Shear strength and yield surface of a partially saturated sandy silt under generalized stress states

This paper studies the hydromechanical behavior of a slightly compacted mixture of sand and clayey silt (30%/70%) under a generalized stress state. The experimental study focused on analyzing the yielding response and shear strength behavior at different stress states (characterized by the intermediate principal stress parameter b, or Lode angle) and at different initial total suctions (as-compacted state). For the investigation, a hollow cylinder apparatus was used. The shear strength results allowed defining the variation of the critical state line with the Lode angle and the suction. Different models were proposed for isotropic and anisotropic yield surfaces, and their shape and rotation were calibrated with experimental results. The modeled yield surfaces fitted reasonably well the experimental results, considering their inclination and dependence on the suction, mean and deviatoric stresses and Lode angle. In addition, some relationships between the stresses and the model parameters were proposed to normalize the yield surface equation.

Calculation of the Deviatoric Stress Field in New Zealand

<p>I model the vertically averaged deviatoric stress field for New Zealand using velocity and crustal density data. I use a thin sheet model of a viscously deforming lithosphere, averaging over a depth of 100 km and solve the stress balance equation. Two methods of solving the stress balance equation are compared: one method solves first for deviatoric stresses due to gravitational potential energy per unit volume before accounting for deviatoric stresses due to boundary conditions; the other method assumes an isotropic viscosity to relate deviatoric stress to strain rate, solving for the viscosity field. Under synthetic testing, the two step method is able to cope with high levels of noise but contains edge effects. The method solving for viscosity is accurate at low noise levels, however, it is unreliable at high noise levels. I apply the two step method to New Zealand using a Quaternary and a GPS-derived velocity model. Vertically averaged deviatoric stress magnitudes are found to be 10-30 MPa, similar to magnitudes found for other plate-boundary zones. Gravitational and boundary stresses each account for approximately half of the full deviatoric stress. Effective viscosities are found to be 1-10×10²¹ Pa s in the regions of most active deformation, which can be interpreted in terms of the long term strength of the lithosphere controlled by temperature and/or lithology.</p>

Calculation of the Deviatoric Stress Field in New Zealand

<p>I model the vertically averaged deviatoric stress field for New Zealand using velocity and crustal density data. I use a thin sheet model of a viscously deforming lithosphere, averaging over a depth of 100 km and solve the stress balance equation. Two methods of solving the stress balance equation are compared: one method solves first for deviatoric stresses due to gravitational potential energy per unit volume before accounting for deviatoric stresses due to boundary conditions; the other method assumes an isotropic viscosity to relate deviatoric stress to strain rate, solving for the viscosity field. Under synthetic testing, the two step method is able to cope with high levels of noise but contains edge effects. The method solving for viscosity is accurate at low noise levels, however, it is unreliable at high noise levels. I apply the two step method to New Zealand using a Quaternary and a GPS-derived velocity model. Vertically averaged deviatoric stress magnitudes are found to be 10-30 MPa, similar to magnitudes found for other plate-boundary zones. Gravitational and boundary stresses each account for approximately half of the full deviatoric stress. Effective viscosities are found to be 1-10×10²¹ Pa s in the regions of most active deformation, which can be interpreted in terms of the long term strength of the lithosphere controlled by temperature and/or lithology.</p>

Rheological stratification in impure rock salt during long-term creep: morphology, microstructure, and numerical models of multilayer folds in the Ocnele Mari salt mine, Romania

At laboratory timescales, rock salt samples with different composition and microstructure show variance in steady-state creep rates, but it is not known if and how this variance is manifested at low strain rates and corresponding deviatoric stresses. Here, we aim to quantify this from the analysis of multilayer folds that developed in rock salt over geological timescale in the Ocnele Mari salt mine in Romania. The formation is composed of over 90 % of halite, while distinct multiscale layering is caused by variation in the fraction of impurities. Regional tectonics and mine-scale fold structure are consistent with deformation in a shear zone after strong shearing in a regional detachment, forming over 10 m scale chevron folds of a tectonically sheared sedimentary layering, with smaller folds developing on different scales in the hinges. Fold patterns at various scales clearly indicate that during folding, the sequence was mechanically stratified. The dark layers contain more impurities and are characterised by a more regular layer thickness compared to the bright layers and are thus inferred to have higher viscosities. Optical microscopy of gamma-decorated samples shows a strong shape-preferred orientation of halite grains parallel to the foliation, which is reoriented parallel to the axial plane of the folds studied. Microstructures indicate dislocation creep, together with extensive fluid-assisted recrystallisation and strong evidence for solution–precipitation creep. This provides support for linear (Newtonian) viscous rheology as a dominating deformation mechanism during the folding. Deviatoric stress during folding was lower than during shearing in the detachment at around 1 MPa. We investigate fold development on various scales in a representative multilayer package using finite-element numerical models, constrain the relative layer thicknesses in a selected outcrop, and design a numerical model. We explore the effect of different Newtonian viscosity ratios between the layers on the evolving folds on different scales. By comparing the field data and numerical results, we estimate that the effective viscosity ratio between the layers was larger than 10 and up to 20. Additionally, we demonstrate that the considerable variation of the layer thicknesses is not a crucial factor to develop folds on different scales. Instead, unequal distribution of the thin layers, which organise themselves into effectively single layers with variable thickness, can control deformation on various scales. Our results show that impurities can significantly change the viscosity of rock salt deforming at low deviatoric stress and introduce anisotropic viscosity, even in relatively pure layered rock.

