## 3 Concrete Pumping Particle Flow Simulation
### Particle Flow Numerical Simulation Verification  
The bend has a diameter of 125 mm and a vertical (90\({}^{\circ}\)) bend with a bend radius of 1000 mm. The density of the pumped C45 concrete mortar is 2100 kg/m\({}^{3}\), while the density of the coarse aggregate particles is 2500 kg/m\({}^{3}\). The aggregate particle size ranges from 5 to 20 mm and follows a normal distribution. The aggregates have a typical uniform mixture of elongated stripes, flakes, and cones, with these three types of particles frequently selected. The three types of aggregate particles were modeled using a HandySCAN non-contact 3D laser scanner to capture their shapes. Geomagic Design X 2017 software was then used to build the geometric models of these particles. These models were imported into particle flow simulation software, where the aggregate particles were approximated as spherical for simulation purposes, as illustrated in Figure 2. The pumping speeds tested were 0.63 m/s, 0.89 m/s, and 1.13 m/s. The concrete slump was 238 mm, with an extension degree of 451 mm. Aggregate particle bond parameters were calibrated through virtual tests of the concrete slump, as detailed in Table 2.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Particle Poisson’s ratio & 0.35 \\ Pipe Poisson’s ratio & 0.30 \\ Particle–particle static friction coefficient & 0.30 \\ Particle–particle rolling friction coefficient & 0.02 \\ Particle–wall static friction coefficient & 0.20 \\ Particle–wall rolling friction coefficient & 0.03 \\ Particle–wall coefficient of restitution & 0.60 \\ Particle–particle coefficient of restitution & 0.70 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Coupling simulation parameter setting.  
In simulating concrete flow within the pumping pipe, a hexahedral mesh is used; the influence of the number of grids and the sparse distribution of grids on the numerical simulation is considered when performing numerical simulation. Considering the computational accuracy and efficiency, this paper adopts 7270 grid elements and 6460 nodes after checking for mesh independence to carry out the simulation analysis of CFD. The inlet is set with a velocity inlet boundary condition, and the wall is modeled as a no-slip boundary. The outlet section of the bend is atmosphere. The standard \(\kappa\)-\(\varepsilon\) turbulence model is employed. The fluid simulation time step is \(10^{-4}\) s, with a convergence accuracy of \(10^{-3}\). The generation rate of coarse aggregate is determined by the pumping speed and the aggregate particle content. The time step for the discrete element calculation of aggregate movement is \(10^{-6}\) s, and the total simulation time for the coupling of mortar and particles is 2 s. The numerical simulation is performed using an 11 th Gen Intel(R) Core(TM) i7-11700 @ 2.50 GHz processor, and the simulation results are presented in Figure 3. The average pressure difference between the inlet and outlet sections represents the pressure loss in the bend. This simulated pressure loss was compared with the experimental data, as shown in Table 3. The relative errors between the simulated and experimental pressure loss values are less than 10%. The feasibility of using particle flow simulations to model concrete pumping behavior is demonstrated.  
Figure 3: The pressure distribution at 1.45 s with a pump velocity of 1.13 m/s.  
Figure 2: Pumping bend model and particle model.