Viscoelastic behaviour of basaltic lavas

Viscoelastic behaviour of basaltic lavas

M.R. James a;b;�, N. Bagdassarov a, K. Mu«ller a, H. Pinkerton b

a Institut fu«r Meteorologie und Geophysik, J.W. Goethe Universita«t Frankfurt, Frankfurt am Main, Germanyb Department of Environmental Science, I.E.N.S., Lancaster University, Lancaster LA1 4YQ, UK

Received 3 December 2001; accepted 15 July 2003

Abstract

The rheological properties of basaltic lavas from Etna, HawaiPi and Vesuvius have been investigated attemperatures between V500 and 1150‡C using a small-strain oscillatory shear. The viscoelastic response of the lavasto small, forced, sinusoidal torques (6 1033 N m) at frequencies between 0.002 and 20 Hz was measured. A purelyviscous regime was only approached during experiments with HawaiPi samples. These experiments indicated that attemperatures between V1070 and 1130‡C, strain rate-independent viscosities (s 109 Pa s) could be measured at strainrates less than V1032^1031 s31. At 800‡C, temporal variations in complex shear modulus and internal frictionsuggest that, over durations of up to 120 h, structural adjustments were occurring within some of the samples. Thistime-varying behaviour of lava samples may be attributed to the slow closing (healing) of microcracks and small porespaces, resulting in the apparent stiffening of lava samples under annealing. Thus, those parts of lava flows thatundergo slow cooling will have more elastic properties. Regions that cool faster possess smaller shear moduli andhigher internal friction due to thermal microcracking and less cohesion between crystals and the bulk glassy matrix.: 2003 Elsevier B.V. All rights reserved.

Keywords: basalt lava; Etna; Vesuvius; HawaiPi ; shear modulus; shear viscosity; oscillatory rheology

1. Introduction

The rheological properties of basaltic lava arecritical parameters in determining the advancerates, morphology and ¢nal dimensions of basal-tic £ows. Rheology is controlled by a number offactors, the most important of which are compo-sition, temperature, crystallinity and bubble con-tent. The e¡ects of these factors on the viscosity

of lavas between eruption and solidi¢cation havebeen analysed by previous workers (Shaw et al.,1968; Sparks and Pinkerton, 1978; Marsh, 1981;Ryerson et al., 1988; Pinkerton and Stevenson,1992; Pinkerton and Norton, 1995; Richet etal., 1996; Dingwell et al., 1998). At temperaturesbelow their eruption temperature, lavas displayviscoelastic behaviour and, at temperatures belowthe glass transition temperature, Tg, of their glassmatrix, they are anelastic (Sakuma, 1953; Bagdas-sarov, 2000). Field measurements carried out athigh stresses (V103 Pa) and typical eruption tem-peratures indicate that basaltic lavas have a rathermoderate viscosity (s 102 Pa s) and an appreci-able static yield strength (V102^103 Pa) (Shaw et

0377-0273 / 03 / $ ^ see front matter : 2003 Elsevier B.V. All rights reserved.doi:10.1016/S0377-0273(03)00340-8

* Corresponding author. Tel. : +44-1524-593574;Fax: +44-1524-593985.

E-mail addresses: [email protected] (M.R. James),[email protected] (N. Bagdassarov),[email protected] (H. Pinkerton).

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Journal of Volcanology and Geothermal Research 132 (2004) 99^113

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al., 1968; Pinkerton and Sparks, 1978; Pinkertonand Norton, 1995; Norton and Pinkerton, 1997).

The sti¡ness of solidifying lava, the temperaturerange over which solidi¢cation and the anelastictransformation occur and the kinetics of fractur-ing and fracture healing processes are importantparameters for lava £ow modelling. Quanti¢ca-tion of these processes may be important, for ex-ample, in the prediction of lava £ow carapacegeneration or break-up. Here, we present the re-sults of viscoelastic measurements carried out onsamples of basalt lava £ows taken from Etna,HawaiPi and Vesuvius at temperatures in therange V500^1150‡C. These reveal the importanceof cooling rate of lava £ows on the strength oflavas.

Experiments designed to characterise the high-temperature anelastic and viscoelastic behavioursof glassy, crystalline and partially molten rocksare based on measurements of elastic modulus(G*) and internal friction (Q31). Traditionally,these measurements are performed using an in-verted torsional pendulum (e.g. Day and Rin-done, 1961; Gueguen et al., 1981; Weiner et al.,1987; Versteeg and Kohlstedt, 1994) or by forcedtorsional oscillation (Berckhemer et al., 1982;Jackson and Paterson, 1987; Bagdassarov andDingwell, 1993; Gribb and Cooper, 1998). Theforced torsional oscillation method used in thiswork has previously been used to study the be-haviour of both rocks (Berckhemer et al., 1982;Jackson and Paterson, 1987; Gribb and Cooper,1998; Bagdassarov and Dorfman, 1998) andglasses (Bagdassarov and Dingwell, 1993; Bag-dassarov et al., 1993, 1994). This technique allowsthe magnitude of the complex shear modulus andangle of internal friction to be measured over arange of temperatures and frequencies.

