Determination of the failure envelope for brittle fracture of Oil Creek Sandstone Part I: (from Marshak \& Mitra) The purpose of this experiment was to determine the failure envelope that characterizes the strength of Oil Creek. Sandstone (a massive, very fine-grained, well-sorted, wellcemented Ordovician sandstone from Grayson County. Texas). To obtain each experimental data point a jacketed cylinder of sandstone was placed in a tri-axial rockdeformation machine. Then the confining pressure was set at a specified value, and the axial stress (1) was increased until the specimen failed. Note that by increasing the value of 1 while 3 was held constant, we increased the differential stress. This increase is represented by an increase in the diameter of the Mohr circle defining the stress state in the sample. Individual experiments differed from one another in the value of the confining. pressure (3) set at the beginning of the experiment. All experiments were carried out at room temperature and at a strain rate of about 103 per second. The raw data of each experiment (run) were replotted on a graph in which the x-axis was axial strain and the y-axis was differential stress. In each case, when the sample achieved its ultimate strength, it failed by brittlely by formation of a discrete shear fracture. In Figure 10-7 three stress-strain curves obtained during the experiment are shown. The confining pressure for each run is indicated on the graph. The strength of the sample under the specified confining pressure is the maximum stress achieved before the sudden stress drop occurred. The stress drop is indicated by the small arrow at the end of the curve. Exercise: (a) Using the stress-strain plots of Figure 10-7, determine the differential stress, 01 and the mean stress at the point of brittle fracture for each run. List these in Table 10-1. (b) Draw the coordinate axes of a Mohr diagram at an appropriate scale. On the diagram draw the Mohr circle showing the stress state at failure for each run (i.e. you should draw three nonconcentric circles centered at the mean stress for the respective experiment). Note that you must first calculate 1 from knowledge of the differential stress and 3. (c) Draw the two curves that are tangent to all three circles. One curve will lie above the x-axis and one curve will lie below the x-axis. These curves define the failure envelope. Are the curves straight or bent? (d) Calculate the equation that approximately describes the curve that lies above the x axis (i.e., determine the appropriate values for the constants in Equation 10-7). This is the Mohr-Coulomb failure criterion for Oil Creek Sandstone. (e) Is the fracture angle indicated by each circle the same? (f) How does confining pressure affect the fracture strength of Oil Creek Sandstone? (g) Complete Table 10-1. Write a paragraph outlining conclusions that can be drawn from the experiments on Oil Creek Sandstone. 2 Equation 10-17: =c+n, where is shear stress at failure, c is cohesion, is the coefficient of internal friction, and n is normal stress. Figure 10-7. Stress-strain curves for Oil Creek Sandstone (adapted from Handin and Hager, 1957). The confining pressure is indicated next to the curve
