PSI - Issue 10

D. Kotsanis et al. / Procedia Structural Integrity 10 (2018) 112–119 D. Kotsanis et al. / Structural Integrity Procedia 00 (2018) 000 – 000

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At this point, it should be emphasized that the choice of the imminent point of failure was in line with the capabilities of our experimental configuration and therefore it was determined as the point where the slope of the axial load-displacement curve became zero.

100 120 140 160 180

100 120 140 160 180

4 th imminent failure point

Peak strength

Peak strength

Residual strength

3 nd imminent failure point

4 th imminent failure point

3 nd imminent failure point

0 20 40 60 80

0 20 40 60 80

Unloading path

Unloading

2 nd imminent failure point

2 nd imminent failure point

AXIAL STRESS (MPa)

AXIAL STRESS (MPa)

1 st imminent failure point

1 st imminent failure point

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5

10

15

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25

0

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(a)

(b)

CONFINING PRESSURE (MPa)

AXIAL DISPLACEMENT ( μ m)

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Fig. 1. (a) Stress path of a multi - stage triaxial test; (b) Axial stress – displacement curves of a multi - stage triaxial test.

4. Failure criteria

In the present work, two failure criteria were considered and shortly discussed in the next section. Their mathemat ical formulations are given in terms of the maximum and the minimum principal stresses, σ 1 and σ 3 , respectively. 4.1. Mohr – Coulomb failure criterion The Mohr-Coulomb (M-C) failure criterion, widely applied in geotechnical practice, can be expressed as follows: σ 1 =k σ 3 +C o =(1+sin φ )/(1-sin φ ) σ 3 +2S o cos φ /(1-sin φ ) (1) where φ and S o represent the internal friction angle and cohesion of the intact rock specimen, respectively. The uniaxial compressive strength of the tested material is given by the constant C o , while k is the slope of the failure envelope in the principal stresses σ 1 - σ 3 space. According to Labuz and Zang (2012), the applicability of this criterion is justified due to its simplicity and ease of use of its mathematical expression, as well as, the clear physical meaning of the derived strength parameters. The Hoek-Brown (H-B) failure criterion is an empirical failure criterion and describes the non-linear increase of the maximum strength of the intact rock when the confining compressive pressure is increased. The derived strength envelope is parabolic, a feature that distinguishes this model from the linear M-C criterion. This criterion was developed by Hoek and Brown (1980), in their effort to adjust a number of mathematical expressions of parabolic type to a large dataset which was obtained from triaxial tests that were conducted on various rock types. The strength envelope of the Hoek – Brown failure criterion for the intact rock, according to Eberhardt (2012), is represented by: σ 1 = σ 3 + C o ( m i σ 3 / C o +1) 0.5 (2) Where C o is the uniaxial compressive strength and m i is a dimensionless empirical constant which is related upon the mineral composition and a number of inherent characteristics of the tested material, like the shape, size and any 4.2. Hoek – Brown failure criterion