2. Apparatus

The experimental method consists of exertingsmall-strain oscillatory torsion deformation on cy-lindrical samples. The equipment (described in de-tail previously (Berckhemer et al., 1982; Kampf-mann and Berckhemer, 1985; Bagdassarov andDingwell, 1993)) exerts a small sinusoidal torque

(of amplitude V1033 N m) to the end of a cylin-drical sample (8 mm in diameter, V20^30 mm inlength). A simple schematic of the device is shownin Fig. 1a. The sinusoidal torque applied to thesample is generated using a pair of electromagnets(two microphone-type coils) connected to a syn-thesiser via a power ampli¢er. The sample is ¢xedbetween two aligned alumina rods, onto whichtwo sets of light aluminium wings are also at-tached. The angular deformation across the sam-ple is measured by pairs of capacitive pick-upswhich respond to the movement of pure ironplates located at the ends of the aluminium wings.The capacitive signal is detected and ampli¢edusing a 5-kHz frequency bridge which is sampledusing a PC. Calibration of the equipment hasbeen described previously (Bagdassarov, 2000),with shear modulus measurements being accurateto 3^5% (due to thermal drift of the calibration athigh temperatures).

Although the mechanical design of the equip-ment has not changed from that used during pre-vious work, the data acquisition hardware andprocessing software have been signi¢cantly im-proved. For each measurement, data are collectedover two periods of the torsional oscillation (Fig.1b). Data are sampled at up to 10 kHz, allowing1000 samples per channel to be acquired at thehighest frequency used during experiments (20Hz). At torsional oscillation frequencies of 2 Hzor lower the number of samples per channel islimited to 10 000. Sinusoids are automatically ¢t-ted to the collected data using a Levenberg^Mar-quardt algorithm, and the shear modulus andphase di¡erence between the applied torque andthe angular displacement across the sample arecalculated from the phase and amplitude param-eters of the ¢tted curves.

Experiments were carried out over the fre-quency range 0.002^20 Hz (at approximately 0.3log intervals) and at temperatures between V500and 1150‡C. At high temperatures, low-frequencymeasurements were prevented by the onset ofnon-linear sample response. This was revealedby Fourier analysis of the data indicating thepresence of harmonics of the torsional drivingfrequency. Automation of sampling and process-ing allows repeated measurements and at high

VOLGEO 3001 16-3-04

M.R. James et al. / Journal of Volcanology and Geothermal Research 132 (2004) 99^113100

frequencies an average of 20 measurements wasused for most temperature^frequency points. Atlow frequencies, individual measurements takeup to 17 min, so fewer experiments were averaged.

During experiments the furnace was purgedwith a £ow of Ar gas (5 cm3 s31). Inspection ofthe samples after experiments showed that oxida-tion (as indicated by growth of Fe^(Ti)-oxides)had taken place only on the surfaces of the sam-ples. Temperatures were recorded using Pt^PtRd(S-type) or Ni^NiCr (K-type) thermocouples. Di-rect measurements of the temperature ¢eld inside

the furnace indicated that temperatures were re-duced by up to 15‡C at distances of 10 mm fromthe hottest point. Although this spatial sensitivityimplies that recorded values were only accurate toV15‡C as indicators of the sample temperature,relative temperature changes within any one ex-periment are much better constrained ( O 3‡C at1000‡C).

The data collected at each temperature^fre-quency point allowed calculation of the magni-tude of the complex shear modulus G*(g, T),and the phase shift B(g,T) between the appliedtorque and the resultant angular strain of thesample, where g is the angular velocity (equal to2Z multiplied by the applied frequency). Fromthese results, the real, GP, and the imaginary, GQ,parts of the complex shear modulus, the internalfriction, Q31, and the complex shear viscosity, R,can be calculated from:

G� ¼ G0 þ iG00 ¼ G�cosðBÞ þ iG�sinðBÞ ð1Þ

Q31 ¼ tanðBÞ ¼ G00

G0 ð2Þ

R ¼ R03iR 00 ¼ G00

g

þ iG0

g

ð3Þ

(e.g. Nowick and Berry, 1972). The zero-rateshear viscosity (macroscopic viscosity), R0, maybe obtained from the frequency dependence ofGQ by:

R 0 ¼ limg!0

G00ðg Þg

ð4Þ

(Marin, 1998).

2.1. Sample bonding

During experiments it is essential that each endof the sample is securely bonded to the aluminarods. In order to do this e⁄ciently, small conicalgrips (angle V1‡, length 4 mm) were machined atboth £at ends of the sample with a diamond tool.Complementary mating grips were produced inthe alumina rods and samples were cemented be-tween the rods with a high-temperature cement(Polytec0). The assembly was placed in the tor-sion apparatus and the sample was then sinteredto the rods for 2 h at 150‡C and then for 24 h at

Fig. 1. (a) Schematic of the torsion oscillation apparatus (re-drawn from Berckhemer et al., 1982). Capacitive pickups de-tect the motion of the iron plates at the ends of the alumi-nium wings, providing two data channels that can becalibrated to provide angular de£ection and the applied tor-que. (b) An example of two periods of data collected in or-der to measure internal friction (from the phase shift) andmagnitude of the complex shear modulus (from the relativeamplitudes of the curves). Further details are given in Bag-dassarov (2000).

