**2. Theoretical and practical background**

Different rocks and rock masses respond in different ways over time. The main factor that controls their behavior is geology. The mineralogical content and the geological structure impact rocks' mechanical behavior; ultimately, the stress regime and the environmental conditions also influence the rock materials' behavior. **Figure 3** provides a roadmap on the material's anticipated mechanical behavior grouped into ductile or brittle behavior based on the conditions the material is initially formed. In general, as the temperature and confining pressure increase, the rock transitions from brittle to ductile (**Figure 3a**). Brittle materials tend to abruptly fail as the stress approaches their short-term strength, and as such, they absorb less energy. In contrast, ductile materials can sustain an applied stress state through more deformation (**Figure 3b** and **c**). When ductile materials (i.e. rock salt or potash) are subjected to constant differential stress below their nominal yield strength, they can behave as visco-elastic materials and further deform as time elapses (**Figure 3d** and **e**). In contrast, brittle materials (i.e., granite or limestone) under similar stress conditions may only exhibit micro-crack damage with progressive crack propagation that results in the eventual interaction of the previously isolated microcracks, which leads to sudden failure (**Figure 3d** and **e**).

#### **Figure 3.**

*Schematic illustration and comparison between brittle and ductile rock materials, (a) transition from brittle to ductile behavior according to confining pressure and temperature conditions; (b) absorbed energy and temperature; (c) general stress – Strain behavior of brittle and ductile materials; (d) stain- rate and time relationship of brittle and ductile materials subjected to constant stress exhibiting creep, and (e) examples of brittle limestone and ductile potash before and after static load (creep) tests.*

### **2.1 Time-dependent phenomena**

Time-dependency refers to the deformation of rock (or other materials) over time. Mechanisms deforming or weakening the rock mass over time are called timedependent phenomena. Since the late 1930s, researchers started investigating the effect of time in rock behavior, trying to apply the theory of creep widely studied and reported on metals [10] to rock behavior. It was not until 1939 when Griggs [11] undertook laboratory experiments to examine the phenomenon of creep of rocks. He constructed two apparatus and performed tests on limestone, anhydride, shale and chalk. He also examined recrystallization under creep conditions at high pressure. At the excavation scale, addressing the effect of time in tunneling and mining engineering has been studied since the 1950s. Researchers introduced the idea of 'stand-up time' in tunnel stability. The 'stand up time', a reflection of timedependent weakening, was also included in the rock mass classification systems [12–14], emphasizing time and its effects by producing charts illustrating the time frame of stable unsupported spans. Since the 1960s many researchers [15–25] have investigated the influence of time on the long-term strength of rock by performing laboratory testing on rock samples, typically using static load (creep) tests by sustaining a constant stress condition. Creep phenomenon is most commonly applied to the study of soft, mono-mineralic rocks such as halite, potash, and limestone [26]. Following this practice, new constitutive and numerical time-dependent models were introduced based on the experimental results and data [27–31]. These models attempt to capture and reproduce the behavior of laboratory tests on the rocks, including time.

In practice, as previously mentioned, there is often a miscomprehension and misinterpretation of the different time-dependent phenomena and the mechanisms acting and resulting in weakening rock and the rock mass over time [9]. This section serves as an attempt to redefine and describe the various mechanisms that can appear to be time-dependent under the appropriate conditions using the composite

*Time-Dependent Behavior of Rock Materials DOI: http://dx.doi.org/10.5772/intechopen.96997*

#### **Figure 4.**

*Nomenclature, defining time-dependent phenomena and the conditions and mechanisms that affect and govern the rock behavior [9].*

nomenclature shown in **Figure 4**. The phenomenon can be either due to a statechange (i.e. stress decrease) or a property-change (i.e. decrease in cohesion). These changes can be further categorized according to their reversibility or recoverability as elastic, inelastic, and irreversible and may increase to visco-elastic or viscoplastic strains. The physical response can be represented as creep (shear strain), contraction or dilation (volumetric strains) over time, as well as relaxation (reduction in shear stress under sustained strain) and degradation (strength loss) depending on loading and boundary conditions. The micro-mechanical mechanisms tend to vary according to the boundary conditions. For instance, the solid rheology (e.g. lattice distortion, dislocation slip, van der Vaal's bonds and/or solid diffusion) may be damaged by new cracks that initiate or pre-existing ones propagate while pores, grain boundaries, and pre-existing cracks creating discontinnuum elements. Besides, the physicochemical changes can be temporal, rheological, and chemical alterations in the micro-scale, leading to swelling, weakening, strain-softening, and hardening. The rate and the magnitude of the time-dependent performance of rock materials are controlled by other environmental, physical, and loading conditions (e.g. temperature, pressure, humidity, and confinement).

Time-dependent phenomena can be a combination of many factors that can result in various physical responses and act either simultaneously or individually. Differentiating and recognizing these phenomena can be a complicated process, and all components in **Figure 4** should be taken into account.

The overall physical response can be a combination/integration of the mechanisms that influence the long-term behavior of intact rock and rock masses and include:

• creep during which visco-elastic behavior governs where time-dependent, inelastic strains and 'indefinite' deformation occur and/or visco-plastic yield where time-dependent plastic strains occur that lead to permanent deformation.


## **2.2 Time-dependent laboratory tests**

Time-dependent behavior of rock materials is usually investigated in the labscale by performing static load (creep) and stress relaxation tests which can be done in uniaxial and triaxial compressive conditions.
