Ductile Layer Research Articles

GPS monitoring of temporal deformation of the Xianshuihe fault

Highly precise (σ ∼1 mm) temporal deformation measurements are taken across the Xianshuihe fault from two pairs of continuous GPS stations straddling the fault. Baseline vector changes of the two pairs of stations show clearly the difference in deformation behavior between the Qianning and Daofu segments of the fault: the former deforms steadily, and the latter deforms with a strong transient component. The transient deformation across the Daofu segment is possibly related to its irregular geometry, where the fault splits into two branches, that is, the east and west branches. An attempt is made to interpret the baseline vector changes using a kinematic fault model composed of a brittle layer in the upper crust, a ductile layer in the lower crust, and a transition zone in between. The slip in the transition zone of the south segment of the Xianshuihe fault is steady. The slips in the transition zones of the north and Daofu segments of the Xianshuihe fault, however, are not steady, and the average slip rates there are higher than that of the south segment. The difference in deformation behavior is probably associated with the rheological properties of the fault interface, suggesting that the overall fault strength of the south segment is greater than those of the north and Daofu segments, corresponding to longer earthquake recurrence time.

Bearing of plate geometry and rheology on shallow-focus mega-thrust seismicity with special reference to 26 December 2004 Sumatra event

We propose a model pertaining to the generation of 26th December 2004 off Sumatra mega-event in the backdrop of other similar type earthquakes along subduction zones around the world. Reconstructions of Benioff trajectories through the hypocenters of historical earthquakes including six mega-earthquakes indicate (i) confinement of hypocenters right within the descending lithosphere, and (ii) natural coincidence of foci of the mega-events around the zones of plate flexing. These observations are discussed in detail with special emphasis on the Sumatra margin considering the role of rheological anomaly across the cross-section of the descending lithosphere; yield strength envelope and residual stress accumulation through time. The intraplate origin of shallow mega-thrust earthquakes allowed us to advocate the ‘zone of flexing’ along the profiles of the subducting plates as nodal area for stress concentration. We propose here that at elevated confining pressure and temperature, loading of unidirectional cyclic stress on time-average bending stress enhanced the material yield strength (i.e., strain-hardening), and leads the semi-brittle portion of the lithosphere into near-brittle condition through rheological transformation. Under subsequent rise in neutral surface and increase in compressive stress field, non-coaxial deformation triggered shear failure on 26th December 2004 preferably at the rheological interface between strain-hardened near-brittle layer and deformed ductile layer within the sub-oceanic mantle. A two-stage fracture mechanism viz. a slow (∼1.1 km/s) bilateral initiation in an essentially strain-hardened near-brittle domain and a follow-up very rapid progression (3.3 km/s) in the brittle, crustal domain was mainly involved in the generation of 2004 off Sumatra mega-event. Estimation shows an amount of 3.38 × 10 22 to 4.50 × 10 22 N m seismic moment ( M o) and 8.95–9.03 moment magnitude ( M w) for the southern part of the 1300 km extended rupture i.e. between the North Andaman to the north and the Sumatra at its south. The study necessitates the reassessment of other shallow-focus mega-thrust earthquakes along the subduction margins around the globe.

The influence of edifice slope and substrata on volcano spreading

Gravitational volcano spreading is caused by flow of weak substrata due to volcanic loading, and is now a process known to affect many edifices. The process produces extension in the upper edifice, evidenced by gräben and normal faults, and compression at the base, seen in strike–slip faults and thrusts. Where spreading is identified, host volcanoes have a range of fault densities, variable rift and gräben shapes, and different degrees of structural asymmetry. Previous studies have suggested a link between edifice shape and structure and the proportion of brittle to ductile material in the substrata or lower edifice. We study this link using refined sand cone analogue models standing on a brittle–ductile/sand–silicone substrata. Two scenarios have been investigated, the first mainly represents oceanic volcanoes with a ductile layer within the edifice (type I), where there is an outer ductile free surface. The second represents most continental volcanoes that have ductile substrata (type II). We apply the model results to natural examples and develop quantitative relationships between slope, brittle–ductile ratio fault density, spreading rate and structural style. Displacement fields calculated from stereophotogrammetry show significant differences between different slope models. We find that more faults are produced when the cone is initially steeper, or when the brittle substratum is thinner. However, the effect of the brittle layer dominates over that of slope. The strike–slip movements are found to be an essential feature in the spreading mechanism and the gräben are in fact transtensional features. Strike–slip and graben faults make a conjugate flower pattern. The structures produced are well-organised for type II edifices, but they are poorly organised for type I models. Type I models represent good analogues for oceanic volcanoes that are commonly affected by large slumps bounded by an extensional zone and lack of well-formed sector gräben. The well-observed connection between oceanic volcano rifts and large landslide-slumps is confirmed to be a consequence of spreading.