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M.R. James et al. / Journal of Volcanology and Geothermal Research 132 (2004) 99^113 101

500‡C, under an axial load of V8 N (e.g. Berck-hemer et al., 1982). Measurements carried out us-ing a dummy sample of Al2O3 have demonstratedthat the e¡ect of the cement on phase delay mea-surements was less than 1033 rad (Bagdassarovand Dorfman, 1998).

2.2. Size and shape factors

When temperatures increased during experi-ments, thermal expansion of the sample and thealumina ceramic rods was accommodated by aspring located at one end of the apparatus. Attemperatures su⁄ciently high for the sample todeform, some of the accumulated stress dissipatesby £ow shortening of the sample. Changes insample length were calculated from micrometerreadings taking at the spring (to a precision ofV0.02 mm) and the correspondingly changedsample diameter (calculated by assuming conser-vation of sample volume) were then used to cal-culate the material properties. However, samplesrecovered after experiments have shown that £owdeformation was not continuously distributedthrough the samples but was concentrated in thecentre, producing distorted, barrel-shaped, cylin-ders. This is a consequence of temperature gra-dients across the sample and due to it being sup-ported at both ends. Thus, despite e¡orts toaccount for changes in the sample shape, the de-viation from a cylindrical form introduced errors(6 2%) in the assumed diameter of the sample,once sample shortening has started.

2.3. Sample description

The experiments were carried out on samples ofbasaltic lavas collected from three di¡erent volca-noes, Etna, HawaiPi and Vesuvius.

2.3.1. EtnaTwo samples from Etna were collected from

lava erupted in 1992 which had ponded afterover£owing from a skylight in the Valle delBove. One of these samples was from the top sur-face and one was taken from the base (V10 cmdown from the surface) and thus represent sam-ples with di¡erent cooling regimes. Digital images

of polished sections were obtained through anoptical microscope and computer-analysed, omit-ting corrections for 3D e¡ects. The surface samplehas smaller vesicles (V0.2^0.5 mm, 15^20 vol%)and smaller crystal content (V20^30 vol%) thanthe basal sample (V20 vol% of 1^2 mm vesiclesand V30 vol% phenocrysts). Images of polishedthin sections are shown in Fig. 2. A further sam-ple was collected from near the southeast cone in1999. This sample was taken from the least vesic-ular area found in a recently emplaced £ow nearhornito H3 (Calvari and Pinkerton, 2002) at thetop of the active £ow ¢eld.

2.3.2. HawaiPiThe Hawaiian basalt was sampled in the east

rift eruption zone of Kilauea, HawaiPi, from alava £ow from a pahoehoe toe in September,1984 (eruption temperature V1147‡C). This pa-hoehoe lava £ow corresponds to episode 25 of theeruption PuPu POPo of Kilauea Volcano. Its bulkchemical composition has been presented else-where (Garcia et al., 1992). The chemical com-position of the groundmass glass obtained bymicroprobe analysis di¡ers from the bulk rockcomposition in SiO2 (52.3 wt%) and CaO (9.2%)content (Bagdassarov, 2000). The vesicularity es-

Fig. 2. (a) Thin section of the crustal sample from Etna,1992. The lava contains V15^20 vol% of vesicles (mean di-ameter between V0.2 and 0.5 mm) and V20^25 vol% ofplagioclase, olivine and magnetite phenocrysts. (b) Thin sec-tion of the 1992 Etna sample that was collected from thebase of an over£ow. This sample contains V20 vol% ofvesicles with a mean diameter of 1^2 mm and about 30 vol%of crystal (from analysis of polished thin sections withoutcorrections for 3D e¡ects).

VOLGEO 3001 16-3-04


timated from 2D image analysis varies from 46.8to 57.6 vol%, or V50 vol% when calculated onthe ‘dry’ density rock basis. The sample has aboutV10 vol% of olivine quenched from magma dur-ing sampling and a few percent of other pheno-crysts.

2.3.3. VesuviusThe Vesuvius samples were collected from the

1834 £ow at Cava Ranieri in the national pro-tected area of Terzigno approximately 6.3 kmESE of the central cone of Vesuvius by the groupfrom University College of London. Chemicalanalysis of the samples is given in Belkin et al.(1993). The same sample was also used by Rocchiet al. (2002) in experiments to determine Young’smodulus and tensile strength.

