Mechanisms of compaction of quartz sand at diagenetic conditions

Mechanisms of compaction of quartz sand atdiagenetic conditions

J.S. Chester �, S.C. Lenz 1, F.M. Chester, R.A. Lang 2

Center for Tectonophysics and Department of Geology and Geophysics, Texas ApM University, College Station, TX 77843, USA

Received 19 June 2003; received in revised form 7 January 2004; accepted 7 January 2004

Abstract

The relative contribution of cracking, grain rearrangement, and pressure solution during experimental compactionof quartz sand at diagenetic conditions was determined through electron and optical microscopy and image analysis.Aggregates of St. Peter sand (2550 60 Wm diameter grain size and porosity of approximately 34%) were subjected tocreep compaction at effective pressures of 15, 34.5, 70, and 105 MPa, temperatures of 22 and 150‡C, nominally dry orwater-saturated (pore fluid pressure of 12.5 MPa) conditions, and for times up to one year. All aggregates displayedtransient, decelerating creep, and volume strain rates as low as 2U10310 s31 were achieved. The intensity of fracturingand degree of fragmentation increase with volume strain and have the same dependence on volume strain at allconditions tested, indicating that impingement fracturing and grain rearrangement were the main mechanisms ofcompaction throughout the creep phase. The increase in fracture density and decrease in acoustic emission rate at longtimes under wet conditions reflect an increase in the contribution of subcritical cracking. No quantitative evidence ofsignificant pressure solution was found, even for long-term creep at 150‡C and water-saturated conditions.Comparison of our findings to previous work suggests that pressure solution could become significant at temperaturesor times somewhat greater than investigated here.8 2004 Elsevier B.V. All rights reserved.

Keywords: compaction; subcritical crack growth; pressure solution; diagenesis ; microstructures; sandstones; deformation;sedimentary basin

1. Introduction

Observations of quartz-rich sandstone reser-voirs document great variability in porosity atsimilar burial depths, and indicate that severaldistinct mechanical and chemical processes con-tribute to consolidation processes over geologictime scales [1^5]. Although porosity loss by ad-vective transfer of solutes from distant sources tosites of cementation may explain porosity varia-tions in some cases, evidence for compaction by

0012-821X / 04 / $ ^ see front matter 8 2004 Elsevier B.V. All rights reserved.doi:10.1016/S0012-821X(04)00054-8

* Corresponding author. Tel. : +1-979-845-1380;Fax: +1-979-845-6162.E-mail address: [email protected] (J.S. Chester).

1 Present address: Unocal Corp., 14141 Southwest Freeway,Sugarland, TX 77478, USA.

2 Present address: Geoscience Data Management, 10003Woodloch Forest Drive, The Woodlands, TX 77380, USA.

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local grain-scale processes is ubiquitous. Grain-scale processes in quartz-rich sands include brittle,frictional (isochemical) mechanisms of intergranu-lar slip, grain rearrangement and pore collapse,microfracture, and grain crushing (e.g. [6^9]), aswell as time- and temperature-dependent mecha-nisms of subcritical crack growth and pressuresolution (stress or strain induced dissolution, dif-fusion, and precipitation) (e.g. [4,5,10^16]). Oftenit is assumed that compaction during early stagesof burial is dominated by brittle processes thatgive way to pressure solution to achieve long-term compaction creep. Characteristic grain sur-face morphologies, such as indentation marks, in-terpenetrating grains and sutured grains have longbeen cited as evidence of porosity reduction bypressure solution. Yet evidence also exists indi-cating that some quartz-rich sandstones developsimilar morphologies by cracking, cataclasis andcementation at grain contacts and that the dis-tinction can only be made through cathodolu-minescence imaging (e.g. [17^19]). For nearly purequartz aggregates, the relative contribution ofeach grain-scale process is uncertain, and quanti-tative expressions predicting the contribution ofeach mechanism to compaction e⁄ciency is lack-ing.

Several laboratory studies have focused on

time-dependent compaction and cementation ofquartz-rich aggregates (e.g. [6,20^26]), yet nostudy has quanti¢ed the contribution of eachcompaction mechanism across the transitionfrom subcritical cracking- to pressure solution-dominated compaction. The purpose of this paperis to document the relative contribution of crack-ing and pressure solution in quartz sand duringcompaction creep at simulated diagenetic condi-tions. The conditions chosen target those exploredin previous studies [23] where the coexistence ofcracks and dissolution features were observed andwhere pressure solution was interpreted as thedominant compaction mechanism.

Microstructures are described for two suites ofexperiments that provide systematic data on thee¡ects of temperature, e¡ective pressure, and timeon the micromechanisms of compaction. The ¢rstsuite is a series of short-term tests (6 1 day induration) designed to explore the relative contri-bution of rapid, mechanical compaction processesand subcritical cracking [27]. Short-term creeptests were compacted under e¡ective pressures of15, 34.5, 70, and 105 MPa (pore £uid pressure of12.5 MPa), and temperatures of 22 and 150‡C.The second suite of experiments was composedof long-term tests [28] designed to explore thetransition from subcritical cracking to pressure

Table 1Compaction experiments and fracture characterization results

Expt. number Pe MPa T ‡C Creep duration s Total inelastic L % grainsfractured

PL Aspectratio

Norm. particlesize

(MPa) (‡C) (s) (%) All Trans. (#/mm)

LSP11 15 150 wet: 1.25U103 0.78 21 1.0 0.47 1.58 1.10LSP03 34.5 22 wet: 1.57U103 1.05 29 1.8 0.59 1.64 0.94LSP15 34.5 150 wet: 3.00U103 1.36 31 4.1 0.66 1.53 1.15LSP01 70 22 wet: 2.20U103 2.13 30 13.9 1.87 1.86 0.73LSP08 105 22 wet: 7.23U103 3.5 ^ ^ ^ 1.95 0.61LSP10 70 150 wet: 3.10U103 6.2 ^ ^ ^ 2.42 0.35SPB 0 22 ^ 0 13 0.2 0.33 1.60 1.00SPSa ^ ^ ^ 0 ^ ^ ^ ^ ^SP35a 34.5 150 dry: 14.39U106 V3.2 ^ ^ ^ ^ ^

wet: 19.82U106

SP37 34.5 150 dry: 4.82U106 1.4 27 5.0 0.56 1.56 1.00SP38 34.5 150 dry: 3.82U106 2.4 59 29.3 2.89 2.14 0.82

wet: 10.81U106

T, temperature; Pe, e¡ective pressure; PL, linear fracture density.a Sample used for grain surface analysis.

