A Constitutive Equation for Nonlinear Stress-Strain Curves in Rocks and its Application to Stress Analysis Around a Borehole During Drilling

Abstract

ABSTRACT The stress-strain behavior of Berea, Ohio, and Pecos sandstone was measured intensively under triaxial loading paths. Both compression and extension tests were performed at different pore fluid pressures. These tests showed that four modes can arise in the stress-strain curves up to failure: an initial nonlinear portion; linear portion; a final nonlinear portion; and volume change of the rock maxtrix due to pore fluid pressure. The characteristics of these modes were studied, and a nonlinear model was developed to represent the important characteristics, i.e., the four modes, of the behavior of sandstones by means of a constitutive equation in such a way as to satisfy certain mathematical requirements. A finite element model using nonlinear stress-strain relationship was developed which simulates the stress state of a structure up to failure. The finite element model was used to predict fracture pressure around a borehole during drilling. The shape of the borehole is either circular or elliptic, and the tectonic stress is directional. Since the nonlinear stress state depends upon loading history, the loads were applied incrementally, simulating phenomena occuring during the drilling process. It is shown that use of conventional linear stress-strain behavior gives significantly erroneous results for well stability problems.