Numerical modelling of the displacement and deformation of ... · were deposited in a strike-slip setting and later in a period of relative tectonic quiescence with broad, regional

Geological Society, London, Special Publications

doi: 10.1144/SP363.24p503-520.

2012, v.363;Geological Society, London, Special Publications Urai and Peter A. KuklaShiyuan Li, Steffen Abe, Lars Reuning, Stephan Becker, Janos L. Basintectonics: A case study from the South Oman Saltdeformation of embedded rock bodies during salt Numerical modelling of the displacement and

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Numerical modelling of the displacement and deformation of

embedded rock bodies during salt tectonics: A case study from

the South Oman Salt Basin

SHIYUAN LI1, STEFFEN ABE1*, LARS REUNING2, STEPHAN BECKER2,

JANOS L. URAI1,3 & PETER A. KUKLA2

1Structural Geology, Tectonics and Geomechanics, RWTH Aachen University,

Lochnerstrasse 4-20, D-52056 Aachen, Germany2Geologisches Institut, RWTH Aachen University, Wullnerstrasse 2, D-52056, Germany

3Department of Applied Geoscience German University of Technology in Oman (GUtech),

Way No. 36, Building No. 331, North Ghubrah, Sultanate of Oman

*Corresponding author (e-mail: [email protected])

Abstract: Large rock inclusions are embedded in many salt bodies and these respond to the move-ments of the salt in a variety of ways including displacement, folding and fracturing. One mode ofsalt tectonics is downbuilding, whereby the top of a developing diapir remains in the same verticalposition while the surrounding overburden sediments subside. We investigate how the differentialdisplacement of the top salt surface caused by downbuilding induces ductile salt flow and the associ-ated deformation of brittle stringers by an iterative procedure to detect and simulate conditions forthe onset of localization of deformation in a finite element model, in combination with adaptiveremeshing. The model set-up is constrained by observations from the South Oman Salt Basin,where large carbonate bodies encased in salt form substantial hydrocarbon plays. The modelshows that, depending on the displacement of the top salt, the stringers can break very soon afterthe onset of salt tectonics and can deform in different ways. If extension along the inclusion dom-inates, stringers are broken by tensile fractures and boudinage at relatively shallow depth. Spacing ofthe boudin–bounding faults can be as close as 3–4 times the thickness of the stringer. In contrast,salt shortening along the inclusion may lead to folding or thrusting of stringers.

Large rock inclusions encased in salt (so-calledrafts, floaters or stringers) are of broad economicinterest. Understanding when and how those rockbodies break and redistribute fluids is of practicalimportance because the inclusions can contain over-pressured fluids or hydrocarbons; as well as beingexploration targets, they also pose drilling hazards(Williamson et al. 1997; Koyi 2001; Al-Siyabi2005; Schoenherr et al. 2007a, 2008; Kukla et al.2011). In addition, stringers are also relevant forthe planning and operation of underground cavernsand waste disposal facilities. The influence ofstringer deformation is of importance in understand-ing the diagenetic evolution and hence reservoirproperties of stringer plays (Schoenherr et al.2008; Reuning et al. 2009). The study of stringershas also contributed to our understanding of theinternal deformation mechanisms in salt diapirs(Talbot & Jackson 1987, 1989; Talbot & Weinberg1992; Koyi 2001; Chemia et al. 2008). Stringergeometries and associated deformation werestudied in surface-piercing salt domes (Kent 1979;Reuning et al. 2009) and in mining galleries in salt

(Richter-Bernburg 1980; Talbot & Jackson 1987;Geluk 1995; Behlau & Mingerzahn 2001). Addi-tionally, recent improvements in seismic imagingallow the visualization and analysis of large-scale3D stringer geometries (van Gent et al. 2011;Strozyk et al. 2012). All these studies reveal highlycomplex stringer geometries such as open to iso-clinal folding, shear zones and boudinage over awide range of scales, and give valuable insightsinto the processes occurring during salt tectonics.However, most salt structures have undergone acombination of passive, reactive and active phasesof salt tectonics (Mohr et al. 2005; Warren 2006;Reuning et al. 2009) which complicates the interpre-tation of stringer geometries. As well as the com-plexity of the internal structural geology, extensivedissolution by groundwater can lead to a structuralreconfiguration of the inclusions (Talbot & Jackson1987; Weinberg 1993). The interpretation of theearly structural evolution of brittle layers in saltgiants (Hubscher et al. 2007) hence remains difficult.

