The goal of our study was to understand how the properties obtained from a deformation test performed on a relatively small portion of a fracture under laboratory conditions can be related back to the in situ properties of the entire fracture. In this paper, we present results of a numerical investigation into the scaling of fracture stiffness with increasing fracture length. Using an efficient boundary element method we were able to simulate hundreds of virtual normal stress tests on entire fracture surfaces and on “sub-fractures” cut from them. In the paper we draw specific attention to the need to perform appropriate numerical processing of the aperture distribution in order that the simulations be representative of relevant experimental configurations. Our results reflect the expected trend with test results performed at small scale resulting in stiffer fracture response than the full fracture according to a power law. In addition, we found that the exponent of the power-law was stress dependent, with less size effect evident as the stress was increased. In this manner, this work provides preliminary insight into the complicated relationship between scale, fracture roughness, stiffness and stress.


We present an efficient numerical method for simulating the deformation and transport properties of fractures, including the effect of detailed surface roughness. Due to its efficiency, this method is suitable for performing extensive parameter studies investigating the interplay between geometrical, mechanical and transport properties in fractures. In our studies of coupled geomechanical phenomena, we are able to perform many detailed, well controlled laboratory experiments at scales ranging from centimeters to approximately one meter at most. Such experiments provide key insights into the fundamental processes at work. However, the phenomena we seek to understand often manifest at scales of tens of meters or more.

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