Particle size distributions in natural carbonate fault rocks:insights for non-self-similar cataclasis

Fabrizio Storti �, Andrea Billi, Francesco SalviniDipartimento di Scienze Geologiche, Universita' degli Studi ‘Roma Tre’, Largo S.L. Murialdo 1, I-00146 Rome, Italy

Received 18 July 2002; received in revised form 8 November 2002; accepted 8 November 2002

Abstract

Particle size distributions of cataclastic rocks influence the mechanical and fluid flow behaviour of fault zones.Available data from natural cataclastic rocks are still controversial and do not fully support a self-similar evolutionfor the cataclastic process, a concept derived from laboratory experiments and micromechanical modelling. Ouranalyses of particle size in carbonate fault rocks show power law distributions with fractal dimensions spanning abroad range. This confirms that the idea of a persistent fragmentation mechanism for describing the entire evolutionof natural cataclastic fault cores in carbonate rocks is inadequate. Conversely, we propose that the fragmentationmechanism progressively changes with the intensity of comminution. Slip localisation within narrow shear bands isfavoured when a favourable cataclastic fabric with fractal dimensions D V2.6^2.7 is achieved in the fault zone.Intense comminution in the narrow shear zones produces the preferential formation of small diameter particlesresulting in particle size distributions characterised by D values approaching or exceeding 3. The non-self-similarevolution of natural cataclastic rocks has an important impact on the frictional and permeability properties of faultzones.3 2002 Elsevier Science B.V. All rights reserved.

Keywords: fault rocks; cataclasis; particle size; fractal; permeability

1. Introduction

Cataclasis is the process of progressive frag-mentation, grinding and compaction of rock par-ticles [1]. During faulting, cataclasis can eventu-ally produce fault gouges, i.e. fault rocks thathave been ground to a very ¢ne-grained powderor clayey material retaining few larger survivor

grains [2]. Cataclastic rocks, and in particularfault gouges, control the frictional fault properties[3^6] and the three-dimensional permeability pat-terns around faults [7,8]. For this reason, theyhave been extensively studied in the ¢eld [9^21],in laboratory experiments [3,4,9,11,22^31] and byanalytical modelling [13,32^34]. Numerical mod-elling has also been used to examine the in£uenceof particle size distribution and inter-particle fric-tion on the nature of deformation in granularfault gouges and on their mechanical behaviour[35].

Many solutions have been proposed for de-

0012-821X / 02 / $ ^ see front matter 3 2002 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 2 - 8 2 1 X ( 0 2 ) 0 1 0 7 7 - 4

* Corresponding author. Tel. : +39-6-54888085;Fax: +39-6-54888201.E-mail address: storti@uniroma3.it (F. Storti).

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scribing cataclastic rock particle size distributionin both two and three dimensions. They includeboth incremental and cumulative relations be-tween mass/volume/number and increasing or de-creasing mass/size [14]. It has been demonstratedthat the best way to characterise particle size dis-tributions [13,14] is by using the fractal relation-ship of particle frequency by size:

NðSÞWS3D ð1Þ

where N(S) is the number of particles less thansize S and D is the fractal dimension. The coef-¢cient D is conveniently determined as the slopeof the best ¢t line on a log N(S) against log Sgraph.

Di¡erent values of D are expected for di¡erentfragmentation processes. In particular, three the-ories of fragmentation have been directly ex-pressed in three-dimensional fractal terms [14] :(i) the ‘pillar of strength’ model of [32], whichpredicts a D value equal to 1.97; (ii) the ‘planeof fragility’ model of [33], which predicts a Dvalue equal to 2.84; (iii) the ‘constrained commi-nution’ model of [13], which predicts a D valueequal to 2.58. Experimental work on simulatedfault gouges has shown their tendency to developD values of about 2.6 [24,26,27], supporting the‘constrained comminution’ model of [13]. In par-ticular, [27] showed that DW2.6 may represent asteady-state value reached after an initial amountof displacement from early values of about 1.8.Only D values in experimental shear bands ap-proached 3 [26] or 4 [27].

