Reply to the discussion by Au and Yeung on ‘‘Forms and sand transport in shallow hydraulic fractures in residual soil’’1

Au and Young have studied our paper carefully, and we appreciate both their interest in our work and the opportunity to address some of the questions that arose from their study. We would like to thank them for pointing out their papers and dissertations, and describing results that resemble those from our work. A significant body of research over the last 50 years describes studies of hydraulic fractures in the laboratory. Hubbert and Willis (1957) were among the first, and the papers by Au and Yeung and their colleagues are solid contributions to this effort. However, our paper focused on a field study and we decided to restrict the discussion of laboratory studies to maintain focus on the field problem. The effects of external boundaries must be carefully considered when evaluating the form of hydraulic fractures created in the laboratory. For example, our results, along with those of many other investigators, suggest that hydraulic fractures curve upward when they interact mechanically with an overlying, stress-free surface. The apparatus used by Au et al. (e.g., Fig. 2, Au et al. 2003) shows rigid plates confining the top and bottom of the sample, along with rigid walls around it—no stress-free surface appears to be present. All of the papers cited by Au and Yeung seem to use this same apparatus. Their apparatus is nicely designed and certainly well suited for studying some aspects of hydraulic fractures, and we do not dispute the importance of the findings described in their papers. However, the boundary conditions imposed by the upper and lower plates were different than the stress-free conditions assumed to influence fracture form at shallow depths in the field. The difference in boundary conditions made it difficult for us to assess the relevance of the forms of the fractures they created in the laboratory to the ones we created in the field. We avoided this comparison in the paper as a result. It is worth noting that experimental techniques were described by Galland et al. (2003) for evaluating interactions between hydraulic fractures and free surfaces in silt-sized material with high lateral stresses. We only recently learned about this work and regrettably did not cite it in our paper. Au and Yeung raised several other good points. Some of their questions can be answered by referring to the theses that form the basis of our paper. We are aware that it can be difficult to access the theses and dissertations through normal channels, so to address this issue we have posted the theses written by Tan (2003), Richardson (2003), and Malin (2005) at http://www.ces. clemson.edu/hydro/ murdoch/Student%20Project/index.htm. That site also has photographs and other supporting material. For the purposes of clarity, the comments of Au and Yueng will be summarized into several questions before presenting a reply. Why did we create hydraulic fractures in the B horizon of the soil? The hydraulic fractures were created in the B horizon primarily because this material is relatively homogeneous and isotropic compared with the underlying saprolite, which has a banded fabric as a weathered relic from the original gneiss. The gneiss is strongly folded and the orientation of the mineral banding in the saprolite can be spatially variable. We wanted to conduct experiments in material with relatively uniform properties because we were interested in evaluating the forms of the fractures independent from the influence of major heterogeneities and complex structures, which could possibly dominate the fracture form. This