**5. Creep tests (materials and experimental program)**

Creep is an irreversible ductile deformation in time under constant stress. Creep strain seldom can be recovered fully when the loads are removed, thus it is largely

*Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone… DOI: http://dx.doi.org/10.5772/intechopen.91720*

"plastic deformation." It is a progressive phenomenon initiated at a certain time after excavation at a certain location around the profile and spreading in time into the rock mass. For the long-duration design life of underground structures, the long-term stability of the tunnel must receive major consideration. For this reason, time-dependent deformation behavior of the surrounding rock must be well understood. Neglecting creep effects during deep excavation may lead to incorrect evaluation of deformation and thus may impact on the criteria for selection of proper design.

Understanding the mechanisms of rock breakdown that have been excavated within ancient monuments requires a thorough study of the mechanical behavior of these rocks, and the importance of the physical and mechanical properties of these rocks to understand the phenomena of instability.

The results of the geotechnical characterization of these rocks will be used in numerical modeling and design of reinforcement measures. For this purpose, a new laboratory testing program will be launched.

Rocks, sample preparation, experimental setup used and the procedure are briefly described below.

#### **5.1 Types of creep**

An idealized creep curve for rock at constant stress consists of three stages: instantaneous elastic strain followed by primary creep with decreasing creep rate, then steady-state creep with constant creep rate, and finally tertiary creep with increasing creep rate leading to failure. Most of the work on time-dependent strain has been conducted on primary and secondary creep phases only and the tertiary phase has not been investigated in appreciable detail.

#### **5.2 Laboratory test specimens**

In this study, the size of the comprehensive laboratory testing program using cylindrical samples with 42-44 mm diameter and height (91–103 mm). Although these rocks do not show distinct layers, the nuclei were extracted from the blocks and their masses in the vertical direction, which was expected to represent the physical properties of these units perpendicular to the layers. However, some samples were also extracted in a vertical direction on the mattress. Some specimens were broken and/or small cracks or cracks appeared on their surfaces. However, in order to achieve reliable assessments, the number of samples was increased as many as possible. Laboratory tests were performed in accordance with the testing procedures proposed ISRM and recommended by ASTM at the Engineering Geology Laboratory, Department of Civil Engineering, University of Aristotle Thessaloniki, Greece.

#### **5.3 Laboratory tests**

Laboratory studies (experimental examination) were performed on surface rock samples and prepared surfaces. The basic mechanical testing of the laboratory includes the behavior of deformation to failure under uniaxial and triaxial compression and we offer a complete creeping rock characterization conducted during the past 2 years from a series of isotropic and isotropic compression tests conducted in the inventory of various stresses, viscosity behavior was determined by following a procedure, the multi-step download, which emphasizes the transit creep side.

Data from microscopic polarization and electron microscopy experiments show that oxygen clarity of NaCl crystals is strongly influenced by the rate and volume of

*(a, b) Photomicrograph of fossiliferous oolitic intraclastic limestone thin section under cross-polarized light (XPL) showing subrounded monocrystalline quartz grains (QTZ) and porous region, El-Shatby Necropolis.*

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

Creep is an irreversible ductile deformation in time under constant stress. Creep strain seldom can be recovered fully when the loads are removed, thus it is largely

moisture changes, and how they shrink with changes in crystal size.

**5. Creep tests (materials and experimental program)**

**Figure 5.**

**22**

## **5.4 Very slow uniaxial creep tests on calcarenitic and sandy oolitic rock specimens under investigation**

Creep in hard brittle rocks is rare as deformation rate is extremely slow. Hard rock shows creep behavior appreciably only at elevated temperatures and pressures generally not encountered in engineering structures. Soft rocks on the other hand creep mostly at the room temperature, atmospheric pressure, and deviatoric stress range normally encountered in engineering structures.

Partial damage was used to explain the reduction of seismic wave velocity, earthquake variation, reduction of elasticity and strength units, and rock failure mechanics. In addition, stress damage can facilitate time-based creep-driven by stress erosion and subcritical crack growth. This creep strongly affects long-term strength and failure stability. For example, granite samples that are exposed to 1 month of nonaxial static pressure under a pressure of approximately 0.65 may fail—or "delayed

*Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone…*

*DOI: http://dx.doi.org/10.5772/intechopen.91720*

The creep test shows how strain builds up over time under constant pressure. The rock usually deforms quickly and then begins to deform more slowly after the yield fatigue, which is called the initial creep. After the initial creep (I), the deformation continues at a constant rate in the linear part of the curve, which is secondary creep (II). Finally, the deformation rate increases rapidly until the rock fails to "fracture" in

fractures" may develop days to years after removal of applicable loads.

the high creep (III), if stress is removed but the strain remains permanent. Three stages of creep behavior can be identified: in the first stage, they are classified as initial creep, and strain occurs at a decreasing rate. In some cases, the primary creep curve approaches a constant rate of strain called secondary creep. In high-stress specimens, secondary creep may turn up in higher creep, which is characterized by an increased strain rate until creep failure occurs suddenly. In the last two stages, the thin vertical cracking begins, accompanied by hardening, and only near failure, large cracks spread rapidly and lead to a sudden collapse. Long-term tests performed on a secondary creep sample revealed even appearance at 40% of estimated strength. The purpose of this research is to make recommendations on the promotion and safety of long-term underground historical structures under load. For this purpose, there is a set of experimental tests and advanced numerical analyses.

**6. Description and discussion of the experimental program**

The research demonstrates an integrated empirical approach aimed at assessing

Long-range uniaxial creep tests were performed on standard cylindrical rock samples collected from the three archeological sites under investigation (diameter D = 4.2–4.4 mm, height H = 90–103 mm); samples were prepared for testing according to ASTM standards with length-to-diameter ratios approximately 2.25, all samples have highly polished end surfaces to minimize final effects. The sample was set between two solid steel plates, with a steel cover between the sample and the two plates. During each test, two high-precision displacement sensors at two vertical levels at a 90° angle allowed both the relative rotation of the two pages and the

Applied loads and the resulting strain were recorded using an automatic data acquisition system, sampling at a rate between 1 and 3 readings per second, thereby

safety and strengthening historic underground structures under high pressure. The purpose of these tests is to obtain data, first, to determine the amount of sticky parameters that govern the long-term behavior of these structures, and

**6.1 Describe full creep tests**

**6.2 Testing device**

**6.3 Sensors**

**25**

secondly, to validate numerical models.

measurement of the average relative displacement.

overcoming any deficiencies in data resolution.

#### **5.5 Analysis of creep behavior of soft rocks in tunneling**

Regarding viscous plasticity, despite much work done on high porous rocks, only over the past years, there has been growing concern about the long-term behavior of deep underground structures in general. The rock mass tests large strain rates of viscosity and plastic. However, after a few years, the stress rates become smaller and reach a fairly stable condition characterized by very small stress rates.

