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To investigate the energy evolution and storage characteristics of the rock during the mixed-mode fracture failure, several single loading-unloading tests under preset different unloading levels were conducted on the cracked straight-through Brazilian disc (CSTBD) red-sandstone specimen with crack inclination angles of 10° and 20°. The input energy, elastic energy, and dissipated energy parameters were obtained by calculating the area integral of the load-displacement curve. Test results display that the total input energy, elastic energy, and dissipated energy of rock specimens increase in quadratic function with the increase of unloading level at different unloading levels. It was found that there are significant linear energy storage and dissipation laws of rock during the mixed-mode fracture process. The concepts of fracture energy storage coefficient (FESC) and fracture energy dissipation coefficient (FEDC) were proposed to express the energy variation of rock in the prepeak stage. Under the same loading conditions, FESC and FEDC remain unchanged regardless of crack inclination angles, indicating that the linear energy storage and dissipation laws are an inherent property of the rock. Besides, the peak fracture elastic-dissipation index W ed (the ratio of peak elastic energy to peak dissipation energy) was obtained through quantitative analysis and demonstrated its invariant feature. [ABSTRACT FROM AUTHOR]

2, the "failure energy" should be "post-peak failure strain energy"; in the line 10, the "failure energy" should be "post-peak failure strain energy"; in line 14, the "input energy" should be "input strain energy". 2, the "peak elastic strain density" should be "peak elastic strain energy"; the "failure energy density" should be "post-peak failure strain energy"; in line 6, the "residual elastic strain energy density" should be "residual elastic strain energy"; in line 14, the "input energy" should be "input strain energy". Correction to Tables b In the line 1 of column "Energy parameters" of Table 1, the "additional input energy" should be "additional input strain energy"; the "total failure energy" should be "post-peak failure strain energy". [Extracted from the article]

• The linear energy storage and dissipation laws during rock flexure are identified. • The elastic and dissipation energies at rock failure are determined using the linear energy storage and dissipation laws. • The relationship between the energy properties and mechanical properties is obtained. • The influence of pre-existing flaws on the linear energy storage and dissipation laws is discussed. To investigate the energy storage and dissipation characteristics during rock flexure fracturing, a series of single cyclic loading–unloading flexural fracture tests was conducted on rectangular rock beams using the three-point loading technique. The results show that under different experimental unloading levels, the elastic and dissipation energies increase linearly as the input energy increases. On this basis, the linear energy storage and dissipation laws were obtained, which were immune to the experimental unloading level. The flexural energy storage coefficient and flexural energy dissipation coefficient were subsequently introduced to characterize the potentials of the rock for storing and dissipating energy, respectively. A positive or negative relationship between the two coefficients and the rock mechanics properties (the brittleness index and average flexural strength) was observed. The influence of pre-existing rock flaws on the linear energy storage and dissipation laws was discussed. In addition, highly quadratic increases in the elastic energy, dissipation energy, and input energy were observed with an increasing experimental unloading level. For the energy characteristics at rock failure (the failure point of the rock specimen), the peak input energy, peak elastic energy, and peak dissipation energy varied considerably under different experimental unloading levels, while the associated peak elastic dissipation index (the ratio of peak elastic energy to peak dissipation energy) remained constant. Similar to the flexural energy storage coefficient, the mean value of peak elastic dissipation index is also positively related to the rock mechanics properties. The linear evolution law of energy storage and dissipation not only permits a quantitative determination of the energy parameters at rock failure (the peak elastic energy and peak dissipation energy), but also relates the energy properties with the rock mechanics properties. [ABSTRACT FROM AUTHOR]