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Four sand-filled hydraulic fractures were created at a depth of 1.5 m, and the vicinities of the fractures were excavated and mapped in detail. All the fractures were shaped like slightly asymmetric saucers between 4.5 and 7.0 m across that were roughly flat-lying in their centers and curved upward to dip between 10° and 15° along their peripheries. Three different colors of sand were injected in sequence to trace the relative ages of the sand in the fracture. The first sand to be injected remained in the vicinity of the injection casing, whereas the last sand moved rapidly to the leading edge. Sand transport occurred through localized, channel-like pathways that extended from the injection casing and then branched into multiple paths as they approached the leading edge. At least four branching pathways of different ages were identified in one fracture, suggesting that this represents a fundamental mechanism of sand transport in these shallow fractures. A theoretical model was developed by adapting Franc2d, a code well-known in structural mechanics, to predict the propagation paths of curved hydraulic fractures at shallow depths. The model predicts fracture forms that are remarkably similar to those in field exposures when properties typical of field conditions are used. [ABSTRACT FROM AUTHOR]

The article presents a response to the discussion made by S. K. Alfred Au and Albert T. Yeung on the authors' paper "Forms and sand transport in shallow hydraulic fractures in residual soil." They appreciate both the interest of Au and Young on their work and the opportunity to address some of the questions that arose from discussers' study. They are grateful for the discussers for pointing out their (Au and Young) papers and dissertations, and describing results that resemble those from their work. In this article, they discuss and clarify some points presented by the discussers.