Purdue University Graduate School

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Rock Anisotropy and Nonlinear Elasticity: Implications for Crustal Stress Measurements 

posted on 2023-06-15, 20:11 authored by Wenjing WangWenjing Wang

Crustal stress measurements play a crucial role in understanding how the subsurface deforms. As one of the most popular methods for stress characterization in deep wellbores, borehole breakout analysis examines the shape of drilling-induced compressive failures to determine stress directions and magnitudes, assuming that the rock formation is both isotropic and linearly elastic. To ensure accurate stress interpretations, the dissertation investigates the validity of underlying presumptions from two perspectives: (1) the effect of rock anisotropy (i.e., elastic anisotropy, and strength anisotropy) on wellbore failure patterns; and (2) the characterization of rock nonlinear elastic mechanical behaviors. 

The developed computer program, EASAfail, has broad applicability in calculating wellbore failure patterns for a wide range of scenarios. It takes into account factors such as elastic stiffness matrices of the rock, stress tensors in the surrounding environment, and the presence of weak planes. The program's generality allows it to handle various rock types with different degrees of symmetry in their elastic properties, as well as weak planes that are weaker than the intact rock matrix. By analyzing these factors, the program reveals that the patterns of wellbore failure in elastic and strength anisotropic rock formations are highly influenced by the sliding of weak planes. Complications from two modes of borehole failure, either in the intact rock matrix or in the weak planes, can cause the breakout azimuth to deviate from the direction of the minimum horizontal stress. 

In addition to hypothetical scenarios generated from numerical models, a case study from the field is presented to underscore the impact of foliations on the anomalous rotations of breakout azimuths. The wellbore was located in Northeastern Alberta, Canada, transecting both the sedimentary column and crystalline basement. Breakout rotations identified from caliper and image logs were highly likely caused by the slippage along foliations, supported by the close correlation between breakout azimuths and dip directions of foliations as well as polarization directions analyzed from dipole sonic logs. Stress magnitudes constrained from Monte Carlo simulations further reveal a lower stress field when rock anisotropy is taken into account, compared to what is inferred conventionally. 

The characterization of rock nonlinear elasticity involves the utilization of the third-order elastic (TOE) model. To measure the TOE moduli in a static manner, test-specific protocols were proposed based on the nonlinear stress-strain behaviors of the rock. By arranging the stress-strain responses obtained from hydrostatic, uniaxial, and triaxial compressive tests into a linear system of equations, it becomes possible to invert the equations for the TOE moduli. These analytical equations were validated through calculations from finite element models. 

By employing the established protocols, the TOE moduli were derived for four different rock types with varying pore structures when subjected to hydrostatic and uniaxial compressions. The TOE model successfully captured the nonlinear stress-strain responses exhibited by Indiana limestone, Vif-type Fontainebleau sandstone, and Snake River Plain basalt. However, it was found to be inadequate for Franc-type Fontainebleau sandstone, which displayed noticeable hysteresis and experienced significant strains. Future geomechanical applications will undoubtedly gain advantages from utilizing the inverted TOE moduli obtained through static measurements, as they allow for the examination of the impacts of nonlinear elasticity in rocks. 


Degree Type

  • Doctor of Philosophy


  • Earth, Atmospheric and Planetary Sciences

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Robert L. Nowack

Additional Committee Member 2

Douglas R. Schmitt

Additional Committee Member 3

Antonio Bobet

Additional Committee Member 4

Julie L. Elliott

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