3. Results

The shear modulus and internal friction results

for the samples are given in Figs. 3^6. The 1992Etna samples (Fig. 3) show marked di¡erences inshear modulus and internal friction between therapidly cooled crustal sample and the more slowlycooled basal sample. As a result of its smallervolume fraction of vesicles, the crustal samplehas a shear modulus V1.5^2 times greater thanthat of the basal sample at high temperatures(s 1050‡C), increasing to Vsix times at low tem-peratures (V500‡C). The internal friction of thecrustal sample shows a relatively low dependenceon frequency at high temperatures (s 800‡C). Attemperatures between V600 and 800‡C (Fig. 3c)a small, wide peak in internal friction suggests acomplicated behaviour at temperatures corre-sponding to that of the glass transition for basal-tic glass (Ryan and Sammis, 1981). For PuPu POPopahoehoe lavas, the glass transition and meltingtemperatures are 655 and 1149‡C, respectively(Burkhard, 2001). In contrast, at temperatures be-low 1000‡C, the internal friction of the basal sam-ple (Fig. 3d) is a strong power law of frequency,

Fig. 3. Shear modulus (a,b) and internal friction (c,d) results from the 1992 Etna lavas. The crustal sample (a,c) shows a highershear modulus than the basal sample, and neither sample has an internal friction approaching 1 over the conditions investigated.

VOLGEO 3001 16-3-04


Fig. 4. In panels and b, temporal variations in shear modulus and internal friction are given for the 1999 Etna sample. After an-nealing for 118 h at 800‡C the sample had attained a greater shear modulus than it originally possessed at 700‡C. The increasingshear modulus and decreasing internal friction with time indicate the sample was becoming increasingly elastic and less viscous.The shear modulus and internal friction results collected after annealing are given in panels c and d.

Fig. 5. Time-dependent shear modulus (a) and internal friction (b) during annealing experiments on the HawaiPi sample. Num-bers in the legend indicate annealing time in hours.

VOLGEO 3001 16-3-04


Q31Og

30:35. The response of a purely elastic ma-terial would be independent of frequency, and thisfrequency dependence indicates a partially viscousresponse even at V600‡C.

Similar experiments carried out on cores cutfrom the 1999 Etna sample not only reproducedthe internal friction peak at low temperatures(V700‡C) but demonstrated considerable tempo-ral variations in the results (Fig. 4). Over periodsof up to V120 h, the measured shear modulusincreased and internal friction decreased. Afterannealing, the 1999 samples produced similarshear modulus and internal friction results (Fig.4c,d) to those of the 1992 Etna crustal material.At temperatures s 1100‡C, Etna samples demon-strated an increase of £uidity of several orders ofmagnitude and it was not possible to maintainthem in the torsion apparatus.

The experiments carried out on the HawaiPisample were extended to higher temperatures be-cause of the higher temperature of the sample’ssoftening point. Similar temporal variations tothose observed with the Etna lavas were foundand are shown in Fig. 5 at a temperature of1102‡C. The results are broadly similar to thoseof the Etna samples, with shear moduli of V18GPa decreasing to V0.2 GPa as sample £uiditystarts to rapidly increase.

The results from the experiments carried out onthe Vesuvius sample are given in Fig. 6. Duringsample annealing the shear modulus increased butto a lesser extent than in Etna samples. An in-crease in tensile strength and Young’s modulus

after annealing was also reported during bendingexperiments (Rocchi et al., 2002). At the highesttemperature attained during experiments (1132‡C)the shear modulus was less than 0.5 GPa andpractically frequency-independent. With a furtherincrease of temperature the sample became too£uid for it to be held within the torsion appara-tus.

4. Discussion

Measurements of the complex shear modulus(G*) and internal friction (Q31) of lava samplesfrom Etna, Vesuvius and HawaiPi show that theypossess an appreciable shear modulus (s 0.5GPa) and an internal friction generally less than1, at temperatures where ¢eld measurements indi-cate viscosities of V103 Pa s. For comparison,polycrstalline rocks at room temperature havetypical values of unrelaxed shear modulus, Gr,of about 50 GPa (Jackson, 1993) and 25 GPa isrepresentative for silicate glasses (Bagdassarov etal., 1993). Between room and high temperaturesprior to the onset of melting, values of Q31 varybetween V1033 and 1031 (Manghnani et al.,1981; Weiner et al., 1987; Jackson, 1993; Bagdas-sarov, 2000).

Natural silicate melts and glasses show a linearviscoelastic behaviour in the glass transition tem-perature range (e.g. Bagdassarov and Dingwell,1993; Bagdassarov et al., 1993). With increasingtemperature and decreasing strain rate, one ex-

Fig. 6. Shear modulus (a) and internal friction (b) results from the Vesuvius lava.

