The rate at which the modulus of elasticity for the inner annulus fibrosus reduces.

I feel like there's information missing in your question. Modulus of elasticity is a physical parameter that reflects the mechanical behaviour of any material in response to the induced stresses due to loading. If the person's on their feet, what weighs them down is gravity. On the earth, gravity has a force of acceleration of about 9.8 meters per second.

Have you been provided any constants related to the inner annulus fibrosus of the intervertebral disc?

In terms of constants, what I found for the inner annulus fibrosus was that the modulus of elasticity ranged from 20MPa to 180MPa and stress on the disc is 0.33MPa and the disc thickness averages 8.5mm. What I really want to know is what happens to the intevertebral discs after you have been awake for 10 days and standing, hypothetically speaking. Do the cells in the discs get severely deprived of nutrients and oxygen and rapidly degenerate?

Thank you

When you're standing for a long period of time, you have all the weight pressing down on those discs - especially the weight of one's head and the effects of gravity. All tissue requires blood and nutrients, and tissues that become fatigued will produce lactic acid. With rest, byproducts of fatigue are eventually cleared. Therefore, I'm assuming that if you were to stand for 10 days straight, the collagen would stretch, and muscles surrounding the backbone will produce biological acids that'll make standing for that long almost impossible.

This is great, thank you so much for shedding some light on this! Now I understand the discs much better!