Homework #4               Glaciology, GEOL 4888,  Spring 2018                        Humphrey

Here are some fairly simple questions to back up some of our thoughts from the lectures on stress and strain.  This shouldn’t take you very long, but will tell me whether people are keeping up.

1. A section of glacier is being stretched, the uniform 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. At this first step we ignore the longitudinal stress, since it is small, what is the approx..overburden pressure near the bed of the glacier?

b. Again ignoring the longitudinal stress, what are the approximate values of s_xx, s_{yy and} s_zz

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

d. Calculate the effective stress (t_effective) for use in the Nye-Glen flow law? (Hint you should only have 2 terms in the sum)

e. Use the effective stress from part c to calculate the shear strain rate (e_xz with a dot over it) near the bed using the full Nye-Glen flow law [ e_xz with a dot over it = A _* (t_effective)² _* t_xz ]. Assume the ice is -5C.

f. Compare the result from part d with the shear strain rate that you would calculate with the Glen flow law approximation, that doesn’t use the effective stress, but only raises the shear stress to the 3^rd power?

Table of Values of A(T), s^-1Pa^-3	Temperature (Celsius)
2.4 x 10^-24	0
9.3 x 10^-25	-5
3.5 x 10^-25	-10
1.2 x 10^-25	-20

g. (hard, but for no points) If this longitudinal stress is uniform over the depth of the glacier, will the longitudinal strain rate also be uniform over the depth?