Fractal dimensions measured in natural cata-clastic rocks are more controversial. Resultsfrom faults in crystalline basement rocks gave ei-ther D values averaging 2.6 [13,36] or a great var-iability in fractal dimensions, ranging from 1.88 to5.52 [9,14,19]. Such large variability of D values isunexpected in a self-similar cataclastic process[24], where the progressive breakdown of particlesis controlled by a scale- and time-independentfragmentation mechanism. In particular, the ‘con-strained comminution’ model of [13], which isbased on the assumption that the failure proba-bility of particles depends largely on the relativesize of nearest neighbours, predicts the tendencyfor cataclastic rocks to develop a self-similar grain

size distribution having a constant fractal dimen-sion equal to 2.58. This D value (D=2.58), infact, describes a cataclastic fabric that minimisesthe fracture probability of particles having similardimensions [13].

Preferential fragmentation of large particlesis a possible explanation for the occurrence incataclastic rocks of D values signi¢cantly higher

Fig. 1. (a) Location map of the sampled fault zones. (b)Chemical analysis of the protolith rocks in the studied faultsites.

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than 2.58. This mechanism has been proposed forexperimental shear bands by [27] and for naturalcataclastic rocks by [14], who also pointed out theimportance of factors such as rock type, altera-tion, and fault kinematics on the ¢nal particle sizedistribution. An additional mechanism for ex-plaining the development of fractal dimensionssigni¢cantly higher than 2.58 is the preferentialincrease of small particles by rotation-enhancedabrasion of larger particles during shear [19,37].The ¢rst mechanism is mainly related to the stateof stress within the deforming cataclastic rocks,while particle grinding essentially depends onslip-enhanced rolling and shearing. Both mecha-nisms likely determine the evolution of particlesize distributions in shear bands. Their relativecontribution is expected to vary through time.

The objective of our study is to get further in-sights into the progression of cataclasis duringfaulting. We studied particle size distributions ofcataclastic rocks developed along outcrop-scalestrike-slip and extensional faults a¡ecting plat-

form carbonate in the Apennines, Italy. Protolithrocks in all studied ¢eld sites are mostly com-posed of CaCO3 and are characterised by verysmall amounts of insoluble materials (Fig. 1).The structural architecture of the fault zones(Fig. 2) is composed of heavily fractured damagezones which bound the fault core where most ofthe displacement is accommodated [8,16]. Thefault cores have a cross-sectional width varyingfrom about 0.3 m to 2.6 m. We sampled boundaryzones adjacent to the damage zone (Fig. 3a), brec-cia zones constituting the bulk of fault core rocks(Fig. 3b), and shear bands within fault cores (Fig.3c). Sampled cataclastic rocks are mainly non-co-hesive to poorly cohesive breccias in the boundaryzones and breccia zones, and gouges in the shearbands.

Particle sizes are power-law-distributed over theanalysed size range and their fractal dimensionshave a large variability. In the following, we dis-cuss the relations between D values and the struc-tural architecture of fault cores as well as theimplications for the evolution of the cataclasticprocess.

2. Particle size analysis

2.1. Methodology

Sampled cataclastic rocks (49 samples) were an-alysed using a sieving and weighing technique[24]. Samples were fully disaggregated by a non-destructive ultrasonic device, dried for 24 h at110‡C, and sieved in a standard dry sieve array(Table 1 in the Background Data Set1). Inspectionof the sieved material allowed removal of grainsin case they were made up of still cemented cata-clasite. This prevented the possible coarsewardbias of the particle size populations. The dryweight of residual material in each sieve wastransformed to the equivalent particle numberby assuming that the grain shapes can be approxi-mated by spheres [37]. The total weight in eachsieve was divided by the weight of the sphere with

Fig. 2. Conceptual sketch of a fault zone sectioned perpen-dicular to the shear direction. The main sectors, characterisedby di¡erent fabrics and particle size distributions, are sche-matically highlighted. Not to scale.

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the same diameter as the mesh aperture of theoverlying sieve. A density of 2670 kg/m3 wasused for computing the weight of the referencespheres. The use of di¡erent reference valuessuch as the weight of the sphere with the samediameter as the mesh aperture of the underlyingsieve, or the weight of the sphere having the aver-age diameter between the mesh apertures of adja-cent sieves does not change the distribution of theresulting equivalent particle numbers. Materials inthe largest and smallest sieves were excluded fromthe procedure because of their intrinsic samplingand sieving limits, respectively. Six particle classeswere obtained, named equivalent particle sizeclasses: 4 mm, 2 mm, 1 mm, 0.5 mm, 0.25 mm,and 0.125 mm.

