Viscosity of the dome of mount St. Helens

Journal of Volcanology and Geothermal Research, 24 (1985) 193-204 Elsevier Science Publishers B.V., Amsterdam -Printed in The Netherlands

VISCOSITY

TSUTOMU

193

OF THE DOME OF MOUNT ST. HELENS

MURASE’,

ALEXANDER

R. McBIRNEY*

and WILLIAM

G. MELSON’

‘Dept. of Physics, Institute of Vocational Training, 1960 Aihara, Sagamihara aGeology Department, University of Oregon, Eugene, OR 97403, U.S.A. %mithsonian Institution, Washington, D.C., 20560, U.S.A. (Accepted

for publication

229,

Japan

June 29, 1984)

ABSTRACT Murase,

T., McBirney,

Helens. In: J. Volcanol.

A.R.

and Melson,

W.G.,

1985.

B.H. Baker and A.R. McBirney Geotherm. Res., 24: 193-204.

Viscosity

(Editors),

of the dome

Processes

of Mount

in Magma

St.

Chambers.

A sample of dacite from the dome of Mt. St. Helens has been studied experimentally and found to have a viscosity that declines from about 10” at 8OO’C to lo3 poise at 1500°C. Its yield strength declines from about 2 x lo6 dynes cm-’ at 8OO’C to less than the precision of our measurements ( lo4 dynes cm-‘) above 1050°C. The geometrical form of the dome is approximately consistent with these properties if the internal temperature of the dome is between 900 and 1000°C. The melting behavior of the crystalline dacite has been determined between 1000 and 1225°C. Data on the composition of the liquid fraction and sizes and proportion of crystals have been used to derive a set of equations for predicting the effective viscosity of crystal-bearing magmas below their liquidus temperatures. Although of the bulk composition of the magma has changed little, the increasing crystallinity and viscosity appear to have influenced eruptive behavior of the volcano during its most recent periods of activity.

INTRODUCTION

Since its return to activity in early 1980, Mt. St. Helens has passed through several stages, each characterized by a different type of activity. Although the bulk composition of the magma has changed only slightly, its crystallinity has increased by more than 50% and its viscosity by orders of magnitude. In order to provide a better basis for interpreting the eruptive behavior in terms of these factors, we have measured the rheological properties of a typical sample of dacite extruded by the currently active dome (Fig. 1). COMPOSITION

AND MELTING

BEHAVIOR

OF THE SAMPLE

The sample used for our studies is believed to have been extruded in early 1981. It was collected in November of that year from a large block, referred

0311-0213/85/$03.30

0 1985

Elsevier

Science

Publishers

B.V.

Fig. 1. Photograph TABLE

of dome

of Mt. St. Helens viewed looking south in late 1981

1

Compositions of the bulk sample and glasses at successive

stages of melting

(all values in

wt .%) Bulk sample

Glass 1000”

Glass 1050”

Glass 1100”

Glass 1150”

Glass 1200”

Glass 1250”

KG P,G,

62.53 0.62 17.78 4.66 0.10 2.32 5.61 4.55 1.23 0.11

76.85 0.27 11.57 0.65 n.d. 0.17 0.61 3.60 3.91 0.11

75.20 0.33 11.56 1.43 n.d. 0.33 0.88 4.01 3.19 0.08

74.41 0.35 12.42 1.91 n.d. 0.38 1.03 4.34 2.82 0.09

73.90 0.38 12.57 2.23 n.d. 0.77 1.54 4.52 2.33 0.07

70.39 0.59 13.66 3.49 n.d. 1.47 2.83 4.34 1.92 0.11

62.97 0.60 16.21 4.11 n.d. 2.11 4.18 4.79 1.48 0.08

Total

99.5 1

97.74

97.01

97.75

98.31

98.80

96.53

7.0

30.7

37.6

42.6

51.5

62.5

81.1

SiO TiO: Al,& FeO* MnO MgG CaO Na,O

% Glass

Microprobe analyses of glass by W.G. Melson, bulk sample by atomic absorption and colorimetry by Christine McBirney. Sodium loss in analyses of glass was minimized but not totally eliminated by moving the electron beam during the analysis. Low totals do not reflect the presence of water or large sodium losses but imprecision resulting from the analytical techniques that were required for the particular samples.

