The triangular stress diagram; a graphical representation of crustal stress measurements

Abstract

A new graphical method is introduced that facilitates the representation and interpretation of the generally anisotropic in situ states-ofstress measured in rocks. The purpose of the method is to clearly and easily display these stress states, each measured in terms of three values, in two-dimensional space; this is done by projecting three-dimensional stress space onto a triangular-coordinate (ternary) diagram and plotting the measured stress states as points. Failure surfaces determined either by experiment or by invoking hypothetical failure criteria are plotted on the diagram to enclose the stability field. Thus, an anisotropic stress condition measured at a given depth in the Earth's crust is represented by a single point on the triangular diagram and its relative position in the enclosed stress space may yield useful information on the degree of mechanical stability of the rock mass at the point of measurement. The method also allows the representation of any number of measured stress states in a given locality, each plotted in its own position. This method is most useful as a reconnaissance tool, provided complete measurements of in situ stress as a function of depth are available, to correlate them with information obtained by different, more indirect methods. A variety of stress paths either associated with the measured stress-depth distribution, or modified by fluid injection or mined excavations, among others, can be traced or extrapolated to establish whether the imposed disturbance leads to failure of crustal rocks.

Estimating in situ Stresses

“…Figure 2.34a shows the geometry of the Earth modeled by Sheorey (1994). Figures 2.34b, c indicate that the model predicts large values of K at shallow depths and a value of 11 MPa for the horizontal stress at the ground surface, which is in agreement with maximum in situ stress values of about 10 MPa measured at the surface of the Earth (Swolfs, 1984). The crust has an average thickness of 35 km and the radius of the Earth is equal to 6371 km.…”

“…Such contrasts were found to occur sometimes on a scale of less than 1 m if the contrast in rock properties was sufficient. Swolfs (1984) compiled data on the variation of ratio of the minimum horizontal stress to vertical stress with depth measured by hydraulic fracturing in sedimentary basins. ) higher in layers with a low Young's modulus and high Poisson's ratio.…”

“…At the Earth's surface the variation of the horizontal stress with time is obtained by taking z = 0 in equation (2.27) (Swolfs, 1984), Eo = 0.5 GPa, a strain rate of 1.0 X 10 -14/ s (0.32 f.l-strain/ year), the relaxation time I] is found to be equal to 31746 years. Assuming that Vo = 0.25, equation (2.30) gives a horizontal stress of 0 at t = 0, a stress of 4.87MPa at t = 31746 years, and a stress of 9.9 MPa at t = 238095 years.…”

“…An exception to this observation is for salt domes for which stresses have been found to be essentially hydrostatic to within 2 MPa (Eriksson and Michalski, 1986). Indeed, measured horizontal stress levels at the surface of the Earth have been found to have an average maximum value of about 10 MPa (Swolfs, 1984). Indeed, measured horizontal stress levels at the surface of the Earth have been found to have an average maximum value of about 10 MPa (Swolfs, 1984).…”

Appalachian Stress Study: 3. Regional scale stress variations and their relation to structure and contemporary tectonics

“…Near-unity R h values are often measured in shales and are usually ascribed to "shale creep" promoting an isotropic stress state [Swolfs, 1984;Warpinski et al, 1983]. Near-unity R h values are often measured in shales and are usually ascribed to "shale creep" promoting an isotropic stress state [Swolfs, 1984;Warpinski et al, 1983].…”