It is known that most rocks have time-dependent behavior, and the viscous and plastic modeling of rocks and soils is of great importance both in petroleum engineering and underground engineering, for example when assessing deformations at the walls of deep fossil sections or considering pressure problems.

Moreover, when smaller time periods are considered, the stress distribution around a cave or exposures is such that the divergent pressure decreases rapidly with respect to the distance to the cave. Very small stress rates are tested at large distances within the rock mass and should be evaluated when predicting the behavior of the cave or photo gallery [40].

The limited available literature may be rooted in the particular problems raised by the long-term creep test, in the short term, as described below.


Tightening of fragile rocks results in distributed damage long before the rocks fail unstable. The damage is usually manifested in small fractures and expansive microcracks [41–43]. These small fractions are usually smaller than the grain size and are often distributed almost uniformly before they are locally cracked. There are no uniform distributions of small fractions associated with the nucleus of error and growth.

#### *Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone… DOI: http://dx.doi.org/10.5772/intechopen.91720*

Partial damage was used to explain the reduction of seismic wave velocity, earthquake variation, reduction of elasticity and strength units, and rock failure mechanics. In addition, stress damage can facilitate time-based creep-driven by stress erosion and subcritical crack growth. This creep strongly affects long-term strength and failure stability. For example, granite samples that are exposed to 1 month of nonaxial static pressure under a pressure of approximately 0.65 may fail—or "delayed fractures" may develop days to years after removal of applicable loads.

The creep test shows how strain builds up over time under constant pressure. The rock usually deforms quickly and then begins to deform more slowly after the yield fatigue, which is called the initial creep. After the initial creep (I), the deformation continues at a constant rate in the linear part of the curve, which is secondary creep (II). Finally, the deformation rate increases rapidly until the rock fails to "fracture" in the high creep (III), if stress is removed but the strain remains permanent.

Three stages of creep behavior can be identified: in the first stage, they are classified as initial creep, and strain occurs at a decreasing rate. In some cases, the primary creep curve approaches a constant rate of strain called secondary creep. In high-stress specimens, secondary creep may turn up in higher creep, which is characterized by an increased strain rate until creep failure occurs suddenly. In the last two stages, the thin vertical cracking begins, accompanied by hardening, and only near failure, large cracks spread rapidly and lead to a sudden collapse. Long-term tests performed on a secondary creep sample revealed even appearance at 40% of estimated strength. The purpose of this research is to make recommendations on the promotion and safety of long-term underground historical structures under load. For this purpose, there is a set of experimental tests and advanced numerical analyses.

## **6. Description and discussion of the experimental program**

#### **6.1 Describe full creep tests**

The research demonstrates an integrated empirical approach aimed at assessing safety and strengthening historic underground structures under high pressure.

The purpose of these tests is to obtain data, first, to determine the amount of sticky parameters that govern the long-term behavior of these structures, and secondly, to validate numerical models.

#### **6.2 Testing device**

**5.4 Very slow uniaxial creep tests on calcarenitic and sandy oolitic rock**

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

Creep in hard brittle rocks is rare as deformation rate is extremely slow. Hard rock shows creep behavior appreciably only at elevated temperatures and pressures generally not encountered in engineering structures. Soft rocks on the other hand creep mostly at the room temperature, atmospheric pressure, and deviatoric stress

Regarding viscous plasticity, despite much work done on high porous rocks, only over the past years, there has been growing concern about the long-term behavior of deep underground structures in general. The rock mass tests large strain rates of viscosity and plastic. However, after a few years, the stress rates become smaller and reach a fairly stable condition characterized by very small stress rates. It is known that most rocks have time-dependent behavior, and the viscous and plastic modeling of rocks and soils is of great importance both in petroleum engineering and underground engineering, for example when assessing deformations at

Moreover, when smaller time periods are considered, the stress distribution around a cave or exposures is such that the divergent pressure decreases rapidly with respect to the distance to the cave. Very small stress rates are tested at large distances within the rock mass and should be evaluated when predicting the

The limited available literature may be rooted in the particular problems raised

1

. The coefficient of thermal expansion of rocks is in order

sample) due to small temperature changes will be greater, in most cases, than the signal to be measured (e.g., the average sample deformation arose from proper creep). The same can be said for moisture variations, which have a

2. Slow creep rates are obtained when small mechanical loads are applied. Most of the crawl test devices are designed to work in a DVR pressure range of 5–20 MPa. Stress control is usually weak when the applied pressure is less than

3.The creep rate is calculated by comparing strains ε1, measured in two different times, τ<sup>1</sup> and τ2, or ε.=(ε<sup>2</sup> ε1)/(τ<sup>2</sup> τ1). When the compression rate is in

accuracy of not less than 10.8, or one-tenth of the expected difference between

Tightening of fragile rocks results in distributed damage long before the rocks fail unstable. The damage is usually manifested in small fractures and expansive microcracks [41–43]. These small fractions are usually smaller than the grain size and are often distributed almost uniformly before they are locally cracked. There are no uniform distributions of small fractions associated with the nucleus

, that is, the "noise" (i.e., elastic thermal deformation

, it can be reasonably evaluated on a daily basis

) only if ε<sup>1</sup> and ε<sup>2</sup> can be measured with an

, a 12-day test results in a strain of

**specimens under investigation**

behavior of the cave or photo gallery [40].

1.When the creep rate is 10 = 10<sup>12</sup> s

significant impact on many rocks.

1

the two successive measured breeds [40].

ε = 10<sup>6</sup>

1 MPa.

of error and growth.

**24**

<sup>α</sup> = 1<sup>4</sup> <sup>10</sup><sup>5</sup> <sup>C</sup><sup>1</sup>

the range ε = 10<sup>12</sup> s

(t2 t1 = 105 s, <sup>ε</sup><sup>2</sup> <sup>ε</sup><sup>1</sup> = 10<sup>7</sup>

range normally encountered in engineering structures.

**5.5 Analysis of creep behavior of soft rocks in tunneling**

the walls of deep fossil sections or considering pressure problems.

by the long-term creep test, in the short term, as described below.

Long-range uniaxial creep tests were performed on standard cylindrical rock samples collected from the three archeological sites under investigation (diameter D = 4.2–4.4 mm, height H = 90–103 mm); samples were prepared for testing according to ASTM standards with length-to-diameter ratios approximately 2.25, all samples have highly polished end surfaces to minimize final effects. The sample was set between two solid steel plates, with a steel cover between the sample and the two plates. During each test, two high-precision displacement sensors at two vertical levels at a 90° angle allowed both the relative rotation of the two pages and the measurement of the average relative displacement.

