*3.2.1 Defining the three stages of stress relaxation*

All the single-step test results showed a similar behavior during stress relaxation for both the limestones. This behavior can be characterized by three distinct stages, which were observed in the stress relaxation versus time graphs. An example of the test results is illustrated in **Figure 12**. The three stages can also be observed in the radial strain response with time, although there is a slight delay during the transition from stage to stage compared to the transition time of the stress relaxation shown as dt in **Figures 12** and **13**.

#### **Figure 11.**

*Maximum stress–relaxation (MPa) to driving stress-ratio normalized to UCS of the single-step tests on the Jurassic and Cobourg samples, as well as the multi-step tests of the Jurassic samples. 'Ax' refers to axial straincontrolled conditions and 'ss' and 'ms' denotes single-step load and multi-step load tests, respectively.*

**Figure 12.**

*The three stages of the stress relaxation process during a relaxation test under axial strain-controlled conditions illustrated on the Jura\_33R sample.*

When the axial deformation is kept constant, the stress relaxes at a decreasing rate; this period is defined as the first stage of stress relaxation (RI). At the end of this stage, the stress decrease approaches a constant rate, which marks the second stage transition (RII). The third stage of relaxation (RIII) follows where no further stress relaxation is measurable. At this stage, the stress reaches an asymptote, and the stress relaxation process is effectively complete, which others have observed [19]. Some samples did not exhibit the second stage of relaxation (RII), and in the first stage, 55% to 95% of the total stress relaxation takes place.

The radial strain does not always reach an asymptote. In this case the material is subject to a practically constant axial stress state with ongoing additional absolute radial strain decrease. This response is possibly related to a combination of threedimensional visco-elastic response and crack behavior during stable propagation (in the axial direction) under constant axial strain.

The significance of this scientific observation should be considered during the excavation of an underground opening. Energy release and stress relaxation in such conditions commonly take place at the face of the excavated tunnel. The created free space disturbs the stress regime of the in-situ conditions. For the stress to re-distribute itself to a new equilibrium state, the rock mass tends to "relax" through the structural geological imperfections (i.e. discontinuities, fractures, joints) of the surrounding rock mass or the newly created fractures due to the excavation method and techniques used. In relation to the scientific observation of the three stages (**Figure 14**), it would be expected that the rock mass would relax in distinct but possibly overlapping stages. This can serve as an explanation of the sound of cracking closer to the tunnel face without observed failure. Another component of stress relaxation is the duration of this phenomenon until it is terminated. Knowing the duration of stress relaxation can be valuable in the support design and the installation timing, avoiding safety implications arising from support overstressing or resulting in cost savings.