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solution as described by Dewers and Hajash [23].Microstructure analyses of three long-term creepexperiments compacted at 150‡C and an e¡ectivepressure of 34.5 MPa are reported. The threesamples document: (1) mechanisms of compac-tion during long-term creep (56 days) under nom-inally dry conditions (SP37; Table 1), (2) mecha-nisms of compaction during long-term creep (125days) under £uid-saturated conditions followingan initial dry creep phase (44 days; SP38; Table1), and (3) changes in grain surface morphologyduring long-term creep (229 days) under £uid-sa-turated, £ow-through conditions and a dry creepphase (167 days; SP35; Table 1).

2. Experiments

2.1. Experimental procedures

Unconsolidated St. Peter sand collected fromthe Ordovician Cave Unit, Minnesota, was usedin all experiments, and is from the same batchused by Dewers and Hajash [23]. A 250^350-Wmsize fraction (s 99% pure quartz), separated bymechanical sieving, was washed in a 20% HCLsolution for 1 h to remove iron oxide contami-nants coating grain surfaces, rinsed repeatedly indistilled water, then agitated in an ultrasonic bathof distilled water to remove ultra-¢ne particlesadhering to grain surfaces following proceduresof Dewers and Hajash [23].

Loose, cylindrical packs of sand were held by atriple-layer jacket that was sealed to an upper andlower piston using nickel^chromium tie wires toisolate the sand from the liquid con¢ning media(kerosene or silicone £uid). Jackets consisted of a50-Wm-thick silver foil (annealed at 700‡C for 10 hminimum) between two 0.64-mm-thick PFA Tef-lon0 sleeves. Silver foil minimized di¡usive trans-port of the pore and con¢ning £uids across thejacket assembly. Starting porosity of each samplewas determined from the mass of sand and totalvolume of the sample. If the sand was to be com-pacted under water-saturated conditions, the sam-ple/piston assembly was £ooded with distilledwater in a vacuum prior to being placed in thepressure vessel.

During the short-term tests, 37-mm-long by 19-mm-diameter samples were compacted under ef-fective pressures of 15, 34.5, 70, and 105 MPa(pore £uid pressure= 12.5 MPa), and tempera-tures of 22 and 150‡C. Con¢ning and pore-£uidpressures, sample pore volume, temperature, andnumber of acoustic emissions (AE) were measured[27]. All samples were subjected to an initial con-¢ning pressure of 15.0 MPa and a pore £uid pres-sure of 12.5 MPa by alternately raising the con-¢ning £uid and pore £uid pressure in 1-MPaincrements, such that the e¡ective pressure wasmaintained between 1.5 and 2.5 MPa. Staring po-rosities are slightly reduced during this stage byporoelastic compaction, thermal expansion, andsome grain rearrangement. Pressure transducersmeasured the con¢ning and pore £uid pressureswith an accuracy of 0.02 and 0.03 MPa, respec-tively, resulting in an accuracy of 0 0.05 MPa fore¡ective pressure.

For short-term experiments run at 150‡C, thepressure vessel was heated externally to the targettemperature after the initial con¢ning and pore£uid pressures were established to prevent boilingthe pore water. The thermocouple, with resolutionof 0 0.05‡C, was located in the wall of the pres-sure vessel, 20 mm from the sample. The maxi-mum temperature variation in the sample was lessthan 1% of the measured temperature in ‡C. Thee¡ective pressure was maintained between 1.5 and2.5 MPa during heating, and the sample and pres-sure vessel were allowed to reach thermal equilib-rium at 1.5^2.5 MPa e¡ective pressure prior toconducting a creep experiment. Compaction wasinitiated by rapidly raising the con¢ning pressureto the desired level. Con¢ning and pore £uid pres-sures were stabilized within 30^100s of initiatingcompaction.

As samples compacted, pore £uid was extractedand con¢ning £uid was added to maintain con-stant con¢ning and pore-£uid pressures. The vol-ume of pore £uid was recorded by the displace-ment of a screw-driven piston-cylinder measuredwith a linear voltage displacement transducer. Forexperiments at temperature, displaced volume wascorrected for changes in temperature of the dis-placed pore £uid [27]. The displaced volume ofpore £uid represents the porosity loss of the sam-

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ple and was used to determine volume strain. Vol-ume strains are accurate to within 0.02% of thetotal strain [27]. Volume strain rates were allowedto decrease to approximately 1038 s31 before ex-periments ended.

Acoustic emissions were measured with a piezo-ceramic transducer a⁄xed to the end of the load-ing piston [27]. The transducer output was ampli-¢ed, band-pass ¢ltered (4^400 kHz), recti¢ed, andintegrated for automated pulse counting by com-puter. Software discrimination of AE from elec-trical noise was based on pulse width and ampli-tude.

During the long-term tests, 85-mm-long by 45-mm-diameter samples were compacted at an e¡ec-tive pressure of 34.5 MPa and temperature of150‡C. The con¢ning pressure, sample volume,sample temperature, room temperature, andpore-£uid pressure were measured and recordedat least four times per day [28,29]. Sample temper-ature was measured by a thermocouple locatedinside the pressure vessel adjacent to the samples.Samples initially were loaded by con¢ning pres-sure under dry conditions and monitored for ap-proximately one week to insure the assembly wasnot leaking. Con¢ning pressure was released, andthen samples were heated to 150‡C while the con-¢ning pressure was maintained at low values (2.8^5.5 MPa). The temperature stabilized after ap-proximately 1 day. Compaction creep at temper-ature was initiated by rapidly raising the con¢ningpressure to the target pressure, which stabilizedwithin 120 s. Samples were allowed to creep underdry conditions for about 1.5 months. At this pointsamples were either removed (dry compactioncreep test, SP37), or saturated with distilled waterand subjected to additional compaction creepover several months (wet creep test, SP38). Satu-ration was achieved in the wet samples in about10 h at constant temperature and e¡ective pres-sure by a synchronous increase in pore pressure to12.5 MPa and con¢ning pressure to 47 MPa.