VOLGEO 3001 16-3-04


pects progressively decreasing shear modulus andincreasing internal friction. However, the visco-elastic behaviour of lavas is often controlled by thepresence of deformable (vesicles) and non-deform-able (crystals) heterogeneities. Viscosity increaseswith increasing crystal content but decreases withincreasing vesicle content (Bagdassarov and Ding-well, 1992) and the presence of these macroscaleobstacles extends the shear stress relaxation spec-trum towards longer relaxation times. Shear mod-ulus relaxation can be extended over several hun-dred ‡C above the Tg of a basaltic groundmassglass (V655‡C) up to V1100^1150‡C. Over thesame range, the frequency dependence of shearmodulus and internal friction becomes weaker,for example, in lavas Q31

Og30:35, compared to

g30:5 for silicate melts.The shear modulus and internal friction of our

lava samples varied signi¢cantly with annealingtime with, at temperatures between V500 and1000‡C, some samples becoming increasingly sti¡and elastic (Fig. 4). Similar temporal variations ofelastic modulus and internal friction have beenpreviously observed in thermally cycled quartzite,granite, dunite and sandstones (Johnson and Tok-

so«z, 1980; Jackson, 1993; Lu and Jackson, 1998)and is thought to be due to the presence andhealing of microcracks and pores. For example,rapid thermal cycling of granite and diabase sam-ples from room temperature to V800‡C results inorder of magnitude increases in crack porosityand a factor of 2 increase in Q31 due to the ther-mal production of cracks (Johnson and Tokso«z,1980). Jackson (1993) interpreted the observed in-crease in shear modulus and decrease in internalfriction with the increasing annealing time to be aresult of the reduction of porosity and increase ofthe grain boundary cohesion by a sintering pro-cess. Progressive decreases in Q31 have been as-sociated with a decrease of centres of stress con-centration. Thus, we interpret our data, whichindicate an increasingly elastic response withtime, as demonstrating the e¡ects of healing mi-crocracks and thermally produced pore space (notvesicles) in the samples. It is likely that the micro-cracks were originally created due to thermalstresses during rapid cooling of the lava £ows;however, we cannot exclude the possibility thatthey could have been produced during samplepreparation or the subsequent heating. In thin

Fig. 7. Thin sections of Etna (A,B) and Vesuvius (C,D) lava samples (each image represents 1250U950 Wm). Panels A and Bgive starting material and show microcracks between crystals and groundmass glass as well as in the interior of phenocrysts. Pan-el B shows the Etna sample after being annealed at 812‡C for 118 h and panel D shows the Vesuvius sample after being an-nealed at 1102‡C for 96 h. The reduction in the number of microcracks demonstrates that healing has occurred both within thegroundmass and the phenocrysts.

VOLGEO 3001 16-3-04


sections, microcracks within crystals and betweencrystals and the groundmass can be observed tohave undergone some healing after annealing(Fig. 7).

The production of microcracks suggests thatrocks which have undergone slow cooling willpossess higher shear moduli and have higherstrengths than rocks which cooled more rapidly.Thus, before annealing, samples taken from thecentre of a cooled £ow would be expected to bemore elastic than samples taken from the top of a£ow. Under annealing at high temperature, thecrack healing process consists of cracks pinchingo¡ and healing to a pore-like shape before subse-quent decreasing of the pore diameter (Atkinson,1984). During this period, the shear modulus maysigni¢cantly increase and the internal friction de-crease. The time dependence of changes in cracklengths can be described as an Arrhenius functionof temperature and, as a ¢rst approximation, alinear dependence between shear modulus and acrack density parameter may be assumed (O’Con-nel and Budiansky, 1974). In Fig. 8a the results ofannealing on the complex shear modulus of the1999 Etna lava sample are presented as a functionof time, t. By ¢tting these data with an exponen-tial time dependence:

MG�M ¼ ðGr3Gð0ÞÞf13e3t=dg þ Gð0Þ ð5Þ

where Gr is the stable shear modulus at any tem-perature, G(0) is the shear modulus at t=0, thecharacteristic time, d, of the crack healing processmay be estimated. The results of the ¢tting arepresented in Fig. 8b in the form of an Arrheniandependence of d, yielding an activation energy of150O 20 kJ mol31. According to Atkinson (1984)this value should relate to the activation energy ofthe e¡ective di¡usion coe⁄cient on grain bound-aries of species participating in the pinching pro-cess at microcrack tips. For example, the activa-tion energy of crack healing in dry quartz atT6 600‡C is about 80^85 kJ mol31 (Atkinsonand Meredith, 1987), corresponding to the activa-tion energy of water di¡usion in quartz (V60 kJmol31, Dersch et al. (1997) or V100 kJ mol31,Brady (1995)). At high temperatures, crystal lat-tice di¡usion is the rate-controlling mechanism ofgrain boundary di¡usion. Thus, the observed ac-

tivation energy for the time dependence of shearmodulus may be associated with an inter-di¡usionof Ca, Mg and alkaline species between olivine,clinopyroxene and plagioclase crystals and basaltglass, with activation energies between 130 and180 kJ mol31 (Brady, 1995). Alternatively, ourresults are also consistent with a self-di¡usion ofSi and O, network formers in basaltic glass, withan activation energy of 170 kJ mol31 (Lesher etal., 1996).