Understanding dilatancy in rocksalt: a microphysical model of rocksalt at the grain-scale

&lt;p&gt;The use of underground repositories excavated in low-permeability formations, such as rock salt, to store high-level, radioactive waste requires the analysis of its isolation properties. Underground excavation disturbs the original stress state of the rocksalt, resulting in a deviatoric stress distribution around the walls of excavated galleries and boreholes. At high deviatoric stresses and low confinement, dense rocksalt produces an increase in porosity and permeability. The extent of dilatancy in this disturbed zone, as well as the impact of dilatancy on the transport properties, are important for assessing the safety of radio-active waste disposal as well as the integrity of salt caverns and boreholes in the context of energy storage, brine cavern abandonment and gas well abandonment. &amp;#160;&lt;/p&gt;&lt;p&gt;The stress conditions at which dilatancy occurs have been measured experimentally, and are typically determined on the basis of macroscopic (sample-scale) measurements of volumetric strain and permeability, and/or acoustic velocity changes or emissions. However, the detailed mechanisms causing dilatancy at the grain-scale are poorly understood. We have developed a microphysical model for dilatancy in rocksalt, both under dry and wet conditions, including mechanisms such as slip and opening of grain boundaries. This model enables us to describe and predict the dilatancy behaviour of rocksalt based on physical, mechanical and chemical processes. The model is presently being independently verified through comparison with existing literature data, and new experiments.&lt;/p&gt;

Porosity and Permeability Evolution with Deviatoric Stress of Reservoir Sandstone: Insights from Triaxial Compression Tests and In Situ Compression CT

Porosity and permeability are the two most important characteristics of underground gas storage in sandstone reservoirs. Injection of gas into reservoir rocks will cause rock deformation. The deformation will influence the porosity and permeability properties of the rocks. We investigate the evolution of these two properties of storage sandstone by triaxial compression tests and a uniaxial in situ compression CT test. As the deviatoric stress increases, the sandstone is compressed firstly (porosity reduction) and then dilates (porosity enhancement). With the increase in confining stress, the occurrence of volumetric dilation will be delayed. Trapped porosity of this sandstone at different deviatoric stresses is very small (0.122%-0.115%) which indicates that nearly all pores are connected. During the compression stage, the decrease in permeability is related to compression of pores and microcracks. During the volumetric dilation stage, it is related to increase in tortuosity. This interpretation can be confirmed by observations of in situ compression CT. The permeability evolution estimated by pore network modeling is consistent with macroscopic testing results.

Study of the Long-Term Deformation Characteristics of Municipal Sludge Solidified Soil under the Coupling Action of Dry-Wet Cycles and Initial Static Deviatoric Stress

A self-developed curing agent is used to solidify the municipal sludge taken from Tianjin. Then, the long-term deformation characteristics of the sludge solidified soil are investigated by means of unconsolidated undrained creep tests with different dry-wet cycles for considering the influence of climate. The experimental results show that the attenuation rate of the shear peak strength of municipal sludge solidified soil decreases gradually with the increase of the number of dry-wet cycles, and the strength remains unchanged when the number of dry-wet cycles is greater than 10. The variation laws under different initial static deviatoric stresses are basically identical. When the applied stress is less than the yield stress of the sludge solidified soil, the duration curves of creep show only attenuated stage, i.e., with very small deformation, and the deformation reaches a constant in a short period of time. When the deviatoric stress reaches the long-term strength of the soil, the instantaneous deformation of the sludge solidified soil becomes large and damage occurs quickly. Under the same deviatoric stress, the creep deformation increases with the increase of the number of dry-wet cycles. When the load applied in each step is of the same magnitude, the higher the initial static deviatoric stress is, the larger the deformation of sludge solidified soil will be. It is found that the stress-strain relationship and the relationship between creep strain and time can be well described by an exponential function and a hyperbolic function, respectively. On this basis, a creep model is proposed for the long-term deformation considering the effect of dry-wet cycle times and initial static deviatoric stress. The model is further validated by comparing the predictions with the test results under different deviatoric stresses; the good agreement between which shows the potential application of the model to relevant practical engineering.

