Quantifying the effect of stress relaxation on excavation

Stress relaxation is relevant to the design of both civil and mining excavations. While many authors refer to the adverse effect of stress relaxation on excavation stability, some present compelling empirical evidence indicating that stress relaxation does not have a significant effect. Establishing clear definitions of stress relaxation was critical to understanding and quantifying stress relaxation of the various types that have been referred to in the literature. This paper defines three types of stress relaxation – partial relaxation, full relaxation and tangential relaxation. Once clear definitions were determined, it became clear that the theoretical arguments and empirical evidence presented by various authors to support their respective cases are not contradictory; rather, the different conclusions can be attributed to different types of stress relaxation. In particular, when the minor principal stress is negative the intermediate principal stress has been identified as significantly affecting jointed rock mass behaviour. The aim of the study was to review and evaluate existing methods of quantifying the effect of stress relaxation around underground excavations and, if necessary, propose a new set of recommendations. An empirical stope stability model, that has been termed the Extended Mathews stability chart, was considered to be the most appropriate method of quantifying the effects of stress relaxation. A new set of guidelines to account for the effect of stress relaxation on excavation stability in the Extended Mathews stability chart has been proposed from a back-analysis of 55 case histories of stress relaxation.

A new relaxation method for roll forming problems

Finite element analysis (FEA) of nonlinear problems in solid mechanics is a time consuming process, but it can deal rigorously with the problems of both geometric, contact and material nonlinearity that occur in roll forming. The simulation time limits the application of nonlinear FEA to these problems in industrial practice, so that most applications of nonlinear FEA are in theoretical studies and engineering consulting or troubleshooting. Instead, quick methods based on a global assumption of the deformed shape have been used by the roll-forming industry. These approaches are of limited accuracy. This paper proposes a new form-finding method - a relaxation method to solve the nonlinear problem of predicting the deformed shape due to plastic deformation in roll forming. This method involves applying a small perturbation to each discrete node in order to update the local displacement field, while minimizing plastic work. This is iteratively applied to update the positions of all nodes. As the method assumes a local displacement field, the strain and stress components at each node are calculated explicitly. Continued perturbation of nodes leads to optimisation of the displacement field. Another important feature of this paper is a new approach to consideration of strain history. For a stable and continuous process such as rolling and roll forming, the strain history of a point is represented spatially by the states at a row of nodes leading in the direction of rolling to the current one. Therefore the increment of the strain components and the work-increment of a point can be found without moving the object forward. Using this method we can find the solution for rolling or roll forming in just one step. This method is expected to be faster than commercial finite element packages by eliminating repeated solution of large sets of simultaneous equations and the need to update boundary conditions that represent the rolls.