# Creep Behavior of Rocks and Its Application to the Long-Term Stability of Deep Rock Tunnels
## 4 Introduction to Creep Test Methods, Monitoring Methods, and Data Processing  
According to the literature, creep properties of rocks are determined from different types of creep tests. Relaxation tests are also commonly employed to determine the creep properties of rocks [61]. All tests are performed under different experimental methods and conditions. The most widely employed experimental methods are indoor creep test methods which mainly include staged incremental loading, staged incremental loading and unloading, and separate loading methods. All the experimental methods are accompanied by monitoring methods. These aim to monitor the evolution of the characteristics of cracks and fractures, as well as the overall creep deformations of the rocks. Briefly, the most famous monitoring methods in this field are computed tomography, ultra-pulse wave velocity, scanning electron microscope, acoustic emission, etc. Each of these monitoring methods has particularities and limitations. The choice of a method mainly depends on the expected results and relevant conditions. For example, computed tomography is generally used to depict the microstructure and meso-structure of rock as well as to detect damage and fractures in rock specimens [70]. As the scan provided by computed tomography (CT) is a bit expensive, it is not commonly employed. Nevertheless, in order to detect experimental damage in rocks, most researchers mainly analyze rock samples before and after creep tests using CT scans. Rock degradation can be monitored using the ultra-pulse wave velocity by accumulating rock damage [71], but not in real time. Moreover, although scanning electron microscope method is quite accurate in detecting rock creep damage by analyzing the variation in rock microstructure [72], it cannot be used in real time. After a rupture due to rock creep, the characteristics of cracks and aperture can be recognized by means of scanning electron microscope [73]. Acoustic emission is typically used to track the progress of cracks and fractures in rocks, as well as to assess damage and strength [74]. Ordinarily, the creep characteristics of rocks are examined from different acoustic emission events. Thus, the acoustic emission method is widely used to study rock failure in different engineering applications [75]. However, despite the existence of several monitoring methods, it remains difficult to effectively monitor the characteristics and conditions of rock creep in real time. The data are usually processed to interpret the results of creep tests. Different methods are usually used to this purpose. The most common are Boltzmann's principle of superposition and viscoelastic-plastic stress separation. Boltzmann's principle of superposition is especially utilized in staged incremental loading, while viscoelastic-plastic stress separation is particularly associated with staged incremental loading and unloading. These methods are briefly presented herein. The Boltzmann principle of superposition consists in superimposing the deformations generated by different loads to obtain the total creep deformation. By applying to a rock specimen, a stress \(\sigma_{0}\) at the instant \(t=0\), its strain (\(\epsilon(t)\)) is given as follows:  
\[\varepsilon(t)=J(t)\sigma_{0} \tag{3}\]  
where \(J(t)\) is the creep compliance which represents the ratio between the creep strain and the applied differential stress [76; 77; 78]. As the experiment progresses, a supplemental stress \(\Delta\sigma\) is applied at \(t=t_{1}\). It should be noted that an additional strain is engendered when \(t>t_{1}\). In such situation, the total strain is accounted as follows:  
\[\varepsilon(t)=J(t)\sigma_{0}+J(t-t_{1})\Delta\sigma \tag{4}\]  
According to [PERSON]'s superposition principle, the calculation of the total creep strain can be generalized as follows:  
\[\varepsilon(t)=J(t)\sigma_{0}+\int_{0}^{t}J(t-t_{1})\frac{d\sigma}{dt_{1}}dt_{1} \tag{5}\]Stress is ordinarily considered a function \(\sigma\left(t\right)\) because it is applied variably and repeatedly over time.