Micromechanics of inelastic compaction in two allochemical limestones

Journal of Structural Geology 43 (2012) 100e117

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Micromechanics of inelastic compaction in two allochemical limestones Veronika Vajdova a,1, Patrick Baud b, *, Lily Wu a, 2, Teng-fong Wong a a b

Department of Geosciences, State University of New York at Stony Brook, NY 11794-2100, USA Institut de Physique du Globe de Strasbourg, UMR 7516 CNRS, Université de Strasbourg/EOST, Strasbourg, France

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 May 2011 Received in revised form 17 July 2012 Accepted 20 July 2012 Available online 13 August 2012

To investigate inelastic compaction in limestone we deformed in conventional triaxial configuration samples of two allochemical limestones: Indiana and Majella limestone with porosity of 14e16% and 30%, respectively. We described the microstructures associated with the damage evolution. Inelastic compaction in both limestones was associated with pore collapse that seemed to initiate from stress concentrations at the surface of a pore. Cataclasis appeared to develop preferentially around the macropores, in agreement with a recent study on a micritic limestone. Our new observations however showed that the spatial distribution of damage in the allochemical limestones can be complicated by its uneven partitioning among the allochems, micrite and sparite. In Indiana limestone, many allochems remain relatively intact even after the cement has undergone significant microcracking, with the implication that significant strength contrast exists between the allochems and cement. In Majella limestone, the asymmetry in damage intensity is not as pronounced, suggesting a less pronounced mechanical contrast between allochems and cement. In both limestones, significant mechanical twinning was observed in samples deformed to relatively high level of strain. We applied to our data a model, that treats a limestone as a dual porosity medium, with the total porosity partitioned between macroporosity and microporosity. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: Micromechanics Porous carbonates Pore collapse Cataclasis Microstructure Experimental

1. Introduction One of the major challenges in carbonate sedimentology is to identify and understand the diagenetic processes by which lime sediments evolve to become limestones, and how they would influence the porosity during burial (Bathurst, 1971; Bjørlykke, 2010). For several decades a widely accepted idea had been that carbonates experience minimal burial compaction, and “distortion by physical squeezing which causes porosity reduction . is a relatively unimportant process in most carbonate rocks” (Wanlass, 1979), with the implication that porosity reduction necessarily requires the massive influx of cement from outside. A field observation that apparently support this idea is the lack of petrographic evidence for mechanical compaction, such as breakage of fossils. However, laboratory studies have since then demonstrated that significant compaction can occur in carbonate sediments with many of the embedded fossils remaining relatively

* Corresponding author. Fax: þ33 368850126. E-mail address: [email protected] (P. Baud). 1 Present address: Talbridge Corporation, P.O. Box 271054, Houston, TX 772771054, USA. 2 Present address: H2M, Melville, NY 11747, USA. 0191-8141/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jsg.2012.07.006

intact, which implies that instead of crushed fossils, more subtle textural indicators should be used to assess the extent of mechanical compaction (Shinn et al., 1977; Bhattacharyya and Friedman, 1979). Guided by such laboratory observations, more systematic studies have subsequently recognized and documented the extent of mechanical compaction in carbonates, especially at shallow burial depths (Meyers, 1980; Shinn and Robbin, 1983; Meyers and Hill, 1983; Choquette and James, 1986). Porosity reduction derives from not only mechanical compaction, but also chemical compaction (involving such processes as pressure solution and subcritical crack growth), which is expected to progressively dominate at greater depths associated with elevated temperature and slower compaction rate (Choquette and James, 1986; Bjørlykke, 2010). There are at least two fundamental questions regarding carbonate compaction that remain unanswered: How much do carbonates compact in comparison to siliciclastics, and what is the interplay between mechanical and chemical compaction during burial diagenesis and at what depths are they operative? Ehrenberg and Nadeau (2005) presented a global compilation of porosityedepth profiles measured in more than 40,000 carbonate and sandstone reservoirs. Observing that the overall trend is for carbonate reservoirs at a given depth to have lower porosities than

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their siliciclastic counterparts, they attributed the difference to the greater chemical reactivity of carbonate relative to siliciclastic rocks, and as a result higher susceptibility to chemical compaction and associated cementation. While this is supported by limited experimental studies on chemical compaction, more systematic investigations in the laboratory under controlled conditions are required before one can constrain better the kinetics of pressure solution and subcritical crack growth, specifically their dependence on stress, temperature and time (Croizé et al., submitted for publication). To constrain its interplay with mechanical compaction, it is also important to characterize the constitutive behavior and damage evolution related to inelastic deformation. Unlike siliciclastic rocks, limited systematic studies of mechanical compaction in porous carbonate rocks have been conducted. Field studies of tectonic deformation in carbonate formations have also documented complex interplay of chemical and mechanical compaction processes. In Majella limestone Tondi et al. (2006) concluded that strain localization in deformation bands was associated with pressure solution complemented by cataclasis, whereas Rath et al. (2011) observed primarily cataclastic mechanisms in deformation bands in Leitha limestone. Carbonate compaction is of importance in many geotechnical applications. Carbonate rocks also hold more than 60% of world’s oil reserves (Schlumberger Market Analysis 2007; http://www.slb. com/services/industry_challenges/carbonates.aspx). Extraction of fluid from a sedimentary rock reservoir reduces the pore pressure and thus increases the effective stress, which can impact the stress field and hydromechanical properties, possibly leading to inelastic deformation and failure manifested by phenomena such as surface subsidence, well failure and induced seismicity (Boutéca et al., 1996; Segall, 1989; Fredrich et al., 2000; Wong et al., 2004). In another application, carbonate formations have been proposed as reservoirs or cap rocks for the geological sequestration of carbonate dioxide as a measure to reduce emission of greenhouse gases (IPCC, 2005; IEA, 2008). A number of technical challenges related to the injectability of supercritical CO2 and integrity of the geologic repository can only be tackled through systematic investigation of the mechanics of dilatant and compactant failure and the influence on permeability evolution (Bemer and Lombard, 2010). Laboratory studies have demonstrated that phenomenologically the compaction behavior in a carbonate rock (Vajdova et al., 2004; Bemer et al., 2004; Baud et al., 2009) is similar to a siliciclastic rock (Wong et al., 1997; Baud et al., 2006). Under hydrostatic loading, compaction is primarily elastic up to a critical pressure, beyond which porosity decreases irreversibly with increasing pressure. Under nonhydrostatic loading, initiation of inelastic compaction would develop at a mean stress that is lower than the critical pressure under hydrostatic loading. At the initiation of inelastic compaction, the mean stress value typically decreases with increasing differential stress, and in terms of the first and second stress invariants these yield points map out a compactant yield “cap” in the stress space (Wong et al., 2004). In spite of these similarities in the phenomenology of compaction, the micromechanical behavior has been observed to be very different in siliciclastic and carbonate rocks. In a siliciclastic rock such as sandstone, inelastic compaction derives primarily from grain crushing initiated by the stress concentrations at grain contacts (e.g., Menéndez et al., 1996). While the micromechanics of compaction and cataclastic flow in a porous siliciclastic rock such as sandstone have been studied extensively (Menéndez et al., 1996; Bésuelle et al., 2000; Wu et al., 2000; DiGiovanni et al., 2000; El Bied et al., 2002; Mair et al., 2002; Baud et al., 2004; Fortin et al., 2006), not much is known about the micromechanical processes related to compaction in a porous carbonate.