Alternative mechanisms that could contributeto the increase of shear modulus during annealingof samples are redox and re-crystallisation pro-

Fig. 8. (a) The complex shear modulus of 1999 Etna lavameasured at 20 Hz and di¡erent temperatures. The temporalchange at each temperature is modelled using a curve ofcharacteristic time constant that is believed to represent thecharacteristic time for crack healing (see text). In panel b,these characteristic times are plotted against absolute recipro-cal temperature. The straight line ¢t represents an Arrheniandependence with an activation energy of 150O 20 kJ mol31.

VOLGEO 3001 16-3-04


cesses in the basalt groundmass glass. Progressivevolatile loss could also be responsible forstrengthening the samples; however, this cannotexplain the power law frequency dependence ofinternal friction in the 1992 Etna samples at lowtemperatures. A contribution to shear modulusincrease from sample oxidation would be dueto the production of interface-controlled inter-growths of pyroxene dendrites and Fe^(Ti)-oxidesbetween 850 and 940‡C (Burkhard, 2001). How-ever, the activation energy of this process is V100kJ mol31, which is less than that observed fromthe time variation curves of shear modulus. Theoxidation kinetics of basaltic glass are determinedprimarily by the di¡usion of divalent cations Ca2þ

and Mg2þ to the surface of the sample, which ischarge-compensated by the inward £ux of elec-tron holes (Cooper et al., 1996). The activationenergy of this process at temperatures below Tg

is 210 kJ mol31. The calculated maximum depth(V1 Wm at 600‡C and V20 Wm at 800‡C) ofsurface oxidation by using the average divalentcation di¡usion coe⁄cient (Cooper et al., 1996)is small compared with the size of lava samplesused in torsion experiments and is in agreementwith observations made from thin sections of thesamples. It should also be noted that these ratesrelate to initially non-oxidised basalt glass sam-ples and the lava samples should be consideredas slow-cooled, partially crystallised glasses, withlong oxidation histories.

At Ts 920‡C, the bulk crystallisation of basal-tic glass and growth of plagioclase crystals mayalso contribute to the increase of sti¡ness of an-nealed lava samples, but the timescales requiredare generally much longer than those of the ob-served changes in shear modulus. For example, anoticeable growth of plagioclase and Fe^Ti-oxideshas been observed at 850^934‡C after s 200 h ofannealing basalt glass (Burkhard, 2001) and thisprocess is likely to have continued for an order ofmagnitude longer time. In contrast, shear modu-lus changes occurred much more rapidly in ourexperiments and generally ceased on a timescaleof 6 100 h. Thus, neither redox nor re-crystalli-sation processes are believed to signi¢cantly con-tribute to the measured changes in the rheologicalproperties of the samples.

Converting the shear modulus and internal fric-tion data into viscosity (Eq. 3) shows that boththe Vesuvius and Etna samples maintained a fre-quency-dependent real component of their viscos-ity (RP) up to the highest temperatures attainableduring the experiments (Fig. 9). Therefore, no‘Newtonian’ viscosity can be given for these tem-peratures at low strain rates. In contrast, the Ha-waiian sample demonstrated marked decreases inthe frequency dependence of RP at high temper-atures and low frequencies (Fig. 10a). The maindi¡erence between the low strain rate behaviourof, on the one side, Etna and Vesuvius basalts,and, on the other, that from HawaiPi, lies in therelative proportion of crystals and vesicles. Thesmall strain rate and small stress viscosity, R0,measured for the Hawaiian sample represent acreep-type mechanism underlying the Binghamyield stress which is expressed under conditionsof slow, small-scale deformation, where the inter-

Fig. 9. Dynamic viscosity as given by GQ(g)/g (see Eq. 4) forthe Vesuvius (a) and Etna (b) samples. At the highest tem-peratures and lowest frequencies used these samples main-tained a frequency-dependent rheology.

VOLGEO 3001 16-3-04


nal structure of the lava sample remains intact.The presence of non-deformable crystals resultsin increases of this e¡ective viscosity, but also in-creases the Bingham yield stress (Bagdassarov etal., 1994). Higher ratios of crystals to vesicles inEtna and Vesuvius lavas increase the Binghamcreep viscosity, R0, and shift it toward smallerstrain rates which were unattainable in our tor-sion experiments. In contrast, the Hawaiian lavasample, with a smaller crystals-to-vesicles ratio,possessed a smaller Bingham creep viscositywhich was observable at the lower strain ratesof the torsion apparatus (1033 s31).

If a material has a strain rate-dependent rheol-ogy then two di¡erent viscosities can be assigned,R0 and Rr, which relate to the low and high strainrate limits, respectively. The Cross model thengives the viscosity as:

R ¼ Rr þ R 03Rr

1þ ðK _QQ Þm ð6Þ

where m and K are empirical constants and _QQ isstrain rate (e.g. Barnes, 1999), with m character-ising a stretching parameter for shear stress relax-ation during the viscoelastic transition. For aMaxwell body rheology, m=2. In the operationalwindow of the oscillatory shear apparatus, onlyR0 can be measured. The high strain rate viscos-ity, Rr, is interpreted as the e¡ective viscosity of a£uid at high strain rates or stresses. In the case oflavas, it corresponds to the results of ¢eld or lab-oratory experiments in which high strains inducedby the measurement disrupt the internal structureof the lava.