Particle size analysis was performed by plottingequivalent particle numbers versus the corre-sponding equivalent size classes in bilogarithmicgraphs and obtaining the corresponding fractaldimensions from the slope of the best ¢t lines. Asensitivity test was made by dividing three sam-ples into two equivalent parts and analysing eachof the two parts separately. Di¡erences in the Dvalues obtained from each sample (vD) are verysmall and start from the third decimal digit (Table2 in the Background Data Set1). The use of sam-ples collected in the same lithology allowed rulingout the in£uence of the rock type on D values.

2.2. Particle size distribution

Equivalent particle abundances in each sizeclass align very well in bilogarithmic graphs(Fig. 4) and this supports the power-law distribu-tions of particle sizes in the 4 mm^0.125 mm sizerange. As a general feature, the contribution oflarger equivalent particles (4 mm, 2 mm, 1 mmequivalent size classes) to the total equivalent par-ticle abundances is negligible. Samples with thelower D values pertain to the boundary regionsof both strike-slip and extensional fault cores (Ta-ble 3 in the Background Data Set1). Fractal di-mensions obtained from the breccia zones vary

from 2.17 to 2.74 in strike-slip fault cores andfrom 2.43 to 2.74 in extensional fault cores (Table4 in the Background Data Set1). Fractal dimen-sions obtained from gouge in shear bands vary

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Fig. 3. Typical fabrics of the main sectors within fault cores: (a) fault core boundary zone; (b) breccia zone; (c) gouge in a shearband within the breccia zone (approximately running from the lower left corner to the upper right corner).

Fig. 4. Examples of linear ¢tting of particle size data in bilog-arithmic graphs. (a) Sample 13MA5, collected in the bound-ary region of the cataclastic fault core. (b) Sample 7MA2,collected in the breccia zone. (c) Sample 2MA2, collected ina shear band.

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from 2.61 to 3.49 in strike-slip fault cores (Table 5in the Background Data Set1). Two gouge samplescollected in extensional fault cores gave D valuesof 3.13 and 2.93 respectively. The summary plotof all data shows the variability of D with faultkinematics and the position within the fault core(Fig. 5). The complete overlap between D valuesobtained from both strike-slip and extensionalfault cores does not support any signi¢cant in£u-ence of fault kinematics on the fractal dimension.On the other hand, there is a direct relation be-tween the position of samples within fault coresand their D values. D values increase from theboundary regions to the shear bands. Partial over-lap between di¡erent D populations indicates agradual transition from di¡erently evolved cata-clastic fabrics.

3. Volumetric analysis

Volumetric data provide complementary infor-mation for a complete sample description. Thedistribution of cumulative volumes is shown inFig. 6 for a representative set of samples selectedaccording to the criterion of progressive increaseof D values from 1.91 to 3.49. Volumes of equiv-

alent particles were computed for samples nor-malised to a 1 kg standard weight. The volumetricfabric of cataclastic rocks constituting the bound-ary regions and breccia zones is dictated by largerparticles, despite their negligible contribution tothe total particle number. Conversely, in faultgouges the cumulative volume of small particlesincreases and eventually controls the rock fabric.This is illustrated by the progressive ‘clockwiserotation’ of the volumetric curves with increasingD. The shape of the volumetric curves evolvesfrom near linear in sample 3MA1, curvilinearwith an increasing downward convexity (samples12MA2, 8MA3, 4MA1, 8MA2), to upward con-vex in sample RIO3 (Fig. 6). These shape changesare dictated by di¡erent behaviours of equivalentsize classes with increasing D values. In particular,the cumulative volume of larger equivalent par-ticles systematically decreases, whereas it system-atically increases for smaller particles.

4. Particle population progression

Availability of samples from di¡erent structuralpositions within a single fault core allows infer-ring the evolution of particle size distributions

Fig. 5. Cumulative plot of the fractal dimensions D as afunction of their position within the cataclastic fault coresand of fault kinematics.

Fig. 6. Cumulative volume of equivalent particles plottedversus the corresponding equivalent size classes. Sampleshave been selected according to the criterion of progressiveincrease of D values from 1.91 to 3.49.

