Sinkholes, pit craters, and small calderas: Analog models of depletion induced collapse analyzed by...

Sinkholes, pit craters, and small calderas: Analog models of depletion-induced collapse analyzed by computed X-ray microtomography

Sam Poppe1,†, Eoghan P. Holohan2,†, Elin Pauwels3,†, Veerle Cnudde4,†, and Matthieu Kervyn1,†

1Department of Geography, Earth System Science, Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium2Helmholtz Centre Potsdam, German Research Centre for Geosciences (GFZ), Section 2.1, Telegrafenberg, 14472 Potsdam, Germany3Centre for X-ray Tomography (UGCT), Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, B-9000 Ghent, Belgium4Centre for X-ray Tomography (UGCT), Department of Geology and Soil Science, Ghent University, B-9000 Ghent, Belgium

ABSTRACT

Volumetric depletion of a subsurface body commonly results in the collapse of over-burden and the formation of enclosed topo-graphic depressions. Such depressions are termed sinkholes in karst terrains and pit cra-ters or collapse calderas in volcanic terrains. This paper reports the fi rst use of computed X-ray microtomography (μCT) to image analog models of small-scale (~< 2 km diam-eter), high-cohesion, overburden collapse induced by depletion of a near-cylindrical (“stock-like”) body. Time-lapse radiog raphy enabled quantitative monitoring of the evo-lution of collapse structure, velocity, and vol-ume. Moreover, μCT scanning enabled non-destructive visualization of the fi nal collapse volumes and fault geometries in three dimen-sions. The results illustrate two end-member scenarios: (1) near-continuous collapse into the depleting body; and (2) near-instan-taneous collapse into a subsurface cavity formed above the depleting body. Even within near-continuously collapsing columns, sub-sidence rates vary spatially and temporally, with incremental accelerations. The highest subsidence rates occur before and immedi-ately after a surface depression is formed. In both scenarios, the collapsing overburden column undergoes a marked volumetric ex-pansion, such that the volume of subsurface depletion substantially exceeds that of the re-sulting topographic depression. In the karst context, this effect is termed “bulking,” and our results indicate that it may occur not only at the onset of collapse but also during pro-gressive subsidence. In the volcanic context,

bulking of magma reservoir overburden rock may at least partially explain why the volume of magma erupted commonly exceeds that of the surface depression.

INTRODUCTION

Closed, near-circular topographic depres-sions with diameters ranging from several tens to thousands of meters are common morphological features on Earth and other planets. In regions underlain by karst rock units, such as limestone or evaporite (rock salt), these depressions are termed sinkholes or dolines. In regions affected by igneous activity, such features are termed pit craters (diameter <~1 km) or calderas (diam-eter >~1 km). As outlined below, differences in geological context lead to some variation of the depression formation mechanisms in detail. An overriding similarity, however, is that sinkholes, pit craters, and calderas commonly form as a result of the volumetric depletion of a subsur-face body and the consequent destabilization and gravitational collapse of the overburden.

Sinkholes, pit craters, and calderas formed in this way can all develop within days and with little advance warning (e.g., Dahm et al., 2011; Poland et al., 2008; Stix and Kobayashi, 2008, and references therein). Nonetheless, modern monitoring methods can yield abun-dant geophysical and geodetic information related to the onset and evolution of such col-lapses. This capacity is illustrated by studies of recent collapses at the basaltic volcanoes of Miyakejima (Japan), Kilauea (Hawaii), and Piton de la Fournaise (La Réunion) (e.g., Geshi et al., 2002; Longpré et al., 2007; Michon et al., 2007; Poland et al., 2008), and at the Wink and Daisetta sinkholes, Texas (Paine et al., 2012), as well as subsurface collapses in the sink-hole-prone city of Hamburg, Germany (Dahm et al., 2011).

For developing early-warning systems and/or remediation schemes from such information, it is important to understand the structural devel-opment of gravitational overburden collapses. An intrinsic problem is that this mostly occurs underground and so cannot be directly observed. Consequently, many researchers have turned to analog and numerical collapse simulations.

Past analytical and numerical modeling stud-ies of collapse have mostly simulated the over-burden to behave as a linearly elastic continuum (e.g., Tharp, 1999; Folch and Marti, 2004). A major limitation of this assumption is that the large and commonly highly discontinuous (i.e., fault- or fracture-related) strains typical of col-lapse are diffi cult or impossible to simulate. More recent studies have surmounted this limi-tation by assuming the overburden to behave as a visco-elastic continuum or by treating the over-burden as an assemblage of distinct elements (e.g., Baryakh et al., 2008; Hatzor et al., 2010; Holohan et al., 2011; Shalev and Lyakhov sky, 2012), but computational expensiveness has hitherto limited them to two dimensions.

Analog models readily simulate such large discontinuous strains in a three-dimensionally complete way (e.g., Sanford, 1959). There have hence been many analog model studies of pit crater or caldera collapse (e.g., Komuro, 1987; Martí et al., 1994; Roche et al., 2000; Walter and Troll, 2001; Kennedy et al., 2004; Lavallée et al., 2004; Geyer et al., 2006; Acocella, 2007; Holo-han et al., 2008, 2013; Burchardt and Walter, 2010; Ruch et al., 2012), but far fewer of sink-hole formation (Parker and McDowell, 1955; Ge and Jackson, 1998; Howard, 2010). Most past analog modeling studies have explored the general structural geometry and kinematics of collapse. Dynamic aspects, such as changes in subsidence velocity or volume through time, are much more diffi cult, even impossible, to scale adequately, but even semi-quantitative

For permission to copy, contact [email protected]© 2014 Geological Society of America

281

GSA Bulletin; January/February 2015; v. 127; no. 1/2; p. 281–296; doi: 10.1130/B30989.1; 9 fi gures; 3 tables; published online 26 August 2014.

†E-mails: sam .poppe@ vub .ac .be; holohan@ gfz -potsdam .de; elin .pauwels@ ugent .be; veerle .cnudde@ ugent .be; [email protected].

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282 Geological Society of America Bulletin, v. 127, no. 1/2

constraints on these could greatly aid the inter-pretation of seismic, geodetic, and gravity data acquired during collapses in nature.

In this paper, we report the novel applica-tion of computed X-ray microtomography (μCT) to image analog models of vertical col-lapse. In nature, collapse events at sinkholes, pit craters, and calderas range in dynamic style from near-instantaneous (“en mass”) to near-continuous (“incremental”), typically occurring over periods of a few minutes to a few months, respectively (Gutiérrez et al., 2008; Stix and Kobayashi, 2008). As shown below, our models reproduce these two end-member scenarios. Our considerations are restricted to a natural length scale of ~< 2 km, and our results are thus most relevant for collapses during which brittle defor-mation is likely to be dominant. We note that the formation of larger calderas is more likely to be infl uenced by thermal effects from the corre-spondingly larger magma reservoir, giving rise to an increased importance of ductile overbur-den behavior (see Burov and Guillou-Frottier, 1999; Gregg et al., 2012). The µCT approach reveals the models’ subsurface collapse evolu-tions as run in a fully three-dimensional (3D) medium, rather than against a glass pane (e.g., Burchardt and Walter, 2010; Ruch et al., 2012). The advantage is that boundary effects at the observed contact between the analog materials and the glass are avoided. After briefl y com-paring our simulated collapse structures and geometries with those of the previous models from the literature, we extract quantitative data on model subsidence rate and volume through time from the μCT imagery. Finally, we discuss implications of these data for development and monitoring of natural collapses at the studied length scale range.

BACKGROUND TO DEPLETION-INDUCED COLLAPSE IN NATURE

Sinkholes form mainly because of undermin-ing of the overburden by subsurface dissolution (“subrosion”) of karst rock (Gutiérrez et al., 2008, and references therein) (Fig. 1). Alterna-tively, uneven dissolution of karst rock directly at or just below the Earth’s surface may produce so-called “solution sinkholes.” Because the study of this latter mechanism is not the aim of our work, we do not consider it any further here. Subsurface dissolution is typically a conse-quence of fresh or undersaturated ground water fl owing through the karst rock body or along its boundaries (Johnson, 2005, and references therein). The overburden may include other karst rock units (bedrock), non-karst rock strata (cap rocks), and/or unconsolidated sediments (cover). Here, we focus on overburden sub-

sidence associated with subsurface dissolution of evaporite (rock salt) bodies (Fig. 1).