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Recent microstructural observations of Vajdova et al. (2010) on the micritic Tavel limestone have shown that the collapse process typically initiates from cataclastic failure in the vicinity of the larger pores, while the conventional micromechanical model (Gurson, 1977; Curran and Carroll, 1979) would predict that theoretically it is equally likely for collapse to initiate from a large or a small pore. The microstructure in compacted samples also shows that cataclasis rather than crystal plasticity seems to be the dominant damage mechanisms in the proximity of a pore that has collapsed. A concentric ring of intense microcracking surrounds the pore and spalled fragments may fill the void. Zhu et al. (2010) have formulated a “cataclastic pore collapse” model that captures these microstructural observations. Solnhofen and Tavel limestones are two carbonate rocks for which the brittleeductile transition and micromechanics of failure have been extensively investigated (Heard, 1960; Rutter, 1974; Fredrich et al., 1990; Baud et al., 2000a; Bemer et al., 2004; Vajdova et al., 2004; Schubnel et al., 2005). Both are micritic limestones with a pore space made up predominately of equant pores and some microcracks that are embedded in a relatively homogeneous micritic matrix. In this investigation we conducted a study on Indiana and Majella limestones, two allochemical limestones with significantly higher porosities and relatively heterogeneous solid constituents (allochems, micrite and sparite) that may show significant contrast in strength and mechanical response. The primary objective of this study is to characterize the damage evolution in deformed and failed samples of these two allochemical limestones, so as to gain insights into the micromechanics of compaction and dilatancy, especially on the partitioning of cataclasis and twinning among the various solid constituents and the extent to which a cataclastic pore collapse model can capture the failure processes. Suites of triaxially compressed samples in dry conditions were acquired at confining pressures 5 and 20 MPa for Indiana and 25 MPa for Majella limestone. For reference we also obtained hydrostatically compacted samples of both limestones. Microstructural observations were performed using the optical and scanning electron microscope. Indiana limestone has already been subjected to numerous rock deformation studies. In particular, brittle faulting and its micromechanics have been investigated by Robinson (1959), Wawersik and Fairhurst (1970), Zheng et al. (1989), and Myer et al. (1992). Brittleeductile transition and compactive yield behavior in Indiana limestone were studied recently by Vajdova et al. (2004). In contrast, there is a paucity of rock physics data on Majella limestone. We are aware of only two previous investigations on the pore structure (Anselmetti et al., 1998) and mechanical compaction (Baud et al., 2009), respectively. 2. Indiana and Majella limestones In a widely used classification system on the basis of composition, Folk (1959) categorized the constituents of a limestone into three principal types: micrite or microcrystalline carbonate (with grain diameter of 4 mm or less), sparite (crystalline carbonate cement made up of crystals >10 mm in diameter), and allochems (any kind of grains that had been transported locally within the environment of origin, including peloids, ooids, bioclasts and intraclasts). Based on the relative proportions of these three endmembers, a limestone can then be classified (Folk, 1959, 1980; Tucker and Wright, 1991) as a microcrystalline limestone (that consists almost entirely of micrite with little or no allochem material and sparry calcite) or an allochemical limestone (with a considerable proportion of allochems embedded in a matrix of micrite and/or sparite). The allochemical family can be further subdivided into microcrystalline allochemical limestone (with

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Table 1 Petrographic description of the rocks used in this study. Rock name

Porosity [%]

Grain size [mm]

Composition

Structure

Origin

Majella grainstone

30

50e400

99% calcite

Central Apennines (Italy)

Indiana limestone

17.9

5e300

97.1% calcite, 1.2% magnesite, 0.8% silica, 0.7% alumina, 0.1% iron oxides

Allochemical: 50% allochems (rudist shells) Allochemical: 65% allochems (fossils, ooids and peloids)a

a

BedfordeBloomington area (Indiana, USA)

Data from ILI (2007).

a mostly micrite matrix) and sparry allochemical limestone (that consists of allochems cemented by sparry calcite). Indiana limestone used in this study is a gray, fossiliferous limestone that is quarried in the BedfordeBloomington area in Indiana. It was formed during Mississippian period and belongs to the Salem Limestone formation (Patton and Carr, 1982). The petrophysical properties are compiled in Table 1. Its average modal composition is: calcite 97.1%, magnesite 1.2%, silica 0.8%, alumina 0.7%, iron oxide 0.1%, and undetermined material 0.1% (Indiana Limestone Handbook, ILI, 2007). The allochems (that include fossils, ooids and some peloids) constitute w65% of the bulk rock volume. They are elongated in shape and tend to align sub-parallel to the sedimentary bedding. In Folk’s (1959) classification, Indiana limestone is an allochemical limestone that would be called a biomicrite and biosparite. According to the petrographical studies of Smith (1966) and Patton and Carr (1982), the chief allochemical constituent is bryozoan with long dimension in the range of 0.2e 1.0 mm, and next in abundance is echinoderm with long dimension in the range of 0.1e2.2 mm. Other than these two bioclasts, Endothyra baileyi, a foraminifer with several whorls of bulbous chambers and with long dimension in the range of 0.6e1.0 mm, is easy to find and identify in Indiana limestone. Many of the ooids contain fossils and fossil fragments which are coated with concentric layers of calcite, that generally do not constitute more than 20% of the radius of the ooids. Our observations of intact Indiana limestone (sample I0-TS, Table 2) show that rims of the allochems in this rock are commonly coated with microcrystalline cement, leaving relatively large open pores at the interstices. Some of the pores are partially filled with sparry cement in the form of blocky calcite crystals. Due to the material heterogeneity associated with three very different solid constituents (allochems, micrite, sparite), the grain sizes in our Indiana limestone samples range from <5 mm for the pore-lining micritic material to >300 mm for the allochems. Besides the macroscopic pores, voids also occur as micropores within the microcrystalline material of allochems and pore-lining cement. Indiana limestone has weak grain boundaries caused in some cases by weak cementation but in majority cases by very porous grain boundary. The porosity of Indiana limestone is

quite variable (ILI, 2007), and a range between 12% and 20% have been reported in the literature. Our Majella limestone samples are from the Madonna delle Mazze quarry in the Apennines, Central Italy. The quarry is situated on the inner part of the forelimb of the Majella Anticline, where fault development has recently been investigated in some detail by Tondi et al. (2006) and Agosta et al. (2009) in relation to the roles of deformation bands and stylolites. Porosity development and diagenesis in the Majella platform have been investigated comprehensively by Mutti (1995). The limestone belongs to the Orfento formation, that derived almost entirely from the breakdown of rudist shells to fragments (ranging in size from silt to gravel) interbedded with megabreccias. The sedimentological characteristics indicate that deposition in Orfento formation occurred in a high energy environment, where the rudist fragments were repeatedly reworked and redeposited, and accordingly the marine cementation was poorly developed. Rudist types include Radiolites and Hippurites. Our block of Majella limestone with composition of >99% calcite is identical to that used by Baud et al. (2009). The block was acquired from the relatively undeformed host rock in the quarry. Allochems in Majella limestone make up about half of the bulk rock volume, and they are primarily in the form of rudist fragments which are somewhat smaller than the fossils and ooids in Indiana limestone. The size distribution of allochems in Majella limestone is also broad, with diameters in the range of 50e400 mm (Table 1). The rest of the solid volume is occupied by a matrix that is made up of bladed sparry calcite cements and microspherules of silica cement. However, since cementation in Majella limestone was not as well developed during and after deposition in a high energy marine environment, it has relatively high porosities in the range of 15e30% (Mutti, 1995; Tondi et al., 2006). We calculated the total porosity from the density of a vacuum dried sample, assuming a solid composition of 100% calcite with density of 2710 kg/m3. For Indiana limestone material from two blocks was used. Samples for the triaxial compression experiments were cored from one block, with porosities ranging from 17.3% to 18.4% (Table 2) and an average value of 17.9%. In addition, we used

Table 2 Deformation history of samples studied. Sample

Confining pressure [MPa]

Initial porosity [%]

I0-TS IH IB1 IB2 IC1 IC2 IC3 IC4 M0-TS MH MC1 MC2 MC3

0 175 5 5 20 20 20 20 0 45 25 25 25

16.5 13.4 17.6 17.3 17.9 31 32.3 32.3 32 31.3

Axial strain [%] 0 0 1.2 0.5 1.5 2.5 10 0 0 6 18 28

Analysis Thin section/2400 Thin section/2400 Thin section Thin section Thin section/2400 Thin section/2400 Thin section/2400 Thin section/2400 Thin section/2400 Thin section/2400 Thin section/2400 Thin section/2400 Thin section/2400

Comments dpi scan dpi scan

dpi dpi dpi dpi dpi dpi dpi dpi dpi

scan scan scan scan scan scan scan scan scan

Intact sample Hydrostat (P* ¼ 60 MPa) Brittle: near peak Brittle: post peak Cataclastic flow: beyond C* Cataclastic flow: near C*0 Cataclastic flow: beyond C*0 Cataclastic flow: beyond C*0 Intact sample Hydrostat (P* ¼ 45 MPa) Cataclastic flow: beyond C* Cataclastic flow: beyond C* Cataclastic flow: near C*0