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during the overall size reduction process fromcoarse-grained boundary zones, to breccia zones,up to the formation of gouge bands. Variations ofnormalised equivalent particle numbers with pro-gressive cataclasis were analysed in sample pairscollected in the same fault cores (Fig. 2). Equiv-alent particle numbers in each size class of thehigher-D sample were divided by the equivalentparticle numbers in the corresponding size classof the lower-D sample. This on the basis of theassumption that D represents an e¡ective param-eter for describing the degree of comminution ofcataclastic rocks and that higher-D cataclasticfabrics evolved from the lower-D ones [21]. Datanormalisation implies the relative dependence ofequivalent particle numbers in the various sizeclasses. As a consequence, any increase of theequivalent particle number in the smaller sizeclasses will induce a slight decrease in the largerones.

In the following, we illustrate particle size pro-gression for sample pairs selected as representa-tive of the whole data set. A sample pair is com-pared for fault core 6MA, which basically consistsof immature cataclastic rocks with a central bandof more comminuted material, represented bysample 6MA2. Analysis of the ratio between cor-responding equivalent particle numbers (Fig. 7a)points out a decrease of the larger equivalent par-ticles, highlighted by a quotient lower than 1, andan increase of all other equivalent particles. Inparticular, the 0.25 mm equivalent size classalmost doubles and the smaller equivalent par-ticles (0.125 mm) are close to triplicate. The pair7MA consists of a sample from the breccia zone(7MA2) and the other from a shear band (7MA1).Equivalent particle ratios (Fig. 7b) show a smallrelative variation of the 4 mm equivalent sizeclass, which decreases by about 15%. All the otherequivalent size classes are characterised by relativeincrements of the corresponding particle numbers,which generally increase with a decrease of theequivalent particle size. Only in the smaller equiv-alent size class is this increment lower than thecorresponding one in the adjacent class. Faultcore 8MA allows inferring the evolution of equiv-alent particle numbers within the breccia zone(samples 8MA1, 8MA3 and 8MA4) and the tran-

sition to fault gouge (sample 8MA2). The pro-gression of the cataclastic fabric in the brecciazone from D=2.4 to DW2.5 occurs through ageneralised increase of equivalent particles apartfrom the larger ones, which remain almost un-changed (Fig. 7c). This increase becomes morepronounced with the decrease of the equivalentparticle size. With increasing D values in the brec-cia zone rocks (samples 8MA3 and 8MA4), butmaintaining the same vD (V0.1), the trend of thecorresponding curve is very similar to the pre-vious one but shifted downward by about 0.5(Fig. 7c). When vD is doubled to about 0.2(8MA4/8MA1) the upward convexity of the cor-responding curve increases due to the preferentialincrease of intermediate and smaller equivalentparticles. This behaviour is much more evidentin the breccia to gouge transition (8MA4 to8MA2), which occurs by a signi¢cant decrementof larger equivalent particles, by a small decre-ment of particles in the 2 mm equivalent sizeclass, and by a large increment in the mediumand small equivalent size classes. The increase ofthe smaller equivalent particle number is almostthree times greater than the decrease of the largerequivalent particle number. The preferential in-crease of the smaller equivalent particles with in-creasing comminution (i.e. D) is con¢rmed by thebehaviour of the weight of material passingthrough the smallest sieve (0.063 mm). Plottingthis weight as a percentage of the total weightagainst the corresponding D value shows an ex-ponentially increasing trend with increasing D(Fig. 8).

Fault core 11MA consists of a sample collectedin the breccia zone (11MA2) and another in ashear band (11MA1). Analysis of the equivalentsize class ratios (Fig. 7d) points out a small dec-rement of the 4 mm equivalent particles, charac-terised by a quotient lower than 1, while all theother equivalent size classes undergo signi¢cantincrements, particularly the two smaller equiva-lent particle size classes. The increment of thesmaller particles, which approaches 400%, ismuch greater than the decrement of the largerparticles. Fault core 13MA is representative ofthe evolution of an immature cataclastic core.Sample 13MA5 was collected in the boundary re-

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gion of the fault core and sample 13MA2 comesfrom the breccia zone. Analysis of the equivalentsize class ratios (Fig. 7e) shows a great incrementcharacterising the small equivalent particles (morethan 300% in the 0.125 mm equivalent size classand about 200% in the 0.25 mm equivalent sizeclass) compared to the almost invariant behaviourof the larger ones. The two intermediate equiva-lent size classes show a comparable increment ofabout 50%. Fault core RIO was selected as rep-resentative of the development of an extremelycomminuted gouge band (RIO3) within the brec-cia zone (RIO2). Di¡ering from all the previouscases, even intermediate particles show nega-tive quotients (Fig. 7f). Particularly, the 4 mm,2 mm and 1 mm classes are characterised by verysmall values, meaning that they underwent a sig-ni¢cant decrement. Only values in the two small-est equivalent particle size classes greatly increase.

