Closure of deep boreholes in ice sheets: a discussion

The most frequently used relation between ice deformation rate, έ, and stress, ፐ, is the power law, commonly called Glen’s flow law, έ = Aፐⁿ , in which A is an ice stiffness parameter and n is an empirical constant. A can be estimated from the simple exponential relation (see paper), where A ₀ is a constant independent of temperature; E, commonly called the enhancement factor, depends on ice crystal orientation, impurity content and other factors; Q is the activation energy for creep; R is the universal gas constant; and T is the absolute temperature. Laboratory experiments yield values of A ₀ = 9.514MPa^–3a^–1 for secondary creep. Typical borehole closure experiments then give E ≈ 0.16. This low value probably results from the fact that, when deforming into a borehole, ice is subject to stresses that are inconsistent with the preferred orientation of c axes that has developed over many years under a stress configuration with no borehole present. Closure data from Vostok hole 3G yield E ≈ 0.7. This higher value may reflect a unique stress environment yielding fabrics that are somewhat better oriented for borehole closure.