Temperature during long-term experiments washeld constant to within 0 0.5‡C and e¡ective pres-sure was held constant to 0 0.3 MPa. Volumestrain was determined using a screw-driven pis-ton-cylinder volumometer to measure the volumeof the con¢ning medium that was displaced to

maintain constant pressure. Volume measure-ments are corrected for small £uctuations in pres-sure, con¢ning vessel temperature, and room tem-perature as well as temperature changes of thedisplaced £uid. Uncertainty in volume strain isapproximately 0 0.03%, which primarily re£ectsthe uncertainty in con¢ning £uid temperature of0 0.1‡C. For measurements spanning one month,uncertainty in volume strain rate is 0 1U10310

s31.The ¢nal porosity of compacted samples in

long-term tests was determined also from the vol-ume of £uid extracted from the samples at thetermination of the wet creep experiments. All £uidwas extracted by passing gas through the sampleto drive pore water into a trap. The remaining£uid was removed from the sample by heatingunder vacuum, and freezing the water vapor ina liquid N2-cooled trap.

2.2. Summary of mechanical data

In the short-term experiments, elastic and in-elastic strains occurred at a very rapid rate duringinitial loading, but could not be measured accu-rately during loading due to the £uctuating e¡ec-tive pressure [27]. The total strain was, however,measured accurately when the e¡ective pressurestabilized to within 1% of the target pressure.The elastic and inelastic strains produced duringloading can be estimated using data from cyclicloading^unloading experiments on the same ma-terials [30]. Pressure-strain paths of the short-termcreep tests indicate that the magnitude of inelasticstrain achieved during rapid loading to creepstress increases with e¡ective pressure and is rel-atively insensitive to temperature during this stage(Fig. 1; Table 1).

After rapid loading, the e¡ective pressure washeld constant and all volume strain achieved dur-ing creep is assumed to be inelastic. All samplesdisplayed decelerating volume strain rates for theduration of the creep experiment (Fig. 2). In gen-eral, the decrease in volume strain rate is morerapid at lower pressures and temperatures. Vol-ume strain rates increase with e¡ective pressureand temperature, and the dependence of creepon pressure and temperature is non-linear. The

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greatest volume strain is achieved in the wet ex-periment run at 150‡C and an e¡ective pressure of70 MPa.

We have no measure of strain during initialloading in the long-term creep experiments. Weassume that the magnitude of inelastic strain isthe same as that achieved during loading in theshort-term experiments because the sand used isthe same and the loading procedure is very sim-ilar. Once the pressure was stabilized to within 1%of the target pressure, subsequent measurementsof volume strain were very accurate. At the end ofeach experiment we measured pore £uid volumeby £uid extraction, and determined the volumestrain produced by loading from the ¢nal poros-ity, volume strain during creep and initial bench-top porosity.

The long-term creep experiments display decel-erating creep subsequent to stabilizing at the tar-get pressure. Volume strain rates are strongly de-pendent on the presence of pore water (Fig. 3). Inall two-stage creep experiments involving water£ooding of nominally dry samples at e¡ective

pressure, a sudden and marked increase in rateof compaction is noted upon introduction ofwater. At times to approximately one month(V2.5U106 s), volume strain rates in dry andwater-saturated tests are 2U10310 s31 and2U1039 s31, respectively. Under wet conditions,volume strain rate decelerates more slowly, drop-ping to 5U10310 s31 after three months.

Fig. 1. E¡ective pressure vs. volume strain for room-temper-ature compaction tests on quartz sand. Elastic and inelasticstrain occurs during rapid loading to creep stress. Inelasticstrain accumulates during the creep stage, and elastic strainis recovered during unloading. Pressure-strain paths at ele-vated temperature conditions are similar except greater strainis achieved during creep phase.

Fig. 2. E¡ect of pressure at (a) room temperature and (b)elevated temperature for short-term creep tests in volumestrain vs. time plots. Volume strain and time are measuredfrom beginning of creep (strain Ls and time ts).

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2.3. Optical and scanning electron microscopy

At the end of the long-term experiments, sam-ples were dried and evacuated prior to reductionof con¢ning pressure to approximately one atmo-sphere. The central portion of each sample wasimpregnated with a low viscosity epoxy (Epotek301) by perforating the jackets and drawing epoxyinto the sample under a vacuum. Maintaining oneatmosphere of e¡ective pressure along with thestrength of the jacket helped preserve the packingarrangement of grains and minimized disruptionof microstructures. The remaining loose sand wascollected for grain surface morphology analysis.For the short-term tests, each sample was impreg-nated throughout; the samples were held tightlyby the jackets such that the sand grains experi-enced little disturbance. A control sample that didnot undergo compaction also was prepared andimpregnated for comparison. All impregnatedportions of each sample were cut into sectionsthat were re-impregnated with epoxy at leasttwo additional times during the cutting and pol-ishing stage to insure minimal plucking and dam-

age during polishing to 0.05 microns. Sections,V2 cm in diameter, were sputter-coated withV200 AU of gold-palladium alloy and examinedin a Leo 1530 VP FE^SEM.

In order to determine the degree of fracturingin the compacted samples, secondary (SE) andbackscatter (BE) electron images were taken at6^10 locations across each polished section at amagni¢cation of 60U, and image resolution of2048U1536 pixels. The number of locations im-aged for each sample was selected to provide ap-proximately 350 grains entirely contained withinthe images. Parameters quanti¢ed using the SE^BE image pairs included: (1) number of wholegrains, (2) size and aspect ratio of particles in 2-D sections, (3) percentage of grains cut by trans-granular fractures, and (4) linear fracture density.Particle size and aspect ratio distributions weredetermined using NIH image analysis software.Fractures were classi¢ed as transgranular if theycut across the entire grain and as intragranular ifthey terminate within a grain. Fracture countswere all made at the same magni¢cation becausevisible aperture and length of a fracture dependon magni¢cation and image resolution. Linearfracture density is the number of fracture inter-cepts per unit length determined along 15 evenlyspaced, parallel lines on each image following themethod of Fredrich and Wong [31]. This measureis appropriate because microfractures developedin sand loaded by hydrostatic stress should berandomly oriented.

To document changes in surface morphologyinduced by compaction creep, SE images weretaken of 100 loose sand grains from the uncom-pacted sample (SPS; Table 1) and 100 loose sandgrains from the longest duration compactioncreep experiment (SP35; Table 1) at 400U mag-ni¢cation. To characterize the particle size distri-bution and shape of grains in the undeformedstarting material, loose grains were immersed inoil and photographed using an optical microscopeat a magni¢cation of 2.5U. Ten images were an-alyzed using NIH image software to determine thearea, and long and short axis dimensions for morethan 300 grains. Axial ratios and equivalentspherical grain diameters were calculated fromthese data.

Fig. 3. Long-term creep tests under dry (SP37) and water-sa-turated (SP38) conditions in volume strain vs. time plots.Volume strain and time are measured from beginning ofcreep (strain Ls and time ts).

