Stress Analysis of Bolt-Resin-Rock Interface

"A general review of major problems concerning mathematical modelling of roof bolting problem is given. A mathematical model (MM) of interactive set Bolt - Resin - Rock and its discretization based on the Finite Element Method (FEM) is developed to calculate numerically course of displacement, stress and strain fields in this set. This new MM enables to get also course of the normal and tangential components of contact stress vector, normal displacement and then mutual tangential slip at the bolt - resin and resin - rock interfaces, respectively.Behavior of system on all interfaces is modelled in the MM as a ""unilateral contact"" governed by so called non-classical boundary condition of Signorini's type including Coulomb's law of friction between resin and rock, and ""a given friction"" law between bolt and resin (see Duvaut, Lions (1972) for mathematical formulation).Numerical example and some values of resulting stresses are shown and remarks on necessary and sufficient conditions for solvability of the problem are also given.IntroductionAs is well known roof bolting has become the primary support system in almost all underground coal mines. But the ""theoretical"" design criteria for roof bolt patterns are rather problematic because: "" ... real mechanisms by which the roof bolts reinforce the immediate roof of underground coal mine entry are still relatively unknown"", see Peng (1986).The aim of this contribution is to present brief description of fundamentals of mathematical theory (see Hlavacek et al., 1988) which could be, according to our opinion and knowledge, very helpful for numerical modelling of a such type of problems. For the sake of brevity we restrict ourselves here to just one of the simplest possible problem: analysis of the behavior of interactive set composed by only single full - length - grouted bolt, resin (or cement) and suitable part of domain of a ""immediate"" neighborhood of bolt which should represent physical action of real rock material."