Results from analogue modelling have shownthat stringers form in the ductile salt mass from

From: Alsop, G. I., Archer, S. G., Hartley, A. J., Grant, N. T. & Hodgkinson, R. (eds) 2012. Salt Tectonics, Sedimentsand Prospectivity. Geological Society, London, Special Publications, 363, 503–520. http://dx.doi.org/10.1144/SP363.24# The Geological Society of London 2012. Publishing disclaimer: www.geolsoc.org.uk/pub_ethics



the earliest stages until the end of halokinesis(Escher & Kuenen 1929; Zulauf & Zulauf 2005;Callot et al. 2006; Zulauf et al. 2009). During thisevolution, the embedded inclusions undergo stretch-ing, leading to boudinage and rotation. It was alsosuggested (Koyi 2001) that the inclusions sink inthe diapir due to negative buoyancy, moving down-wards as soon as diapir growth and salt supply arenot fast enough to compensate for this.

In numerical models, salt is often treated as rela-tively homogeneous material. The few studies thathave addressed the evolution of stringers withinthe salt focus on the rise and fall of viscous stringersduring salt diapir growth (Weinberg 1993; Koyi2001; Chemia et al. 2008). To our knowledge, nonumerical study has investigated the brittle defor-mation of individual stringers during the initialphases of salt tectonics.

The aim of this study is to report the first resultsof a study aimed at contributing to our understand-ing of brittle stringer dynamics during downbuild-ing. We use the finite element method (FEM) tomodel the deformation and breaking of brittlelayers embedded in ductile, deforming salt bodies.

Geological setting

The study area is situated in the southwestern part ofthe South Oman Salt Basin (SOSB), in the south ofthe Sultanate of Oman (Fig. 1). The SOSB is lateNeoproterozoic–Early Cambrian in age and is partof a salt giant consisting of a belt of evaporiticbasins from Oman to Iran (Hormuz Salt) and Paki-stan (Salt Range) and further to the East Himalaya(Mattes & Conway Morris 1990; Allen 2007).

The SOSB is an unusual petroleum-producingdomain. Self-charging carbonate stringers embed-ded into the salt of the SOSB represent a uniqueintra-salt petroleum system with substantial hydro-carbon accumulations, which has been successfullyexplored in recent years (Al-Siyabi 2005; Schoen-herr et al. 2008, Grosjean et al. 2009). However,predicting subsurface stringer geometries and reser-voir quality remains a major challenge. The SOSBstrikes NE–SW and has a lateral extension of c.400 × 150 km. Its western margin is formed bythe Western Deformation Front (Fig. 1), a structu-rally complex zone with transpressional character(Immerz et al. 2000). The eastern margin is theso-called Eastern Flank (Fig. 1), a structural high(Amthor et al. 2005).

The eastwards-thinning basin fill overlies anEarly Neoproterozoic crystalline basement and com-prises Late Neoproterozoic–Recent sediments witha total thickness of up to 7 km (Heward 1990;Amthor et al. 2005; Al-Barwani & McClay 2008).Oldest deposits of the basin are the Neoproterozoic–

Early Cambrian age (c. 800–530 Ma) Huqf Super-group (Gorin et al. 1982; Hughes–Clarke 1988;Burns & Matter 1993; Loosveld et al. 1996;Brasier et al. 2000; Bowring et al. 2007). The lowerpart of the Huqf Supergroup comprises continentalsiliciclastics and marine ramp carbonates of theAbu Mahara and Nafun Group (Fig. 2), whichwere deposited in a strike-slip setting and later ina period of relative tectonic quiescence with broad,regional subsidence (Amthor et al. 2005). Concomi-tant to the deposition of the terminal Nafun Groupsediments (c. 550.5–547.36 Ma, Fig. 2), an upliftof large basement blocks led to segmentation ofthe basin and to the formation of fault-boundedsub-basins (Immerz et al. 2000; Grotzinger 2002;Amthor et al. 2005). Basin restriction during Edia-caran times led to first Ara-salt sedimentationwithin these fault-bounded sub-basins at veryshallow water depths (Mattes & Conway Morris1990; Schroder et al. 2003; Al-Siyabi 2005). Periodsof differential subsidence in the SOSB led to trans-gressive–highstand conditions which caused growthof isolated carbonate platforms. Six carbonate to eva-porite (rock salt, gypsum) sequences of the Ara Groupwere deposited in total, termed A0/A1 to A6 frombottom to top (Mattes & Conway Morris 1990;Fig. 2). Bromine geochemistry of the Ara Salt (Schro-der et al. 2003; Schoenherr et al. 2008) and marinefossils in the 20–200 m thick carbonate intervals(Amthor et al. 2003) clearly indicate a seawatersource for the Ara evaporates.