The high-temperature data in Fig. 10a havebeen ¢tted with Cross curves (assuming thatR0ERr, and using m=1) and the values of R0

Fig. 10. Dynamic viscosity of the HawaiPi sample. In panel a,the high temperature values of GQ(g)/g are given, demonstrat-ing the decreasing dependence on frequency at low frequen-cies. The curves show the results of using a Cross model inorder to extract the zero-shear viscosity (see text). Fitting pa-rameter of Eq. 5 m=1 at all temperatures, K=1.6log(R0 Pas) = 9.23 at 1126‡C, 3.7 and 9.7 at 1100‡C, 30 and 10.65 at1072‡C. In panel b, the zero-shear viscosity values R0 ob-tained for the HawaiPi lava sample are compared with thosegiven by dilatometer (Bagdassarov, 2000) and rotational vis-cometer (Shaw, 1969; Shaw et al., 1968; Ryan and Blevins,1987; Ryerson et al., 1988; Pinkerton et al., 1995) experi-ments on Hawaiian basalt lavas. There is good agreementbetween the dilatometer and the torsional results, with theslightly greater values from the dilatometer being expecteddue to the e¡ect of compression viscosity on extracting shearviscosity values from the pure shear experiments (Bagdassa-rov and Dingwell, 1992). The gradient of the dashed best ¢tlines represents an activation energy for viscous £ow ofV950 kJ mol31. The plot demonstrates the Vthree order ofmagnitude change in viscosity which occurs around7.0U1034 K31 (V1155‡C) and separates the high-tempera-ture, Newtonian region from the lower-temperature, visco-plastic region. The 1 s31 line indicates the torsion results atunit shear rates which are more applicable for comparisonwith the rotational viscometer measurements. High values ofR0 obtained in torsion and dilatometer, small strain^stressexperiments relate to the creep-type rheology displayed bylava when its internal structure is not destroyed by the mea-surements. Field experiments carried out at high stresses andstrains show Rr, or a viscoplastic viscosity, expressed whenthe internal structure (the organisation of vesicles and crys-tals) of the lava is altered by the viscometer or the £ow it-self.

VOLGEO 3001 16-3-04


obtained are plotted in Fig. 10b along with otherviscosity measurements made with a parallel-plateviscometer (a Ba«hr0 high-temperature dilatome-ter, University Bayreuth (Bagdassarov, 2000))and rotational viscometers (Shaw, 1969; Shaw etal., 1968; Ryan and Blevins, 1987; Ryerson et al.,1988; Pinkerton et al., 1995). The parallel-plateviscometer uses shear rates of 1035^1037 s31,compared with equivalents of V1032^102 s31

for the torsion apparatus. The activation energyfor viscous £ow obtained by the dilatometer andtorsion experiments (given by the gradient of thedashed lines in Fig. 10b) is V950O 5 kJ mol31.The small o¡set (0.67 log units) between the twolines is due to the e¡ect of the volume (or bulk)viscosity of a porous sample, Rv, which a¡ects theparallel-plate deformation results of the dilatom-eter experiments. The pure shear deformationused in the dilatometer gives a compressional vis-cosity, Rc, which is usually related to the shearviscosity by Rc/3. However, this is valid only forincompressible samples (which have an in¢nitevolume viscosity), and is therefore not applicableto material with V50% porosity, which will havea ¢nite volume viscosity. For high-porosity mate-rials, the relationship:

R c ¼ R v þ 43R s ð7Þ

is appropriate (e.g. Bagdassarov and Dingwell,1992). Thus measured values should be correctedfor a ¢nite-volume viscosity, the value of which isunknown. From Fig. 10b the compressional vis-cosity data from the dilatometer experiments arerelated to the simple shear viscosity results of thetorsion experiments, Rs, by RcW3U100:67Rs, or101:15Rs. Applying Eq. 7 thus gives RvW12.7Rs

(at V50% porosity). The theoretical dependenceof the volume viscosity as a function of porosityhas been considered elsewhere (Prud’homme andBird, 1978; Aksel, 1995), with the classical formu-la:

R v ¼43

b2

b 0ðb 03b ÞR0s ð8Þ

derived for small concentrations of vesicles in a£uid, where b0 is the density of £uid, b is thedensity of the suspension and R

0s is the viscosity

of the £uid without vesicles. Converting R0s to Rs

by R0sW0.2Rs (for V50% porosity, Fig. 5, Rust

and Manga, 2002), gives the theoretical relationof RvW3.3Rs. The discrepancy between our resultand this theoretical estimation may be easily at-tributed to experimental errors in viscositiy aswell as the non-spherical shape of some vesiclesand their non-uniform size distribution in the lavasamples.

