A method of estimating the stress exponent in the flow law for rocks using fold shape

Lan, Labao; Hudleston, Peter J.

doi:10.1007/bf00879592

Cited by 12 publications

(3 citation statements)

References 26 publications

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“…For example, Q/n values estimated for pressure solution creep (n = 1) range from 15 to 113 [e.g., Kawabata et al , 2009]. The ability, demonstrated here, to estimate Q/n without relying on high‐temperature laboratory experiments is a useful approach to better constrain rock rheology, and would be particularly powerful if used in combination with independent constraints on n [e.g., Grigull et al , 2012; Kenis et al , 2005; Lan and Hudleston , 1995; Treagus and Treagus , 2002]. …”

Section: Discussionmentioning

confidence: 99%

Constraints from rocks in the Taiwan orogen on crustal stress levels and rheology

2012

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[1] Taiwan's Hsüehshan range experienced penetrative coaxial deformation within and near the brittle-plastic transition between $6.5 and 3 Ma. This recent and short-lasting deformation in an active, well-studied orogen makes it an ideal natural laboratory for studying crustal rheology. Recrystallized grain size piezometry in quartz and Ti-in-quartz thermobarometry yield peak differential stresses of $200 MPa at 250-300 C that taper off to $80 MPa at $350 C and $14 MPa at $400-500 C. Stress results do not vary with lithology: recrystallized quartz veins in slates and metasiltstones yield equivalent stresses as recrystallized grains in quartzites. A minimum strain rate of 2.9 Â 10 À15 s À1 associated with this deformation is calculated by dividing a strain measurement (axial strain $0.3) in a strongly deformed quartzite by the available 3.5 m.y. deformation interval. We estimate a maximum strain rate of 7.0 Â 10 À14 s À1 by distributing the geodetic convergence rate throughout a region homogeneously deformed under horizontal compression. These stress, strain rate and temperature estimates are consistent with the predictions of widely applied dislocation creep flow laws for quartzite. The samples record stress levels at the brittle-plastic transition, indicating a coefficient of friction (m) of 0.37 in the upper crust consistent with results based on critical taper. Integrated crustal strength of the Hsüehshan range amounts to 1.7 Â 10 12 N/m based on our analysis, consistent with potential energy constraints based on topography. Other strength profiles are considered, however high crustal stresses (>300 MPa) conflict with our analysis. The study supports the use of the recrystallized grain size piezometer in quartz as a quick and inexpensive method for resolving stress histories in greenschist facies rocks. For consistency with the independent constraints presented here, we find it accurate to within +20%/À40%, significantly better than previously recognized.

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Section: Discussionmentioning

confidence: 99%

Constraints from rocks in the Taiwan orogen on crustal stress levels and rheology

2012

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“…14a). Lan and Hudleston (1995) presented a method to estimate the power-law exponent from observed fold shapes. Estimates of the viscosity ratios from fold shapes in combination with microstructural analysis have also been applied to estimate the stress levels during folding (Trepmann and Stöckhert, 2009).…”

Section: Some Applicationsmentioning

confidence: 99%

Folding and necking across the scales: a review of theoretical and experimental results and their applications

Schmalholz¹,

Mancktelow²

2016

Preprint

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Abstract. Shortening and extension of mechanically-layered ductile rock generates folds and pinch-and-swell structures (also referred to as necks or continuous boudins), which result from mechanical instabilities termed folding and necking, respectively. Folding and necking occur in layered rock because the corresponding mechanical work involved is less than that associated with a homogeneous deformation. The effective viscosity of a layered rock decreases during folding and necking, even when all material parameters remain constant. This mechanical softening due to viscosity decrease is solely the result of fold and pinch-and-swell structure development and is hence termed structural softening (or geometric weakening). Folding and necking occur over the whole range of geological scales, from microscopic up to the size of lithospheric plates. Lithospheric folding and necking are evidence for significant deformation of continental plates, which contradicts the rigid-plate paradigm of plate tectonics. We review here some theoretical and experimental results on folding and necking, including the lithospheric scale, together with a short historical overview of research on folding and necking. We focus on theoretical studies and analytical solutions that provide the best insight into the fundamental parameters controlling folding and necking, although they invariably involve simplifications. To first order, the two essential parameters to quantify folding and necking are the dominant wavelength and the corresponding maximal amplification rate. This review also includes a short overview of experimental studies, a discussion of recent developments involving mainly numerical models, a presentation of some practical applications of theoretical results, and a summary of similarities and differences between folding and necking.

