## 4 Pressure Loss Correction Model for Bend Section
### Sensitivity Analysis of Parameters in Bend Section  
Horizontal inclination affects the configuration of the pumping pipe on the pump truck. An excessively large or small radius of curvature can increase the risk of pipe clogging. Additionally, concrete conveying resistance varies with changes in both the horizontal inclination and the radius of curvature of the pumping pipe. Concrete conveying resistance varies with different pumping flow rates. Therefore, it is important to analyze how the horizontal inclination angle of the pumping pipe, the radius of curvature, and the pumping flow rate affect concrete pressure loss. Additionally, since the curved pipe tension angle is typically \(90^{\circ}\) in the current market, this paper does not include a sensitivity analysis of the curved pipe tension angle. According to the particle flow numerical simulation process, with a concrete pumping pipeline diameter of 125 mm, the combined effects of centrifugal force, particle collisions, and collisions with the pipe wall create blocking effects at the elbow. To better simulate the concrete flow, an adjustment section is added: a 500 mm straight pipe section is placed before the elbow, and a 400 mm straight pipe section is added after the elbow. The concrete model and aggregate particle shape remain consistent with the validation model, with a radius of curvature of 195 mm and a pumping speed of 0.905 m/s. The inlet axis is  
Figure 5: Geometric reconstruction of coarse aggregate [10]. parallel to the horizontal plane, and the outlet axis is at an angle to the horizontal plane. The pumping pipes are arranged at angles of \(90^{\circ}\), \(45^{\circ}\), \(0^{\circ}\), \(-45^{\circ}\), and \(-90^{\circ}\) relative to the horizontal direction. The bend model is meshed using hexahedral elements, totaling 5470 elements and 5092 nodes. The simulation duration is 2 s, with a fluid simulation time step of 0.0001 s and a particle simulation time step of 0.000001 s. The interaction forces between the fluid and the particles are calculated using a coupled drag force model. After the numerical simulation of particle flow, the pressure distribution in the pumping pipeline is as illustrated in Figure 6. The figure shows that the pressure at the pipeline inlet increases with the horizontal inclination angle. When the inclination angle is perpendicular to the ground, the pressure loss during concrete pumping is highest. This is because, in addition to overcoming resistance along the pipeline, the concrete must also overcome the flow resistance generated by its own weight. In other words, as the horizontal inclination of the pipeline increases, the concrete must overcome not only the increased resistance to flow caused by its own weight but also greater flow resistance within the pipe. This leads to higher energy loss. For a concrete pumping pipeline with a diameter of 125 mm, a horizontal arrangement of the bend, and a flow rate of 0.905 m/s. The simulation analysis for C45 concrete is conducted using curved pipes with radii of curvature of 195 mm, 235 mm, 275 mm, 315 mm, and 355 mm. The pressure distribution in the pipe is illustrated in Figure 7. The figure shows that as the radius of curvature increases, the average pressure at the inlet section of the bend also increases. This is because a larger radius of curvature extends the pumping time and path, which raises the energy required to overcome resistance along the pipeline. Consequently, the increased pressure loss due to the larger radius of curvature results in a higher average pressure at the inlet. Figure 6: Bend section of different horizontal inclination pressure distribution cloud map. Figure 7: Pressure distribution of different radii of curvature in the bend section. A bend with a curvature radius of 195 mm is used, and the pumping flow rates are 40 m\({}^{3}\)/h, 55 m\({}^{3}\)/h, 70 m\({}^{3}\)/h, 100 m\({}^{3}\)/h, and 120 m\({}^{3}\)/h. The elbow is positioned at a 90\({}^{\circ}\) inclination to the horizontal direction.