PSI - Issue 32

Ivan Pankov et al. / Procedia Structural Integrity 32 (2021) 166–172 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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lower and the rock plasticity becomes higher. The strength criterion parameters obtained as a result of the experiments have been used to formulate theoretical dependences of changes in the rock strength on the intermediate and minimum principal stresses for load patterns with a proportionate change of applied loads. The graphs of change in siltstone strength depending on the influence of the minimum and intermediate principal stresses, used as an example, are presented in Fig. 2. a b

Fig. 2. Theoretical dependences of changes in siltstone strength for load patterns: (a) is the proportionate change of ͵ ƒ† ʹ ; (b) is the proportionate change of ʹ ƒ† ͳ The analysis of the obtained theoretical dependences has revealed the manner, in which the ultimate strength changes depending on ʹ during a proportionate change of the minimum and intermediate principal stresses (Fig. 2a). As can be seen from the figure, in the compression area ( ʹ ൐ Ͳ ), an increase in ͵ causes quite a significant increase in the siltstone strength. The nature of the strength change depending on σ 3 during a proportionate change in the intermediate and the maximum principal stresses is somewhat different (Fig. 2b). As illustrated by the figure, the maximum increase in strength occurs in the tensile area ( ͵ ൏ Ͳ ). When moving to the compression area ( ͵ ൐ Ͳ ), a proportionate increase in the principal stress no longer causes such a significant change in siltstone's strength. a b

Fig. 3. Comparing the theoretical strength with the experimental data obtained with various load patterns: (a) are the results obtained by Karman (1911) and Becker (1915) on Carrara marble samples; (b) are the results obtained by Mogi (1967) on Westerly granite samples