The Shape and Volume of the Skaergaard Intrusion, Greenland: Implications for Mass Balance and Bulk Composition

Re-examination of the Skaergaard intrusion in the context ofits regional setting, combined with new data from explorationdrilling, has resulted in a revised structural model for theintrusion. It is modelled as an irregular box, c. 11 km fromnorth to south, up to 8 km from east to west, and 3·4–4km from the lower to the upper contact. The walls of the intrusionare inferred to follow pre-existing and penecontemporaneoussteep faults, and the floor and roof seem largely controlledby bedding planes in the host sediments and lavas, similar toregional sills. The suggested shape and volume are in agreementwith published gravimetric modelling. Crystallization alongall margins of the intrusion concentrated the evolving meltin the upper, central part of the intrusion, best visualizedas an ‘onion-skin’ structure inside the box. Thetotal volume is estimated to c. 280 ± 23 km³, of which13·7% are referred to the Upper Border Series (UBS),16·4% to the Marginal Border Series (MBS) and 69·9%to the Layered Series (LS). In the LS, the Lower Zone (LZ) isestimated to constitute 66·8%, the Middle Zone (MZ) 13·5%and the Upper Zone (UZ) 19·7%. The new volume relationshipsprovide a mass balance estimate of the major and trace elementbulk composition of the intrusion. The parental magma to theSkaergaard intrusion is similar to high-Ti East Greenland tholeiiticplateau basalts with Mg number c. 0.45. The intrusion representsthe solidification of contemporary plateau basalt magma trappedand crystallized under closed-system conditions in a crustalreservoir at the developing East Greenland continental margin. KEY WORDS: bulk composition; emplacement; mass proportions; Skaergaard intrusion; structure     

Curve-Fitting Schemes for Fragmentation Data

Fragmentation measurements in the form of sieve passing and mass fraction data were used to test the capability of three different distributions to fit the observed data over a wide range in fragment size and mass. These distributions were based on Rosin-Rammler, lognormal and simple sigmoidal (S-shaped) functions, having 2 input parameters for the single-component versions and 5 input parameters for the two-component versions. Provided convergence was achieved in the non-linear curve-fitting technique, the two-component versions always provided superior fits to the observed data. However, these versions were very sensitive to variations in the values chosen for the input parameters. In this particular regard, the two-component sigmoidal function was the most robust. The present results also show that the two-component lognormal function provided the best fit to the fragmentation data in a general sense, and the two-component Rosin-Rammler function provided the worst fit. However, there was not a significant difference between any of the three methods.     

Fuzzy set approaches to classification of rock masses

Rock mass classification is analogous to multi-feature pattern recognition problem. The objective is to assign a rock mass to one of the pre-defined classes using a given set of criteria. This process involves a number of subjective uncertainties stemming from: (a) qualitative (linguistic) criteria; (b) sharp class boundaries; (c) fixed rating (or weight) scales; and (d) variable input reliability. Fuzzy set theory enables a soft approach to account for these uncertainties by allowing the expert to participate in this process in several ways. Hence, this study was designed to investigate the earlier fuzzy rock mass classification attempts and to devise improved methodologies to utilize the theory more accurately and efficiently. As in the earlier studies, the Rock Mass Rating (RMR) system was adopted as a reference conventional classification system because of its simple linear aggregation.

The proposed classification approach is based on the concept of partial fuzzy sets representing the variable importance or recognition power of each criterion in the universal domain of rock mass quality. The method enables one to evaluate rock mass quality using any set of criteria, and it is easy to implement. To reduce uncertainties due to project- and lithology-dependent variations, partial membership functions were formulated considering shallow (<200 m) tunneling in granitic rock masses. This facilitated a detailed expression of the variations in the classification power of each criterion along the corresponding universal domains. The binary relationship tables generated using these functions were processed not to derive a single class but rather to plot criterion contribution trends (stacked area graphs) and belief surface contours, which proved to be very satisfactory in difficult decision situations. Four input scenarios were selected to demonstrate the efficiency of the proposed approach in different situations and with reference to the earlier approaches.     

