# A Numerical Study of the Behavior of Micropile Foundations under Cyclic Thermal Loading
## 2 Basis for Numerical Analyses  
### Geometry  
The numerical analyses presented here were undertaken using the finite-element program ABAQUS 2016 [35]. A two-dimensional (2D) axisymmetric pile geometry was considered, which comprised a 200 mm diameter micropile with a TA length of either 30 m (designated MP-30) or 15 m (MP-15), embedded in a domain that was either 91 m or 45.5 m deep, Figure 1b,c). Utilizing a 2D axisymmetric modeling approach provides notable advantages in computational efficiency, precision, and simplified configuration for geotechnical challenges exhibiting rotational symmetry, as exemplified by the case of piles and the soil domain. The thermally-activated part of the pile started 1.0 and 0.5 m below ground level for MP-30 and MP-15 respectively, to provide a buffer between the thermal boundary conditions applied in the pile and along the ground surface; this had only a minor effect on the reported pile behavior. This is a generic study, however, the pile lengths modeled are representative of typical micropile installations and also allowed the influence of the effect of the changes in geometry between the large diameter (LD) piles considered previously [34] and the micropiles considered herein.  
The model was discretized, as shown in Figure 2, by means of a mesh defined by 5421 quadrilateral elements of type CA4 XT [35], i.e., coupled temperature-displacement elements for which the stress analysis depends on the temperature solution and the thermal analysis depends on the displacement solution.  
The lateral dimension of the finite element mesh was set to provide mesh radius to pile diameter ratios, R/D of 30, 8 and 4 (R = 6, 1.6 and 0.8 m). Initial analyses (not presented, and see, e.g., [34]) showed that when R/D = 30, the pile could be considered to be isolated and not influenced by mechanical and thermal boundary conditions on the side boundary. With smaller values of R/D, the problem could be considered as a \"unit cell\" that represents an idealized pile group that extends to infinity. [PERSON] (2019) [36] undertook a full three-dimensional analysis of the same problem and demonstrated that the unit cell approach approximated this reasonably closely, with the benefit of a much-reduced computational effort, confirming the results of previous studies including [37; 38; 39], among others.  
Figure 1: (a) Profile of soil stiffness; (b) Large Diameter (LD) pile geometry and boundary conditions; (c) Micropile (MP) geometry and boundary conditions (U1: horizontal fixity, U2: vertical fixity, T: temperature).  
The bottom boundary was fixed in the vertical and horizontal directions while the side boundary was only fixed in the horizontal direction, Figure 1b,c. Thermal boundary conditions are outlined in Section 2.3, with climatic boundary conditions based on those for a humid subtropical climate such as Milan, Italy ([[https://www.timeanddate.com/weather/italy/milan/climate](https://www.timeanddate.com/weather/italy/milan/climate)]([https://www.timeanddate.com/weather/italy/milan/climate](https://www.timeanddate.com/weather/italy/milan/climate)) (accessed on 20 May 2022).