#### **6.3 Sensors**

Applied loads and the resulting strain were recorded using an automatic data acquisition system, sampling at a rate between 1 and 3 readings per second, thereby overcoming any deficiencies in data resolution.

#### **6.4 Loading**

The approved test procedure consisted of loading samples at a constant rate of about 1.35 MPa up to 1.75 MPa for samples from Catacomb in Kom El-Shoqafa, 1.55 MPa up to 2.17 MPa for samples from Mustafa Kamel Necropolis, and 2.6 MPa up to 3.44 MPa for samples from El-Shatby cemetery. In order to keep the applied pressure as stable as possible, dead weights were used and steel cylinders were placed on the upper steel plate on the upper face of the cylindrical sample. The applied stress is calculated by dividing the weight of the steel cylinders placed on the top plate by the initial cross-sectional area of the sample.

#### **6.5 Temperature and hygrometry**

The temperature changes during a long-term creep test must be as a small as possible and must be measured precisely enough to allow correction of the raw strain data for thermoelastic strains; in our study, all the periods of test were in the room temperature between 24 and 26° in the laboratory by controlling the air condition.

### **7. Test results**

Uniaxial creep tests were performed on three rock samples from each site. Rock samples are loaded through fixed uniaxial compression at 1, 35, 1, and 75 MPa (one stress per sample) for Catacomb of Kom El-Shoqafa rock samples collected, at 2.6 and 3.44 MPa for rock samples collected from El-Shatby archeological site, and at 1.55 and 2.17 MPa for rock samples collected from Mustafa Kamel Necropolis.

The experimental procedure follows ASTM standards (ASTM D4405 and D4341). The compression machine is used to apply continuous axial load to the samples. Digital scales are installed at 0.001 millimeters to measure the axial displacement of the samples, see **Figures 6**–**9**. Samples are loaded continuously for 1 to 2 years until the samples fail without any acceleration, depending on the displacement results. During testing, axial distortion, time, and failure modes are recorded. The readings are repeated every minute at the beginning of the test, and gradually decrease to twice a day after the first few days of testing. This also depends on the deformation rate of each sample. The results are presented by strain time curves. Axial stress and axial pressure values are calculated by:

$$
\sigma\_{\text{axial}} = \mathbf{P} \mathbf{a} / \mathbf{A},
\tag{1}
$$

pressures. Axial stress also increases crawling strains. In the transit crawl stage, the stress rate increases with the applied stressors. In most cases, the stress rate under high axial pressure is greater than the low axial pressure rate. The effect of embedding in the sample may make the compression rate under low pressure higher than

*The collected intact sandy oolitic limestone specimens from Εl-Shatby Necropolis site under creep testing devices.*

*Rock creep testing devices. Samples are 90–105 mm high, 42–44 mm2 diameters. Two displacement sensors*

*Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone…*

*DOI: http://dx.doi.org/10.5772/intechopen.91720*

On May 5, 2016 (Day 1), Catacomb of Kom El-Shoqafa no\_1 began testing on a sample of sandy limestone, loading it to a vertical stress of σ1 = 1.75 MPa, 65% of the coaxial compression strength of the rock material (peak sample strength). **Figure 10** displays the strain curve versus time; this curve averages the data provided by two displacement sensors. Strains do not correct for elastic thermal differences. In this test, the crawl was faster than the Catacomb of Kom El-Shoqafa site. Test no\_2: From day 130 to day 200 after the start of each test, the cumulative strain was 4.5

the pressure under high pressure.

**Figure 6.**

**Figure 7.**

**27**

*were used during each test.*

**7.1 Catacomb of Kom El-Shoqafa, Test No. 1**

$$
\varepsilon\_{\text{axial}} = \Delta \mathcal{L} / \mathcal{L},\tag{2}
$$

where σ axial is the axial pressure, Pa is applied axial load, A is the normal crosssection area of the direction of the load, ε axial is the geometric axial strain, ΔL is the axial deformation, and L is the original length.

**Table 2** summarizes the results of a uniaxial creep test. The axial stress time curves are shown in **Figures 10–16**, and the curves represent instantaneous, transient, and triple creeps of rock samples under a fixed axial load. Samples are loaded quickly and then the axial strains increase. The immediate breeds range from 0.07 to 3.5.

Most samples, under constant axial pressure, show a complete creep stage: transient, steady, and triple creep stages.

Increasing the value of the instantaneous creep strain with hard axial stress gives strain time curves of rock samples tested under constant high and low axial

*Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone… DOI: http://dx.doi.org/10.5772/intechopen.91720*

#### **Figure 6.**

**6.4 Loading**

**7. Test results**

0.07 to 3.5.

**26**

The approved test procedure consisted of loading samples at a constant rate of about 1.35 MPa up to 1.75 MPa for samples from Catacomb in Kom El-Shoqafa, 1.55 MPa up to 2.17 MPa for samples from Mustafa Kamel Necropolis, and 2.6 MPa up to 3.44 MPa for samples from El-Shatby cemetery. In order to keep the applied pressure as stable as possible, dead weights were used and steel cylinders were placed on the upper steel plate on the upper face of the cylindrical sample. The applied stress is calculated by dividing the weight of the steel cylinders placed on

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

The temperature changes during a long-term creep test must be as a small as possible and must be measured precisely enough to allow correction of the raw strain data for thermoelastic strains; in our study, all the periods of test were in the room temperature between 24 and 26° in the laboratory by controlling the air condition.

Uniaxial creep tests were performed on three rock samples from each site. Rock samples are loaded through fixed uniaxial compression at 1, 35, 1, and 75 MPa (one stress per sample) for Catacomb of Kom El-Shoqafa rock samples collected, at 2.6 and 3.44 MPa for rock samples collected from El-Shatby archeological site, and at 1.55 and 2.17 MPa for rock samples collected from Mustafa Kamel Necropolis. The experimental procedure follows ASTM standards (ASTM D4405 and D4341). The compression machine is used to apply continuous axial load to the samples. Digital scales are installed at 0.001 millimeters to measure the axial displacement of the samples, see **Figures 6**–**9**. Samples are loaded continuously for 1 to 2 years until the samples fail without any acceleration, depending on the displacement results. During testing, axial distortion, time, and failure modes are recorded. The readings are repeated every minute at the beginning of the test, and gradually decrease to twice a day after the first few days of testing. This also depends on the deformation rate of each sample. The results are presented by strain time curves.

where σ axial is the axial pressure, Pa is applied axial load, A is the normal crosssection area of the direction of the load, ε axial is the geometric axial strain, ΔL is the

**Table 2** summarizes the results of a uniaxial creep test. The axial stress time curves are shown in **Figures 10–16**, and the curves represent instantaneous, transient, and triple creeps of rock samples under a fixed axial load. Samples are loaded quickly and then the axial strains increase. The immediate breeds range from

Most samples, under constant axial pressure, show a complete creep stage:

strain time curves of rock samples tested under constant high and low axial

Increasing the value of the instantaneous creep strain with hard axial stress gives

σaxial ¼ Pa*=*A, (1) εaxial ¼ ΔL*=*L, (2)

the top plate by the initial cross-sectional area of the sample.

