Numerical simulation of bolt‐supported tunnels by means of a multiphase model conceived as an improved homogenization procedure

This paper examines the possibility of applying a homogenization procedure to analyze the convergence of a tunnel reinforced by bolts, regarded as periodically distributed linear inclusions. Owing to the fact that a classical homogenization method fails to account for the interactions prevailing between the bolts and the surrounding ground and thus tends to significantly overestimate the reinforcement effect in terms of convergence reduction, a so‐called multiphase model is presented and developed, aimed at improving the classical homogenization method. Indeed, according to this model, the bolt‐reinforced ground is represented at the macroscopic scale as the superposition of two mutually interacting continuous phases, describing the ground and the reinforcement network, respectively. It is shown that such a multiphase approach can be interpreted as an extension of the homogenization procedure, thus making it possible to capture the ground–reinforcement interaction in a proper way, provided the constitutive parameters of the model and notably those relating to the interaction law can be identified from the reinforced ground characteristics. The numerical implementation of this model in a finite element method‐based computer code is then carried out, and a first illustrative application is finally presented. Copyright © 2008 John Wiley & Sons, Ltd.     

General coupling extended multiscale FEM for elasto‐plastic consolidation analysis of heterogeneous saturated porous media

This paper presents a general coupling extended multiscale FEM (GCEMs) for solving the coupling problem of elasto‐plastic consolidation of heterogeneous saturated porous media. In the GCEMs, the numerical multiscale base functions for the solid skeleton and fluid phase of the coupling system are all constructed on the basis of the equivalent stiffness matrix of the unit cell, which not only contain the interaction between the solid and fluid phases but also consider the time effect. Furthermore, in order to improve the computational accuracy for two‐dimensional problems, a multi‐node coarse element strategy for the GCEMs is proposed, and a two‐scale iteration algorithm for the elasto‐plastic consolidation analysis is developed. Some one‐dimensional and two‐dimensional homogeneous and heterogeneous numerical examples are carried out to validate the proposed method through the comparison with the coupling multiscale FEM and standard FEM. Numerical results show that the newly developed GCEMs can almost preserve the same convergent property as the standard FEM and also possesses the advantages of high computational efficiency. In addition, the GCEMs can be easily applied to other coupling multifield and multiphase transient problems. Copyright © 2014 John Wiley & Sons, Ltd.     

Macroscopic diffusivity in concrete determined by computational homogenization

Effective moisture and chloride ion diffusivity coefficients for concrete are determined by computational homogenization, where concrete is modeled on the mesoscale as a heterogenous three‐phase composite material. By imposing moisture and chloride ion gradients on a representative volume element, effective macroscale properties are obtained through finite element analysis. A parametric study of the effects of the ballast content was carried out. The numerical results correspond well with an estimate of the Hashin–Shtrikman type available in the literature. The computational homogenization strategy proposed here also includes the interfacial transition zone, and its influence on the effective diffusivity coefficients is assessed. Copyright © 2012 John Wiley & Sons, Ltd.     

Geochronological Constraints Using 40Ar/39Ar Dating on the Mineralization of the Hishikari Epithermal Gold Deposit, Japan

Abstract. Ages for thirty adularia samples collected from various veins were in the Hishikari gold deposit determined by ⁴⁰Ar/³⁹Ar dating to constrain the timing of adularia‐quartz vein formation and to determine the temporal change in temperature of hydrothermal fluid. Plateau ages were obtained from all adularia samples, and significant excess ⁴⁰Ar is not recognized from inverse isochrones. The duration of mineralization within individual veins was determined by adularia ages from the early and late stages of mineralization within the same vein. The durations of mineralization in the Daisen‐1, Daisen‐3, Hosen‐2 and Keisen‐3 veins in the Honko‐Sanjin zone were 7,000, 140,000, 160,000 and 170,000 years, respectively. The durations of mineralization in the Seisen‐2 and Yusen‐1–2 veins in the Yamada zones were 360,000 and 320,000 years, respectively. Mineralization lasted for a relatively longer period in individual veins at the Yamada zone. Mineralization ages from the Honko‐Sanjin zone range from 1.04 to 0.75 Ma, and most mineralization ages are concentrated in a short period from 1.01 to 0.88 Ma. In contrast, mineralization ages for the Yamada zone range from 1.21 to 0.64 Ma. These results indicate that fracturing and subsequent vein formation lasted for a longer period in the Yamada zone (about 570,000 years) compared with those events in the Honko‐Sanjin zone (about 290,000 years). The homogenization temperatures of liquid‐rich fluid inclusions in columnar adularia used for age determination were determined to be 223°C on average, and most of these temperatures range from 180 to 258d?C. No significant temporal change in homogenization temperature is recognized in this study. However, adularia in the Keisen veins indicated higher homogenization temperatures compared with elsewhere in the deposit, suggesting that the principal ascent of mineralizing hydrothermal fluid was via the Keisen veins.     