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one sample with porosity 14.6% cored from another block and deformed in hydrostatic compression by Vajdova et al. (2004). The intact sample comes from the block used by Vajdova et al. (2004) as well. A saturation test with distilled water indicates that interconnected porosity forms about 3/4 of the total porosity. For Majella limestone, the average total porosity (inferred from density of vacuum dried sample) is 31.7%, which is almost identical to the interconnected porosity values of 31% and 30% determined by pycnometer and water saturation techniques, respectively (Baud et al., 2009). 3. Experimental procedure 3.1. Sample preparation Cylindrical samples of the Indiana and Majella limestones were cored perpendicular and parallel to the sedimentary bedding, respectively. Indiana limestone cores have been ground to diameter of 18.4 mm and length of 38.1 mm. After it had been dried in vacuum at 80  C for 48 h, each sample was first jacketed in a thin copper foil (of thickness 0.05 mm), and then polyolefine (heatshrinkable) tubings were used to separate the rock from the confining medium (kerosene). Electric resistance strain gages (TML type PFL10-11) were attached in orthogonal directions to the copper jacket to measure axial and transverse strains. The strain gages were easily broken due to pore collapse near the sample surface. To avoid this problem, we first pressurized the samples to 5 MPa, filled the pores near the surface with an epoxy (BLH SR-4 EPY-150) and then smoothed the surface by sanding it after the epoxy had cured. The sample was then jacketed with copper foil and strain gages were then attached. Majella limestone cores have been ground to diameter of 20 mm and length of 40 mm and the procedure for drying and jacketing have been the same as for Indiana limestone. No strain gages were used with Majella limestone. 3.2. Triaxial experiments The jacketed samples of Indiana limestone were deformed in the conventional triaxial configuration at room temperature at the laboratory at Stony Brook University, USA, using the same procedure as Vajdova et al. (2004). The triaxial compression experiments were performed at confining pressures of 5 and 20 MPa and will be denoted as IB and IC series for brittle deformation and cataclastic flow, respectively. The confining pressure was measured with accuracy of 0.1 MPa, and during triaxial loading it was held constant to within 1%. The axial load was measured with an external load cell with an accuracy of 1 kN. To calculate the axial stress from the recorded axial load, the effect of bulging in a deformed sample was accounted for by evaluating the relative increase in cross-sectional area from the transverse strain. The displacement was measured outside the pressure vessel with a displacement transducer (DCDT) mounted between the moving piston and the fixed upper platen. With the knowledge of the stiffness of the loading frame (2.38  108 N/m) the axial displacement of the sample was obtained by subtracting the displacement of the loading frame from the apparent displacement recorded by the DCDT. The axial displacement was servo-controlled at a fixed rate (corresponding to a nominal strain rate of 1.3  105 s1). The load, displacement, and strain gage signals were acquired by a 14-bit A/D converter at a sampling rate of 0.5 s1 with resolutions of 0.3 MPa, 1 mm and 105, respectively. Uncertainty in strain was estimated to be 2  104 (when calculated from the DCDT signal) and 105 (when measured directly by the strain gages). The volumetric strain was calculated using the relation εv ¼ εj:j: þ 2εt , where εj:j: and εt are

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the axial and transverse strains, respectively. This formula neglects second-order contributions of strains to the volume change that may be appreciable at relatively large strain. While the transverse strains were generally small, the axial strains in some experiments exceeded 3%, and it is difficult to assess to what extent such strain gage data beyond 3% or so are reliable. For these cases we prefer to use the axial strain values as inferred from the DCDT data. Acoustic emission (AE) activity was monitored via a piezoelectric transducer (PZT-7, 5 mm diameter, 1 MHz longitudinal resonant frequency) positioned on the flat surface of one of the end-plugs. However, it is typical of limestone deformation experiments that very little AE activity can be resolved, and accordingly the AE data were not of use in this study. Jacketed samples of Majella limestone were deformed in conventional triaxial configuration at room temperature at Ecole et Observatoire des Sciences de la Terre (EOST) in Strasbourg, France, using the same procedure as Klein and Reuschlé (2004). The triaxial compression experiments were performed at confining pressures of 25 MPa. In these experiments (MC series in the following text), a computer-controlled stepping motor connected to a pressure transducer regulated the confining pressure and held it constant within 0.03 MPa. The axial load was applied by a piston controlled by a second computer-controlled stepping motor. Axial displacement was measured outside the pressure vessel with a capacitive transducer with accuracy 0.2 mm mounted on the moving piston and servo-controlled at a fixed rate (corresponding to a nominal strain rate of 105/s). Axial strain of a sample was calculated from the axial displacement data and initial sample length while considering stiffness of the loading frame. Volumetric strain was inferred from the displacement of the piston of the confining pressure generator measured with an angular encoder. The samples were stressed to different stages of deformation and then unloaded. Upon retrieval from the apparatus, they were encapsulated with epoxy and thin-sections were then cut along the central vertical plane of each sample. For each limestone, thinsections of a hydrostatically compacted sample and an intact sample were also prepared for reference. The samples and their deformation histories are summarized in Table 2. 3.3. Microstructural analysis Microstructure of the intact and deformed samples was studied under optical microscope and scanning electron microscope (SEM) on thin-sections. Optical microscopy was performed using a Nikon polarizing microscope. For SEM observations, the gold-coated thinsections were studied using a LEO 1550 microscope with a voltage up to 10 kV. All SEM micrographs presented here were acquired in the backscattered electron mode. To study the material heterogeneity and its influence on deformation in Indiana limestone, four microstructural components (micrite cement, sparry cement, allochems and pores) were distinguished and their geometric attributes characterized quantitatively by image analysis. The image analysis used a mosaic of 48 micrographs (4  12 micrographs, 640  480 pixels each) taken in the center of each thin-section with a black&white Hitachi CCD camera mounted on the polarizing microscope. The investigated area formed approximately a rectangle (3  7 mm2), with the longer side stretched across bedding to allow for averaging features that vary with sedimentary history. For sample IB2 where shear zone cut near the center of the thin-section the mosaic has been shifted slightly to one end of the sample to avoid the shear zone and its immediate vicinity. Boundaries between the four microstructural components were mapped manually after automated detection techniques (e.g. Heilbronner, 2000) were found ineffective for the complex grain structure of Indiana limestone. The boundary

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maps were analyzed with the public domain image processing software Scion Image (http://www.scioncorp.com/pages/scion_ image_windows.htm) to quantify the areal fraction, equivalent diameter, aspect ratio and preferred orientation of the four microstructural components. Equivalent diameter of a grain was evaluated as a diameter of a circle with area equal to that of the grain. Aspect ratio and orientation of a grain were evaluated from the best fitting ellipse. Due to the limitations of the manual mapping, camera resolution and time constraint, only objects with diameter larger than 10 mm or so were analyzed. Objects smaller than that were considered a part of microcrystalline matrix. We also used an Epson PerfectionÔ V700 photo scanner to characterize the pore size statistics of the two intact limestone samples I0-TS and M0-TS. The thin sections were scanned at a resolution of 1800 dpi or higher. Our experience is that the scanner can resolve the macroporosity as effectively as an optical microscope, with the advantage that it can cover the whole area of the thin section, thus circumventing the need to assemble a mosaic of numerous optical micrographs. The macropores were identified using a brightness thresholding approach (Russ, 1990), and the binarized image was then analyzed using ImageJ, a public domain image processing program developed at the National Institutes of Health. The area of each individual pore was determined and the equivalent diameter was evaluated. 4. Mechanical data The convention is adopted that compressive stresses and compactive strains (i.e. shortening and porosity decrease) are positive. The maximum and minimum principal stresses will be denoted by s1 and s3, respectively. We summarize in Fig. 1a and b the mechanical data in terms of the differential stress s1  s3 as a function of axial strain for Indiana and Majella limestones, respectively. When deformed at confining pressure of 5 MPa, the Indiana limestone samples failed by brittle faulting. Sample IB2 attained a peak stress and then underwent strain softening accompanied by a gradual stress drop (Fig. 1a). A shear zone developed at an angle of 30 to s1. Sample IB1 was deformed to just past the peak stress, and no strain localization was observed. At confining pressure of 20 MPa, Indiana limestone failed by cataclastic flow. The differential stress increased monotonically. The exception is sample IC4 that underwent two stress drops of several MPa at axial strain w4.5% and w7.5% (Fig. 1a). These stress drops were probably related to small-scale strain localization features that were observed under the microscope and will be discussed later. At a confining pressure of 25 MPa, Majella limestone also failed by cataclastic flow. The differential stress increased monotonically and significant strain hardening was observed in all three samples deformed (Fig. 1b). To illustrate the development of inelastic volume change in Indiana limestone, we show in Fig. 2a data for the mean stress (s1 þ 2s3)/3 as a function of volumetric strain for the IB and ICseries. For reference the data of Vajdova et al. (2004) for hydrostatic compression of Indiana limestone (sample IH) is shown as the dashed curve, with the critical pressure for the onset of inelastic compaction marked by P* at w60 MPa. As noted by Vajdova et al. (2004), in the cataclastic flow regime the volumetric strain evolves over three distinct stages with the progressive increase of differential stress (and mean stress). In the first stage, the triaxial compression curves more or less coincided with the hydrostat up to a critical stress state indicated by C*. In the second stage at stress levels beyond C*, there was an accelerated decrease in volume in comparison to the hydrostat, which implies that the deviatoric stress field provided significant inelastic contribution to the compactive strain. This phenomenon of “shear-enhanced compaction”

Fig. 1. Principal stress difference s1  s3 versus axial strain for the triaxially compressed samples of (a) Indiana limestone of the IB and IC series deformed at 5 and 20 MPa of confining pressure, respectively and (b) Majella limestone of the MC-series deformed at 25 MPa of confining pressure.

