Forced folding and fracturing induced by differential compaction during post-depositional inflation of sandbodies: insights from numerical modelling

7 Three series of numerical models based on the discrete element method were constructed to 8 simulate forced folding and fracturing triggered by postdepositional inflation of fluidised sandbody. 9 The models consist of numerous particles that have relatively low to high interparticle bonds to 10 represent overburden sediments with a relatively low to high cohesion, and cohesionless, 11 frictionless particles to represent fluidised sands. The modelling results show that normal faults 12 were produced due to the upward inflation of sand domes and the resulting flexed overburden, 13 when the cohesion of the host sediments is low. Opening voids were created as a result of strata 14 collapse, when the intrusion-related normal faults terminated within the host sediments as blind 15 faults. Conical fractures that are aligned along sandbody margins were produced, which consist of 16 closed, lower segments with a reverse displacement, and opening, middle-upper segments with a 17 minor to zero shear component. Forced folds were generated in most models with a moderate to 18 high cohesion, resulting in differential compaction in the overlying sediments that can account for 19 the formation of fold-related fractures, which are either shear, hybrid or pure tensile, depending 20 on their structural positions. The amplitude of forced folds is closely associated with both cohesion 21 * Corresponding author. E-mail address: qingfeng.meng@manchester.ac.uk and thickness of sediments in the overburden, whilst fold wavelength is mainly controlled by 22 sediment cohesion. Based on the modelling results, three types of preferential sites for the storage 23 of injected sands were suggested, which are believed to be instructive for subsurface sandbody 24 detection and prediction. This study demonstrates that differential compaction induced by sand 25 inflation can play an important role in overburden folding and fracturing. 26 27


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The study on large-scale sandstone intrusions has become increasingly common in the past two The discrete element modelling method, based on elastic interactions between frictional rigid 80 particles, was first developed by Cundall and Strack (1979) to simulate behavior and interaction 81 of granular materials. The modelled materials consist of numerous elastic particles that displace 82 independently from one another, and interact with neighbouring particles only at contacts between 83 particles. Particle contact is defined as a linear spring in compression that resist particle overlap, 84 and a frictional strength that resists shear motion (Fig. 2a). More complex behavior of a particle 85 assembly can be simulated by allowing the particles to be bonded together so as to resist both shear 86 and extensional displacements. The bonds will be broken once the bond strength is exceeded, bonded particles with radii ranging from 1.0 to 3.2 m, to represent overlying sediments in the 116 overburden. A 0.2 km high, right-angled equilateral triangle, located below the central part of the 117 rectangular box, is filled with 18,516 non-bonded particles with radii ranging from 0.5 to 1 m, to 118 represent fluidized sands. Notably, the geometry of the sandbody is highly simplified, and the aim 119 of such a geometry is to allow the particles within the sandbody to radially spread upwards. Particle 120 sizes in both the sandbody and the overburden follow a Gaussian distribution, which can help 121 avoid hexagonal close packing of particles.

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The particle stiffness is assigned with a value of 1e7 N/m for both normal (Kn) and shear (Ks) is set to zero. The particle density ρ is 2600 kg/m 3 . The bonding cohesion for particles in the 128 overburden is set to be between 1 to 8 MPa (see model configurations in Table 1), to represent 129 sediments with a relatively low to high cohesion.

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The packing of particles was achieved by allowing an assembly of randomly-generated particles 132 to settle to the bottom of the model under their own weight. The system was considered to have 133 reached static equilibrium when the mean unbalanced force within the particle assembly have 134 dropped to a negligible value. The particle assembly was then trimmed to the desired height, which 135 led to a small amount of vertical elastic rebound and elevated the surface. We then repeated the trimming process that allowed the system to be settled. The particle assembly in the overburden respectively. The overburden sediments are mechanically homogeneous. Colours were assigned 139 to the overburden sediments simply for bedding correlations.

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The model boundaries are defined by elastic walls that share the same mechanical properties with 142 their contacting particles. Deformation of the system was driven by a horizontal wall underneath 143 the sandbody that moved upward. This helps represent a lithostatic stress condition during sand 144 fluidization and inflation. The models were gravitationally loaded by 1 g.

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We mainly focused on the macroscopic deformations and structures generated as a result of 147 sandbody inflation, especially on forced folds and faults/fractures. The models that reproduced 148 classical, widely reported structures were selected for a more detailed analysis, regarding their 149 sequential deformation processes and evolving stress fields. By varying the cohesion and thickness  Models 1-4 with a relatively thin overburden exhibited varied deformation patterns in the fault scarps in the uppermost layer during normal slipping. F1 and F3, which are dipping towards opposite directions, constitute a small horst located above a symmetrical sand dome. F2 and F4 161 occur along the margins of the sandbody, with the fault-bounded blocks acting as footwalls.

