Homework 1

Due Wednesday, Feb.5.

Show all work.

You may work with others if you like, but please list their names if you do.

1) The director of a California experiment station used to offer visitors a free acre of California. When they gladly accepted, he gave them a glass vial with soil in it, explaining that soil has such a large specific surface that an entire acre’s worth of area fit into the vial. How much loam (20% clay, 40% sand, 40% silt), in grams, does it take to make an acre’s worth of soil surface area? Assume that the clay is montmorillonite.

2) You are analyzing a soil sample for particle size distribution. After destroying the organic matter, you sieve the solids through a nest of sieves and weigh what is retained on each sieve. Then you take the fine residue (“pan”), disperse it in 1 liter of a dispersing solution (sodium hexametaphosphate), mix it, and allow particles to settle. Every now and again, you pipette out a 10 ml water sample at 20 cm depth.

a) plot the particle size distribution, using a log X-axis for size, and a linear Y-axis going from 0 to 1 for cumulative fraction.
See fig. 3.4 in Hillel as an example. Watch your units!

b) what is the texture?

Sieve: Pipette:

Sieve size (mm)	mass retained (g)	sample time (s)	sample mass (g)
1.0	0.07	171	0.0011
0.5	0.12	1070	0.0008
0.2	0.21	4280	0.0004
0.1	0.33	1700	0.0001
0.05	0.28	Density of solution	1.03 g/cm³
pan	1.32	Viscosity:	1.25x10^-2 kg/m s

3) Suppose you have packed spheres of radius 1 cm. What is the largest size sphere you can fit inside the matrix if the original spheres are packed cubically? What if they are packed tetrahedrally?

4) You perform 2 triaxial shear experiments on identical samples of a soil. For the first, the confining pressure is 20 and the load 60 MPa at failure. In the second, the confining pressure is 50 and the load 110 at failure.

a) what is the angle of internal friction?

b) what might be the texture of the soil, and why?