Subsequent deposition of continental siliciclas-tics on the mobile Ara Salt led to strong salt tectonicmovements. Differential loading formed 5–15 kmwide clastic pods and salt diapirs, which led tofolding and fragmentation of the carbonate platformsinto isolated stringers floating in the Ara Salt. Earlystages of halokinesis started with deposition of thedirectly overlying Nimr Group, derived from theuplifted basement high in the Western DeformationFront and the Ghudun High. This early halokinesiswas controlled by pre-existing faults and formedasymmetric salt ridges and minibasins (Al-Barwani& McClay 2008). During deposition of the massiveAmin Formation the depositional environmentchanged from proximal alluvial fans to a more distalfluvial-dominated environment, whereas the existingsalt ridges acted as barriers until salt welds wereformed (Hughes-Clark 1988; Droste 1997). Furthersalt ridge rises and/or shifts of accommodationspace during deposition of the Mahwis Formationled to the formation of several listric growth faultsin the post-salt deposits. Salt dissolution during theMahwis and Lower Ghudun period formed small1–2 km wide sub-basins on the crest of selectedsalt ridges. The end of salt tectonics is marked bythe Lower Ghudun group, because salt ridge risecould not keep pace with the rapid sedimentation of

S. LI ET AL.504



Fig. 1. Overview map of the Late Ediacaran to Early Cambrian salt basins of Interior Oman (modified from Schroderet al. 2005; Reuning et al. 2009, reprinted by permission from GeoArabia). The study area (marked by the yellowsquare) is located in the south-western part of the South Oman Salt Basin. The eastwards-thinning basin with sedimentfill of up to 7 km is bordered to the west by the transpressional Western Deformation Front and to the east by thestructural high of the Eastern Flank.

MODELLING STRINGER DEFORMATION DURING SALT TECTONICS 505



this formation (Al-Barwani & McClay 2008). Exten-sive near-surface dissolution of Ara Salt affectedthe Eastern Flank in particular during the Permo-Carboniferous glaciations, forming the present-dayshape of ‘stacked’ carbonate platforms without sep-arating salt layers (Heward 1990).

During the Carboniferous, reactivated basementfaults led to movement of a number of salt ridgesforming new point-sourced diapirs. This reneweddownbuilding changed into compressional salt dia-pirism during the Cretaceous (Al-Barwani &McClay 2008). This complex sequence of salt tec-tonics led to present-day variable salt thicknessesfrom a few metres up to 2 km in the SOSB.

Salt tectonics in the study area

The salt tectonic evolution of the study area wasstudied from seismic lines supplied by PDO

Exploration (Fig. 3). Here the deposition of theNimr Group on the mobile Ara substrate led toearly downbuilding and the formation of first gener-ation Nimr minibasins and to small salt pillows onthe flanks around the pods. Ongoing siliciclasticsedimentation made the pods sink deeper into thesalt and caused further salt flow (cf. Ings & Beau-mont 2010). The first salt pillows evolved into saltridges due to vertical rise and lateral thinning ofthe salt body. Ongoing salt squeezing promoted theactive rise of salt ridges with listric growth faultsforming above or on their flanks. The growth faultcreated locally new accommodation space whichled to differential loading during deposition of theAmin conglomerates. This differential loadingformed a second generation ‘pod’ on the top of anexisting salt ridge. The new evolving pod developedtwo new ridges. The growth faults in the SW of thestudy area, located on the flanks of the salt ridge,

Fig. 2. Chronostratigraphic summary of rock units in the subsurface of the Interior Oman (modified from Reuning et al.2009, reprinted by permission from GeoArabia). The geochronology was adopted from Al-Husseini (2010). Thelithostratigraphy of the lower Huqf Supergroup was adapted from Allen (2007) and Rieu et al. (2007). Thelithostratigraphy of the upper Huqf Supergroup and the Haima Supergroup was adapted from Boserio et al. (1995),Droste (1997), Blood (2001) and Sharland et al. (2001). The lithostratigraphic composite log on the right (not to scale)shows the six carbonate to evaporite sequences of the Ara Group, which are overlain by siliciclastics of the Nimr Groupand further by the Mahatta Humaid Group. Sedimentation of the siliciclastics on the mobile evaporite sequence led tostrong halokinesis, which ended during sedimentation of the Ghudun Formation (Al-Barwani & McClay 2008).

S. LI ET AL.506



Fig. 3. (a) Uninterpreted seismic line crossing the study area. (b) Interpretation of the seismic line shown in (a). Theformation of salt pillows and ridges is caused by passive downbuilding of the siliciclastic Nimr minibasin leading tostrong folding and fragmentation of the salt embedded carbonate platforms.




were associated with growth of the existing salt ridge.Small sub-basins formed by salt dissolution were ofminor importance in the study area. The end of thesalt tectonics is indicated by the Ghudun layer withlateral constant thickness.

