Application fields for numerical models of discontinuous systems – examples:
Applications showcased on VGeST
We focus here on examples studied during the 5-year EPSRC funded VGW project (2004-2009) and will add further past projects under development and future research project highlights in this section. We have modelled discontinuous systems in geoscience using both the combined finite–discrete element method FEMDEM, and DEM. Where the representative sample requires extremely high numbers of particles, there are increasing advantages in using DEM over FEMDEM. A robust approach that couples FEMDEM or DEM to powerful generic fluids models would greatly expand the range of application opportunities and for this reason considerable effort to couple fluid flows can also be seen in the applications discussed. Here, we focus on geoscience and geoengineering applications and concentrate VGeST on granular matter at scales where gravitational forces dominate.
Granular materials, packing and flow
One indicative problem for discontinuous systems where understanding is relatively incomplete is the effect of shape and friction on packing and packed structures. This has been thoroughly addressed in both 2D using FEMDEM to reveal stress architecture within grains carrying force chains and in 3D studies looking at ellipsoidal and real-shaped grains. While granular flow has not been a focus of study, the potential to model the dynamics of hopper flow or silo discharges is very apparent in 2D FEMDEM simulations. 3D transient dynamics within a simple silo filling operation was also modelled.
Rock slide avalanching has been modelled in 2D using FEMDEM. It has been shown to be an ideal tool for studying the details behind the emergent complexity of these important geohazards. Initiation of motion, internal strain and breakup by fracture and fragmentation during motion, selective transportation and deposition through to state of rest can all be modelled as one process. In another study with a 3D model, angle of repose at initiation of avalanching was determined using DEM simulations employing a clustered sphere model for particle shape. The research study had the objective to explore how much shape resolution (i.e. number of spheres to fit within the cluster) is needed to determine the static angle of repose of certain granular systems.
The vast majority of coastal structures rely on granular materials to combat the forces of storm waves and to stop water overtopping in to harbours and causing flooding or erosion. Concrete seawalls and caissons are also widely employed. The applications considered here include stresses in gigantic systems of granular layers mad up of armour units. The modelling of waves is also developed as a pre-requisite to wave-structure interaction models. Energetic wave breaking can be achieved with remarkable realism using our preferred fluids solver, “Fluidity”. Waves breaking over assemblies of concrete units are simulated and the vertical and horizontal drag forces exerted by the waves on the units have been calculated for illustrative purposes.
Flow inside grain packs
This is a hugely significant problem for industry for both oil and gas as well as carbon sequestration, requiring accurate modelling of the physics. The opportunity exists to build process models mimicking the sedimentation compaction and diagenesis history of sedimentary rock. One study using VGST generates realistic sedimentary fabrics artificially with numerical models and then applies fluid flow solvers to model permeability assuming the grains form a static solid skeleton. Models of typical sand grain packs have been created. The emerging simulated pressure drop as fluid flows through all the interstices has been modelled with both a full Navier-Stokes solver for larger Reynolds numbers and also using a Darcy flow solver. The simulations help towards a fuller understanding of the contribution of grain characteristics and compaction on flow and geophysical properties important for reservoir engineers.
Geomechanics, fractures and tectonic structures (page under construction)
VGeST is well-suited to stress analysis of rock masses and for obtaining the bulk deformability characteristics for rock engineering projects from geothermal energy, geological respository, tunnel, slope stability, excavation or foundation design. Deterministically measured or statistically derived discontinuity geometries can be introduced within a solid medium to represent an in-situ blocky rock mass or sedimentary layered jointed system after some experience is gained in model building. Boundary constraints and geometries can be varied to examine stress heterogeneity and the destabilization and motion of sliding blocks. Currently, the fracture modelling in VGeST is constrained to quasi-2D FEMDEM. Block caving with different rock mas characteristics, openings and sublevel draw configurations can be investigated. The propagation of fractures and growth of fracture networks has been modelled with VGeST using a cohesive crack model. Modelling demonstrates that crack apertures and directions may vary dynamically and models of flow in the network of fractures indicate an evolving permeability anisotropy with potentially rapid jumps as connectivity becomes established during a disturbance in the applied stress state.