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3. Microstructural observations

3.1. Starting material: surface morphology ofgrains, fractures, and initial porosity

The 250^350-Wm size fraction of St. Peter sand

produced by sieving is composed of grains ofequivalent spherical grain diameter between 140and 420 Wm (Fig. 4a). The mean equivalent spher-ical grain diameter is 255 Wm with a standarddeviation of 60 Wm. The mean size is skewed to-ward the lower limit of sieves used, and graindimensions have a wide range because grains aresomewhat elliptical in shape (Fig. 4b). In general,ellipticity increases with a decrease in grain size.

Acid-washed grains of the starting material dis-play a characteristic surface morphology that isdominated by linear approximately parallel ridges(Fig. 5a) referred to as ‘upturned plates’ [32,33],

Fig. 4. Grain size distribution and shape of 250^350-Wmsieved size fraction. Frequency is number of grains in eachbin relative to total number of grains. (a) Distribution ofgrain sizes in terms of equivalent spherical grain diameter.Grains have an average spherical grain diameter of 255 Wmwith standard deviation of 60 Wm. (b) Ellipticity is character-ized by the ratio of long to short axis dimensions.

Fig. 5. SE images of grain surfaces showing microroughnessand smooth spots (arrows) in an (a) uncompacted grain and(b) compacted grain.

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or a ‘brain-like’ texture [23]. The plates, inter-preted to re£ect subaerial or aeolian abrasion[32,33], served as sites for minute incipient quartzovergrowths. Some overgrowths display well-de-veloped rhombohedral terminations, others arerounded, smoothing the upturned plate texture.Smoothing has been attributed to modi¢cationof the abrasion texture by dissolution and repre-cipitation of silica between plate edges [32] or me-chanical abrasion of asperity peaks with the plas-tering of attrition debris in surface hollows [34].The upturned plate surface texture is punctuatedoccasionally by smooth spots that may be rimmedby silica overgrowths (Fig. 5a). Both features have

been interpreted as evidence of grain^grain con-tact dissolution/precipitation processes associatedwith diagenesis [33], although experiments show-ing such features may be produced without con-tact dissolution [15]. Large quartz overgrowthsare absent in samples collected from the south-eastern Minnesota locality [33].

The control sample, SPB, that was preparedbut not compacted, yielded an initial porosity of34%. This value was determined from image anal-ysis of SE and BE images of a polished surfaceand has an uncertainty of about 0.5% re£ectingthe uncertainty in de¢ning grain boundaries indigital images. The porosity value for SPB com-

Fig. 6. BE images of sand showing increase in fracture intensity and development of complex systems as function of increase involume strain. (a) LSP11, 0.8% strain. (b) LSP01, 2.1% strain. (c) LSP08, 3.5% strain. (d) LSP10, 6.2% strain.

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pares well with the range of initial porosities (32^37%) determined for 9 compacted samples on thebasis of mass of sand and sample volume [27].

Few fractures are found within quartz grainstaken from the uncompacted sample (SPB). Whenpresent, cracks are short, intragranular fracturesthat have extremely narrow apertures and are notvisibly ¢lled with blue epoxy; in some cases frac-tures intersect grain surfaces (Table 1). The frac-tures may be inherited or possibly produced dur-ing sample preparation. Fluid inclusion planesalso are present, and clearly are inherited fea-tures.

3.2. Fractures produced during short-term creep

The wet, short-term creep experiments (LSP11,LSP01, LSP08, LSP10) show a de¢nitive increasein density of intragranular and transgranular frac-tures, and fragmentation with increasing magni-tude of volume strain (Fig. 6; Table 1). Both iso-lated and more complex fracture systems arepresent. Isolated fractures dominate at relativelylow magnitudes of compactive strain and consistof relatively sharp, single fracture traces havingnarrow apertures, an opening-mode geometry,and often emanate from grain boundaries athigh angles (Fig. 6b). Complex fracture systemsare composed of numerous intragranular or trans-granular fractures, or both (Figs. 6d and 7). Frac-tures within these systems also display sharp edgesand tend to emanate at a high angle from grainboundaries, and often are arranged in parallel,radiating, or cone geometries (e.g. [6]). Examplesof both isolated and complex systems that areclearly associated with grain^grain contacts canbe documented. In some cases, particularly insamples compacted to the largest volume strain,fractures transecting an entire grain and linkingopposing points of contact are evident, indicatingthat impingement (Hertzian) fracturing occurred(Fig. 7a). The aperture and number of transgra-nular fractures increase with an increase in vol-ume strain. At large strains, individual grains mayshow numerous parallel or radiating intragranularand transgranular fractures. At the highest strain,fractures often fragment a grain into numerousangular particles. In many cases, matching parts

Fig. 7. BE images of complex impingement fractures for wet,long-term creep test (SP38).

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of fragments are obvious, and the fractures dis-play opening-mode separations with little or noshear displacement parallel to fracture walls. Atthe intermediate (LSP08) and large (LSP10) vol-ume strains, however, particles with angularshapes often are observed in isolation with noevidence of matching fragments (Fig. 6). Suchgrains clearly are fragments of original grainsthat have been displaced signi¢cantly. Fracturedensity characterizations of samples that containdisplaced, isolated fragments are inaccurate be-cause fracture densities are underestimated. Noevidence of £attening, interpenetration or suturingat grain^grain contacts was observed in any of theshort-term tests, regardless of temperature, indi-cating that impingement fracturing was the dom-inant compaction mechanism at all volume strainsachieved.

3.3. Fractures produced during long-term creep

Fracture densities and morphologies of thelong-term dry and wet creep experiments are con-sistent with trends and morphologies producedduring short-term wet creep. Multiple subparallelcracks with di¡erent apertures that link two op-posing points of contact are evident (Fig. 7). Thenumber of fractures increases with proximity tograin^grain contact sites often in the form of suc-cessively branching fractures that have narrowerapertures towards the contact. Numerous small,angular fragments are visible at many grain^graincontact sites. In some cases, matching fragmentscan be identi¢ed, even for particles on the orderof several Wm in length. In other cases, cataclasishas completely disrupted the region and grain re-construction is not possible. It is important tonote that fragments less than 1 Wm in length inthe long-term wet creep test (SP38) are angularand do not show obvious evidence of roundingby dissolution (Fig. 7).