5. Discussion

5.1. Fractal dimensions

The main point arising from the particle sizedata is that the fractal dimensions of the studiedcataclastic rocks do not cluster around a speci¢cvalue but are distributed over a wide intervalfrom 1.88 to 3.49. It should be noted that D val-ues greater than 3 are not possible in the absenceof fractal limits, because this would mean thattotal particle volume should be greater than avail-able, i.e. particle interpenetration. It follows thatthe distributions of equivalent particles with Dgreater than 3 should have upper and lower frac-tal limits, above and below which these particlesize distributions are no longer fractal [17,38]. Thelinear ¢ts of our data imply that measured sizeclasses lie within the linear (fractal) segments ofthe bilogarithmic distributions and that the upper

and lower fractal limits are external to the 0.125^4mm size interval.

The occurrence of large variations of D valuesquestions the idea that cataclasis can be conve-niently described by the thoroughgoing persis-tence of a fragmentation mechanism describedby a fractal dimension DW2.6 [13]. Conversely,our data suggest a progressive change of the frag-mentation mechanism with increased intensity ofcomminution. This is indicated by the increase ofD values from immature core boundary rocks, tobreccia zones, up to intensely comminuted gougein shear bands. The evidence that 2.6^2.7 is thehighest fractal dimension in cataclastic rocks frombreccia zones may suggest the idea that it repre-sents a threshold value associated with a particu-larly favourable fragmentation mechanism [13].When cataclastic rocks in breccia zones developa fabric corresponding to this threshold value,their further evolution may continue in a nearsteady-state way [27].

An alternative hypothesis is that the cataclasticfabric associated with fractal dimensions of about2.6^2.7 may enhance slip localisation [39] and theconsequent formation of narrow shear bandswhere most displacement is accommodated. Sliplocalisation, in turn, induces a negative velocitydependence and a lowering of friction in theseshear zones [40], facilitating the persistence oftheir activity. A self-enhancing cataclastic processmay thus be triggered in narrow shear bands oflocalised slip, where intensely comminuted gougedevelops, likely preventing further reworking ofthe cataclastic fabric in the adjacent breccia zones.

Relative comparison among di¡erently evolvedcataclastic rocks in the same fault core shows thatthe development of D values higher than 2.6^2.7occurs, at least in ‘massive’ carbonate rocks, bythe preferential relative increase of smaller par-ticles rather than by the selective decrease of larg-er particles, as proposed for crystalline basement

6

Fig. 7. Ratios between the equivalent particle numbers in corresponding size classes in sample pairs collected from the same faultcores. These graphs show the relative increase or decrease of equivalent particles in each size class during the progression of cata-clasis. See text for a discussion of the e¡ect of data normalisation. (a) Ratio between samples 6MA2 and 6MA3. (b) Ratio be-tween samples 7MA1 and 7MA2. (c) Ratio between samples 8MA3 and 8MA1, 8MA4 and 8MA1, 8MA4 and 8MA3, 8MA2and 8MA4 respectively. (d) Ratio between samples 11MA1 and 11MA2. (e) Ratio between samples 13MA5 and 13MA2. (f) Ra-tio between samples RIO3 and RIO2. C. breccia means coarse-grained breccia, sampled in fault core boundary regions.

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cataclastic rocks [14,27]. The increment of smallerequivalent particles is up to four times greaterthan the decrement of the larger equivalent par-ticles (Figs. 7b^d,f and 8). A preferential increaseof small particles with fault slip has been docu-mented by [29] in large displacement laboratoryexperiments on quartz fault gouge.