Axial stress and axial pressure values are calculated by:

axial deformation, and L is the original length.

transient, steady, and triple creep stages.

**6.5 Temperature and hygrometry**

*Rock creep testing devices. Samples are 90–105 mm high, 42–44 mm2 diameters. Two displacement sensors were used during each test.*

pressures. Axial stress also increases crawling strains. In the transit crawl stage, the stress rate increases with the applied stressors. In most cases, the stress rate under high axial pressure is greater than the low axial pressure rate. The effect of embedding in the sample may make the compression rate under low pressure higher than the pressure under high pressure.

#### **7.1 Catacomb of Kom El-Shoqafa, Test No. 1**

On May 5, 2016 (Day 1), Catacomb of Kom El-Shoqafa no\_1 began testing on a sample of sandy limestone, loading it to a vertical stress of σ1 = 1.75 MPa, 65% of the coaxial compression strength of the rock material (peak sample strength). **Figure 10** displays the strain curve versus time; this curve averages the data provided by two displacement sensors. Strains do not correct for elastic thermal differences. In this test, the crawl was faster than the Catacomb of Kom El-Shoqafa site. Test no\_2: From day 130 to day 200 after the start of each test, the cumulative strain was 4.5

#### **Figure 8.**

*The collected sandy οοlitic limestone specimens from the catacombs of Kom El-Shoqafa site under creep testing devices.*

#### **Figure 9.**

*The collected intact calcarenitic rock specimens from Mustafa Kamel Necropolis site under creep testing devices.*

microns for Catacomb of Kom El-Shoqafa. 1 and 2.8 microns for Catacomb of Kom El-Shoqafa test site 2. This difference is fully in line with what is known in previous tests conducted at greater pressures on these samples. When the stress rate in the transient pressure zone is increased, followed by a similar decrease, it can be observed from day 44 to day 130, immediately followed by a steady slope (steady state crawl) up to 205 days. Finally, a more stable condition followed with a smaller stress rate until the sudden sample failure on day 368. Stress rate developments were more progressive in this case. There is no specific explanation for these changes in compression rate. At the end of the test, the observed pressure rate is <sup>ε</sup> = 2.30 <sup>10</sup><sup>8</sup> <sup>s</sup> 1 , the sample was suddenly broken after the 368 day (end of the test) on June 1, 2017, while the sample showed a higher creep phase.

Test no\_2, which began on another sample significantly purer than the previous, loaded on a vertical stress σ1 = 1.35 Mpa, 50% of the axial compression strength of the rock material (peak strength), the applied stress until the end of the test was not adjusted without sample failure on July 2, 2018, during a steady slope or steady state and a creep with a small strain rate was observed. **Figure 11** displays a curve versus time. This curve averages the data provided by two displacement sensors. The compression rate (ε.) is calculated every 5 days; it is calculated for 10 days. Strains are corrected for temperature variation. Initially, the strain experienced a long initial transient period until the first few days characterized by a slow decline in

*Strain versus time curve during the catacomb of Kom El-Shoqafa, uniaxial creep test no. 1.*

**Specimen No. Testing period Time (days)**

*Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone…*

From **5/5/2016** to **1/6/2017 σ<sup>1</sup> = 1.35 MPa**

From **1/9/2016** to **2/7/2018 σ<sup>1</sup> = 1.75 MPa**

From **12/4/2016** to **4/7/2018 σ<sup>1</sup> = 2.60 MPa**

From **5/5/2016** to **3/7/2018 σ<sup>1</sup> = 3.44 MPa**

From **11/4/2016** to **28/3/2017 σ<sup>1</sup> = 2 MPa**

From **6/4/2016** to **7/4/2016 σ<sup>1</sup> = 2.50 MPa**

From **3/4/2016** to **22/3/2017 σ<sup>1</sup> = 1.55 MPa σ<sup>1</sup> = 1.86 MPa**

**Catacomb of Kom El-Shoqafa** test Ν\_1 (sandy oolitic

*DOI: http://dx.doi.org/10.5772/intechopen.91720*

**Catacomb of Kom El-Shoqafa**

**El-Shatby Necropolis**. test Ν\_1 (oolitic intraclastic limestone)

**El-Shatby Necropolis**. test Ν\_2 (oolitic intraclastic limestone)

**Mustafa Kamel** Necropolis .test Ν\_1 (intact Calcarenite)

**Mustafa Kamel** Necropolis. test Ν\_2 (intact Calcarenite)

**Mustafa Kamel** Necropolis. test Ν\_3 (intact Calcarenite)

*Uniaxial creep test, testing program.*

limestone)

test Ν\_2

**Table 2.**

**Figure 10.**

**1 9 100 135 178 375 667 786 813**

contractions), with long-term amplitude fluctuations ++20%; this is probably associated with moisture fluctuations. This phase was followed by a long steady slope or steady-state creep to the end of the test while the observed compression rate was ε.

<sup>1</sup> (positive sample

<sup>1</sup> was at the beginning of the test.

rate, with the average stress rate stabilizing to <sup>ε</sup> = 5.85 <sup>10</sup><sup>10</sup> <sup>s</sup>

, while it was 1.50 <sup>10</sup><sup>9</sup> <sup>s</sup>

= 3.21 <sup>10</sup><sup>9</sup> <sup>s</sup>

**29**

1

## **7.2 Catacomb of Kom El-Shoqafa, Test No. 2**

On September 1, 2016, (Day 1) after the start of the previous tests, an identical creep device on the same table was assigned to the catacomb of Kom El-Shoqafa

*Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone… DOI: http://dx.doi.org/10.5772/intechopen.91720*


#### **Table 2.**

*Uniaxial creep test, testing program.*

#### **Figure 10.**

microns for Catacomb of Kom El-Shoqafa. 1 and 2.8 microns for Catacomb of Kom El-Shoqafa test site 2. This difference is fully in line with what is known in previous tests conducted at greater pressures on these samples. When the stress rate in the transient pressure zone is increased, followed by a similar decrease, it can be observed from day 44 to day 130, immediately followed by a steady slope (steady state crawl) up to 205 days. Finally, a more stable condition followed with a smaller stress rate until the sudden sample failure on day 368. Stress rate developments were more progressive in this case. There is no specific explanation for these changes in compression rate. At the end of the test, the observed pressure rate is

*The collected intact calcarenitic rock specimens from Mustafa Kamel Necropolis site under creep testing devices.*

*The collected sandy οοlitic limestone specimens from the catacombs of Kom El-Shoqafa site under creep testing*

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

On September 1, 2016, (Day 1) after the start of the previous tests, an identical creep device on the same table was assigned to the catacomb of Kom El-Shoqafa

test) on June 1, 2017, while the sample showed a higher creep phase.

