DISTRIBUTION OF JOINTS - PROBABILISTIC MODELING AND CASE-STUDY NEAR CARDIFF (WALES, UK)

In this paper a new probabilistic two-dimensional model for simulating joint development in a single vertical set cutting horizontally layer ed rocks is presented. The problem of considering the probability of j oints nucleating within limestone beds and the probability of joints p ropagating across mudstone interbeds is solved using matrix analysis. Sources of dispersion, relationships between joint spacing and bed thi ckness, and the influence of pre-existing joints on vertical propagati on were taken into account. Simple assumptions were made concerning th e sense of vertical joint propagation, poorly constrained by field dat a in most cases. We demonstrate that, with the input of just a few geo metrical and statistical parameters, realistic cross-sections can be c onstructed based on the probabilistic modelling. Our field analysis ai med to: (1) provide real values for the statistical parameters; and (2 ) compare actual and simulated patterns in order to check our results. Input parameters include bed thicknesses, average numbers of joints a nd the proportion of joints cutting two adjacent limestone beds. Field data were collected from coastal exposures in Liassic rocks at Llantw it Major (Wales, U.K.). At the sample sites, tabular layers comprise a lternating decimetric limestones and centimetric mudstone interbeds. T hey are cut by two orthogonal sets of vertical joints. We studied the distribution of the dominant joint set striking N170 degrees. Both the models and the outcrops display similar characteristics, e.g. a log-n ormal distribution of joint spacing and a negative exponential distrib ution of the number of joints vs the number of beds crossed. Our proba bilistic modelling is applicable to other situations with a limited nu mber of numerical constraints obtained from field or sub-surface obser vations. (C) 1997 Elsevier Science Ltd.