In grouping the fracture intensity measurementsfrom the long- and short-term creep experimentswe see that the number of grains cut by trans-granular fractures increases monotonically withvolume strain up to a strains of 2.5% (Fig. 8a).Similarly, linear fracture density in the solid frac-tion of each sample also increases monotonically

with strain (Fig. 8b). At volume strains greaterthan approximately 2.5%, transgranular fracturesand displaced fragments are so numerous that itis di⁄cult to determine the number of originalgrains and accordingly, di⁄cult to determine thepercentage of original grains cut by transgranularfractures. These trends indicate that fracture den-sity depends on total volume strain regardless ofstrain rate, saturation by water, magnitude of ef-fective pressure during creep, proportion of total

Fig. 8. Fracture intensity as function of strain. (a) Fractionof grains cut by transgranular fractures vs. total inelastic vol-ume strain. (b) Linear fracture density vs. total inelastic vol-ume strain. Linear fracture density includes measure of allintragranular and transgranular fractures.

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strain achieved by creep relative to that achievedduring loading, and temperature (Fig. 8). Further-more, the data also suggest that the dominantcompaction creep mechanism at all volumestrains, for all conditions tested, was fracture.

3.4. Fragmentation

The degree of fragmentation can be quanti¢edby the ratio of particle size of a compacted samplerelative to particle size of the uncompacted sam-ple, and the average aspect ratio of particles (Fig.9). These measures re£ect fragmentation, and donot demand knowledge of the number of originalgrains in a particular volume. Fragmentationleads to a reduction in average particle size of apopulation of particles, and tends to produceelongate fragments that increase the average as-pect ratio of the population of particles (Figs. 6and 7). At volume strains of less than about 2%only a few transgranular, opening-mode fracturesare produced. The apertures of these fracturesoften are below detection limits and thus fragmen-tation is not observed in measurements of particlesize and aspect ratio (Fig. 9). Measurements doshow some variations at low strain, but these areattributed to local variations in particle sizes seenin images. In contrast, at strains greater thanabout 2%, the average particle size decreasesand aspect ratio increases (Fig. 9). The overallincrease in fragmentation with strain is signi¢-cantly greater than the variation in fragmentationobserved within a sample or between two small-strain samples. Similar to the relationships be-tween total strain and measures of transgranularfractures and linear fracture density, the variationin fragmentation among all the samples observedcan be related to total strain. These data suggestthat to ¢rst-order, fragmentation is not directlydependent on saturation by water, magnitude ofe¡ective pressure during creep, proportion of totalstrain achieved by creep relative to that achievedduring loading, or temperature (Fig. 9).

3.5. Surface morphology of grains duringlong-term creep

To quantify changes in surface morphology

that result from long-term compaction creep, sur-faces of individual grains of the starting materialwere compared to those of the long-term creeptest at water-saturated conditions and 150‡C for229 days (SP35). In particular, the number andsize of smooth spots on grain surfaces were quan-

Fig. 9. Degree of fragmentation as a function of total inelas-tic volume strain as measured by average particle size andparticle aspect ratio. Particle size and aspect ratio were deter-mined by image analysis of BE images of sections from un-deformed and deformed samples. Due to magni¢cation andresolution of images, only particles with areas greater than200 Wm2 could be measured. Average particle size of eachsample is normalized by the average particle size of the un-deformed sample. Fragmentation becomes signi¢cant at vol-ume strain greater than approximately 2%.

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ti¢ed and the roughness of the spots was qualita-tively assessed.

SEM analysis indicates that uncompacted andcompacted samples display a similar number ofsmooth, £at spots on the surfaces of individualgrains in all size categories, except for the smallestcategory of 18^36 Wm average spot diameter (Fig.10). In the smallest size category, the number ofspots is slightly increased in the compacted sam-ple relative to the uncompacted sample. Smoothspots in both samples are elliptical and displaydi¡erent micro-roughness characteristics and moreplanar geometries than do adjacent grain sur-faces (Fig. 5). These data indicate that smoothspots on surfaces were only slightly modi¢ed dur-ing long-term creep at 150‡C and relatively fewnew spots were created. In contrast, individualgrains from the compacted sample (SP35) displaynumerous new fractures and fractured surfaces,consistent with data from the polished sectionsof SP38 (Figs. 6 and 7).

4. Discussion

4.1. Mechanisms of creep: short-term runs at roomtemperature

Lenz [27] documents that AE rates are propor-tional to volume strain rate throughout the creepstage in the short-term tests run at room temper-

ature and lower pressures. This ¢nding is consis-tent with earlier results of Brzesowsky [6] for uni-axial (laterally constrained) compaction of quartzsand at room temperature. In both studies, AEevents during the creep phase are interpreted tore£ect the onset of unstable propagation oncesubcritical cracks achieve a critical length. It isalso recognized that not all cracks produce AEand that AE can result from slip between grains[35,36]. Given the low temperature and short timefor creep, it is unlikely that measurable straincould be achieved through pressure solution in-volving dissolution at grain^grain contacts anddi¡usion of solute (e.g. [10]).

On the basis of the poroelastic and inelasticresponse of St. Peter sand (same particle sizeused herein) to cyclic application of e¡ective pres-sures up to the critical pressures for grain crush-ing, P*, Karner et al. [30] conclude that the dom-inant process of compaction at room temperatureevolves with pressure and strain. At small perma-nent strain and pressures up to approximately 1/3P*, Karner et al. [30] suggest that grain rearrange-ment and pore collapse, facilitated by some crack-ing and frictional slip along grains boundaries, arethe primary compaction mechanisms. At pres-sures greater than 1/3 P*, cracking is thought todominate. Our observations of intragranular frac-tures that emanate from points of grain^graincontact and some rearrangement of fracturedfragments, as well as the non-linear but progres-sive overall increase in degree of cracking withstrain (and pressure) at room temperature sup-ports the interpretations of Brzesowsky [6], Lenz[27] and Karner et al. [30] (Figs. 6, 8 and 9). Thusthe microstructures of the wet, short-term creepexperiments run at room temperature provide thebaseline of fracture-dominated compaction forcomparison with other tests at elevated temper-atures and long times.

4.2. Mechanisms of creep: short-term runs atelevated temperatures and pressures

Lenz [27] shows that the proportionality be-tween AE rate and creep rate decreases withtime in the short-term tests run at higher pressuresand temperatures. The greatest decrease is seen in

Fig. 10. Occurrence of smooth spots on grains as a functionof spot size (area) for starting material and for a sampleafter long-term creep in the presence of water. Frequency isthe number of spots observed in SE images of 100 grains.An increase in the occurrence of spots due to creep is sug-gested only by the smallest size class.

