Theoretical relation between water flow rate in a vertical fracture and rock temperature in the surrounding massif

TL;DR

This paper presents an analytical model linking water flow rate in vertical fractures to surrounding rock temperature, aiding tunnel drilling by predicting flow rates from thermal anomalies.

Contribution

It introduces a mathematical relation between fracture flow rate and rock temperature, validated with real tunnel data, enhancing predictive capabilities during tunnel excavation.

Findings

Good agreement between observed and theoretical temperatures.

Predicted and observed flow rates are consistent in case studies.

Model can estimate flow rates before fracture intersection.

Abstract

A steady-state analytical solution is given describing the temperature distribution in a homogeneous massif perturbed by cold water flow through a discrete vertical fracture. A relation is derived to express the flow rate in the fracture as a function of the temperature measured in the surrounding rock. These mathematical results can be useful for tunnel drilling as it approaches a vertical cold water bearing structure that induces a thermal anomaly in the surrounding massif. During the tunnel drilling, by monitoring this anomaly along the tunnel axis one can quantify the flow rate in the discontinuity ahead before intersecting the fracture. The cases of the Simplon, Mont Blanc and Gotthard tunnels (Alps) are handled with this approach which shows very good agreement between observed temperatures and the theoretical trend. The flow rates before drilling of the tunnel predicted with the theoretical solution are similar in the Mont Blanc and Simplon cases, as well as the flow rates observed during the drilling. However, the absence of information on hydraulic gradients (before and during drilling) and on fracture specific storage prevents direct predictions of discharge rates in the tunnel.