Uncertainty in predicting geological conditions often leads to postulating worst conditions and thus to conservatism in design and construction. Savings are possible by adapting design and construction methods to the conditions actually encountered during excavation. Specifically, among the excavation and support methods that can be technically used for a given combination of geological parameters, only one will be the most economical. Usually, however, the cost of changing construction method is such that adapting to different geologic conditions is only economical if these conditions persist over long segments of the tunnel. It follows that in defining a set of design-construction options prior to construction and in adaptively selecting them in the course of the excavation, one has to take into account the variability of geologic conditions. This can be done by probabilistically describing the geologic conditions, and by then selecting excavation-support methods using the tools of decision theory under uncertainty. Information that becomes available during construction should of course be used to update the probabilistic description of the geologic condition ahead of the tunnel face. A simple model that accomplishes these objectives is proposed here. Its viability is demonstrated through a case study analysis of the Seabrook Power Station discharge tunnel. Prior to this example, modeling assumptions are stated and a few results from mathematical analysis of the model are given here.
2. PROBABILISTIC GEOLOGICAL PREDICTION
An attractive feature of the probabilistic method for geological prediction described in this section is that it makes more complete use of information already available, without requiring new or more sophisticated exploration programs. Therefore, the approach is implementable under standard practices and procedures. It is based on a Markov-process representation of the spatial variation of geologic parameters. The form of this process makes it possible to easily reduce parameter uncertainty as more information becomes available during preliminary exploration and subsequently during tunnel excavation. Mathematical analysis readily provides initial and updated geological predictions which form the key data for decision making.
2.1 Modeling Assumptions
Tunneling operations and financial planning depend on such parameters as rock type, faulting, degree of jointing and permeability. Some parameters are discrete. For example, "rock type" X 1 may be Schist (X1=1) , Metaquartzite (X1=2) , and Diorite (X1=3). Other parameters are continuous but can be conveniently discretized. For example, "degree of jointing" X2 may be classified as not severe (X2=1) or severe (X2=2). Discretization corresponds to accepted practice and greatly simplifies the analytical model. From a mathematical point of view, the generic parameter Xi can be regarded as a scalar random function of distance from the portal of the tunnel (Fig. 1). Simultaneous characterization of the vector Random process X (l)=[X1(l) .... Xn(l)]T can be either through the joint characteristics of its components (through the distribution of X(l) for each l, the joint distribution of x(l1 ) and x(l2) for each l1 and l2' and so on) or through the marginal characteristics of one component and the conditional characteristics of the other components.