Geomechanical modelling of salt tectonics

Geomechanical modelling of geological structures isa rapidly developing area of research. The numericaltechniques allow incorporation of realistic rheolo-gies, complex geometries and boundary conditions,and are especially useful for sensitivity analyses toexplore the dependence of the system on variationsin different parameters. The disadvantages are num-erical problems with modelling localization of defor-mation with poorly known initial conditions andcontroversy on the appropriate rheologies.

In addition to simplified analytical models whichserve well to elucidate some critical problems (Trian-tafyllidis & Leroy 1994; Fletcher et al. 1995; Lehner2000), most work is based on numerical techniques,usually applying finite elements (Woidt & Neuge-bauer 1980; Last 1988; Podladchikov et al. 1993;Poliakov et al. 1993; Schultz-Ela & Jackson 1993;Van Keken 1993; Daudre & Cloetingh 1994; Ismail-Zadeh et al. 2001; Kaus & Podladchikov 2001;Schultz-Ela & Walsh 2002; Gemmer et al. 2004;Ings & Beaumont 2010).

Almost all work to date has been in 2D andfocuses on forward modelling of systems at differentscales, incorporating different levels of complexityin different part of the models. For example, somemodels try to incorporate realistic two-componentrheology of the salt while others use simpletemperature-independent rheology. Other modelsfocus on a detailed description of the stress field inapplied studies of hydrocarbon reservoirs aroundsalt domes, but only consider small deformations.Overburden rheology is in some cases modelled asfrictional-plastic with attempts to consider localizeddeformation, while other models assume linearviscous overburden. Although most models produceresults which are in some aspects comparable to thenatural prototypes, it is at present unclear how thecombination of simplifications at different stagesof the modelling might produce realistic-lookingresults. Numerical modelling of salt tectonics istherefore a rapidly evolving field which, in recentyears, has started to produce quite realistic results;however, much remains to be done until the fullcomplexity of salt tectonic systems is understood.

Methods

While the interpretation depicted in Figure 3 servesto illustrate the most important profiles, it is

important to remember that the SOSB salt tectonics(Al-Barwani & McClay 2008) is strongly non-plane-strain; for a full understanding, 3D analysisand modelling is required. The models presentedhere provide the first step towards full understand-ing of stringer dynamics in this complex system.

In this study we used the commercial finiteelement modelling package ABAQUS for our mod-elling, incorporating power-law creep, elasto-plasticrheologies and adaptive remeshing techniques.

Model set-up

To capture and explore the essential elements of thesystem, a simplified generic model (Fig. 4) was

12 000 m

1600

m

600 m

360 m

80 m

18 000 m

Pre - Salt Sequence

Ara Salt

Carbonate - Stringer

HaimaPod

Salt ridge

Salt ridge

Fig. 4. Simplified model set-up discussed in this paper(Fig. 3), not drawn to scale.

Table 1. Boundary conditions and input parameters

Parameter Value

Width of salt body(W )

18 000 m

Height of salt body(H )

1600 m

Stringer thickness(h)

80 m

Stringer length (l ) 12 000 mSalt density 2040 kg m23

Stringer density 2600 kg m23

Salt rheology A ¼ 1.04 × 10214 MPa25 s21,n ¼ 5

Salt temperature 50 8CStringer elastic

propertiesE ¼ 40 GPa, y ¼ 0.4

Basement elasticproperties

E ¼ 50 GPa, y ¼ 0.4

Basement density 2600 kg m23

Calculation time 6.3 Ma

S. LI ET AL.508



defined, based on the SW-part of the interpretedseismic line, between the two major salt highs (cf.Fig. 3).

The model with SW-dipping basement has awidth of 18 km. The dip angle is 3.28. The saltinitially has a thickness up to 1600 m and thinstowards the NE to 600 m. The carbonate stringerwith a length of 12 km and a thickness of 80 m islocated 360 m above the basement (Table 1). Thepassive downbuilding of the Haima pod is strongestin the centre of the model and the volume of saltremains constant during deformation, while theHaima pods accumulate and subside in the centre.In this simple model, we start with a sinusoidalshape of top salt and increase amplitude over time.

The duration and rate of deformation was esti-mated using thickness variations of the overlyingsiliciclastic layers. The interpreted seismic line(Fig. 3) indicates that the Nimr group, forming thecharacteristic pods in our study area, has the highestlateral thickness variations. This suggests that themain salt deformation took place during the depo-sition of the Nimr group. A deformation time ofc. 6.3 Ma (2 × 1014 s) was therefore used.

An important tool to validate the models is tocompare the calculated differential stress with re-sults of subgrain-size piezometry using core sam-ples of SOSB Ara salt samples (Schoenherr et al.2007a). Table 1 lists a number of key properties ofthe model.