Dynamics and structural development of metamorphic core complexes

The development of metamorphic core complexes (MCCs) in a thickened continental lithosphere is studied using fully coupled thermomechanical numerical code, accounting for elastic‐brittle‐ductile properties of constituent rocks. For MCCs to develop, the middle lower crust and the sub‐Moho mantle are required to be weak enough to flow laterally, so as to simultaneously feed the exhuming dome and enable the Moho to keep a flat geometry. The conditions are satisfied with initial Moho temperatures of 800°C or higher, with crustal thicknesses of 45 km or greater, and with initial effective viscosities lower than 1020 Pa s and 1022 Pa s in the lower crust and the underlying mantle, respectively. A compositional (mainly density) anomaly with the properties of granite is placed centrally in the crust to localize strain at the onset of deformation. During a first stage of “upper crust necking,” the deformation pattern is relatively symmetrical and dominated by graben formation in the upper crust. When the first ductile layers reach the surface, a second stage of “dome amplification and widening” occurs. Dome amplification is accommodated by horizontal flow in the ductile crust, giving an early symmetrical pattern of conjugate shear zones with no obvious detachment zone. The system then rapidly becomes asymmetric, with the localization of a detachment zone along one dome limb, further accommodating dome widening. Thus the exhumation process of a metamorphic dome results in the progressive development of a detachment zone. Depending on initial Moho temperature, the detachment zone can migrate in space or die out and be replaced by a new one with an opposite dip.

Deep-crust strike-slip earthquake faulting in southern Italy aided by high fluid pressure: insights from rheological analysis

Abstract I present the results of a crustal rheological analysis of the Potenza 1990 and Molise 2002 (southern Italy) deep foci (10–25 km) strike–slip earthquake sequences ( M max =5.7) located in the upper half of the middle crust. The analysis consists of geotherms and two-mechanism (brittle frictional v. ductile plastic flow) strength envelopes. Strength envelopes are calculated along a sub-vertical E–W-striking inherited crustal-scale fault zone reactivated under a strike–slip tectonic regime. The effects of high pore-fluid pressure ( Pf ) and strain rate increase due to afterslip processes during the co-seismic and early post-seismic phases are evaluated. The results are compared with the depth-distribution of seismicity. Under long-term strain rates, the rheology predicts a brittle layer in the upper part of the middle crust embedded by two plastic horizons: the base of the carbonates and the Verrucano layer (above) and the lower part of middle crust (below). The best rheological model for the observed seismicity is that considering high Pf in the middle crust (λ≥0.65). Brittle faulting aided by high Pf in the middle crust is in agreement with the focal depths and magnitudes of the main shocks. The upward and downward widening of the brittle layer in the middle crust, due to the increased strain rate in the co-seismic and early post-seismic phases (afterslip), agrees with the width of the aftershock zones. The weak ductile layer at the base of the carbonates (and possibly within the Verrucano) appears to have an important role in delimiting the seismogenic faulting upwards and probably played a role in defining a seal to fluid up-flow along the fault zone.

Extension during active collision in thin-skinned wedges: Insights from laboratory experiments

The occurrence of strike-normal extension in mountain belts undergoing active contraction is not predicted by analytical solutions for the mechanics of purely frictional orogens. To test the idea that ductile rocks at depth might allow extensional deformation to occur in otherwise frictional and contractional orogens, we have conducted a series of analog experiments with purely frictional and layered frictional-ductile rheologies. By precisely measuring the horizontal deformation field, we have quantitatively confirmed the qualitative observation that analog frictional wedges do not extend. This is consistent with published numerical models, and is in contrast to purely viscous models that commonly display coeval extension with contraction. Our modeling also demonstrates that layered frictional-ductile models can, during active convergence, result in discrete extensional normal faulting even when only a relatively thin ductile layer is present. The resulting extension, though relatively small in magnitude compared to the active contraction, can greatly modify the final profile of a convergent orogen and can lead to the formation of a broad plateau between the pro-wedge and the retro-wedge.

