Numerical Modeling Of Deformation Research Articles

Numerical Modeling of Deformation in a Shaft in the Interstratified Salt Rocks

Deformation of rocks is modeled with allowance for their creep, brittle and plastic failure in the vicinity of an unlined shaft under interaction between a monolithic concrete support and inhomogeneous enclosing massif. In calculations conducted by the finite-element method, failure is modeled by a decrease in strength in different directions that can vary in time along with the loading conditions.

Ascent and emplacement of buoyant magma bodies in brittle‐ductile upper crust

The emplacement of silicic magma bodies in the upper crust may be controlled by density (such that there is no buoyancy to drive further ascent) or temperature (such that surrounding rocks are too cold to deform significantly over geological timescales). Evidence for the latter control is provided by negative gravity anomalies over many granitic plutons. Conditions of diapir ascent and emplacement in this case are studied with a numerical model for deformation and heat transport allowing for ductile, elastic and brittle behavior. A large‐strain formulation is used to solve for temperature, stress, strain, and strain rate fields as a function of time for a range of diapir sizes, density contrasts, and background geotherms. The method allows for large viscosity contrasts of more than 6 orders of magnitude and determines the dominant deformation mechanism depending on the local values of temperature, strain, and strain rate. Emplacement depth and final deformation characteristics depend on diapir size and buoyancy. Small diapirs (less than about 5 km in diameter) cannot reach shallow crustal levels and do not involve brittle deformation. In the ductile regime the diapir flattens significantly upon emplacement due to stiff roof rocks and to the free surface above. Late stage deformation proceeds by horizontal spreading, with little upward displacement of roof rocks and is likely to be interpreted as “ballooning.” Large diapirs (more than about 5 km in diameter) rapidly rise to shallow depths (1–5 km) and induce brittle faulting in the overlying rocks. In this regime, buoyancy forces may lead to faulting in roof rocks. In this case, late stage ascent proceeds by vertical intrusion of a plug of smaller horizontal dimensions than the main body. Buoyant diapirs keep on rising after solidification, long after the relatively short‐lived high‐temperature magmatic stage. This may account for some phases of late caldera resurgence in extinct volcanic systems.

A numerical modelling approach to fluid flow in extensionalenvironments: implications for genesis of large microplaty hematite ores

Numerical modelling of deformation and fluid flow on a regional scale was utilised to test recent models for deep (≥ 5 km)penetration of surface fluids involved in genesis of Whaleback style microplaty hematite ores in the Pilbara, Western Australia. Current models suggest they formed in the waning stages of the ca. 2300 Ma Ophthalmian Orogeny. This study uses a finite difference continuum modelling code, Fast Lagrangian Analysis of Continua (FLAG), to test whether deep penetration of surface fluids is mechanically feasible in relation to ore formation. Several “conceptual models” were tested and model boundary conditions were conducive to an extensional collapse of the mountain range. During extensional deformation, downward fluid flow is evident along a subvertical fault for reasonable strain rates and topographic elevation. Throughout deformation, fluids move progressively deeper into the model. Deeper seated fluid is forced upwards from the base of the model due to perturbations in hydraulic head and pore pressure. Both fluids mix at intermediate levels and this mixing process becomes progressively deeper within the model as extension takes place. Fluid mixing is apparent at the banded iron formation (BIF) and fault boundaries, as is lateral fluid migration along the BIF layers. This study supports the hypothesis that downward flow of meteoric fluid may have played a role in the evolution of the microplaty hematite ores. However, unlike the model of Morris [Morris. R.C., 1985. Genesis of iron ore in banded iron formation by supergene and supergene-metamorphic processes—a conceptual model. In: Wolff, K.H. (Ed.), Handbook of Strata-Bound and Stratiform Ore Deposits, vol. 13, Elsevier, Amsterdam, pp. 73–235] in which downward penetration is essentially superficial, the association of fluid flow with extension may have allowed deep fluid penetration (≥ 5 km) and potential fluid mixing, as proposed by Powell et al. [Geology 27 (1999) 175] and Taylor et al. [Econ. Geol. 96 (2001) 837].

Comparison of Satellite Altimetry to Tide Gauge Measurement of Sea Level: Predictions of Glacio-Isostatic Adjustment

Abstract Modern rates of sea level change are of interest because of concerns that global warming may be causing glacier retreat. Both tide gauges and satellite radar altimetry are used to measure the present rates of change in sea level. Tide gauges measure sea level relative to the ocean floor whereas the reference for satellite altimetry is the earth's center. A numerical model of deformation of the earth's solid surface and its geoid forced by melting ice sheets, both past and present, is used to predict the present rate of sea level change as measured by tide gauges and satellites. Sea level change observed by both tide gauges and satellites are predicted to be spatially nonuniform. Considering only past ice sheets tide gauges in glaciated regions would record a fall in sea level of −13 mm yr−1, whereas satellite altimetry would record a rise in sea level of 0.7 mm yr−1. In the region peripheral to the glaciated zone a tide gauge would record a rise in sea level (3 mm yr−1) in contrast to a predicted...

