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A new method is proposed in order to estimate the shear strength of schistosity planes in slate in terms of Mohr-Coulomb cohesion and internal friction angle. The procedure consists in carrying out the Brazilian method under different loading-foliation angles, for which experimental tests were achieved in slates from the northwest of the Iberian Peninsula (Spain). The experimental fracture patterns were analytically studied and justified by simulating the stress field in the discontinuity planes contained in the whole sample, taking into account the first failure registered in the tests. By combining experimental and analytical studies and a procedure based on the representation of the threshold state of stresses-in the elastic regime-in the failure plane, it is possible to estimate the foliation's strength envelope through a lineal adjustment according to the Mohr-Coulomb criterion and, thus, to characterize the layering. Finally, the proposed procedure was validated by the direct shear test. The cohesion and the internal friction angle obtained with this convenctional test were very close to that calculated by the proposed method, verifying the methodology developed by the authors. This procedure may be interesting in various engineering applications, either in the study of the properties of cleavage in slate, which is commonly used as an industrial rock, or in dam foundations, underground excavations and slope engineering, since one of the main failures in civil engineering is due to sliding along weak planes. KeywordsBrazilian test . Slate . Foliation . Internal friction angle . Cohesion . Strength parameters finished thickness. For this reason, slate is commonly used as 39 roofing or flooring, being an important economic sector in 40 Spain, which is the world leader in roofing slate production. 41 Besides its popular use in building, slate is frequently encoun-42 tered in various engineering applications, such as dam foun-43 dations, underground excavations and slope engineering 44 (Chen et al. 2016). Thus, to establish the mechanical proper-45 ties of jointed rocks along weak planes is important for 46 the exploitation, design and construction of civil engineering 47 works. 48 Direct shear testing is the favorable way to characterize the 49 discontinuities. The portable shear box described by Brown 50 and Walton (1975) is one of the most used testing systems in 51 order to calculate the cohesion and the internal friction angle 52 by assuming the Mohr-Coulomb criterion. Once the specimen * C. Gonzalez-Nicieza

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A new method is developed in order to determine the stress state inside a disk subjected to arbitrary radial compressive distributions along its boundary, obtaining both numerical and closed-form solutions, which is analytically verified through accepted formulations; additionally, alternative expressions for uniform, sinusoidal and parabolic distributions are proposed. Based on the hypothesis of a smooth stress transition along the loaded and unloaded part of the rim, two new distributions (spline and new cosine) are proposed and analysed. Even if closed-form solutions were not feasible, the latter may be accurately solved numerically since the error committed is that of the numerical technique used. Main differences are observed in radial and shear components, whereas hoop ones are relevant on the vicinity of the load application area and the vertical axis. Special attention is paid to the centre of the sample, of which stress state depends on the distribution shape and the contact angle. Finally, it is concluded that there is always a deviation from the values predicted due to the concentrated load as a consequence of the deformation induced by the jaw, which is especially significant in the uniform stress distribution and also influences the determination of the tensile strength in the material.

The present research analyses the configuration of jaws to avoid the premature failure of the disc in the Brazilian test. The objective is to depict the loading device configuration that most likely produces results comparable to the Hondros' analytical stress solution. To this end, several numerical analyses have been carried out for different contact angles with the Finite Element Method. It was deduced that the final contact angle plays an important part in the success of the Brazilian test and that the Griffith criterion can be fulfilled if the equivalent stress is calculated. Additionally, the orientation of the forces in the contact between the loading device and the disc has been studied for different friction conditions. According to the numerical results, it was found that a loading arc configuration of 20º shows the best agreement with the probable values given by the analytical stress model when the uncertainty of its magnitudes is taken into account. The study also demonstrates that the friction in the contact between the optimal loading configuration and the disc does not seem to significantly affect the theoretical predictions in the centre of the disc.