Flow and fracture maps for basaltic rock deformation at high temperatures
Introduction
Pervasive fracturing of rock at high temperatures is a dominant feature of volcanic systems: whether this is fracturing of the country rock surrounding magma chambers (inferred from seismic activity; Newhall and Punongbayan, 1996), or fracturing of lava domes (Fink and Griffiths, 1998), fracturing of the crust of mobile lava flows (Fig. 1), or their solidifying fronts (Kilburn, 1993, Kilburn, 2000). As a result, understanding how the strength of rock varies with the specific extrinsic conditions of stress state, pressure and temperature, and the intrinsic conditions of composition and water content, joints, flaw and crack damage, crystal and vesicle size, content and anisotropy is fundamental to understanding the dynamics of volcanic systems. Two diverse examples are the conditions for magma ascent and the emplacement of lava flows. Thus, magma ascent is affected by many independent factors such as the tectonic setting and pressure changes within the magma. However, it is the failure of the host rock below the volcanic edifice, involving fracture at elevated temperatures, that leads to the opening of new pathways through which fresh magma is able to reach the surface (Gudmundsson, 1998, Gudmundsson, 1995, Ryan, 1994, Shaw, 1980). The second example, lava flows, involves the primary hazard from effusive volcanoes, and modelling rates of flow advance and maximum potential length are important goals for hazard mitigation (Kilburn, 1996, Kilburn, 2000). Again, many factors affect the way a flow evolves, including effusion rate, cooling processes, channel pressures and the topography of the ground over which it travels. It has long been recognised that material properties, such as rheology are important controls on lava behaviour (Nichols, 1939), but only recently has the importance of lava strength also been addressed (Kilburn, 1996).
Indeed, fracture in general plays a crucial role in limiting material strength (Griffith, 1921). To understand how rock strength at high temperatures varies with extrinsic and intrinsic conditions it is essential to understand how these affect both flow and fracture, and how flow ‘strength’ is limited by fracture. Sometimes this is counter-intuitive. We advocate that principal stress failure maps, introduced by Hallam and Ashby (1990) and employed for instance by Sammonds et al. (1998) to describe sea ice fracture, are the best means of representing rock flow and fracture and interpreting for ductile–brittle transition, under conditions of stress, pressure and temperature relevant to volcanic systems.
In this paper, we introduce the use of principal stress failure maps and discuss their application to investigating the deformation of predominantly basic igneous rocks. The principal stress failure map is a graphical representation of ductile and brittle experimental data together with mechanical models of flow and fracture plotted in two dimensions on maximum and minimum principal stress axes, σ1 and σ3, shown in schematic form in Fig. 2. (We use the convention that the principal stresses are denoted by σ1≥σ2≥σ3; tension positive.) When σ1=σ2=σ3=P, the rock is subject only to hydrostatic pressure, P, and the axis of symmetry on the map, σ3=σ1 is called the hydrostat. The map has a tension–tension quadrant where simple and biaxial tensile test data are plotted, a compression–compression quadrant, and two tension–compression quadrants where data from confined extension tests are plotted. For the conventional triaxial deformation test, which is the most common rock mechanics test, two of the applied stresses have equal values, σ1=σ2>σ3, (they are referred to as the confining pressure, p) and results are plotted in the compression–compression quadrant on the map for axial stress, σ3, against confining pressure, P=σ1. Ductile deformation results fall on creep envelopes for a particular creep strain rate, which are parallel to the hydrostat. The fracture envelope truncates the creep envelopes as fracture limits strength. (A fuller description of the principal stress failure map is given below.)
Models and data for rock failure are also commonly plotted on two other representations: the Mohr construction and the deformation mechanism map (Frost and Ashby, 1982, Murrell, 1990). The Mohr construction plots shear stress against normal stress, but is poor at representing strain rate dependent processes. The deformation mechanism map plots shear stress against temperature, but is poor at representing the effect of normal stress (or pressure). The principal stress failure map can be employed to demonstrate both the effects of pressure and strain rate dependent processes. Therefore it is the best means of representing ductile flow, which is strongly dependent on strain rate, and the role of fracture in limiting strength, as fracture is strongly dependent on normal stress or pressure.
