# Triaxial Compression Test in Rock

#### Introduction

Triaxial tests are widely used in geotechnical engineering both in soil and rock mechanics. Specimens are axially loaded to failure while a confining pressure is constantly applied. As a result, the behavior of geomaterials is investigated in a three-dimensional stress state.

The principal stresses (the maximum and minimum normal stresses acting on a plane at which the shear stress is zero) in 3-dimensional objects are three (σ1> σ2> σ3). In nature, the principal stresses may differ. However, in laboratory triaxial tests, the intermediate stress σ2 is equal to σ3. Conducting laboratory tests in which all applied principal stresses differ is challenging and is not widely used. Such a procedure would be referred as polyaxial or true triaxial test. Moreover, research has shown that the effect of the intermediate stress is minor.

The principal stresses applied during a triaxial test are presented in Figure 1.

The confining pressure is determined and remains constant during a test. The sample is initially loaded isotropically until the principal stresses are equal to the predetermined confining pressure. Then, the axial stress, σ1, increases at a certain rate until the specimen fails and the maximum σ1 is recorded.

#### Sample preparation

Test samples are obtained by core drilling and must be selected to be representative of the rock formation examined.

The specimens should be tested within 30 days of the drilling date to preserve their initial conditions (e.g. natural water content).

It should be pointed out, that saturation or pore-pressure built up is not a critical issue in rock mechanics since the porosity of rocks is much lower than that of soils, thus testing a dry or a saturated sample would not significantly affect the results.

The sample shape is cylindrical and the diameter must range from 38 to 54 millimeters. The diameter is derived by taking measures at the top, mid and the bottom parts of the specimen with a tolerance of 0.1 millimeters.

The height to diameter (H/D) ratio must be between 2.0 and 3.0. The height should be determined to the nearest millimeter. Moreover, the size of the largest frock fragment should be maximum 10% of the sample’s diameter.

The ends of the samples must be smoothed so that the top and bottom surfaces are flat with a tolerance of ±0.01 mm. This ensures that the applied loads are uniformly transmitted to the sample and there is no loading eccentricity.

The lateral sides of the specimen must be smooth and not present irregularities within 0.3mm tolerance.

#### Testing Procedure

A cylindrical rock specimen is placed in a specifically designed cell (such as a Hoek cell). A specially designed membrane is attached to the cell so that it remains airtight. The lateral pressure is hydrostatic and is applied through a liquid (usually oil) which is pumped into the membrane. A hydraulic pump or a servomotor capable of regulating pressure within 1% accuracy is utilized. The specimen is axially enclosed by steel spherical seats. To derive the vertical and circumferential deformation of the sample, strain gauges can be used. However, it is not mandatory to record the strain response when conducting a triaxial test. A schematic of the Hoek cell and the parts assembled together to conduct a triaxial test is presented in Figure 2.

The Hoek cell is then placed in the loading apparatus that is used to apply a vertical load to the specimen. Modern loading systems are servo-control devices that apply a hydraulic pressure at a constant rate. The loading rate (kN/s) is selected so that the specimen fails in approximately 10 minutes (5-15 min). If there is already data about the maximum σ1 under a constant σ3 (derived from previous tests), this rate can be calculated. Otherwise, a logical assumption should be made based on existing knowledge on the behavior of the tested material.

The lateral pressure is applied at the same rate selected for the axial load until it reaches the prescribed value. Once this confining pressure is reached, it should be maintained within 2% accuracy.

The loading machine must be stiff and sufficient of applying the maximum required pressure for a rock specimen to fail. In addition, it should be frequently calibrated to correctly derive the loading measures.

#### Results and Calculations

The raw data of a triaxial test include the dimensions of the sample, the lateral pressure σ3, the axial load P, the duration of the test, which must be within the required limits, and, if strain gauges are utilized, the deformation measurements.

Firstly, the cross-sectional area of the sample is calculated as:

where D is the diameter of the sample.

The axial stress is derived by dividing the axial load with the specimen’s cross-sectional area:

where P is the axial load.

If deformations measurements are recorded, the stress-strain response of the sample is plotted. The axial and circumferential strains, eA and eC, respectively are both calculated as:

where R is the initial electrical resistance of the strain gauge, ΔR is the change in resistance due to deformation and k is a gage factor. After a sequence of at least 3 triaxial tests, failure envelopes of the rock samples are derived. The most common failure criteria used in rock mechanics are:

- The Mohr-Coulomb (M-C) Failure Criterion
- The Hoek-Brown (H-B) Failure Criterion

The M-C Failure Criterion correlates the shear strength and the normal effective stress that act on the failure plane. It can be also expressed in terms of principal stresses as:

Where t is the shear strength of the material, c is the cohesion, φ is the friction angle, σn is the normal stress acting on the failure plane, σ1 and σ3 are the principal stresses.

The M-C criterion is utilized due to its simplicity and its universal acceptance in geotechnical engineering. However, the H-B criterion was developed based on a series of laboratory tests in many rock types that showed there is a non-linear correlation between principal stresses in rocks’ brittle failure.

The principal stresses correlation in H-B Criterion is expressed as:

where σci is the uniaxial compressive strength, mi is a constant based on the rock type, σ1 and σ3 are the principal stresses.

After conducting at least 3 triaxial tests in different lateral pressures, the best-fit envelopes of the criterion selected are plotted and the parameters of each one (cohesion, friction angle in M-C and mi, σci in H-B) are derived. Nevertheless, in H-B criterion, most of the times σci is already determined from Uniaxial Compression Tests on the material. It is critical to ensure that the samples derive from the same core or rock block and present similar properties. This can be achieved by visual observation.

#### Example of deriving the M-C and the H-B criteria parameters

Assume 4 triaxial tests were conducted on a specific type of rock specimens. The pre-determined lateral stresses and the corresponding axial stresses on failure are presented in Table 1:

The results are plotted with the best-fit M-C and H-B envelopes in Figure 3.

Based on the best-fit curves, the parameters for the two failure criteria are derived and presented in Table 2.

*References*

Suggested methods for determining the strength of rock materials in triaxial compression: Revised version, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Volume 20, Issue 6, 1983, Pages 285-290, ISSN 0148-9062, doi.org/10.1016/0148-9062(83)90598-3.