Rheological and physical characteristics of crustal-scaled materials for centrifuge analogue modelling

We characterize a set of analogue materials used for centrifuge analogue modelling simulating deformation at different levels in the crust simultaneously. Specifically, we improve the rheological characterization in the linear viscoelastic region of materials for the lower and middle crust, and cohesive synthetic sands without petroleum-binding agents for the upper crust. Viscoelastic materials used in centrifuge analogue modelling demonstrate complex dynamic behaviour, so viscosity alone is insufficient to determine if a material will be an effective analogue. Two series of experiments were conducted using an oscillating bi-conical plate rheometer to measure the storage and loss moduli and complex viscosities of several modelling clays and silicone putties. Tested materials exhibited viscoelastic and shear-thinning behaviour. The silicone putties and some modelling clays demonstrated viscous-dominant behaviour and reached Newtonian plateaus at strain rates < 0.5 × 10⁻² s⁻¹, while other modelling clays demonstrated elastic-dominant power-law relationships. Based on these results, the elastic-dominant modelling clay is recommended as an analogue for basement cratons. Inherently cohesive synthetic sands produce fine-detailed fault and fracture patterns, and developed thrust, strike-slip, and extensional faults in simple centrifuge test models. These synthetic sands are recommended as analogues for the brittle upper crust. These new results increase the accuracy of scaling analogue models to prototype. Additionally, with the characterization of three new materials, we propose a complete lithospheric profile of analogue materials for centrifuge modelling, allowing future studies to replicate a broader range of crustal deformation behaviours.     

Finite strain effects in experimental mullions

Mullions are cylindrical structures developed at the interface between rocks of different competence shortened along the layering. Natural examples include phyllosilicate-rich meta-igneous sheets and massive sulfides in silicate country rocks. In axial profiles they consist of rounded lobes convex into the less competent material which alternate with sharp cusps pointing toward the more competent material. Mullions have been produced experimentally in incompetent single layers of silicone putty (viscosity n_L = 2.9 × 10⁴ Pa s and power law exponent n = 1) embedded in a strain-rate softening host of plastilina + silicone putty mixture (n_h = 5.5 × 10⁶ Pa s and n = 7.1). The initiation, development and changes in geometry of mullions in the two interfering interfaces of a single incompetent layer shortened along its length by pure shear, are reported. Up to ∼10% bulk shortening (% BS) gentle flexures develop first in one interface, then, by ∼17% BS, in both. These rounded irregularities become cuspate at ∼25% BS. Where a lobe develops on one contact, a cusp is slightly preferred on the opposite side. Such antisymmetric mullions contrast with the symmetrical (pinch-and-swell) mullions predicted by Smith, but are like natural examples and those figured in the literature. The amplitudes of the cusps increase while their wavelength range decreases with finite shortening. It has been found that mature cusps distort but do not transgress the original contact even if the viscosity contrast is ∼-1/1000. Beyond 40% BS, cusps either mature to flames or combine to horns, and after 60% BS even the last surviving mullions cease to amplify dynamically and the layer only thickens uniformly. Most stages seen in the models can be matched by natural field examples.     

Another word on the rheology of silicone putty: Bingham

Silicone putty, a material commonly used as a rock-analog in tectonic scale-model studies, exhibits rheological behavior that is similar to the Bingham rheological model over a wide range of strain rate. Nevertheless, at low strain rates a power law is a useful approximation. Similarly, at high strain rates a linear viscous model can be applied. Thus, the choice of rheologic expression can be based on knowledge of the range of stress levels that are achieved in a given model. Conversely, models can be designed to develop appropriate stress levels so that the rheological formulation appropriate to the relevant prototype material will be applicable.     

A biaxial press for model deformation and rheological tests

A biaxial press has been designed and constructed specially for: (1) deforming geological scale models (initial dimensions, 30 × 7.5 × 5 cm; final ones, 7.5 × 30 × 5 cm); and (2) measuring rheological properties of modelling materials (clays, waxes, gelatine, plasticine, putty). At all stages of an experiment, a model can be photographed or observed in ordinary light or in transmitted polarized light. There are facilities for automatic recording and control of temperature, displacements, average longitudinal strain-rate and applied normal load or stress. The boundaries of the model remain planar and orthogonal. By using tested lubricants, one can obtain good approximations to conditions of: (a) frictionless boundaries; or (b) uniformly extended boundaries.     