The abundance of smaller particles in intenselycomminuted cataclastic rocks cannot be explainedby their preferential fragmentation because thiscontrasts with the notion of particle strength in-crease with decreasing size [41]. More likely, theincrease of small particles in gouge bands is in-duced by slip-enhanced surface abrasion [37] dur-ing the progressive decrease of the average par-ticle size, as pointed out by [26] in laboratoryexperiments, and by [21] in natural fault coresdeveloped in granites. Survivor larger particlesin intensely comminuted gouge are fully sur-rounded by small particles and this decreases theircapability of being fractured [4,13,26,39]. Theproposed evolutionary pathway for cataclasticrock fabrics in carbonate fault cores is schemati-cally illustrated in Fig. 9. Early stages of faultcore formation are dominated by particle frag-mentation while particle abrasion controls the dis-tribution of particle size and shape in fault gouge.

5.2. In£uence on permeability properties

The broad variability of D values and theevidence of a preferential increase of smallerparticles with increasing comminution have im-portant consequences for the space and timeevolution of fault permeability. The three-dimen-sional architecture of poorly evolved (i.e. low-D)cataclastic fabrics is dominated by the packingproperties of larger particles and this favours ahigh porosity and an e⁄cient permeability. Anincrease of D indicates an increased capability(i.e. greater number) of smaller particles to ¢llthe available space between larger particles. Theexponential direct relation between D and theamount of particles in the silt and clay size range(6 0.063 mm) obtained from fault core 8MA(Fig. 8) indicates that even very small voids are¢lled in fault gouges, which thus attain an ex-tremely low permeability. This contributes to ex-plain the hydraulic seal behaviour of gouge bandsin natural fault zones [42,43] and in laboratoryexperiments [29]. The hydraulic seal behaviourof fault gouge developed in massive carbonateplatform rocks can be inferred from some faultcores in the studied ¢eld sites. The boundary re-gions of these fault cores show strong impregna-tion by iron hydroxides, abruptly terminating atmore comminuted breccia zone or gouge band

Fig. 8. Direct relationship between fractal dimensions andpercentage weight of material having size smaller than 0.063mm in the corresponding samples of fault core 8MA. Theweight of the sample fraction with a particle size smallerthan 0.063 mm was obtained by subtracting the residual dryweight after sieving to the total dry weight of the sample.Note that for DW3 the weight of material with a particlesize smaller than 0.063 mm is more than 26% of the sampletotal weight.

Fig. 9. Cartoon showing the proposed evolution of the cata-clastic fabric with increasing displacement. The role of par-ticle fragmentation in the comminution process progressivelydecreases and is replaced by particle abrasion. The incrementof smaller particles produced by surface abrasion is muchgreater than the decrement of the larger particles, caused bytheir fragmentation.

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boundaries, which are characterised by the occur-rence of almost continuous bands of iron hydrox-ides (Fig. 10). The lack of any evidence of hydrox-ide impregnation within the breccia zones or thegouge bands indicates that they acted as barriersto the across-fault migration of £uid phases. Thelack of comminuted feldspars and phyllosilicatesin these fault cores rules out the role of water-induced clay formation [11,43] on fault permeabil-ity properties. Conversely, the extremely low per-meability of fault gouge in carbonate platformrocks is mainly related to the particle size distri-bution and packing.

Development of a fault zone is a four-dimen-sional process where di¡erent evolutionary stagesoccur in di¡erent structural positions. Faulting inlimestone typically evolves from early joint andsolution cleavage arrays (the damage zone), whichare then overprinted by the formation of cataclas-tic rocks during slip localisation and the develop-ment of fault cores [44^46]. The progressive devel-opment of fault cores from damage zones impliesthat di¡erent permeability properties occur in dif-ferent regions of fault zones at di¡erent evolution-ary stages (Fig. 11). In the tip regions, fault zonegrowth is in an immature stage, where only the

damage zone developed. The progression of frac-turing in the damage zone increases permeabilityand connectivity and the whole fault zone behavesas a conduit for £uid £ow. The lateral propaga-tion of the low-permeability fault core dissects theacross and along strike continuity of the conduit,causing its progressive compartmentalisation intosectors with low hydraulic exchanges. In this ma-ture stage, the contrast between high-permeabilitydamage zones and fault core boundary regions,and very low-permeability gouge bands withinbreccia zones imparts a directional anisotropy topermeability in fault zones, which act as conduitsfor £uid £ow parallel to the fault strike and asbarriers for £uid £ow perpendicular to the faultstrike [8,29].

