ABSTRACT
ABSTRACTThe principles of the Boundary Element Method ofstress analysis are reviewed briefly, and the maindifferences between two alternative formulations of themethod are described. The concept of Complete PlaneStrain is discussed. Problems involving thedetermination of stress and displacement distributionsassociated with the development of long undergroundopenings arbitrarily inclined in a triaxial field maybe resolved into two subsidiary problems, which can besolved independently by direct formulations of theBoundary Element Method. When excavations aredeveloped in a non-homogeneous medium, boundaryconstraint equations can be established for eachdistinct region in the medium, and these may becombined into complete boundary constraint equationsfor the connected regions, again allowing independentsolution of each of the subsidiary problems. Once theboundary value problems have been solved for theunknown excavation and inclusion surface data, boundarystresses around excavations and inclusions may bedetermined directly. Stresses and displacements atselected internal points in the medium can also becalculated from the known surface data. Theperformance of a Boundary Element program is assessedby comparison of the results of B.E. analysis of somesimple problems involving non-homogeneous media, withresults calculated from the closed form solutions forthese problems.INTRODUCTIONThe Boundary Element Method is a relatively newnumerical technique for analysis of underground designproblems, although the principles exploited in themethod are well established in classical elasticity.The attractions of the method for the analysis ofstress and displacement distribution in infinite bodyproblems such as the underground design problem areboth fundamental and operational. Fully continuousvariation of the field parameters is achieved in theproblem area, and discretization errors are confinedto excavation boundaries. A problem is definedcompletely in terms of the excavation boundaries, theconditions imposed on these boundaries,
