Int J Earth Sci (Geol Rundsch) (2006) DOI 10.1007/s00531-006-0070-1
O R I GI N A L P A P E R
M. Ho¨lzel Æ B. Grasemann Æ M. Wagreich
Numerical modelling of clast rotation during soft-sediment deformation: a case study in Miocene delta deposits
Received: 2 March 2005 / Accepted: 19 January 2006 Springer-Verlag 2006
Abstract A numerical model for a rotated clast in a sedimentary matrix is presented, quantifying the deformation in associated soft-sediment deformation structures. All the structures occur in a southwards prograding deltaic sequence within the Miocene Ingering Formation, deposited at the northern margin of the Fohnsdorf Basin (Eastern Alps, Austria). Debris flow and pelitic strata contain boudins, pinch-and-swell structures, ptygmatic folds, rotated top-to-S reverse faults and rigid clasts, developed under different stress conditions within the same layers. The deformation around a 24·10 cm trapezoid-shaped rigid clast, resembling the d-clast geometry in metamorphic rocks, has been modelled using a 2D finite element modelling software. Under the chosen initial and boundary conditions the rotational behaviour of the clast mainly depends on the proportions of pure and simple shear; best fitting results were attained with a dominantly pure shear deformation (65–85%), with stretching parallel and shortening normal to the bedding. In this specific model set-up, the initial sedimentary thickness is reduced by 30%, explained by stretching due to sediment creeping and compaction. The high amount of pure shear deformation proposed is compatible with the observed layer-parallel boudinage and pinch-and-swell structures. Rotated faults and ptygmatic folds were caused by the minor component of bedding-parallel simple shear. Keywords Soft-sediment deformation Æ Numerical modelling Æ Rigid clast Æ Neogene List of symbols sij : deviatoric components of the stress tensor Æ e_ ij : components of the strain rate tensor Æ i, j: M. Ho¨lzel (&) Æ B. Grasemann Æ M. Wagreich Department of Geodynamics and Sedimentology, University of Vienna, UZA II-Althanstr. 14, 1090, Vienna, Austria E-mail:
[email protected] Tel.: +43-1-427753435 Fax: +43-1-42779534
reference to two horizontal and vertical Cartesian directions Æ g: viscosity Æ u: velocity Æ xi, xj: spatial directions Æ p: pressure
Introduction Examples of numerical modelling of soft-sediment deformation (e.g. Kurabayashi et al. 2002) are scarce compared to the voluminous literature on modelling of structures, especially the behaviour of rigid clasts and their use as kinematic indicators in metamorphic rocks (e.g. Bons et al. 1996; Mandal et al. 2001; de Meer et al. 2002; Samanta et al. 2002; Schmid and Podladchikov 2003; Marques et al. 2005; Schmid 2005 and references cited therein). However, modelling of soft-sediment deformation may significantly contribute to our understanding of soft-sediment deformation processes as well as to the conditions and geological setting of syn- to early postdepositional sediment failure. In addition, models of soft-sediment deformation are rarely compared to natural examples and thus lack the direct control given by the natural laboratory, although this can give significant quantitative information about the processes involved, which cannot be obtained otherwise. In forward modelling, simulations under defined initial conditions are carried out. The results of these are compared with natural examples, leading to conclusions about their genesis or to a prediction of future processes. The paper presented here outlines a model for a rigid clast rotating in a weak sediment matrix, based on a natural example of a syn- to early postdepositional rotated clast in Neogene deltaic deposits. The main interest was in observing the rotational behaviour of the clast under differing components of pure and simple shear. Comparable examples of deformed sedimentary nodules or aggregates have been described by Maltman (1994), Fritsche (1997) and Knaust (2001), but neither numerical modelling nor quantitative rheological considerations have been taken into account.
Geological setting The investigated sedimentary succession forms part of the Neogene basin fill of the Fohnsdorf Basin (Styria, Austria), which is the largest intramontane basin in the Eastern Alps (Fig. 1). The tectonic history of the basin started in the Early to Middle Miocene with the formation of a NE–SW oriented pull-apart basin, followed by Middle Miocene basin inversion (Strauss et al. 2001). The Neogene succession has been divided into three formations (Sachsenhofer et al. 2000a; Strauss et al. 2001, 2003): the fluvio-deltaic Fohnsdorf Formation (Upper Karpatian to Lower Badenian, thickness 800 m), the deltaic Ingering Formation (Lower/Middle Badenian, 2,000 m) and the alluvio-deltaic Apfelberg Formation (Middle?/Upper Badenian, 1,000 m). Detailed sedimentological and stratigraphic descriptions of the basin fill, especially of the Ingering Formation, are given in Sachsenhofer et al. (2003), Strauss et al. (2003) and Ho¨lzel and Wagreich (2004).