Holocene calcrete crust deposits on the moraine of Batura Glacier, northern Pakistan

Abstract   Calcretes can be observed on the surface of old moraines around Batura Glacier in the upper Hunza Valley, Karakoram Mountains, Pakistan. They develop as a calcareous crust cementing small gravels under boulders. In order to understand the genesis of the calcrete crust, a variety of methods were employed: (i) study of mineralogy and geochemistry of a calcrete crust precipitated on the lateral moraine using X-ray diffractometer and electron probe microanalysis; (ii) analysis of solute chemistry of surface water and ice bodies around the Batura Glacier; and (iii) accelerator mass spectrometry ¹⁴C dating of the crust itself. The results indicate that the calcrete crust has definite laminated layers composed of a fine-grain and compact calcite layer, and a mineral fragment layer. The chemical composition of the calcite layer is approximately 60% CaO and 1% MgO. The mineral fragment layer consists of rounded grain materials up to 0.2 mm in diameter. It shows a graded bedding structure with fine grains of quartz, albite and muscovite. Meanwhile, as the Paleozoic Pasu limestone is distributed around the terminal of Batura Glacier, Ca cations dissolve in the melt water of the glacier. Accordingly, the calcrete crust is precipitated by decreases in CO₂ partial pressure from glacier ice and evaporation of the melt water, including high concentration of Ca²⁺ at ephemeral streams and small ponds stagnating between the moraine and glacial ice. On the basis of the AMS ¹⁴C age, the calcrete is considered to have formed approximately 8200 calibrated years bp under the Batura glacial stage.     

Probabilistic approach for active control of structures: experimental verification

In our previous study (Earthquake Engineering and Structural Dynamics 2003; 32 :2301), we have developed a probabilistic algorithm for active control of structures. In the probabilistic control algorithm, the control force is determined by the probability that the structural energy exceeds a specified target critical energy, and the direction of a control force is determined by the Lyapunov controller design method. In this paper, an experimental verification of the proposed probabilistic control algorithm is presented. A three‐story test structure equipped with an active mass driver (AMD) has been used. The effectiveness of the control algorithm has been examined by exciting the test structure using a sinusoidal signal, a scaled El Centro earthquake and a broadband Gaussian white noise; and, especially, experiments on control have been performed under different conditions to that of system identification in order to prove the stability and robustness of the proposed control algorithm. The experimental results indicate that the probabilistic control algorithm can achieve a significant response reduction under various types of ground excitations even when the modeling error exists. Copyright © 2004 John Wiley & Sons, Ltd.     

在卸荷产生拉剪情况下裂隙岩体的力学行为

据岩体在卸荷情况下的拉剪应力状态,确定了节理岩体的线弹性断裂力学模型。依照此模型,可以得到相对远离裂隙(该位置的点到裂隙中心的距离比裂缝长度大)且受裂隙影响区域内应力、应变和变形方程。这些对评估裂隙岩石变形有重要的参考意义。通过用理论方程的计算结果和卸荷情况下试验观测所得的数据对比,证明该模型应用于实际工程中具有可行性。     

Assimilation and Fractional Crystallization Controlled by Transport Process of Crustal Melt: Implications from an Alkali Basalt-Dacite Suite from Rishiri Volcano, Japan

Mechanisms of fractional crystallization with simultaneous crustalassimilation (AFC) are examined for the Kutsugata and Tanetomilavas, an alkali basalt–dacite suite erupted sequentiallyfrom Rishiri Volcano, northern Japan. The major element variationswithin the suite can be explained by boundary layer fractionation;that is, mixing of a magma in the main part of the magma bodywith a fractionated interstitial melt transported from the mushyboundary layer at the floor. Systematic variations in SiO₂ correlatewith variations in the Pb, Sr and Nd isotopic compositions ofthe lavas. The geochemical variations of the lavas are explainedby a constant and relatively low ratio of assimilated mass tocrystallized mass (‘r value’). In the magma chamberin which the Kutsugata and Tanetomi magmas evolved, a strongthermal gradient was present and it is suggested that the marginalpart of the reservoir was completely solidified. The assimilantwas transported by crack flow from the partially fused floorcrust to the partially crystallized floor mush zone throughfractures in the solidified margin, formed mainly by thermalstresses resulting from cooling of the solidified margin andheating of the crust. The crustal melt was then mixed with thefractionated interstitial melt in the mushy zone, and the mixedmelt was further transported by compositional convection tothe main magma, causing its geochemical evolution to be characteristicof AFC. The volume flux of the assimilant from the crust tothe magma chamber is suggested to have decreased progressivelywith time (proportional to t^–1/2), and was about 3 x 10^–2m/year at t = 10 years and 1 x 10^–2 m/year at t = 100years. It has been commonly considered that the heat balancebetween magmas and the surrounding crust controls the couplingof assimilation and fractional crystallization processes (i.e.absolute value of r). However, it is inferred from this studythat the ratio of assimilated mass to crystallized mass canbe controlled by the transport process of the assimilant fromthe crust to magma chambers. KEY WORDS: assimilation and fractional crystallization; mass balance model; magma chamber; melt transport; Pb isotope     

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.     

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.