# One-Dimensional Modeling of the Pressure Loss in Concrete Pumping and Experimental Verification
## 5 Analysis of Results  
### Analysis of Experimental Results  
A high-rise residential building under construction with 32 floors and a total floor height of 100 m is taken as the object of study. The site uses a certain type of truck-mounted pump; the maximum theoretical conveying capacity of the pump is 90 m\({}^{3}\)/h, the pumping concrete cylinder diameter is 230 mm, and the conveying cylinder stroke is 1600 mm. The pumping pipe has an internal diameter of 125 mm, a wall thickness of 10 mm, an elastic modulus of 210 GPa, and a Poisson's ratio of 0.3. The pumping pressure is adjusted according to the construction floor, with a minimum pressure of 10 MPa and a maximum pressure of 20 MPa. In the experiment, the concrete used for on-site pumping is ordinary commercial C30 concrete produced by a manufacturer in Wuhan, and the experiments are carried out according to the standard \"Slump Test of Concrete Mixes (T0511-94)\" specifications. The mix ratios are shown in Table 1.  
The slump experiment is mainly used to observe the slump shape of concrete and mortar under the action of dead weight, to determine their flow characteristics. Sampling of the mixer truck before the experiment is required. Before sampling, the mixer truck rapidly rotates at a rate of 20-30 rpm for 30 s so that the concrete in the mixer truck is fully mixed, and the tank opening is opened so that the concrete mixture is discharged into a trolley, completing the sampling before pumping. The concrete and mortar in the cart are tested for several times, respectively, and a stopwatch is used to record the time T100 when the mortar slump reaches 100 mm. The slump experimental results are shown in the table. In this study, the average flow rate of concrete in the conveying pipe is measured to be 0.905 m/s. The average density of the concrete is measured to be 2400 kg/m\({}^{3}\), and the average density of cement mortar is 2182 kg/m\({}^{3}\). The measured slumps of the concrete and mortar are shown in Table 2. The average slump \(S\) of the concrete is 210 mm, the measurement process of the mortar is the same as that of the concrete, and the average slump \(S_{1}\) of the mortar is 230 mm. According to Equations (2), (3), and (10), the empirical formula giving the pressure loss per unit length is calculated as follows:  
\[\Delta p_{c}=10033\;\mathrm{Pa}\approx 0.01\;\mathrm{MPa}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Concrete Type** & **Cement (kg)** & **Water (kg)** & **Fly Ash II. (kg)** & **Mineral Powder (kg)** & **Water-Reducing Agent (kg)** & **Sand (kg)** & **Coarse Aggregates** & **Wet Bulk Density** (kg)** \\ \hline C30 & 200 & 102 & 60 & 70 & 9 & 1031 & 919 & 2400 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Content of each component in C30 concrete. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Experiment No.** & **1** & **2** & **3** & **4** \\ \hline Slump of concrete/mm & 212 & 210 & 205 & 213 \\ Slump of mortar/mm & 225 & 230 & 232 & 235 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Slump experiment results. According to the coarse aggregate particle size of the same specifications to meet the concrete grade, a gravel pile of 5-25 mm coarse aggregates is randomly selected several times, and Figure 5 shows the actual particle size distribution of coarse aggregates obtained through sampling analysis. The randomly sampled aggregate particles are classified into three fractions according to their elongated, vertebral, or flake shape, and the randomly sampled aggregate particles are divided into three components: strip, cone, and schistose. Particles are randomly selected from each component, and the total mass of the coarse aggregates selected from the three components is measured. The average mass of the coarse aggregate particles is considered to be the average mass of the particles when the average mass of the particles is within a 5% error after repeated experiments.