The rheology of salt was described by a power-law relationship between the differential stress andstrain rate:

1 = A(Ds)n = A0 exp − Q

RT

( )(s1 − s3)n (1)

where 1 is the strain rate, (s1–s3) is differentialstress, A0 is a material parameter, Q is the activationenergy, R is the gas constant (R ¼ 8.314 Jmol21

K21), T is temperature and n is the power lawexponent.

The two main deformation mechanisms in saltunder the stress conditions and temperatures ofactive diapirism are pressure solution creep withn ¼ 1 and dislocation creep with n ¼ 5 (Urai et al.2008). As argued in Urai et al. 2008, under activediapirism deformation occurs at the boundary ofthese two mechanism and therefore rheology canbe simplified to n ¼ 5 with the appropriate materialparameters. Here we used parameters measured forAra rock salt in triaxial deformation experiments:A0 ¼ 1.82 × 1029 MPa25 s21, Q ¼ 32400 Jmol21,n ¼ 5 (Schoenherr et al. 2007b; Urai et al. 2008).Under the differential stresses observed within thesalt, in our models this results in an effective viscosityheff of 2.5 × 1019 to 7.3 × 1020 Pa s during activedeformation.

In order to simplify the models we used a con-stant temperature of 50 8C for the whole salt body.This simplification is justified by the relatively smalltotal thickness of the salt layer which would resultonly in small temperature and rheological differ-ences if a realistic temperature gradient was applied.

The mechanical properties of the stringers usedin the models are based on those of typical carbonaterocks in the SOSB. The elastic properties are rela-tively well known, but the fracture strength wasdetermined experimentally on small samples. Ittherefore remains difficult to extrapolate theseresults to the scale of 10–100 m, which is relevantfor the models presented here. At that scale, addi-tional less-well-known properties (e.g. small-scalefracture density) have a strong influence on thefracture strength.

In our models we take a conservative approachand assume that the large-scale fracture strength isclose to that of an undamaged carbonate rock. Wetherefore chose a Mohr–Coulomb fracture criterionwith a cohesion of 35 MPa, a tensile strength of25 MPa, a friction angle of 30 degrees and theelastic properties E ¼ 40 GPa and a Poisson ratioof y ¼ 0.4. If we consider a thickness of the com-bined salt and sediment cover above the stringerof c. 1000 m we obtain an absolute vertical stressof c. 25 MPa and therefore, assuming hydrostaticpore pressure, an effective vertical stress of c.15 MPa. Given these stress conditions, the relevantfailure mechanism for the stringer is tensile. Wehave therefore used a test comparing the minimumprincipal stress in the stringer with the tensilefailure strength to determine if the stringer is break-ing during a given time step.

Displacement of top salt

Our models are constrained by the displacement ofthe top Ara salt over time as shown by the sedimentpackage above. One approach to developing amodel with the correct displacement would be for-ward modelling and progressive deposition of sedi-ment (Gemmer et al. 2004, 2005; Ings & Beaumont2010), and adjusting the model to produce theobserved displacement. However, this would bevery time-consuming and probably produce non-unique solutions. We therefore chose a modellingstrategy where the displacement of the top salt isachieved by applying a predetermined displacementfield. At this stage of the modelling we do not allowhorizontal motion at this boundary (the equivalentof a fully coupled salt–sediment interface). Themodel is validated against differential stressmeasured in the salt using subgrain-size piezometry.We keep the total vertical load on the top salt surfaceconstant by applying a displacement boundary con-dition on the top of the model as discussed, together




with a constant total upwards load at the bottom ofthe model. The right and left sides of the modelare constrained not to move horizontally but arefree to move vertically.

As discussed before, in the initial models pre-sented above we start with a sinusoidal shape oftop salt, increasing in amplitude at constant rateover a time interval of c. 6.3 Ma (2 × 1014 s). Infuture work, the model can be easily adapted toinclude the results of 2D or 3D palinspastic recon-struction of the overburden (Mohr et al. 2005).

Iterative scheme for stringer breaking

One of the main challenges of the current study is tomodel the breaking of the brittle layers embedded in

salt which deforms in a ductile manner. Full descrip-tion of the opening and propagation of a fracture andits filling with the ductile material is beyond thecapabilities of current numerical modelling. Wetherefore adopted a strongly simplified, iterativeprocedure in ABAQUS to detect the onset of con-ditions of fracturing and model the subsequentbreak-up of the stringers.

