Temperature diffusion and thermal strain from embedded fiber optic sensors installed at the Deep Underground Science and Engineering Laboratory (DUSEL) site Lead, South Dakota

We are monitoring temperature and rock deformation at the 4100’-level of DUSEL using six Micron Optics Inc. OS3600 temperature-compensated Fiber Bragg Grating (FBG) strain gages. This study is part of a larger project to measure mechanical and thermal strain on the meter-scale within an intact rock mass. Each sensor measures one-dimensional strain and changes in environmental temperature at the sensor. Two of the six sensors are embedded ~1 meter into the rock mass. The other four sensors are mounted on the rock surface on two perpendicular walls of an alcove (2 x 6 m and 2 m tall). Temperature and strain measurements have been recorded continuously at 1 minute intervals since October 1, 2009. Temperature data from the surface mounted sensors show both long-term (> 1 week) and short-term (instantaneous to > 5 days) temperature changes in the alcove. The long-term temperature changes in the alcove propagate into the rock mass creating a thermal gradient between the rock surface and the embedded sensors. Temperature changes measured by the embedded sensors do not record the short-term temperature effects seen at the surface, and temperature changes in the embedded sensors lag behind changes in temperature in the drift; this lag is attributed to thermal diffusion into the rock mass. In order to model thermal diffusion, we use a model for the heating of a semi-infinite half-space due to a time-dependent surface temperature as a boundary condition. The predicted temperature trend is then compared to the measured temperature from the embedded FBG temperature gages. The model gives a good approximation of temperature at both embedded sensors at depths of 0.8 and 0.9 meters. The shape of the temperature trend at the embedded sensors is accurately modeled, and the 0.1 m difference in depth between the two embedded sensors is resolvable using this model. The model fit to the data is based on a coefficient of thermal diffusivity of κ = ~2.0 x 10-6 m2/s for both sensors independently. This coefficient of thermal diffusivity is reasonable for a quartz and mica-rich metamorphic rock. Further, we can use the thermal model and the measured strain to estimate moduli of the rock mass, assuming no other sources of strain.