This paper presents a model for the “plane of weakness” theory applied to a deviated borehole that penetrated laminated shale contains numerous bedding parallel weakness planes. Two conditions determine whether the rock fails along a weakness plane: the relative magnitude of the two normal stresses, and the angle between the borehole and the bedding plane. The model is applied to a deviated well that penetrated a tight fold in the northeastern British Columbia foothills belt in Canada. The well was associated with severe borehole failure prior to this geomechanical study. Subsequent drilling operations utilizing results of this study lead to a successful completion of the project.
Strength properties of bedded rocks have been known for some time. Anderson (1951) presented an early analysis of the phenomenon. Jaeger (1960) gives a thorough analysis of the various loading scenario that explain bedding failure. In particular, Jaeger includes friction in his analysis. A common way to model shear failure using Jaeger’s approach is to use the Mohr Coulomb failure model, but vary the cohesive strength and the angle of internal friction, depending on the loading relative to bedding plane inclination.
The plane of weakness was introduced in the oil industry by Aadnoy (1988). In modeling highly inclined boreholes, he investigated the effects of wellbore inclination, anisotropic elastic rock properties, anisotropic stresses, and anisotropic rock strength. It was shown that under certain conditions, the rock would fail along planes of weakness. Because of the geomechanical properties of shale (common high pore pressure, alignment of phyllosilicates due to overburden diagenesis), slip surfaces may exhibit significantly more potential to fail as compared to stronger rock units, such as limestone and sandstone. For this reason, shale instability is an extremely important and potentially costly problem in many foothills drilling operations in western Canada.
Layered rocks such as shales often exhibit different properties along or across bedding planes. Elastic properties like bulk modulus, Young’s modulus and Poisson’s ratio, show directional properties. The same can be concluded for compressive and tensile rock strength. Figure 1 shows compressional strength data for Arkansas sandstone. Clearly, rock strength is high when force vectors are applied at a high angle to bedding. At lower angles, on the order of 15° and 30°, stratal compressive strength is low. For this case, rock failure will occur along bedding planes. This type of rock behavior is often termed “plane of weakness”. Empirical data indicates that core plugs will fail along similar shear planes, despite varying confining loads.
Figure 1 is a plot showing typical rock response to applied stress. However, the plane of weakness is not so pronounced, generally. Figure 2 shows strength of a Green River Shale under laboratory applied stresses. Although the minimum strength is at about 30° to bedding inclination, reduced rock strength is seen at all inclinations except a where principle compress ional stresses are parallel to bedding.
