Soil Mechanics (continued)

stress is proportional to strain (Hooke’s law) in an elastic solid. But if you try this with, say, a steel spring, it will obey Hooke’s law for only a finite range, then deform plastically, then break. So: elastic, then plastic, then shear.

Boussinesq equation - purely elastic, developed for stress at a point, can be used for stress over an area if you assume superposition.

60 degree approximation

application: don’t undermine your foundation.

how do you measure shear?

In the lab:

Direct shear

triaxial

In the field:

Shear vane

penetrometer: not really shear, but penetrometer ~ plant root. In other words, suitability for plants. Why are the mechanisms different?

compaction versus consolidation

Compaction: the soil is reduced in volume and air moves out.

Consolidation: the soil is reduced in volume and water moves out.

Why is the difference important?

σ_t = σ_e + p: if soil is saturated before compression, some of the stress is borne by the water, so the soil itself is not stressed as much.

The water will leave over time, and the load will be shifted to the soil. This is how buildings settle over time.

“Optimum water content” for compressability - Proctor test:

some water lubricates the particles, allowing compaction

too much water bears the stress, slows compaction

: so Proctor test is for short times - unlike a building.

Proctor test at different levels of energy

Maximum compression: great for foundations, precisely wrong for tillage

The big picture: like pulling on a spring, compaction of soil typically leads first to elastic deformation, then plastic, then shear.

This is shown in the diagram below. Notice the axes: log(stress) versus void ratio.

A: Elastic deformation range. If stress is released, the void ratio will return to its original state alone the same line (that’s part of the definition of elastic).

B: The transition from elastic to plastic: the angle changes. Now the soil is encountering stress greater than it had experienced before. The line below this is sometimes called the “virgin compression line” to emphasize that.

C: A hysteresis loop. When stress is relieved, the void ratio won’t return along the original line (so it’s not elastic). But it’s not plastic either, or it would go straight to the left (change in stress, but no change in void ratio). This intermediate state is called elasto-plastic.

D: The soil fails.