# Failure in Confined Brazilian Tests on Sandstone
## 2 Materials and Methods  
### Experimental Methods  
Slabs of Royal Red sandstone quarried southeast of Kanab, Utah were provided by New Mexico Travertime, Inc. The sandstone was selected because it is a widely available  
Figure 2: Strength data for (**a**) Berea Sandstone [10] and (**b**) Carrara Marble [1]. Results include confined extension tests, as well as direct tension (DTS), uniaxial compression (UCS) and triaxial tests. The Hoek Brown failure criteria is shown for the confined extension tests, as well as the tension cut off. Modified from [PERSON] and Martin [6] and Patel and Martin [4]. and common rock type, and is homogenous, consisting of a small grain size ranging from 20 to 100 microns with no large aggregate particles. The slabs were cored, and the ends were cut with a masonry saw to produce samples for subsequent testing. Uniaxial compression tests [16] were performed on cylindrical specimens with a diameter of 50.8 mm and a height of 101.6 mm using an applied axial force at a rate of 30,000 N/min. A compressive strength of 62.24 MPa was derived from averaging the maximum applied principal stress for five tests. [PERSON]'s modulus was estimated as 2.74 GPa from the stress and strain data interpreted from the measured force and deformation. A density of 2480 kg/m\({}^{3}\) was calculated by measuring the weight and volume of each sample used in the uniaxial compression tests. Samples for Brazilian tests were produced with a 50.8 mm diameter and a 25.4 mm thickness, consistent with recommended sample dimensions for Brazilian tests [17]. The samples were flattened to address the problem of localized cracking produced near the region of the applied force [4; 18]. To produce flattened loading surfaces, the cylindrical samples were flattened 1 mm on the top and bottom of the disk using a sanding belt. Unconfined flattened Brazilian tests were performed at a rate of 0.2 mm/min [19]. Thin wood strips were placed between the loading frame and the sample to evenly distribute the load along the flattened end. An average tensile stress at failure of 6.05 MPa was obtained from four repeated unconfined Brazilian tests. For confined Brazilian testing, sandstone disks were jacketed to allow loading while under confinement providing by a confining fluid (Figure 3). The disks were first placed between two aluminum endcaps which are ported for fluid access to the ends of the sample if desired. Perforated Teflon spacers with a thickness of 1.6 mm were placed between the sandstone and the endcaps to limit friction between the samples and the end caps. The perforated Teflon spacers also allowed an even distribution of gas across the surface of the sandstone. A latex membrane was then placed around the sample, Teflon, and endcaps. This assembly was cast in a low stiffness polyurethane rubber compound, PMC-121/Dry from Smooth-On Inc. Two loading platens were embedded in the polyurethane rubber cast to allow direct contact with the sample when loading. The jacketed samples were tested in a pressure vessel rated to 34 MPa internal pressure. The pressure vessel was placed in a 433 kN Instron load frame which was used to apply the diametric load through a loading ram. A hydraulic oil pump was used to apply a confining pressure on the sample. Quasi-static confined Brazilian strength tests were carried out with this system by applying a diametric load at a prescribed deformation rate and observing permeability changes. After an initial seating period, the samples were loaded at a rate of 0.04 mm/min. Tests were performed at five confining pressures: 2.76, 8.27, 13.79, 20.68, and 27.58 MPa. Figure 3: Schematic of the sample jacketing construction modified from [PERSON] [15]. The principal stresses at the center of the sample are calculated from the loading conditions based on the elastic solution developed by [PERSON] [20] for the unconfined Brazilian test. [PERSON] and [PERSON] [13] extended [PERSON]'s solution to account for a confining pressure, \(\mathrm{P_{C}}\), used in the confined Brazilian test.