Development And Application of Infinite Elements For Analysis of Openings in Rockmass

Abstract

In several branches of engineering and sciences, problems frequently arise in which the domain of analysis extends to large distances in one or more directions. Such problems which are termed as 'unbounded- are difficult to analyse.. Many problems of Rock Engineering are unbounded. These problems are characterised by uncertainties in the form of unknown geological features, many unreliable strength properties, and initial stress field which is difficult to determine accurately. Further, rockmass contains discontinuities like joints, fissures, faults and bedding planes etc. In many such cases an elastic analysis is often adequate to determine rockmass behaviour provided nonhomogeneity, anisotropy and effect of discountinuities are taken into account. Such an analysis clearly indicates zones of tensile stress, slip and plastic failure. In recent years, the underground space is utilised for storage of solar energy and radioactive nuclear waste which applies thermal loads on underground structures. It is, therefore, desirable to make design and analysis of underground structures systematic, scientific and comprehensive to achieve economy, safety and reliability. In this study, infinite elements with improved features are formulated. Anew (finite element analysis) computer program is also developed. The above infinite elements are implemented in this computer program. The interface or joint elements are also implemented. The infinite elements are derived by stretching a finite element to become an infinite element as well as by compressing an jgHaLta element to become a finite element. The infinite elements of the seW approach are used in the analysis because mass and stiffness properties of these elements may be derived by using Gaus s -Legendre numerical integration scheme. Further, these infinite elements may have (1/r), (1/r ) and (l//r) type decay. The location of mid-side nodes is fixed based on (ii) theoretical considerations. In the class of static unbounded problems which are solved, infinite elements with an inverse decay are found adequate. The infinite elements with (1/r2) decay may be useful in the analysis of wave propagation problems. The above software is used in the analysis of following problems, Analysis of surface loaded isotropic homogeneous rockmass, Analysis of multi-layered rockmass with rough interface, Analysis of nonhomogeneous semi-infinite rockmass, Analysis of cross-anisotropic semi-infinite rockmass, Analysis of deep openings in isotropic/cross-anisotropic rockmass, Analysis of shallow openings in isotropic /cross-anisotropic /non-homogeneous semi-infinite rockmass, Analysis of parallel and adjacent openings, Analysis of lined tunnels in initial stress field, Analytical derivation of thermal stresses in circular underground openings and its numerical verification, Analysis and design of power tunnels. The conventionally employed truncation approach works only when the truncation boundary is located deep inside far-field. Such a restriction does not apply in the coupled finite/infinite element method of analysis. This feature leads to a smaller FEM mesh than that in the truncation approach. Further, the infinite elements are applicable in the analysis of nonhomogeneous and cross-anisotropic materials. In the abovementioned problems, the infinite element with an inverse decay and a 2 x 2 Gauss-Legendre numerical integration is sufficient. The numerical results are in a satisfactory agreement with the available analytical solutions. Several interesting and important extensions of this study are possible. (iii) The effect of nonhomogeneity and cross-anisotropy on both dis placement and stress field in surface loaded semi-infinite rockmass is significant. In the analysis of power tunnels, rock sharing pressure is found to be uniformly distributed even for the anisotropic rockmass. This may, however, not be true for an extreme case of anisotropy. The thermal stresses in the lining and also the support pressure are found to be significant, but fortunately, the temperature distribution in the rockmass has no effect. This finding is of significant consequence in the design of nuclear waste depositories. Finally, Jaeger>. solution for a power tunnel is extended to include anisotropy, thermal effect and plane strain conditions. The proposed equation may be used for the design of lining in power tunnels even in cold regions