Computation of Ice Borehole Closure By the Finite Element Method

The ice borehole closure may affect the drilling operation when the closure rate reaches some critical level. It is essential to estimate the closure rate of ice boreholes for drilling program planning. To examine Nye's formula and to obtain more accurate estimates of ice borehole closure to various ice conditions, a finite element modeling was used. The ice was treated as non-linear visco-incompressible fluid. Glen's ice flow power law was used. The effects of change in ice density and temperature versus depth were considered. Computation was carried out by the direct iteration method.

Tests with Nye's formula show that the model can give quite accurate results in closure rate, strain rate and stresses with errors at the 4th digit number in strain rate. Nye's formula gives more conservative values. Tests with field measurements show that the exponent of power law should be considered as a variable of ice-effective stress was obtained by modeling with field measurements. Ice density variation has small effect on the ice closure rate, while a temperature increase of 15 degrees Celsius may lead to 8 times the increase in the closure rate at the 1,500-m depth. Borehole diameters have a linear effect on the closure rate. Modeling results also show that the ice bottom boundary conditions can only affect borehole closure rate within, at most, 50 m from the bottom, and the effect decreases quickly within 5m from the bottom. The ice flow has little effect on the ice borehole closure.