## 5 Conclusions  
In this study, a new methodology to understand how compaction affects the hydrodynamic and thermal properties of a porous medium was developed. This methodology was used to investigate the effects of compaction on the coupled water and heat transport in green roof substrates through numerical simulations. The results showed that as the substrate was compacted, the pore-size of the substrates was reduced. As a result, the capillary forces increased and the water storage volume decreased. These results agree with other investigations performed in natural soils. However, because the foundations of the new methodology are based on compaction methods developed for natural soils that have higher residual water contents and bulk densities compared to the artificial substrates, the new approach failed to produce reasonable results for some substrates. For instance, for substrates S3 and S4 the methodology predicted compacted residual water contents that were lower than those of the uncompacted state. For this reason, the proposed method could be used for green roof substrates that present residual volumetric water contents larger than 0.05 cm\({}^{3}\) cm\({}^{-3}\).  
Regarding the substrate's thermal properties, the thermal conductivity curves increased their values as the bulk density increased. This increase in the thermal conductivity occurred because there was more physical contact between the solid particles of the media. The effect of compaction on the thermal conductivity curve was more relevant in the saturated part of the curves for all the substrates.  
Also, when considering that compaction also affects the hydrodynamic properties of the substrates, the variations of the thermal conductivity curve are now restricted to the new limits of moisture, which reduces the possible fluctuations of the thermal conductivity. When the substrates have a very low bulk density (\(<\)0.5 g cm\({}^{-3}\)), the proposed method can present problems, so care must be taken when analyzing the results.  
The numerical simulations showed that the water and thermal behaviors of the roof system changed with compaction, reducing the amplitude of the fluctuations in the volumetric water content daily cycles, increasing the average water content and reducing the breakthrough time of the green roof substrates.  
When comparing the overall thermal behavior within the substrates studied, the S2 substrate reduced the vertical heat diffusion through the roof. Compaction changes the thermal behavior of the green roof substrates in different ways for each substrate due to the dependence of the air, water, and soil fraction of each substrate. The results showed that compaction affected the coupled water and heat fluxes in a hypothetical green roof. However, the compaction methodology needs an experimental validation for artificial substrates that have low bulk densities and residual water contents. Future research should focus on performing an appropriate experimental validation of this methodology to further confirm the results from the numerical simulations.  
Conceptualization, methodology, writing original draft, review and editing, F.S. and V.S.; Formal analysis and investigation, V.S.; Supervision, F.S.  
This research and the APC were funded by the Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT), by grant CONICYT/FONDECYT/1170850.  
The authors thank the Centro de Desarrollo Urbano Sustentable (CEDEUS--CONICYT/FONDAP/15110020) and the Centro de Excelencia en Geotermia de los Andes (CEGA--CONICYT/FONDAP/15090013) for supporting this investigation.  
The authors declare no conflict of interest and declare that the funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.