In this study, it was assumed that three-dimensional penny-shaped cracks existed in deep rock masses. A new non-Euclidean model was established, in which the effects of penny- shaped cracks and axial in-situ stress on...In this study, it was assumed that three-dimensional penny-shaped cracks existed in deep rock masses. A new non-Euclidean model was established, in which the effects of penny- shaped cracks and axial in-situ stress on zonal disintegration of deep rock masses were taken into account. Based on the non-Euclidean model, the stress intensity factors at tips of the penny- shaped cracks were determined. The strain energy density factor was applied to investigate the occurrence of fractured zones. It was observed from the numerical results that the magnitude and location of fractured zones were sensitive to micro- and macro-mechanical parameters, as well as the value of in-situ stress. The numerical results were in good agreement with the experimental data.展开更多
Recently, Zhang and Li presented five mock theta functions as q-hypergeometric double sums by using a Bailey pair. In this paper, employing the same Bailey pair, we further establish two new mock theta double sums in ...Recently, Zhang and Li presented five mock theta functions as q-hypergeometric double sums by using a Bailey pair. In this paper, employing the same Bailey pair, we further establish two new mock theta double sums in terms of Appell-Lerch sums and theta series.Indeed, identities between a new mock theta function and classical mock theta functions are obtained.展开更多
基金supported by the 973 Project(No.2014CB046903)the National Natural Science Foundation of China(Nos.51325903 and 51279218)the Natural Science Foundation Project of CQ CSTC(Nos.CSTC2013KJRC-1JRCCJ30001 and CSTC2013JCYJYS0005)
文摘In this study, it was assumed that three-dimensional penny-shaped cracks existed in deep rock masses. A new non-Euclidean model was established, in which the effects of penny- shaped cracks and axial in-situ stress on zonal disintegration of deep rock masses were taken into account. Based on the non-Euclidean model, the stress intensity factors at tips of the penny- shaped cracks were determined. The strain energy density factor was applied to investigate the occurrence of fractured zones. It was observed from the numerical results that the magnitude and location of fractured zones were sensitive to micro- and macro-mechanical parameters, as well as the value of in-situ stress. The numerical results were in good agreement with the experimental data.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 1187125812271234)+2 种基金the Young Backbone Teachers in Henan Province (Grant No. 2020GGJS194)the First-Class Courses in Henan Province (Grant No.[2020]13099)the Young Backbone Teachers in Luoyang Normal College (Grant No. 2019XJGGJS10)。
文摘Recently, Zhang and Li presented five mock theta functions as q-hypergeometric double sums by using a Bailey pair. In this paper, employing the same Bailey pair, we further establish two new mock theta double sums in terms of Appell-Lerch sums and theta series.Indeed, identities between a new mock theta function and classical mock theta functions are obtained.
