Effective Stress

From GEOtechref

Most analytical evaluations of soil properties, strengths and applications utilize the theory of effective stress. The effective stress is defined as the total stress minus the pore pressure...

$\sigma' = \sigma - u$

Where $\sigma'$ is the effective stress, $\sigma$ is the total stress, and $u$ is the pore pressure.

All three of these parameters depend on depth, that is, that they are functions of depth...

$\sigma'(z) = \sigma(z) - u(z)$

Where $z$ is the depth from some known and assumed datum, most commonly the ground surface.

Total Stress

The total stress is the stress felt by a soil particle at some depth from both soil and water, above and surrounding the soil particle. In general...

$\sigma(z) = \gamma \cdot z$

Where $\gamma$ is the total unit weight of the soil and $z$ is the depth.

However, because soil is inherently heterogenuous, the soil properties differ with depth, including unit weight. Therefore, a more general approach...

$\sigma(z) = \int_{0}^{Z} \gamma(z)\, dz$

Where $0$ is the starting depth (typically the ground surface) and $Z$ is the ultimate depth in question.

Pore Pressure

Similarly to its custom essay, the pore pressure is a function of depth...

$u(z) = \gamma_w \cdot z$

Where $\gamma_w$ is the unit weight of water, which can be assumed to remain constant.

In absence of a perched water table and/or confined aquifers the pore pressure increases linearly with depth from the water surface.

$u(z) = \int_{0}^{Z} \gamma_w\, dz$

Where $0$ is the depth of the water surface and $Z$ is the ultimate depth in question.

In the case of a confined aquifer, the starting depth $0$ should be the piezometric surface, which may or may not be above the ground surface. Read more about the reasons to buy essay papers

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Category: Soil Mechanics