Pit craters and small calderas (~< 2 km diam-eter) form mainly through destabilization of the overburden by drainage and critical depres-surization of a subsurface magma body (see Roche et al., 2001; Geshi et al., 2002; Stix and Kobayashi, 2008; Michon et al., 2011) (Fig. 2). The overburden usually comprises partly to fully consolidated igneous material, which may be of highly heterogeneous mechanical character. Depending on the level of emplace-ment of the magma body below the free surface, the overburden may also include non-igneous “basement” rocks. Another pit crater–forming process involves collapse of material into an open subsurface fracture formed by the intru-sion and drainage of a dike. Such a mechanism is evidenced from a detailed study of pit crater chains on Hawaii (Okubo and Martel, 1998), and may be considered a variation on the main mechanism explored here.

There is a remarkably similar range of over-burden subsidence mechanisms observed at sinkholes, pit craters, and small calderas (Gutiér-rez et al., 2008, and references therein; Branney, 1995; Lipman 1997; Okubo and Martel , 1998; Harris, 2009). Based on these observations, overburden subsidence in both terrain types may involve: (1) sagging of strata; (2) foundering of large intact blocks delimited by ring faults; or (3) “caving” or “stoping,” whereby pieces of overburden detach and subside in conjunction with the progressive upward migration of sub-surface cavities. Many natural cases show com-binations of more than one such mechanism. A fourth subsidence mechanism particular to the sinkhole literature is termed “suffosion.” This refers to the relatively long-term downward fl ushing, tumbling, granular fl ow, and/or vis-cous creep of unconsolidated cover deposits into pipes or fi ssures in the bedrock. In volcanic ter-rains, suffosion may also occur in materials such as poorly consolidated tephras, although the ori-gins of the underlying fi ssures or pipes may or may not be directly connected to movements of magma (Ferrill et al., 2004).

The development of each of the sub-sidence mechanisms (1–3 above) depends on the mechanical and geometric properties of the overburden and on those of the under-lying body of rock salt or magma. The most important mechanical and geometric factors are, respectively, the strength (i.e., cohesion) of the overburden and the ratio of overburden thickness to depletion zone diameter (T/D) (e.g. Whittaker and Reddish, 1989; Ge and Jackson, 1998; Roche et al., 2000, 2001; Gutiérrez et al., 2008; Holohan et al., 2011). The shape of the depletion zone exerts a secondary infl uence (Ge

and Jackson, 1998; Roche et al., 2000; Holohan et al., 2011). In general, (1) sagging is promoted by low rock mass strength and low T/D ratio; (2) foundering of one or more large coherent blocks enclosed by a ring fault occurs at inter-mediate rock mass strength and intermediate to high T/D ratio; and (3) stoping and ephemeral cavities develop at high rock mass strength and high T/D ratio (e.g., Roche et al., 2000, 2001; Holohan et al., 2011).

Of these three common subsidence mecha-nisms, coherent-block foundering and stoping are associated with sharply defi ned depressions bounded by steep sides that are cliffed or over-hanging (Gutiérrez et al., 2008). Such a steep-sided morphology gives rise to the term “pit crater” in volcanic terrains. Time-averaged sub-sidence rates of up to several tens or hundreds of meters per day have been observed during the formation of pit craters and calderas (Poland et al., 2008; Geshi et al., 2002; Michon et al., 2007, 2011). Although many sinkholes show much slower subsidence rates of 0.2–30 cm/yr (Soriano and Simón, 2002; Dahm et al., 2011; Paine et al., 2012), some also collapse at rates of up to several tens of meters per day (e.g., Walters , 1978; Johnson, 2005). These high rates are typically seen with sudden, en-mass over-burden collapses into large underground cavities.

Such observations point to an overriding importance of brittle overburden deformation in those collapses of highest geohazard. Con-sequently, we focus here on the more brittle mechanisms (2–3) by considering the effects of subsurface volume depletion on overburden rock masses of relatively high cohesion and of intermediate T/D ratios of roughly 0.8–1.3.

METHODOLOGY

Experiment Setup and Material

Dry silica sand sieved to 50–180 µm grain size and mixed with 5% or 10% by volume of dry plaster served as an analog for a brittle over-burden rock mass. The sand and plaster mixes (SP mix) had bulk densities of ~1.6 × 103 kg m–3 and ~1.75 × 103 kg m–3, respectively. Following the method of Donnadieu (2000), we estimated cohesions of ~180 Pa and ~300 Pa, respectively, by averaging 20 measurements of maximum vertical cliff height. In contrast to pure dry sand, which is theoretically cohesionless, the cohesive SP mix can support near-vertical cliffs, as seen in the natural collapse-related depressions (Figs. 1 and 2; see also Hubbert, 1937; Roche et al., 2001; Holohan et al., 2008).

Our depletion zone comprised a cylindrical body of golden syrup (GS), a Newtonian fl uid with a density of 1.4 × 103 kg m–3 and a viscos-

Sinkholes, pit craters, and small calderas

Geological Society of America Bulletin, v. 127, no. 1/2 283

ity of 50 Pa s at 22 °C laboratory temperature (Mathieu et al., 2008). The use of an uncon-strained fl uid allows for “freer” gravity-driven deformation of the brittle overburden (Roche et al., 2000), in contrast to the use of an elastic balloon (e.g., Martí et al., 1994) or a solid piston (e.g., Ruch et al., 2012).

As the attainable µCT image resolution depends on the object diameter, among other

factors (see below), the analog setup was down-scaled to a feasible size. The analog materials were hence contained within a plastic cylinder of 6.5 cm diameter (Fig. 3), which yielded an average µCT voxel size of 80–84 µm (“CCT12” models) and 110–111 µm (“CCT14” models). This is necessary to image the smallest faults, which may be only two sand grains thick (Kervyn et al., 2010).

The plastic cylinder was fi xed upon a hori-zontal plastic base with a 0.8 cm circular per-foration. A GS body of height 1.5 cm and diameter 2 cm was emplaced within a tempo-rary cylindrical mold upon the plastic base, and was connected to an external GS silo via the basal perforation and a fl exible tube. The mold was surrounded by SP mix and then removed. Following this, SP mix was added until reach-

Cargill sinkhole, Kansas

Inner cylinderOuter cylinder

500

450

400

350

Crater Lake sinkhole, SaskatchewanA C

200

600

1000

SE NW

SE NW

Dep

th in

met

er

Met

er a

.s.l.

SW NE

Dep

th in

met

er

0

50

100

200

50 500Distance in meter

B D

VoidVoid

Gray shale

Red shale

Roof fall rubble

Sand

Salt+ shale

150

500

450

400

350

200

600

1000

Figure 1. Examples of sinkholes and their potential subsurface structure. (A) Crater Lake sinkhole, Saskatchewan, Canada (adapted from Christiansen, 1971). This structure resulted from natural salt dissolution. Gray (near-)horizontal lines de-limit lithological boundaries as interpreted from borehole data. The Sutherland Group marker layer is presented in gray. These indicate that the near-surface sinkhole structure comprises two ring fault sets. a.s.l.—above sea level. (B) Seismic data indicate that the Crater Lake sinkhole overlies a downward-widening overburden column of increased porosity relative to the surrounding undisturbed rock mass (adapted from Gendzwill and Hajnal, 1971). When the surface trace of the outer cylinder is projected down to meet the subsurface structure, as defi ned by seismic refl ectors, an overall hour glass shape can be seen. (C) Cargill sinkhole, Hutchinson, Kansas (from Walters, 1978). This resulted from sudden collapse in 1974 into a subsurface cavity produced over many years previously by salt-solution mining. (D) Subsurface structure of the Cargill sinkhole (adapted from Walters, 1978). Although the near-surface structure as shown in the cross-section is relatively well known from boreholes drilled into the sinkhole after collapse, the deep structure of the collapse column and exact dimen-sions of the subsurface cavity are unknown.

Poppe et al.


ing to a desired height above the GS body and was levelled. Finally, the model was placed on the scanning rotor. Following past works (e.g. Holohan et al., 2011; Roche et al., 2000; Ruch et al., 2012), the main variables explored here were the SP mix’s cohesion and the over-burden’s thickness to diameter ratio T/D (see model descriptions in Table A1).

To enable clearer imaging of deformation structures in the µCT scans, several horizontal garnet sand layers with a thickness of ≤1 mm were interlayered within the SP mix above the GS body. To further improve the imaging of structural offsets in radiography images, the widths of the garnet layers in the direction of the beam were reduced in the CCT14 models; such layers were thus strip-like in form. The garnet sand’s bulk density of 2.28 × 103 ± 0.06 × 103 kg m–3 provides a readily detectable density contrast to the SP mix. Sieved at <250 µm, the garnet sand’s mean grain size (~200 µm) exceeded that of the silica sand (~150 µm). As only thin layers or strips were emplaced, however, there were no signifi cant differences detected between models with or without garnet sand layers and no signifi cant changes in fault dip at SP mix–garnet interfaces.