Ingering Formation The lower part of the Ingering Formation (600 m) of the Ingering Formation, a coarsening upward trend, resulting in the predominance of quartz-rich coarse sands and pebbles/gravel, is
Fig. 1 Geological sketch map of the Eastern Alps, showing the position of the intramontane Fohnsdorf Basin
Fig. 2 Stratigraphic overview and schematic map of the Neogene sediment fill in the Fohnsdorf Basin (Strauss et al. 2001, 2003). The rectangle in the stratigraphic log shows layers included in the
investigated deformation structures. MMF Mur-Mu¨rz-Fault System; PLF Po¨ls-Lavanttal Fault, AB Austroalpine basement. The overlying quaternary basin fill is marked in grey
present. The brackish character disappears and geochemical investigations indicate freshwater conditions (Sachsenhofer et al. 2000b, 2003). This sandy sequence has been interpreted as part of a prograding delta frontfluvial delta plain depositional system with large-scale cross bedding (2–3 m sets) and coarse channel fills (Ho¨lzel and Wagreich 2004).
pinch-and-swell structure (Ramsay and Huber 1983). Space problems due to stretching of the competent breccia beds resulted in deformation in the surrounding less-competent pelitic layers, which flowed into the boudin necks. Rotated fault planes and asymmetrical folds
Soft-sediment deformation structures In the study area, soft-sediment deformation mainly occurs in the lower part of the Ingering Formation. The best outcrop, which lies in the western bank of the river Ingering (Ingering river section, see Fig. 2 and Ho¨lzel and Wagreich 2004), NW of Knittelfeld (N 4713¢58.0¢¢, E 1446¢31.2¢¢), is 100 m long, exposing 25.4 m of sediments comprising mollusc-bearing breccia beds alternating with pelitic layers. Boudins and pinch-and-swell structures Individual breccia beds display strong variations in thickness and some layers are interrupted or pinch out laterally within a few meters; this boudinage indicates layer-parallel extension (Fig. 3a). In the up to 3 m thick more competent beds, boudins with a barrel-shaped cross-section formed (Fig. 3b), whilst in thinner, less competent beds, stress concentrations did not rupture the layer but led to a lenticular cross-section, known as
Although most of the stretched layers observed record an orthorhombic symmetry, reverse fault planes with a monoclinic symmetry offset some breccia boudins by a few millimetres (Fig. 3d). These shear planes, which have a surprisingly constant orientation dipping towards NW (303/39), suggest a shearing component during sediment deformation. Taking into account the other structural criteria (see below) as well as the southward prograding delta system, the shear planes are interpreted as S- to SE-directed thrusts. Ptygmatic folding of thin, fine-grained breccia layers indicate layer-parallel shortening (Fig. 3c). Most of these folds have N- to NW-dipping axial planes and therefore are S- to SE-facing, confirming a S-directed shear component during sediment deformation. Rigid clasts Angular rock fragments, with diameters ranging from 1 to 24 cm, are embedded in the breccia beds without any preferred orientation.
Fig. 3 Investigated outcrop along the Ingering river: top drawing shows sketch of parts of the main outcrop displaying deformational structures; a picture of the main outcrop; b mega-boudin in Congeria breccia bed; c S-facing folds of thin Congeria breccia layers; d Breccia bed boudins separated by reverse fault planes with an offset of several millimetres
One clast lies at the transition between breccia and pelitic layers. Although genetically unrelated, this clast’s shape geometrically resembles d-clasts (Fig. 4a), used by structural geologists to establish the sense of shear within deformed rocks (cf. Passchier and Trouw 1996). Such porphyroclasts have elongated mantles of the same mineral as the clast, stretched in the direction of the foliation. Dependent on the finite deformation, the relative mantle width, the shape of the clast and the coupling between the mantle matrix and the clast, h-, d- and r-type clasts have been distinguished (Passchier and
Trouw 1996). d-clasts generally reflect a rotation of the clast and a distortion of the wings in convex and concave sides; the resulting monoclinic geometry is considered to be a reliable criterion for determining the sense of shear (Fig. 4a). In this study this 14·24 cm2 large, trapezoidal shaped mylonite clast has been investigated in detail with numerical modelling. The clast, which lies on top of a 20 cm thick breccia bed, is surrounded by pelitic fringes (Fig. 4a) showing a convex and a concave side. In fact the pelitic layer is dragged by the rotating clast
apparent shear sense
A
simple shear deformation as well as various progressive deformation histories between these end-members. The results of the numerical forward models have been compared with the natural example (Fig. 4a) to explain the apparent conflicting rotation sense of the clast (north directed) within a southward sloping delta (compare sediment transport direction and shear sense of ideal d-clast geometry in Fig. 4a). Rheology
S
N
sediment transport direction
B
Because we describe a linear viscous rheology, we assume a simple constitutive relationship where stress is proportional to the strain rate. This may be written as: sij ¼ 2g_eij ;
2:1 Fig. 4 a Comparison of an ideal d-clast and the natural example. Note the conflicting southerly sediment transport direction and north-directed shear sense given by the ideal d-clast geometry. b Initial geometry of the clast in the numerical model
and no slip surface between the clast and matrix has been observed. The geometry of the clast suggests a north- to northwest-directed (top-to-right in Fig. 4) rotation sense, but, as discussed above, sedimentological, structural and palaeogeographical criteria indicate S- to SE-directed sediment slumping. Note that layerparallel shortening and extension occur within the same layers. This apparent north-directed shear could indicate either a polyphase deformation history or progressive deformation, which has been frequently observed in gravity-induced downslope slumping sediments (e.g. Williams and Prentics 1957; Woodcock 1976; Farrell 1984).
