A finite-element model which includes joint friction and cohesion is presented for the analysis of bedded formations. The intact rock in each layer is modeled by a continuum element while a separate joint element is placed between the layers and at possible fracture planes. Under the action of body forces, the beds separate and cracks are allowed to form for different values of joint friction and cohesion. The stability of the immediate roof is examined for a typical mine opening in a bedded deposit. Comparisons are made with analyses that use elementary beam theory and comments are made concerning the magnitude of the factors of safety that exist for the roof structure.
In the past, theoretical analyses of underground openings were not well received because the assumption of homogeneous elastic material was not suitable for the jointed and sometimes fractured rock mass. However, with the advent of the finite-element method, discrete models which simulate changing properties from point to point have been developed. For example, Zienkiewicz, Valliappar and King  considered the rock mass to have many cracks and fissures and therefore could carry no tension stresses. To improve the model and to include the effect of joint behavior between blocks of intact rock; Goodman, Taylor, and Brekke  presented a joint element which includes shearing stress, friction and cohesion. These developments have allowed a more realistic description of the behavior and state of stress around openings cut into rock masses. It is the purpose of this paper to apply these techniques to the specific problem of a mine opening in a well structured bedded formation.
The nature of the problem is best discussed in reference to Fig. 1 which gives a perspective view of a typical coal seam in a bedded deposit . The major joints run parallel to the strike while minor joints run parallel to the dip of the formation. Two classes of
FIG. I- ORIENTATION FORMATIONS (Available in full paper)
FIG. 2 - OVERBURDEN LOADS NOT CARRIED BY IMMEDIATE ROOF (Available in full paper)
openings are identified depending on the orientation of the joint sets. In a Class I opening the immediate roof is characterized by fairly intact rock with only minor joints present. A Class II opening may have major joints perpendicular to the span of the roof and may be subject to severe fracturing. The analysis of these two classes of openings will be discussed herein.
The immediate roof over the opening can be separated from the formation and investigated as a body-loaded structure without including the overburden pressure. The justification for this assumption is given in Fig. 2 which shows the overburden being transmitted around the opening and into the supporting pillars. When this pressure arch is developed little, or no, overburden loads are carried by the roof strata and it can reasonably be considered as loaded only by its own weight.
The paper will be divided into three parts. First, a description of the finite-element idealization used to model the rock and joint behavior will be given.