A stable isotope study of the migmatitic rocks in the Ballachulish contact aureole, Scotland

The highest grade pelitic and semipelitic rocks of the Ballachulish aureole are dominantly potash feldspar + cordierite + biotite hornfelses with widely variable amounts of quartz, plagioclase, andalusite, sillimanite and corundum (together with accessory phases). On a microscopic scale these hornfelses show textural evidence of the presence of melt, whilst on a mesoscopic scale they contain a variety of leucosomes. Oxygen isotope studies have been carried out on both whole rocks and mineral separates in order to: (1) assess the sources of molten and volatile constituents and (2) determine the extents of isotopic homogenization and equilibration. Data from localities with both restricted and extensive evidence of leucosomes and melt development are compared, as well as one locality with petrographic evidence of melt incursion from the igneous complex. The whole-rock δ¹⁸O values of the leucosomes (10.5–14.9%.) are in general similar to the immediately adjacent mesosomes (9.9–14.5%.) which are typically cordierite- and feldspar-rich hornfelses. Isotopic evidence is thus consistent with an in-situ partial melt origin for the leucosomes, without the substantial addition of externally derived components. In the area of extensive melt development, the ‘chaotic zone’, it is possible there was addition of an H₂O-rich fluid phase (6-13 wt%) from the igneous complex which resulted in a slight lowering of δ¹⁸O values by 0.5–1.0%. Quartz mineral separates were used to assess the degree of local isotopic homogenization. In the extensively molten area (chaotic zone) there is extensive homogenization between rock layers (quartz δ¹⁸O usually within 1.0%), whilst in less molten areas δ¹⁸O quartz has a range of c. 3.0%. The greater homogenization in the chaotic zone is attributed to the increased degree of melting and infiltration of H₂O-rich fluid from the igneous complex.     

Spatial distribution of dust deposition within a small drainage basin: Implications for loess deposits in the Negev Desert

Loessial colluvial sediments and aeolian aprons are common deposits in the Negev Desert Highlands. In an attempt to monitor the amounts and distributional pattern of loess, monthly dust measurements were carried out during 2004 to 2006 in 10 cm diameter traps located at 18 stations along four slopes, north‐facing, south‐facing, east‐facing and west‐facing in a second‐order drainage basin near Sede Boqer, Negev Desert Highlands, Israel. Annual total dust depositions ranged between 110 g and 178 g m^?2 with an average of 151·1 g m^?2. The average annual dust deposition in the catchment was 23·5% higher than the average amount recorded at the hilltops (122·4 g m^?2) and may be a consequence of sheltering opportunities in the hilly topography. When analysed according to season and aspect, significantly higher monthly amounts were received during the wet rainy season of December to March (17·0 g m^?2), in comparison with the rest of the year (8·1 g m^?2). As for the aspect, while no significant differences characterized north‐facing and south‐facing slopes, east‐facing slopes received significantly higher amounts (by 43·3%) than west‐facing slopes, pointing to preferential dust deposition at the leeward slope. Concurring with the classical model that anticipates higher dust deposition at the leeside slope, but in disagreement with some reports published in the literature, the findings of this study were also supported by a field survey that showed preferential loess accumulation at the eastern and north‐eastern aspects. These findings may shed light on distributional patterns of colluvial sediments and aeolian aprons in the Negev, on soil‐forming processes and on past cycles of dust deposition.     