Edge effects may infl uence the model stress fi eld due to the fi nite size of the experimental setup, as vertical stresses could be redistrib-uted laterally through arch effects to the con-tainer walls (Roche et al., 2000). These can be assumed to be of secondary importance as long as the container diameter is large with respect to the area affected by deformation. The cylinder diameter of 6.5 cm is more than twice the 2 cm diameter of the analog depletion zone, and as such, we regard edge effects in our models to be suffi ciently small.

Depletion was started by lowering the GS silo to slightly below, or to the same level as,

MiyakejimaDolomieu, Piton de la Fournaise

CA Ring faultsurface

Funnel-like crater

Outer ring fault

Wall debris

Inner ring faultWall debris

200 m100 m

500 m

Ring fault

Magmareservoir

Magmadepletion

NS

Magmareservoir

Ringfault

Closedcavity

Wall debris

Magma depletioninto dyke

?

500 m

N N

B D

Figure 2. Examples of pit craters or small calderas and their potential subsurface struc-ture. (A) Dolomieu pit crater, Piton de la Fournaise volcano, La Réunion Island, collapsed during the depletion of a subsurface reservoir in 2007 (adapted from Staudacher et al., 2009). (B) Interpretation of Dolomieu pit crater subsurface structure after the 2007 collapse (adapted from Michon et al., 2007). The lateral intrusion of a dike from the magma reser-voir was evidenced geophysically. Marginal benches within the pit crater indicate several ring fault splays. (C) Miyakejima caldera, during its 2000 collapse (adapted from Geshi et al., 2002). (D) Interpretation of Miyakejima subsurface structure after the 2000 collapse (adapted from Geshi et al., 2002). Magma injection into a lateral dike and several subsur-face cave collapses were evidenced in geophysical data before ring faults reached the surface and formed the caldera. The caldera itself fi lled progressively with debris from wall failures.

17

2

3

4

5

8

2 cm

D

T

6

Figure 3. X-ray tomography setup at the Ghent University Centre for X-ray Tomog-raphy for imaging analog caldera models. 1—X-ray beam source; 2—plastic stand with central perforation and outlet; 3—plas-tic cylindrical container; 4—sand-and-plaster mix; 5—thin garnet sand intercalations; 6—golden syrup (GS) analog fl uid body; 7—external GS container, adaptable in ele-vation; 8—PerkinElmer fl at panel detector; T—overburden thickness; D—GS reservoir diameter.



the model’s plastic base. GS hence fl owed later-ally from the reservoir into the silo. For evapo-rite karst terrains, this is comparable to lateral removal of salt by groundwater fl ow or by salt withdrawal into an adjacent diapir (Ge and Jack-son, 1998). For volcanic terrains, it represents magma withdrawal from a subvolcanic reservoir without any concurrent eruptive or explosive activity in the collapsing depression itself, a sce-nario documented several times in nature (e.g., Hildreth and Fierstein, 2000; Geshi et al., 2002; Michon et al., 2007).

The experimental series is described in Table A1. No direct control was exercised on the depletion volume or rate. Depletion typically lasted 200–900 min, and stopped automatically when the subsiding overburden touched the bottom of the GS body and plugged the out-fl ow pipe.

Model Scaling

To ensure similarity, the physical and mechan-ical properties of our analog models should be downscaled with respect to those of the natural prototypes (Hubbert, 1937). A dimensionless ratio Π* was defi ned for each key physical parameter, where Π* is the ratio of model (Πm) to nature (Πn). The key physical ratios are: typi-cal length, L*; density, ρ*; angle of internal fric-tion, φ*; cohesion, C*; gravity acceleration, g*; viscosity, μ*; and vertical stress, σ* (Table 1).

In terms of scaling the brittle overburden behavior, both the SP mix and natural rock masses behave to a large degree as Mohr-Coulomb materials (Byerlee, 1968; Schellart, 2000). They hence have a linear failure enve-lope defi ned as τ = C + σn × tanφ, where τ is the shear stress in Pa, C is the cohesion in Pa, σn is the normal stress in Pa, and φ is the angle of internal friction in degrees. As they pos-sess the same units, C* = σ* = ρ* × g* × L* = 1.4 × 10–5 (Table 1). A high laboratory-scale rock cohesion of 108 Pa is typically lowered by one or two orders of magnitude at larger rock mass scales, due to large jointing and fracturing

(Schultz, 1996), and so we assume Cn = 107 Pa. For a length ratio L* = 2.5 × 10–5, i.e., 1 cm = ~400 m (Table 1), Cm should hence equal 140 Pa for volcanic and (evaporite) karst rock. The SP mix cohesion of 180 Pa lies fairly close to this value. The angles of internal friction in nature and in the SP mix are approximately the same, and thus φ* ≈ 1.

Scaling of the depletion zone behavior is less straightforward, given the differences in deple-tion zone materials and depletion processes in volcanic and karst terrains. In principle, viscos-ity is scaled through the equation: η* = σ*T*, where T* = L* / V* and V is the time-averaged subsidence velocity (Ge and Jackson, 1998; Holohan et al., 2008). From Vm = 1.4–2.8 × 10–6 m s–1 (~1 cm in 2–4 h) and Vn = 2.3 × 10–4 m s–1 (~20 m per day; e.g., Geshi et al., 2002), the GS viscosity of ηm = 50 Pa s scales up to a natu-ral magma viscosity of ηn ~108 Pa s. This value approaches that of rhyolitic magmas (~105–108 Pa s; Dingwell, 1998) and lies between those of basaltic magmas (~101–103 Pa s; Murase and McBirney, 1973) and rock salt (~1017–1019 Pa s; Ge and Jackson, 1998). The imprecise scaling of viscosity should not result in dramatically different structural outcomes, because brittle deformation of the overburden, the focus of this work, is theoretically time independent (Ge and Jackson, 1998). In addition, although salt disso-lution drives the formation of natural sinkholes, rather than salt withdrawal, a geometric and kinematic analysis by Ge and Jackson (1998) indicates that structural differences between withdrawal- or dissolution-driven collapses should be slight. These premises are ultimately supported by the above-outlined morpho-struc-tural similarities of collapse-related sinkholes, pit craters, and small calderas in nature.

X-Ray Microtomography Methodology

µCT has been used as a non-destructive approach for imaging the internal kinematic development of regional-tectonic analog mod-els since the early 1990s (see Schreurs et al.,

2003). More recently, Kervyn et al. (2010) fi rst applied µCT to analog volcanological models. Imaging of models presented here was carried out at the Ghent University (Belgium) Centre for X-ray Tomography (UGCT; http:// www .ugct .ugent .be; Masschaele et al., 2007; Cnudde and Boone, 2013). For technical specifi cations, see Appendix 2.

µCT is based on the attenuation of X-rays as they pass through a volume of material and yields the local linear attenuation coeffi cient in that material. This coeffi cient depends on the material density and mean atomic number (Kervyn et al., 2010, and references therein). Material thickness in our models is constant. Thus, the attenuation observed in a radiograph, as well as the linear attenuation coeffi cient observed in a voxel of a µCT image, are primarily affected by changes in material density within the SP mix, and by shifts in chemical composition within model zones where, e.g., SP mix comes to replace GS. Den-sity changes arise in space and time in two ways: (1) by using materials of different initial density, and (2) by increasing or decreasing the material volume (i.e., volumetric strain). For instance, fault formation in the models is associated with dilation of granular packing. Consequently, fault-affected material volumes have a lighter gray value on the µCT imagery compared to the sur-rounding material volumes unaffected by fault formation (Panien et al., 2006).

The setup has two limitations. Firstly, a full scan for each model takes slightly less than one hour, during which time no deformation should take place in order not to induce any image noise. Secondly, rotation of the sample is required during scanning. Even at the lowest rotation speed possible, acceleration upon start-ing the rotor can trigger collapse of metastable portions of the models (see below).

