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The industry has embraced self-compacting concrete (SCC) to overcome deficiencies related to consolidation, improve productivity, and enhance safety and quality. Due to the large deformation at the flowing process of SCC, an enhanced Lagrangian particle-based method, Smoothed Particles Hydrodynamics (SPH) method, though first developed to study astrophysics problems, with its exceptional advantages in solving problems involving fragmentation, coalescence, and violent free surface deformation, is developed in this study to simulate the flow of SCC as a non-Newtonian fluid to achieve stable results with satisfactory convergence properties. Navier-Stokes equations and incompressible mass conservation equations are solved as basics. Cross rheological model is used to simulate the shear stress and strain relationship of SCC. Mirror particle method is used for wall boundaries. The improved SPH method is tested by a typical 2D slump flow problem and also applied to L-box test. The capability and results obtained from this method are discussed.

Industrialization of construction is the main trend in scientific and technical progress in construction, including the extensive use of prefabricated factory-finished elements and the conversion of production into a mechanized and continuously flowing process of assembly and installation of buildings and structures made of prefabricated assemblies and elements. It will lead to higher-quality materials and more cost-effectiveness and energy efficiency for infrastructure construction. Self-consolidating concrete (SCC) is a thixotropic mixture, created by tailoring different materials and securing excellent deformability and adequate resistance to segregation to insure the exceptional rheology behavior of concrete [

While simulation is a mature science in homogeneous fluids, simulation of the flow of SCC is difficult because of the need to track the boundaries between the liquid and solid phases. Few previous studies have focused on finding the rheological material model for certain paste or concrete [

In considering the large deformation nature of SCC flow and great complexity of concrete-infilling behavior, the conventional methods such as discrete element method (DEM) and finite element method (FEM) have two critical drawbacks including the limitations in modeling free surfaces and nonguaranteed conservation of mass. The recently developed Smoothed Particles Hydrodynamics (SPH) method offers a glimpse of the future of fresh concrete flow simulation. Although SPH was first developed to study astrophysics problems [

However, the existing SPH still has limitations when applied to non-Newtonian fluid. Firstly, it cannot measure the velocity divergence and pressure gradient accurately. Secondly, it cannot treat the nonslip boundary condition exactly, which is an issue for SSC. Hence, further enhancement of the existing SPH method will be the focus of this study fluid to achieve accurate and stable results with satisfactory convergence properties. And the improved SPH algorithm is tested by a typical 2D slump flow problem and then applied for an L-box flow problem. The SCC is modeled using Cross rheological model. The capability and results obtained from this method are discussed. The simulation provides reasonable good agreement with available data from the literature. The findings may be of engineering interests in view of the flowability and pressure caused by fresh SCC on structures.

In the current study, the SCC is assumed as viscous non-Newtonian fluid, which is governed by the Navier-Stokes (NS) equation. The 2D Lagrangian form is [

The SCC flow is the incompressible flow and (

The SPH is an interpolation method, which transforms the Partial Difference Equation (PDE) to integration form and allows any function to be expressed in terms of the value at a set of disordered particles. Following Gingold and Monaghan [

The SCC domain may be represented by discrete particles and (

In the current study, the quintic kernel function [

Many forms have been proposed to evaluate the gradient and divergence in the SPH literatures. In the current study, the velocity divergence is computed by the antisymmetric form to improve the accuracy [

The gradient of shear stress is computed similar to the pressure gradient and can be expressed by

The particle assigns the initial smoothing length

If

If

The particle will continue to increase the smoothing length until the smoothing length becomes larger than

There are several methods to model the boundary condition including the virtual force method [

In this section, the improved SPH model is applied to a benchmark slump test model to simulate the slum flow of SCC to demonstrate the capability of the proposed model in SCC flow modeling. And the model is also used to simulate the filling ability of SCC by using the L-box test.

Figure

The initial configuration of the placement for slump flow.

The SCC is a high performance mix and the density and rheological properties of SCC used for slump test are presented in Table ^{3}.

Density and rheological properties of SCC for simulation [

Density (kg/m^{3}) |
Plastic viscosity (Pa s) | Yield stress (Pa) | |
---|---|---|---|

SCC | 2380 | 48.4 | 56.3 |

The simulation domain is discretized by particles with size

Figures

The velocity distribution during slump flow.

Final spread

The pressure distribution during slump flow.

Final spread

The shear strain rate distribution during slump flow.

Final spread

In order to understand the filling ability in addition to the flow characteristics of SCC, the classic L-box filling test is also simulated by using the improved SPH method. Figure

The configuration of the L-box test for SCC [

The same SCC mix properties as presented in Table ^{3}. Figures

Simulation of L-box testing for SCC with velocity distribution.

Simulation of L-box testing for SCC with pressure distribution.

Simulation of L-box testing for SCC with shear strain rate distribution.

The simulation domain is discretized by particles with size

Due to the large deformation at the flowing process of SCC, an enhanced Lagrangian particle-based method—an improved SPH method—with its exceptional advantages in solving problems involving fragmentation, coalescence, and violent free surface deformation is developed in this study to simulate the flow of SCC as a non-Newtonian fluid to achieve stable results with satisfactory convergence properties. Navier-Stokes equations and incompressible mass conservation equations are solved as basics. Cross rheological model is used to simulate the shear stress and strain relationship of SCC. Mirror particle method is used for wall boundaries. The improved SPH method is tested by a typical 2D slump flow problem and also applied to L-box flowing problem. The results obtained from this method are reasonably agreeing with the experimental data. This enables the modeling of the flow of SCC by enhancing the current particle method and also provides an efficient tool to estimate the lateral pressure of the SCC exerted on structures. Moreover, it will benefit the industry and practical concrete applications by using this method to estimate the flowability, the mould filling performance of concrete, and also the interactions between the concrete and mould during casting. The proposed method could also become an efficient method to study the mix design to optimize the workability of the concrete.

The authors declare that they have no competing interests.

Grateful acknowledgment is made to ECARD Research Grant scheme from Queensland University of Technology and the National Natural Science Foundation of China (Project no. 51508294) to collectively support this project.