# Prediction of Friction Resistance for Slurry Pipe Jacking
## 4 The Verification of the Effectiveness of the Proposed New Approach
### Comparison between the Predicted Friction Resistances and the Numerical Simulation Result  
Some excellent work of numerical simulation has been conducted for the estimation of the jacking force (or friction resistance) of pipe jacking. For example, [PERSON] et al. [5,40] and [PERSON] [41] presented a novel discrete 2D numerical model to evaluate the normal force acting on the pipe. Then, the friction resistance is determined by multiplying the interface friction coefficient by the normal force. Three different drives in a pipe jacking projects were analyzed, where the calculated pattern of jacking force was compared with the measured data, which demonstrated the effectiveness of the proposed approach. [PERSON] and [PERSON] [25] used a model coupling finite element method and a displacement control method to estimate the required jacking force in pipe jacking. The displacement control option in the numerical analysis software ABAQUS (Abaqus Inc., (Palo Alto, CA, USA) 2012) was used to designate the displacement at the end cross section of the pipe in the launch shaft. Accounting for the contact property and the contact range between the pipes and the soil during the jacking process, the stresses exerted on the pipes were used to back-calculate the jacking forces [25]. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Cases** & **C 1** & & **C 2** & & **C 3** & & **C 4** & \\ \hline  & & **Ratio** & & **Ratio** & & & **Ratio** & & **Ratio** \\ \hline \(f_{\text{mea. (kN/m)}}\) & 1.5 & & 36.16 & & 3.78 & & 9.75 & \\ \hline  & M 7 \({}^{*}\) & 2.44 & 163\% & 43.37 & 120\% & 3.55 & 94\% & 5.19 & 53\% \\  & M 8 \({}^{*}\) & 3.46 & 231\% & 58.53 & 162\% & 4.02 & 106\% & 5.69 & 58\% \\  & M 9 \({}^{*}\) & 1.93 & 129\% & 41.19 & 114\% & 3.43 & 91\% & 10.74 & 110\% \\ \(f_{\text{cal. (kN/m)}}\) & M 10 \({}^{*}\) & 4.30 & 287\% & 56.99 & 158\% & 3.84 & 101\% & 9.80 & 101\% \\  & M 11 \({}^{*}\) & 2.09 & 140\% & 48.22 & 133\% & 4.62 & 122\% & 14.08 & 144\% \\  & M 12 \({}^{*}\) & 1.26 & 84\% & 36.51 & 101\% & 4.08 & 108\% & 15.72 & 161\% \\  & M 13 \({}^{*}\) & 1.89 & 126\% & 35.02 & 97\% & 3.31 & 88\% & 10.27 & 105\% \\ \hline \hline \end{tabular} The superscript \({}^{***}\) is used to distinguish from the number of models in Table 2.  
\end{table} 
Table 6: Comparison of the friction resistances calculated by the new approach and the measured data. The numerical simulation strategy of Yen and Shou [25] is quite consistent with the analytical approach of this paper. Therefore, the numerical simulation approach of Yen and Shou will be described in the next section and its estimated result of friction resistance will be discussed and compared with that calculated by the analytical approach of this paper. One of the analyses focused on a case of slurry pipe jacking in the Taichung Science Park, the basic parameters of this case were summarized in Table 7. In the numerical simulation, the lateral boundaries were fixed by roller, and hinges were used to constrain the bottom boundary. The three dimensional hexahedron element (C3D8R) with eight nodes was used in the simulation. To verify the jacking force obtained from the displacement control simulation, overcut and lubrication were included in the model by setting the contact range (1/3, 1/2, and 1 pipe-soil contact) and the frictional coefficient (Figure 7a-c). The results suggested the 1/3 contact case can estimate the jacking force with a better accuracy towards the middle and the final stage of the pipe jacking process (Figure 8). In Figure 8, the slope of the linear regression for the scattered points represents frictional resistance, and the intercept represents face resistance. For the calculated result of this paper, the measured face resistance is used, and the frictional resistance (\(f_{\text{cal. }}=57.7\) kN/m) is calculated by the new approach (Section 3) using parameters of UK PJA in [PERSON]'s silo model (Table 1).