Deformation Quantifi cation on µCT Imagery

Unlike a full µCT scan, a radiograph image requires only a short exposure time of 2000 ms

TABLE 1. COMPARISON OF PHYSICAL PARAMETERS IN MODELS AND NATURE

ParameterBulk density, ρ

(kg m–3)Gravity acceleration, g

(m s–2)

Typicallength, L

(m)Stress, σ

(Pa)

Angle of internal friction, φ(degrees)

Cohesion, C0

(Pa)Viscosity, µ

(Pa s)

Πmodel 1560–1750 ~9.8 3 × 10–2 1.6 × 10²–5.5 × 10² 22–25 180–300 50

Πvolcano † 2400 ~9.8 1.2 × 103 2.8 × 107 25–30 107 10–10³

Π*volcano 0.65–0.73 1.0 2.5 × 10–5 1.4 × 10–5–2.0 × 10–5 0.7–1.0 1.8 x 10–5–3.0 × 10–5 0.05–5

Πsinkhole § 2400 ~9.8 0.2 × 10³ 4.7 × 105 25–30 107 1017–1019

Π*sinkhole 0.65–0.73 1.0 1.5 × 10–4 9.8 × 10–4–1.2 × 10–5 0.7–1.0 1.8 × 10–5–3.0 × 10–5 5 × 10–18–5 × 10–16

Π* = Πmodel /Πnature

Note: The calculation of stress and cohesion is explained in the section METHODOLOGY—Model Scaling.†Natural properties of basaltic volcanic rock and basaltic magmas from Lockwood and Hazlett (2010).§Natural properties of carbonate-evaporitic rock from Selby (1993).

Poppe et al.


and no rotation of the sample. The 3D spatial information of the model is projected on a 2D plane, and so a sequence of time-lapse radio-graphs taken every 0.5 min provided a “2.5D” documentation of the model deformation evolu-tion. In addition, a radiograph taken at the start of depletion enabled any deviations from the ideally cylindrical geometry of the GS body, induced by the emplacement and retraction of the temporary mold, to be constrained.

To quantify the velocity evolution of the model, the central point at the base of each gar-net sand layer was tracked through each image in the sequence. In addition, syn-deformation volume changes of certain entities could be estimated through revolution of their outlines in the radiographs, under the assumption that these entities were more or less axisymmetric volumes (see Appendix 3). These entities, which include the total affected overburden, the depression, the subsided overburden column, and the reservoir, are shown in Figure 4.

For complete µCT scans, all data sets were processed in the Octopus software package (Vlassenbroeck et al., 2007) and rendered into 3D by using VGStudioMax software (http:// www .volumegraphics .com). A digital elevation model was then extracted from the fi nal 3D ren-dered model surface by using a LabView user-defi ned interface (http:// www .ni .com). This enabled the calculation of the surface depres-sion’s fi nal volume in ArcMap software (http:// www .esri .com/).

RESULTS

Here we present results from models rep-resenting the two end-member collapse sce-narios mentioned above: (1) near-continuous collapse into a gradually depleting fl uid body; and (2) near-instantaneous collapse into a sub-surface metastable cavity. For model param-eter descriptions, refer to Table A1. In some experiments, radiograph sequences showed how several small cavities formed in an upward-migrating succession, similar to that observed by Ruch et al. (2012). Consequently, these mod-els showed a collapse scenario between the end members. Radiographs taken at drainage onset showed that metastable cavity formation at the lower T/D ratios occurred when GS bodies had a notably convex-upward top surface. This is in line with results of previous studies (e.g., Holo-han et al., 2011), as is the observation that cavity formation occurred in all cases with a combina-tion of highest cohesion and highest T/D ratio (Table A1).

Previous modeling studies (cited in the Intro-duction) have extensively documented the main geometric and kinematic features of collapse.

Consequently, we only briefl y describe such aspects here to contextualize novel observations revealed by µCT analysis, such as: (1) the effects of downward-varying depletion zone geometry on collapse kinematics; (2) structural similari-ties and dissimilarities between the end-member dynamic collapse styles; and (3) the quantifi ed volumetric evolution of the collapse.

For each collapse scenario, we begin by describing the collapse evolution as seen in the radiography sequences. We then present the fi nal collapse structures as observed in full-3D µCT scans, and compare the structural out-comes of each collapse scenario. Finally, we examine the evolution of subsidence rates and collapse volumes during several representa-tive near-continuous collapses, as derived from quantitative radiograph analysis, and quantify the fi nal deformation-related volume changes for both scenarios.

Near-Continuous Collapse into a Gradually Depleted Subsurface Body

This scenario is illustrated and described by the representative models CCT12-12 (T/D ~0.80), CCT14-5 (T/D ~1.2), and CCT14-6 (T/D ~1.2) (Table A1), as each shows aspects of interest par-ticularly well.

Results of Radiograph SequencesAs described in many previous works, early

evolution of collapse involves the formation of a conical deformation zone within the lower two-thirds of the overburden (Fig. 5). This conical

zone was typically enclosed within an outward-dipping ring fault. Garnet sand layers within the deformation zone were slightly down-sagged and their dips increased toward the fault sur-face. The upper section of the overburden sub-sequently collapsed in discrete upward-propa-gating steps, as newer and progressively steeper ring fault surfaces splayed from the older ring fault bounding the lower roof section (see also Burchardt and Walter, 2010). After formation of a surface depression, the initially overhanging ring fault scarp degraded by means of numerous failures of various sizes (see also Geshi et al., 2012). Consequently, the surface depression’s diameter increased, and the retreating ring fault scarp steepened and became near-vertical to inward-inclined (e.g., Fig. 5). Along the trace of the ring fault itself, progressive drag of garnet sand layers formed a tight footwall syncline.

The radiograph sequences in Figure 5 also show some previously unreported structural effects stemming from the initial depletion zone geometry. In the late stages of both models CCT12-12 and CCT14-6, one or more centrally located ring faults (F4 in Fig. 5A, F4 and F5 in Fig. 5B) formed within the previously coher-ently subsiding column. These new faults all dipped outward, but whereas the one in model CCT12-12 had a normal slip sense, those in model CCT14-6 had reverse slip senses. The late-stage formation of these faults and their dif-fering slip senses can be related to whether the overburden column subsided into a downward-widening or downward-narrowing depletion zone. The normal fault in CCT12-12 accommo-

Reservoir /

Subsidedoverburden

Depression

Total

overburdenaffected

Reservoir / DiapirDiapir

Surface

materialBrittle

Surface

materialBrittle

Figure 4. Sketch of volumetric entities within a depletion-induced col-lapsing system as defi ned in the radiograph analysis (see Fig. 9). The lateral outline of the “total affected overburden” column is defi ned on the last radiograph of a radiograph sequence, while its lower limit is defi ned as the reservoir ceiling on the fi rst radiograph.



dated a horizontal extension of the column as it subsided into a markedly downward-widening GS body. Conversely, the new reverse faults in CCT14-6 accommodated a horizontal contrac-tion of the column as it progressed into a mark-edly downward-narrowing GS body.

Results of 3D scansFigures 6 and 7 show the rendered 3D

scans of models CCT12-12 and CCT14-5, the latter’s initial parameters and fi nal struc-ture being very similar to those of CCT14-6. Vertical slices through these models indicate

that collapses of the unstable overhanging ring fault scarp, probably during the scanning process, further changed the shape and diam-eter of the surface depression. In CCT12-12, a secondary near-cylindrical intra-column col-lapse structure (Fig. 6) formed immediately

1 cm

min. 20 min. 60 min. 120

min. 140 min. 180 min. 220

reservoir / diapir

top

collapsingoverburden

depression

F1F1F2F2

F3F3

F4F4F4

F4

Mod

el C

CT1

2-12

min. 2 min. 100 min. 300

min. 600 min. 900

Mod

el C

CT1

4-6

top

depression

1 cm

F1 F2

F3

F5

F1

F2

F3

F5F5

F4

collapsingoverburden

reservoir / diapir wetting

aureole

A

B

C

100 min0

50 min0

300 min0

1

2

3

2

Figure 5. Time-lapse radio-graphs of models undergoing gradual depletion-induced col-lapse. Dark and light gray values represent respectively dense and less dense materials (see Kervyn et al., 2010). The model surface and ring faults are shown by black dashed lines. (A) Model CCT12-12, with ratio of over-burden thickness to syrup res-ervoir diameter (T/D) ~0.8. Images were acquired respec-tively 20, 60, 100, 140, 180, and 220 min after initiation of deple-tion. Note the concave-upward geometry of the reservoir roof, allowing for the development of a secondary, outward-inclined, normal ring fault F4. (B) Model CCT14-6, with T/D ~1.2. Images were acquired respectively 2, 100, 300, 600, and 900 min after initiation of depletion. Note the time for complete depletion here was longer relative to CCT12-12 due to a higher fl uid reservoir. (C) Temporal sequence of out-lines of the collapsing overbur-den column of model CCT14-6, displaying the three main pro-cesses involved in expanding the column: 1—lateral enlarge-ment; 2—downward sub sidence with density decrease, i.e., “bulking”; 3—addition of mate-rial from failure of the surface depression scarp. Note how the lateral inclusion of unaffected brittle material, i.e., process 1, plays a major role in the fi rst 100–200 min, but is very limited afterwards.

