# A Numerical Study of the Behavior of Micropile Foundations under Cyclic Thermal Loading
## 3 Results and Discussion
### Comparison with Previous Studies  
In related studies, [PERSON] et al. (2022b) [62] and [PERSON] et al. (2021) [59] examined the behavior of LD piles in frictional and cohesive media, respectively. In both studies, it was demonstrated that the degree of initial mobilization of the shaft resistance, M, controlled the subsequent cyclic thermal response. They concluded that in these cases, the cyclic thermal response was largely stable for values of M less than about 80% to 90% ([PERSON] et al., 2022b) [62]. Figure 14 compares the normalized thermal stress-displacement response of the reported behavior of LD piles in frictional media ([PERSON] et al., 2022a) [34] and the micropiles from this study. Following [PERSON] et al. (2022a) [34] and [PERSON] et al. (1999) [56], the pile head thermal displacement, \(\mathrm{y}_{\mathrm{th,0}}\), and the maximum axial thermal stress, \(\mathrm{\sigma}_{\mathrm{th,max}}\), were normalized by the theoretical values for unrestrained pile expansion, \(\mathrm{y}_{\mathrm{th,free}}\), and the thermal stress due to perfect restraint, \(\mathrm{\sigma}_{\mathrm{th,fixed}}\), respectively (as defined in Section 3.3.1). When normalization is positive, this means that the stress/displacement changes are in the same sense, i.e., compression and expansion upwards during pile heating, and vice versa. \begin{table}
\begin{tabular}{l c c c c c} \hline  & & \multicolumn{4}{c}{**MP-30**} \\ \hline
**R/D** & **R,m** & \multicolumn{2}{c}{**Outside**} & \multicolumn{2}{c}{**Inside**} \\ \hline  & & Injection & Extraction & Injection & Extraction \\
30 & 6.0 & +23.7 & \(-\)24.8 & +18.4 & \(-\)31.7 \\
8 & 1.6 & - & - & - & - \\
4 & 0.8 & +16.8 & \(-\)16.6 & +13.3 & \(-\)16.9 \\ \hline  & & \multicolumn{4}{c}{**MP-15**} \\ \hline
**R/D** & **R,m** & \multicolumn{2}{c}{**Outside**} & \multicolumn{2}{c}{**Inside**} \\ \hline  & & Injection & Extraction & Injection & Extraction \\
30 & 6.0 & +17.1 & \(-\)23.4 & +13.4 & \(-\)28.7 \\
8 & 1.6 & +14.3 & \(-\)16.6 & +13.3 & \(-\)20.4 \\
4 & 0.8 & +1.8 & \(-\)3.4 & +2.4 & \(-\)5.6 \\ \hline \end{tabular}
\end{table} 
Table 7: Effect of micropile spacing and surface temperature boundary condition on the peak heat transfer (W/m) in Year 10. Figure 13: Effect of pile layout and surface temperature on heat exchange potential. (a) _Isolated piles (R/D = 30)_  
Despite the differences in physical dimensions, pile stiffness and M-values (50 to 70% but less than 80%), the piles showed similar behavior in terms of the thermal stress-displacement response with an increase in stress as pile head movement reduced, and vice versa, which was qualitatively similar to that observed in field tests of isolated piles ([PERSON] et al., 2019) [63]. Even MP-30, where the response was conditioned somewhat by the slenderness of the pile and its low relative axial stiffness compared with the other cases, fell into the same pattern of behavior, although with rather larger thermal stresses. (b) _Pile group (unit cell with R/D = 4)_  
For the three cases illustrated, the group effect was similar, with a reduction in thermal stress associated with an increase in average thermal pile head movement. However, the general trend in the stress-displacement response was maintained. It should be noted that it is expected that when micropiles are used with a higher initial mobilization of the shaft resistance, which might be the case when they are used for settlement control, then the cyclic thermal response may follow that seen in previous studies of large diameter piles, with the potential for significant irrecoverable settlement developing. Therefore, the thermal activation of piles used to stabilize and limit the settlements of existing foundations will require careful consideration. In terms of heat transfer, the relative effect between the LD pile and micropile cases is for a reduction.