The role of crustal models in the dynamics of the India–Eurasia collision zone

SUMMARY We investigate how different crustal models can affect the stress field, velocities and associated deformation in the India–Eurasia collision zone. We calculate deviatoric stresses, which act as deformation indicators, from topographic load distribution and crustal heterogeneities coupled with density driven mantle convection constrained by tomography models. We use three different crustal models, CRUST2.0, CRUST1.0 and LITHO1.0 and observe that these models have different crustal thickness and densities. As a result, gravitational potential energy (GPE) calculated based on these densities and crustal thicknesses differ between these models and so do the associated deviatoric stresses. For GPE only models, LITHO1.0 provides a better constraint on deformation as it yields the least misfit (both orientation and relative magnitude) with the surface observations of strain rates, lithospheric stress, plate motions and earthquake moment tensors. However, when the stresses from GPE are added to those associated with mantle tractions arising from density-driven mantle convection, the coupled models in all cases provide a better fit to surface observations. The N–S tensional stresses predicted by CRUST2.0 in this area get reduced significantly due to addition of large N–S compressional stresses predicted by the tomography models S40RTS and SAW642AN leading to an overall strike-slip regime. On the other hand, the hybrid models, SINGH_S40RTS and SINGH_SAW that are obtained by embedding a regional P-wave model, Singh et al., in global models of S40RTS and SAW642AN, predict much lower compression within this area. These hybrid models provide a better constraint on surface observations when coupled with CRUST1.0 in central Tibet, whereas the combined LITHO1.0 plus mantle traction model provides a better fit in some other areas, but with a degradation of fit in central Tibet.

Understanding deformation of cratons in presence of mid-lithospheric discontinuity

&lt;p&gt;The recent discovery of mid-lithospheric discontinuity (MLD) within most cratons has added a new dimension in the understanding of cratonic survival. The MLD shows up as a seismic discontinuity at ~80-160 km depth. However, there is controversy regarding the strength of this layer. While some studies suggest that this layer is as strong as the craton itself, others advocate that under some special conditions (e.g. metasomatism) MLD can become weak and aid in the delamination of cratons. In this study, we develop 3-D full spherical mantle convection models to understand the effect of MLD in the survival of cratons. In our models, we incorporate MLDs of variable strength, depth and thickness. Along with varying the strength of MLDs, we use different combinations of craton and asthenosphere viscosity to quantitatively estimate how deformation pattern varies. Results obtained from the models suggest that in the presence of a weak MLD stress magnitudes decrease but strain-rates increase&amp;#160; ~2-3 times. This could potentially lead to delamination of cratons. To constrain the present-day strength of MLDs, we predict deviatoric stresses from these different models and compare them to the observed SH&lt;sub&gt;max&lt;/sub&gt; directions obtained from the World Stress Map. The deviatoric stress pattern changes as the viscosity, depth and thickness of MLD changes.&lt;/p&gt;

Measuring stress and strain in rocks by spectroscopy

&lt;p&gt;Microstructures and the different thermoelastic properties of minerals ensure that no rock is ever under perfect hydrostatic stress at the grain level. If deviatoric stresses and strains significantly modify thermodynamic properties of minerals so that the equilibrium assemblage and compositions are different from that predicted from hydrostatic conditions, it is crucial to be able to measure the stress state of minerals in-situ in rocks. Forty years ago it was considered that &amp;#8216;Analysis of residual stresses at the scale of mineral grains within a polycrystalline aggregate such as a rock is virtually intractable&amp;#8217; [1]. This is no longer true.&lt;/p&gt;&lt;p&gt;Confocal Raman spectroscopy allows spectra to be collected from small volumes of mineral grains within a section. The positions of Raman peaks depends on the elastic strains in the minerals through the phonon-mode Gr&amp;#252;neisen tensors [2]. The development of precise DFT simulations of crystal structures and their Raman spectra now allows the components of the phonon-mode Gr&amp;#252;neisen tensors to be calculated [3]. With these tensors it is possible to determine the strains from measured Raman peak positions, to thereby map the strain, and hence the stress state, of individual mineral grains. We have now extended the DFT simulations to show that the Raman shifts of crystals subject to symmetry-breaking stresses (e.g. around inclusions) are, as expected, not solely determined by the phonon-mode Gr&amp;#252;neisen tensors of the ideal crystal. We have also recently developed the measurement of the change in peak intensities in cross-polarised Raman spectra to determine the stress [4] in these cases. For minerals such as garnets, this effect is stronger and therefore more sensitive to stress than the shifts in peak positions and offers at the moment the possibility to quickly visualise stress and strain fields in minerals in-situ in rocks. Quantitative stress values from this method await the determination of the piezo-phonon tensors for garnets, but comparison of peak positions and intensities show that the two methods return consistent results.&lt;/p&gt;&lt;p&gt;This work was supported by ERC-StG TRUE DEPTHS grant (number 714936) to M. Alvaro. N. Campomenosi was also supported by the University of Genova.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;[1] Holzhausen &amp; Johnson (1979) Tectonophysics 58, 237.&lt;/p&gt;&lt;p&gt;[2] Angel et al. (2019) Zeitschrift f&amp;#252;r Kristallographie, 234, 129.&lt;/p&gt;&lt;p&gt;[3] Murri et al. (2018) American Mineralogist, 103, 1869.&lt;/p&gt;&lt;p&gt;[4] Campomenosi et al. (2020) Contributions to Mineralogy and Petrology, accepted.&lt;/p&gt;