# 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 Field Data  
Before comparison analysis, the existing prediction equations were numbered from M 1 to M 13 (Table 2). For M 7\(\sim\)M 13, the Equations (7), (14), (18), and (22) should be used and the parameters (\(b\), \(\delta\), and \(K\)) of [PERSON]'s silo model (Equation (22)) in the calculation of earth pressure should be determined by their approaches that are shown in Table 1.  
As has been mentioned before, the new approach of this paper introduces an effective friction coefficient \(\mu\) (Equation (28)) to replace the original pipe-soil friction coefficient \(\mu_{s}\) (Equation (7)). The calculation of \(\mu\) (Equation (28)) should follow the flow chart shown in Figure 2. Equations (18) and (22) are also used to calculate the normal force \(N\) and vertical earth pressure \(\sigma_{v}\), respectively. The new prediction equations were numbered from M 7 * to M 13 * (Table 3). Some parameters required by the predicted equations (such as \(\mu_{s}\), \(P_{m}\), and \(W\)) might not be given in the literature. In principle, during the calculation, the parameters given in the field case should be used, and the missing parameters can be evaluated by the following rules:  
1. The pipe-soil friction coefficient \(\mu_{s}\) is uniformly calculated by \(\mu_{s}\) = tan (\(q\)/2). 2. The slurry pressure \(P_{m}\) is usually set as equal to the vertical soil stress \(\sigma_{v}\) plus 30 kPa [28], so \(P_{m}\) = \(\sigma_{v}\) + 30 kPa is adopted. 3. The weight of pipe \(W\) is evaluated by \(W\) = \(\gamma_{p}S\), where \(\gamma_{p}\) = 24 kN/m\({}^{3}\) is for reinforced concrete [38], \(S\) is the area of pipe cross section. 4. When the overcut \(\Delta R\) (usually between 0-50 mm) is missed, \(\Delta R\) = 10 mm is taken. 5. The cohesion of pipe-slurry \(c_{m}\) is usually less than 0.1 kPa [39], \(c_{m}\) = 0.1 kPa is used. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Models** & **Equations** & **Approaches** \\ \hline M 1 & Equations (6) and (7) & \\ M 2 & Equations (7)–(10) & \\ M 3 & Equations (7), (11) and (12) & \\ M 4 & Equations (7), (15), (18) and (19) & CTTA (China) \\ M 5 & Equations (7), (16), (21) and (22) & JSA 1 (Japan) \\ M 6 & Equations (7), (17), (21) and (22) & JSA 2 (Japan) \\ M 7 & Equations (7), (14), (18) and (22) & JMTA (Japan) \\ M 8 & Equations (7), (14), (18) and (22) & Terzaghi (Japan) \\ M 9 & Equations (7), (14), (18) and (22) & PJA (UK) \\ M 10 & Equations (7), (14), (18) and (22) & BS EN 1594-09 (UK) \\ M 11 & Equations (7), (14), (18) and (22) & ATV A 161 E-90 (Germany) \\ M 12 & Equations (7), (14), (18) and (22) & ASTM F 1962-11 (US) \\ M 13 & Equations (7), (14), (18) and (22) & GB 50332-2002 (China) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The numbering of the existing friction resistance prediction equations. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Models** & **Equations** & **Approaches** \\ \hline M 7 * & Equations (14), (18), (22) and (28) & JMTA (Japan) \\ M 8 * & Equations (14), (18), (22) and (28) & Terzaghi (Japan) \\ M 9 * & Equations (14), (18), (22) and (28) & PJA (UK) \\ M 10 * & Equations (14), (18), (22) and (28) & BS EN 1594-09 (UK) \\ M 11 * & Equations (14), (18), (22) and (28) & ATV A 161 E-90 (Germany) \\ M 12 * & Equations (14), (18), (22) and (28) & ASTM F 1962-11 (US) \\ M 13 * & Equations (14), (18), (22) and (28) & GB 50332-2002 (China) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The numbering of the new friction resistance prediction equations. The average values of soil parameters (such as \(\gamma_{s}\), \(c_{s}\), \(\varphi\), and \(e\)) can be obtained from the Geological Engineering Handbook. Parameters in each of the four cases were finally determined, which are given in Table 4 [2; 9; 22]. These cases encountered some representative soils, such as silt, clay, sand, and gravels.