硅酸盐熔体包裹体均匀化过程的动力学性质

硅酸盐熔体包裹体的研究,和以模拟实验为主的实验岩石学,实验矿物学一样,已经成为现代岩浆岩石学,尤其是理论岩浆岩石学研究的一个必不可少的组成部分。均匀化测温研究,是硅酸盐熔体包裹体研究的一个重要组成部分。其方法是对于呈封闭系统的硅酸盐熔体包裹体进行加热,在反方向上,再造这些包裹体从结晶到熔融的所有阶段,直至其完全均匀化,也就是恢复到它们被生长着的矿物包含、捕获时的状态,借以测量矿物近液相线或固相线的结晶温度。     

B‐bar based algorithm applied to meshfree numerical schemes to solve unconfined seepage problems through porous media

The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous media. The Biot's equations are formulated in displacements (or u − w) assuming an elastic solid skeleton. The free surface location and its evolution in time are obtained by interpolation of pore water pressures throughout the domain. Shape functions based on the principle of local maximum entropy are chosen for the meshfree approximation schemes. In order to avoid the locking involved in the fluid phase of the porous media, a B‐bar based algorithm is devised to compute the average volumetric strain in a patch composed of various integration points. The efficiency of such an implementation for one phase problems is shown through the Benchmark problem, Cook's membrane loaded by a distributive shear load. The proposed methodology is firstly applied to various classical examples in unconfined steady seepage problems through earth dams, then to the dynamic consolidation of a soil column. The results obtained for both problems are quite satisfactory and demonstrate the feasibility of the proposed method in solving coupled problems in porous media. Copyright © 2015 John Wiley & Sons, Ltd.     

Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite‐element method

The scaled boundary finite‐element method, a semi‐analytical computational scheme primarily developed for dynamic stiffness of unbounded domains, is applied to the analysis of unsteady seepage flow problems. This method is based on the finite‐element technology and gains the advantages of the boundary element method as well. Only boundary of the domain is discretized, no fundamental solution is required and singularity problems can be modeled rigorously. Anisotropic and non‐homogeneous materials satisfying similarity are modeled with no additional efforts. In this study, firstly, formulation of the method for the transient seepage flow problems is derived followed by its solution procedures. The accuracy, simplicity and applicability of the method are demonstrated via four numerical examples of transient seepage flow – three of them are available in the literature. Homogenous, non‐homogenous, isotropic and anisotropic material properties are considered to show the versatility of the technique. Excellent agreement with the finite‐element method is observed. The method out‐performs the finite‐element method in modeling singularity points. Copyright © 2014 John Wiley & Sons, Ltd.     

A multiphase approach for evaluating the horizontal and rocking impedances of pile group foundations

This paper advocates the use of a multiphase model, already developed for static or quasi‐static geotechnical engineering problems, for simulating the behaviour of piled raft foundations subject to horizontal as well as rocking dynamic solicitations. It is shown that such a model, implemented in a FEM code, yields appropriate predictions for the foundation impedance characteristics, provided that shear and bending effects in the piles are taken into account, thus corroborating the findings of the asymptotic homogenization theory. Besides, it is notably pointed out that such a multiphase‐based computational tool makes it possible to assess the dynamic behaviour of pile groups in a much quicker way than when using direct numerical simulations, which may face oversized problems when large pile groups are concerned. Copyright © 2016 John Wiley & Sons, Ltd.     

Geology,Fluid Inclusion,and Sulfur Isotope Studies of the Chehugou Porphyry Molybdenum–Copper Deposit,Xilamulun Metallogenic Belt,NE China