Poppe et al.


above the drainage pipe at the very end of the simulation, as the GS withdrew slightly below the plastic cylinder’s base. Also visible in each model are remnants of the initial GS reservoir and a ring-shaped wetting aureole where some of the GS permeated locally into the SP mix.

In general, the 3D collapse structures and morphology in our models agree with those

of previous analog studies: debris fans from depression wall erosion covering the initial topographic surface; an overall hourglass shape from the combination of a funnel-shaped shal-low-level morphology and cone-shaped deeper-level structure; down-sagging of layers close to the collapse-bounding ring faults; and repeated stratigraphy stacks or the break-up of the over-burden column into several distinct blocks (see,

e.g., Roche et al., 2000; Geshi et al., 2012; Ruch et al., 2012).

Importantly, the slices through the 3D scans also illustrate how the collapse geometry seen in any plane of section can vary markedly depend-ing on the horizontal or vertical position of that section. In particular, the further a vertical section lies from the true center of the collapsed region, the more strongly exaggerated the col-

H1H2

H3H4

H3 H4

V1

V1

V2

V3

V4V2V3

V4

Ring Fault

Collapsed column(sagged layers) Wetting aureole

Collapsed column

RingFault

Collapsedcolumn

(sagged)

Topographic margin

Wettingaureole

Intra-columncollapse structure

Reservoir / diapirremnants

Debrisfans

HorizontalSlices

secilSlacitreV

3 cm

2.5 cm

H1Ring Fault (buried)

Topographicmargin

H2Ring Fault

Infill

Intra-columncollapse

RingFault

Mod

el C

CT1

2-12

Figure 6. Three-dimensionally scanned and rendered volume of model CCT12-12 with ratio of overburden thickness to golden syrup reservoir diameter (T/D) ~0.8, with horizontal and vertical cross-sections. Note that here, and in Figures 7 and 8, the dark and light gray values represent less dense and dense materials, respectively, i.e., the inverse of the radiograph gray scale. Note the intra-column collapse above the drainage opening in slice V4, due to post-collapse subsidence of the sand-and-plaster mix within the drainage tube.



lapse’s hourglass geometry becomes and the more the collapse’s true width may be under-estimated.

In addition, the 3D scans show that the gray value of the subsided overburden column dif-fers markedly from that of the surrounding, undeformed SP mix. This indicates a density contrast that, in the absence of mass transfer, can be interpreted as arising from volumetric expansion (dilation) of grain packing within the overburden column (see also Kervyn et al., 2010). The radiographs demonstrate that this difference in gray value, and hence volumetric expansion, develops from the onset of collapse (e.g., Fig. 5A). Moreover, sequential tracings of the column growth in model CCT14-6 (Fig. 5C) illustrate that the volumetric expansion there is primarily a result of vertical extension

of the column that occurs progressively through the course of subsidence.

Near-Instantaneous Collapse into a Metastable Cavity

This scenario is described by the representa-tive model CCT14-2 (T/D ~1.25) (Table A1).

Results of Radiography SequenceAs in the cases of near-continuous collapse,

collapse began with development of a coni-cal deformation zone in the lower part of the overburden (Fig. 8A). However, the conical deformation zone developed into an overbur-den block that detached from the overlying brittle material and subsided coherently into the depleting GS body. Consequently, a subsurface

cavity formed above the block and grew down-ward as the block subsided. The cavity remained stable until the end of GS depletion.

Results of 3D ScanAcceleration at the onset of rotation for 3D

µCT scanning was insuffi cient to trigger col-lapse in this case, but shaking the model cylin-der only very slightly after scanning was suf-fi cient. Consequently, 3D scans of the model could be made before (Fig. 8B) and after (Fig. 8C) a “dynamically triggered” collapse of the cavity roof.

The pre-collapse 3D scan shows that the lower part of this cavity coincided with the former location of the GS body (Fig. 8B). The upper part of the cavity lies within the overburden, where upward propagation of collapse halted

H1

H2H3

H4

H1 H2 H3 H4

V1

V1

V2

V3

V2V3

Ring fault (buried) Ring fault

Collapsed column (sagged)

Ring Fault

Collapsed column(sagged layers)

Wetting aureole

Collapsedcolumn

Ringfault

Collapsedcolumn

(sagged)Topographic margin

Wettingaureole

Reservoir / diapirremnants

Debrisfans

HorizontalSlices

secilSlacitreV

Topographicmargin

3 cm

5 cm

Mod

el C

CT1

4-5

Topographic margin

Ringfault

Wettingaureole

Preserved garnetsand strips

Figure 7. Three-dimensionally (3D) scanned and rendered volume of model CCT14-5, with ratio of overburden thickness to golden syrup reservoir diameter (T/D) ~1.2, with horizontal and vertical cross-sections. The collapse evolution and fi nal structure is very similar to the one of model CCT14-6, of which no 3D scan is available (Table A1). Note the overall preserva-tion of sand-and-plaster mix–garnet sand stratifi cation.

Poppe et al.


about halfway between the reservoir ceiling and the surface. Radiographs illustrate that model CCT14-2 had an initially fl at-topped GS body. Furthermore, both the radiographs and the 3D scan show clearly that a ~1–2-mm-thick GS–SP mix wetting aureole formed initially around the GS body itself, and later detached from the

un affected SP mix. The cavity’s stability is there-fore a consequence of neither an arched reservoir geometry nor any increase in cohesion caused by the local wetting. Instead, the cavity likely formed spontaneously, and its roof remained self-supporting under the appropriate combina-tion of high T/D ratio and high cohesion.

The post-collapse 3D scan (Fig. 8C) exhibits an overall collapse geometry that has a similar hourglass shape to that seen in the near-contin-uous collapses. Consequently, and although not shown here for brevity, the points made above on how the collapse geometry and dimensions in section view depend strongly on the plane of section’s position with respect to the collapse center also pertain to the cases of near-instan-taneous collapse into a large cavity. In addition, the gray value of the collapsed column is again markedly different from that of the surrounding unaffected SP mix, and so indicates a collapse-related volumetric expansion. Importantly, and although a remnant pre-collapse stratigraphy is preserved within it, the upper part of the over-burden column that collapsed en mass into the cavity is much more structurally disturbed on a small scale (Fig. 8C) than in the near-continuous collapses (compare with Fig. 7 in particular).

Quantitative Analysis of Near-Continuous Collapse

Vertical subsidence rates of garnet sand levels and the reservoir–SP mix interface were recorded for model CCT14-6 (Fig. 9A). The volumes of the GS body, collapsed SP mix col-umn, and depression were also tracked through time (Fig. 9B). The evolution of collapse veloc-ity and volume in this and in several other ana-lyzed models (e.g., CCT12-8, CCT12-12, and CCT14-4), whose results are not shown for brevity, are quite similar, and may be divided into a minimum of three phases.

Phase 1Phase 1 (pre–surface collapse) is character-

ized by an upward-propagating zone of elevated subsidence velocity and rapid increase in col-lapsed column volume. This refl ects the upward propagation of the column-bounding ring fault(s) (Figs. 5A, 5B). Because deformation is confi ned to the subsurface during this phase, the model top surfaces remained at a constant level, and there were hence no surface depressions.

Phase 2Phase 2 (post–surface collapse) is marked

by initially high subsidence rates down the whole column, with periodic accelerations affecting mainly its upper part. The collapsed overburden column continues to grow, and depression volume begins to increase. These changes refl ect the rapid collapse of the upper-most part of the overburden and the formation of a depression at the surface. With time, sub-sidence velocities decrease along the whole column length, although sporadic accelerations are still seen at different levels. Depression and

A

4 cm

B Pre-collapse

Cavity

V

5 cm

C Post-collapse

Depression

Wetting aureole (collapsed)

Peak of roof block

Coherentroof block

L1

L2L3

L4

Coherent roof block

Outlineof latercollapse

Outline ofpre-collapsecavity

L1

L2

L3

L4 Highlydisrupted roof material

During depletion

Initial

Cavity

Cavityoutline

Initial depletionzone outline

Peak of roofblock

Coherentroof block

Peak of roofblock

Wetting aureole (collapsed)

Intermediate

Final

Reservoir / diapir

Mod

el C

CT1

4-2

Reservoir /diapir remnant

Figure 8. Evolution of collapse into a major subsurface metastable cavity in model CCT14-2. (A) Time-lapse radiographs at the beginning, halfway during, and after golden syrup depletion. A roof block detached above the reservoir ceiling along a bell-shaped rupture plane, and subsided coherently during depletion. Note in the fi nal radio graph how the wetting aureole also collapsed; thus, the roof above the cavity is self-supporting and not reliant on the wetting aureole for stability. (B) Central vertical slice of the three-dimensionally (3D) scanned and rendered volume of the metastable cavity prior to trig-gered collapse. The apex of the cavity lies about halfway between the initial reservoir ceiling and the model surface. (C) Central vertical slice of the 3D scanned and rendered volume of the overburden collapsed into the cavity space. The coherent roof block is still observed in the bottom part of the column, and the layering of the collapsed roof is highly disrupted if compared to results from more gradual collapse models (Figs. 6 and 7).



column volumetric growth trends seem more closely linked to depletion rate during this sec-ond phase (Fig. 9B).

