# Deviatoric stress

*δσ _{ij}* is 2

^{nd}order tensor represented by a 3x3 matrix of form:

σ_{11}-σ_{m} |
σ_{12} |
σ_{13} |

σ_{21} |
σ_{22}-σ_{m} |
σ_{23} |

σ_{31} |
σ_{32} |
σ_{33}-σ_{m} |

with
six independent stress parameters (*σ _{12} = σ_{21}, σ_{13} = σ_{31}, σ_{23} = σ_{32}*) and

*σ _{m} = (σ_{11} + σ_{22} + σ_{33})/3*

In
a triaxial test it is possible to arrange the stress components in a way that
the diagonal stress components *σ _{11}, σ_{22}* and

*σ*are oriented parallel to the applied Cartesian coordinate system. Consequently, these three stress components become the principal stresses

_{33}*σ*and

_{1}, σ_{2}*σ*and the off-diagonal components equal zero. Therefore, in a laboratory situation the deviatoric stress tensor

_{3}*[δσ*can be simplified to:

_{ij}]σ_{1}-σ_{m} |
_{0} |
_{0} |

_{0} |
σ_{2}-σ_{m} |
_{0} |

_{0} |
_{0} |
σ_{3}-σ_{m} |

According
to **Engelder (1994)** deviatoric stress is very often confused with other types of
stresses such as **differential stress** and **effective stress**. **Engelder (1994)** recommends
not to use the term “deviatoric stress” unless for fault slip problems.

# Differential stress

*ΔS* is the difference between the maximum principal stress *S _{1}*
and the minimum principal stress

*S*.

_{3}*ΔS = S_{1} - S_{3}*

is also the diameter of a Mohr circle.

# Effective stress

*σ _{ij}* (with

*i*=

*j*and the main principle stresses

*σ*

_{1}≥ σ_{2}≥ σ_{3}) is the difference between the applied external stress

*S*and the pore pressure

_{ij}*P*. In its simple form (

_{p}**Terzaghi 1923**):

*σ _{ij }= S_{ij }- δ_{ij}P_{p}*

it denies the importance of pore volume and
its compressibility by disregarding the **Biot coefficient** *α*. This equaition is applied generally in soil mechanics where full
efficacy of pore pressure (i.e. *α* =
1) can be assumed.

In case of solid rock things appear more
complicated and pore pressure efficacy never is at 100%. Consequently, the **Biot
coefficient** has to be considered and the exact form of the equation according to
**Nur & Byerlee 1971** is:

*σ _{ij }= S_{ij }- δ_{ij}αP_{p}*.

# Entry pressure

See "**Threshold pressure**"

# News

## Tests results for the first deep borehole Bülach are now published on NAGRA's website

In September 2019 the Swiss National Cooperative for the Disposal of Radioactive Waste (NAGRA) commisioned Gesteinslabor with UCS, Brazilian and triaxial tests on neighbouring rocks of the Opalinus Clay - the rock which will host Switzerland's future facilities for nuclear waste disposal.

Read more … Tests results for the first deep borehole Bülach are now published on NAGRA's website

## Gesteinslabor receives funding grant for the development of a novel test rig to determine capillary threshold pressure with hydrogen

Gesteinslabor receives funding from BMWi for the development of a new test rig. With this funding, our company will open up a new business field in renewable energies by implementing an innovative technology to determine the **capillary threshold pressure with hydrogen** on cap rock of underground gas storage facilities.