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experiments that achieve the greatest creep strain.One possible explanation for the decrease in pro-portionality is that the increment of strainachieved by rapid failure associated with an AEevent increases in magnitude with an increase intotal volume strain. Yet our microstructural ob-servations document an overall non-linear in-crease in degree of fracturing with volume strain(Fig. 8), suggesting just the opposite, i.e. a de-crease in the increment of strain achieved byeach additional crack as total strain increases.Lenz [27] suggests that the decrease in the propor-tionality re£ects the decreasing importance of AE-generating cracking relative to other silent, butunidenti¢ed, mechanisms of creep that are pro-moted by increases in temperature, pressure andtime. Our observations of fracture density as afunction of strain for short-term creep at elevatedpressures and temperatures are consistent withdata for short-term creep at room temperature(Figs. 8 and 9). This consistency, and the factthat the only deformation mechanisms noted arefracture and grain rearrangement, suggest that thesilent mechanism discussed by Lenz [27] re£ectsthe increased importance of subcritical cracking.

4.3. Mechanisms of creep at elevated temperaturesand long times

At all conditions tested, the quartz sand exhib-its transient, decelerating creep [28,29]. Volumestrain follows a simple transient creep relationwhere strain increases linearly with the logarithmof the time since experiment conditions were es-tablished, as given by L3Ls = Lc*log{1+(t3ts)/tc},where L is volume strain, t is time, Lc and tc arethe characteristic strain rate and time, respec-tively, and Ls is the strain at time ts [27,28]. Thistype of transient creep is demonstrated by a lineardependence of strain with log t (Fig. 11). A sim-ilar response for quartz sand was demonstratedby Dewers and Hajash [23] and implied by plotspresented by Brzesowsky [6]. In the short-termtests, the volume strain rates and time for decel-eration increase (as given by Lc and tc) as thetemperature and pressure increase [27].

The creep behavior of nominally dry quartzsand during long-term creep at 150‡C (SP37) is

consistent with the extrapolation of the behaviordisplayed during short-term wet creep at 150‡C(LSP15) to longer times. This consistency is illus-trated graphically by the slope of curves in vol-ume strain vs. log time plots (Fig. 11). The similarslope suggests that the microscopic processes thatlead to AE and that achieve strain at short timesin the presence of water also are responsible forstrain at long times in the dry experiments. Themicrostructure observation that the degree offracturing in the dry, long-term creep test is con-sistent with the degree of fracturing in the short-term tests supports the conclusion that the creepmechanisms are the same (Figs. 8 and 9).

The creep behavior of wet quartz sand duringlong-term creep at 150‡C (SP38) is markedly dif-ferent. Comparison with the long-term dry test(SP37) demonstrates that greater strain rates andmuch greater strain are achieved under water-sa-turated conditions after times of approximately105 to 106 s (Fig. 11). We interpret the di¡erenceto re£ect the e¡ect of liquid water on subcriticalcracking at times greater than approximately 106

s, rather than the activation of pressure solution.This interpretation is supported by the fact thatthe degree of fracturing in the long-term wet testis consistent with that in all other creep tests, in-cluding the short-term tests run at room temper-

Fig. 11. Volume strain from select short- and long-term creeptests plotted as a function of log time.

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ature (Figs. 8 and 9). The abrupt change in slopeof the volume strain vs. log t curves (Fig. 11)could re£ect a change in the rate-controlling pro-cess or reaction mechanism of subcritical cracking[37,38]. It is possible that during long-term creep,cracks remain subcritical during the entire processof grain failure, which would be consistent withthe inference of Lenz [27] that the silent mecha-nism in the short-term tests is the same as thatresponsible for the greater strain rates achievedduring long-term wet creep.

Even though volume strain rates generally in-crease with an increase in availability of chemi-cally reactive water, the grain-size dependence ofcreep and functional form of transient creep aresimilar regardless of conditions (i.e. nominallydry, or saturated with water vapor, static wateror percolating water) during long-term creep ofwet quartz sand [28]. Such similarity in mechan-ical behavior would be unlikely if the dominantmicroscopic mechanism of compaction was fun-damentally di¡erent in the wet and dry tests.

On the basis of all observations, we concludethat intragranular cracking, accompanied bygrain rearrangement, dominates in all creep teststo 150‡C and can explain the mechanical compac-tion measured in long- and short-term experi-ments as well as the AE of the short-term tests.At short times under wet and dry conditions andat long times under dry conditions, cracks thatare initiated by locally high grain contact stressesgrow across grains and can accelerate to highrates leading to AE, grain rearrangement, porecollapse, and compaction. At long times underwet conditions, the rapid cracking that producesAE is reduced in signi¢cance relative to subcriticalcracking.

4.4. Implications for the transition to pressuresolution-dominated creep

Production of new smooth spots on grain sur-faces is not de¢nitive evidence of pressure solution[15]. Nevertheless, our measurements documentthat if new spots did form as a result of contactdissolution during long-term creep, or originalspots were enlarged, these processes were of mi-nor extent. The spot data are consistent with the

conclusion, based on the fracture data, that dis-solution at grain contacts did not contribute sig-ni¢cantly to the total volume strain during long-term creep (V7 months) at 150‡C. Our conclu-sion is contrary to previous interpretations basedon mechanical data and qualitative microstructur-al observations that pressure solution was thedominant compaction process in the long-term,wet creep experiments discussed herein (e.g.SP38) [26] and in previous experiments on similarmaterials at similar conditions [23].

Dewers and Hajash [23] reported a progressiveenlargement of smooth spots on grain surfacesand production of small quartz overgrowthsalong the edges of the spots with increasing strainat 150^200‡C and e¡ective pressures of 34.5 MPa.Spot sizes reported ranged up to approximately80 Wm in diameter [23]. Our data indicate thatthe distribution of spot sizes in the deformedand undeformed samples are statistically thesame. Furthermore, the only new spots that mayhave been produced during the longest of ourcreep tests at 150‡C (SP35) range in size from18 to 36 Wm diameter. Our observations raisethe question of what magnitude of strain couldbe achieved from the production of spots of thissize.

