# Splitting Tensile Strength Test (Brazilian)

## Introduction

** The Brazilian Test **is a laboratory test conducted in rock mechanics to indirectly determine the tensile strength of rocks.

The tensile strength of rock materials is an important parameter in designing a geotechnical project since it is significantly lower than the rocks’ compressive strength. This phenomenon is also presented in concrete, a fact that led to the utilization of steel reinforcement to increase the tensile capacity of the material.

Research has also shown that during compression, the tensile strength in the tips of microcracks is exceeded and those cracks tend to propagate through the specimen leading to failure.

The tensile strength of a rock is mainly derived by two testing procedures:

- The Direct Tensile Strength test
- The Brazilian Test

The Direct Tensile Strength test is considered as the most proper method to derive the tensile capacity of a specimen. However, it is not widely utilized since sample preparation is challenging and the failure is usually invalid (the specimen should fail through its middle part so that the test is reliable).For this reason, the Brazilian Test is widely used as the sample preparation and the testing procedure are far more efficient.

#### Sample Preparation

The Brazilian test is conducted on disk specimens that are cut and smoothened so that any irregularities across their surfaces are less than 0.25 millimeters. The two surfaces must also be parallel to within 0.25° accuracy.

Samples must be chosen to be representative of the rock material examined. The selection can be conducted via visual observation of the minerals and grains while certain defects such as cracks and cavities should be avoided.

A sample’s diameter must not be less than 54 millimeters while its thickness must be between 0.2 and 0.75 times its diameter and optimally, approximately equal to the half of the diameter. Both the diameter and the thickness must be derived to the nearest 0.25 millimeter by obtaining at least three measurements.

The geometric characteristics of a typical sample prepared for a Brazilian Test are presented in Figure 1.

The water content slightly affects the results of a Brazilian test; therefore, it is recommended that the samples are preserved and tested based on their field moisture.

#### Brazilian Test Cell

The cylindrical specimen is placed in a specially designed cell which consists of two steel parts that are assembled together so that they make contact with the sample in two opposite ends. The upper jaw contains a spherical opening where a circular half-ball bearing is placed. A schematic of the Brazilian Test Configuration is presented in Figure 2.

#### Testing Procedure

The sample is placed into the cell and masking tape (a 0.2-0.4mm adhesive paper) is wrapped around its surface. The system is then placed in the loading apparatus which must be capable of applying a constant loading rate so that the specimen fails within 15-30 seconds. The maximum load is recorded.

Typical loading devices designed for Brazilian Tests have a maximum loading capacity of 100kN. Nevertheless, loading devices utilized for Uniaxial Compression Tests can also be used as long as they are capable of applying the aforementioned rate.

The specimen must fail along its diameter so that the test is considered valid.

#### Calculations

To derive the tensile strength of a single sample the following equation is applied:

Where,

σt: The Tensile Strength of the specimen

P: The recorded Load

D: The Diameter of the specimen

#### t: The Width of the specimen

Equation 1 is derived using the theory of elasticity for isotropic media considering the loading and boundaries conditions during a Brazilian Test. The failure stress (tensile strength) is determined at the center of the disc when the applied load is equal to P and its vector is perpendicular to the loading diameter.

The stress distribution along the loading axis of the specimens is depicted in Figure 3. While the sample’s ends are under compressive stress, the rest of the loading diameter is under tensile stress with its maximum value presented in the central part of the sample.

To derive a reliable result on the tensile strength of a rock, at least 10 Brazilian Tests must be conducted. However, if the results do not have significant variation (the coefficient of variation must be less than 5%), a smaller number of samples can be utilized.

#### Calculation Example

Assume that 10 disk specimens are prepared for Brazilian Tests. The diameter and thickness of the samples are derived to ensure that they comply with the aforementioned regulations. The samples are then positioned into the cell and the system is placed into the loading apparatus. The loading rate is selected so that the samples fail within 15-30 seconds and the maximum load is recorded. If the tensile strength of the material had been derived before, the loading rate can be calculated. Otherwise, a logical assumption, based on characteristics and information regarding the tested material, can be made.

The results of the Brazilian Tests example are presented in Table 1.

**Table 1:** Example of Brazilian Tests Results for 10 disk specimens

Given that every failure is valid and the selected loading rate was appropriate (since all specimens’ failure within the desired time frame), the tensile strength of the rock is calculated as the average value between the 10 tests.

References

ASTM C496 / C496M-17 (2017), Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens, ASTM International, West Conshohocken, PA, www.astm.org

ASTM D3967-16 (2016), Standard Test Method for Splitting Tensile Strength of Intact Rock Core Specimens, ASTM International, West Conshohocken, PA, www.astm.org

ISRM (1978) Suggested Methods for Determining Tensile Strength of Rock Materials Part 2: Suggested Method for determining indirect tensile strength by the Brazil Test. International Journal of Rock Mechanics and Mining Sciences, 15, 99-103. http://dx.doi.org/10.1016/0148-9062(78)90003-7