To construct principal stress failure maps specific experimental data are needed. After a comprehensive literature review of numerous deformation experiments on basaltic rocks over a wide range of test conditions we have constructed the failure maps which we present below, and then used them to re-interpret the experimental data and the ductile–brittle transition. Basaltic lava forms and evolves from fluid to solid state, under limited temperature and pressure conditions: between about 1200 and 500°C and from atmospheric pressure to about 3–4 MPa. In the case of magma host rock, temperatures may range from 1200°C to as low as 100–200°C, but pressures may reach 75 MPa, corresponding to about 3-km depth in the crust. However few laboratory deformation experiments have been done on basaltic rocks under conditions of high temperature and comparatively low pressure: only a handful of fracture experiments have been done under these conditions (see below). We have therefore constructed failure maps for conditions relevant to volcanic systems by extrapolation from experimental data gathered over a wide range of conditions, but point out where further experimental research is required to validate these extrapolations. We then show, conceptually, how these failure maps can be applied to volcanic systems, using lava flows as an example. (A complete solution requires a detailed stress analysis, which is beyond the scope of this paper.)
Section snippets
High-temperature mechanical tests on basic igneous rocks
The rheology of molten lava, besides temperature, is strongly controlled by silica content, water content, crystal content, polymerisation, vesiculation and degassing (for a review, see Dragoni, 1993). Kilburn (1993) pointed out that as molten lava cools, in the crystallisation interval (nominally from 1200 to 950°C for basalts) compressive strength increases from 0 to ∼108 Pa, thereafter remaining at about 108 Pa during cooling to room temperature (Murrell and Chakravarty, 1973) and the
Principal stress maps of flow and fracture
The principal stress failure map (Fig. 2) can be used to plot results from creep and fracture tests of creep-brittle materials obtained from laboratory deformation experiments (Hallam and Ashby, 1990). Fully dense flow is driven by the shear stress alone and is independent of pressure, or mean stress, except at very high pressures of the Earth’s mantle (Frost and Ashby, 1982). Steady-state isotropic flow can be described by the power law creep equation. On the principal stress map, the flow
Experimental data and their representations
We have constructed the creep envelopes using the power-law creep equation (Eq. 3) with data from laboratory triaxial deformation tests on basaltic rocks only. The peak differential stresses required for ductile deformation attained during constant strain rate ‘strength’ tests have been shown to be the same as the stresses required to induce minimum strain rates in constant stress ‘creep’ tests (Mellor and Cole, 1982). Ductile strength data can therefore be expected to conform to the power-law
Discussion
The principal stress maps shown above were constructed using experimental data from at least 20 different volcanic rock types, including mainly basalts but also diabase and andesite. Fracture models, power-law creep models and the failure data plotted on the maps belong to different rock types and used different test conditions. Nevertheless all data conform to the same fracture criterion and all equal rock types conform to the same creep power law. The fracture criterion predicts well the
Application to lava flow
Lava flows are subject to a number of characteristic forces such as gravity and the resistance of the solidifying crust and strengthening lava crust and interior. The combination of such forces causes the rock to deform by both viscous flow and brittle fracture. Understanding the influence of tensile and shear stress, strain and temperature on each dynamic regime and how these factors interrelate with each other is a key to understanding how far a flow will advance and by what mechanisms.
Conclusions
The deformation mechanisms and the deformation properties of several intrusive and extrusive igneous rock types, all of which have been studied by laboratory experiments, have been collected and plotted on the same 2-D principal stress maps. The power law creep equation and the fracture criterion were also plotted on the same map to show where the transition from ductile to brittle behaviour occurs within this stress space.
Analysis of the maps shows that key data are missing for conditions
Acknowledgments
This research was supported through the European Union Framework V Environment Programme Contract No. ENV4-CT98-0713. Peter R. Sammonds is a Royal Society University Research Fellow. This paper has been improved by the helpful comments of Harry Pinkerton.
References (62)
- et al.
High-temperature behaviour of basalts; role of temperature and strain rate on compressive strength and KIc toughness of partially glassy basalts at atmospheric pressure
Int. J. Rock Mech. Min. Sci. Geomech. Abs.
(1991) Infrastructure and mechanics of volcanic systems in Iceland
J. Volcanol. Geotherm. Res.
(1995)- et al.
Experimental deformation of a glassy basalt
Tectonophysics
(1991) - et al.
Water in the Oceanic upper mantle: implications for the rheology melt extraction and the evolution of the lithosphere
Earth Planet. Sci. Lett.
(1996) - et al.
Some studies of low temperature rock strength
Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
(1984) - et al.
The dynamic strength and fracture properties of Dresser basalt
Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
(1974) - et al.
Deformation and failure of ice under constant stress and strain rate
Cold Reg. Sci. Technol.