Mechanical and electrical yielding for an electrically insulated crack in an interlayer between piezoelectric materials

A plane problem for a crack in a thin ductile layer between two piezoelectric materials under remote electromechanical loading is considered. The piezoelectric substrates are of the same material. They are modeled by half-spaces. For the interlayer thickness tending to zero, electrical and mechanical yielding zones of different unknown lengths are introduced at the crack continuations. These zones are modeled by jumps of electric potential and mechanical displacement jumps, respectively. A vector Hilbert problem is formulated and solved exactly. The lengths of the yield zones are found from the conditions of finiteness of the normal stress and of the electrical displacement. The crack opening and the electric potential jumps at the initial crack tip are found in closed form for the cases of electrical yield zone longer and shorter than the mechanical one. Simple formulae for energy release rate are presented for Griffith crack and the developed electromechanical yield models. Also, an approximate model for eliminating the mechanical and electrical singularities is suggested. Numerical results are presented for different values of yield parameters and of remote electromechanical loading. A good agreement between the energy release rate values obtained for a Griffith crack, exact and approximate yield zone models are established.

Micromechanics of toughening in ductile/brittle polymeric microlaminates: Effect of volume fraction

Ductile/brittle microlaminates, comprised of alternating layers of ductile polymer [e.g., polycarbonate (PC)] that inelastically deform by shear yielding, and brittle polymer [e.g., styrene-acrylonitrile (SAN), polymethylmethacrylate (PMMA)] that undergo crazing in tension, offer a strategy for tensile toughening by capitalizing on the synergistic interactions between crazing and shear yielding. This work presents a micromechanical model for PC/PMMA ductile/brittle laminates that captures the constituent volume fraction dependence of the macroscopic behavior, as well as the underlying micro-mechanisms of deformation and tensile failure, in particular the synergy between crazing and shear yielding. The finite element implementation of the model considers both two-dimensional and three-dimensional representative volume elements (RVEs), and incorporates continuum-based physics-inspired descriptions of shear yielding and crazing, along with failure criteria for the ductile (PC) and brittle (PMMA) layers. The interface between the ductile and brittle layers is assumed to be perfectly bonded. The 3D RVE models successfully capture the macroscopic tensile stress–strain behavior of the ductile/brittle laminates at varying constituent volume fractions and the corresponding underlying micromechanisms of deformation and failure. The transition from brittle to ductile laminate behavior is in agreement with experimental data and is found to occur as the fraction of the ductile layer is increased to 0.60. The simulations reveal the brittle to ductile cross-over to be governed by the ability of the ductile layers to constrain the dilation and growth of crazes in the brittle layer. In particular, after the critical volume fraction of the ductile constituent is attained, surface edge crazes are inhibited from tunneling across the width of the specimen which then leads to reduced crazing/cracking and increased shear yielding. 2D RVE models are unable to adequately account for the deformation and toughness of PC/PMMA microlaminates as a function of the constituent volume fractions, as they neglect any distribution of inelastic events in the laminate-width (out-of-plane) direction.

Transfer zones and fault reactivation in inverted rift basins: Insights from physical modelling

Lateral transfer zones of deformation and fault reactivation were investigated in multilayered silicone–sand models during extension and subsequent co-axial shortening. Model materials were selected to meet similarity criteria and to be distinguished on CT scans; this approach permitted non-destructive visualisation of the progressive evolution of structures. Transfer zones were initiated by an orthogonal offset in the geometry of a basal mobile aluminium sheet and/or by variations of layer thickness or material rheology in basal layers. Transfer zones affected rift propagation and fault kinematics in models. Propagation and overlapping rift culminations occurred in transfer zones during extension. During shortening, deviation in the orientation of frontal thrusts and fold axes occurred within transfer zones in brittle and ductile layers, respectively. CT scans showed that steep (58–67°) rift-margin normal faults were reactivated as reverse faults. The reactivated faults rotated to shallower dips (19–38°) with continuing shortening after 100% inversion. Rotation of rift phase faults appears to be due to deep level folding and uplift during the inversion phase. New thrust faults with shallow dips (20–34°) formed outside the inverted graben at late stages of shortening. Frontal ramps propagated laterally past the transfer structure during shortening. During inversion, the layers filling the rift structures underwent lateral compression at the depth, the graben fill was pushed up and outwards creating local extension near the surface. Sand marker layers in inverted graben have showed fold-like structures or rotation and tilting in the rifts and on the rift margins. The results of our experiments conform well to natural examples of inverted graben. Inverted rift basins are structurally complex and often difficult to interpret in seismic data. The models may help to unravel the structure and evolution of these systems, leading to improved hydrocarbon exploration assessments. Model results may also be used to help predict the location of basement discontinuities which may have focused hydrothermal fluids during basin formation and inversion.

