The striated and polished glacial pavements on the farm Nooitgedacht 66, northwest of Kimberley, developed at the base of the Dwyka Group, on a substrate of basic lavas of the Pniel Group, Ventersdorp Supergroup, are very well known as both geological and archaeological monuments. First discovered by Stone Age people who left numerous engravings on the striated rock surfaces, the pavements were rediscovered soon after the discovery of diamonds in the Kimberley area in 1870. Despite the extensive studies and abundant geological and archaeological literature on these pavements since 1880, certain peculiar features have been found that seem to have escaped the notice of previous researchers. The newly-discovered features are circular or oval shaped fractures, sometimes concentric sets of fractures, usually arranged around a central circular or oval shaped depression of the smooth glacially striated substrate of Ventersdorp lava, with, in many cases, radial fractures emanating from the central depression. In this paper these structures are analysed, and they are shown to be a form of Hertzian fracture, which forms through impulsive or static loading of an elastic medium by an indenter. Large quartz porphyry erratic boulders found in the Dwyka tillites overlying the glacial pavements are presumed to have acted as the indenters. By the use of Hertzian fracture theory, the average radii of the Hertzian fractures, and the radii of the largest glacial erratics, are used to infer the total maximum thickness of the Karoo Supergroup strata which once covered the area of the glacial pavements. The thicknesses estimated from this preliminary analysis (5.86 km) are about a factor of 2.6 to 2.3 times higher than estimates derived from studies of crustal xenoliths from kimberlite pipes in the Kimberley area. This may be attributed to the assumptions and the many uncertainties inherent in the calculations performed, but it hints at an independent method of calculating the former thickness of eroded Karoo strata in the area, if some of the parameters involved can be refined by further studies.