For this purpose an initial model is set up withthe material properties in a gravity field. Themodel is then run (i.e. the salt body is deformed)and the stresses in the stringer are monitored. Ifthe stresses in a part of the stringer exceed thedefined failure criterion, the simulation is stopped,the stringer is ‘broken’ by replacing the materialproperties of one column of elements in the stringer

Continous Stringer Stringer FramentsMininum principal Mininum principal stressstress

−152.2 MPa−152.2 MPa

−122.7 MPa−122.7 MPa

−93.14 MPa−93.14 MPa

−63.61 MPa−63.61 MPa

−34.07 MPa−34.07 MPa

−4.536 MPa−4.536 MPa

+25.00 MPa+25.00 MPa

(a) (b)

(c) (d)

Fig. 5. Breaking of a stringer and subsequent separation of the fragments. (a) The minimum principal stress is used todetect tensile failure in stringer in step 1. If tensile strength is exceeded, the stringer is broken in this location. (b) Afterthe first break, the salt flows inside the fractured part. The minimum principal stress in stringer decreases. With thefurther displacement on the top, the minimum principal stress around stringer also decreases. (c) With the furtherdisplacement of the top surface, the two stringers continue moving apart. (d) The two stringers continue moving apartand the minimum principal stress decreases in the salt.

S. LI ET AL.510



by those of salt (Fig. 5) and the simulation is contin-ued until the failure criterion is exceeded again inanother part of the stringer. This procedure isrepeated until the final deformation of the saltbody is reached while the stress does not exceedthe failure criterion in any part of the stringer.

Adaptive remeshing of the model

The model contains material boundaries which, inthe standard FEM, need to be located at an ele-ment boundary. Deformations of the model there-fore also require the deformation of the FEM mesh.

The heterogeneous deformation of the salt bodyaround the stringers leads locally to high strainswhich therefore result in local strong distortions ofthe FEM mesh. However, if the distortion of themesh becomes too large, it can cause numericalinstabilities and inaccuracy. This process limits themaximum achievable deformation of a FEMmodel with a given mesh.

To overcome these limitations we have used thebuilt-in adaptive remeshing routines of ABAQUS tocreate new elements while mapping the stress anddisplacements of the old mesh on this new one.

Since the mesh needs to deform to follow the movingmaterial boundaries in our model, this would lead tomesh distortions which will eventually become toolarge. After a certain amount of deformation, a newmesh is built according to the new locations of thematerial boundaries and the field variables aremapped from the old to the new mesh. The calcu-lation is continued using the new mesh until anotherremeshing step is needed.

Results

Figure 4 illustrates the simplified model set-up, drawnto scale. Figure 6 shows the deformed mesh and thesequence of breaks in the stringer together with thedisplacement of top salt during downbuilding.

The first break in the stringer occurs slightlyupslope from the centre of the model, in the regionwhere the downward movement of the top saltsurface with respect to the sloping basement isfastest. After the break, the two stringer fragmentsmove apart and the velocity field of the salt is redis-tributed. In Figure 7 the maximum vertical displace-ments are given relative to the initial datum. The

1km

1st break (50m)

2nd break (190m)

3rd break (290m)

4th break (310m)

Final configuration (500m)

Fig. 6. The geometry of model evolution and the location of the 1st, 2nd, 3rd, 4th and final configuration of thebreakages. The displacements of the mid node on the initial top salt for each step are 50, 190, 290, 310 and 500 m. Giventhe sinusoidal shape of the prescribed displacement of the top salt surface, this results in a total deformation amplitudethat is twice as large, that is the height difference between the highest and lowest point of the top salt surface is 100, 380,580, 610 and 1000 m in the respective time steps. Position of the break indicated by the grey arrow. Salt is shown in blue,carbonate stringer in red and pre-salt sequence in yellow. Dotted line shows the position for initial top salt.




second and third break also occur in the central regionof the model whereas the fourth break is located inthe right part of the model where the salt layerabove the stringer is significantly thinner than inthe left part. The length of the boudins can be as

small as 3–4 times the thickness of the stringer. Inthis model, the regions where the most intensefolding or thrusting of the stringers is expected withincreasing displacement (i.e. in the areas of horizon-tal shortening near the side boundaries of the model)

Minimum Principal Stress

−152.2 MPa

−122.7 MPa

−93.14 MPa

−63.61 MPa

−34.07 MPa

−4.536 MPa

+25.00 MPa

Fig. 7. The minimum principal stress during the model evolution from step 1 to step 5. Dotted line shows the positionfor initial top salt.

S. LI ET AL.512



do not contain stringers, so only minor folding androtation of the stringers occurs around the ends ofthe boudins.

As described above, the Mohr–Coulomb cri-terion and the values of the minimum principalstress (Fig. 7) were used as a criterion for failurein the stringer. If the criterion is exceeded, the strin-ger is broken at the location where the stress exceedsthe breaking strength, as shown in Figure 8.

