Abstract
Before the excavation of underground engineering, joints, fissures, and voids already exist in the rock—that is, there are defects in the rock. Due to the existence of these defects, the rock produces plastic deformation, which can lead to incompatible deformation. Therefore, the classic continuum theory cannot accurately describe the deformation of the rock. In this paper, a relationship between the strain tensor and metric tensor was studied by analyzing the three states of elastic plastic deformation, and the elasto-plastic incompatible model was built. Additionally, the stress and deformation of a thick-walled cylinder under hydrostatic pressure was investigated by using a finite element program written in the FORTRAN language. The results show that the plastic strain is associated with not only deviator stress but also the distribution of defects (represented by the incompatible parameter R). With the value of R increasing, the defects in the rock increased, but the elastic plastic stiffness matrix decreased. Thus, as more rock enters the plastic state, the deformation of the surrounding rock is enlarged.
Highlights
The size and shape of an object will change under external forces, namely the deformation of objects
The important characteristic of elastic deformation is reversibility—that is, deformation occurs after the force is applied and disappears after the force is removed
This indicates that the elastic deformation is determined by the binding force between atoms
Summary
The size and shape of an object will change under external forces, namely the deformation of objects. After the external force is removed, the part of the deformation that has disappeared is called elastic deformation, and the remaining deformation is plastic deformation. The important characteristic of elastic deformation is reversibility—that is, deformation occurs after the force is applied and disappears after the force is removed. The actual object contains defects such as dislocations and disclinations; with a small elastic deformation, the stress is capable of activating the dislocation and making it move, resulting in plastic deformation. The classical continuum theory is not suitable for analyzing the defected rocks, and the incompatible deformation theory can be used. Kondo first introduced differential geometry into the defect theory. He established the relationship between the dislocation theory and non-Riemannian geometry [4]. Fiisnawllyri,ttthene eilnasttohpelaFsOtiRc TfiRnAiteNelleamngenutagper,ogarnadmtihsewsrtirtetesns ianntdhe deFfOorRmTaRtAioNn olafnagcuiarcgue,laarntdutnhneeslturensdsearnhdydderfoosrtmataictiponreossfuarceiricsuallasrotaunnanleylzuendd. er hydrostatic pressure is analyzed
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
