Use of Universal Kriging as a tool to estimate mountain temperature distribution affected by underground infrastructures: the case of the Brenner Base Tunnel

Mountains represent huge low enthalpy geothermal reservoirs. The correct estimation of underground temperature values is relevant for both the design of the tunnel ventilation system and for the assessment of the potential exploitation of geothermal energy. An accurate three-dimensional (3D) model of the ground temperature distribution can be therefore considered as an important goal in the preliminary design stage of mountain tunnels. Numerical modelling and spatial interpolation of the available temperature data need an appropriate estimation methodology, due to the generally limited number of values compared to the dimension of the investigated area. The common deterministic temperature models, based on local surface datasets, average geothermal heat flux and underground thermal properties, possibly integrated with borehole data, cannot be considered sufficiently accurate. The traditional interpolations are generally characterised by low accuracy since they do not take into account the spatial structure of data (i. e. the distance among them). This drawback can be avoided using geostatistical approaches such as Universal Kriging (UK). The UK method, presented in this paper, is a valuable tool for the improvement of temperature measurement interpolation at different depths. In particular, it allows an unbiased estimation of the distribution of the mountain temperature. This type of model can also be continuously updated with new temperature data measured during construction, allowing the estimation of the temperature inside the tunnel at locations that may also be very far from the entrance. Finally, the estimation of the temperature variance, which is possible with this technique, provides a local probability mapping and shows the uncertainty of the temperature estimates. The present work illustrates the application of this methodology to the Italian segment of the Brenner Base Tunnel. In this particular case, the temperature distribution model was added to the specific Geographic Information System available for the underground infrastructure.