Joint lineal density is one of the most important joint characteristic elements which describes rock mass properties such as deformability, permeability and so on. This paper suggests joint lineal density diagram in order to describes the joint lineal density measured in the arbitary direction and permeability anistropy diagram in order to describe permeability anistropy of the jointed rock masses estimated in the arbitary direction.


Stereographic projection has been used as a graphic device for solving geological problem. For instance, we often use it to grasp the orientational distribution of discontinuities in rock masses. It also has been applied to examine stability of a rock slope and underground excavern by Hoek and Bray¹) and Hoek and Brown2), respectively and also plays important role in Key Block analysis which is suggested by Goodman and Shi3). Since the mechanical and hydraulic behaviour of jointed rock mass are strongly affected by joint distribution, we have to grasp rock masses anisotropy in order to improve rock masses using grouting technique or reinforce rock masses using Rockbolt and/or anchor effectively. Although it is important subject to grasp it, stereographic projection has not been used to describe rock masses anisotropy directly. So the authors suggest new graphic device in order to express the anisotropy of rock masses by stereographic projection. In this paper the authors suggest Joint lineal density diagram and anisotropic permeability diagram which give us an effective information when we attempt to reinforce or improve joints effectively.


Before referring to JLD diagram and JP diagram the estimation for joint orientation distribution is examined. Since a lot of joints exist in the objective foundation, it is necessary to estimate joint orientation distribution statistically.

2.1 Correction for sampling biases

Joint sampled population usually has sampling biases because joint information that we can obtain from the site, differs with the method of the survey. Scanline or Scanwindow survey is often used in order to sample joint data. Joint orientation distribution which is estimated from the field data directly, usually differ from the genuine distribution in rock masses because of the sampling biases. Therefore it is necessary to remove or minimize these biases caused by each sampling method. Statistically, each sample should not be dealt with equally, but have to be weighted according to the probability of its sampling. As the method to estimate the genuine orientation distrinution of joints, spherical net can be used to calculate the orientation density which is the probability density of orientation distribution. The orientation density is measured at each measuring pole which are established at interval of η=. The coordination of measuring pole is given by zenithal angle θ= and argument angle = in polar coordinate. The measuring pole must be located at a certain interval in order to measuring the density homogeniously on the sphere. It is difficult to established the point at a certain interval on the sphere. Using the following equation, However, we can obtain the location of the point which is homogenious for the engineering purpose on the sphere.


Joint lineal density is defined as the number of joints per unit length that appear on the scanline, and has been applied to the design and construction of the civil engineering structure in various way. For instance, joint mean spacing, which is a reciprocal number of joint lineal density, has been used for a principal element of some notable rock classification methods.

This content is only available via PDF.
You can access this article if you purchase or spend a download.