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“…Several authors have used field observations to test the experimentally derived flow laws for quartz and quartz-dominated rocks against natural examples. For example, Kenis et al (2004) and Kenis et al (2005) have investigated the relationship between the shape of mullions and the power law stress exponent as well as the competence contrast between quartz and psammite, Treagus (1999) discussed the relationship between effective viscosity ratios and cleavage refraction in different rock layers, and Hudleston and Lan (1993, 1994 and Lan and Hudleston (1995a, 1995b, 1996 used fold shapes and scaling relationships between the amplitude, wavelength, and layer thickness in folds to deduce information about rock rheology in the form of viscosity ratios. Treagus and Treagus (2002) modelled viscosity ratios from strain variations in conglomerates with varying rock phase fractions.…”

Section: Introductionmentioning

confidence: 99%

Insights into the Rheology of Rocks under Brittle-Ductile Deformation Conditions from an Exhumed Shear Array in the Southern Alps, New Zealand

Grigull¹

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<p>A suite of brittle-ductile faults in the central Southern Alps, New Zealand is used as a natural laboratory into the rheology of quartz rocks. The fault array is ~2 km wide and formed in the hanging-wall of the SE-dipping Alpine Fault during the late Cenozoic at >= 25 km depth. It was exhumed in the past few Myr and is now exposed 5-7 km east of the Alpine Fault. The faults are near-vertical, extend laterally and vertically over tens of metres, and strike sub-parallel to the Alpine Fault. They displace quartzofeldspathic Alpine Schist (metagreywacke) in a predominantly brittle way. The faults impinge upon and displace abundant centimetre-thick quartz veins that are discordant to the dominant schist foliation. These quartz veins exhibit a full range of slip from fully brittle to fully ductile. In most quartz veins, a ductile component of slip and a 1-3 cm (n=72) wide ductile shear zone are present. The mean total slip measured in the veins is (7.2 +/- 5.8 ) cm (n=72). This study first develops a method to determine the true shape and displacement of a geological marker from any outcrop orientation. It then uses a set of geometrical scaling relationships exhibited by the ductilely-to-brittlely sheared quartz veins, and the observed interaction between brittle faults and ductilely deforming quartz veins to develop a series of finite-element models that reproduce the field observations. A flow law of the form de/dt = A*(f_H2O)^m*(sig_d)^n*exp(-Q/(R*T)) is used to model the behaviour of the quartz veins. Flow law parameters for the quartz veins and viscous and frictional strength ratios between quartz and schist are determined from these models. For Q = 135 kJ mol^-1, f_H2O= 200 MPa and m = 1.0, the results show that the scaling relationships in the quartz veins are successfully reproduced for A = 10^(-10 +/- 2) MPa^-n s^-1, and n = 4. The ratio between ductile-to-total slip (D) were measured for 72 veins throughout the brittle-ductile shear array and are highly variable. In order to understand what has led to this variability, we investigate the following parameters: original vein thickness, deformation temperature, water content, microfracturing, calcite fraction, and total slip. D-ratios appear to scale with original vein thickness, however, significant scattering of the D-values indicates that other factors also control D. The temperature resolution (from Titanium-in-Quartz geothermometry and oxygen isotopy) is not high enough to determine whether temperature influenced the D-values. Fourier Transform Infrared Spectroscopy (FTIR), and optical microscopy reveal that water content, microfracturing, and calcite fraction were very similar from one vein to another and therefore did not control the D-ratios either. Detailed outcrop maps of the brittle-ductile shears and displacement-length profiles along five individual faults indicate that the total slip varied rapidly and on short distances (cm- to m-scale) along the faults. We infer that these varying slip rates led to different flow strain rates in the deforming quartz veins and therefore can explain the variations in D-values. Optical microscopy reveals abundant fluid inclusions in both the deformed and undeformed parts of the veins. These inclusions indicate that the quartz was ‘wet’ and the veins were weakened with respect to the surrounding schist. We therefore infer that the location of the shear zones was predetermined by the position of the brittle faults propagating through the stronger schist and impinging on the weaker quartz veins.</p>

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A method of estimating the stress exponent in the flow law for rocks using fold shape

Cited by 12 publications

References 26 publications

Constraints from rocks in the Taiwan orogen on crustal stress levels and rheology

Constraints from rocks in the Taiwan orogen on crustal stress levels and rheology

Folding and necking across the scales: a review of theoretical and experimental results and their applications

Insights into the Rheology of Rocks under Brittle-Ductile Deformation Conditions from an Exhumed Shear Array in the Southern Alps, New Zealand

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