A comparison of natural and experimental strain patterns around fold hinge zones

Patterns of finite strain around fold hinges in incompetent layers in buckled interlayered materials have been investigated in a series of experimental tests conducted with a view to comparing the results with a recently described anomalous slaty cleavage pattern from northern Norway. As well as compressing rubber, putty and plasticene models, a photoelastic strain analysis of buckled rubber strips in gelatine has been carried out. Strain patterns from the various tests are strikingly similar to the natural cleavage patterns, and a discussion of the factors favouring their development is presented.     

Experiments simulating surface deformation induced by pluton emplacement

We present centrifuge experiments to study the surface deformation induced by shallow pluton emplacement in a rheologically stratified crust. Sand simulates the topmost brittle crust; plastilina and denser silicone represent more and less competent crustal portions, respectively; lighter silicone simulates a buoyant intrusion. In the models, density differences affect the rate of intrusion but not their evolution or shape, whereas viscosity and strength stratifications control both the shape and rate of the intrusions. With a higher viscosity contrast (10^2–4) between the intrusion and the embedding media, the rise of the lighter silicone induces a laccolith-like intrusion, responsible for doming and thinning of the overburden; an apical depression may form, inducing silicone extrusion. Conversely, with a lower (10¹) viscosity contrast, the overburden and the intrusion exhibit a lens-shaped form, with a broad central depression bordered by an upward flexure towards the periphery. A sag in the floor of the intrusion is commonly observed; no silicone extrusion occurred. The intrusion is a hybrid between a laccolith and a lopolith. The comparison with nature (1) confirms roof uplift as an important means of accommodating space during pluton emplacement and (2) suggests that, where roof uplift plays a major role, pluton emplacement can induce a well-correlated sequence of events at surface: doming, the development of a depression and extrusion.     

高粘度非牛顿模型材料流变性能的实验测定

本文介绍了一种高粘度非牛顿模型材料流变性能的实验测定原理和方法。此法不仅可以得到材料的表观剪应变速率和非牛顿剪应变速率,还可以得到流变指数、应力指数和表观粘度。采用夹心式流变仪对M503模型材料进行了试验测定。M503是一种聚合物模型材料,由橡胶腻子XM-50(一种黑色密封材料)与滑石粉按重量1:1混炼而成。实验结果表明:M503是一种假塑性材料,当非牛顿剪应变速率控制在7.52-105.56×10-5s-1范围时,其应力指数n变化范围为1.15-3.33,表观粘度变化范围为4.69-0.99×107Pa·s。      

Physical analog (centrifuge) model investigation of contrasting structural styles in the Salt Range and Potwar Plateau,northern Pakistan

We use scaled physical analog (centrifuge) modeling to investigate along- and across-strike structural variations in the Salt Range and Potwar Plateau of the Himalayan foreland fold-thrust belt of Pakistan. The models, composed of interlayered plasticine and silicone putty laminae, comprise four mechanical units representing the Neoproterozoic Salt Range Formation (basal detachment), Cambrian–Eocene carapace sequence, and Rawalpindi and Siwalik Groups (Neogene molasse), on a rigid base representing the Indian craton. Pre-cut ramps simulate basement faults with various structural geometries.A pre-existing north-dipping basement normal fault under the model foreland induces a frontal ramp and a prominent fault-bend-fold culmination, simulating the Salt Range. The ramp localizes displacement on a frontal thrust that occurs out-of-sequence with respect to other foreland folds and thrusts. With a frontal basement fault terminating to the east against a right-stepping, east-dipping lateral ramp, deformation propagates further south in the east; strata to the east of the lateral ramp are telescoped in ENE-trending detachment folds, fault-propagation folds and pop-up structures above a thick basal detachment (Salt Range Formation), in contrast to translated but less-deformed strata with E–W-trending Salt-Range structures to the west. The models are consistent with Salt Range–Potwar Plateau structural style contrasts being due to basement fault geometry and variation in detachment thickness.     

