In laboratory tests, the onset of dilation occurs at stress levels far below the peak strength but yielding of the laboratory specimen is not synonymous with the onset of dilation, and is seldom measured or reported in traditional laboratory testing. In field tests, the on-set of dilation is often associated with stress-induced extension fracturing. The displacements associated with these stress-induced fractures, cannot be replicated using traditional constitutive modelling and associated or non-associated flow rules. In this paper a methodology is developed for modeling dilation using the Particle Flow Code (PFC) that captures many of the observations reported in conventional laboratory test results. The findings from this research show that clumped-particle geometry provides the best agreement with laboratory test results for both tensile and compressive loading paths.
Experience with underground excavations at depth indicates that one of the most significant phenomena observed in brittle rocks is extensile fracturing. This fracturing occurs as a result of tangential stress concentrations. Direct observation of brittle rock failure around underground openings reveals that this extensile fracturing exhibits significant dilation (Fig. 1). A detailed description of the spalling process observed around a circular test tunnel was given by Martin et al.  and Lajtai  showed that in laboratory samples the brittle failure process resulted in the opening of fractures.
In materials such as metals and clays, yielding can occur without significant volume change. However, in brittle rocks on the boundary of underground openings overstressing results in the development of micro- and macro-cracks. In the mining industry, the process is often referred to as 'spalling' or 'dog-earing'. In the petroleum industry, the problem is often cast as 'well-bore breakouts'. One of the early descriptions in civil engineering was given by Terzaghi  and referred to as 'popping rock'. Modeling of this process has always been challenging and has received a lot of attention in the mining, nuclear waste and petroleum industries since the 1950's.
With the advent of modern computers, both continuum mechanics and traditional fracture mechanics approaches have been used to model this fracturing process [3-6]. The use of continuum mechanics to
(available in full paper)
Fig. 1: Dilation associated with stress-induced fracturing observed in a 600-mm-diameter borehole.
simulate a fracturing process that results in an open rough fracture, as described by Lajtai  and shown in Fig. 2, is extremely problematic as the displacement field across the fracture in a continuum must be continuous. But if the fracture is open, this requirement cannot be satisfied. In traditional fracture mechanics, the fracture has zero width, again suggesting that this approach is not applicable for representing a process that results in open fractures. In all these approaches specific flow rules are required to capture the displacement field. In continuum mechanics an associated or non-associated flow rule is assumed.
For the fracture mechanics approach the control of the fracture growth is related to the fracture toughness (KIC) [4, 6-8]. In both approaches there are fundamental shortcomings.