Phase 3Phase 3 (post–surface settling) is marked by

very low to no central subsidence and by even-

tual tapering off and fi nal cessation of growth of the depression and column, while the GS deple-tion also tapers off (Fig. 9B). In this last phase, the central part of the subsiding overburden col-umn has met the base of the GS body, ending through-going subsidence of the column’s top surface and growth of the depression.

The fi nal depression volumes are substan-tially smaller than their related depletion vol-umes (Fig. 9B). For CCT12-12, the fi nal “pla-teau” value of the estimated depression volume is within error of the fi nal 3D-defi ned depression volume of 1180 ± 20 mm3, and thus our volume estimates on radiographs may be considered as reliable within error.

Table 2 reports the quantifi ed volumes for six representative models. In all models, differences between depleted GS volumes and fi nal surface depression volumes are on average 39%, with a minimum of 28% ± 9% and a maximum of 51% ± 7%. On the other hand, fi nal overburden column volumes are substantially greater than the respective initial volumes. Final column volume values, determined at the last radio-graph, are on average 23% larger than the ini-tial volumes of the affected overburden before subsidence, with a minimum of 10% ± 10% and a maximum of 40% ± 13%. These effects are illustrated by model CCT14-6, where the fi nal depression volume is 30% ± 9% smaller than the depleted volume and the fi nal affected over-burden column increased 17% ± 11% in volume compared to the initial volume of the affected overburden before subsidence (Fig. 9B). The surface depression volume being substantially less than the depletion volume is thus accounted for by volumetric expansion of the column.

DISCUSSION

The Use of µCT for Imaging Analog Depletion-Induced Collapses

A key advantage of µCT is that it is non-destructive (Schreurs et al., 2003; Cnudde and Boone, 2013, and references therein), and so 3D model scans can be sliced in any direction and revisited at any time. The 3D geometry of fault surfaces can hence be assessed in a spa-tially complete manner, in contrast to extrapo-lation between multiple but spatially restricted planes of cross-section when sectioning wetted models. The µCT shows clearly how the outcrop pattern of a collapse structure, in map view or in cross-section, can vary dramatically depending on the depth and lateral position of the plane of section (Figs. 6 and 7). This is because collapse is accommodated by a system of annular faults whose geometry is highly variable in three dimensions. Consequently, structural or topo-graphic dimensions given for ancient eroded sinkholes, pit craters, or small calderas must be treated with caution.

A second advantage is that radiographs enable a check on the pre-collapse geometry of a fl uid depletion zone, which can often devi-

Vert

ical

dis

pla

cem

ent

(mm

)Vo

lum

e (m

m³)

A Phase

1

Phase

2

Phase

3

0 100 300 500 700 900

2.10

6.10

10.10

14.10

VerticalsubsidencerateTopographical surface

Reservoir ceiling

0.20

0.00

0.10(mm/min)

overburden,initialV

V

V

Vovb

dep

res

Time (min) Subsidence endStoping

3

3

3

3

B

–10

–20

–30

–40

Figure 9. Quantifi ed subsidence rates and volume evolution of model CCT14-6 (ratio of overburden thickness to golden syrup reservoir diameter (T/D) ~1.2), representing near-continuous collapse into a gradually depleting body. The three designated collapse stages are discussed in the text. (A) Vertical subsidence rate interpolated from measurements of the vertical positions of fi ve garnet sand layers and the reservoir ceiling on 2.5-min-spaced radiographs. (B) vol-ume changes for the depression (“dep,” blue), overburden (“ovb,” green) and reservoir (“res,” orange), as calculated from 5-min-spaced radiographs. Errors are designated by shaded areas. No fi nal topographic depression volume could be measured as a three-dimensional computed X-ray microtomography scan failed techni-cally. Note the ~17% difference between initial and fi nal affected overburden volume, refl ecting brittle material volumetric expan-sion (i.e., dilation or bulking) during collapse.

Poppe et al.


ate from that planned (see also Ge and Jackson, 1998). Here, radiographs reveal that differing late-stage structures formed within the column can be related to whether the depletion zone (i.e., magma reservoir or salt diapir) is markedly downward widening or downward narrowing (Fig. 5), rather than ideally cylindrical. Such structural effects are undocumented in other modeling studies, but could manifest themselves in nature under similar geometrical conditions.

Thirdly, radiograph sequences provide a high-temporal-resolution “2.5D” insight into subsurface model development as generated in a true 3D space. It is thereby unnecessary either to stop and cross-section multiple models run to different deformation stages (e.g., Roche et al., 2000) or to construct a model against a glass pane with attendant edge effects (e.g., Geyer et al., 2006; Burchardt and Walter, 2010; Ruch et al., 2012). A limitation of radiograph images is that the central collapsed zone is overprinted by the projection of unaffected material located between the source and the detector. This study hence shows how such µCT imagery, even if limited scanning time and costs require careful beforehand planning, can be used for quantita-tive analyses of analog model evolution, a main area of technical development in recent years (e.g., Burchardt and Walter, 2010; Ruch et al., 2012; Holohan et al., 2013). These analyses are discussed further below.

Near-Continuous versus Near-Instantaneous Collapse: Morphological and Structural Features

The analog models shown here reproduce many of the main structural and morphological features observed in or inferred for the collapse of sinkholes, pit craters, and small calderas in nature. Structures include steeply dipping normal or reverse ring faults, ephemeral cavi-ties, and sagged strata. Morphological features include overhanging to cliffed depression boundaries, intra-depression debris fans, and an overall hourglass geometry from a combination of cone-like and funnel-like shapes of the lower and upper sections of the collapsed overburden column (e.g., Figs. 1A, 2A, and 2B).

As shown by previous studies, the conical lower section geometry develops during the pro-gressive upward failure of the overburden along multiple conical ring fault splays, with the even-tual establishment of a single ring fault that cuts through to the surface (see also Roche et al., 2000; Ruch et al., 2012; Geshi et al., 2012).

The funnel-like upper section geometry develops as the hanging wall of the conical ring fault system becomes gravitationally unstable.

Failure of the hanging wall, either by normal faulting (e.g., Martí et al., 1994; Roche et al., 2000) or by mass wasting (e.g., Roche et al., 2001; Geshi et al., 2012; this study), ultimately produces an inward-inclined annular scarp at the surface (Figs. 1 and 2). Our study further shows that these morphological and structural features develop in both end-member scenarios of: (1) near-continuous collapse into a slowly depleting body; and (2) near-instantaneous col-lapse into a large, metastable cavity.

Subsurface cavities are known or inferred to have developed prior to the formation of many sinkholes, pit craters, and small calderas. Exam-ples in karst terrains include natural caves and caverns and related sinkholes in the Kunguras-kaya cave complex, Russia (Andrejchuk and Klimchouk, 2002), in the Delaware Basin gyp-sum deposits of Texas and New Mexico (John-son, 2005, and references therein), and in and around the city of Hamburg, Germany (Dahm et al., 2011). There are also numerous examples of collapses into cavities formed by manmade salt dissolution, such as the 1974 Cargill col-lapse in Kansas (Fig. 1C, 1D) and the 1980 Wink Sink collapse in Texas (Johnson, 1989). Examples in volcanic terrains include cavities with arched ceilings exposed in pit crater chains on Hawaii (Okubo and Martel, 1998) and in the scarp of the 2002 pit crater collapse at Piton de la Fournaise (Carter et al., 2007, their fi gure 9). At Miyakejima volcano (Figs. 2C, 2D), seismic, gravity, and magnetic data indicated upward migration of a steam-fi lled cavity toward the volcano summit over the course of ~12 days before a caldera developed at surface (Geshi et al., 2002, and references therein).