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Model 2 produced multiple small blind normal faults in the sediments below the magenta layer 164 (Fig. 3b). These faults correspond to the concaves and convexes on the irregular sandbody surface.

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Notably, a forced fold was formed in the overburden. An opening-mode fracture was generated in

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Model 7 produced two minor blind normal faults that cut layers between the sandbody and the magenta layer (Fig. 4c). These two faults define a minor horst that was formed due to the uplift of  and reached the red layer (Fig. 4e). The fracture tip can be subdivided into a hybrid-mode, inclined 207 segment, and an opening-mode sub-vertical segment. Notably, the inclined segment is aligned 208 normal to the surface of the underlying sandbody.

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Model 10 produced a rather symmetric forced fold in the overburden (Fig. 4f). Similar to model 4,

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The tensile stresses became more intensified, and the stress trajectories were aligned in a half-      The modelling results presented demonstrate that shear, tensile and hybrid fault/fractures (both 362 normal and reverse) can be induced in the overburden by inflation of sandbodies and forceful 363 intrusion of sands into the overlying sediments. These fault/fractures are predominantly fold-related, due to differential compaction in the adjacent sediments during progressive fold development, which largely agrees with Cosgrove and Hillier (1999).

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The fold-related faults/fractures can be subdivided into three main types, including 1) normal (Figs  3a-b, 4a-e, 5a-b,) and reverse faults (Fig. 5b-g) that correspond to the irregularities of the sandbody surface, and also along sandbody margins; 2) inclined or sub-horizontal pure tensile fractures 370 aligned along the channel margins, and are not directly connected to the sandbody (Fig. 5d-g)

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Faults/fractures of type 1 can be attributed to differential compaction induced by the intrusive 375 bodies, and their formation mechanism is further discussed in the following section.

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suggests that differential compaction would lead to nucleation and upward propagation of reverse 435 faults along sandbody margins rather than pure opening-mode, upward-tapering fractures (Fig. 5d-436   g, 10b). The reverse faults passed into opening-mode fractures as they propagated upwards, either 437 in a hybrid mode or in a pure tensile mode. The reverse sense of shear becomes neglectable in the 438 tips of those opening-mode fractures (Fig. 5f).

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Such fractures can serve as preferential sites for subsequent storage of remobilised sands, and 449 evolve into sills. It is, therefore, argued that the formation of sib-horizontal sills, especially the 450 frontmost segments of wing-like structures, may not result from mechanical heterogeneities, such 451 as bedding. Instead, they may be produced as tensile wing cracks at the end of the main shear 452 fractures, and be associated with rapid decrease in displacement towards the fracture tips (Fig. 10).  (Fig. 4b); 2) opening spaces created on top of grabens due to strata collapse (Fig.  (Fig. 5d-g). These sites provide opening spaces that can preferentially accommodate fluidised along its propagation direction. The lower segment of the wing exhibits a downward tapering tip, and is not directly connected to the sub-horizontal basal sandbody in the 2D section. The wing 478 sheet shares the same grain size and mineral composition with the basal sandbody, and has been 479 suggested to be sand injectites sourced from the basal sandbody during its remobilisation (Meng

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It is worth mentioning that the models presented are highly simplified, without aiming to directly 487 simulate any specific natural prototypes. The main limitations of our models are that the roles of 488 fluid pressure, mechanical stratigraphy and sandbody geometry were not considered. It is, 489 therefore, suggested that future studies can incorporate these factors, especially for specific case 490 studies with regional and local geological contexts being provided.

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This study utilized the discrete element modelling method to simulate overburden forced folding 494 and fracturing induced by inflation of fluidised sandbodies. We conclude the following:

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(1) Inflation of fluidised sands can trigger normal faulting of the overburden when the host 496 sediments have a low cohesion, i.e. a low level of lithification. The formation of normal faults can 497 be attributed to sand doming-induced differential compaction in the overlying sediments.
(2) Sandstone inflation can result in forced folding of the overlying, cemented sediments and 500 thereby a flexed overburden. Differential compaction across the inflated sandbody can produce 501 faults/fractures along channel margins and also in fold hinge zones.

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Modified from (Jackson, 2007). Note the domes that uplifted the sediments on the footwall of F2.