Stability analysis of tunnels driven in jointed rocks by means of a homogenized limit analysis approach

Conceived as a potential alternative to the classical design methods employed for analyzing the stability of underground structures driven in jointed rocks, the homogenization approach stems from the heuristic idea that, from a macroscopic point of view, a rock mass cut by a network of joints may be perceived as a homogenized continuum. The strength properties of the latter can be theoretically obtained from the failure conditions of its individual constituents: rock matrix and joint interfaces. At the material level, the limit analysis reasoning is used in the context of homogenization to formulate the homogenized strength criterion of a jointed rock mass in the particular situation of a single set of parallel joints. As it could be expected, the obtained closed‐form expressions show the strength anisotropy induced by joint preferential orientation. The support functions (π functions) associated with the homogenized strength criterion are also determined in both plane strain and three‐dimensional cases. This criterion is then applied to the investigation of stability analysis of a tunnel excavated in a jointed rock mass. Upper bounds estimated of the stability factor are derived from the implementation of the kinematic approach directly on the homogenized underground structure. Finally, the approach is applied to analyze and discuss the collapse of the Pinheiros subway station (São Paulo, Brazil). Copyright © 2014 John Wiley & Sons, Ltd.     

A numerical study of mechanical behavior of a cement paste under mechanical loading and chemical leaching

Based on relevant experimental data of a petroleum cement paste under mechanical loading and chemical leaching, an elastic‐plastic model is first proposed by taking into account plastic shearing and pore collapse. The degradation of mechanical properties induced by the chemical leaching is characterized by a chemical damage variable which is defined as the increase of porosity. Both elastic and plastic properties of the cement paste are affected by the chemical damage. The proposed model is calibrated from and applied to describe mechanical responses in triaxial compression tests respectively on sound and fully leached samples. In the second part, a phenomenological chemical model is defined to establish the relationship between porosity change and calcium dissolution process. The dissolution kinetics is governed by a diffusion law taking into account the variation of diffusion coefficient with calcium concentration. The chemical model is coupled with the mechanical model, and both are applied to describe mechanical response of cement paste samples subjected to progressive chemical leaching and compressive stresses. Comparisons between experimental data and numerical results are presented.     

Insights into the complexity of crustal differentiation: K2O‐poor leucosomes within metasedimentary migmatites from the Southern Marginal Zone of the Limpopo Belt,South Africa

Differentiation of the continental crust is the result of complex interactions between a large number of processes, which govern partial melting of the deep crust, magma formation and segregation, and magma ascent to significantly higher crustal levels. The anatectic metasedimentary rocks exposed in the Southern Marginal Zone of the Limpopo Belt represent an unusually well‐exposed natural laboratory where the portion of these processes that operate in the deep crust can be directly investigated in the field. The formation of these migmatites occurred via absent incongruent melting reactions involving biotite, which produced cm‐ to m‐scale, K₂O‐poor garnet‐bearing stromatic leucosomes, with high Ca/Na ratios relative to their source rocks. Field investigation combined with geochemical analyses, and phase equilibrium modelling designed to investigate some aspects of disequilibrium partial melting show that the outcrop features and compositions of the leucosomes suggest several steps in their evolution: (1) Melting of a portion of the source, with restricted plagioclase availability due to kinetic controls, to produce a magma (melt + entrained peritectic minerals in variable proportions relative to melt); (2) Segregation of the magma at near peak metamorphic conditions into melt accumulation sites (MAS), also known as future leucosome; (3a) Re‐equilibration of the magma with a portion of the bounding mafic residuum via chemical diffusion (H₂O, K₂O), which triggers the co‐precipitation of quartz and plagioclase in the MAS; (3b) Extraction of melt‐dominated magma to higher crustal levels, leaving peritectic minerals entrained from the site of the melting reaction, and the minerals precipitated in the MASs to form the leucosome in the source. The key mechanism controlling this behaviour is the kinetically induced restriction of the amount of plagioclase available to the melting reaction. This results in elevated melt H₂O and K₂O and chemical potential gradient for these components across the leucosome/mafic residuum contact. The combination of all of these processes accurately explains the composition of the K₂O‐poor leucosomes. These findings have important implications for our understanding of melt segregation in the lower crust and minimum melt residency time which, according to the chemical modelling, is <5 years. We demonstrate that in some migmatitic granulites, the leucosomes constitute a type of felsic refractory residuum, rather than evidence of failed magma extraction. This provides a new insight into the ways that source heterogeneity may control anatexis.     