persisted until the volumetric strain switched from compaction to a third stage: dilation. This transition from compactive to dilatant cataclastic flow occurred at the critical stress state indicated by C*0 . Fig. 2a shows that the sample IC1 was loaded somewhat beyond the onset of shear-enhanced compaction C*, the sample IC2 was loaded to well beyond C* and the sample IC3 to beyond the transition C*0 . Sample IC4 was loaded significantly past the transition C*0 . At confining pressure 5 MPa, inelastic sample deformation is associated with dilatancy, even before the peak stress has been attained. The stress at the onset of dilatancy is marked by C0 in Fig. 2a. Both samples IB1 and IB2 were unloaded after significant dilatancy had developed before (IB1) and after (IB2) the formation of a shear zone. The stress drop associated with the shear zone formation is

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loading, the critical pressure P* for the onset of pore collapse was 37 MPa (Baud et al., 2009), significantly lower than that for the less porous Indiana limestone (Fig. 2a). As demonstrated by Vajdova et al. (2004), this critical pressure generally decreases with increasing porosity. Our hydrostatically compacted sample MH was subjected to a maximum pressure of 45 MPa. The onset of shear-enhanced compaction occurs at critical stress states that map out a yield cap in the stress space (differential versus mean stress). We have compiled in Fig. 3 the compactive yield stress (C* and P*) data of Indiana and Majella limestones reported by Vajdova et al. (2004) and Baud et al. (2009), respectively. We also include data for the critical stresses (C*0 ) at the transition from compactive to dilatant cataclastic flow for Indiana limestone from Vajdova et al. (2004) and for Majella limestone (this study). For reference we show the loading paths and maximum stresses attained by the samples for microstructural investigation in this study. 5. Microstructural observations In terms of rock fabric, both Indiana and Majella limestones can be classified according to Dunham’s (1962) classification as calcitecemented grainstones: grain supported structure with no mud and original component not bound together during deposition. Fig. 4a illustrates the microstructure of intact Indiana limestone (I0-TS) observed under an optical microscope. The allochems are commonly coated with micrite cement around their rims, and the interparticle porosity is made up of relatively large pores (areas with lightest color). Some of these pores are partially filled with sparry cement. For comparison we also show in Fig. 4b an image scanned at 2400 dpi of a larger area of the thin section. The image highlights the diversity of allochems (including ooids and different

Fig. 2. Mean stress (s1 þ 2s3)/3 versus volumetric strain for (a) samples of Indiana limestone of the IB and IC series triaxially deformed at 5 and 20 MPa of confining pressure, respectively. The mechanical data for the sample IH deformed hydrostatically are presented for reference (dashed curve) (b) samples of Majella limestone of the MCseries deformed at 25 MPa of confining pressure. Critical pressure for pore collapse is marked by P*. C0 indicates the onset of dilatancy in experiments at confining pressure 5 MPa, C* and C*0 indicate the onset of shear-enhanced compaction and the transition from compactive to dilatant cataclastic flow. Mechanical data for hydrostatic compaction of Majella limestone from Baud et al. (2009) are presented for reference.

indicated by an arrow in Fig. 2a as no volumetric data are available past the brittle failure due to some damage on the strain gages. The development of inelastic volume change in Majella limestone is qualitatively similar to Indiana limestone (Baud et al., 2009). We show in Fig. 2b data for the mean stress as a function of volumetric strain for the MC-series. While the sample MC1 was unloaded just beyond the onset of shear-enhanced compaction C*, the sample MC2 was loaded to well beyond C* and the sample MC3 to near the transition C*0 . For Majella limestone under hydrostatic

Fig. 3. Failure envelopes shown in the stress space (P, Q) for Indiana limestone (circles) after Vajdova et al. (2004) and Majella limestone (squares) after Baud et al. (2009). The open symbols represent the onset of shear-enhanced compaction C* (compactive yield cap). Symbols with a cross inside and a dark background represent the peak stresses for brittle deformation of Majella and Indiana limestones, respectively. The critical stress (C*0 ) data of samples IC3 and MC3 are indicated as dark symbols. The stress path for the triaxial experiments performed on Indiana (20 MPa confining pressure) and Majella limestone (25 MPa confining pressure) are also indicated as dashed lines.

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Fig. 4. (a) Optical micrograph of an intact sample of Indiana limestone sample in polarized light (sample I0-TS). Pore, allochem, micrite and sparry cement are marked in the image. (b) Scanned image of intact Indiana limestone sample at a resolution of 2400 dpi.

fossil types) and their geometric attributes. In addition to macroporosity, micropores occur especially within allochems, and can be resolved under the SEM as illustrated by some of the micrographs presented in Section 5.1. High microporosity is concentrated along boundaries of allochems forming a weak zone favorable for microcrack propagation. This strength contrast seems to significantly affect the deformation in Indiana limestone. Under the SEM, the larger macropores (dark areas) in Majella limestone (sample M0-TS) were observed to have dimensions comparable to the allochems (Fig. 5a), whereas numerous mm-sized micropores are embedded in the allochems and cemented regions (Fig. 5b). Fig. 5c highlights numerous micropores that can be found in the periphery of a macropore. For comparison we show in Fig. 5d the spatial partitioning of allochems, matrix and porosity in a Majella limestone sample that was mapped manually by Tondi et al. (2006) under an optical microscope. The gray areas correspond to the matrix, that is made up of bladed sparry calcite cements and microspherules of silica cement (Mutti, 1995). The allochems (light areas) are primarily in the form of rudist fragments that are quite angular and poorly sorted. We used a ternary diagram (Fig. 6) to characterize the partitioning of allochem, matrix and total porosity. For Indiana

limestone, we characterized under the optical microscope areal fraction of allochems in selected regions of six thin sections (I0-TS, IB1, IB2, IC1, IC2 and IC3). From geometric probability theory, it can be demonstrated that the areal fraction can be used to estimate the volumetric fraction if the sample is isotropic (Underwood, 1970). Since the allochems remain relatively intact even in the highly deformed samples, allochem fractions in the deformed samples are expected to be basically the same as those in the samples before they were stressed. We calculated the total porosity from density of the dry sample, and the matrix fraction as the remainder of the bulk volume after the allochem fraction and porosity have been deducted. Our Indiana limestone data show that even though the total porosity fell in a narrow range of 16.5e18.4%, the allochem fraction varies appreciably among the samples, ranging from 57% to 70%. It should be noted that this analysis assumes implicitly that the allochem, matrix and total porosity are three mutually exclusive features. However, the total porosity actually includes micropores, many of which can be located inside the allochems and cements. Partly due to this complication, our microstructural measurements gave apparent cement fraction values in the range of 25e37%, which are appreciably higher than the values of 11.6e26.5% we obtained by subtracting the total porosity and allochem fraction.

Fig. 5. Backscattered SEM images of an intact sample of Majella limestone (sample M0-TS). (a) Clusters of allochems and cement (light) separated by macropores (dark). The larger macropores (dark areas) have dimensions comparable to the allochems. (b) Micropores embedded in the allochems and cemented regions. (c) Numerous micropores in the periphery of a macropore. (d) Map performed manually under optical microscope (Tondi et al., 2006) showing the partitioning of allochems (rudists), matrix (mostly cement) and porosity in a Majella limestone.

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Fig. 6. Percentage of pores, allochem and matrix cement in Indiana (open circles) and Majella (close squares) limestones. The data for Majella are from Tondi et al. (2006).

Using maps such as Fig. 6, Tondi et al. (2006) characterized the allochem and matrix fractions and total porosity in five Majella limestones samples obtained from the host rock in Madonna della Mazza quarry. Their samples have porosities ranging from 15.3% to 28.5% and allochem fractions from 47.0% to 60.3% (Fig. 6). It should be noted that our Majella limestone block is comparable to the more porous samples of the suite analyzed by Tondi et al. (2006). 5.1. Damage evolution in Indiana limestone Our SEM observations underscore the different mechanisms, by which cataclasis contributes to dilatant failure and inelastic compaction. Microcracking seems to be the dominant mechanism of dilatant failure in brittle faulting in Indiana limestone, although twinning was also observed with increasing density as the deformation progressed. In the Indiana limestone sample IB1 that was retrieved after loading to the peak stress, a variety of stress-induced cracking was observed (Fig. 7a). Many cracks have developed along grain boundaries, mostly due to relative movement of the allochems or delamination of the pore-lining micrite. Sliding along such cracks may in turn nucleate wing cracks that propagate subparallel to thes1 direction. Extensile intragranular cracks (within allochems and cement) also nucleated and propagated from stress concentrations in the vicinity of pores or impinging grain contacts. The stress-induced cracking was observed to develop at many different scales. As illustrated in Fig. 7b, complex intragranular and intergranular cracking may develop near shear zone. In the postfailure sample IB2, we observed a shear zone 0.5e1.0 mm wide, made up of grain fragments and intensely comminuted calcite particles. Intense microcracking has also developed in zones with relatively high microporosity concentrated along allochem boundaries. A shear-crack following boundaries of two allochems separates the shear zone (on the right) from the less deformed material on the left. The transition between shear zone and the surrounding material is relatively sharp in Indiana limestone. Our observations of the progressive development of microcracking and shear localization are qualitatively similar to earlier investigations of brittle faulting in limestone by Wawersik and Fairhurst (1970), Olsson (1974), Zheng et al. (1989) and Myer et al. (1992).