, the sample was suddenly broken after the 368 day (end of the

<sup>ε</sup> = 2.30 <sup>10</sup><sup>8</sup> <sup>s</sup>

**28**

**Figure 8.**

**Figure 9.**

*devices.*

1

**7.2 Catacomb of Kom El-Shoqafa, Test No. 2**

*Strain versus time curve during the catacomb of Kom El-Shoqafa, uniaxial creep test no. 1.*

Test no\_2, which began on another sample significantly purer than the previous, loaded on a vertical stress σ1 = 1.35 Mpa, 50% of the axial compression strength of the rock material (peak strength), the applied stress until the end of the test was not adjusted without sample failure on July 2, 2018, during a steady slope or steady state and a creep with a small strain rate was observed. **Figure 11** displays a curve versus time. This curve averages the data provided by two displacement sensors. The compression rate (ε.) is calculated every 5 days; it is calculated for 10 days. Strains are corrected for temperature variation. Initially, the strain experienced a long initial transient period until the first few days characterized by a slow decline in rate, with the average stress rate stabilizing to <sup>ε</sup> = 5.85 <sup>10</sup><sup>10</sup> <sup>s</sup> <sup>1</sup> (positive sample contractions), with long-term amplitude fluctuations ++20%; this is probably associated with moisture fluctuations. This phase was followed by a long steady slope or steady-state creep to the end of the test while the observed compression rate was ε. = 3.21 <sup>10</sup><sup>9</sup> <sup>s</sup> 1 , while it was 1.50 <sup>10</sup><sup>9</sup> <sup>s</sup> <sup>1</sup> was at the beginning of the test.

Transient reverse crawl was observed on day 214 to day 244, sometimes referred

On May 5, 2016 (after the start of the previous tests), an identical crawl device was assigned to the same table, and El-Shatby test of Q2 was started on a cylindrical sample with geometric dimensions similar to that used in El-Shatby test of cemetery no\_1, loaded on a vertical stress of σ1 = 3.44 MPa, 65% of the coaxial compression strength of the rock material (**Figure 13**). A long transient period can be observed followed by a constant inclination or a steady-state crawl until the last day of recording. In this test, the crawl was faster than at El-Shatby Cemetery, test number 1: from day 70 to 270 after the beginning of each test, the cumulative strain was 2.5 μm for El-Shatby Cemetery, test number 2 and 1.8 microns for El-Shatby Cemetery site, test number 1. This difference corresponds exactly to what is known from previous tests conducted at greater pressures on these samples. An increase in the stress rate can be observed, followed by an equivalent decrease, at day 260 and at around day 324, and stress rate developments were more progressive in this case. There is no specific explanation for these changes in compression rate. At the end of

to as "hypotension." During this test, this reverse crawl lasted much longer (20 days) than is currently observed in tests with greater stress. The stress rate stabilized one way or another after day 260, but at the end of the test, the observed

*Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone…*

1 .

the test on July 3, 2018, the observed pressure rate was <sup>ε</sup>. = 3.41 <sup>10</sup><sup>10</sup> <sup>s</sup>

after, the applied pressure was adjusted once, and was constructed up to

*Strain versus time curve during El-Shatby Necropolis, uniaxial creep test no. 2.*

On April 3, 2016, (Day 1) Mustafa Kamel's # 1 test began on an intact sample initially loaded at 1.55 MPa but no creep was observed until 9 days after the test began. Perhaps the pregnancy is too small to produce any detectable strain. There-

σ1 = 1.86 MPa (+10%) after the 9th day 60% of the uniaxial compression strength of the rock material. The numbers in parentheses indicate that the compression value is adjusted. **Figure 14** shows the pressure curve versus time; this curve averages the data provided by two displacement sensors. The compression rate (ε.) is calculated

1 .

pressure rate was <sup>ε</sup>. = 1.62 <sup>10</sup><sup>9</sup> <sup>s</sup>

**7.4 El-Shatby Necropolis, Test No. 2**

*DOI: http://dx.doi.org/10.5772/intechopen.91720*

**7.5 Necropolis of Mustafa Kamel, Test No. 1**

**Figure 13.**

**31**

**Figure 11.** *Strain versus time curve during the catacomb of Kom El-Shoqafa, uniaxial creep test no. 2.*

#### **7.3 El-Shatby Necropolis, Test No. 1**

On April 12, 2016, (Day 1) testing of Shatby Tombs No. 1 began on a sample of sound rock-limestone that was loaded to = 1 = 2.60 MPa, 50% of the axial compression strength of the rock material (peak strength) is not Stress adjustment until the end of the test on July 4, 2018. **Figure 12** shows the stress curve versus time, where the elastic strain is followed by a long transient creep characterized by a slow rate of decline, followed by a slope or creep constant in a steady state with a small stress rate until end of the test without sample failure; this curve averages the data provided by two displacement sensors. The compression rate (ε.) is calculated every 1 h at the beginning of the test, and after the first few days it is calculated every day. Strains are corrected for temperature variation. The strain experienced a long initial transient period, where the average stress rate stabilized on <sup>ε</sup> = 1.3 <sup>10</sup><sup>9</sup> <sup>s</sup> <sup>1</sup> (positive sample contractions.), with long-term amplitude fluctuations ++15%; this is probably associated with moisture fluctuations.

**Figure 12.** *Strain versus time during El-Shatby Necropolis, uniaxial creep test no. 1.*

*Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone… DOI: http://dx.doi.org/10.5772/intechopen.91720*

Transient reverse crawl was observed on day 214 to day 244, sometimes referred to as "hypotension." During this test, this reverse crawl lasted much longer (20 days) than is currently observed in tests with greater stress. The stress rate stabilized one way or another after day 260, but at the end of the test, the observed pressure rate was <sup>ε</sup>. = 1.62 <sup>10</sup><sup>9</sup> <sup>s</sup> 1 .