We observe (Fig. 9) that there is a stress shadow(i.e. an area where the differential stress is smallerthan in the surrounding region) in the salt under-neath the stringer at the location of the futurebreak, with a stress increase after the stringer breaksand the salt on the two sides in communication. InFigure 8, we can also see that the fracturing con-dition is reached due to both extension and bend-ing of the stringers. There is no further fracturingof the stringer between the 4th break shown inFigure 6, that is, after the displacement in thecentre of the top salt has reached 310 m and theend of the simulation which is at a central top saltdisplacement of 500 m.

The salt flow around stringers leads to an exten-sion which is dependent on the flow patterns in thesalt and length of the stringer fragments (Ramberg1955). If the length of stringer is small enough, thestress therefore cannot exceed the failure strengthand no further fracturing takes place.

Figure 9 shows contours of the differential stresss1–s3 in the model. It can be seen that the differen-tial stress inside the salt is between c. 600 kPa and c.1.4 MPa. This agrees well with the differential stressof c. 1 MPa in Ara salt measured from subgrain-sizedata (Schoenherr et al. 2007a). This suggests thatour model and the boundary conditions chosen areinternally consistent.

Comparison of stress orientations during thedifferent stages of model evolution (Fig. 10) shows

how principle stress orientations change due to thebreaking of the stringer (Fig. 11). This is visible inthe central part of the model. In step 1, the stressorientation changes at the breaking part. On thetop of the stringer, we can see that the orientationof the principal stresses rotates by up to 908. The sameevolution can be observed in other steps (Fig. 12).Before the break in the stringer occurs, it can beseen in Figure 13 that the flow pattern in the salt isorganized in such a way that there is a particularlystrong horizontally diverging flow above the regionof the stringer where the break will happen. It isalso noticeable that flow in the salt layer betweenthe basement and the stringer has a much lower vel-ocity than above, as expected for the dominantlyCouette flow in this region. After the stringer hasbeen broken into two separate fragments, the flowpattern is reorganized as shown in Figure 14. Thereis now a strong flow though the gap between thetwo stringer fragments which are moving apart,leading to bending moments and rotation of the strin-gers. Due to this movement there is now also a morerapid flow of the salt in the relatively thin layerbetween the stringer and the basement rock.

Discussion

We presented an approach to numerically model thedeformation and break-up of brittle layers embeddedin ductile salt. While full and comprehensive treat-ment of boudinage is a very complex process, thisapproach is reasonably practical and describesmany of the critical processes in the developmentof salt stringers. Although the basic principles forthe onset of boudinage have been recognized for along time, much less is known of the evolution of aset of boudins after their initial formation. Thedetails of the evolution of the boudin-neck and the

Strength (25MPa) exceeded

Minimum Principal Stress

−152.2 MPa

−122.7 MPa

−93.14 MPa

−63.61 MPa

−34.07 MPa

−4.536 MPa

+25.00 MPa

Fig. 8. The minimum principal stress to cause tensile failure is exceeded in stringer in step 1. Where the tensile strengthis exceeded, the stringer is broken at this spot. Dotted line shows the position for initial top salt.




evolution of pore pressure in the stringers (e.g.Schenk et al. 2007) are also unknown. Thecalculations are therefore regarded as stronglyconservative considering the high strength assigned

to the stringers. Considering the evidence for over-pressures in many carbonate stringers in the SOSB,in reality the stringers probably failed much earlierthan in this model (Kukla et al. 2011).

1km

Differential stress in salt

+0.432 MPa

+0.694 MPa

+0.955 MPa

+1.217 MPa

+1.478 MPa

+1.739 MPa

+2.001 MPa

Fig. 9. The differential stress in salt during the model evolution from step 1 to step 5. The differential stress is plottedhere on the undeformed FEM mesh. The reason that it has not been plotted on the deformed mesh as all the otherdata presented is a limitation in the current version of the software used. The differential stress for step 5 is plotted ona partially deformed mesh here because the model has been remeshed due to the large local deformations betweensteps 4 and 5.

S. LI ET AL.514



The carbonate stringers embedded in the saltare modelled as brittle elasto-plastic materialwhile the salt is modelled as non-Newtonianviscous fluid (n ¼ 5). This is in contrast to previousstudies that have used viscous material for both thesalt and the embedded rock bodies (Weinberg1993; Koyi 2001; Chemia et al. 2008). In the numeri-cal model of the sinking anhydrite blocks on saltdiapirs (Koyi 2001), the anhydrite is given a 104

times higher viscosity than the salt; however, bothmaterials are considered as Newtonian (n ¼ 1)viscous fluids. In contrast, the analogue model pre-sented in the same paper uses a Mohr–Coulombmaterial, that is, sand, as an analogue for theanhydrite stringers. In the model of Chemia et al.(2008), the salt is again considered to be Newtonian;however, the anhydrite is treated as non-Newtonian

fluid with a power-law rheology (n ¼ 2). In addition,the overlaying sediments are also modelled asnon-Newtonian viscous material, but with a power-law exponent n ¼ 4. Chemia et al. 2009 havedemonstrated the influence of non-Newtonian saltrheologies on the internal deformation of a saltdiapir containing heavy inclusions such as anhydritebodies.