Magma-induced strain localization in centrifuge models of transfer zones

Scaled centrifuge experiments have been used to investigate the dynamic relations between deformation and magma distribution in rift-related transfer zones. The physical models were built using suitable analogue materials, such as sand to represent the brittle upper crust, various kinds of silicone mixtures to simulate the lower crust and upper mantle and glycerol to reproduce magma. Models simulated the development of transfer zones across pre-existing glycerol reservoirs placed at the base of the analogue continental crust. In plan view, different geometries, dimensions and positions of subcrustal reservoirs were reproduced in three different sets of experiments; to compare results, models were also performed without magma-simulating glycerol.Set 1 experiments, incorporating a narrow rectangular glycerol reservoir, show that the low-viscosity material is able to localise deformation into the overlying crust, giving rise to discrete transfer zones. This concentrated surface deformation corresponds at depth to major magma accumulation. Set 2 experiments, with an initial wide squared glycerol reservoir, show instead that deformation is distributed across the whole model surface, corresponding at depth to relatively minor magma accumulation. Set 3 experiments explored various positions of a small squared reservoir that invariably localised faulting in the overlying analogue brittle crust at the onset of model deformation.The overall model behaviour suggests that magma distribution at depth can effectively control the strain distribution in the overlying crust and the deformative pattern of transfer zones. Strain distribution, in turn, may control magma emplacement as localized deformation would favour major accumulation of magma at transfer zones. Coupled to a strong thermal weakening of the country rocks, this process may ultimately lead to a positive feedback interaction between magma and deformation.     

The influence of different rheological parameters on the surface deformation and stress field of the Aegean–Anatolian region

The Aegean–Anatolian region is characterised by an inhomogeneous deformation pattern with high strain rates and a high seismicity both at the boundaries and in the plate interior. This pattern is controlled by the geometry and rheology of the structural units involved and their tectonic setting. A numerical analysis with a finite-element model of the region is used to quantify the influence of different rheological parameters. Viscoelastic material behaviour is implemented for the mantle lithosphere, whereas the crust is modelled with an elastic–plastic rheology. The variation of the inelastic material properties (viscosity and plastic strength) quantifies the influence of these material parameters on the deformation, stress, and strain patterns. Comparison of the modelled results with geodetic and geophysical observations reveals that the viscosity of the mantle lithosphere is the key to explaining the inhomogeneous deformation pattern. The best-fit model yields a viscosity of 10²⁰ Pa s beneath Anatolia, whereas adjacent regions have viscosities between 10²¹ and 10²³ Pa s. The model also explains the intra-plate seismicity and the stress field as well as its partitioning into regions with strike-slip and normal faulting. The final model is in good agreement with seismological, geodetic, and geological observations. Local deviations can be tracked down to small-scale structures, which are not included in the model.     

Strength and stiffness of compacted chalk putty–cement blends

Chalk breaks easily when subjected to human action such as mechanical handling, earthworks operations or pile installation. These actions break the cemented structure of chalk, which turns into a degraded material known as putty, with lower strength and stiffness than the intact chalk. The addition of Portland cement can improve the behaviour of chalk putties. Yet, there are no studies determining the tensile strength of chalk putty–cement blends, the initial stiffness evolution during the curing time and other design parameters such as friction angle and cohesion of this material. This paper addresses this knowledge gap and provides an interpretation of new experimental results based on the dimensionless index expressed as the ratio between porosity and volumetric content of cement (η/C_iv) or its exponential modification (η/C_iv^a). This index aids the selection of the amount of cement and density for key design parameters of compacted chalk putty–cement blends required in geotechnical engineering projects such as road foundations and pavements, embankments, and also bored concrete pile foundations.

