Theoretical and experimental bifurcation analysis of rock under plane strain compression
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ORIGINAL PAPER
Theoretical and experimental bifurcation analysis of rock under plane strain compression Kang Qinrong 1,2 & Zhang Weizhong 1 & Huang Gun 2 & Zhang Dianji 1 Received: 16 June 2019 / Accepted: 18 October 2019 # Saudi Society for Geosciences 2019
Abstract A new plane strain apparatus for rock testing was designed and built, and a series of plane strain tests on sandstone was performed. The formation and orientation of localization in sandstone were studied theoretically within the framework of equilibrium bifurcation theory. Corresponding elastoplastic constitutive models with nonlinear yield and potential functions were developed and fitted on the plane strain test data. The inclination of the shear band and the bifurcation point were predicted using the acoustic tensor method. The comparison of the computational and experimental results indicates that the initiation of a shear band predicted by a two-dimensional model could occur within the strain hardening region (i.e. prior to the peak stress), and the predicted orientations of the shear bands agreed qualitatively with those measured. Keywords Plane strain . Plane strain apparatus for rock . Shear band . Bifurcation
Introduction Many geotechnical problems can be attributed to plane strain problems such as tunnels, slopes, retaining walls, and dams. (Jaeger and Cook 1979; Zhang 1987). Instability is a common phenomenon in geotechnical engineering, resulting in landslides, wall collapses, and sand liquefaction. The destruction of the material is often triggered by local stress concentration, which causes the crack tip of the material to expand, merge, and form a large fracture zone, which continuously expands into a fracture surface. In the study of geotechnical instability, the localization phenomenon is currently of immense concern. Deformation localization is the unique loss of material or the structural deformation field, and different deformation rate fields appear under the same load state. Therefore, it is
Responsible Editor: Zeynal Abiddin Erguler * Zhang Weizhong [email protected] 1
School of Xingfa Mining Engineering, Wuhan Institute of Technology, Wuhan 430073, People’s Republic of China
2
State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, People’s Republic of China
meaningful to study the causes and mechanisms of the localized destruction of materials. Regarding the research on the bifurcation theory, scholars worldwide have conducted a significant amount of research that has been extensively used in medicine, mathematics, mechanics, and other fields. The study of deformation localization can be roughly divided into two stages. The first stage was before the 1970s: from the earlier Hadamard (1903) and then Thomas (1961), Nadai (1937), Hill and Hutchinson (1975); Hill (1958, 1959, 1962), Drucker (1950, 1952, 1959), Mandel (1966), and Desruse and Chambon (1989) conducted extensive research on this problem and established a large number of theories describing the localization phe
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