Advanced Strain Analysis by High Energy Synchrotron X-Ray Diffraction

Diffraction experiments using high energy, high intensity synchrotron X-ray beams are a powerful method of compiling two or three-dimensional orientation and phase-specific scans of the lattice parameter. This information can be converted into strain and stress maps of high accuracy and resolution, and used for the validation of numerical models of deformation. The present paper describes the use of monochromatic and white beam configurations at ESRF, Grenoble and SRS, Daresbury to study problems of fracture mechanics and plasticity. The characteristic strain variation in the vicinity of the crack front was studied in a nominally single-phase aluminium alloy and in a composite reinforced with SiC particles. Quantitatively, the experimental map of matrix strain in a composite was matched to the LEFM prediction to determine the value of the stress intensity factor. Qualitatively, the transition was clearly identified between the surface and the bulk of a specimen containing a crack. The use of an energy dispersive detector and a white beam is also described to obtain a two-dimensional map of the residual strains in a cross section of a plastically bent beam.

A numerical model of deformation and fluid-flow in an evolving thrust wedge

To investigate deformation and fluid-flow in an actively deforming tectonic wedge, we model the evolution of a large, two-dimensional (100 km long, 5 km thick), mechanically and hydrologically homogeneous and isotropic pile of sedimentary strata that is deformed to become a thrust wedge. We compare both ‘dry’ and ‘wet’ cases, in order to illustrate: (1) the relative importance of fluids on wedge evolution, and (2) the effect of brittle deformation on fluid-flow. We use an elastic–plastic constitutive relation, including a Mohr–Coulomb failure criterion and a non-associated flow rule, and coupled fluid flow, with bulk rock properties that approximate typical foreland sedimentary strata. Simulations are made both with and without dilation. The model is fully dynamic, but inertial forces remain small. Results show that deformation within the wedge is accommodated by reverse-slip movement on shear bands, which migrate in both directions through the wedge as both fore- and back-thrusts. The model has features predicted by the critical-taper theory: (1) overall wedge geometry; (2) crudely self-similar growth during evolution; (3) more intense deformation toward the rear of the wedge. The models show strong overall in-sequence faulting behavior with major thrusts isolating relatively undeformed packages, which are moved in a piggyback manner upon the active thrusts. Intermittent out-of-sequence faulting does however occur, in order to maintain the wedge taper. Fluid-flow in the deforming wedge is dominated by topography, but is also strongly affected by dilational plastic deformation. In all simulations, there is focused fluid flow within fault zones. When mechanical time-stepping is shut off (uncoupled), flow systems evolve to steady-state where inflow equals outflow. By subtracting the two ‘states’ we isolate the mechanical fluid response from the total coupled system response. The mechanical fluid response is manifest as contours of head and pressure difference and focusing of fluid-flow in areas of active deformation. In non-dilational simulations, these zones are quite localized and are a result of the contrasting stresses in and adjacent to a brittle shear zone. In simulations with dilation, the zones of head and pressure difference are broad and regional in extent. They are ten times greater in magnitude than in non-dilation simulations, and they track a rock-damage front that moves through the wedge.

Crustal rheology and faulting at strike‐slip plate boundaries: 2. Effects of lower crustal flow

We present a numerical model of deformation at a strike‐slip plate boundary within a linear viscoelastic crust, which is driven by far‐field plate motions and basal mantle velocities. The crust is assumed to have uniform elastic properties but continuously varying viscosity as a function of depth. Brittle faulting is represented by static elastic dislocations that are imposed when stresses exceed a critical threshold for fracture or frictional sliding. The locations and depth extents of faults in this model are not prespecified but, instead, are governed by stress evolution within the crust. We find that when a primarily elastic upper crust is underlain by a low‐viscosity lower crustal layer, the deformation zone broadens in time to encompass many parallel strike‐slip faults in an interacting network. In contrast, when the entire crust behaves elastically, the deformation zone remains narrow and focused on a single plate‐bounding fault, reflecting imposed mantle motions. Surface strain rate patterns within the interacting fault network are complex and reflect significant faulting‐related strain rate perturbations that decay over timescales of postseismic relaxation in the lower crust (10–100 years). The fault network has a characteristic spacing, with complex fault interactions and with the depth extents of faults increasing with time to a maximum depth governed by crustal rheology. The maximum depth of faults is limited by stress relaxation and large‐scale viscous flow in the lower crust, which confines brittle failure to shallow and midcrustal levels.

Computational mesomechanics of particle-reinforced composites

Numerical models of deformation, damage and fracture in particle-reinforced composite materials, based on the method of multiphase finite elements (MPFE) and element elimination technique (EET), are presented in this paper. The applicability of these techniques for different materials and different levels of simulation was studied. The simulation of damage and crack growth was conducted for several groups of composites: WC/Co hard metal alloys, Al/Si and Al/SiC composites on macro- and mesolevel. It is shown that the used modern techniques of numerical simulation (MPFE and EET) are very efficient in understanding deformation and damage evolution in heterogeneous brittle/ductile materials with inclusions.