195

to as the “Federal Building”, near the eastern base of the dome. In hand specimen, the rock is medium-grained with faint flow banding and scattered xenoliths and xenocrysts of coarse-grained basement rocks. In thin section, nearly half the volume is seen to consist of seriate plagioclase with maximum dimensions reaching about 1.5 mm and zoned from calcic labradorite to medium oligoclase. Smaller phenocrysts of pleochroic hypersthene, greenish augite, and russet oxyhornblende together account for another 5 or 6% of the volume. Opaque minerals, including products of breakdown of the amphibole, amount to about 5%, and apatite is a common accessory. The hyalopilitic groundmass contains microlites of plagioclase, pyroxene, and iron oxides set in a matrix of colorless glass. The chemical composition of the bulk rock is given in Table 1. In order to determine the state of the sample under the conditions of the rheological measurements, melting experiments were carried out on samples of the original rock and of glass prepared by melting and quenching a finely ground aliquot of the same specimen. Samples were held at successive temperatures from 1050 to 1225°C and at oxygen fugacities close to the Ni-

Fig. 2. Compositions atures between 1000

of glass, proportions and 1225’C.

and sizes of crystals,

over a range of temper-

NiO buffer for five to ten hours then quenched, examined petrographically, and analyzed by microprobe. Samples that started as glass remained totally liquid, and in no case were crystals (other than quench products) detectable by optical methods. Samples that started as solid rock contained differing amounts of residual crystals throughout the entire temperature range of the experiments. At temperatures between 1050 and llOO”C, the main effect of heating was to melt the fine-grained groundmass and relict crystals of amphibole. Above llOO”C, microphenocrysts, particularly mafic phases, showed evidence of melting, but about 30% crystals still remained at 1225”C, the highest temperature reached in this series of experiments. The composition of the glass changed in a regular fashion with progressively higher temperatures (Table 1). Using these analytically determined compositions, the fraction of melt was calculated by assuming that all of the KzO of the original bulk rock was concentrated in the melt. Proportions of glass and crystals determined in this way do not conflict with petrographic estimates. Calculated values are plotted against temperature in Fig. 2. RHEOLOGICAL

MEASUREMENTS

Two techniques were used to determine viscosity and yield strength, a bending method at temperatures below 1150°C (Fig. 3a) and a counterbalanced sphere method (Fig. 3b) at higher temperatures. For the bending method, a small slab of the rock was cut and ground to dimensions of approximately 6.0 X 1.2 X 0.4 cm. The sample was supported near its ends by two porcelain prisms, and a load was applied vertically downward at the middle of the sample by means of a loose stirrup of silica glass with a knife edge resting at the center of the specimen. Weights were suspended from the lower end of the rod just below a small opening at the base of the furnace. Rates of deflection resulting from the applied stresses were measured by means of a linear transformer mounted directly below the furnace. Measurements were started soon after the sample reached a constant temperature and the thermal expansion of the silica glass rod had become negligible compared to the deflection due to bending of the sample. At higher temperatures where the degree of melting was too great for the rock to support its own weight, finely ground rock was melted at 1450°C quenched to glass, and remelted in a platinum crucible 5 cm in diameter and 5.5 cm high to form a homogeneous nearly bubble-free liquid. A platinum sphere, 0.50 cm in diameter, was suspended in the molten sample from a platinum wire, 0.059 cm in diameter. Differing stresses were applied to the sphere by changing the weights on an analytical balance, and, as in the first method, rates of strain were measured with a linear transformer and chart recorder. The maximum vertical displacement of the sphere was 0.351 cm. In both methods, the atmosphere of the furnace was held close to the NiNiO buffer by mixtures of CO, and CO and monitored by a zirconia electrolitic cell. Temperature was measured by a thermocouple positioned close to the sample, as indicated in Fig. 3.

197

Llneor transfor.&&a& mer to record< v

1 cerom

MI

/1( (

[

-Silica ~_tube Lineor

transformer

recorder\2 L_

Weight

Fig. 3. Apparatus for measuring viscosity. (a) Bending method used at low temperatures. Oxygen fugacity is controlled by mixtures of CO, and CO flowing downward through the furnace. (b) Counter-balanced-sphere methods used for measurements at high temperature. See text for details.