Previous analog or numerical collapse stud-ies that produced cavities (e.g., Roche et al., 2001; Holohan et al., 2011; Ruch et al., 2012) have simulated an intermediate behavior to the abovementioned end members, whereby several, relatively small “metastable” cavities open and close at the top of the upward-grow-ing collapse column. The collapsed over burden column in these cases typically comprises an assemblage of structurally disrupted blocks (e.g., Roche et al., 2001). This intermediate behavior was also observed in some of our mod-els with relatively lower cohesions, and is prob-ably refl ective of natural collapses such as that at Miyakejima.

Complementary to this, our highest-cohesion models also include the end member of near-instantaneous collapse of most of the roof into a single, relatively large, subsurface cavity. Here, coherent detachment of the lowermost part of the overburden gave rise to a stable compressive arch-like geometry in the remainder of the over-burden, such that further upward growth of the

TAB

LE 2

. QU

AN

TIF

IED

AF

FE

CT

ED

OV

ER

BU

RD

EN

CO

LUM

N V

OLU

ME

S

Mod

el n

ame

Col

laps

e m

ode

Initi

al v

olum

e of

affe

cted

ov

erbu

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(mm

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Fin

al v

olum

e of

affe

cted

ov

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(mm

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Vol

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row

th

of a

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ed

over

burd

en(m

m³)

Vol

umet

ric g

row

th

of a

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ed

over

burd

en(%

)

Fin

al v

olum

e of

de

pres

sion

(mm

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Fin

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plet

ed fr

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Vol

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mis

mat

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m³)

Vol

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ric

mis

mat

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ver

sus

depl

etio

n(%

)

CC

T12

-8N

ear-

cont

inuo

us15

,059

± 7

5316

,618

± 8

3115

59 ±

158

410

± 1

061

85 ±

310

8574

± 4

2923

89 ±

739

28 ±

9

CC

T12

-12

Nea

r-co

ntin

uous

3138

± 2

0044

05 ±

200

1267

± 4

0040

± 1

311

80 ±

20

2348

± 4

0011

68 ±

420

50 ±

18

CC

T14

-2N

ear-

inst

anta

neou

s13

,784

± 6

8917

,715

± 8

8639

31 ±

157

529

± 1

133

33 ±

167

6793

± 3

4034

60 ±

507

51 ±

7

CC

T14

-4N

ear-

cont

inuo

us14

,915

± 7

4819

,190

± 9

6042

75 ±

170

829

± 1

149

10 ±

246

7287

± 3

6423

77 ±

610

33

± 8

CC

T14

-5N

ear-

cont

inuo

us16

,252

± 8

1317

,904

± 8

9516

52 ±

170

810

± 1

044

60 ±

223

7570

± 3

7931

10 ±

602

41 ±

8

CC

T14

-6N

ear-

cont

inuo

us12

,368

± 6

1814

,493

± 7

2521

25 ±

134

317

± 1

147

93 ±

240

6823

± 3

4120

30 ±

581

30 ±

9



column was prevented. The cavity formed above the detached block instead grew to a large size relative to the remaining overburden. Collapse into the cavity was ultimately “dynamically trig-gered”; a similar mechanism is suspected at sev-eral sinkholes in nature (Walters, 1978; Dahm et al., 2011; Jousset and Rohmer, 2012).

The structure of this end-member collapse differs slightly from the intermediate scenarios seen in the previous studies cited above. On a large scale, the collapsed material formerly overlying the cavity is seemingly coherent, in that stratigraphic order is preserved. On a small scale, however, the material is highly disrupted. These observations are characteristic of other gravity-driven collapse processes that involve the fragmentation of the collapsing mate-rial upon its rapid initial acceleration into an unconfi ned region, such as rockslide avalanches (Glicken, 1996; Shea and van Wyk de Vries, 2008; Thompson et al., 2010).

Evolution of Velocity and Volume During Collapse

Vertical subsidence rates calculated at dis-crete levels inside the collapsing model overbur-den column indicate that even within an appar-ently coherent column, there may be spatially and temporally distinct slip events during model subsidence (Fig. 9A). This observation in a fully 3D medium validates the assumption that simi-lar patterns obtained previously in 2D experi-ments against a glass pane (Ruch et al., 2012) are only minimally affected by related edge effects. In agreement with Ruch et al. (2012), our models suggest that such discrete velocity changes could be a cause of collapse-related earthquakes in nature (cf. Dahm et al., 2011; Shuler et al., 2013). Future analysis and model-ing of collapse-related earthquakes could hence include non-uniform displacements along a down-going overburden column.

Estimations of volume evolution during model collapses reveal that the depletion zone, affected overburden column, and surface depression show partly different, but also partly mirroring, trends of volumetric change in the post–surface collapse phases (Fig. 9B). The depletion zone undergoes near-linear or power-function trends of volume decrease, while the overburden column and surface depression con-versely undergo near-linear or power-function trends of volume increase.

A similar near-linear growth of depression volume was observed during the 2000 collapse of Miyakejima (see Geshi et al., 2002, their fi g-ure 4d). Our models indicate that this relates to a near-linear volumetric depletion of the under-lying reservoir, behavior deduced independently

from analysis of related very-long-period (VLP) seismic signals by Kumagai et al. (2001).

The volumetric growth of the collapse-affected overburden over the three phases takes place via three processes. Firstly, material is added to the column as deformation propagates upward and laterally within the overburden. As seen in the temporal evolution of the outline of the overburden column in Figure 5C, lateral col-umn growth diminishes rapidly and comes to a halt relatively early in phase 2. Secondly, mate-rial within the overburden column undergoes a volumetric expansion, as evidenced by lighter gray values in it than in the surrounding SP mix. Thirdly, material is added as debris derived from the failure of ring fault scarps once the collapse reaches the surface. The synchronous occur-rence of the fi rst and second processes explains the rapid increase in column volume at the onset of collapse in the subsurface (Figs. 5 and 9). The more gradual increase of column volume thereafter is mainly derived from a combination of the second and third processes, of which the second (volumetric expansion) is more domi-nant (Fig. 5C).

The volumetric expansion of collapsed over-burden is well known in studies of mining collapse (e.g., Whittaker and Reddish, 1989) and sinkhole formation (e.g., Andrejchuk and Klimchouk, 2002). This is termed “bulking,” and is particularly prevalent in overburden rock masses of high cohesion. The effect of bulking is seen geophysically as reduced seismic veloci-ties (e.g., Gendzwill and Hajnal, 1971) and potentially also as a negative gravity anomaly (e.g., Paine et al., 2012). Our model results indicate that bulking occurs not only during the initial upward propagation of the overburden deformation (e.g., Andrejchuk and Klimchouk, 2002) but may also continue, albeit to a lesser extent, as an overburden column progressively subsides.

Bulking of the collapse column compen-sates for a substantial portion of the subsurface body’s volumetric depletion. This volumetric compensation, which reached 10%–40% in our models, leads to a depression volume at sur-face that is 28%–51% smaller than the depleted volume at depth. A similar observation is often made for natural pit crater and small caldera collapses, albeit with uncertainties concerning intrusive magma volumes at depth. At Piton de la Fournaise in 2007, for example, 1.0–1.4 × 108 m3 in dense rock equivalent (DRE) of magma was erupted but the fi nal Dolomieu pit crater volume was only 9.6 × 106 m3 (Michon et al., 2007). At Katmai, a slightly larger caldera of ~2.5 km by 4 km, 13.5 km3 of DRE volume of magma was erupted, but the caldera volume was only 8 km3 (Hildreth and Fierstein, 2000).

In addition, Geshi et al. (2012, and references therein) reported values for several other (explo-sive) caldera-forming eruptions that exhibited a similar apparent volume mismatch. As shown by our models, the process of bulking could, perhaps in combination with magma compress-ibility, help explain this longstanding “volume mismatch” problem in volcanic terrains, par-ticularly for small-scale collapses (depression diameter <~2 km).

CONCLUSIONS

This study illustrates a fi rst use of combined “2.5D” and 3D computed X-ray microtomog-raphy (µCT) techniques to quantitatively study analog models of small scale (<2 km diameter), gravity-driven collapses, induced by deple-tion of a subsurface body. Two end-member scenarios were actively investigated: (1) near-continuous collapse into a gradually depleting subsurface body, and (2) near-instantaneous col-lapse into a subsurface cavity. The main fi ndings of this work are as follows:

1. Time-lapse radiographs show that late-stage structures formed during near-continuous col-lapse of an overburden column into a slowly depleting subsurface body depend on downward changes in the body’s geometry. Within the sub-siding overburden column, late-stage outward-inclined normal faults may form if the body widens downward; late-stage outward-inclined reverse faults may form if the body narrows downward.

