# The Construction of Equivalent Particle Element Models for Conditioned Sandy Pebble
## 5 Calibration of Model Parameters
### Calibration Process  
#### 5.3.1 Range of Parameters  
Before the establishment of LS-SVM, the correlations between the slump value and three undetermined parameters, as well as the value range of each parameter are analyzed by single-variable method. Figure 10 shows the established discrete element models for slump test. Similarly, the slump cone has been enlarged 6 times with top diameter of 600 mm, bottom diameter of 1200 mm, and height of 1800 mm. In the simulation, the lifting speed is 0.36 m/s and the whole lifting process is completed in 5 s. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Input Parameter** & **Unit** & **Value** & **Comment** \\ \hline \multicolumn{4}{c}{**Material Parameter**} \\ \hline Density \(\rho\) & kg/m\({}^{3}\) & 2700 & Measured by overflow method \\ Poisson’s ratio \(\
u\) & n/a & 0.15 & [PERSON] et al. (2013) [35] \\ [PERSON]’s modulus \(E\) & MPa & \(5\times 10^{4}\) & [PERSON] et al. (2013) [35] \\ Shear modulus \(G\) & MPa & \(2.17\times 10^{4}\) & \(G=\frac{E}{2(1+v)}\) \\ \hline \multicolumn{4}{c}{**H-M Contact parameter**} \\ \hline Restitution coefficient \(e\) & n/a & To be calibrated & \\ Static friction coefficient \(\mu_{s}\) & n/a & 0.6891 & \(\mu_{s}\approx\tan\varphi_{u}\) \\ Rolling friction coefficient \(\mu_{r}\) & n/a & To be calibrated & \\ \hline \multicolumn{4}{c}{**Cohesion parameter (JKR model)**} \\ \hline Surface energy \(k\) & J/m\({}^{2}\) & To be calibrated & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The input parameters for the simulation model. Figure 10: Slump test model of sphere (**a**) and cluster (**b**). Figure 11 records the slump value against the surface energy \(k\) in the cases of single sphere (a) and cluster (b) when \(e=0.15\) and \(\mu_{\rm r}=0.02,0.05,0.1,0.15,0.2\), successively. As is indicated in the figures, the slump value is in negative correlation to \(k\). It can be explained by (1) low surface energy: the mutual cohesion is rather weak and the interparticle forces cannot resist the particle weight, therefore the aggregation is easy to scatter into single particles, which makes for a large slump value (Figure 12a,e). (2) When the surface energy improves, the internal contact force is strong enough to resist gravity, thus the aggregation can deform continuously and displays good fluidity and plasticity as the actual conditioned soil. Consequently, the slump value is reduced (Figure 12b,f). (3) If the surface energy is excessively high, the soil presents poor fluidity thus leading to a small slump (Figure 12c,g). In addition, it can be seen from Figure 11 that the slump value is also negatively correlated to \(\mu_{\rm r}\). This is because the strong rolling friction contributes to a strong interlocking action and makes it harder to deform. Figure 13 shows the variation of slump value versus \(e\) in six different scenarios of \(\mu_{\rm r}\) and \(k\) (taking sphere model as example). It is obvious that no strict correlation exists between slump value and restitution coefficient \(e\). On the whole, the slump value increases as \(e\) improves. Figure 11: The variation of slump value versus surface energy: (**a**) sphere model and (**b**) cluster model. Figure 12: The simulation result of slump test: (**a–c**) sphere model and (**e–g**) cluster model. On the basis of literature research, the range of the restitution coefficient is set as \(0<e\leq 0.6\), while the scope of the other two parameters are determined according to their correlation with the slump value. Figure 14a,b shows the slump value against rolling friction coefficient when \(k=0\) respectively in the case of sphere and cluster. It can be concluded that once \(\mu_{\rm r}>0.22\) for sphere or \(\mu_{\rm r}>0.15\) for cluster, the slump value is less than 160 mm regardless of the value of \(e\). It means even without cohesive force between particles, the frictional interaction is strong enough to resist the flow of soil. In such a situation, the slump value can no more meet the requirements.