One key difference between our work and pre-vious numerical studies in the outcome of the simu-lations of the deformation of the rock bodiesembedded in salt is that we allow for breaking ofthe (brittle) stringers in our work, whereas most pre-vious numerical studies have tended to producefolding or pinch and swell of the (viscous) stringers.From the results of the simulations presented in thiswork (Figs 6–13), it can be seen that the stringers

Fig. 10. The stress orientations during the model evolution process from step 1 to step 5. Stress orientations aroundstringers are clearly visible. Minimum principal stress in stringer is horizontal. Dotted line shows the position for initialtop salt.




deform in different ways depending on the localstress and strain conditions. In the central part ofthe model where the laterally diverging flow patternsin the salt cause extension of the stringer, the strin-gers are broken by tensile fractures and boudinaged.The spacing of the boudin–bounding faults can be asclose as 3–4 times the thickness of the stringer.Interpretations of seismic data (Fig. 3) indicate thatthe stringers in the Ara salt are indeed broken andboudinaged underneath the Haima pod, in agreementwith the model. However, the stringers are also inter-preted as folded. This is also in agreement withobservations in salt mines (Borchert & Muir 1964)

and 3D seismic observations of stringers in salt inthe Central European Basin where resolution of theseismic data is much better (Strozyk et al. 2012).This might be an effect of the mechanical propertiesassumed for the stringers. In this study the stringersare treated as elasto-plastic, whereas in nature theyshow a combination of brittle and ductile behaviour.When the brittle stringer in our models is stretched,the stress change will result in failure of the stringerand boudinage. Under compressive loading themodel shows shortening, bending and, under suit-able salt flow conditions, thrusting may also occur(Leroy & Triantafyllidis 2000). Progressive salt

Step 1

Stress orientation changesat the breaking part

Minimum In−Plane Principal StressMaximun In−Plane Principal StressOut−of−Plane Principal Stress

Fig. 11. The stress orientations during the model evolution process in step 1. Stress orientation change at the breakingpart is clearly visible. Minimum principal stress in stringer is horizontal. Dotted line shows the position for initialtop salt.

Stress orientation changesaround the stringer

Step 3

Minimum In−Plane Principal StressMaximun In−Plane Principal StressOut−of−Plane Principal Stress

Fig. 12. The stress orientations during the model evolution process in step 3. Stress orientations around stringers areclearly visible. Minimum principal stress in stringer is horizontal. Dotted line shows the position for initial top salt.

S. LI ET AL.516



deformation may lead to complex combinations ofthese effects, for example to boudinage followedby overthrusting.

In future work, we will attempt to include theductile behaviour of the stringer in the model byconsidering visco-plastic material properties for

Fig. 13. The velocity gradient in salt localizes at the position of the future break in stringer. The part beneath the stringerhas very small flow. Blue arrow points to stringer. Grey arrow indicates location of future break. Dotted line shows theposition for initial top salt.

Fig. 14. A strong flow through the gap between the separating stringer fragments develops. A significant flow can alsobe observed in the relatively thin salt layer between the stringer and the basement. Dotted line shows the position forinitial top salt.




the stringers in addition to the current elasto-plastic material.

Conclusions

We presented first results of a study of the dynamicsof brittle inclusions in salt during downbuilding.Although the model is simplified, it offers a practi-cal method to explore complex stringer motionand deformation, including brittle fracturingand disruption.

Under the conservative conditions modelledhere, stringers are broken by tensile fractures andboudinaged very early in downbuilding (c. 50 mtop-salt minibasin subsidence) in areas where hori-zontal salt extension dominates. Ongoing boudinageis caused by reorganization of the salt flow aroundthe stringers. Rotation and bending of the stringersis caused by vertical components of the salt flow.Flow stresses in salt calculated in the numericalmodel are consistent with those from grain-size data.The model can easily be adapted to model morecomplex geometries and displacement histories.

We thank the Ministry of Oil and Gas of the Sultanate ofOman and Petroleum Development Oman LLC (PDO)for granting permission to publish the results of thisstudy. We also thank PDO for providing the seismic dataand Z. Rawahi, A. Brandenburg, M. van den Berg andG. Lopez Cardozo for useful discussions.

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Numerical modelling of the displacement and deformation of ... · were deposited in a strike-slip setting and later in a period of relative tectonic quiescence with broad, regional