Three-Dimensional Numerical Modeling of Deformation and Stress in the Himalaya and Tibetan Plateau with a Simple Geometry.

The Himalaya-Tibetan region is the most active continent-continent collision zone in the world. To understand the tectonics of the region, we have numerically modeled the deformation and stress fields in the region by using a three-dimensional finite element technique. For the sake of simplicity, our model space has a simple geometry. It covers a fan-shaped region including the Himalayan Arc of about 2, 000 km in length in the south and the Tibetan Plateau in the north, and extends to a depth of 250 km. We consider several combinations of boundary conditions. In a typical case, the boundary conditions are as follows: on the southern boundary of the model space, we impose a uniform velocity of 50 mm/year northward in the direction normal to the Himalayan Arc; the northern and basal boundaries of the model space are constrained by roller conditions; and other boundaries of the model space are left free. We do not consider the gravitational forces. In this case, the deformation field shows that the region far inside the Tibetan Plateau is experiencing an east-west extension at a rate of 6 mm/year and that the maximum uplift at a rate of -4 mm/year occurs mostly along the Indus-Tsangpo suture zone. The stress field has interesting features; the magnitudes of the near-surface stresses beneath the Lesser and Greater Himalaya varies considerably along the arc. It is large in the western and eastern Himalaya (the maximum rate of stress build-up is - 0.003 MPa/year) and small in the central Himalaya. In the Tibetan Plateau, the stresses are quite large in the central portion. The modeled stresses far inside the Tibetan Plateau agree with strike-slip faulting predominantly observed there, while those in southern Tibet are not consistent with normal faulting revealed by focal mechanism solutions.

Modeling of molten droplet impingement on a non-flat surface

Numerical modeling of deformation and interaction of molten tungsten, nickel and titanium droplets impinging on a non-flat surface during thermal spraying has been performed in the present study. This research represents a significant advance relative to earlier published theoretical and numerical studies which were limited to a flat surface. Under the practical conditions in thermal spray processes, the complex physical phenomena of droplet spreading and consolidation take place at a microscopically rough and non-flat surface on a target substrate. The present study, therefore, provides a novel approach to the practical impingement behavior of molten droplets. On the basis of the present study, some fundamental mechanisms governing pore formation in spray processed materials may be established and the concomitant effects of important processing parameters may be determined.

Modeling of periodic great earthquakes on the San Andreas Fault: Effects of nonlinear crustal rheology

We analyze the cycle of great earthquakes along the San Andreas fault with a finite element numerical model of deformation in a crust with a nonlinear viscoelastic rheology. The viscous component of deformation has an effective viscosity that depends exponentially on the inverse absolute temperature and nonlinearly on the shear stress; the elastic deformation is linear. Crustal thickness and temperature are constrained by seismic and heat flow data for California. The models are for anti plane strain in a 25‐km‐thick crustal layer having a very long, vertical strike‐slip fault; the crustal block extends 250 km to either side of the fault. During the earthquake cycle that lasts 160 years, a constant plate velocity νp/2 = 17.5 mm yr−1 is applied to the base of the crust and to the vertical end of the crustal block 250 km away from the fault. The upper half of the fault is locked during the interseismic period, while its lower half slips at the constant plate velocity. The locked part of the fault is moved abruptly 2.8 m every 160 years to simulate great earthquakes. The results are sensitive to crustal rheology. Models with quartzite‐like rheology display profound transient stages in the velocity, displacement, and stress fields. The predicted transient zone extends about 3–4 times the crustal thickness on each side of the fault, significantly wider than the zone of deformation in elastic models. Models with diabase‐like rheology behave similarly to elastic models and exhibit no transient stages. The model predictions are compared with geodetic observations of fault‐parallel velocities in northern and central California and local rates of shear strain along the San Andreas fault. The observations are best fit by models which are 10–100 times less viscous than a quartzite‐like rheology. Since the lower crust in California is composed of intermediate to mafic rocks, the present result suggests that the in situ viscosity of the crustal rock is orders of magnitude less the rock viscosity determined in the laboratory.

Interaction between Strike-Slip and Thrust-Shear: Deformation of the Bullbreen Group, Central-Western Spitsbergen

Field mapping and strain measurement data are used to infer a deformation history for synorogenic, subgreenschist facies sedimentary rocks of the Ordovician Bullbreen Group in central-western Spitsbergen. Evidence for true extension parallel to fold axes, and comparison of incremental strains preserved by fiber-filled extension veins with numerical deformation models, suggest that strike-slip shear was a significant component in what was generally a thrust-shear deformation regime. Initial dextral strike-slip shear parallel to the fault-controlled Bullbreen sedimentary basin subsequently decreased in importance relative to thrusting perpendicular to the basin margin. Although the presumed Caledonian-aged dextral strike-slip motion described here may have been a local phenomenon, it is difficult to reconcile with existing models of N-S orientated, large-scale, sinistral strike-slip in western Spitsbergen.