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Damage in the inelastically compacted samples is primarily associated with collapse of macropores. In the sample IH which was hydrostatically compressed to an additional 100 MPa beyond the critical pressure P* (Fig. 2a), macropores at different stages of collapse were observed. Intragranular cracking at an early stage can be observed in allochems, such as the one marked “A” in Fig. 7c with numerous microcracks near the segment of the allochem boundary along which the micritic cement had delaminated. In this hydrostatically compacted sample, cataclastic pore collapse seems to involve largely the cement, with most of the allochems remaining relatively intact. Fig. 7d illustrates the later stage of collapse of a macropore within cement surrounded by five allochems, supplemented by a close-up view of the collapsed macropore in Fig. 7e. Intense microcracking had developed in the cement surrounding the macropore, but the damage mode and intensity were heterogeneously distributed around the pore, possibly due to the mechanical contrast between the micrite and sparry cement. Numerous cracks had emanated from the micropores and coalesced. Large and small spalled fragments have imploded into the cavity. Unlike a micritic limestone such as Tavel limestone which has many quasi-spherical macropores (Vajdova et al., 2010), the geometry of a macropore in an allochemical limestone can be quite irregular, adding to the heterogeneity of the spatial distribution of cataclastic damage in the periphery of a collapsed pore (Fig. 7c and e). In the samples IC2 and IC3 triaxially compressed at 20 MPa confining pressure, the development of shear-enhanced compaction was manifested by pervasive collapse of macropores (Fig. 7f), accompanied by cataclastic damage in their peripheries analogous to those observed in the hydrostatically compacted sample IH. While cataclastic pore collapse is mostly confined to within the cement and the allochems are relatively intact in IC2, many extensile intragranular cracks were observed to have propagated sub-parallel to s1 within the allochems in sample IC3 (Fig. 7g), which was loaded to past C*0 (Fig. 2a). It is likely that the significant stress perturbation triggered by collapse of the macropores had induced many such microcracks to propagate, which would cooperatively contribute to dilatancy in competition with the inelastic compaction from pore collapse. The transition C*0 from compaction to dilatancy occurs when growth of dilatant microcracking becomes dominant. The style of stress-induced cracking in IC3 and IC4 is somewhat similar to that in the dilatant sample IB2, with an important difference in that pore collapse is significantly more pervasive in IC3 and IC4, which had undergone intensive shearenhanced compaction before they began to dilate. Sample IC4 also revealed several shear cracks that stretched over 4 to 6 grains and had offset up to 0.1 mm.

5.2. Damage evolution in Majella limestone Inelastic compaction in Majella limestone is also associated primarily with collapse of macropores. Again microcracking seems to be the dominant mechanism, although twinning was also observed with increasing density as the deformation progressed. Fig. 8a shows extensive cataclastic damage in the periphery of a relatively large macropore in the hydrostatically compacted sample MH. Unlike Indiana limestone in which the damage is often confined to the cemented regions, crack intensity in allochems and cements of Majella limestone is comparable. Numerous cracks surrounding a pore began to coalesce. Such a scenario is pervasive in this hydrostatically compacted sample. Fig. 8b shows pattern of cataclastic damage in the periphery of a relatively small macropore, which is qualitatively similar to that of a large macropore (Fig. 8a). In addition to pore-emanated cracking, Hertzian cracking (Zhang

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Fig. 7. Microstructure of deformed Indiana limestone. Direction of s1 is vertical. (a) Microcracks in sample IB1, optical micrograph in plain transmission light: (GB) grain boundary crack, (B) bending a long fossil, (EM) elastic mismatch crack. (b) Shear zone and its vicinity in sample IB2, backscattered SEM. A shear crack (SC) follows grain boundary and separates shear zone on the right (C, comminuted material) from less deformed material on the left. A microcrack deflection (DC) indicates a weak grain boundary. (c) Sample IH deformed hydrostatically beyond P*. Intragranular cracking at an early stage can be observed in allochems, such as the one marked “A”. (d) Collapsed macropore within a cemented region that is surrounded by five allochems in sample IH. (e) High magnification view of this collapsed macropore. (f) Sample IC2 failed by cataclastic flow. Pervasive collapse of macropores accompanied by cataclastic damage in their peripheries. (g) Sample IC3 also failed by cataclastic flow and was deformed beyond C*0 . Extensile intragranular cracks have propagated sub-parallel to s1 within the allochems.

et al., 1990) associated with tensile stress concentration at impinging grain contacts was also observed. Baud et al. (2009) reported that at low confining pressure (5e 10 MPa), their Majella limestone samples failed by development of compactive shear bands with intensely comminuted grains. Their microstructure observations indicate that the bands have thickness of about 2e3 grains and are oriented at a low angle (45e50 ) with respect to the major principal stress. In contrast, distributed cataclastic flow was observed in our samples triaxially compressed at 25 MPa confining pressure. Cataclastic damage in our three

samples (MC1, MC2 and MC3) is qualitatively similar to that observed in MH, with two important differences. First, many stress-induced cracks are preferentially aligned sub-parallel to s1, as illustrated in Fig. 8c and d for samples MC1 and MC3, respectively. Second, these two samples have developed more intensive cracking and comminution. In MC3 deformed to the transition stress C*0 (Fig. 2b) most of the macropores have basically collapsed (Fig. 8e), and in localized regions the comminution was so intense that grain fragments have been reduced to sub-micron size (Fig. 8f).

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Fig. 8. (a) Backscattered SEM images of deformed samples of Majella limestone. Direction of s1 is vertical. (a) Sample MH hydrostatically beyond P*. Cataclastic damage in the periphery of a relatively large macropore. (b) Hertzian cracking associated with tensile stress concentration at impinging grain contacts. Stress-induced cracks are preferentially aligned sub-parallel to s1 in samples MC1 (c) and MC3 (d) failed by cataclastic flow. (e) Sample MC3 failed by cataclastic flow. Most of the macropores have collapsed near C*0 and (f) in localized regions grain fragments have been reduced to sub-micron size.

5.3. Pore size statistics and inelastic compaction Our SEM observations have identified cataclastic pore collapse as an important mechanism for inelastic compaction in both limestones. It is likely that the progressive development of pore collapse would be accompanied by corresponding changes in the pore size statistics. Since our observations also indicate that the collapse is primarily associated with the macropores which can be readily resolved in scanned image or optical micrograph, the pore size statistics revealed by such measurements provide useful insights into the evolution of macropore collapse. Scanned images of five Indiana and four Majella limestone samples were acquired. We scanned the thin-section (covering an area of w38  18 mm2 for Indiana limestone and w40  20 mm2 for Majella limestone) at a resolution of 1800 dpi or higher, and the whole image was analyzed unless the thin section has domains with numerous grains plucked out, which had to be excluded. Furthermore, isolated holes that appeared to be grains plucked out in the thin section were manually filled in using the paintbrush tool in ImageJ and considered as a solid phase. Due to variability among samples and thin-sections, the settings for the scanner had to be adjusted appropriately for each sample. The brightness level of an 8-bit scanned image ranges from 0 to 255, and for our limestone samples the pore space is typically associated with a range of w40

in brightness level. For example, for the scanned image of I0-TS (Fig. 4a) we segmented the pores using lower and upper threshold brightness levels of 192 and 232, respectively. The binarized image was then analyzed to determine the area of each individual pore, from which the equivalent diameter was evaluated. Given the thickness of the thin section and limited resolution of the scanned image, we arbitrarily used a lower limit of 33 mm on pore size, and therefore a macropore in this data set is defined to be a feature with equivalent diameter of 33 mm or larger. From geometric probability theory, it can be demonstrated that the areal porosity (sum of the pore areas normalized by the total area) can be used to estimate the macroporosity of the sample if it is isotropic (Underwood, 1970). Symbols in Fig. 9a correspond to our macroporosity data so determined from the scanned images of the intact Indiana limestone sample I0-TS, as well as the shear-compacted samples IC1, IC2 and IC3. (In sample IC4 the pore space was so pulverized that we could not resolve the quantity.) To assess the sensitivity of the porosity estimate to threshold selection, we also determined the macroporosity values corresponding to increasing or decreasing the lower threshold brightness level by 4, which are shown as the upper and lower bars attached to the symbols. Since the range of brightness level for the pores is w40, this represents shifting the lower threshold by w10% of the full range. For comparison, we also