     

Interaction of metamorphism, deformation and exhumation in large convergent orogens

Coupled thermal‐mechanical models are used to investigate interactions between metamorphism, deformation and exhumation in large convergent orogens, and the implications of coupling and feedback between these processes for observed structural and metamorphic styles. The models involve subduction of suborogenic mantle lithosphere, large amounts of convergence (≥ 450 km) at 1 cm yr^?1, and a slope‐dependent erosion rate. The model crust is layered with respect to thermal and rheological properties — the upper crust (0–20 km) follows a wet quartzite flow law, with heat production of 2.0 μW m^?3, and the lower crust (20–35 km) follows a modified dry diabase flow law, with heat production of 0.75 μW m^?3. After 45 Myr, the model orogens develop crustal thicknesses of the order of 60 km, with lower crustal temperatures in excess of 700 °C. In some models, an additional increment of weakening is introduced so that the effective viscosity decreases to 10¹⁹ Pa.s at 700 °C in the upper crust and 900 °C in the lower crust. In these models, a narrow zone of outward channel flow develops at the base of the weak upper crustal layer where T≥600 °C. The channel flow zone is characterised by a reversal in velocity direction on the pro‐side of the system, and is driven by a depth‐dependent pressure gradient that is facilitated by the development of a temperature‐dependent low viscosity horizon in the mid‐crust. Different exhumation styles produce contrasting effects on models with channel flow zones. Post‐convergent crustal extension leads to thinning in the orogenic core and a corresponding zone of shortening and thrust‐related exhumation on the flanks. Velocities in the pro‐side channel flow zone are enhanced but the channel itself is not exhumed. In contrast, exhumation resulting from erosion that is focused on the pro‐side flank of the plateau leads to ‘ductile extrusion’ of the channel flow zone. The exhumed channel displays apparent normal‐sense offset at its upper boundary, reverse‐sense offset at its lower boundary, and an ‘inverted’ metamorphic sequence across the zone. The different styles of exhumation produce contrasting peak grade profiles across the model surfaces. However, P–T–t paths in both cases are loops where P_max precedes T_max, typical of regional metamorphism; individual paths are not diagnostic of either the thickening or the exhumation mechanism. Possible natural examples of the channel flow zones produced in these models include the Main Central Thrust zone of the Himalayas and the Muskoka domain of the western Grenville orogen.     

Modelling Nd-isotopes with a coarse resolution ocean circulation model: Sensitivities to model parameters and source/sink distributions

The neodymium (Nd) isotopic composition (?_Nd) of seawater is a quasi-conservative tracer of water mass mixing and is assumed to hold great potential for paleoceanographic studies. Here we present a comprehensive approach for the simulation of the two neodymium isotopes ¹⁴³Nd, and ¹⁴⁴Nd using the Bern3D model, a low resolution ocean model. The high computational efficiency of the Bern3D model in conjunction with our comprehensive approach allows us to systematically and extensively explore the sensitivity of Nd concentrations and ?_Nd to the parametrisation of sources and sinks. Previous studies have been restricted in doing so either by the chosen approach or by computational costs. Our study thus presents the most comprehensive survey of the marine Nd cycle to date.Our model simulates both Nd concentrations as well as ?_Nd in good agreement with observations. ?_Nd covaries with salinity, thus underlining its potential as a water mass proxy. Results confirm that the continental margins are required as a Nd source to simulate Nd concentrations and ?_Nd consistent with observations. We estimate this source to be slightly smaller than reported in previous studies and find that above a certain magnitude its magnitude affects ?_Nd only to a small extent. On the other hand, the parametrisation of the reversible scavenging considerably affects the ability of the model to simulate both, Nd concentrations and ?_Nd. Furthermore, despite their small contribution, we find dust and rivers to be important components of the Nd cycle. In additional experiments, we systematically varied the diapycnal diffusivity as well as the Atlantic-to-Pacific freshwater flux to explore the sensitivity of Nd concentrations and its isotopic signature to the strength and geometry of the overturning circulation. These experiments reveal that Nd concentrations and ?_Nd are comparatively little affected by variations in diapycnal diffusivity and the Atlantic-to-Pacific freshwater flux. In contrast, an adequate representation of Nd sources and sinks is crucial to simulate Nd concentrations and ?_Nd consistent with observations. The good agreement of our results with observations paves the way for the evaluation of the paleoceanographic potential of ?_Nd in further model studies.     