We use an idealized model to determine therelationship between spot size and volume strainassuming strain occurs by dissolution at contactsbetween grains. For cubic-close-packing of spher-ical grains of the same size, volume strain is givenby L=3(13(R23a2)1=2/R), where R is the originalgrain radius and a is the radius of the dissolutioncontact spot. By this relationship spot sizes on theorder of 15^30 Wm diameter would be produced ingrains 250 Wm in diameter by 0.5^2.2% strain. Forcubic-close packing, there would be six new spotsper grain, of which at least two should be visibleon a SE image of an individual grain. If this sim-plistic model were correct, it suggests that approx-imately 200 new spots should have been observedon the 100 individual grains from SP35 if allstrain (total volume strain of 3%) achieved duringcreep was accommodated by dissolution at graincontacts. Although some dissolution likely oc-curred, the similarity in size of spots in the start-ing material and compacted sample support our

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interpretation that cracking, accompanied bygrain rearrangement, dominated the compactionprocess.

Our ¢ndings are consistent with the results ofSchutjens [22]. On the basis of qualitative micro-structural observations, Schutjens [22] concludedthat the grain scale mechanism of compaction inquartz sand changes from £uid-assisted time-de-pendent microcracking to stress-induced intergra-nular pressure solution at about 300^350‡C. Rel-ative to Schutjens’ [22] experiments, our long-termtests were conducted for much longer periods oftime but achieved considerably lower rates ofstrain. Using the activation enthalpy determinedfor creep by Schutjens [22] and Dewers and Ha-jash [23], which is similar to values determined forquartz dissolution [39] and subcritical cracking inquartz [37], and assuming an Arrhenius type rela-tionship between temperature and time, we ¢ndthat the mechanisms activated in our long-termexperiments should be similar to those activatedin the higher temperature and faster strain ratetests of Schutjens [22]. Experiments conducted at300‡C achieved strain rates in the range of 1036 to1038 s31, which correlate to rates of 1038 to 10310

s31 at 150‡C; the conditions of the long-term ex-periments reported here. These data suggest thatdissolution at grain contacts may just begin to beevident at 150‡C (at strain rates of 10310 s31), andthe transition from subcritical cracking- to pres-sure solution-dominated creep could begin in ear-nest at temperatures as low as 200‡C at strainrates of 10310 s31 (see also, [23]).

4.5. Implications for grain-scale mechanisms ofcompaction in nature

In a survey of quartz-rich sandstones of di¡er-ent ages and burial histories, Milliken and Lau-bach [19] use cathodoluminescence imaging todocument that brittle deformation of detritalgrains occurs in many sandstones. Many fracturesare cemented by secondary quartz, and becausethe cement is in optical continuity with the detri-tal grains, fractures cannot be seen in convention-al light microscopy. Through cathodolumines-cence imaging the secondary quartz cement maybe distinguished from detrital quartz, and quartz-

sealed fractures may be imaged [17]. In some casesapparent pressure solution features, such as con-cave^convex and sutured grain boundaries, areassociated with complex fracture systems similarto those seen in our short-term and long-termcreep experiments in which grain impingement isaccommodated by intense fragmentation at thecontact [18,19]. The secondary quartz cementa-tion in natural sandstone clearly documents solu-tion transfer processes were important. Further-more, the association of fracture and apparentpressure solution features is consistent with a re-lationship between brittle deformation and pres-sure solution. However, as shown in our experi-ments, natural compaction of quartz sands solelyby cracking may occur through purely mechanicale¡ects from large e¡ective pressure during burial(see also [9]), or through subcritical cracking overlong times under low e¡ective pressure. Futureexperiments combined with detailed microscopywill be useful to determine the relation betweenpressure solution and cracking in natural sand-stones, and the relative contribution of di¡erentgrain-scale processes to volume strain as a func-tion of intrinsic and extrinsic parameters.

5. Conclusions

(1) Intensity of fracturing and degree of frag-mentation increase with volume strain and havethe same dependence on volume strain at all con-ditions tested.

(2) Cracking and grain rearrangement are thedominant compaction creep mechanisms in quartzsand at temperatures to 150‡C and volume strainrates as low as 10310 s31. At these conditions,strain achieved through pressure solution atloaded grain contacts is insigni¢cant relative tocracking.

(3) The increase in fracture density and de-crease in acoustic emission rate at long timesunder wet conditions re£ect an increase in thecontribution of subcritical cracking.

(4) The greater rate of compaction of quartzsand during long-term wet creep at 150‡C, rel-ative to dry conditions, likely re£ects a changein the rate-controlling process or reaction mecha-

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nism of subcritical cracking and grain rearrange-ment.

Acknowledgements

We thank A.K. Kronenberg, W. He, A. Ha-jash, Jr., and S.L. Karner for helpful discussions,and B. Evans, S.L. Karner, A.K. Kronenberg, D.Sparks, and T.-F. Wong for thoughtful reviews ofthe manuscript. We acknowledge the capable as-sistance of R. Guillemette (Cameca SU50 elec-tron microprobe) and T. Stephens (Leo VP1530FE^SEM), and use of the facilities of the Micros-copy and Imaging Center of Texas ApM Univer-sity. The FE^SEM acquisition was supported bythe National Science Foundation under GrantNo. DBI-0116835. This research was supportedby the O⁄ce of Basic Energy Sciences, Divisionof Chemical Sciences, Geosciences, and Bioscien-ces, Department of Energy, under Grant No. DE-FG03-ER14887.[SK]

References

[1] J.C. Maxwell, In£uence of depth, temperature, and geo-logic age on porosity of quartzose sandstone, Am. Assoc.Pet. Geol. Bull. 48 (1964) 697^709.

[2] M.A. Addis, M.E. Jones, Volume changes during diagen-esis, Mar. Pet. Geol. 2 (1985) 241^246.

[3] D.W. Houseknecht, Assessing the relative importance ofcompaction processes and cementation to reduction ofporosity in sandstones, Am. Assoc. Pet. Geol. Bull. 71(1987) 633^642.

[4] E.H. Oelkers, P.A. Bjorkum, W.M. Murphy, A petro-graphic and computational investigation of quartz cemen-tation and porosity reduction in North Sea sandstones,Am. J. Sci. 296 (1996) 420^452.

[5] M.R. Rezaee, N.M. Lemon, In£uence of depositional en-vironment on diagenesis and reservoir quality: Tirrawarrasandstone reservoir, southern Cooper Basin, Australia,J. Pet. Geol. 19 (1996) 369^391.

[6] R. Brzesowsky, Micromechanics of Sand Grain Failureand Sand Compaction, Ph.D. Thesis, University ofUtrecht, Utrecht, 1995, 180 pp.

[7] B. Menendez, W. Zhu, T.-F. Wong, Micromechanics ofbrittle faulting and cataclastic £ow in Berea sandstone,J. Struct. Geol. 18 (1996) 1^16.

