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

116

Table 1 (continued). M-C peak and residual strength parameters along with the range of confining pressures. Rock type Rock code

Range of confining pressures (MPa)

Peak strength parameters

Residual strength parameters

φ (o)

(o)

S o (MPa)

S

φ R

oR (MPa)

Compact Limestone Compact Limestone Compact Limestone

S4 PAIAN S6-8 S4 THOR S3-4 S8 THOR S1-1 S4 SPAT S3-2 S8 RAF S2-2 S15 PAL S1-2 S2 SPAT S1-2 S9 PAL S2-2

3.0-22.1 2.4-25.1 2.0-18.1 1.1-9.3 3.0-11.0 0.6-15.0 2.5-10.0 3.2-10.0

27.3 24.8 18.1

30.4 36.4 29.5 35.1 35.6 37.8 34.6 33.4

6.1 8.2 ---- 1.8 2.1 2.8 3.1 1.8

41.3 36.9

----

Sandstone Sandstone Sandstone

9.5 7.4

42.1 44.2 42.6 40.9 40.5

15.9 11.6 14.7

Breccia Breccia

Peak strength data were proved to fit well with the M-C criterion, exhibiting a coefficient of determination ( r 2 ) greater than 0.93 in all cases. Some characteristic fit lines (dashed lines) from the three rock types are shown in Fig.2.

100 120 140 160 180 200

σ 1 = 3.3σ 3 +133.3

σ 1 = 4.1σ 3 +97.9

σ 1 = 4.2σ 3 +65

S15 PAL S1-2 S22 LAV S1-2 S1 SPAT S2-4 S3 MARK S1-3 S6 THOR S5-1

σ 1 (MPa)

0 20 40 60 80

σ 1 = 3.1σ 3 +53.6

σ 1 = 3.8σ 3 +18.3

0

5

10

15

20

25

σ 3 (MPa)

Fig. 2. Peak strength data along with their M-C fit lines.

Residual strength data also fits well, exhibiting a coefficient of determination ( r 2 ) greater than 0.92 in all the above cases. The derived strength envelope, however, seems to behave more or less in a non-linear fashion, as it can be seen in Fig.3b, where the peak and residual strength data along with their fit lines (dashed lines) of a sandstone sample, (S15 PAL S1-2), are shown. Through the above results it is obvious that in the residual state, the “apparent” cohesion was reduced dramatically, as it was expected, and the friction angle was increased. This is in accordance with a cohesion weakening-friction strengthening model for brittle rock failure, such as that proposed by Renani and Martin (2018). It should be noted that the cohesion value in the post-failure state of the specimens is used herein only to describe the M-C fit to the residual strength envelope over the used range of the confining pressure and not as an inherent property of the material.