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D. Veneziano

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Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 31st U.S. Symposium on Rock Mechanics (USRMS), June 18–20, 1990

Paper Number: ARMA-90-0261

Abstract

ABSTRACT INTRODUCTION Rock fracture parameters such as size, attitude, spacing and shape vary in space in a way that can be practically described only in probabilistic terms. Stochastic fracture geometry models have been developed by Baecher, et al. (1977), Veneziano, (1979), Dershowitz, (1985), Long et al. (1985, 1987), Hestir et al., (1987) and La Pointe and Hudson (1985) among others. These models are not completely satisfactory because: -They do not account for spatial nonhomogeneities such as fracture clustering (An exception is the parent/daughter model of Long et al., 1987). -The models are only loosely tied to the geologic genesis of the fractures. In particular, most models assume independence among fracture sets. From a physical viewpoint, this assumption is often incorrect. -Only in a few cases have the models been validated using actual fracture data. A way to address these concerns is proposed here. The main features of our model are that fracture sets are described in a hierarchical order and dependencies among fractures of the same set or of different sets are accounted for. The sequential generation and correlation of fracture sets correspond to what happens in nature. Equally important as the modelling principle is the availability of statistical procedures to estimate parameters and validate the model. In its present form, the model is two-dimensional, i.e. it can be used to describe fracture trace patterns on outcrops. Some comments will be made at the end of the paper how to extend the hierarchical model. The model will be presented by first introducing the basic ideas and then developing the details, the latter simultaneously with showing an application to actual data.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 22nd U.S. Symposium on Rock Mechanics (USRMS), June 29–July 2, 1981

Paper Number: ARMA-81-0361

Abstract

ABSTRACT 1. INTRODUCTION 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 (X 1 =1) , Metaquartzite (X 1 =2) , and Diorite (X 1 =3). Other parameters are continuous but can be conveniently discretized. For example, "degree of jointing" X 2 may be classified as not severe (X 2 =1) or severe (X 2 =2). Discretization corresponds to accepted practice and greatly simplifies the analytical model. From a mathematical point of view, the generic parameter X i 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)=[X 1 (l) .... X n (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(l 1 ) and x(l 2 ) for each l 1 and l 2 ' and so on) or through the marginal characteristics of one component and the conditional characteristics of the other components.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the 19th U.S. Symposium on Rock Mechanics (USRMS), May 1–3, 1978

Paper Number: ARMA-78-0090

Abstract

ABSTRACT: The Probabilistic Model for Shearing Resistance of Jointed Rock is a step in the development of complete methods for reliability analysis of rock slopes. The model derives the probability distribution of the strength of a discontinuous rock mass taking uncertainty on the joint pattern into consideration. The distributions of joint spacing and length from field surveys, the shear resistance parameters of intact rock and rock discontinuities, and the in-situ stress field are input data to the model. The paper describes the two main parts of the method, the stochastic model of joint geometries and the mechanical model. The results of actual computations are then presented and discussed to show the practical applicabilities of the method and to examine the sensitivity to various input parameters. The main qualitative, conclusion is that the probability distribution of apparent persistence is insensitive to variations of the stress field and of the joint orientation relative to the stress field. Apparent persistence depends strongly however on the distribution parameters of joint spacing and length together with cohesion of intact rock. 1. INTRODUCTION Probabilistic approaches to rock slope stability analysis have become increasingly common because they provide a rational incorporation of the uncertainty of parameters affecting slope stability. Risk analyses and Bayesian updating techniques used in site exploration require the use of probabilities of failure rather than the traditional factor of safety. Complete probabilistic modeling is theoretically possible but may be somewhat premature because the assumed mechanisms and associated parametric relations may introduce inaccuracies that have a greater effect than the uncertainty of individual parameters. In this paper a limited topic, the effect of discontinuity geometry on slope stability, will be treated. This partial model can later be incorporated into a complete probabilistic slope stability analysis.