There are several factors supporting or enhancing formation of a joint set rather than a single runaway joint. First, multiple flaws distributed throughout a rock volume. Hence at the initiation of a joint array or during its evolution there are numerous individual joints competing for the opportunity for the next incremental growth. Second, stress relief or stress shadow around a joint resulting in a highly heterogeneous stress distribution such that other joints can only develop outside the immediate sphere of influence of an incipient joint. As shown by Lachenbruch (1962), formation of a joint releases stresses perpendicular to the joint in a region whose lateral dimension scales with joint height (Figure 1). This concept provides a basis for estimating the distance from an existing joint by which another joint can form and is relevant to how joint spacing is related to the joint height or layer thickness.

Figure 1. Theoretical values of elastic stress relief due to a vertical tension crack from Lachenbruch (1962). Plot of horizontal stress at the surface versus distance from the fracture for different loading distributions. Inset shows idealization of the fracture as well as defines symbols.

A similar argument can be made for an array of joints growing away from a surface (Figure 2). If one of the joint elements advances by a small increment, this reduces the propagation energy available for the nearby joints and this reduction is proportional to the amount of increment and inversely proportional with the distance from the joint with the growth increment (DeGraff and Aydin, 1993). Interested readers may also want to see Pollard and Aydin (1988), and Nur (1982), the latter of which focused on lineaments primarily based on geomorphic expressions.

Figure 2. The influence of a fracture with a small increment of growth on the propagation energy available for subparallel fractures in an array. The decrease of the propagation energy for the neighboring fractures is proportional to the amount of increment and inversely proportional to the distance from the fracture with the growth increment. Redrawn from from DeGraff and Aydin (1993).

As we pointed out earlier, interaction among neighboring joints and their propagation velocity are important factors in influencing joint set properties.