A correction for sampling bias on joint orientation for finite size joints intersecting finite size exposures

In joint surveys, biases are introduced in sampling for orientation. Terzaghi (1965) developed a correction for orientation bias which depends only on the orientation of the joint with respect to the sampling domain. This bias is applicable only for joints of infinite size intersecting infinite size exposures. In reality, both the joint sizes and the size of the sampling domain are finite. The paper provides a methodology to derive corrections for orientation bias in the case of finite size joints intersecting finite size exposures. The derivation of the correction for a thin circular joint intersecting a finite size rectangular domain is given in the paper. The obtained expression for the correction clearly shows that the bias depends on the sizes and shapes of both the joint and the sampling domain in addition to the orientation of the joint with respect to the sampling domain. For joints of infinite size intersecting infinite size domains, the developed corrections get reduced to the Terzaghi’s (1965) correction. The ways one can apply this derived correction in practice are discussed.