Browsing by Author "Wang, CD"

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Computing displacements in transversely isotropic rocks using influence charts
(1999-01-01)
Wang, CD
;
Liao, JJ
;
土木工程學系
;
Department of Civil Engineering
This paper presents a simple graphical method for computing the displacement beneath/at the surface of a transversely isotropic half-space subjected to surface loads. The surface load can be distributed on an irregularly-shaped area. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the half-space. Based on the point load solutions presented by the authors, four influence charts are constructed for calculating the three displacements at any point in the interior of the half-space. Then, by setting z = 0 of the derived solutions, another four influence charts for computing the surface displacements can also be proposed. These charts are composed of unit blocks. Each unit block is bounded by two adjacent radii and arcs, and contributes the same level of influence to the displacement. Following, a theoretical study was performed and the results showed that the charts for interior displacements are only suitable for transversely isotropic rocks with real roots of the characteristic equation; however, the charts for surface displacements are suitable for all transversely isotropic rocks. Finally, to demonstrate the use of the new graphical method, an illustrative example of a layered rock subjected to a uniform, normal circular-shaped load is given. The results from the new graphical method agree with those of analytical solutions as well. The new influence charts can be a practical alternative to the existing analytical or numerical solutions, and provide results with reasonable accuracy.
Computing displacements in transversely isotropic rocks using influence charts
(1999-01-01)
Wang, CD
;
Liao, JJ
;
土木工程學系
;
Department of Civil Engineering
This paper presents a simple graphical method for computing the displacement beneath/at the surface of a transversely isotropic half-space subjected to surface loads. The surface load can be distributed on an irregularly-shaped area. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the half-space. Based on the point load solutions presented by the authors, four influence charts are constructed for calculating the three displacements at any point in the interior of the half-space. Then, by setting z = 0 of the derived solutions, another four influence charts for computing the surface displacements can also be proposed. These charts are composed of unit blocks. Each unit block is bounded by two adjacent radii and arcs, and contributes the same level of influence to the displacement. Following, a theoretical study was performed and the results showed that the charts for interior displacements are only suitable for transversely isotropic rocks with real roots of the characteristic equation; however, the charts for surface displacements are suitable for all transversely isotropic rocks. Finally, to demonstrate the use of the new graphical method, an illustrative example of a layered rock subjected to a uniform, normal circular-shaped load is given. The results from the new graphical method agree with those of analytical solutions as well. The new influence charts can be a practical alternative to the existing analytical or numerical solutions, and provide results with reasonable accuracy.
Displacements and stresses due to a vertical point load in an inhomogeneous transversely isotropic half-space
(2003-07-01)
Wang, CD
;
Tzeng, CS
;
Pan, E
;
Liao, JJ
;
土木工程學系
We present the solutions for displacements and stresses subjected to a vertical point load in a continuously inhomogeneous transversely isotropic half-space with Young's and shear moduli varying exponentially with depth. Planes of transverse isotropy are assumed to be parallel to the horizontal surface. The solutions for the half-space are obtained by superposing the solutions of two full spaces, one with a point load in its interior and the other with opposite traction of the first full space along the z = 0 plane. The Hankel transform in a cylindrical co-ordinate system is employed for deriving the solutions. However, the resulting integrals for displacements and stresses involve polynomial, exponential function, and Bessel function that cannot be given in closed form; hence, numerical techniques are adopted in this work. In order to check the accuracy of numerical procedures, the comparisons are carried out with the homogeneous solutions of Liao and Wang, and the calculated results agree with those to nine decimal places. Furthermore, two illustrative examples are presented to elucidate the effect of inhomogeneity, and the type and degree of rock anisotropy on the vertical surface displacement and vertical normal stress in the inhomogeneous isotropic/transversely isotropic rocks subjected to a vertical concentrated force acting on the surface. The calculated results show that the induced displacement and stress are decisively influenced by the inhomogeneity, and the degree and type of material anisotropy. The proposed solutions can more realistically simulate the actual stratum of loading problem in many areas of engineering practice. (C) 2003 Elsevier Ltd. All rights reserved.
Elastic solutions for a transversely isotropic half-space subjected to a point load
(1998-06-01)
Liao, JJ
;
Wang, CD
;
土木工程學系
;
Department of Civil Engineering
We rederive and present the complete closed-form solutions of the displacements and stresses subjected to a point load in a transversely isotropic elastic half-space. The half-space is bounded by a horizontal surface, and the plane of transverse isotropy of the medium is parallel to the horizontal surface. The solutions are obtained by superposing the solutions of two infinite spaces, one acting a point load in its interior and the other being free loading. The Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions. These solutions are identical with the Mindlin and Boussinesq solutions if the half-space is homogeneous, linear elastic, and isotropic. Also, the Lekhnitskii solution for a transversely isotropic half-space subjected to a vertical point load on its horizontal surface is one of these solutions. Furthermore, an illustrative example is given to show the effect of degree of rock anisotropy on the vertical surface displacement and vertical stress that are induced by a single vertical concentrated force acting on the surface. The results indicate that the displacement and stress accounted for rock anisotropy are quite different for the displacement and stress calculated from isotropic solutions. (C) 1998 John Wiley & Sons, Ltd.