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scanned image of the hydrostatically compacted sample IH shows that it has a macroporosity of 2.1%, comparable to that of the triaxially compressed sample IC2. Fig. 9b shows our macroporosity data determined from the scanned images of the intact Majella limestone sample M0-TS, as well as three shear-compacted samples MC1, MC2 and MC3. We also determined the macroporosity values corresponding to changing the lower threshold brightness level by 4, which are shown as the upper and lower bars attached to the diamond symbols. Again comparison with the total porosity indicates that a very significant fraction (about one-third) of the total porosity is occupied by the macropores. Analogous to the Indiana limestone data, there is an overall trend for the macroporosity to decrease with increasing strain. The evolution of pore collapse is also reflected in the pore size statistics. We considered the stereological parameter nA, number of macropores per unit area in the scanned image. Fig. 10a compares the statistical distribution of equivalent pore diameter of two Indiana limestone samples. In the intact sample I0-TS, the macropore size ranges over one order of magnitude, with a maximum diameter of 621 mm. In the hydrostatically compacted sample IH, there is an overall reduction in nA over the whole diameter range, which implies pervasive collapse of the macropores induced by inelastic compaction. Fig. 10b shows the statistical distribution of equivalent pore diameter of the three triaxially compressed samples. In comparison to the undeformed sample I0-TS (Fig. 10a), there is an overall reduction in nA over the whole diameter range in the highly strained sample IC3. In contrast, the number of larger pores decreased while the number of smaller pores increased in the two samples IC1 and IC2 deformed to lower strains. This implies that at the initiation of shear-enhanced compaction, the larger pores are more vulnerable to cataclastic collapse which would shift the pore size distribution toward the small diameters. With accumulation of further inelastic strain, many of the smaller macropores would also collapse, which would result in an overall reduction in all diameter range as seen in sample IC3. Of course numerous tiny pores (with equivalent diameter <33 mm) not resolved in our measurements would also be created by the inelastic deformation. Qualitatively similar results were obtained for Majella limestone. In the intact sample M0-TS, there are more macropores than in Indiana limestone but overall they are smaller (Fig. 10c). In the hydrostatically compacted sample MH, there is again an overall reduction in nA over the whole diameter range related to pervasive collapse of the macropores. Similar decrease in nA with the progressive development of shear-enhanced compaction was also observed (Fig. 10d). Fig. 9. Initial porosity (circles) and macroporosity (squares) as a function of axial strain for (a) Indiana limestone samples I0-TS, IC1, IC2 and IC3, (b) Majella limestone samples M0-TS, MC1, MC2, and MC3. The stressestrain curves are given for reference for the samples deformed triaxially. Error bars correspond to standard deviations.

evaluated the macroporosity values determined by tracing the pores manually under the optical microscope in selected areas. Since the overall agreement between the macroporosity values from the two measurement techniques is very good, we have not included this second set of data in the figure. For reference we also show in Fig. 9a the initial total porosities. For the undeformed sample I0-TS, we determined the macroporosity to be only about one-third of the total porosity of 16.5%, with the implication that the microporosity represents a very significant fraction. Our data show an overall trend for the macroporosity to decrease with increasing strain (Fig. 9a), related to the progressive development of cataclastic pore collapse in Indiana limestone. Although not included in Fig. 9a, our analysis of the

5.4. Interplay of cataclasis, deformation twinning and rigid allochem motion Calcite requires relatively low shear stresses to initiate mechanical twinning and dislocation slip even at room temperature (Turner et al., 1954; Griggs et al., 1960). As noted by Vajdova et al. (2004) the differential stress levels in our experiments are comparable to the shear stresses required to activate e-twinning in calcite. It should also be noted that twinning and microcracking are intertwined, in that the former can result in significant tensile stress concentration for the nucleation of microcracks (Olsson and Peng, 1976; Fredrich et al., 1989). While details of microcracking can be observed under the SEM, twinning is easier to resolve under an optical microscope. In an Indiana limestone sample, optical microscope observations of Groshong (1974) indicate appreciable twinning activity in a sample compacted hydrostatically to 100 MPa. Fig. 11a shows the interplay of pore collapse, cleavage cracking and twinning in our hydrostatically compacted sample IH.

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Fig. 10. Size distribution of pores resolved from a scanned image at a resolution of 2400 dpi. The number of pores per unit area nA is plotted versus equivalent diameter. (a) Indiana limestone samples I0-TS intact (white) and IH deformed hydrostatically (black). (b) Indiana limestone samples deformed at 20 MPa of confining pressure IC1 (white), IC2 (black) and IC3 (gray). (c) Majella limestone samples M0-TS intact (white) and MH deformed hydrostatically (black). (d) Majella limestone samples deformed at 25 MPa of confining pressure MC1 (white), MC2 (black) and MC3 (gray).

Under nonhydrostatic loading, the interaction between cataclasis and crystal plasticity can be quite complex, as illustrated in Fig. 11b for Indiana limestone sample IC3. Twin lamellae emerging on a grain boundary may lead to microcracking in a neighboring grain. The twins in Fig. 11b evidently interacted with the microcracks, although it is difficult to categorically conclude whether the twinning induced microcrack initiation or the opposite. In the relatively compact Tavel limestone, Vajdova et al. (2010) recently documented a progressive increase of twinning density with increasing strain in the cataclastic flow regime and similar trend is apparent also on thin-sections of Indiana limestone. The twinning activity in Majella limestone is qualitatively similar. Fig. 11c shows deformation twins observed in the hydrostatically compacted sample MH. Under nonhydrostatic loading, twinning activity was observed to be quite pervasive in sample MC2 (Fig. 11d). More intense twinning was observed in sample MC3 deformed to higher stresses (Fig. 11e), and an example of twinning near a macropore in MC3 is shown in Fig. 11f.

In their study of the use of calcite twinning for paleotress estimation, Rowe and Rutter (1990) considered three different measures of twinning activity and investigated comprehensively their dependences on grain size, stress, strain, strain rate and temperature. One of their measures is “twinning incidence”, defined to be the percentage of grains in a given grains size class interval which contain optically visible twin lamellae. They observed that this measure of twinning activity increases with grain size (at constant level of differential stress) and linearly with stress (at a given grain size). Furthermore all three measures of twinning activity were observed to be independent of strain, strain rate and temperature. Since Rowe and Rutter (1990) focused on compact carbonate rocks, it requires further systematic investigation to assess the extent to which their conclusions on calcite twinning activity can be generalized to limestones of significantly higher porosity. Our observations and the recent data of Vajdova et al. (2010) on Tavel limestone indicate an increase of twinning activity with increasing strain and in this sense should be

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Fig. 11. Interplay between microcracking and mechanical twinning. Optical micrographs, direction of s1 is vertical. (a) Indiana limestone sample IH deformed hydrostatically, in polarized light. Pore collapse (PC), cleavage cracks (C) and twinning (T) were observed. (b) Sample IC3 of Indiana limestone deformed triaxially at confining pressure 20 MPa, crossed nicols. Emergence of twin lamellae on a crystal surface leads apparently to microcrack formation. (c) Majella limestone sample MH deformed hydrostatically, plain light. Twins formed in the monocrystalline part of a grain and interacted with a microcrack. (d) Sample MC2 of Majella limestone deformed triaxially at 25 MPa confining pressure: twinning was observed to be quite pervasive. (e) Sample MC3 of Majella limestone deformed triaxially at 25 MPa confining pressure until C*0 : More intense twinning (T) was observed. (f) Twinning close to a macropore.

interpreted as due to the increase in differential stress that accompanied strain hardening in these samples. Our SEM observations underscore an important difference in allochem deformation between the two limestones: while the rudists in Majella limestone show pervasive and intense microcracking and comminution, the fossils and ooids in Indiana limestone have remained relatively intact even in the highly strained samples. Since the allochem boundaries appear to be weak and attract grain boundary cracks in Indiana limestone, it is possible that the progressive deformation would induce relative motion of the basically rigid allochems within this high porosity matrix. Our data on geometry and orientation of the allochems corroborate this scenario. In the undeformed Indiana limestone sample I0-TS, the equivalent diameters of the allochems have a mean value of 0.35 mm. In five deformed samples (IB1, IB2, IC1, IC2 and IC3) the mean diameters are comparable and fall in a narrow range of 0.25e0.32 mm.