(1982) Experimental deformation of diopside and websterite
Tectonophysics
(1978)- Balme, M.R., Rocchi, V., Sammonds, P.R. and Vita-Finzi, C., 2002. Experimental and Theoretical Fracture Mechanics...
- Bauer, S.J. Friedman, M. and Handin, J., 1981. Effects of water-saturated on strength and ductility of three igneous...
Mechanical twinning in experimentally deformed plagioclase
Contrib. Mineral. Petrol.
Strength characteristics of rock samples under hydrostatic pressure
Trans. Am. Soc. Mech. Eng.,
Transient creep and semi-brittle behaviour of crystalline rocks
Pure Appl. Geophys.
Steady state flow of rocks
Rev. Geophys.
The deformation of flat ellipsoidal cavities under large confining pressures
Bull. Seismol. Soc. Am.
Morphology, eruption rates, and rheology of lava domes: Insights from laboratory models
J. Geophys. Res.
Strength and ductility of four dry igneous rocks at low pressures and temperatures to partial melting
Proc. Symp. Rock Mech.
The phenomena of rupture and flow in solids
Phil. Trans. R. Soc., London
Deformation of rocks at 500°C to 800°C
Geol. Soc. Am. Mem.
Magma chambers modelled as cavities explain the formation of rift zone central volcanoes and their eruption and intrusion statistics
J. Geophys. Res.
Measurements of creep in igneous rocks
J. Earth Sci., Nagoya Univ.
Cited by (26)
Experimental investigation on dynamic mechanical behavior and fracture evolution of fissure-filled red sandstone after thermal treatment
2021, Engineering GeologyCitation Excerpt :In practice, natural rocks usually contain numerous fissures such as diagenetic fissures, weathering fissures, tectonic fissures, engineering fissures, etc. (Noda and Kiremidjian, 1991) which are often filled with materials such as mineral veins, weathering products and cement mortar due to the geological action and artificial intervention. The studies on the effect of temperature on the mechanical characteristics and failure patterns of rocks under static and dynamic conditions have mainly focused on intact rocks (Rocchi et al., 2003; Wan et al., 2009; Masri et al., 2014; Liu and Xu, 2015b; Andreev et al., 2019; Yin et al., 2019, 2020; Wang et al., 2020; Li et al., 2020; Li et al., 2021a,b). Nevertheless, the effect of temperature on the dynamic mechanical behavior and damage characteristics of rock masses containing fractures may be more comparatively realistic.
Non-local structural derivative Maxwell model for characterizing ultra-slow rheology in concrete
2018, Construction and Building MaterialsCitation Excerpt :When α = 1, the creep compliance of the ultra-slow Maxwell model can be degenerated into the Lomnitz creep model in Eq. (1), where q = E/η and τ = 1. It confirms that the ultra-slow Maxwell model is much slower than the Lomnitz creep model reported by various scholars [18,21,22]. Similarly, Fig. 6 shows that the smaller structural parameter leads to the slower relaxation and the smaller relaxation deformation.
Influence of loading and heating processes on elastic and geomechanical properties of eclogites and granulites
2018, Journal of Rock Mechanics and Geotechnical EngineeringStudy on dynamic characteristics of marble under impact loading and high temperature
2013, International Journal of Rock Mechanics and Mining SciencesCitation Excerpt :De Bresser et al. [9] focused on the question if water affects the strength of marble deforming at high temperature and established criteria that allowed assessment of the role of water in microstructure development in marble. Rocchi et al. [10] collated and analyzed laboratory data for basaltic rocks from over 500 rock deformation experiments and plotted these on principal stress failure maps. Mufundirwa et al. [11] monitored the natural rock slope deformation across fractures predominantly in a chert rock mass using six surface fracture displacement sensors, and predicted the deformations arising from thermal stresses using (5 m×5 m) two-dimensional(2D) finite element (FE) plane strain analysis coupled with a model for rock mass expansion due to freezing of pore water.
Deformation modes in an Icelandic basalt: From brittle failure to localized deformation bands
2013, Journal of Volcanology and Geothermal ResearchCitation Excerpt :Note that pore pressure is one of the most variable parameter in the earth crust. The role of pore fluid in the mechanics of the crust has been extensively studied in the past (Rocchi et al., 2002; Kato et al., 2003; Balme et al., 2004; Ramsey and Chester, 2004). More recently, a specific fluid-induced rupture experiment was performed on a Fontainebleau sandstone recording acoustic emissions (Schubnel et al., 2007).