#### **7.4 El-Shatby Necropolis, Test No. 2**

On May 5, 2016 (after the start of the previous tests), an identical crawl device was assigned to the same table, and El-Shatby test of Q2 was started on a cylindrical sample with geometric dimensions similar to that used in El-Shatby test of cemetery no\_1, loaded on a vertical stress of σ1 = 3.44 MPa, 65% of the coaxial compression strength of the rock material (**Figure 13**). A long transient period can be observed followed by a constant inclination or a steady-state crawl until the last day of recording. In this test, the crawl was faster than at El-Shatby Cemetery, test number 1: from day 70 to 270 after the beginning of each test, the cumulative strain was 2.5 μm for El-Shatby Cemetery, test number 2 and 1.8 microns for El-Shatby Cemetery site, test number 1. This difference corresponds exactly to what is known from previous tests conducted at greater pressures on these samples. An increase in the stress rate can be observed, followed by an equivalent decrease, at day 260 and at around day 324, and stress rate developments were more progressive in this case. There is no specific explanation for these changes in compression rate. At the end of the test on July 3, 2018, the observed pressure rate was <sup>ε</sup>. = 3.41 <sup>10</sup><sup>10</sup> <sup>s</sup> 1 .

#### **7.5 Necropolis of Mustafa Kamel, Test No. 1**

On April 3, 2016, (Day 1) Mustafa Kamel's # 1 test began on an intact sample initially loaded at 1.55 MPa but no creep was observed until 9 days after the test began. Perhaps the pregnancy is too small to produce any detectable strain. Thereafter, the applied pressure was adjusted once, and was constructed up to σ1 = 1.86 MPa (+10%) after the 9th day 60% of the uniaxial compression strength of the rock material. The numbers in parentheses indicate that the compression value is adjusted. **Figure 14** shows the pressure curve versus time; this curve averages the data provided by two displacement sensors. The compression rate (ε.) is calculated

**Figure 13.** *Strain versus time curve during El-Shatby Necropolis, uniaxial creep test no. 2.*

**7.3 El-Shatby Necropolis, Test No. 1**

**Figure 11.**

**Figure 12.**

**30**

probably associated with moisture fluctuations.

*Strain versus time during El-Shatby Necropolis, uniaxial creep test no. 1.*

On April 12, 2016, (Day 1) testing of Shatby Tombs No. 1 began on a sample of sound rock-limestone that was loaded to = 1 = 2.60 MPa, 50% of the axial compression strength of the rock material (peak strength) is not Stress adjustment until the end of the test on July 4, 2018. **Figure 12** shows the stress curve versus time, where the elastic strain is followed by a long transient creep characterized by a slow rate of decline, followed by a slope or creep constant in a steady state with a small stress rate until end of the test without sample failure; this curve averages the data provided by two displacement sensors. The compression rate (ε.) is calculated every 1 h at the beginning of the test, and after the first few days it is calculated every day. Strains are corrected for temperature variation. The strain experienced a long initial

*Strain versus time curve during the catacomb of Kom El-Shoqafa, uniaxial creep test no. 2.*

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

transient period, where the average stress rate stabilized on <sup>ε</sup> = 1.3 <sup>10</sup><sup>9</sup> <sup>s</sup>

itive sample contractions.), with long-term amplitude fluctuations ++15%; this is

<sup>1</sup> (pos-

stress rate was not observed in this test, followed by an equivalent decrease, while a long transient strain was encountered and a slow decline in rates was followed by a creeping phase in a steady state with a very small stress rate until day 91, after acceleration or the third stage of creep began. The 135th day in a large stress rate

*Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone…*

On April 6, 2016, an identical creep device was set on the same table, and Mustafa KAM # 3 test was started on another heavily loaded sample on a stress of σ1 = 2.5 MPa, 80% of the uniaxial pressure force of the material rock (peak

strength). Strains do not correct for elastic thermal differences. **Figure 16** displays a curve versus time. This curve averages the data provided by two displacement sensors. In this test, the crawl was faster than the site of Mustafa Kamel's tombs, test number 1 and test number: from the first day after the start of the test, the cumulative strain was 7 microns for the site of Mustafa Kamel Necropolis, test number 3. This difference corresponds exactly to what is known from the tests previously conducted at smaller pressures on these samples. The sample fractured 26 h after the start of the test, the crawl begins with a short elastic strain followed by a short transient strain followed by a steady-state crawl with a very small stress rate up to 23 h after the start of acceleration or triple crawl resulting in a sudden failure of the sample with a high stress rate after 26 h exactly. At the end of the test, the observed

<sup>ε</sup>. = 1.11 � <sup>10</sup>�<sup>9</sup> <sup>s</sup>

�1 .

*DOI: http://dx.doi.org/10.5772/intechopen.91720*

pressure rate was ε. = 0.30 per second.

**7.8 Comparison with tests performed under larger stresses**

*Strain versus time curve during Mustafa Kamel Necropolis, uniaxial creep test no. 3.*

lasts much longer during tests under greater stress.

creep.

**33**

**Figure 16.**

Qualitatively, the behavior of soft rocks under small pressure (0.1 = 0.1–3 MPa) exhibits the same general features as observed under large pressures (e.g., σ = 5– 20 MPa). The rapid accumulation of stress leads to a transient creep characterized by a slow rate of decline. The creep rate then becomes almost constant (a steady state is reached) or, more precisely, its average value remains constant, but the rate faces long-term fluctuations that may be affected by slow changes in moisture measurement. Reducing the load ("low pressure") creates an inverse crawl, which

Norton-Hoff's constitutive equation is often proposed to describe stable state

<sup>ε</sup>*:* <sup>¼</sup> <sup>A</sup><sup>∗</sup> exp *:*ð Þ �Q*=*RT <sup>σ</sup><sup>n</sup> (3)

**7.7 Necropolis of Mustafa Kamel, Test No. 3**

**Figure 14.** *Strain versus time curve during Mustafa Kamel Necropolis, uniaxial creep test no. 1.*

every 5 days; it is calculated for 10 days. Strains are corrected for temperature variation. The strain experienced a long initial transient period characterized by a low slow rate followed by a steady slope or a steady-state creep with a small stress rate, at which time the average stress rate stabilized to <sup>ε</sup> = 1.62 <sup>10</sup><sup>9</sup> <sup>s</sup> <sup>1</sup> (positive sample contractions.), with long-term capacity fluctuations of + \_20%; this is probably associated with moisture fluctuations.

The transient inverse creep has not been observed, and is sometimes referred to as "stress drop." Strain rate more-or-less stabilized after day 160, and strain rate ε . = 4.86 <sup>10</sup><sup>9</sup> <sup>s</sup> <sup>1</sup> and the sample has been broken suddenly after 178 days (the end of the test 22/3/2017); the specimen showed the complete three phases of creep end with the tertiary or acceleration creep stage.