Alternatives to the Cross model were reviewedby Yue and Bru«ckner (1994), who suggested astrain rate-dependent viscosity model dependingon three phenomenological constants. Their mod-el is appropriate for parallel-plate viscometry inwhich signi¢cant strain increases during experi-ments can produce thermal e¡ects and violationsof non-slip boundary conditions. However, in thetorsion experiments the maximum torque was1033 N m, and maximum angle deformation1035 rad, resulting in a negligible heat production(6 1037 J s31) even at the highest strain ratesused.

Field measurements, corrected to unit strainrate, have reported signi¢cantly smaller shear vis-cosities for Hawaiian basalts. Shaw et al. (1968)measured plastic viscosities of 650^750 Pa s at1130‡C and Pinkerton et al. (1995) measured vis-cosities of 234^548 Pa s at 1146‡C (Fig. 8b). Unitshear rate results from the torsion experiments (asgiven by the ¢tted Cross models) are ¢ve orders ofmagnitude greater than these ¢eld measurements.For Mount St. Helens dacite, Pinkerton and Ste-venson (1992) demonstrated that a combinationof factors was responsible for a 10 order of mag-nitude variation within measured and calculatedapparent viscosities at sub-liquidus temperatures.For Hawaiian basalt, although di¡erences in vol-atile content, crystallinity and vesicularity existbetween the experimental and the ¢eldwork sam-ples, the main di¡erence in the results (Fig. 10b) isdue to the magnitude of the strain used, withrotational viscometry producing high strains andtorsion and dilatometer experiments producingsmall strains.

When magmas or lavas are subjected to smallstrains, the rheology is in£uenced by the deforma-tion of gas bubbles and by the rotation, interac-tion and small displacement of crystals suspendedin the viscous melt matrix. In this case, the rheol-

VOLGEO 3001 16-3-04


ogy is controlled by the ‘structure’ of the materialand is consequently relatively high (see Fig. 10b,torsion and dilatometric experiments). For rota-tional viscometry (either in the ¢eld or in labora-tory experiments) the strains are much higher and,with time, the material ‘structure’ becomes dis-rupted. The increasingly ‘unstructured’ nature ofthe material results in a viscous shear thinningresponse (Barnes, 1997), producing decreased ap-parent viscosities.

The small stress and strain rate experimentscarried out in torsion and dilatometer equipmentdemonstrate a second, relatively high-viscosity(creep-type rheology), plateau in the viscosity^strain rate dependence (Barnes, 1999) that cannotbe observed with high stress or strain rate mea-surements. However, at temperatures aboveV1145^1150‡C the groundmass of lava becomesso £uid that the viscosity decreases a few ordersof magnitude (Fig. 10b) and the high-viscosityplateau is no longer present. Fig. 10b demon-strates the di¡erence between the R0 (creep-type)and Rr (viscoplastic) viscosities. In the smallstrain and small stress torsion equipment, the in-ternal structure of the lava sample is not de-stroyed, and the measured viscosity is of a creeptype. This type of viscosity may be expressed inlava dome growth or relaxation processes. In ex-periments with rotational viscometers, wherestrains and stresses are considerable, the internalstructure of the lava is destroyed and the apparentviscosity is several magnitudes smaller. This typeof viscosity will control lava £ows over steep to-pography. Thus, at the same temperature, lavasmay possess two viscosities depending on astress^strain scale and numerical modelling oflava £ows should consider the high viscosity andviscoelasticity of lavas when strain rates are belowunity.

5. Conclusions

(1) The oscillatory torsional apparatus allowslow-strain investigations of shear modulus andinternal friction. Experiments carried out on lavasover a range of temperatures (V500^1150‡C) andfrequencies (20^0.002 Hz) demonstrate that in

general the complex shear modulus of lavas de-creases with decreasing frequency and increasingtemperature. Internal friction is usually 6 1.

(2) At temperatures close to their eruption tem-perature (V1080^1100‡C) no purely viscous re-gime was detected for the Etna and Vesuvius sam-ples and their measured creep-type viscosityremained frequency-dependent over the range20^0.002 Hz. However, results for the HawaiPisample indicate a shear rate-independent regimefor low shear rates at temperatures betweenV1070 and 1130‡C, with viscosities s 109 Pa s.

(3) The samples from Etna and Vesuvius exhib-ited extended anelastic behaviour at temperatureswithin the ‘glass transition’ temperature of thegroundmass, and that may be attributable to thebad cohesion between crystal grains and thegroundmass glass. Annealed lava at V900^950‡C possesses a shear modulus of about 15^20GPa. Below V800‡C, but still within basalt glasstransition temperature range, when the dilatomet-ric e¡ects between groundmass glass and crystalsare signi¢cant, intensive microcracking may beexpected and can decrease the shear modulus to7^10 GPa. By reheating between 700 and 950‡C,the characteristic time constant of the lava hard-ening process may be on a scale of several to ahundred hours.

Acknowledgements

We thank J. Deubener and one anonymous ref-eree for helpful comments that improved themanuscript.

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Viscoelastic behaviour of basaltic lavas