Strain distribution within arcuate diapiric ridges of silicone putty

Twenty crescent-shaped diapiric models of silicone putty were made in two high-capacity centrifuges. The strain distribution within the models was studied by means of coloured rectangular elements, a method which led to large errors at random locations. Most elements affected by large errors could be identified in repeated experiments.The deformation pattern within the central segment of the diapiric ridges is dominated by two large regions of contrasting principal strain normal to the radial symmetry plane (axial plane of the crescents). This principal strain is tensile near the concave boundary of a ridge and compressive near the convex boundary of a ridge.Within the radial symmetry plane, the orientation pattern of long axes of the total-strain ellipses resembles an open fan which diverges toward the crest of the diapiric ridge. In the high-amplitude models, there is a narrow crestal region in which the long axes are subhorizontal. A similar region has been noted in comparable models of cylindrical diapiric ridges.In one of our models (WMS 20), the arcuate hinge line has pronounced culminations at both ends of the diapiric ridge. This results in a strong crestal depression at the radial symmetry plane where the strain analysis was performed. Accordingly, the characteristic region of tensile normal strain occupies most of the radial section.     

A modified normalized model for predicting effective soil thermal conductivity

Effective soil thermal conductivity (λ _eff) describes the ability of a multiphase soil to transmit heat by conduction under unit temperature gradient. It is a critical parameter for environmental science, earth and planetary science, and engineering applications. Numerous models are available in the literature, but their applicability is generally restricted to certain soil types or water contents (θ). The objective of this study was to develop a new model in the similar form of the Johansen 1975 model to simulate the λ _eff(θ) relationship of soils of various soil textures and water contents. An exponential type model with two parameters is developed and a new function for calculating dry soil thermal conductivity is presented. Performance of the new model and six other normalized models were evaluated with published datasets. The results show that the new model is able to well mimic λ _eff(θ) relationship of soils from sand to silt loam and from oven dry to full saturation. In addition, it has the best performance among the seven models under test (with root-mean-square error of 0.059 W m^?1 °C^?1, average deviations of 0.0009 W m^?1 °C^?1, and Nash–Sutcliffe efficiency of 0.994). The new model has potential to improve the reliability of soil thermal conductivity estimation and be incorporated into numerical modeling for environmental, earth and engineering studies.     

Active and passive measurements of radon diffusion coefficient from building construction materials

The gaseous state and chemical inert behavior of radon make it important tracer for the radon transport study through the building materials. The radon resistant property of building construction materials is important parameter to control the indoor radon levels in living and workplaces. The materials with higher radium content can be made less severe by the use of some building materials of low diffusion coefficient and diffusion length. This makes the study of radon diffusion through building material more important along with the study of exhalation and radioactivity content. Keeping this in mind the radon diffusion study was carried out through different building construction materials used for wall and floor by active and passive techniques. The diffusion coefficient from these building materials measured by passive methods varied from (0.9 ± 0.5) × 10^?7 to (22.95 ± 13.19) × 10^?6 m²s^?1 and radon diffusion length varied from 0.21 to 3.31 m for cement, soil, sand, wall putty and plaster of Paris (POP) etc. The radon diffusion coefficient measured by active technique varied from 1.93 × 10^?10 to 1.36 × 10^?7 m²s^?1 for samples with definite geometry like paper, polyethylene, marble, granite etc. The radon diffusion coefficient and diffusion length depend upon the porosity and density of materials for powder samples.     

引入非线性瞬时弹性模量的软土流变模型

软土是一种非线性流变物质,但现行流变模型却忽略了加载瞬时的非线性变形;软土流变试验参数是数学模型参数而非物理模型参数,一个土样一般只对应一种材料参数,但现行流变模型的模型参数常随着荷载变化,且变化无规律,离散性大。基于以有机质为流变相物质的人工土试样室内一维压缩蠕变试验,建立了各级荷载作用下具有相同模型参数的7组件流变模型,用非线性弹簧H描述软土加载瞬时弹塑性变形、并联的三元件组件模拟软土随时间变化的黏弹塑变形。结果表明：引入三次非线性瞬时弹性模量的7组件流变模型能够较准确地反映软土的流变特性。