Analyses of Cavitation Instabilities in Ductile Metals

Cavitation instabilities have been predicted for a single void in a ductile metal stressed under high triaxiality conditions. In experiments for a ceramic reinforced by metal particles a single dominant void has been observed on the fracture surface of some of the metal particles bridging a crack, and also tests for a thin ductile metal layer bonding two ceramic blocks have indicated rapid void growth. Analyses for these material configurations are discussed here. When the void radius is very small, a nonlocal plasticity model is needed to account for observed size-effects, and recent analyses for the influence of such size-effects on cavitation instabilities are presented. When a metal contains a distribution of micro voids, and the void spacing compared to void size is not extremely large, the surrounding voids may affect the occurrence of a cavitation instability at one of the voids. This has been analyzed for a material containing a periodic distribution of spherical voids with two different void sizes, where the stress fields around larger voids may accelerate the growth of smaller voids. Another approach has been an analysis of a unit cell model in which a central cavity is discretely represented, while the surrounding voids are represented by a porous ductile material model in terms of a field quantity that specifies the variation of the void volume fraction in the surrounding metal.

Modeling constrained metal behavior in ceramic/metal laminates

The toughening of brittle materials with a ductile layer greatly enhances the composite fracture toughness. The behavior of a single constrained ligament is what characterize this enhancement. In this article, an approach based on geometrical correction function of necking is proposed to model the bridging ligament response and compared with experimental single Ni-ligament test using digital image correlation (DIC) technique.

Displacement fields and finite strains in a sandbox model simulating a fold-thrust-belt

This thesis uses geodetic satellite data to measure present-day crustal deformation in the Zagros fold-thrust belt (SW Iran). Geodetic-type measurements are also used in down-scaled models that simulate the surface deformations seen in convergent settings like the Zagros fold-thrust belt.Global Positioning System (GPS) measurements of three surveys between 1998 and 2001 indicate 9 ± 3 mm/yr and 5 ± 3 mm/yr shortening across the SE and NW Zagros respectively. GPS results show that in addition to the different rates and directions of shortening on either side of the NS trending Kazerun fault, local along-belt extension occurs to the east. Differential SAR interferograms of ERS1 & 2 images between 1992 and 1999 detect 8 ± 4 mm/yr uplift rate across a newly recognized fault in SW Qeshm Island. This can be attributed to a steep imbricate thrust that may still represent the local Zagros deformation front.The salt diapirs in the Zagros rise from a source layer that acts as a low-frictional decollement that decouples the deformation of the cover sediments from their basement in the eastern Zagros whereas the cover to the west deforms above a high-friction decollement. Physical models were prepared to simulate cover deformation in the Zagros by shortening a sand pack above adjacent high- and low-frictional decollements (represented by a ductile layer). The strain distributions differed above the two types of decollements; it was more heterogeneous above the salt where local extension in the shortening direction was dominant. A separate work also investigated systematically the role of basal friction on cover deformation in convergent settings. Accurate height measurements of the model surface by laser-scanner indicated a deformation front more distal than usual, particularly in the low-basal frictional models. The volume reduction in our shortened sand models correlated directly with their basal friction.

