## 1 Introduction
The standard \(\kappa\)-\(\varepsilon\) turbulence model is a semi-empirical formulation, which is widely used in engineering applications due to its moderate computational volume and relatively high accuracy of solution [18]. Foreign scholars have carried out relevant research on arrest and wear. [PERSON] et al. investigated fresh concrete pumping arrest using a CFD modeling approach [19]. [PERSON] et al. studied the pumping wear characteristics of a concrete pipeline based on CFD-DEM coupling [20]. The layout of pumping pipes for pump truck boom pumping affects the rheological behavior of concrete. [PERSON] et al. used particle flow simulations to analyze the impact of conical and combined conveying pipe model parameters on pressure loss and optimized the pipe arrangement to minimize pressure loss [21]. Concrete pumping flow is influenced by the interaction of factors such as pipe layout, aggregate particles, and pumping speed. In the design and construction of pumping systems, it is crucial to consider specific project requirements, concrete characteristics, conveying distance, and pumping height. As the demands for precise engineering management and high-quality concrete control increase, traditional empirical methods, time-consuming high-precision simulations, and costly coiled-tube experiments are proving inadequate for adapting to industry development trends. In optimizing the pumping pipe layout and determining suitable pumping pressure, the Morinage empirical formula [22] for flow resistance in straight pipe sections is considered to lack precision as it does not account for the influence of aggregate particles. The converted horizontal length method [23] equates the horizontal inclination angle and radius of curvature of the pump pipe, while ignoring the influence of pumping speed on pressure loss. Particle flow numerical simulation [24] fully considers the interactions between aggregate and mortar, offering high calculation accuracy. However, the complexity of the model significantly increases computation time, making it unsuitable for the energy-saving optimization and intelligent control of the boom. Therefore, building on the one-dimensional flow model formula for straight pipe section pressure loss proposed earlier, this paper introduces an engineering correction method for pressure loss in curved pipe sections. This method utilizes high-precision granular flow numerical simulations and considers the effects of curvature radius, horizontal inclination angle, and pumping speed on pressure loss. In summary, a method for correcting the pressure loss of one-dimensional flow in a concrete pumping bend section based on particle flow is proposed in this paper. The paper is structured as follows: Section 2 introduces the experimental measurement and equivalent calculation methods for concrete pumping pressure loss in engineering construction. Section 3 describes the principles of numerical simulation for granular flow, simulatesthe typical flow state of concrete pumping in elbows, and verifies the results through experiments. Section 4 introduces a one-dimensional flow model for horizontal straight pipe sections and analyzes the impact of pumping pipe profile parameters and flow rate on pressure loss. It constructs a correction model for pressure loss in curved pipe sections and verifies the validity of this correction method by comparing it with experimental results. Finally, Section 5 summarizes the main conclusions.