Numerical Analysis of Fracture Characteristics of Elliptic Porous Sandstone and its Filling Gypsum Based on Statistical
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ORIGINAL PAPER
Numerical Analysis of Fracture Characteristics of Elliptic Porous Sandstone and its Filling Gypsum Based on Statistical Damage Theory Ying Xu . Shi Hu
Received: 24 March 2020 / Accepted: 1 April 2020 Ó Springer Nature Switzerland AG 2020
Abstract In view of the fact that less attention has been paid to the failure characteristics of rock mass structures with different elliptical shapes, based on the statistical damage theory, the finite element calculation model of sandstone with elliptical holes and its filled gypsum is established, the meso-parameters are calibrated by laboratory test results, and the fracture damage process, peak intensity and acoustic emission law are numerical simulated. Based on the acoustic emission results, the concept of damage degree is defined, and the damage process of the specimen is quantitatively described. The results show that with the increase of k value, the ‘‘main crack’’ produced by tensile stress in the hole gradually evolves into a tension-shear compound ‘‘wing crack’’. After the grain ‘‘,’’ main crack ‘‘and’’ wing crack ‘‘developed to a certain extent, shear failure appeared on the left and right sides of the hole, and then developed into horizontal inclined tension-shear composite failure. The peak strength of elliptical pores and sandstone filled with gypsum sandstone increased at first and then decreased. The peak strength of filled gypsum sandstone increased by 6.92%, 4.61%, 11.21%, 13.64%, 15.31%, 10.6% and 11.50%, respectively, compared with that of unfilled gypsum sandstone, and
Y. Xu S. Hu (&) School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, Anhui, China e-mail: [email protected]
the peak strength of sandstone filled with gypsum sandstone increased by 6.92%, 4.61%, 11.21%, 13.64%, 15.31%, 10.6% and 11.50%, respectively. Damage and variation of concrete during loading. There are four stages: linear elastic deformation stage, crack initiation stage, crack acceleration stage and damage stable development stage. With the increase of k value, the maximum damage degree increases at first and then decreases, and the damage degree of sandstone filled with gypsum is larger than that of unfilled sandstone sample as a whole. Keywords Statistical damage Elliptical holes Filling characteristics Fracture process Damage degree Numerical simulation
1 Introduction Defects and holes are one of the inevitable and difficult problems in rock mechanics engineering (Li et al. 2015; Yang et al. 2012; Du et al. 2017). The hole problem is the classical problem of elastic mechanics (Zhu et al. 2015). The classical analytical solutions have been extended and applied to various industries such as rock mechanics and have played a great role in predicting disaster protection in rock mechanics engineering such as tunnels and roadways (Hao and Nie 2019; Jiang and Song 2018). There also exists large amounts of cracks, joints and holes in rock slopes
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