Cavity expansion analyses of crushable granular materials with state‐dependent dilatancy

Crushability is one of the important behaviors of granular materials particularly under high stress states, and affects both the deformability and strength of the materials that are in essence associated with state‐dependent dilatancy. In this presentation, first, a new critical state model is proposed to take into account the three different modes of compressive deformation of crushable granular materials, i.e. particle rearrangement, particle crushing and pseudo‐elastic deformation. Second, the governing equations for cavity expansion in crushable granulates are introduced, in which the state‐dependent dilatancy as well as the bounding surface plasticity model are used. Then, the procedure to obtain semi‐analytical solutions to cavity expansion in the material is described in detail, in which a commercial differential equation solver is employed. Finally, cavity expansion analyses are carried out on Toyoura sand, a well‐documented granular material, to demonstrate the effects of crushability and state‐dependent dilatancy. The study shows that particle crushing does occur at both high stress and critical states and affects the stress fields and the deformation behavior of the material surrounding the cavity in association with state‐dependent dilatancy. This leads to conclusion that particle crushing and state‐dependent dilatancy have to be taken into account when cavity expansion theory is used to interpret cone penetration tests and pressuremeter tests. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of connecting rain barrels on the storage size reduction

In this article, the possibility of sharing rain barrels and the potential benefit of reducing storage size through physical and non‐physical connections of rain barrels in a community are investigated. Using the concepts of homogeneous/heterogeneous users in rainwater harvesting systems (RWHS), two simple cases of a community composed of four prospective users are examined. The first is performed with the users who have the same mean and variance in water demands (homogeneous users), and the second is with the users with different means and variances (heterogeneous users). To take account for the rainfall characteristics in different places, historical records from six cities in the USA are used for storage–reliability–yield analysis. The result indicates that required total storage can be reduced by connecting multiple rain barrels. In addition, a significant difference is found between homogeneous and heterogeneous user groups. Homogeneous users do not achieve a substantial benefit from connecting their rain barrels; these users may even be disadvantaged by sharing. In contrast, heterogeneous users receive benefit by reducing the total required storage. Most benefit is expected between users with maximum difference in mean water demands. The reduction in storage size was as considerable as 37% in this study. The quantity of storage reduction depends on locations and target reliabilities. Knowledge of the benefits and limitations of rain barrel connections can improve RWHS performance through ability to customize a network plan for individual users. Copyright © 2011 John Wiley & Sons, Ltd.     

Cavity expansion in cross‐anisotropic rock

Schistous rock can be considered—in a first approximation—as cross‐anisotropic linear elastic material. The determination of the corresponding material constants on the basis of the laboratory investigation of rock samples often fails, as the extraction of appropriate cores proves to be unfeasible (the cores disintegrate if the schistosity is pronounced). In this paper a new method is presented to determine the material constants of a linear elastic cross‐anisotropic rock on the basis of cavity expansion field tests, e.g. with a radial jack. To this purpose, an analytic approximation for the deformation of a hydrostatically loaded cylindrical cavity in cross‐anisotropic rock is derived which serves to the inverse analysis of the material parameters. Copyright © 2010 John Wiley & Sons, Ltd.     

Investigation of highly efficient algorithms for solving linear equations in the discontinuous deformation analysis method

Large‐scale engineering computing using the discontinuous deformation analysis (DDA) method is time‐consuming, which hinders the application of the DDA method. The simulation result of a typical numerical example indicates that the linear equation solver is a key factor that affects the efficiency of the DDA method. In this paper, highly efficient algorithms for solving linear equations are investigated, and two modifications of the DDA programme are presented. The first modification is a linear equation solver with high efficiency. The block Jacobi (BJ) iterative method and the block conjugate gradient with Jacobi pre‐processing (Jacobi‐PCG) iterative method are introduced, and the key operations are detailed, including the matrix‐vector product and the diagonal matrix inversion. Another modification consists of a parallel linear equation solver, which is separately constructed based on the multi‐thread and CPU‐GPU heterogeneous platforms with OpenMP and CUDA, respectively. The simulation results from several numerical examples using the modified DDA programme demonstrate that the Jacobi‐PCG is a better iterative method for large‐scale engineering computing and that adoptive parallel strategies can greatly enhance computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd.     

A constitutive model for mechanical and chemo‐mechanical compaction in sedimentary basins and finite element analysis

Compaction and associated fluid flow are fundamental processes in sedimentary basin deformation. Purely mechanical compaction originates mainly from pore fluid expulsion and rearrangement of solid particles during burial, while chemo‐mechanical compaction results from Intergranular Pressure‐Solution (IPS) and represents a major mechanism of deformation in sedimentary basins during diagenesis. The aim of the present contribution is to provide a comprehensive 3D framework for constitutive and numerical modeling of purely mechanical and chemo‐mechanical compaction in sedimentary basins. Extending the concepts that have been previously proposed for the modeling of purely mechanical compaction in finite poroplasticity, deformation by IPS is addressed herein by means of additional viscoplastic terms in the state equations of the porous material. The finite element model integrates the poroplastic and poroviscoplastic components of deformation at large strains. The corresponding implementation allows for numerical simulation of sediments accretion/erosion periods by progressive activation/deactivation of the gravity forces within a fictitious closed material system. Validation of the numerical approach is assessed by means of comparison with closed‐form solutions derived in the context of a simplified compaction model. The last part of the paper presents the results of numerical basin simulation performed in one dimensional setting, demonstrating the ability of the modeling to capture the main features in elastoplastic and viscoplastic compaction. Copyright © 2016 John Wiley & Sons, Ltd.     

