In a broad sense, there are three elements of soil mechanics. This discipline involves an understanding of the different types of soil, such as sand, gravel, silt and clay. It includes knowing the different conditions these soils can be found in, whether dry or fully saturated. It also requires understanding how each type of soil behaves under each set of conditions. These elements gives engineers an understanding of how any type of soil will behave when put under a particular type of stress.
The study of how soil responds to stresses put upon it involves six elements. The internal friction of a soil helps determine how likely the soil is to slide. The cohesion, or stickiness, of soil is also a determining factor in the slide rate. A soil's compressibility measures how much a given force will cause it to compress. Elasticity determines how much soil will re-expand after compression. The rate at which soil draws up water from the water table, called capillarity, determines how wet the soil will get. Permeability measures how well a soil allows water to spread out.
An understanding of these six elements involves both physics and math. The mathematical elements of soil mechanics are algebra, trigonometry and calculus. Engineers use algebraic and trigonometric equations to model forces and conditions that soil is exposed to. They use calculus to determine how these relationships change over time. The calculus involved includes both derivative and integral calculus, along with an understanding of differential equations.
The fundamental physics elements of soil mechanics include Hooke's Law and Darcy's Law. Hooke's Law describes how different materials compress and expand under different pressures. Darcy's Law describes how water flows through soil. These principles involve such measurements as stress, strain, density and elastic constants. Wave mechanics is another form of physics necessary for soil mechanics as it is used to describe how seismic waves travel through soil.