Dynamic analysis of strain localization in water‐saturated clay using a cyclic elasto‐viscoplastic model

A computational framework is presented for dynamic strain localization and deformation analyses of water‐saturated clay by using a cyclic elasto‐viscoplastic constitutive model. In the model, the nonlinear kinematic hardening rule and softening due to the structural degradation of soil particles are considered. In order to appropriately simulate the large deformation phenomenon in strain localization analysis, the dynamic finite element formulation for a two‐phase mixture is derived in the updated Lagrangian framework. The shear band development is shown through the distributions of viscoplastic shear strain, the axial strain, the mean effective stress, and the pore water pressure in a normally consolidated clay specimen. From the local stress–strain relations, more brittleness is found inside the shear bands than outside of them. The effects of partially drained conditions and mesh‐size dependency on the shear banding are also investigated. The effect of a partially drained boundary is found to be insignificant on the dynamic shear band propagation because of the rapid rate of applied loading and low permeability of the clay. Using the finer mesh results in slightly narrower shear bands; nonetheless, the results manifest convergency through the mesh refinement in terms of the overall shape of shear banding and stress–strain relations. Copyright © 2013 John Wiley & Sons, Ltd.     

U–Pb SHRIMP data constraints on calc-alkaline granitoids with 1.3–1.6 Ga Nd TDM model ages from the central domain of the Borborema province,NE Brazil

The Tabira, Itapetim and Timbaúba granitoids are intruded into metasedimentary sequences and Cariris Velhos (Tonian) orthogneisses from the Central Domain of the Borborema Province, NE Brazil. They have U–Pb SHRIMP ages of 593 ± 7 Ma; 615 ± 9 Ma and 616 ± 5 Ma respectively. The studied granitoids have zircon cores inherited from the protholith, with a large number of analyses showing ²⁰⁶Pb/²³⁸U ages ranging from 950 to 1200 Ma. Oscillatory zoning typical of magmatic zircon is common, although it is faint in some inherited cores.The studied granitoids are calc-alkaline and show Nd T_DM model ages ranging from 1.30 to 1.56 Ga and ?Nd (600 Ma) ranging from ?2.40 to ?5.34. These values are similar to those recorded in the country rocks. The lowest values of ?Nd (600 Ma) were recorded in enclaves of dioritic composition. Nd and U–Pb SHRIMP data suggest a significant participation of the metasedimentary rocks in the protholith of these granitoids. The Mesoproterozoic Nd T_DM model ages recorded in the studied granitoids are interpreted as the result of a hybrid source involving melting of metagraywackes, metamafic rocks of Tonian ages and/or biotite – bearing orthogneisses (Cariris Velhos Orthogneisses). The resulted melting was modified by mingling with juvenile Brasiliano melts, diorite in composition.The Timbaúba granitoids intrusions are coeval with high-T metamorphism and flat-lying foliation forming event in an intracontinental setting, during the Brasiliano convergence and contractional deformation. The Itapetim Pluton was emplaced in the convergence - lateral escape setting and the Tabira granitoids were intruded after the flat-lying foliation event, representing sin transcurrent intrusions.Our data show that within the Central Domain of the Borborema Province, granitoids with similar petrographic and geochemical compositions can have distinct ages and be intruded in distinct tectonic regimes.