The linear transformer used to measure displacement of the bending slab or counter-balanced sphere has a sensitivity of 0.533 V mm-’ along a stroke of 0.8 cm in each direction from the center position. The transformer is connected through an amplifier to a chart recorder on which displacement is scaled at 2 to 5 mV inch-‘. The precision of the measurements of strain obtained by this method is within about 0.0001 mm, while that for strain rates is about 1 X 1O-6 cm set-’ at the most rapid rate and as low as 1 X lo-” or less for very slow strain rates. Results Results for the two methods are shown graphically in Fig. 4a, b. Figure 4a shows that the dacite has an apparent yield strength of about lo6 dynes above cme2 at 800°C and 1.5 X lo6 degrees cm -2 at 950°C. At temperatures 105O”C, we could detect no yield strength within the precision of the method (lo4 dynes cm-‘). Relations between logarithmic viscosity and temperature are shown in Fig. 5. The viscosity of the largely crystalline rock decreased sharply from 1Ol5 to 10’ poise with increasing temperature from 900 to 1150°C. The viscosity of the molten rock above its liquidus during the cooling cycle can

198 0

x10

6 900°C

7' 6-

Strain rote (S') b x103 00 2.c

1400

1300

. 1500°C .

- 1.5 N

‘E ”

.

.

: x :

YI f w

1.c

. <

0.:

L

I

5

10 Velocity

75 (cm

I 20x10-2

se')

Fig. 4. a. Stress vs. strain rate by the bending method at temperatures between 800 and 1000°C. b. Stress vs. velocity of ascending sphere above 1200°C. Measurements obtained by counter-balanced sphere method.

199

be expressed

by the Arrhenius

relation:

n = A exp (E/RT)

(1)

where n is viscosity, A is the pre-exponential constant (10W5.” for this specimen), E is the activation energy for viscous flow (67.72 kcal per mole), R is the gas constant, and T is temperature in degrees Kelvin. The large difference between the viscosity of the crystalline and molten rock at temperatures below 1200” can be ascribed in part to the mechanical effect of suspended crystals and in part to the change of chemical composition of the liquid fraction of the sample. The effect of suspended solids on the viscosity of a fluid can be estimated using the Einstein-Roscoe equation: 77= qo(l-

Rc#I)-~.~

(2)

in which Q,, is the viscosity of the crystal-free liquid, R is a factor, which for uniform spheres is 1.35, and @ is the volume fraction of solids. It is possible to calculate q0 using the compositions of the liquid fractions given in Table 1 and the empirical equations for viscosity obtained by Shaw (1972). Taking the volume fractions of crystals given in Fig. 2 for @, the measured values of effective viscosity can be approximated from eq. (2), if a value of 1.7 is assigned to R at $J = 0.57. This value is close to that deduced by Marsh (1981) from a study of the crystallinity and limiting viscosity of lavas. The relation does not, however, predict effective viscosities for a wide range of crystal contents.

14 -

o* 600

1 700

Fig. 5. Summary ties of crystal-free

I 800

900

2

q

4

l

heating

heating

1

I

I

I

1000

1100

1200

1300

run

run

, 1400

1500

‘C

of viscosity variations as a function of temperature. Calculated liquids with 0, 1, and 2 wt.% H,O are shown by fine lines.

viscosi-

Fig. 6. Measured and calculated effects of crystal contents on the effective viscosity of a Hawaiian tholeiitic basalt (MLB) and Mount St. Helens dacite (SHD). For SHD, the solid dots are observed data. (The two points at small values of $ were calculated using extrapolated viscosities.) Open circles are calculated from eq. (3) assuming a water content of 0.5 wt.% in the liquid fraction. Relative viscosity is defined as the ratio of the viscosity of a crystal-liquid suspension to that of the crystal-free liquid at the same temperature, Curves labeled U and S are calculated for spheres of uniform and serial sizes respectively, using the Einstein-Roscoe equation (eq. 2). Viscosities calculated by this method are plotted against measured values in Fig. 6. The effect of 1 or 2 wt.% water on the viscosity of the sample can be calculated by the method of Shaw (1972) as also shown in Fig. 6. The interior of the dome could have as much as a percent or so of water and, if so, would have a viscosity correspondingly lower than the values we have measured for a degassed sample. For small proportions of crystals, the effects of size can be neglected, but this factor becomes important for magmas like that of St. Helens which has many large crystals. If the viscosity of the liquid fraction, vo, can be estimated from the composition of the groundmass, the effective viscosity of such magmas can be calculated from the equation (McBirney and Murase, 1984; the constant 0.019 is a new value based on additional work.): log 77eff = log 170 +

0.019 D, (l/@)-“J--

1

(3)