Elastic solutions for a transversely isotropic half-space subjected to buried asymmetric-loads
(1999-02-01)
Wang, CD
;
Liao, JJ
;
土木工程學系
;
Department of Civil Engineering
Elastic closed-form solutions for the displacements and stresses in a transversely isotropic half-space subjected to various buried loading types are presented. The loading types include finite line loads and asymmetric loads (such as uniform and linearly varying rectangular loads, or trapezoidal loads). The planes of transverse isotropy are assumed to be parallel to its horizontal surface. These solutions are directly obtained from integrating the point load solutions in a transversely isotropic half-space, which were derived using the principle of superposition, Fourier and Hankel transformation techniques. The solutions for the displacements and stresses in transversely isotropic half-spaces subjected to linearly variable loads on a rectangular region are never mentioned in literature. These exact solutions indicate that the displacements and stresses are influenced by several factors, such as the buried depth, the loading types, and the degree and type of rock anisotropy. Two illustrative examples, a vertical uniform and a vertical linearly varying rectangular load acting on the surface of transversely isotropic rock masses, are presented to show the effect of various parameters on the Vertical surface displacement and vertical stress. The results indicate that the displacement and stress distributions accounted for rock anisotropy are quite different for those calculated from isotropic solutions. Copyright (C) 1999 John Wiley & Sons, Ltd.
Elastic solutions for stresses in a transversely isotropic half-space subjected to three-dimensional buried parabolic rectangular loads
(2002-12-10)
Wang, CD
;
Liao, JJ
;
土木工程學系
;
Department of Civil Engineering
In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half-space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half-space, induced by three-dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian coordinate system for a transversely isotropic half-space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half-spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. Copyright (C) 2002 John Wiley Sons, Ltd.
Elastic solutions of displacements for a transversely isotropic half-space subjected to three-dimensional buried parabolic rectangular loads
(2002-09-01)
Wang, CD
;
Liao, JJ
;
土木工程學系
;
Department of Civil Engineering
This paper presents the closed-form solutions for estimating the displacements in a transversely isotropic half-space subjected to three-dimensional buried linearly varying, uniform, and parabolic rectangular loads. The loading types include an upward linearly varying load, a downward linearly varying load, a uniform load, a concave parabolic load, and a convex parabolic load on a rectangle. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the half-space. The presented solutions are obtained from integrating of the point load solutions in a Cartesian co-ordinate system for the transversely isotropic half-space. The solutions for a transversely isotropic medium subjected to parabolic rectangular loads are never mentioned in the literature. The parabolic loads might be more realistic than linear variable or uniform loads acting on foundations. The buried depth, the dimensions of loaded area, the type and degree of material anisotropy, and the loading type for transversely isotropic half-spaces influence these solutions. An illustrative example is presented to investigate the effect of the type and degree of rock anisotropy, and the loading types on the displacement. The proposed solutions can provide reasonably results to estimate the induced displacements in the isotropic/transversely isotropic geomaterials subjected to three-dimensional buried parabolic rectangular loads for practical purposes. (C) 2002 Elsevier Science Ltd. All rights reserved.
Stress influence charts for transversely isotropic rocks
(1998-09-01)
Wang, CD
;
Liao, JJ
;
土木工程學系
;
Department of Civil Engineering
A graphical procedure to calculate stresses in a transversely isotropic halfspace subjected to a three-dimensional surface load has been developed. The surface load can be distributed on an irregularly-shaped area. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the half-space. The closed-form solutions for stresses at a point under the vertex of a loading sector, with a unit load intensity are presented first. Based on these solutions, five influence charts are constructed for calculating the six components of a stress tensor at any given point in the half-space. The charts are composed of unit blocks. Each unit block is bounded by two adjacent, radii and arcs, and contributes the same level of influence to the stress within the half-space. An example is presented to demonstrate the use of the new graphical method for the case analyzed, results from the new graphical method agree with those of analytical solutions within 3%. The new influence charts can be a practical alternative to the existing analytical or numerical solutions, and provides results with reasonable accuracy. (C) 1998 Elsevier Science Ltd.
The influence of surface ruptures on building damage in the 1999 Chi-Chi earthquake: a case study in Fengyuan City
(2004-01-01)
Dong, JJ
;
Wang, CD
;
Lee, CT
;
Liao, JJ
;
Pan, YW
In addition to the main surface rupture along the Chelungpu fault associated with the 1999 Chi-Chi, Taiwan earthquake, numerous secondary or branch ruptures on hangingwall were also observed. These secondary surface ruptures are parallel or sub-parallel to the main rupture within a distance of a few meters to 1-2 km. The rupture length of these secondary ruptures varies from a few tens of meters up to 5 km. The surface deformation resulted in serious damages of buildings. The present work studied the features of surface deformation on the hangingwall around the Chung-Cheng Park, Fengyuan, Taichung. Three distinct surface ruptures, minor ruptures and tension cracks were observed in this area. The observed distribution and types of building damage on the hangingwall are demonstrated. Due to the difference in geological condition and complex pattern of surface deformation, the resulted building damages on the hangingwall vary. A series of site investigation including field survey, drilling, seismic prospecting, P-S logging tests and laboratory tests were carried out in the interested area. A geological structure model was proposed on the basis of the results of site investigation. Numerical simulation was carried out to model the surface deformation as well as subsurface potential damage zone of an active fault. It reasonably explains the observed pattern of surface deformation and indicates that the surface deformation zone during a catastrophic earthquake is predictable. (C) 2003 Elsevier Science B.V. All rights reserved.