Pressure-sensitive ductile layers – II. 3D models of extensive damage

The mechanisms of void growth and coalescence in ductile polymeric layers, taking into account the effects of pressure-sensitivity, α, and plastic dilatancy, β, are explored in this two-part paper. In Part I, a two-dimensional model containing discrete cylindrical voids was used to simulate void growth and coalescence ahead of a crack. This paper extends the previous work by explicitly modeling initially spherical voids in a three-dimensional configuration. Damage predictions from the present 3D model for low yield strain adhesives are found to be in good agreement with both the 2D model in Part I and the computational cell element model. Significant discrepancies in the damage predictions, however, exist among all three models for high yield strain adhesives (e.g. polymers). The present 3D study also discusses the increasing damage level and its spatial extent with pressure-sensitivity, as well as the exacerbation of these effects arising from the deviation from an associated flow rule. In fact, both high porosity and high pressure-sensitivity promote void interaction. In addition, pressure-sensitivity increases the oblacity of the voids and reduces the intervoid ligament spacing over a wide range of load levels. These effects are compounded as the fracture process zone thickness decreases relative to the adhesive thickness. Results further show that both the adhesive toughness levels and the critical porosity governing the onset of void coalescence are significantly lowered with increasing pressure-sensitivity.

Direct Wafer Bonding Enhanced by Ductile Layers Inserted Near the Interface

This work demonstrates that the insertion of thin dissipative interlayers can substantially increase the resistance to fracture of interfaces obtained by wafer bonding. A multiscale numerical modelling strategy has been developed in order to quantify the protective effect resulting from the presence of a plastically deforming interlayer. The concept has been applied, for experimental demonstration, to a system known to be difficult to bond, i.e. PECVD SiO2/PECVD SiO2 interface. The introduction of a 1 micrometer thick aluminium interlayer next to the interface has lead, on average, to an increase by 67% of the overall interface fracture toughness. Proper combinations of interlayer thicknesses and mechanical properties can theoretically lead to improvement of the fracture energy by a factor of up to 10.

Basin inversion and fault reactivation in laboratory experiments

A series of analogue models have been performed to get insights into the relationships between the reactivation of pre-existing normal faults and the orientation of a successive compressive stress field. The models were deformed in two phases: (1) a first extension phase ( σ h ≈ σ 3) generating a graben, and (2) a successive compressive phase with the orientation of the shortening direction ( σ h ≈ σ 1) trending between 0° and 90° (obliquity angle α) to the faults bounding the graben. The deepening of this graben was accompanied by syn-tectonic sedimentation that included a basal ductile layer (simulating salt in nature) overlain by a brittle sand pack. The experimental results suggest that the development of compressive structures is strongly controlled by the pre-existing normal faults and by the obliquity angle α. The experiments have invariably shown that the extensional faults were reactivated during shortening whatever the value of the angle α. Whereas strike-slip reactivation of major normal faults is favoured by low obliquity angles α, mostly dip-slip reactivation of pre-existing structures is instead promoted for high obliquity angles α. The analysis of model results highlights the important role played by a ductile layer at the base of the basin fill, and the obliquity angle α in controlling both strain partitioning and brittle–ductile decoupling.

Analytical approach for the toroidal relaxation of viscoelastic earth

This paper is concerned with post-seismic toroidal deformation in a spherically symmetric, non-rotating, linear-viscoelastic, isotropic Maxwell earth model. Analytical expressions for characteristic relaxation times and relaxation strengths are found for viscoelastic toroidal deformation, associated with surface tangential stress, when there are two to five layers between the core–mantle boundary and Earth's surface. The multilayered models can include lithosphere, asthenosphere, upper and lower mantles and even low-viscosity ductile layer in the lithosphere. The analytical approach is self-consistent in that the Heaviside isostatic solution agrees with fluid limit. The analytical solution can be used for high-precision simulation of the toroidal relaxation in five-layer earths and the results can also be considered as a benchmark for numerical methods. Analytical solution gives only stable decaying modes—unstable mode, conjugate complex mode and modes of relevant poles with orders larger than 1, are all excluded, and the total number of modes is found to be just the number of viscoelastic layers between the core–mantle boundary and Earth's surface—however, any elastic layer between two viscoelastic layers is also counted. This confirms previous finding where numerical method (i.e. propagator matrix method) is used. We have studied the relaxation times of a lot of models and found the propagator matrix method to agree very well with those from analytical results. In addition, the asthenosphere and lithospheric ductile layer are found to have large effects on the amplitude of post-seismic deformation. This also confirms the findings of previous works.

06/02138 Assessment of the WWER-440N-213 reactor condition: Timofeev, B. T. and Karzov, G. P. International Journal of Pressure Vessels and Piping, 2006, 83, (3), 216–226.