#### **7.6 Necropolis of Mustafa Kamel, Test No. 2**

On April 11, 2016, (after the start of the previous tests) an identical crawl device was set on the same table, and Mustafa KAM # 2 test started on another sample that is significantly purer than the previous, loaded on the stress of σ1 = 2 MPa, 65% of the uniaxial compression force for rocky materials, and applied pressure was not modified until the end of the test on 28/3/2017 (**Figure 15**). It displays the strain curve versus time; this curve averages the data provided by two displacement sensors. In this test, the creep was faster than the site of Mustafa Kamel's tombs, test number 1: from day 11 to 91 after the start of each test, the cumulative strain was 3.7 microns for the Mustafa Kamel test site Necropolis. 2 and 3.5 microns of the graves of Mustafa Kamel site No. 1. This difference corresponds exactly to what is known from previous tests conducted at greater pressures on these samples. An increase in

**Figure 15.** *Strain versus time curve during Mustafa Kamel Necropolis, uniaxial creep test no. 2.*

*Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone… DOI: http://dx.doi.org/10.5772/intechopen.91720*

stress rate was not observed in this test, followed by an equivalent decrease, while a long transient strain was encountered and a slow decline in rates was followed by a creeping phase in a steady state with a very small stress rate until day 91, after acceleration or the third stage of creep began. The 135th day in a large stress rate <sup>ε</sup>. = 1.11 � <sup>10</sup>�<sup>9</sup> <sup>s</sup> �1 .

#### **7.7 Necropolis of Mustafa Kamel, Test No. 3**

On April 6, 2016, an identical creep device was set on the same table, and Mustafa KAM # 3 test was started on another heavily loaded sample on a stress of σ1 = 2.5 MPa, 80% of the uniaxial pressure force of the material rock (peak strength). Strains do not correct for elastic thermal differences. **Figure 16** displays a curve versus time. This curve averages the data provided by two displacement sensors. In this test, the crawl was faster than the site of Mustafa Kamel's tombs, test number 1 and test number: from the first day after the start of the test, the cumulative strain was 7 microns for the site of Mustafa Kamel Necropolis, test number 3. This difference corresponds exactly to what is known from the tests previously conducted at smaller pressures on these samples. The sample fractured 26 h after the start of the test, the crawl begins with a short elastic strain followed by a short transient strain followed by a steady-state crawl with a very small stress rate up to 23 h after the start of acceleration or triple crawl resulting in a sudden failure of the sample with a high stress rate after 26 h exactly. At the end of the test, the observed pressure rate was ε. = 0.30 per second.

**Figure 16.** *Strain versus time curve during Mustafa Kamel Necropolis, uniaxial creep test no. 3.*

#### **7.8 Comparison with tests performed under larger stresses**

Qualitatively, the behavior of soft rocks under small pressure (0.1 = 0.1–3 MPa) exhibits the same general features as observed under large pressures (e.g., σ = 5– 20 MPa). The rapid accumulation of stress leads to a transient creep characterized by a slow rate of decline. The creep rate then becomes almost constant (a steady state is reached) or, more precisely, its average value remains constant, but the rate faces long-term fluctuations that may be affected by slow changes in moisture measurement. Reducing the load ("low pressure") creates an inverse crawl, which lasts much longer during tests under greater stress.

Norton-Hoff's constitutive equation is often proposed to describe stable state creep.

$$
\varepsilon = \mathbf{A}^\* \cdot \exp \left. \left( -\mathbf{Q} / \mathbf{R} \mathbf{T} \right) \sigma^\mathbf{n} \right. \tag{3}
$$

every 5 days; it is calculated for 10 days. Strains are corrected for temperature variation. The strain experienced a long initial transient period characterized by a low slow rate followed by a steady slope or a steady-state creep with a small stress

sample contractions.), with long-term capacity fluctuations of + \_20%; this is prob-

the test 22/3/2017); the specimen showed the complete three phases of creep end

The transient inverse creep has not been observed, and is sometimes referred to as "stress drop." Strain rate more-or-less stabilized after day 160, and strain rate ε

On April 11, 2016, (after the start of the previous tests) an identical crawl device was set on the same table, and Mustafa KAM # 2 test started on another sample that is significantly purer than the previous, loaded on the stress of σ1 = 2 MPa, 65% of the uniaxial compression force for rocky materials, and applied pressure was not modified until the end of the test on 28/3/2017 (**Figure 15**). It displays the strain curve versus time; this curve averages the data provided by two displacement sensors. In this test, the creep was faster than the site of Mustafa Kamel's tombs, test number 1: from day 11 to 91 after the start of each test, the cumulative strain was 3.7 microns for the Mustafa Kamel test site Necropolis. 2 and 3.5 microns of the graves of Mustafa Kamel site No. 1. This difference corresponds exactly to what is known from previous tests conducted at greater pressures on these samples. An increase in

<sup>1</sup> and the sample has been broken suddenly after 178 days (the end of

<sup>1</sup> (positive

. =

rate, at which time the average stress rate stabilized to <sup>ε</sup> = 1.62 <sup>10</sup><sup>9</sup> <sup>s</sup>

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

*Strain versus time curve during Mustafa Kamel Necropolis, uniaxial creep test no. 1.*

*Strain versus time curve during Mustafa Kamel Necropolis, uniaxial creep test no. 2.*

ably associated with moisture fluctuations.

with the tertiary or acceleration creep stage.

**7.6 Necropolis of Mustafa Kamel, Test No. 2**

4.86 <sup>10</sup><sup>9</sup> <sup>s</sup>

**Figure 15.**

**32**

**Figure 14.**

where σ is the applied deviatoric stress; T is the absolute temperature; and A\*, n, and Q/R are constants. For Etrez salt, Pouya suggests the following parameter values:

$$\mathbf{A}^\* = \mathbf{0.64 MPa}^{-n} \text{ yr.}^{-1}, \mathbf{Q}/\text{R} = \mathbf{4100 K}, \text{and } \mathbf{n} = \mathbf{3.1}.\tag{4}$$

Berest et al. [40] found that if the Norton-Hoff Law of Conditions was derived in Creep Test 1 (σ = 0.108 ΜPa, T = 286.5 K), the calculated compression rate (ε. = 10�<sup>17</sup> s �1 ) is smaller. Start by from the observed compression rate (ε. = 1.4 � <sup>10</sup>�<sup>12</sup> <sup>s</sup> �1 ). The observed pressure rates, even if they are too small, are much larger than expected. Spears et al. suggest that the pressure solution (rather than infiltration and slip, the mechanism that controls high stresses) is the most effective mechanism for crawling at very small pressures; the exponent of stress in this context would be n = 1 instead of n = 3–5, which is observed during standard tests. If this proposal is adopted, the Creep law should be modified when considering small pressures, with significant consequences in predicting the cave or gallery convergence rate.