Numerical modelling of soft-sediment deformation To investigate the rotation of a rigid clast deforming within a viscous matrix, the finite element model BASIL (Barr and Housemann 1992, 1996) was used. BASIL sets up a finite element mesh for simple 2D geometries, obtains a time-zero solution and proceeds in an adaptive time-stepping mode to compute successive solutions as finite deformation proceeds, using velocity boundary conditions which define pure and
ð1Þ
where sij are the deviatoric components of the stress tensor, e_ ij the components of the strain rate tensor and g a proportionality constant, called the viscosity. The subscripts i and j refer to the horizontal and vertical Cartesian directions, respectively. The strain rate is defined in terms of the components of velocity u, in the spatial xi- and xj- directions: 1 @ui @uj þ : ð2Þ e_ ij ¼ 2 @xj @xi BASIL calculates isochoric plane strain deformation using Eq. 1 with the force balance equations in two dimensions: @ @ sij þ p ¼ 0; @xj @xi
ð3Þ
where the summation is over the i and j indices and p is the pressure. After each time increment, the step velocity u and the pressure p are recorded at every node of the grid shown in Fig. 5. Geometry A rectangular region with an aspect ratio of 2 and a resolution of 32 and 16 elements in the two spatial directions is considered (Fig. 4b). The left side of the model region is numerically welded to the right side so that all components of stress and deformation are continuous across this boundary, which thus describes a cylindrical infinite shear zone. In the centre, a rigid trapezoid-shaped clast has been defined with the same aspect ratio as the natural example. Since BASIL works with relative rather than absolute values, the clast has been taken to be 100 times stronger than the matrix. The shape of the laminationdrag and overall deformation of the sediment, which implies a maximum clast rotation of 40, was used to determine the initial clast orientation in the experiments (Fig. 4b).
Wk = 1.0 (simple shear)
modelled results can explain the north-directed rotation of the investigated clast.
A Wk = 0.97
B Wk = 0.87
C Wk = 0.5
D
Wk = 0.29
E
Wk = 0.0 (pure shear)
F
Fig. 5 Results of the numerical model under different finite deformation conditions including the end-members simple shear (Wk=1) and pure shear (Wk=0). In each figure the kinematic vorticity number (Wk), the initial and the deformed rectangles for every step (black/grey) and the passive marker lines after deformation are illustrated. a, b show a co-rotating clast, in c coand counter-spins are balanced (no rotation) and in d–f the clast is counter-rotating. Experiment e, marked with a rectangle, shows the best fitting result compared to the natural clast (cf. Fig. 4a)
Boundary conditions Displacement boundary conditions at the upper and lower boundaries of the modelled shear zone are given by velocity components resulting in homogeneous plane strain deformation. Depending on these velocity components, all strain combinations, including pure, simple and general shear, can be modelled. To quantify the relative contribution of shearing, stretching and thinning of the modelled rock volume, the kinematic vorticity number Wk (Truesdell 1954) was used; for pure shear Wk=0 and for simple shear Wk=1. Details for finding velocity components with different Wk resulting in comparable finite strains are given in Grasemann et al. (2003). Note that a top-to-left (south-directed) shear sense (Fig. 4) has been modelled, consistent with the south-directed sediment transport, to determine whether
Results Figure 5 shows the model results for different finite deformations, including the end-members simple and pure shear (Fig. 5a, f). Each figure shows the corresponding kinematic vorticity number Wk, the deformed initial rectangle, the finite element grid and the passive marker lines after deformation. Since Wk is non-linear, Wk values of 0.0, 0.29, 0.5, 0.87, 0.97 and 1 relate to a 0, 17, 33, 67, 83 and 100% simple shear contribution. The most important result is that the rotational behaviour of the trapezoid-shaped clast is clearly controlled by Wk. Whereas the simple shear component induces a co-rotational spin of the clast (Wk>0.87, Fig. 5a, b), the pure shear component rotates the longest diameter of the clast, which is inclined against the shear direction, into parallelism with the shear zone boundary, resulting in a counter-rotational spin (Wk
