromechanical models in which the second phase aggregates are treated as rigid spheres and the short steel fibres as slender rigid bodies. The basic equations solved in the SPH are the incompressible mass conservation and Navier-Stokes equations. The solution procedure uses prediction-correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting temporal velocity field is then implicitly projected on to a divergence-free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. The results of the numerical simulation are benchmarked against actual slump tests carried out in the laboratory. The numerical results are in excellent agreement with test results, thus demonstrating the capability of SPH and a proper rheological model to predict SCC flow and mould-filling behaviour.

### MSC:

76M28 | Particle methods and lattice-gas methods |

76A05 | Non-Newtonian fluids |

74E30 | Composite and mixture properties |

### Keywords:

self-compacting concrete; self-compacting fibre-reinforced concrete; non-Newtonian Bingham fluid; viscosity; flow modelling; smooth particle hydrodynamics (SPH)
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\textit{S. Kulasegaram} et al., Int. J. Numer. Anal. Methods Geomech. 35, No. 6, 713--723 (2011; Zbl 1274.76282)

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### References:

[1] | Petersson, Proceedings of the 3rd International RILEM Symposium, Pro 33 pp 202– (2003) |

[2] | Noor, Proceedings of the 1st International RILEM Symposium on Self-compacting Concrete pp 35– (1999) |

[3] | Dufour, Numerical modelling of concrete flow: homogeneous approach, International Journal for Numerical and Analytical Methods in Geomechanics 29 pp 395– (2005) · Zbl 1178.76064 |

[4] | Roussel, Computational modelling of concrete flow: general overview, Cement and Concrete Research 37 pp 1298– (2007) |

[5] | Monaghan, Smoothed particle hydrodynamics, Annual Review of Astronomy and Astrophysics 30 pp 543– (1992) · Zbl 1361.76019 |

[6] | Monaghan, Simulating free surface flows with SPH, Journal of Computational Physics 110 pp 399– (1994) · Zbl 0794.76073 |

[7] | Bonet, Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulation, International Journal for Numerical Methods in Engineering 47 pp 1189– (2000) · Zbl 0964.76071 |

[8] | Bonet, Variational and momentum aspects of smooth particle hydrodynamics formulations, Computer Methods in Applied Mechanics and Engineering 180 pp 97– (1999) · Zbl 0962.76075 |

[9] | Cummins, An SPH projection method, Journal of Computational Physics 152 (2) pp 584– (1999) · Zbl 0954.76074 |

[10] | Kulasegaram, A Variational formulation based contact algorithm for rigid boundaries in two-dimensional SPH applications, Computational Mechanics 33 pp 316– (2004) · Zbl 1067.74072 |

[11] | Papanastasiou, Flows of materials with yield, Journal of Rheology 31 pp 385– (1987) · Zbl 0666.76022 |

[12] | Ghanbari, Prediction of the plastic viscosity of self-compacting steel fibre reinforced concrete, Cement and Concrete Research 39 pp 1209– (2009) |

[13] | Chorin, Numerical solution of the Navier-Stokes equations, Mathematics of Computation 22 pp 745– (1968) · Zbl 0198.50103 |

[14] | Koshizuka, Numerical analysis of breaking waves using moving particle semi-implicit method, International Journal for Numerical Methods in Fluids 26 pp 751– (1998) · Zbl 0928.76086 |

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