The Chehugou Mo–Cu deposit, located 56 km west of Chifeng, NE China, is hosted by Triassic granite porphyry. Molybdenite–chalcopyrite mineralization of the deposit mainly occurs as veinlets in stockwork ore and dissemination in breccia ore, and two ore‐bearing quartz veins crop out to the south of the granite porphyry stock. Based on crosscutting relationships and mineral paragenesis, three hydrothermal stages are identified: (i) quartz–pyrite–molybdenite ± chalcopyrite stage; (ii) pyrite–quartz ± sphalerite stage; and (iii) quartz–calcite ± pyrite ± fluorite stage. Three types of fluid inclusions in the stockwork and breccia ore are recognized: LV, two‐phase aqueous inclusions (liquid‐rich); LVS, three‐phase liquid, vapor, and salt daughter crystal inclusions; and VL, two‐phase aqueous inclusions (gas‐rich). LV and LVS fluid inclusions are recognized in vein ore. Microthermometric investigation of the three types of fluid inclusions in hydrothermal quartz from the stockwork, breccia, and vein ores shows salinities from 1.57 to 66.75 wt% NaCl equivalents, with homogenization temperatures varying from 114°C to 550°C. The temperature changed from 282–550°C, 220–318°C to 114–243°C from the first stage to the third stage. The homogenization temperatures and salinity of the LV, LVS and VL inclusions are 114–442°C and 1.57–14.25 wt% NaCl equivalent, 301–550°C and 31.01–66.75 wt% NaCl equivalent, 286–420°C and 4.65–11.1 wt% NaCl equivalent, respectively. The VL inclusions coexist with the LV and LVS, which homogenize at the similar temperature. The above evidence shows that fluid‐boiling occurred in the ore‐forming stage. δ³⁴S values of sulfide from three type ores change from ?0.61‰ to 0.86‰. These δ³⁴S values of sulfide are similar to δ³⁴S values of typical magmatic sulfide sulfur (c. 0‰), suggesting that ore‐forming materials are magmatic in origin.     

Numerical Homogenization of Two-Phase Flow in Porous Media

Homogenization has proved its effectiveness as a method of upscaling for linear problems, as they occur in single-phase porous media flow for arbitrary heterogeneous rocks. Here we extend the classical homogenization approach to nonlinear problems by considering incompressible, immiscible two-phase porous media flow. The extensions have been based on the principle of preservation of form, stating that the mathematical form of the fine-scale equations should be preserved as much as possible on the coarse scale. This principle leads to the required extensions, while making the physics underlying homogenization transparent. The method is process-independent in a way that coarse-scale results obtained for a particular reservoir can be used in any simulation, irrespective of the scenario that is simulated. Homogenization is based on steady-state flow equations with periodic boundary conditions for the capillary pressure. The resulting equations are solved numerically by two complementary finite element methods. This makes it possible to assess a posteriori error bounds.     

The genesis of sandstone‐type uranium deposits in the Ordos Basin,NW China: constraints provided by fluid inclusions and stable isotopes

Quartz from sandstone‐type uranium deposits in the east part of the Ordos Basin contains abundant secondary fluid inclusions hosted along sealed fractures or in overgrowths. These inclusions consist mainly of water with NaCl, KCl, CO₂ (135–913 ppm) and trace amounts of CO (0.22–16.8 ppm), CH₄ (0.10–1.38 ppm) and [SO₄]^2? (0.35–111 ppm). Homogenization temperatures of the studied fluid inclusions range from 90 to 210°C, with salinities varying from 0.35 to 12.6 wt‐% (converted to NaCl wt%), implying multiple stages of thermal alteration. Although high U is associated with a high homogenization temperature in one case, overall U mineralization is not correlated with homogenization temperature nor with salinity. The H and O isotopic compositions of fluid inclusions show typical characteristics of formation water, with δ¹⁸O ranging from 9.8 to 12.3‰ and δD from 26.9 to ?48.6‰, indicating that these fluid inclusions are mixtures of magmatic and meteoric waters. The oxygen isotope ratios of carbonates in cement are systematically higher than those of the fluid inclusions. Limited fluid inclusion‐cement pairs show that the oxygen closely approaches equilibrium between water and aragonite at 150°C. Highly varied and overall negative δ¹³C in calcite from cement implies different degrees of biogenetic carbon involvement. Correlations between U in bulk rocks and trace components in fluid inclusions are lacking; however, high U contents are typically coupled with high [SO₄]^2?, implying pre‐enrichment of oxidized materials in the U mineralization layer. All these relationships can be plausibly interpreted to indicate that U (IV), [SO₄]^2? as well as Na, K were washed out from the overlying thick sandstone by oxidizing meteoric water, and then were reduced by reducing agents, such as CH₄ and petroleum, likely from underlying coal and petroleum deposits, and possibly also in situ microbes at low temperatures.     

