Brazilian test

The Brazilian test is performed on a solid disc using diametrical compression. In this test the pressure increases to value when the sample is broken. The compression induces tensile stresses normal to the loaded diameter which reach a maximum value at the center [1]. Assumption for this test is that failure occurs at the point with maximum tensile stress (figure 3).

Figure 3. Machine with mounted specimen that uses in Brazilian test

This method is very simple in terms of specimen preparation. The appropriate shape of sample for Brazilian test is form of drill core and after slicing core into the disk it can possible use this sample for testing. If the orientation of the disk is varied, the tensile strength can be measured across all cross-section of the core [1]. So, if disk is diametrically loaded by two platens that is mounted in direction perpendicular to the length of sample, it is derived the tensile strength perpendicular to the cross-section. Because of this all components with differential direction (x,y,z) of the tensile strength can be obtained with a minimum of sample preparation.

The stress distribution within a thin disc loaded by uniform pressure radially applied over an arc its circumference subtending an angle 2α at the center, has been analyzed by Hondros (1957) assuming that the material was homogeneous, isotropic and linearly elastic. At the center, the stress component normal to the loaded diameter was found to be [1]:

(2)

where

P – applied force, MN;

D – diameter of disk, m;

T – thickness of disk, m;

2α – angular distance over which P is assumed to be distributed

When α = о i.e. а line lоаd [1]:

(3)

The tensile strength is obtained by means of equation 3. It should be noted that using this equation it is assumed that stress value at the center is independent of the loading configuration [1].

The results and calculation of the Brazilian test is represented in figure 4 and table 2 respectively.

№ of samples	d, m	,	Maximum of N	, Mpa
R3	0.055	0.00475	3562.5	1.5
R4			4500	1.895
W3			19312.5	8.133
W4			20812.5	8.765

Table 2. Results of determination tensile strength during Brazilian testing

Figure 4. Noted axial displacement and axial load due to Brazilian testing

Elastic constants test

This test is carried out on saturated or unsaturated samples with cylindrical shapes from 1 to 1.5 inch in diameter. Specimen loaded in a Hoek cell and then static elastic constants are measured with increasing pressure or stress level. This test measures axial strain and horizontal strain due to loading of core. It should be noted that specimen is not failed. But at the beginning axial load is increased to some big value and then it is decreased to zero. So, the unloading curve is often used for determine the elastic constants since it is considered that on unloading no possible fracture of the grains will take place. Modulus of elasticity calculated as ratio between the axial load change and the axial strain changes at 50% failure stress:

(4)

It is used the central part of graph because this part is characterized with elastic rock properties in deep depth and there are all micro fractures are closed due to high value of lithostatic pressure.

Poisson’s ratio calculated from the ratio between the change in radial strain and the change in axial strain [1]:

(5)

The results of test are represented on the figures 5,6:

Figure 5. Relationship between axial load and strain for Red sandstone

Figure 6. Relationship between axial load and strain for white sandstone

№ of samples	r, m	,				ν	E, GPa
White sandstone	0.019	0.0011335	69.88	428.82	8821.920709	0.163	25.377
Red sandstone			157.09	746.18	7057.536567	0.21	10.418

Table 3. Results of determination Poisson’s ratio and modulus of elasticity during test