We report the structural geometry and facies architecture of a small diapir-related carbonate-dominated basin from the Jurassic rift of the Moroccan High Atlas. The Azag minibasin is a lozenge-shaped depocenter completely enclosed by tectonic boundaries that we interpret as welds after former salt anticlines or salt walls. The exposed ca. 3000 m-thick infill of the Azag minibasin is asymmetric; layers are tilted to the W defining a rollover geometry. Areally-restricted sedimentary discontinuities and wedges of growth strata near the basin margins indicate sedimentation contemporaneous with diapiric rise of a Triassic ductile layer. Facies evolution through the basin reflects local accommodation by salt withdrawal and regional events in the High Atlas rift. The early basin infill in the Sinemurian and Pliensbachian shows thickness variations indicative of low-amplitude halokinetic movements, with reduced exposed thicknesses compared to surrounding areas. The exposed Toarcian and Aalenian deposits are also reduced in thickness compared to areas outside the basin. Subsidence increased dramatically in the Bajocian-early Bathonian (?), the main phase of downbuilding, when over 2600 m of carbonates and shales accumulated at a rate > 0.5 mm/a in the depocentral area of the minibasin governed by W-directed salt expulsion. The stratigraphic units distinguished often show maximum thicknesses and deeper facies in the depocentral area, and rapidly change to shallower facies at the basin margins. The Bajocian carbonate facies assemblage of the minibasin include: reservoir facies as microbialite-coral reefs in the basin margins (formed during periods of strong diapir inflation and bathymetric relief), basin-expansive oolite bars (formed during episodes of subdued relief), and organic-rich, dark lime mudstones and shales that show source-rock characteristics. The Azag basin is a good analog for the exploration of salt-related carbonate plays in rifts and continental margins where source-rock and reservoir can form in a same minibasin.

Pressure-sensitive ductile layers – I. Modeling the growth of extensive damage

Polymeric adhesives sandwiched between two elastic substrates are commonly found in multi-layers and IC packages. The non-elastic deformation and flow stress of such adhesive joints are highly pressure-sensitive. In this work, we study the effects of pressure-sensitivity, α, and plastic dilatancy, β, on void growth and coalescence ahead of a crack in ductile adhesive joints. To this end, a single layer of discrete voids is placed ahead of the crack in a pressure-sensitive dilatant adhesive sandwiched between two elastic substrates. The adhesive joint is subjected to small-scale yielding conditions. Using an associated flow rule ( α = β), we show that pressure-sensitivity not only intensifies damage levels but also increases its spatial extent several fold. The damage level as well as its spatial extent is found to be even greater when a non-associated flow rule ( β < α) is deployed. A reduction in the damage process zone’s thickness further increases the voiding activity in the adhesive, thereby resulting in brittle-like failure. This work also examines the fracture toughness trends using a material failure criterion for crack growth.

A combined dislocation—cohesive zone model for fracture in a confined ductile layer

The collective dislocation behavior near a crack tip in a ductile layer sandwiched between two brittle solids is analyzed via two-dimensional dislocation dynamics (DD) simulations that incorporate a cohesive zone (CZ) model. The cohesive crack tip is treated as part of a much larger finite crack confined in the ductile layer. The underlying boundary value problem is formulated with a set of boundary integral equations and numerically evaluated with a collocation method. The fracture energy of the layered composite material is shown to be strongly correlated with the layer thickness and is directly influenced by the cohesive strength of the ductile layer (Hsia KJ et al. (1994) J Mech Phys Solids 6 877–896).

The effect of energy feedbacks on continental strength

The classical strength profile of continents is derived from a quasi-static view of their rheological response to stress--one that does not consider dynamic interactions between brittle and ductile layers. Such interactions result in complexities of failure in the brittle-ductile transition and the need to couple energy to understand strain localization. Here we investigate continental deformation by solving the fully coupled energy, momentum and continuum equations. We show that this approach produces unexpected feedback processes, leading to a significantly weaker dynamic strength evolution. In our model, stress localization focused on the brittle-ductile transition leads to the spontaneous development of mid-crustal detachment faults immediately above the strongest crustal layer. We also find that an additional decoupling layer forms between the lower crust and mantle. Our results explain the development of decoupling layers that are observed to accommodate hundreds of kilometres of horizontal motions during continental deformation.