This is my Ph.D. dissertation entitled: “Three-dimensional modeling of underground excavations and estimation of boundary conditions in rock with fabric”. My advisor was Prof. B. Amadei, and the rest of my graduate committee was composed of Profs. S. Sture, R. Pak, D.M. Frangopol, K.J. Willam, W. Savage. The thesis was prepared at the Department of Civil Engineering, University of Colorado, Boulder, and defended in summer 2000.
Abstract: The complex formation and geologic history of rock masses make them anisotropic and initially stressed in their natural state. Efficient tools are needed to predict the response of an
anisotropic rock mass, and to estimate boundary conditions controlling the in situ state of stress. At the outset, this dissertation proposes an implementation of Green’s functions, Green’s
stresses and stress derivatives for three-dimensional, generally anisotropic bodies. Subsequently, this implementation is incorporated into existing Boundary Element and coupled Boundary
Element-Finite Element codes. An extensive numerical investigation shows that the proposed implementation is efficient, precise, and robust even when degenerate materials are used, such as
transversely isotropic or isotropic materials.
Then, the numerical codes developed in the first part are used to investigate the effect of transverse isotropy on underground excavations. The following problems are considered: the
importance of boundary conditions in anisotropic rock masses; the detection of rock mass weakness ahead of the face of an advancing tunnel; the amount of deformation that has taken
place before installation of the lining/support; staged tunnel excavation and tunnel lining. It is shown that: (i) it is possible to predict the presence of rock mass weakness ahead of a
tunnel face by simply monitoring the tunnel wall displacements, even in anisotropic ground and/or under non-hydrostatic state of stress; (ii) when the plane of transverse isotropy strikes
parallel to the tunnel axis, it is possible to use expressions valid for isotropic media in order to calculate the amount of deformation that has taken place before installation of the lining/support;
(iii) when the plane of transverse isotropy does not strike parallel to the tunnel axis, a threedimensional analysis of the rock mass-structure interaction is necessary; (iv) the yielded rock
mass zone around a tunnel and the state of stress in the lining are governed by the spatial attitude of the plane of transverse isotropy.
Finally, a Bayesian approach which can be used to estimate the boundary conditions for rock mass models is presented. Both linearly elastic and non-linear rock mass models are
considered; in the first case, the solution is achieved in a one-step calculation, in the second case an iterative algorithm must be followed. Applications are given pertaining to tunneling and to the
Underground Research Laboratory (URL) of Atomic Energy Canada Limited (AECL), Canada. It is shown that: (i) the proposed procedures allow engineers to incorporate a priori
information, and to update the boundary conditions as soon as new information becomes available; (ii) the proposed procedures are quite general because mixed basic data (displacement
components, stresses, strains) and mixed boundary conditions (stresses, displacement components) may be used without difficulty; (iii) any model of the rock mass can be used, thus
engineers can continue utilizing their own software used for analyzing the rock mass; (iv) the iterative procedure displays fast convergence rate, despite the high degree of non-linearity
involved and/or the complex geology of the site; (v) in tunneling applications, when the objective is to determine the pre-mining state of stress, it is necessary to use absolute displacement
measurements, as opposed to traditional relative displacement measurements, in order for the problem to be well-posed; (vi) it is possible to reproduce the complex in situ state of stress at the
URL site; (vii) discontinuity geometry and slickenside direction and magnitude alone are not always sufficient in order to infer the present in situ state of stress in a rock mass. Measurements
of the current response of the rock mass (in terms of displacement components, stresses, strains) to disturbances (e.g. excavation) must be conducted in order to pin down the current boundary
conditions of a rock mass model.