The strain‐dependent spatial evolution of garnet in a high‐P ductile shear zone from the Western Gneiss Region (Norway): a synchrotron X‐ray microtomography study

Reaction and deformation microfabrics provide key information to understand the thermodynamic and kinetic controls of tectono‐metamorphic processes, however, they are usually analysed in two dimensions, omitting important information regarding the third spatial dimension. We applied synchrotron‐based X‐ray microtomography to document the evolution of a pristine olivine gabbro into a deformed omphacite–garnet eclogite in four dimensions, where the 4^th dimension is represented by the degree of strain. In the investigated samples, which cover a strain gradient into a shear zone from the Western Gneiss Region (Norway), we focused on the spatial transformation of garnet coronas into elongated garnet clusters with increasing strain. The microtomographic data allowed quantification of garnet volume, shape and spatial arrangement evolution with increasing strain. The microtomographic observations were combined with light microscope and backscatter electron images as well as electron microprobe (EMPA) and electron backscatter diffraction (EBSD) analysis to correlate mineral composition and orientation data with the X‐ray absorption signal of the same mineral grains. With increasing deformation, the garnet volume almost triples. In the low‐strain domain, garnet grains form a well interconnected large garnet aggregate that develops throughout the entire sample. We also observed that garnet coronas in the gabbros never completely encapsulate olivine grains. In the most highly deformed eclogites, the oblate shapes of garnet clusters reflect a deformational origin of the microfabrics. We interpret the aligned garnet aggregates to direct synkinematic fluid flow, and consequently influence the transport of dissolved chemical components. EBSD analyses reveal that garnet shows a near‐random crystal preferred orientation that testifies no evidence for crystal plasticity. There is, however evidence for minor fracturing, neo‐nucleation and overgrowth. Microprobe chemical analysis revealed that garnet compositions progressively equilibrate to eclogite facies, becoming more almandine‐rich. We interpret these observations as pointing to a mechanical disintegration of the garnet coronas during strain localization, and their rearrangement into individual garnet clusters through a combination of garnet coalescence and overgrowth while the rock was deforming.     

Consolidation in spatially random unsaturated soils based on coupled flow‐deformation simulation

This paper integrates random field simulation of soil spatial variability with numerical modeling of coupled flow and deformation to investigate consolidation in spatially random unsaturated soil. The spatial variability of soil properties is simulated using the covariance matrix decomposition method. The random soil properties are imported into an interactive multiphysics software COMSOL to solve the governing partial differential equations. The effects of the spatial variability of Young's modulus and saturated permeability together with unsaturated hydraulic parameters on the dissipation of excess pore water pressure and settlement are investigated using an example of consolidation in a saturated‐unsaturated soil column because of loading. It is found that the surface settlement and the pore water pressure profile during the process of consolidation are significantly affected by the spatially varying Young's modulus. The mean value of the settlement of the spatially random soil is more than 100% greater than that of the deterministic case, and the surface settlement is subject to large uncertainty, which implies that consolidation settlement is difficult to predict accurately based on the conventional deterministic approach. The uncertainty of the settlement increases with the scale of fluctuation because of the averaging effect of spatial variability. The effects of spatial variability of saturated permeability k_sat and air entry parameters are much less significant than that of elastic modulus. The spatial variability of air entry value parameters affects the uncertainties of settlement and excess pore pressure mostly in the unsaturated zone. Copyright © 2016 John Wiley & Sons, Ltd.     

High‐ to ultrahigh‐temperature metamorphism in the lower crust: An example resulting from Hikurangi Plateau collision and slab rollback in New Zealand

Lower crustal xenoliths erupted from an intraplate diatreme reveal that a portion of the New Zealand Gondwana margin experienced high‐temperature (HT) to ultrahigh‐temperature (UHT) granulite facies metamorphism just after flat slab subduction ceased at c. 110–105 Ma. P–T calculations for garnet–orthopyroxene‐bearing felsic granulite xenoliths indicate equilibration at ~815 to 910°C and 0.7 to 0.8 GPa, with garnet‐bearing mafic granulite xenoliths yielding at least 900°C. Supporting evidence for the attainment of HT and UHT conditions in felsic granulite comes from re‐integration of exsolution in feldspar (~900–950°C at 0.8 GPa), Ti‐in‐zircon thermometry on Y‐depleted overgrowths on detrital zircon grains (932°C ± 24°C at aTiO₂ = 0.8 ± 0.2), and correlation of observed assemblages and mineral compositions with thermodynamic modelling results (≥850°C at 0.7 to 0.8 GPa). The thin zircon overgrowths, which were mainly targeted by drilling through the cores of grains, yield a U–Pb pooled age of 91.7 ± 2.0 Ma. The cause of Late Cretaceous HT‐UHT metamorphism on the Zealandia Gondwana margin is attributed to collision and partial subduction of the buoyant oceanic Hikurangi Plateau in the Early Cretaceous. The halt of subduction caused the fore‐running shallowly dipping slab to rollback towards the trench position and permitted the upper mantle to rapidly increase the geothermal gradient through the base of the extending (former) accretionary prism. This sequence of events provides a mechanism for achieving regional HT–UHT conditions in the lower crust with little or no sign of this event at the surface.