201

is the mean diameter of crystals in microns. For the composiin which D, tions, liquid fractions, and mean crystal sizes given in Table 1 and Fig. 2, the calculated effective viscosity is close to the observed values for the entire range of our measurements (Fig. 6). RHEOLOGICAL

CONTROL

OF THE SHAPE OF THE DOME

Several studies have been made of the relationship between the physical properties and geometric form of viscous lavas. The most simple of these is one based on flow of a viscous Newtonian fluid under the force of gravity. Estimates of the viscosity of the dome from the observed flow of lobes of the St. Helens dome are in the range of 10” to 10” poise (U.S. Geol. Surv., 1982). Judging from the measured Vancouver Office, written commun., relations between viscosity and temperature shown in Fig. 5 and Table 1, a viscosity in this range would be consistent with a temperature of about 1100°C if, as seems likely, the lava is nearly water-free. But at this temperature, the magma would have about 62.5% liquid, and this value is much greater than what is seen in the dacite of the currently growing dome. Huppert et al. (1982) have analyzed a domical extrusion of basaltic andesite in the crater of Soufriere Volcano on the island of St. Vincent, and showed that its shape during active growth can be approximated from the equilibrium form of a viscous Newtonian fluid spreading under its own weight on a horizontal surface. Their equation (5.4): h

=~)[e(a)] -’ ( y ) 1’4 t(a-i)14 [l

- (r/rN)] 1’3

(4)

gives the height, h, in terms of kinematic viscosity, v, time, t, radius, r, and total radius, i-N. S is the rate of supply which, for the present dome can be taken as 0.385 m3 s-‘. Density, p, is close to 2.4 g cmW3 in the range of our measurements. If the rate of supply is assumed to be constant, (Y is 1.00, and C(Q) has a value of about 0.72. It is possible to solve eq. (4) for viscosity by taking a height of about 120 m for the center of the dome (r = 0) at the time the photograph was taken. This gives such an unreasonably high value (about 5.1 X 1016 poise) that we conclude that eq. (4) is not appropriate for the conditions of growth of the observed dome. The discrepancy may be due to the assumption of a constant rate of growth and Newtonian properties of the magma. The profile we obtain for this viscosity (Curve A in Fig. 7) has somewhat steeper edges than the observed one, as would be expected from these assumptions. Johnson (1970), Hulme (1974), and Moore et al. (1978) have considered the behavior of viscous non-Newtonian magmas and related the configuration of flow-fronts and other stable boundaries to an apparent yield strength. Most calculations of this kind are based on the model proposed by Orowan (1949) for a perfectly plastic ice sheet. Orowan obtained the following relation between the thickness, h, at the center of the body and the radius, R, at static equilibrium on a horizontal base:

202

h/R’12 = (2Y/pg)1i2

(51

where Y is yield strength in dyness2. Taking the height (45 m) and radius (183 m) reported for the dome in June 1980 when it had its simplest form (Moore et al., 1981), one can solve eq. (4) for the yield strength and obtain: Y = 1.3 X lo6 dynes crne2 This value is close to those determined experimentally at 950°C and suggests that when the main part of the dome spreads and cools to a temperature near this value, its motion is arrested. An equilibrium profile calculated from the equation based on the same argument by Orowan (1949) (Fig. 7, curve B) is close to but slightly flatter than the observed one.

A,

x-Huppert

B,

0-

et al

Orowon

m

7. Comparison of of Fig. 1 by theoretical equations. A is calculated from eq. of Huppert et a dynamically stable at its center rate of 0.385 s-’ a horizontal surface. B is calculated from eq. of Orowan ( 1949) for a statically stable body with a yield strength of 1.3 X 10’ dyne cm-* on a horizontal surface. Possible explanations for the differences are discussed in the text.

As in other methods of estimating yield strengths, this calculation does not take into account the inhomogenity of the body resulting from differences in temperature between the cold crust and hotter interior of the dome. Pinkerton and Sparks (1978) have shown that these differences are very large, and Mcl3irney and Mm-we (1984)pointedout that estimates of yield strength that ignore temperature effects deviate widely from experimentally determined values. We conclude, as did Kilburn (1984), that none of the theoretical models so far derived is strictly adaptable to the problem of viscous lavas.