Transient infinite elements for seepage problems in infinite media

In this paper, a time-dependent infinite element which can be used to simulate transient seepage problems in infinite media is presented. The hydraulic head distribution function of the element has been derived in detail and the property matrices of the element have been well formulated. Since both space and time variables are used in the course of constructing the hydraulic head distribution function of the element, the present infinite element can be referred to as a transient one. Using the present infinite element to model the far field of a system, the mechanism of transient seepage problems in infinite media can be rigorously simulated because the property matrices of the element are evaluated at any time of interest in the analysis. Since explicit expressions can be written for the property matrices of the infinite element, they may be evaluated quite easily and this can be carried out by writing a simple subroutine in a computer program. In order to examine the accuracy and efficiency of the present infinite element, both a one-dimensional (ID) transient seepage problem in a semi-infinite medium and a 2D transient seepage problem in a full plane have been solved using the finite and infinite element technique. It has been demonstrated that the present infinite element is very useful for the numerical simulation of transient seepage problems in infinite media.     

Multiple Dolomitization and Fluid Flow Events in the Precambrian Dengying Formation of Sichuan Basin,Southwestern China

The Precambrian Dengying Formation is a set of large-scale, extensively dolomitized, carbonate reservoirs occurring within the Sichuan Basin. Petrographic and geochemical studies reveal dolomitization was a direct result of precipitation by chemically distinct fluids occurring at different times and at different intensities. Based on this evidence, dolomitization and multiple fluid flow events are analyzed, and three types of fluid evolution models are proposed. Results of analysis show that Precambrian Dengying Formation carbonates were deposited in a restricted peritidal environment(630–542 Ma). A high temperature and high Mg~(2+) concentration seawater was a direct result of dolomitization for the micrite matrix, and for fibrous aragonite in primary pores. Geochemical evidence shows low δ~(18)O values of micritic dolomite varying from-1.29‰ to-4.52‰ PDB, abundant light rare earth elements(REEs), and low dolomite order degrees. Microbes and meteoric water significantly altered dolomite original chemical signatures, resulting in algal micritic dolomite and the fine-grained, granular, dolosparite dolomite having very negative δ~(18)O values. Finely crystalline cement dolomite(536.3–280 Ma) and coarsely crystalline cement dolomite have a higher crystallization degree and higher order degree. The diagenetic sequence and fluid inclusion evidence imply a linear correlation between their burial depth and homogenization temperatures, which closely resemble the temperature of generated hydrocarbon. Compared with finely crystalline dolomite, precipitation of coarsely crystalline dolomite was more affected by restricted basinal fluids. In addition, there is a trend toward a more negative δ~(18)O value, higher salinity, higher Fe and Mn concentrations, REE-rich. Two periods of hydrothermal fluids are identified, as the exceptionally high temperatures as opposed to the temperatures of burial history, in addition to the presence of high salinity fluid inclusions. The early hydrothermal fluid flow event was characterized by hot magnesium-and silicon-rich fluids, as demonstrated by the recrystallized matrix dolomite that is intimately associated with flint, opal, and microcrystalline quartz in intergranular or intercrystalline pores. This event was likely the result of a seafloor hydrothermal chimney eruption during Episode I of the Tongwan Movement(536.3±5.5 Ma). In contrast, later hydrothermal fluids, which caused precipitation of saddle dolomite, were characterized by high salinity(15–16.05 wt% NaCl equivalent) and homogenization temperatures(250 to 265°C), δ~(18)O values that were more enriched, and REE signatures. Geochemical data and the paragenetic sequence indicate that this hydrothermal fluid was related to extensive Permian large igneous province activity(360–280 Ma). This study demonstrates the presence of complicated dolomitization processes occurring during various paleoclimates, tectonic cycles, and basinal fluids flow; results are a useful reference for these dolomitized Precambrian carbonates reservoirs.     