The outline of an allochem (manually mapped in the optical micrograph) was fitted with an ellipse automatically by Scion Image software, and its aspect ratio (ratio of major and minor axis lengths) and orientation of the major axis were evaluated. Aspect ratio of allochems in the five deformed samples have mean values in the range of 1.9e2.0, while that of the sample I0-TS is 2.0. Overall the allochem data on Indiana limestone indicate that the size and shape of the allochems were not modified by the deformation. In contrast, the major axis orientation shows systematic changes due to inelastic deformation, as illustrated by the rose diagrams for the orientation statistics in Fig. 12. In the undeformed sample I0-TS, many of the allochems are preferentially aligned parallel to the bedding (identical to the s3 direction in our triaxial experiments conducted on samples cored perpendicular to bedding). There is also a second set of allochems with preferred orientations dipping at w60 to bedding (i.e. w30 to s1). It can be seen in Fig. 12 that in the five deformed samples this second preferred orientation

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Fig. 12. Evolution of preferred orientation of allochem with axial strain in Indiana limestone. The rose diagrams show the major axis orientations: a scenario consistent with rigid body motion. This is not due to the matrix being intrinsically ductile but rather the allochems to move about and align.

became less pronounced with increasing strain. In fact only one preferred orientation was observed in some of the highly strained samples. A likely explanation is that the inelastic deformation and cataclastic damage were accompanied by rigid body rotations of the allochems that were controlled by the stress field to align their long axis perpendicular to s1 (and parallel to s3). 6. Discussion The mechanics of inelastic compaction and cataclastic flow in porous carbonate rocks are similar to siliciclastic rocks in many respects (Baud et al., 2000a; Vajdova et al., 2004). Notwithstanding these similarities in phenomenological behavior, observations of Vajdova et al. (2010) and this study on allochemical and micritic limestones have demonstrated that the micromechanics can be very different. In a siliciclastic rock such as sandstone, inelastic compaction derives primarily from grain crushing initiated by the stress concentrations at grain contacts, that induce intragranular cracks to radiate in a conical pattern toward the interior of the impinging grains (e.g., Menéndez et al., 1996; Wu et al., 2000). In contrast, Vajdova et al. (2010) observed in Tavel limestone that inelastic compaction in this micritic limestone is associated with pore collapse that seems to initiate from stress concentrations at the surface of a relatively equant pore, which induce a ring of localized cataclastic damage in its periphery. While our observations here for Indiana and Majella limestones suggest that the micromechanical process is qualitatively similar, they also show that the spatial distribution of damage in the allochemical limestones can be complicated by its uneven partitioning among the allochems, micrite and sparite. 6.1. Cataclastic pore collapse and damage development in allochems and cements In compacted samples of Tavel limestone, Vajdova et al. (2010) observed cataclastic damage distributed in the periphery of a macropore which indicates that the micritic matrix can be approximated as mechanically homogeneous. In a Tavel limestone

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sample hydrostatically stressed to beyond the critical pressure P*, a halo of cataclastic damage was observed to develop symmetrically around the circumference of a macropore. In the two allochemical limestones under study the cataclastic damage is also localized in the periphery of a macropore, but in contrast it is often associated with appreciable spatial heterogeneity, even for the hydrostatically stressed samples (Figs. 7 and 8). Nevertheless, the collapse of pores is expected to result in significant reduction of permeability. In a recent study, Selvadurai and Glowacki (2008) observed in Indiana limestone compacted to an effective pressure of 60 MPa an irreversible decrease in permeability by an order of magnitude. Under nonhydrostatic loading, inelastic compaction can result in an overall permeability decrease that is often accompanied by an enhancement of permeability anisotropy, as was recently observed by Dautriat et al. (2008) in an oolitic limestone. In Indiana limestone, many allochems remain relatively intact even after the cement has undergone significant microcracking and fragmentation, with the implication that significant strength contrast exists between the allochem and cement. This observation is in agreement with some of the more systematic field and laboratory studies of carbonate compaction which have recognized that as a consequence of such strength contrast, a highly compacted limestone may not exhibit any signs of breakage in shells, foraminifera, or ooids (Shinn et al., 1977; Bhattacharyya and Friedman, 1979; Shinn and Robbin, 1983). Detailed observations on Indiana limestone indicated that the high porosity layer that outlines most allochems attracts microcracks and apparently represents a low strength zone. Many microcracks that approach an allochem deflect as grain boundary cracks upon reaching this high porosity layer and the allochems can become free to move and so accommodate pore collapse without apparent damage. In Majella limestone, the asymmetry in damage intensity between allochem and cement is not as pronounced as in Indiana limestone, possibly because the mechanical contrast between the cements and allochems is not as pronounced. The allochems in this weakly cemented limestone are rudist shells that had undergone significant fragmentation and breakage in a high-energy sedimentary environment. Fig. 13 provides a synopsis of the deformation mechanisms associated with mechanical compaction in porous limestones that have been documented here and in the previous study of Vajdova et al. (2010). The onset of inelastic compaction at the critical stress state (P* or C*) is primarily due to the collapse of macropores accompanied by cataclastic damage in the surroundings. This allows the allochems to be debonded from the matrix and undergo rigid body rotation. Stress concentration in the vicinity of a macropore induces cracks to emanate from micropores, which then coalesce into a ring of cataclastic damage (Fig. 13b). As the sample undergoes strain hardening and attains a higher stress level, twinning and possibly dislocations are activated to accommodate the accumulation of inelastic strain (Fig. 13c). In his comprehensive study of compaction in Mississippian skeletal limestones, Meyers (1980) analyzed 390 samples and concluded after close examination that about 90% of the skeletal grainstone and 99% of the skeletal packstones exhibit some compaction features, including grain breakage, plastic grain deformation and grain reorientation. He also demonstrated that the bulk of mechanical compaction in skeletal grains occurs in multicrystalline skeletal grains (bryozoans, brachiopods, ostracodes, solitary corals), whereas deformation of single crystal echinoderms (which are often found in Indiana limestone) is rare. Our observations of twinning (Fig. 11), cement damage and allochem rotation (Fig. 12) in compacted samples of Indiana limestone are qualitatively similar to many of the field examples presented by Meyers (1980).

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Analogous deformation mechanisms were observed by Rath et al. (2011) in Leitha limestone. It is a poorly sorted grainstone made up of w99% calcite, predominantly bioclasts. The total porosity of the host rock ranges from 22% to 35%. Early formation of deformation bands involved particulate movement of grains with relatively little cementation, with some of the bioclasts induced by the applied stress to rotate by as much as 90 . After the precipitation of cements along the bioclasts, tectonic deformation was accommodated by cataclastic deformation of bioclasts and cement. 6.2. Compaction localization and shear-enhanced compaction Compaction bands are planar structures that have undergone inelastic compaction predominantly due to shortening in a direction sub-perpendicular to their planar surface with negligible shear offset (Mollema and Antonellini, 1996). In the field such compaction bands have been extensively observed in the Aztec sandstone at Valley of Fire State Park, Nevada (Hill, 1989; Sternlof et al., 2005) and in the Navajo sandstone at the Kaibab Monocline, Utah (Mollema and Antonellini, 1996; Schultz, 2009). In the laboratory analogous structures of discrete compaction bands have also been observed, mostly in sandstones with porosities >20% or so. In contrast to siliciclastic rocks, there has not been to date any laboratory evidence of compaction bands in porous limestone. In Majella limestone particularly, Baud et al. (2009) explored the compactive yield behavior over a broad range of stress conditions in the laboratory and found no compaction localization. In contrast, Tondi et al. (2006) did observe in the Madonna della Mazza quarry a number of bed-parallel deformation bands that lack any evidence of shearing, which they categorized accordingly as compaction bands. Even though not pervasive throughout the formation, these bands correspond to the oldest deformation structures that typically developed within the coarse-grained beds with the highest porosities (w30%). During burial the overburden pressure was inferred to range from 10 to 70 MPa, comparable to the mean stress involved in laboratory deformation of Majella limestone (Figs. 2b and 3). A plausible explanation of this apparent discrepancy between laboratory and field observations is that localized compaction may develop more readily in a porous medium that is spatially heterogeneous. We plot in Fig. 14 the critical pressure P* for the onset of pore collapse in limestones (with porosities up to 30%) compiled recently by Zhu et al. (2010). To help define the overall trend for the porosity sensitivity of P*, they also included data for chalk (with porosities ranging from 38% to 45%) compiled by Vajdova et al. (2004). The laboratory data show that the pore collapse pressure is sensitively dependent on the total porosity, especially in the range of 10e23% with a significant drop of P* by an order of magnitude. Tondi et al. (2006) analyzed five samples from the Madonna della Mazza quarry (Fig. 6), three of which have porosities in the range of 15e22% while the two more porous samples have porosities of 25% and 29%. According to the laboratory data (Fig. 14), while pore collapse and inelastic compaction can readily develop in the more porous layers at a relatively low pressure of w30 MPa, such processes would initiate in the more competent layers only if significantly higher pressures (by as much as a factor of 5) were attained. In the quarry the more porous samples are often located in relatively thin coarse-grain beds, and it is possible that the compaction bands found in such beds were due to the preferential

Fig. 13. Deformation mechanisms associated with compaction in dry experimentally deformed porous limestone. (a) Cataclasis in the surrounding of the allochems allows them to be debonded from the matrix and undergo rigid body rotation. (b) Stress

concentration in the vicinity of a macropore induces cracks to emanate from micropores, which then coalesce into a ring of cataclastic damage. (c) As the sample undergoes strain hardening and attains a higher stress level, twinning and possibly dislocations are activated to accommodate the accumulation of inelastic strain.

