How hydrofractures become arrested Agust Gudmundsson* and Sonja L. Brenner Geological Institute, University of Bergen, Allegt. 41, N-5007 Bergen, Norway Introduction Fractures that are partly, or entirely, generated by internal ¯uid pressure are referred to as hydrofractures. They include dykes, inclined sheets, many joints and mineral veins, as well as man-made hydraulic fractures. Hydro- fractures are among the most common brittle tectonic structures in the earth's crust. They appear to be primarily extension fractures (Gudmundsson et al., 2001) and can thus be modelled as mode I cracks. Except for some magma-driven fractures in the upper crust, hydrofractures are driven by ¯uids that are less dense than the host rock. It follows that a hydrofracture normally has a positive buoyancy term with the potential of driving the fracture to the surface. Despite their positive buoyancy, most hydrofractures do not reach the surface, but instead become arrested at various crustal depths. Hydrofracture pathways are among the main conduits for transporting ¯uids in the crust, so that the conditions of hydrofracture arrest or, alternatively, propagation to the surface, are very important in ®elds such as petroleum and geothermal exploration, waste studies, seismology, volcanology and hydrogeology (e.g. Bonafede and Danesi, 1997; Ingebrit- sen and Sanford, 1998; Hardebeck and Hauksson, 1999; Dahm, 2000; Econo- mides and Nolte, 2000). This paper explores the conditions of hydrofracture arrest and, brie¯y, hydrofracture propagation, in the Earth's crust. This exploration is made, ®rst, by summarizing some basic ®eld observations concerning arrested hydrofractures; secondly, by present- ing analytical models as to crack-tip stresses; and, thirdly, by presenting numerical models on the common conditions for hydrofracture arrest. Field observations In many hydrofractures, for example fractures generated by gas or oil pressure, the ¯uid may disappear once the fracture has formed. Other hydro- fractures, however, are driven open by ¯uids that solidify in the fracture after its formation. These include dykes, sills, inclined sheets and mineral veins, in which case the fracture tips, and their mechanism of arrest, can be studied. The main types of hydrofracture tips are perhaps best illustrated by using well-exposed dyke and vein tips as examples. Some hydrofractures end vertically by tapering away in relat- ively homogeneous and isotropic rock layers (Fig. 1). Others end at discon- tinuities such as contacts, joints or faults. These hydrofractures either thin gradually towards the disconti- nuity or end bluntly (Figs 2 & 3). Where the host rock consists of alternating soft and sti layers, hy- drofractures commonly become arres- ted at layer contacts. For example, many dyke tips in Tenerife and Ice- land are arrested at contacts between soft layers of pyroclastic rocks and sti layers of basaltic lava ¯ows (Fig. 2; Gudmundsson et al., 1999; Marinoni and Gudmundsson, 2000). Also, many veins tips are arrested at contacts between layers of soft marl and stiff limestone (Fig. 3). Crack-tip stresses If a hydrofracture is an extension fracture subject to internal ¯uid pres- sure, the two basic models used to calculate the tensile stresses at its tip are the mathematical crack and the elliptic hole. For a 2D mathematical crack model, a hydrofracture located on the vertical y-axis is de®ned by x  0, )a £ y £ a. The internal ¯uid overpressure (driving pressure or net pressure) of the hydrofracture is given by the even function p(y)  p()y), so that the pressure is the same on the walls above and below the horizontal x-axis. Analytical solutions for tip stresses and opening displacements of elastic cracks are reviewed by Sneddon and Lowengrub (1969), Valko and Econo- mides (1995) and Maugis (2000), whereas Bonafede and Rivalta (1999) provide solutions for stress-concentra- tion eects of interfaces between dis- similar half-spaces on hydrofractures crossing the interfaces. Because the hydrofractures considered here are extension fractures, the normal stress on the crack is the minimum principal compressive stress, r 3 . Consider the case of a constant overpressure, so that p(y)  )P 0 . Then inside the frac- ture, r 3  P 0 , for 0 £ y £ a, whereas outside the fracture tips, for y>a, the crack-tip tensile stress r 3 (y, 0) is: ABSTRACT Fluids in the earth's crust are commonly transported by hydrofractures, such as dykes and mineral veins, many of which become arrested at various crustal depths. Hydrofractures are commonly arrested ± some showing blunt tips ± at contacts between soft (low Young's modulus) and stiff (high Young's modulus) layers. For example, many dyke tips are arrested at contacts between soft pyroclastic rocks and stiff basaltic lava ¯ows, and vein tips at contacts between soft marl and stiff limestone. Theoretical models indicate that overpressured, buoyant hydrofractures in homogeneous, isotropic host rocks should normally reach the surface. In layered host rocks, however, abrupt changes in Young's moduli, horizontal discon- tinuities, and layers with unusually high fracture-perpendicular stresses encourage hydrofracture arrest. It is proposed that for layer-parallel loading, stiff layers favour hydrofracture arrest during active compression but soft layers during extension. It is concluded that for hydrofracture propagation to occur, the stress ®eld along its potential pathway must be essentially homogenous. Terra Nova, 13, 456±462, 2001 *Correspondence: Agust Gudmundsson, Geological Institute, University of Bergen, Allegt. 41, N-5007 Bergen, Norway. E-mail: agust.gudmundsson@geol.uib.no 456 Ó 2001 Blackwell Science Ltd