[8] T.-F. Wong, C. David, W. Zhu, The transition from brit-tle faulting to cataclastic £ow in porous sandstones: Me-chanical deformation, J. Geophys. Res. 102 (1997) 3009^3025.

[9] F.A. Chuhan, A. Kjeldstad, K. Bjorlykke, K. Hoeg, Po-rosity loss in sand by grain crushing-experimental evi-dence and relevance to reservoir quality, Mar. Pet.Geol. 19 (2002) 39^53.

[10] E.H. Rutter, The kinetics of rock deformation by pressuresolution, Philos. Trans. R. Soc. Lond. A 283 (1976) 203^219.

[11] R. Raj, Creep in polycrystalline aggregates by mattertransport through a liquid phase, J. Geophys. Res. 87(1982) 4731^4739.

[12] G.M. Pharr, M.F. Ashby, On creep enhanced by a liquidphase, Acta Metall. 31 (1983) 129^138.

[13] E.H. Rutter, Pressure solution in nature, theory, and ex-periment, J. Geol. Soc. Lond. 140 (1983) 725^740.

[14] R. Tada, R. Siever, Pressure solution during diagenesis,Annu. Rev. Earth Planet. Sci. 17 (1989).

[15] S.H. Hickman, B. Evans, Kinetics of pressure solutionat halite^silica interfaces and intergranular clay ¢lms,J. Geophys. Res. 100 (1995) 13113^13132.

[16] P.A. Bjorkum, How important is pressure in causing dis-solution of quartz in sandstone?, J. Sediment. Res. 66(1996) 147^154.

[17] R.F. Sipple, Sandstone petrology evidence from lumines-cence petrography, J. Sediment. Petrol. 38 (1968) 530^554.

[18] W.W. Dickinson, K.L. Milliken, The diagenetic role ofbrittle deformation in compaction and pressure solution,Etjo sandstone, Namibia., J. Geol. 103 (1995) 339^347.

[19] K.L. Milliken, S.E. Laubach, Brittle deformation in sand-stone diagenesis, in: M. Pagel, V. Barbin, P. Blanc, D.Ohnenstetter (Eds.), Cathodoluminescence in Geoscien-ces, Springer, New York, 2000, pp. 225^243.

[20] J.J. Renton, M.T. Heald, C.B. Cecil, Experimental inves-tigation of pressure solution of quartz, J. Sediment. Pe-trol. 39 (1969) 1107^1969.

[21] R.B. deBoer, Pressure solution: Theory and experiments,Tectonophysics 39 (1977) 287^301.

[22] P.M.T.M. Schutjens, Experimental compaction of quartzsand at low e¡ective stress and temperature conditions,J. Geol. Soc. Lond. 148 (1991) 527^539.

[23] T. Dewers, A. Hajash Jr., Rate laws for water-assistedcompaction and stress-induced water-rock interaction insandstones, J. Geophys. Res. 100 (1995) 13093^13112.

[24] E.H. Rutter, P.H. Wanten, Experimental study of thecompaction of phyllosilicate-bearing sand at elevated tem-perature and with controlled porewater pressure, J. Sedi-ment. Res. 70 (2000) 107^116.

[25] A. Niemeijer, C.J. Spiers, B. Bos, Compaction creep ofquartz sand at 400^600 degrees C: Experimental evidencefor dissolution-controlled pressure solution, Earth Planet.Sci. Lett. 195 (2002) 261^275.

[26] W. He, A. Hajash, D. Sparks, Creep compaction ofquartz aggregates: E¡ects of pore-£uid ^ A combinedexperimental and theoretical study, Am. J. Sci. 303(2003) 73^93.

[27] S.C. Lenz, Subcritical Crack Growth in Creep Compac-tion Experiments, M.Sc. Thesis, Texas ApM Univ., Col-lege Station, TX, 2002.

EPSL 7003 17-3-04


[28] W. He, R.A. Lang, F.M. Chester, J.S. Chester, A. Hajash,A.K. Kronenberg, Creep compaction of quartz aggregatesunder dry and £uid-saturated conditions, EOS Trans.AGU 80 (1999) F1020.

[29] W. He, Experimental and Theoretical Modeling of CreepCompaction of Quartz Sand: Rate Laws and Evolution ofPorosity and Fluid Chemistry, Ph.D. Thesis, Texas ApMUniv., College Station, TX, 2001, 140 pp.

[30] S.L. Karner, F.M. Chester, A.K. Kronenberg, J.S. Ches-ter, Subcritical compaction and yielding of granularquartz sand, Tectonophysics 377 (2003) 357^381.

[31] J.T. Fredrich, T.-F. Wong, Micromechanics of thermallyinduced cracking in three crustal rocks, J. Geophys. Res.91 (1986) 2743^2764.

[32] D. Krinsley, J.C. Doorkamp, Atlas of Quartz Sand Sur-face Features, Cambridge University Press, Cambridge,1973, 91 pp.

[33] J. Mazzullo, Origin of grain shape types in the St. PeterSandstone: Determination by Fourier shape analysis andscanning electron microscopy, in: J.R. Marshall (Ed.),Clastic Particles Scanning Electron Microscopy andShape Analysis of Sedimentary and Volcanic Clasts,Van Nostrand Reinhold, New York, 1987, pp. 302^313.

[34] J.R. Marshall, W.B. Whalley, D.H. Krinsley, The originof some ‘chemical’ textures on quartz-grain surfaces: In-terpretation and environmental implications, in: J.R.Marshall (Ed.), Clastic Particles Scanning Electron Mi-croscopy and Shape Analysis of Sedimentary and Vol-canic Clasts, Van Nostrand Reinhold, New York, 1987,pp. 248^253.

[35] R.M. Korner, A.E. Lord, Acoustic emissions in stressedsoil samples, J. Acoust. Soc. Am. 56 (1974) 1917^1924.

[36] D. Lockner, The role of acoustic emission in the study ofrock failure, Int. J. Rock Mech. Min. Sci. 30 (1993) 883^900.

[37] B.K. Atkinson, Subcritical crack growth in geological ma-terials, J. Geophys. Res. 89 (1984) 4077^4114.

[38] P.M. Dove, Geochemical controls on the kinetics ofquartz fracture at subcritical tensile stresses, J. Geophys.Res. 100 (1995) 22349^22359.

[39] P.M. Dove, D.A. Crerar, Kinetics of quartz dissolution inelectrolyte solutions using a hydrothermal mixed £ow re-actor, Geochim. Cosmochim. Acta 54 (1990) 955^970.

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Mechanisms of compaction of quartz sand at diagenetic conditions