**3.3 Static load testing series**

Single-step static load tests were conducted on 10 Jurassic, and 4 Cobourg samples and they were held at stress levels above CI for seconds to several days

#### **Figure 14.**

*The three stages of the stress relaxation process during a relaxation test under axial-strain–strain-controlled conditions and the response of the material during each stage, dashed lines on the right photo show axial stabilization of damage.*

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

until failure occurred. Most of the single-step tests failed within the first few hours. Several samples did not fail after several days to weeks, at which time the test was terminated. While more practical and convenient, the single-step tests require the testing of more specimens to fully cover the spectrum of the expected range of time to failure. Multi-step tests were performed on three samples, 2 Jurassic and 1 Cobourg, to compare with stress levels derived from the single-step tests. The stress difference between the steps (varying between 2–4) was 5 MPa, and the duration of each step varied from 1 hour up to 10 days until failure took place. A few Jurassic samples did not fail, and it was decided to terminate these tests and unload the samples. To examine the long-term strength and time to failure of a material, the specimens need to fail under a constant load.

The static load testing began at load levels close to the peak strength, based on the Baseline Test results. Subsequent tests were conducted at lower driving stress levels approaching CD and below. In these tests, the constant target stress is applied and maintained by controlling the axial load while measuring the strains (axial and lateral) that increase as the sample proceeds toward failure. Samples loaded close to the peak strength fail catastrophically into many fragments, while samples loaded closer to CD fail less violently. Selected results are presented in this section, serving as examples to describe the main influencing factors during the two limestone tests' creep process.

Two aspects of time-dependency were examined: the first was to derive visco-elastic (creep) parameters for use in the Burgers model (or related models), and the second, the time to failure. Samples that did not fail were also examined to assess the potential reason why some samples fail, and others do not, even at the same driving stress-ratio. For this reason, this section focuses on analyzing and comparing the data from this testing series to other data available in the literature.

However, during the loading phase, the properties of the sample can be determined, such as the stiffness or the damage thresholds. The steps of the analysis procedure were:


All the results presented refer to unconfined conditions.

### *3.3.1 Estimating the driving stress-ratio*

In the literature, most of the testing results are presented in the form of time against the driving-stress-ratio, defined and used as the stress normalized by the strength of the sample. In most cases, the UCS is taken as an average value from standard UCS tests. In this section, a new solution is presented to examine similar datasets.

[45] suggested that there is a consistent relationship between UCS and CI for brittle rocks. The author has found this to be true for a number of test series with similar lithologies and compatible testing protocols [46]. It was decided to convert the CI values from this study's static load tests to an equivalent UCS value. The CI and UCS values from the Baseline testing series for the two types of limestone were used to develop the conversion factor (here: 2.66 for Jurassic and 2.52 for Cobourg), shown in **Figure 15**. The conversion factors were multiplied with the CI values estimated from the loading portion of the static load test for each sample. [26] suggested that the modified UCS\* can be calculated using Eqs. (3) and (4):

$$UCS^\* = a\*CI \tag{3}$$

$$\mathfrak{a} = \frac{\text{UCS}^{\mathcal{B}}}{\text{CI}^{\mathcal{B}}} \tag{4}$$

where: UCS\* is the estimated UCS, CI is the Crack Initiation value derived from the static load test, α is a constant and describes the slope of the CI versus UCS graph, and the superscript B denotes values from the Baseline Testing.

When the data (red circles and squares) are compared with other static load test results from various rock types, the time to failure of the samples from this

#### **Figure 16.**

*Static load test data for hard rocks performed at room temperature in wet or dry conditions (where the driving stress-ratio is the stress level at failure to unconfined compressive strength of the material).*

study seems to follow a similar trend (**Figure 16**). There are no samples loaded below the CI threshold that fail from the data presented and gathered from the literature.

**Figure 17** categorizes the data according to the main rock type, sedimentary, metamorphic, and igneous.

The sedimentary rocks appear to follow a similar trend with the metamorphic rocks. In contrast, igneous rocks show more scatter because most test results have been on igneous rocks and that there are fewer results on sedimentary and metamorphic. There could also be due to different grain sizes of the granitic rocks tested characterized by grain-scale heterogeneity.

Granites and limestones, even though they fail similarly following brittle failure theory principles, their long-term strength is directly dependent on lithology, as better shown in **Figure 18**. Due to heterogeneous mineralogy and their different intrinsic properties, granitic rocks allow other creep behavior within different constituent crystal grains. Steady creep creates mechanical conflicts between the different grains and damage results. This creep-induced damage process is less dominant in monominerallic limestones, and therefore creep can occur with less resultant weakening.

Differences in the trend start to emerge when examining individual sample sets. The latter is partly because there is a lack of statistically representative data sets on an individual sample set, except the lac du bonnet set.

From **Figure 19**, it is evident that above 0.8 ucs or the cd threshold, all samples failed within an hour. Below the ci threshold, where pre-existing cracks are closing, and elastic strains govern, no failure should occur as [47, 48] reported from testing cobourg limestone samples for up to 100 days. Commonly, the static load stress levels fall between the ci and the cd thresholds. This region is an uncertain region since between ci and cd crack propagation, and accumulation of damage occurs in the short-term. Still, in the long-term, the time component can degrade the rock,

further leading it to failure. However, below 0.7 ucs, no failure is shown. These nofailure points could be the result of not holding the load constant for long enough. Data from the literature suggests that failure could be expected at such driving stress-ratios. Tests from 6 months to 1 year are advised to examine if samples of the limestones in this study would fail at such driving stress-ratios over the long-term. The time-dependent behavior discussed in this section is interpreted to be, in part, the result of the behavior of new microcracks, the intensity of which impacts the final ucs value [49].

#### **Figure 17.**

*Static load test data for: (a) sedimentary, (b) metamorphic, (c) igneous rocks performed at room temperature in wet or dry conditions (where the driving stress-ratio is the stress level at failure to unconfined compressive strength of the material).*

#### **Figure 18.**

*comparison of static load test data on limestone and granite performed at room temperature in dry conditions (where the driving stress-ratio is the stress level at failure to unconfined compressive strength of the material).*

#### **Figure 19.**

*static load test data of jurassic and cobourg limestone performed at room temperature in dry conditions (where the driving stress-ratio is the stress level at failure to unconfined compressive strength of the material). The 'nf' in the legend indicates samples or tests did not fail whereas the 'f' denotes samples or tests reach failure.*