203 EFFECTS

OF CRYSTALLINITY

AND VISCOSITY

ON ERUPTIVE

BEHAVIOR

Viewing the activity of Mt. St. Helens since May of 1980 as a whole, one sees a general tend from highly explosive outbursts of gas-rich pumice to slow extrusions of very viscous lava. During this time, the character of the magma has become progressively more crystal-rich and viscous (Table 2). A change to slightly less differentiated compositions, together with decreasing water contents has been accompanied by a steady increase of crystallinity. This sequence of change suggests that the discharge comes from a single body of magma starting with an accumulation of gas-charged liquid in the upper part of the column and drawing on successive levels of a body that was vertically zoned in water content and crystallinity. The present magma is near the upper limit of viscosity beyond which magmas can be extruded only by viscous plug-like flow (Marsh, 1981). Barring a change of composition, future activity could be confined to endogenous growth and blocky protrusions, possibly with pockets of high pressure gas. An abrupt change to more basic and less viscous magma would indicate that the base of the zone of differentiated magma has been reached.

TABLE

2

Eruptive present.

modes of Mount St. Numbers in parentheses

Period

Phase

27 March to 18 May, 1980

Emplacement cryptodome

Helens during the period between March 1980 give approximate length of each phase in days

and

the

Description of

Growth of bulge, sions. No essential

periodic small phreatic ejecta; only lithic debris

explo-

(51) 18 May 1980 (a few minutes)

Destruction cryptodome

of

18 May to 12 June 1980

Plinian pumice eruptions

Breaching of the “main magma” as white pumice in mainly Plinian eruptions. Tapping of H,O-rich (5--7%) magma with about 40% crystals

Transient

Alternation between emplacement of domes of water-poor (l-2% H,O) crystal-rich (-60%) mag ma with dome-destroying eruptions of more H,Orich (2-5%) magma with fewer crystals (40-50%)

(25) 12 June 17 Oct.

to 1980

domes

(126) 17 Ott present (600+)

1980

to

Dome

building

Catastrophic phreato-magmatic explosions. Ejection of much of the cryptodome as the “blast faties”, a grey dacite with 60 to 100% crystals

Repeated extrusion of viscous H,O-poor (l-3%) crystal-rich (60%) magma. Rare pyroclastic eruptions, smaller volumes and lower H,O than earlier phases

204 ACKNOWLEDGEMENTS

The experimental work was made possible by Grant No. EAR-7909458 of the National Science Foundation to A.R. McBirney, Dr. T.J. Casadevall and H.E. Huppert kindly reviewed the manuscript.

REFERENCES Hulme, G., 1974. The interpretation of lava flow morphology. Geophys. J. R. Astron. Sot., 39: 361-383. Huppert, H.E., Shepherd, J.B., Sigurdson, H. and Sparks, R.S.J., 1982. On lava dome growth with application to the 1979 lava extrusion of the Soufriere of St. Vincent. J. Volcanol. Geotherm. Res., 14: 199-222. Johnson, A.V., 1970. Physical Processes in Geology. Freeman and Cooper, San Francisco, 577 pp. Kilburn, C.R.J., 1984. A study of the morphological and rheological development of the basaltic aa lavas of Mt. Etna, Sicily. PhD Thesis, Univ. of London, (unpubl.). Marsh, B.D., 1981. On the crystallinity, probability of occurrence, and rheology of lava and magma. Contrib. Mineral. Petrol., 78: 85598. McBirney, A.R. and Murase, T., 1984. Rheological properties of magmas. Annu. Rev. Earth Planet. Sci., 12: 337-357. Moore, H.J., Arthur, D.W.G. and Schaber, G.G., 1978. Yield strengths of flows on the Earth, Mars, and Moon. Proc. Lunar Planet. Sci. Conf., 9: 3351-3378. Moore, J.G., Lipman, P.W., Swanson, D.A. and Alpha, T.R., 1981. Growth of lava domes in the crater, June 1980. January 1981. U.S. Geol. Surv., Prof. Pap., 1250: 541. 547. Orowan, E., 1949. Discussion. In: Meeting of the British Glaciological Society, the British Rheologists Club, and the Institute of Metals. J. Glacial., 1: 231-240. Pinkerton, H. and Sparks, R.S.J., 1978. Field measurements of the rheology of lava. Nature, 276: 383-385. Shaw, H.R., 1972. Viscosities of magmatic silicate liquids: an empirical method of prediction, Am. J. Sci., 212: 870-893. Sparks, R.S.J. and Pinkerton, H., 1978, Effect of degassing on rheology of basaltic lava. Nature, 276: 385-386.