# A Numerical Study of the Behavior of Micropile Foundations under Cyclic Thermal Loading
## 3 Results and Discussion
### _Pile axial thermal displacement_  
In all cases, a small irrecoverable settlement developed in the first few thermal cycles. For the isolated pile case (R/D = 30), the irrecoverable vertical displacement averaged \(-1.3\) and \(-0.22\) mm for MP-30 and MP-15, respectively, and reduced as R/D (pile spacing) reduced to an average of \(-0.74\) mm and about zero, respectively (Table 3). A cyclic thermoelastic displacement response developed on top of these irrecoverable settlements: for both isolated pile cases, the amplitude of the movement was about 1 mm but when R/D was reduced to 4, the movement amplitude increased significantly, to 3.2 and 2.5 mm respectively (Table 3). For comparison, the results from the analysis of a 30 m long, LD pile are also in Figure 10; these showed similar behavior, with regular cyclic thermal movements about a small permanent settlement developing in the first few cycles. The permanent movement reduced with reduced pile spacing, but again, the cyclic amplitude increased. Examining in more detail the response of the two micropile cases, it was observed that during cooling cycles, downwards (negative) axial thermal displ \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**MP-30**} & \multicolumn{2}{c}{**MP-15**} \\ \hline
**R/D** & **Average** & **Amplitude** & **Average** & **Amplitude** \\ \hline
30 & \(-1150\) (52) & \(\pm 2480\) (112) & \(-150\) (7) & \(\pm 1160\) (52) \\
4 & \(-1580\) (71) & \(\pm 170\) (8) & \(80\) (4) & \(\pm 480\) (22) \\ \hline \hline \end{tabular} Values in brackets are %-\(\sigma_{\text{th,free}}=100\), \(\sigma_{\text{th,max}}/\sigma_{\text{th,fixed}}\) values.  
\end{table} 
Table 4: Maximum thermal axial stress (kPa) in pile, averaged between years 6 and 10. Figure 10: Effect of pile proximity on cyclic thermal axial load-transfer response of micropile unit cell groups. cases, though of differing magnitude--larger downward pile head movements occurred at closer pile spacing which even exceeded \(y_{\text{th,free}}\) due to the thermal activation of the ground, as discussed in Section 3.2. During heating cycles, there were marked differences which were most obvious for the isolated MP-30 case: here, in the first pile heating, the pile head expanded upwards and the base downwards as expected; in subsequent cycles, however, the upwards expansion was restrained and the resultant thermal movement was downwards (settlement) with respect to the start of the thermal activation of the pile (this effect is further discussed below, in relation to the thermal stress response). At the pile base, on the other hand, the thermal movements were small (\(\pm\) a few tenths of a millimeter, Table 3) and in line with expectations, i.e., downwards during heating and upwards during cooling. This led to significant nonlinearity in the profile of axial thermal movements for the isolated MP-30 case shown in Figure 9a. This effect was still present for MP-30 at R/D = 4 but was much smaller due to the more extensive thermal activation of the surrounding ground. The effect also appeared to be present in the isolated MP-15 case, but due to its shorter length, axial restraint was reduced, and the effect was not so obvious. This response had a direct impact on the axial thermal stress, as will be discussed below. Finally, considering typical settlement limits for isolated piles and large pile groups, the values of average irrecoverable settlement obtained are unlikely to be of concern in terms of their impact on design. The amplitude of the pile head movement was somewhat larger and may require verification against project serviceability criteria. However, this also needs to be considered in terms of the overall group settlement under external mechanical load only, which was several times larger (see Figure 7), and the thermal movements remained a small proportion of the overall vertical movement which increased as R/D reduced.