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Fig. 14. Comparison of theoretical predictions with laboratory data on critical pressures for pore collapse (P*) of limestones. micritic (circles) and allochemical (squares) limestones and chalks (diamonds). Experimental data (Zhu et al., 2010) of micritic, allochemical limestones and chalk are shown as circles, squares and diamonds, respectively. They are bounded by the theoretical curves for S* ¼ 20 MPa and S* ¼ 130 MPa.

development of pore collapse at a relatively low critical pressure related to their high porosities. Additionally in natural environments, reactive fluid may be present, possibly allowing stressdriven chemical compaction at strain rates several orders of magnitude lower than those accessible in the laboratory. Tondi et al. (2006) emphasized the importance of pressure solution processes in the Orfento formation. It is also possible that these processes played some role in the formation of the bed parallel compaction bands observed in the field. 6.3. Porosity reduction of carbonates in sedimentary formation The critical stress level as a function of porosity compiled in Fig. 14 represents an upper bound on what is necessary for the development of inelastic compaction by pore collapse. The data are for hydrostatic loading on nominally dry limestone samples. If the sedimentary formation is subjected to a deviatoric stress field due to tectonic loading, the mean stress level for the onset of shearenhanced compaction can be lower by as much as a factor of 2 (Vajdova et al., 2004; Baud et al., 2009). Nevertheless, these upper bounds on the stress level are so high that although they may be pertinent to geotechnical applications such as oil reservoir and geological repository, it is not likely that such high stresses are attained at burial depths corresponding to typical sedimentary basins, and accordingly chemical compaction is expected to dominate the porosity reduction observed in such settings at depths beyond 2 km or so. However, it should be noted that in sedimentary and tectonic settings, mechanical and chemical compactions are probably coupled in a complex manner, and therefore significant uncertainty remains regarding constraints on the stress and kinetics that one derives for individual mechanisms idealized as decoupled endmembers. Therefore experimental studies under controlled conditions are necessary for identifying the operative mechanisms,

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which then provide a useful framework for a deeper investigation into how they may be coupled in geologic settings. In the presence of water, the compactive yield stress of a limestone is expected to be lower due to chemical weakening processes. Solution-precipitation and related mass transfer processes can result in porosity reduction significantly larger than that in a dry rock. Furthermore cataclastic damage represents significant increase in reactive surface area, which would enhance the kinetics. Ratedependent subcritical crack growth may also result in cataclastic damage at a stress level lower than that operative in a dry rock, and a fracture mechanics model can be used to analyze the effect. To model the micromechanics of inelastic compaction in porous limestone, Zhu et al. (2010) recently developed a cataclastic pore collapse model that is based on linear elastic fracture mechanics. It considers the limestone as a dual porosity medium (with the total porosity partitioned between the macroporosity FM and microporosity Fm), which first yields by the collapse of the macropores, that are surrounded by an effective medium containing the microporosity (Fig. 13b). This micromechanical model predicts that the critical pressure P* for the onset of pore collapse depends on the total porosity F according to a power law: P* ¼ ð0:883=F0:414 Þ S*, with the parameter S* related to the micropore size a* (Fig. 13), fracture toughness KIC, and the partitioning of microporosity and macroporosity ðF* ¼ Fm =ð1  FM ÞzFm Þ according to: S* ¼ KIC = pffiffiffiffiffiffiffiffi ðF* =FÞ0:414 pa*. Zhu et al. (2010) observed that the laboratory data for P* fall between two limiting curves (corresponding to the two solid curves in Fig. 14) according to their dual porosity model. Two relatively compact micritic limestones (Solnhofen and Tavel) lie on the upper curve corresponding to S* ¼ 130 MPa, corresponding to a micropore radius of 0.8 mm, assuming a KIC value of 0.2 MPa m1/2 considered to be appropriate for calcite (Atkinson and Meredith, 1987). The P* data for samples with porosities beyond w23% fall on a plateau given by the lower limit S* ¼ 20 MPa, which implies that a*  32 mm. Our Majella limestone sample with a total porosity of 30% fall on this lower plateau. Between the two limits at porosities in the range of about 10e 23%, the inferred value of S* decreases rapidly with increasing porosity. Since changes in the porosity partitioning factor F*/F is unlikely to be large enough to result in this decrease, a significant part of this decrease is probably related to corresponding increase in micropore size from submicron to tens of micron. Our Indiana limestone sample fall into this intermediate porosity range, and as noted earlier, the more compact Majella limestone samples analyzed by Tondi et al. (2006) also have porosities in this range. In the presence of water, two effects may result in mechanical weakening. The first is the reduction of surface energy in the presence of water. Analyses of porous limestones and sandstones by Baud et al. (2000b, 2009) indicate such a weakening effect of up to 20%. The second is stress corrosion, which would result in subcritical crack growth (with the stress intensity factor K1 connected to crack velocity) and cataclastic damage development that are sensitive to strain rate and fluid chemistry. There is a paucity of laboratory data on this effect, and as emphasized by Croizé et al. (submitted for publication) in their recent review, more systematic investigations in the laboratory are warranted to elucidate the coupling of chemical compaction (including pressure solution and subcritical crack growth) and mechanical compaction (including cataclasis and crystal plasticity) and better constrain their interplay in relation to porosity and permeability evolution in carbonate formations. 7. Conclusion In this study, the evolution of microstructural damage was described for the compressive failure of two porous allochemical

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limestones deformed in the laboratory. Shear-enhanced compaction is associated both in Indiana and Majella limestones primarily with cataclastic damage although mechanical twinning was also observed. Microcracks initiate as pore-emanated cracks from micropores and macropores alike but macropores represent the dominant stress concentrators and seem to drive the crack propagation, which eventually leads to pore collapse. The pore-emanated microcracks do not show any preferred orientation at low strain. With increasing strain majority of microcracks aligns with s1 direction. Our new results are overall in qualitative agreement with recent observations in a micritic limestone (Vajdova et al., 2010). In Indiana limestone, microcracking occurs first in the cement and many allochems remain intact even after a significant amount of strain. In Majella limestone, damage appeared more evenly distributed between the allochems and cement. The stress perturbation resulting from the pore collapse promotes the opening of additional microcracks. Beyond a certain level of non-elastic strain, the interplay of compaction and dilatancy leads to the transitional state C*0 in both rocks as dilatancy overcomes compaction at high strain. No compaction localization was observed in our failed samples. This contrasts with field observation particularly in Majella limestone, in which Tondi et al. (2006) observed bed-parallel compaction bands. The discrepancy between the laboratory and field observations could result from the fact that localized compaction may develop more readily in a porous medium that is spatially heterogeneous. Detailed observations of the field compaction in Majella limestone in the Madonna delle Mazze quarry are currently being performed to confirm this opinion. We applied to our data the dual porosity model for cataclastic pore collapse in limestone, recently proposed by Zhu et al. (2010). This model considers the limestone as a dual porosity medium (with macroporosity and microporosity), which first yields by the collapse of macropores in agreement with our microstructural observations. The model predicts the onset of pore collapse under hydrostatic conditions to be dependent on the total porosity, the microporosity and the size of the micropores embedded in the effective medium surrounding the macropores. The efficiency of such an approach hinges on an accurate description of the microporosity in limestone. Acknowledgments We are grateful to Roberto Suarez-Rivera who furnished us with blocks of Indiana limestone some years ago. The block of Majella limestone was kindly provided by Emanuele Tondi, who with Fabrizio Agosta took PB and TfW on a very informative field trip to Majella. We want to thank Jim Quinn and Wei Zhu for assistance with SEM microscopy, and Sergio Vinciguerra for logistic support. We have benefited from discussions with José-Luis Alves, Christian David, Jerome Fortin, Nicholas Gland, Troy Rasbury, Emanuele Tondi, Sergio Vinciguerra and Wei Zhu. We thank the associate editor and two anonymous reviewer for critical reviews on this manuscript. This research was partially supported by the Office of Basic Energy Sciences, Department of Energy under grant DE-FG0299ER14996, and the National Science Foundation under grant EAR1044967. Patrick Baud was partially supported by CNRS (PICS). The authors would also like to thank the CAPES-COFECUB program for stimulating fruitful discussions on compaction in carbonates. References Agosta, F., Alessandroni, M., Tondi, E., Aydin, A., 2009. Oblique normal faulting along the northern edge of the Majella Anticline, central Italy: inferences on hydrocarbon migration and accumulation. J. Struct. Geol. 31, 674e690.

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