2. 3D X-ray µCT scans of models represent-ing both end-member scenarios reveal that the fi nal collapse morphology and geometry of both end members are quite similar. The main difference is a greater small-scale disruption of the overburden during near-instantaneous collapse into a large cavity, probably resulting from large acceleration and free fall upon col-lapse. The susceptibility of both volcanic and evaporite terrains to such cavity formation and near-instantaneous collapse is to be considered for hazard-risk assessment purposes.

3. Subsidence velocity analysis of the time-lapse radiographs reveals subtle differential movements of discrete sections of even appar-ently coherently collapsing overburden col-umns formed in 3D space. This supports similar results from a recent study made in quasi-2D space (Ruch et al., 2012). Future modeling of collapse-related earthquake sequences should hence consider non-uniform displacements along a down-going column.

4. The density reduction in the collapsing overburden occurs from its volumetric expan-sion, which accounted for 10%–40% of expanded brittle material volume in our models.

Poppe et al.


This phenomenon, termed “bulking” in studies of mining and sinkhole collapses, occurs not only at the onset of collapse but also during pro-gressive subsidence of the overburden column. Final surface depression volumes in our mod-els were consequently 28%–51% lower than the volumes depleted from the subsurface fl uid reservoir. For small-scale (<2 km diameter) caldera and pit crater collapses, this volumet-ric increase of the overburden column may—at least partially—play a role in producing the long-standing “volume mismatch” observed at several volcanoes, whereby the volume depleted from the subsurface body exceeds the volume of the depression formed at surface, or Vdepletion > Vdepression.

ACKNOWLEDGMENTS

This work is based upon an Master of Science thesis conducted by SP at Ghent University. EPH acknowledges support from GFZ-Potsdam and from a Marie Curie International Mobility Fellowship co-funded by Marie Curie Action and the Irish Research Council. EP acknowledges the Special Research Fund of Ghent University (BOF) for fi nancial support (GOA01GO1008). MK acknowledges the support of the Flemish Fund for Scientifi c Research (FWO-Flanders) for developing the volcano analog lab at VUB. Pieter Vanderniepen and Matthieu Boone and the entire UGCT team are greatly acknowledged for technical support, scanning, and initial data set reconstruction. We thank P. Jacobs and A. Delcamp for commenting on the original work and the devel-opment of our analog models, and for enthusiastic moral support. Reviews of the original manuscript by Shan de Silva, Olivier Roche, Nobuo Geshi, and two anonymous reviewers helped to considerably improve the fi nal version of this paper.

APPENDIX 2. TECHNICAL SPECIFICATIONS OF THE X-RAY MICROTOMOGRAPHY SCANNING SETUP

µCT imaging of the models was carried out at the Ghent University Centre for X-ray Tomography (UGCT; http:// www .ugct .ugent .be; Masschaele et al., 2007) with the following technical specifi cations. The beam source was a high-power directional tube head, used at a voltage of 150 kV and a tube current of 400 µA target current. This resulted in an effective target power of 60 W. To avoid beam hardening ef-fects, 3 mm Al fi ltered the X-ray beam. A PerkinElmer XRD 1620 CN3 CS a-Si fl at panel detector with CsI screen was placed vertically behind the models, al-lowing an image width of 2048 pixels of 200 × 200 µm2. While the model rotated, 1200 projection images were acquired, where each projection was one frame with 2000 ms exposure time. A magnifi cation of 4.74 was obtained through a source-to-object dis-tance of 282 mm and a source-to-detector distance of 1338 mm. The detector was used in binning 2 mode, which means that four pixels are averaged out in one pixel, dividing the amount of pixels in the height and in the width by two. Such a binning method comes at the expense of the spatial resolution, but attenuates noise. The corresponding voxel size is 80–84 µm, which yields a much better resolution than in medical CT scanners. For the CCT14 models, a Varian Paxscan a-Si fl at panel detector with CsI screen was placed horizontally behind the models, allowing image di-mensions of 2000 × 1600 pixels of 127 × 127 µm2. A magnifi cation of 2.30, through a source-to-object dis-tance of 375.77 mm and source-to-detector distance of 862.8 mm, combined with binning 2 mode, yielded a corresponding voxel size of 110–111 µm.

APPENDIX 3. METHOD FOR VOLUME ESTIMATION FROM RADIOGRAPHS

Syn-deformation volume changes of specifi c enti-ties could be estimated through an axisymmetric revolution of a half polygon defi ned by the outline

of the object of interest in a radiography image. It is acknowledged that the assumption in this procedure that all structural entities are axisymmetric volumes may lead to signifi cant error in some cases. The edge of the area of each entity was tracked through each radiograph in a sequence by defi ning a polygon, the node coordinates of which were recorded. After defi n-ing the central gravity axis of each polygon for each object of interest (e.g., depression or overburden col-umn) in one model, polygons were split into left and right half polygons. The area A of the half polygon (in pixels) was then calculated from the so-called “Shoe-lace” or “Gauss’s area” formula:

A = 12

xi yi+1i=1

n−1∑ + xn y1 − xi+1i=1

n−1∑ − x1yn . (1)

The x-coordinate of the centroid of the half polygon Cx is then defi ned by:

Cx = xi + xi+1( )i=1

n−1∑ xi yi+1 + xi+1yi( ) 6A, (2)

where xi and yi represent the respective x- and y-coordinates of each half-polygon node. The volume V described by revolving the half polygon about the axis is defi ned by the Guldinus theorem as V = A × 2Π × d, where d is the horizontal distance between centroid and revolving axis: d = Cx – Xaxis, where the latter is the revolving axis’s x-coordinate. Finally, the two re-sulting half-polygon volumes (in voxels) for each time step were averaged and converted to volumetric units by using the voxel size specifi c to each model.

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APPENDIX 1.

TABLE A1. DESCRIPTION OF THE EXPERIMENTAL SERIES

Model name

Brittle overburden thickness, T

(cm)

Brittle cohesion, τ0

(Pa)

GS reservoir height(cm)

GS reservoir diameter, D

(cm)

Roof aspect

ratio, ~T/D Roof shape Collapse mode† Comments§

CCT12-1 2.5 ~180 2.0 3.0 0.8 Curved Near-instantaneous No radiograph series, no 3D scan

CCT12-2 1.5 ~180 2.0 3.0 0.5 Curved Near-instantaneous No time-lapse radiographsCCT12-3 2.0 ~180 2.0 3.0 0.65 Horizontal Near-continuous No time-lapse radiographsCCT12-4 2.5 ~180 1.9 2.0 1.25 Curved Near-instantaneous No time-lapse radiographsCCT12-5 1.5 ~180 1.5 2.6 0.6 Horizontal Near-continuous No time-lapse radiographsCCT12-6 1.5 ~180 2.0 2.0 0.75 Horizontal Near-continuous No time-lapse radiographsCCT12-7 2.5 ~180 1.5 3.0 0.8 Horizontal Near-continuous No time-lapse radiographsCCT12-8 2.8 ~180 2.2 2.4 1.2 Gently curved Near-continuous –CCT12-11 1.5 ~180 0.9 2.2 0.7 Horizontal Near-continuous No time-lapse radiographs,

no 3D scanCCT12-12 1.6 ~180 0.9 2.0 0.8 Curved Near-continuous –CCT14-1 3.4 ~300 2.0 2.7 1.25 Horizontal Near-instantaneous Radiographs only fi rst

45 minCCT14-2 3.1 ~300 2.0 2.5 1.25 Horizontal Near-instantaneous Radiographs only fi rst

75 minCCT14-3 2.7 ~300 2.0 2.5 1.1 Gently curved Near-instantaneous No 3D scanCCT14-4 3.0 ~180 2.0 2.5 1.2 Horizontal Near-continuous –CCT14-5 3.0 ~180 1.8 2.5 1.2 Horizontal Near-continuous –CCT14-6 2.6 ~180 1.9 2.15 1.2 Horizontal Near-continuous No 3D scan

Note: Tests or failed models are not included; radiographs were acquired systematically from CCT12-8 onward, but the X-ray source sometimes stopped inmid-experiment due to unidentified technical reasons. GS—golden syrup; 3D—three-dimensional.

†Near-instantaneous collapse into a metastable subsurface cavity versus near-continuous collapse through to the surface.§An initial and fi nal radiograph were acquired in most cases, even for models for which no time-lapse series was available.



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SCIENCE EDITOR: CHRISTIAN KOEBERL

ASSOCIATE EDITOR: SHANAKA DE SILVA

MANUSCRIPT RECEIVED 6 SEPTEMBER 2013REVISED MANUSCRIPT RECEIVED 4 JULY 2014MANUSCRIPT ACCEPTED 29 JULY 2014

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Sinkholes, pit craters, and small calderas: Analog models of depletion induced collapse analyzed by...

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