5.3. Role of dissolution

Removal of material by dissolution, either syn-or post-tectonic, is a well-known phenomenon incarbonate rocks [47,48]. The e⁄ciency of dissolu-tion in limestone is maximised at low strain rates,high £uid £ows, high ratios between surface andvolume of particles, and when a certain amountof clay minerals occurs [49^51]. In the studied

Fig. 10. Detail of the abrupt transition from the fault core boundary zone to the breccia zone. The former is strongly impreg-nated by iron hydroxides (dark material on the left side of the photo). Whitish breccias are not impregnated attesting to theirlower permeability. Note the dark stream of hydroxides at the boundary between the two sectors.

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fault zones, pressure solution cleavage arrays arewell developed in damage zones [46], despite thevery poor content of clayish material in the pro-tolith rocks. This suggests low strain rates ande⁄cient £uid circulation in the very early stagesof faulting. Conversely, the preservation of the¢nest fraction in the sampled cataclastic rocks in-dicates a negligible role of dissolution during faultactivity because smaller particles have the highestsurface^volume ratio and thus should have beeneasily dissolved. Possible reasons for their preser-vation include high strain rates and/or ine⁄cient

£uid circulation. The latter is in agreement withthe sub-aerial environmental conditions of defor-mation in the study faults, many of which arecurrently active [52,53].

Post-faulting £uid £ow within the studied faultcores might have altered their original particle sizedistributions. The capability of meteoric water todissolve carbonate fault rocks depends on D val-ues. The increase of D from fault core boundariesto intensely comminuted gouge in shear bandsimplies a corresponding decrease of permeabilityand, consequently, of possible dissolution-relatedbias. The higher permeability of cataclastic rocksin the fault core boundary regions may have fa-voured the partial removal by dissolution of partof the smaller particles, producing a further de-crease of D. Conversely, the lower permeability ofcataclastic rocks in breccia zones may have inhib-ited a signi¢cant alteration of D values by disso-lution. The same reasoning applies to fault gouge,whose very low permeability likely prevents anyin£uence of dissolution, despite the extremely ¢neparticle size.

6. Conclusions

We analysed particle size distributions in car-bonate cataclastic rocks from fault cores in theApennines, Italy. Particle sizes are power-law-dis-tributed over the analysed size range and theirfractal dimensions increase from the boundaryzones of fault cores, to the breccia zones consti-tuting the bulk of fault cores, up to intensely com-minuted gouge in shear bands within brecciazones. Such a large variability of the fractal di-mensions and its relationships with the structuralarchitecture of fault cores indicate that the idea ofa persistent fragmentation mechanism for describ-ing the entire evolution of natural cataclastic faultcores in carbonate rocks is inadequate. We pro-pose that the evolution of the cataclastic processin the studied fault cores involved: (i) a progres-sive change of the dominant fragmentation mech-anism with increasing displacement; (ii) a relationbetween particle size distributions and fault slip;(iii) an increased contribution of surface abrasionwith increasing displacement; (iv) the variation of

Fig. 11. Cartoon showing the permeability structure of anideal fault zone in carbonate platform fault rocks. The tipline of the fault is imaged to propagate upward and fromleft to right. The two qualitative graphs schematically showthe transition from a conduit to a barrier behaviour of thefault zone passing from an early (only damage zone) to amature structural architecture. Arrows show the expectedpathway of £uid phases within the fault zone. Not to scale.

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particle strength with size and shape. The non-self-similar evolution of cataclasis has importantimplications for the four-dimensional evolution ofthe permeability structure in carbonate fault coresand for their frictional behaviour.

Acknowledgements

This paper strongly bene¢ted of critical readingand suggestions from EPSL reviewers M. Anto-nellini and T. Blenkinsop. This work has beenfunded by MURST grants awarded to F. Salvini,and by Enterprise Oil Italiana S.p.A. We aregrateful to R. Gambini (formerly at EnterpriseOil Italiana S.p.A.) for encouraging our workand to P. Impagliazzo, S. Merlo and M. Musac-chio for their help during ¢eld and laboratorywork. A. Taddeucci and P. Tuccimei providedthe chemical analyses of the protolith rocks.[RV]

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