Homework #5               Glaciology, GEOL 4888,  Spring 2018 Humphrey

So many of you had trouble with deviatoric and non-deviatoric stresses on the midterm that I am asking question 1 again.

1. A section of glacier is being stretched, the deviatoric longitudinal stress (t_xx) is 200KPa. The only stresses in the glacier are this extensional stress and the basal shear stress (t_xz) which is about 100KPa, and, of course, the overburden stress or pressure. The glacier is about 600m deep.

a. What is the overburden pressure? (ignore the longitudinal stress)

b. The longitudinal stress is a deviatoric stress, so what is the approximate total (non-deviatoric) stress (s_xx) near the bed?

c. What is the approximate (non-deviatoric) stress (s_yy)

d. Calculate the effective stress (t_effective) for use in the Nye-Glen flow law?

2.    We did a regelation experiment in class.  We used a copper wire with a thickness of 0.4mm.  We loaded a 2kg weight on each side of the wire, and hung it over a piece of ice that had a diameter of 7cm.  The wire regelated about 1cm in an hour. In your notes you will find an expression for regelation velocity.  On the basis of your equation: how does the calculated velocity compare to the observed?

Couple of hints: to do this correctly you need to take into account the curvature of the wire as it is dragged through the ice, but it turns out that the forces can be fairly well approximated by assuming the copper is a rigid straight bar and horizontal. Also note that you will need the thermal conductivity of copper (in Joule/(m s C).

[If you like math problems: it is possible to calculate the shape of the curve of the wire. As far as I know, nobody has ever published this shape!]

3. Consider a glacier in coastal Alaska that is 10 km long, 200m deep and 1km wide. The mass balance curve shows the average net accumulation in the accumulation region is 0.5m per year. The ELA is about 4 km up from the snout. What is the approximate balance velocity at the ELA?