Date of Award

Fall 2013

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Civil Engineering

First Advisor

Antonio Bobet

Second Advisor

Laura J. Pyrak- Nolte

Committee Chair

Antonio Bobet

Committee Member 1

Laura J. Pyrak- Nolte

Committee Member 2

Maria c. Santagata

Committee Member 3

Pablo D. Zavattieri


Results from a series of laboratory experiments to determine fracture specific stiffness, for a fracture subjected to shear and normal stress, are presented and analyzed. The experimental work focuses on the determination of relations between normal and shear fracture specific stiffness and between spatial distribution of fracture specific stiffness and fluid flow through the fracture

The ratio of shear to normal fracture specific stiffness is experimentally investigated on a fracture subjected to shear as well as normal stress. Synthetic fractures made of gypsum and lucite were prepared with different fracture surface conditions: either well-mated or non-mated. For well-mated fracture surfaces, asperities were created by casting gypsum against sandpaper. A block of gypsum was cast against the sandpaper and then a second block was cast against the first block such that the two contact surfaces were well-mated. The surface roughness was controlled by using the sandpapers with different average grit size. Non-mated fracture surfaces were fabricated with two lucite blocks that were polished (lucite PL) or sand-blasted (lucite SB) along their contact surface. In the experiments, each specimen was subjected to normal and shear loading while the fracture was probed with transmitted and reflected compressional and shear waves. Shear and normal fracture specific stiffnesses were calculated using the displacement discontinuity theory. For non-mated fractures, the stiffness ratio was not sensitive to the application of shear stress and, as normal stress increased, approached a theoretical ratio which was determined assuming that the transmission of compressional and shear waves was equal. The stiffness ratio obtained from well-mated fractures ranged from 0.5 to 1.4, which deviated from the conventional assumption that shear and normal fracture specific stiffness are equal. The stiffness ratio increased with increasing surface roughness and with increasing shear stress. For well-mated surfaces under normal compression and no shear, the theoretical ratio gave a good approximation to experiment measurements. During shear, at constant load, and for well-mated fractures with large surface roughness, the stiffness ratio strongly depended on the shear fracture specific stiffness and increased with shear up to a maximum prior to failure.

The spatial variability of fracture specific stiffness along a fracture was investigated seismically on granite specimens with a single fracture. Seismic measurements on intact and fractured granite specimens were obtained as a function of stress. The granite matrix exhibited stress-sensitivity due to the existence of micro-cracks and was weakly anisotropic, with a ratio of about 0.9 for shear wave velocities in two orthogonal directions. For fractured granite specimens, transmission of P- and S- waves across a fracture significantly increased as the fracture compressed. The increase of transmission was interpreted as the increase of fracture specific stiffness. Spectral analysis on the transmitted waves showed that the transmission of high frequency components of the signals increased and the dinant frequency approached the value of the intact specimen. The heterogeneity of the granite material resulted in a ±8∼12% variation in stiffness, which depended on the selection of an intact standard. Fracture specific stiffness was estimated at the dominant frequency of 0.3 MHz for normal specific stiffness and 0.5 MHz for shear. Fracture specific stiffness was non-uniformly distributed along the fracture plane and changed locally as a function of stress. The spatial variability of stiffness exceeded the variation of stiffness caused by the heterogeneity of granite matrix. It was found that local fracture geometry, e.g. local surface roughness distribution or local micro slope angles, influenced the magnitude of local shear fracture specific stiffness. The more uniform the asperity heights, the stiffer the fracture. Also, high micro-slope angles increased the shear fracture specific stiffness.

The seismic response of the rock matrix (granite) and fracture with and without flow was utilized to correlate fluid flow with fracture specific stiffness. Experiments of fluid invasion into a rock matrix and along a fracture showed an increase in wave velocity and a decrease in wave amplitude when the rock became wet. Invasion velocity was determined seismically by tracking the fluid front in the rock matrix.