Permeability determination of porous media using large‐scale finite elements and iterative solver

The problem of finite element simulation of incompressible fluid flow in porous medium is considered. The porous medium is characterized by the X‐ray microtomography technique in three dimensions. The finite calculus‐based stabilization technique is reviewed to implement the equal order finite element interpolation functions for both velocity and pressure. A noble preconditioner, the nodal block diagonal preconditioner, is considered whose performance is thoroughly investigated. Combining this preconditioner with a standard iterative solver during the computational homogenization procedure, it is possible to carry out the large‐scale fluid flow simulation for estimating permeability of the porous medium with reasonable accuracy and reliability. Copyright © 2013 John Wiley & Sons, Ltd.     

Dating and Fluid Geochemistry of the Sarkobu Gold Deposit in Altay, Xinjiang, China

The dating of fluid inclusions of quartz yields an Ar-Ar isochrone age of 320.4±6 Ma. Three types of fluid inclusions have been identified with the homogenization temperature ranging from 157℃ to 362℃. The homogenization temperature consists of two groups. The first group varies from 157℃ to 166℃, and the second from 232℃ to 362℃. Their chemical composition is dominated by Na+-Ca2+-Mg2+ and Cl-. The relative concentration of ions is characteristic by Na+>Ca2+>K+>Mg2+ and C1->SO42-> F-. The δD and δ18O values indicate that the ore-forming fluid originates from mixing of multi-source water. The Sarkobu gold deposit has experienced two mineralization stages: gold was enriched during the volcanic-exhalative-sedimentary process in the early stage, while the gold deposit was finally formed under compression-shearing during the orogenic period.     

An artificial boundary approach for unbounded transient seepage problems

A new artificial boundary approach for transient seepage problems in unbounded domain is presented. The artificial boundary condition at the truncated boundary is derived from the analytical solutions for transient seepage problems in one dimension, including solutions, respectively, for flow in one‐dimensional infinite space and for radial flow in an infinite layer, and then it is tentatively applied for some two dimensional problems in addition to the one‐dimensional problems mentioned above. The boundary conditions derived relate the time‐dependent boundary flux with the time derivative of the hydraulic head at the truncated boundary, which makes the implementation much easier compared with the infinite element method. The accuracy and efficiency of the artificial boundary are validated by several numerical examples, which shows that the proposed boundary can give very good results for one‐dimensional transient seepage problems, as expected, whereas reasonable results can be also obtained for two‐dimensional problems, such as two‐dimensional axisymmetric flow and flow in an infinite plane. Copyright © 2014 John Wiley & Sons, Ltd.     

Time homogenization for clays subjected to large numbers of cycles

This paper discusses the reliability and the efficiency of a time homogenization method employed to reduce the computational time during cyclic loading for two common geotechnical tests and two elastoplastic models for clays. The method of homogenization is based upon splitting time into two separate scales. The first time scale relates to the period of cyclic loading and the second to the characteristic time of the fatigue phenomenon. The time homogenization method is applied to simulate an undrained triaxial test (homogeneous stress state) and a pressuremeter test (nonhomogeneous stress state) under one‐way cyclic loading on normally consolidated clay. This method is coupled with two elastoplastic models dedicated to cyclic behavior of clay (a bounding surface plasticity model and a bubble model). Both linear and nonlinear elasticities are considered. The difficulty encountered when applying this method to models introducing nonlinear elasticity and kinematic hardening is pointed out. The performance of time homogenization related to the main parameters is numerically investigated by comparison with conventional finite element simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Characterization of an internal slope movement structure by hydrogeophysical surveying

A hydrogeophysical study was carried out by a water controlled injection within a landslide situated on an active part of the La Clapière landslide foot (Alpes Maritimes, France). Coupling of both real‐time geophysical and hydrological follow ups allowed the representation and quantification of the surface water drainage in space and time within the slipped mass. Thus, 30% of the injected water is quickly drained by a complex slipping surface meanly situated at 10‐m depth. The transit time between injection and outflow of the water allowed an overloading of about 10 m³ (i.e. 10 tons) comparable with classical rain events in the area. This weight and the associated interstitial pressures increase have not led to any movements asking for the origin of the water volumes which could induce destabilizations. This experiment enabled an accurate redefinition of the internal slope structure and the understanding of the dynamics of the slipped mass with a surface hydraulic request.