Publication Date: 2004
International Journal of Rock Mechanics and Mining Sciences (13651609)41(SUPPL. 1)
There are various structural and geological stratigraphies in study area. The main lithology includes the shale, marl, limestone and dolomite that belong to the Cambrian to upper Cretaceous besides Quaternary deposits. To identify the engineering and geotechnical characteristics of the rock mass along the tunnel route, the results of laboratory and in situ tests, geophysical explorations (geoelectrical methods), field observations and borehole logging charts have been used. The well-known rock mass classification systems for tunnelling purposes (RMR, GSI and Q-system) have been used. Using the GSI classification system for rock mass, the modified Hock- Brown criterion parameters of the rock mass for typical section were determined. The RMR was used to determine the required support for the entire length of tunnel. Also the Q system was used to compare the required support from Q system with the RMR system. Finally rock-support interaction analysis was conducted for a typical cross section of the tunnel. Using the above empirical and analytical methods, the required supports were compared for a typical section. © 2004 Elsevier Ltd.
Publication Date: 2005
International Journal for Numerical Methods in Engineering (00295981)64(4)pp. 427-460
In this part of paper we shall extend the formulation proposed by Babuška and co-workers for robustness patch test, for quality assessment of error estimators, to more general cases of patch locations especially in three-dimensional problems. This is performed first by finding an asymptotic finite element solution at interior parts of a problem with assumed smooth exact solution and then adding a correction part to obtain the solution near a kinked boundary irrespective of other boundary conditions at far ends of the domain. It has been shown that the solution corresponding to the correction part may be obtained in a spectral form by assuming a suitable proportionality relation between the nodal values of a mesh with repeatable pattern of macro-patches. Ha ving found the asymptotic finite element solution, the performance of error estimators may be examined. Although in this paper we focus on the asymptotic behaviour of error estimators, the method described in this part may be used to obtain finite element solution for two/ three-dimensional unbounded heat/elasticity problems with homogeneous differential equations. Some numerical results are presented to show the validity and performance of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd.
Publication Date: 2005
International Journal for Numerical Methods in Engineering (00295981)64(4)pp. 461-502
In this part of the paper we shall use the formulation given in the first part to assess the quality of recovery-based error estimators using two recovery methods, i.e. superconvergent patch recovery (SPR) and recovery by equilibrium in patches (REP). The recovery methods have been shown to be asymptotically robust and superconvergent when applied to two-dimensional problems. In this study we shall examine the behaviour of the recovery methods on several three-dimensional mesh patterns for patches located either inside or at boundaries. This is performed by first finding an asymptotic finite element solution, irrespective of boundary conditions at far ends of the domain, and then applying the recovery methods. The test procedure near kinked boundaries is explained in a step-by-step manner. The results are given in a series of tables and figures for various cases of three-dimensional mesh patterns. It has been experienced that the full superconvergent property is generally lost due to presence of boundary layer solution and the definition of the recoveries near boundaries though the results of the robustness test is still within an acceptable range. Copyright © 2005 John Wiley & Sons, Ltd.
Publication Date: 2005
Building and Environment (03601323)40(10)pp. 1413-1427
Nature displays profound preference for certain specific ratios to design her life-forms. These are geometric relationships that are transcendent and originated from Sacred Geometry. The view that geometry had a ritual origin is a part of a wider view that civilisation itself had a ritual origin, and therefore the history of utilisation of Sacred Geometry by man goes back to many centuries ago. The Pythagorean tradition, and the Egyptian and Babylonian sciences from which it derived, and Persian mathematics, a part of which reflects a Pythagorean intellectuality, are based on the sacred conception of numbers and their symbolism. In the traditional world, geometry was inseparable from the other sciences of the Pythagorean Quadrivium, namely arithmetic (numbers), music and astronomy. Traditional geometry is related to the symbolic configurations of space. Geometric forms such as the triangle, square and various regular polygons, the spiral and the circle are seen in the traditional perspective to be, like traditional numbers, as aspects of the multiplicity of the Unity. Architecture itself has always had a sacred meaning to all traditional civilisations through millennia, by which means man has tried to provide for himself a manifestation of heavens. Persian architecture always emphasised on Beauty, and by means of Sacred Geometry Persians measured the proportions of heaven and reflected them in the dimensions of buildings on the earth. A comprehensive utilisation of proportions in Persian architecture, such as in the design of plans, elevations, geometric and architectural patterns, and mechanical and structural features, can be proved through geometrical analysis of Persian historical buildings. In this paper, the sacred conception of geometry and its symbolism in the Pythagorean tradition, and Sacred Geometry and proportions in natural life-forms will be explained. The use of the science of geometry in design of a number of Persian historical buildings will be presented. The geometric factors upon which the design of these buildings, from both architectural and structural viewpoints, is made will be discussed. © 2004 Elsevier Ltd. All rights reserved.