Many lessons were learned during the test under these unusually low pressures. This first series of tests opened the way for further research on the behavior of rocks under very small pressures, long-term single-axis crawl tests were performed for geological and engineering applications on rock samples (for 850 days), and the applied loads were as small as 1.35 MPa. Slow stress rates such as 1.11 � <sup>10</sup>�<sup>10</sup> <sup>s</sup> �1 were observed in some cases. These small loads and pressure rates pose several specific problems: potential drift of sensors during long 2-year tests, interference with small changes in room temperature and moisture measurement, and effects related to irregular load distribution applied to sample surfaces. These difficulties have been recognized and at least partially addressed. The qualitative results are in good agreement with what is known as the behavior of soft rocks under greater pressure; however, the observed pressure rates, even if they are extremely small, were much greater than expected.

The initiation, accumulation, and growth of cracks caused by stress in rocks are generally referred to as rock damage. Referring to the pressure caused by the crack is the load at which the sample will eventually fail, under prolonged loading, which they propose correspond to about 70–80% of the peak strength of the sample. It is also believed that the damage to the crack damage or the crack damage threshold point corresponds to the point at which the stress reflection or sample expansion begins. Corresponding to the volumetric stress gradient is approximately 70% of the estimated unrestricted compressive strength of the rock.

These stresses are well above the stress threshold for damage. It has been suggested that sample composition for unrestricted compression force tests reduces the spread of cracks. Many researchers suggest that the strain of the ring is generated between a stretch crack and the outer surface of a cylindrical sample. This breed may generate a confinement collar that limits the growth of continuous cracks.

Preliminary test results suggest that an alternative mechanism may affect the spread of unstable cracks. Under pure uniaxial loading conditions, a split can be expected parallel to the maximum pressure direction. The failure may ultimately be at the microscopic level due to the curvature of the rock slabs resulting from tensile fractures directed toward the maximum compressive pressure, as shown in **Figure 17**.

#### **7.9 Triaxial creep tests on the calcarenitic and sandy oolitic rock specimens under investigation**

The purpose of triaxial creep tests is to determine the viscosity and plastic parameters of the soft rock samples under confined conditions and to investigate the effects of axial stress and fortified pressure. Time-related parameters are mon-

*Rock specimens under investigation, after uniaxial creep test. (a) Calcarenitic rock specimens, Necropolis of Mustafa Kamel. (b) Oolitic intraclastic limestone specimens, El-Shatby Necropolis. (c) Sandy oolitic limestone*

*Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone…*

*DOI: http://dx.doi.org/10.5772/intechopen.91720*

itored, recorded, and analyzed.

*specimens, Catacombs of Kom El-Shoqafa.*

**Figure 17.**

**35**

*Uniaxial and Triaxial Creep Performance of Calcarenitic and Sandy Oolitic Limestone… DOI: http://dx.doi.org/10.5772/intechopen.91720*

#### **Figure 17.**

where σ is the applied deviatoric stress; T is the absolute temperature; and A\*, n, and Q/R are constants. For Etrez salt, Pouya suggests the following parameter values:

) is smaller. Start by from the observed compression rate

). The observed pressure rates, even if they are too small,

Berest et al. [40] found that if the Norton-Hoff Law of Conditions was derived in Creep Test 1 (σ = 0.108 ΜPa, T = 286.5 K), the calculated compression

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

are much larger than expected. Spears et al. suggest that the pressure solution (rather than infiltration and slip, the mechanism that controls high stresses) is the most effective mechanism for crawling at very small pressures; the exponent of stress in this context would be n = 1 instead of n = 3–5, which is observed during standard tests. If this proposal is adopted, the Creep law should be modified when considering small pressures, with significant consequences in

Many lessons were learned during the test under these unusually low pressures. This first series of tests opened the way for further research on the behavior of rocks under very small pressures, long-term single-axis crawl tests were performed for geological and engineering applications on rock samples (for 850 days), and the applied loads were as small as 1.35 MPa. Slow stress rates such as 1.11 � <sup>10</sup>�<sup>10</sup> <sup>s</sup>

The initiation, accumulation, and growth of cracks caused by stress in rocks are generally referred to as rock damage. Referring to the pressure caused by the crack is the load at which the sample will eventually fail, under prolonged loading, which they propose correspond to about 70–80% of the peak strength of the sample. It is also believed that the damage to the crack damage or the crack damage threshold point corresponds to the point at which the stress reflection or sample expansion begins. Corresponding to the volumetric stress gradient is approximately 70% of the

These stresses are well above the stress threshold for damage. It has been suggested that sample composition for unrestricted compression force tests reduces the spread of cracks. Many researchers suggest that the strain of the ring is generated between a stretch crack and the outer surface of a cylindrical sample. This breed may

Preliminary test results suggest that an alternative mechanism may affect the spread of unstable cracks. Under pure uniaxial loading conditions, a split can be expected parallel to the maximum pressure direction. The failure may ultimately be at the microscopic level due to the curvature of the rock slabs resulting from tensile fractures directed toward the maximum compressive pressure, as shown in **Figure 17**.

**7.9 Triaxial creep tests on the calcarenitic and sandy oolitic rock specimens**

The purpose of triaxial creep tests is to determine the viscosity and plastic parameters of the soft rock samples under confined conditions and to investigate

generate a confinement collar that limits the growth of continuous cracks.

were observed in some cases. These small loads and pressure rates pose several specific problems: potential drift of sensors during long 2-year tests, interference with small changes in room temperature and moisture measurement, and effects related to irregular load distribution applied to sample surfaces. These difficulties have been recognized and at least partially addressed. The qualitative results are in good agreement with what is known as the behavior of soft rocks under greater pressure; however, the observed pressure rates, even if they are extremely small,

, Q*=*R ¼ 4100 K, and n ¼ 3*:*1*:* (4)

�1

<sup>A</sup><sup>∗</sup> <sup>¼</sup> <sup>0</sup>*:*64 MPa�<sup>n</sup> yr*:* �<sup>1</sup>

predicting the cave or gallery convergence rate.

estimated unrestricted compressive strength of the rock.

rate (ε. = 10�<sup>17</sup> s

(ε. = 1.4 � <sup>10</sup>�<sup>12</sup> <sup>s</sup>

�1

were much greater than expected.

**under investigation**

**34**

�1

*Rock specimens under investigation, after uniaxial creep test. (a) Calcarenitic rock specimens, Necropolis of Mustafa Kamel. (b) Oolitic intraclastic limestone specimens, El-Shatby Necropolis. (c) Sandy oolitic limestone specimens, Catacombs of Kom El-Shoqafa.*

the effects of axial stress and fortified pressure. Time-related parameters are monitored, recorded, and analyzed.
