Deviatoric stress

δσij is 2nd order tensor represented by a 3x3 matrix of form:

σ11-σm σ12 σ13
σ21 σ22-σm σ23
σ31 σ32 σ33-σm

with six independent stress parameters (σ12 = σ21, σ13 = σ31, σ23 = σ32) and

σm = (σ11 + σ22 + σ33)/3

In a triaxial test it is possible to arrange the stress components in a way that the diagonal stress components σ11, σ22 and σ33 are oriented parallel to the applied Cartesian coordinate system. Consequently, these three stress components become the principal stresses σ1, σ2 and σ3 and the off-diagonal components equal zero. Therefore, in a laboratory situation the deviatoric stress tensor [δσij] can be simplified to:

σ1-σm 0 0
0 σ2-σm 0
0 0 σ3-σm

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 S1 and the minimum principal stress S3.

ΔS = S1 - S3

is also the diameter of a Mohr circle.

Effective stress

σij (with i=j and the main principle stresses σ1 ≥ σ2 ≥ σ3) is the difference between the applied external stress Sij and the pore pressure Pp. In its simple form (Terzaghi 1923):

σij = Sij - δijPp

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:

σij = Sij - δijαPp.

Entry pressure

See "Threshold pressure"



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.

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.