# A Numerical Study of the Behavior of Micropile Foundations under Cyclic Thermal Loading
## 3 Results and Discussion
### _Pile axial thermal displacement_
(b) _Pile axial thermal stress_  
The axial deformation responses of the MP-30 and MP-15 cases were discussed above and were directly related to the axial stress response which is also shown in Figures 9 and 10. Here, the thermal stress changes represented around 15 to 20% of the maximum axial stress generated by the mechanical load alone, and the curves are shown in the Figures separately from the mechanical ones. The isolated MP-30 pile exhibited much larger average thermal stress changes than those mobilized in MP-15 (Table 4), in terms of both the average value and amplitude of the thermal stress fluctuations. This was a direct consequence of the strong restraint able to be imposed on pile movements along the shaft, which also acts to lock-in a large compression stress in the first few thermal cycles. In the first heating cycle, the maximum thermal compression stress generated was about two-thirds of \(\sigma_{\text{th,fixed}}\), but in the subsequent cycles this more than doubled to about 1.6 \(\sigma_{\text{th,fixed}}\). The generation of the large compression stress arose from the low initial shaft resistance mobilization in the lower part of the pile (Figure 7) and from the reversal of shearing on the shaft as the pile expanded upwards in the top half of the pile. By comparison, the thermal stress generated in cooling cycles was consistent from cycle-to-cycle with the maximum thermal stress (tensile) occurring in the lower third of the pile. The profile of thermal stress along the pile during cooling (Figure 9) was clearly affected by the large locked-in compression stress discussed above, as tensile stress was suppressed in the middle part of the pile. The isolated MP-15 pile showed more typical behavior with the pile expanding and contracting, to generate thermal compression and tensile stress during heating and cooling respectively and with maximum thermal stress changes of less than about 0.5 \(\sigma_{\text{th,fixed}}\). The tensile thermal stress changes discussed above may be of concern in design. However, most micropiles are constructed with full depth reinforcement such as a steel tube, as considered in this study, or a central high-strength steel bar. This means that the micropile is able to carry tensile loads along its full length. Further, in this study, remembering that the piles are in compression due to the mechanical load, the only resultant tensile axial stress occurred for the isolated MP-30 pile and this amounted to only a few-hundred kPa. For the pile group unit cells (R/D = 4), the MP-15 response was the reverse of the isolated pile (Figure 10), with heating leading to tensile stress due to the thermal activation and expansion of the surrounding soil, and vice versa for cooling. The LD pile did not show this reversal (Figure 10) because of its larger absolute unit cell radius, R = 4 m, compared with 0.8 m on the micropiles and, thus, the more limited thermal activation of the ground. The MP-30 pile response differed markedly from MP-15: while the thermal axial stress reversed in the first heating and all cooling cycles, from the second heating cycle onward, the maximum thermal stress reverted to be a compression irrespective of the heating mode. This would appear to be a similar effect to the isolated piles, in the first cooling cycle, the pile head moved down and when reheated, the soil restraint on the shaft was sufficient to restrain the thermal expansion of the pile and maintain the compression. Over the next few cycles, the effect developed, and only after Year 6 did the pile settlement and compression stress development stabilize. Tension did develop, towards the pile base, however the magnitude of this was always less than the maximum compression.