This paper studies experimentally the coalescence mechanism between two parallel three-dimensiona... more This paper studies experimentally the coalescence mechanism between two parallel three-dimensional (3-D) pre-existing surface cracks in granite specimen under uniaxial compression. The bridge angles between the two pre-existing cracks vary from 01 to 1351. The digital speckle correlation method (DSCM) is used to analyze the captured images producing strain fields during the cracking process, and thus reveals the mode of cracking (either tensile, shear or their combination). Petal crack that initiates from internal crack fronts of the pre-existing surface cracks plays an important role in crack initiation, propagation and coalescence. Microcracks underneath the specimen surface appear as white patches on the surface, which always appear preceding the appearance of surface macrocracks (either wing or antiwing cracks). Cracks, which grow in a direction opposite to that of wing cracks, were consistently observed before the appearance of wing cracks; and these cracks are therefore called "anti-wing cracks". In addition, DSCM results suggest that wing crack and anti-wing crack are tensile during initiation but may subsequently turn into mixed mode. The coalescence between the two 3-D pre-existing surface cracks takes place both on the specimen surface (through wing, anti-wing cracks or secondary cracks) and inside the specimen (through internal petal cracks). Depending on the bridge angle β between the two pre-existing cracks, there can be no crack coalescence, coalescence in forms of tensile cracks (tensile mode), coalescence by mixed mode cracks (mixed mode), and finally coalescence in forms of a secondary crack jointing an initiated wing or anti-wing crack, emanating from one tip, to the other tip (secondary crack mode).
This paper derives a new three-dimensional (3-D) analytical solution for the indirect tensile tes... more This paper derives a new three-dimensional (3-D) analytical solution for the indirect tensile tests standardized by ISRM (International Society for Rock Mechanics) for testing rocks, and by ASTM (American Society for Testing and Materials) for testing concretes. The present solution for solid circular cylinders of finite length can be considered as a 3-D counterpart of the classical two dimensional (2-D) solutions by Hertz in 1883 and by Hondros in 1959. The contacts between the two steel diametral loading platens and the curved surfaces of a cylindrical specimen of length H and diameter D are modeled as circular-tocircular Hertz contact and straight-to-circular Hertz contact for ISRM and ASTM standards respectively. The equilibrium equations of the linear elastic circular cylinder of finite length are first uncoupled by using displacement functions, which are then expressed in infinite series of some combinations of Bessel functions, hyperbolic functions, and trigonometric functions. The applied tractions are expanded in Fourier-Bessel series and boundary conditions are used to yield a system of simultaneous equations. For typical rock cylinders of 54 mm diameter subjected to ISRM indirect tensile tests, the contact width is in the order of 2 mm (or a contact angle of 4°) whereas for typical asphalt cylinders of 101.6 mm diameter subjected to ASTM indirect tensile tests the contact width is about 10 mm (or a contact angle of 12°). For such contact conditions, 50 terms in both Fourier and Fourier-Bessel series expansions are found sufficient in yielding converged solutions. The maximum hoop stress is always observed within the central portion on a circular section close to the flat end surfaces. The difference in the maximum hoop stress between the 2-D Hondros solution and the present 3-D solution increases with the aspect ratio H/D as well as Poisson's ratio m. When contact friction is neglected, the effect of loading platen stiffness on tensile stress in cylinders is found negligible. For the aspect ratio of H/D = 0.5 recommended by ISRM and ASTM, the error in tensile strength may be up to 15% for both typical rocks and asphalts, whereas for longer cylinders with H/D up to 2 the error ranges from 15% for highly compressible materials, and to 60% for nearly incompressible materials. The difference in compressive radial stress between the 2-D Hertz solution or 2-D Hondros solution and the present 3-D solution also increases with Poisson's ratio and aspect ratio H/D. In summary, the 2-D solution, in general, underestimates the maximum tensile stress and cannot predict the location of the maximum hoop stress which typically locates close to the end surfaces of the cylinder.
Chau, K.T. (2013). Analytic Methods in Geomechanics. CRC Press, Boca Raton (457 pages)., Jan 2013
Bringing together a range of areas including tensor analysis, elasticity, plasticity, fracture me... more Bringing together a range of areas including tensor analysis, elasticity, plasticity, fracture mechanics and viscoelasticity, among others, this book is an indispensible guide to the fundamentals of geomechanics. It provides explanations of each subject area, using a step-by-step process with numerous worked examples. The more advanced material, such as complex variables in 2-D elasticity and application of J-integral to model slipping slopes then supplies a gateway into understanding the latest research results and applying them to practical problems. The book is suitable for undergraduate and graduate students as well as professionals and researchers.
The free-field strong ground motions recorded at 64 sites within 200 km from the ruptured Longmen... more The free-field strong ground motions recorded at 64 sites within 200 km from the ruptured Longmen Shan fault during the 12 May 2008 M w 7.9 Wenchuan earthquake were used to examine the near-source strong ground motioncharacteristics. The magnitude of vertical and horizontal peak ground accelerations (PGAs), frequency content, and duration of acceleration histories are analyzed. The observed peak ground accelerations at distances exceeding 60 km from the ruptured fault were significantly higher than those predicted by the Next Generation Attenuation (NGA) model, whereas, for periods of larger than 1 s, the spectral accelerations are much smaller than those of the NGA model. The same is also true for the observed peak ground velocities (PGVs). The duration of ground shaking is longer than for most earthquakes of comparable similar magnitude. For sites within 60 km from the ruptured fault, the accelerations observed on the hanging wall are larger than those observed on the footwall. The duration of ground shaking along the rupture direction (or the forward direction) is shorter than that opposite to the rupture direction (or the backward direction). There is also a systematic increase of PGA and PGV at sites located in the direction of the rupture propagation, whereas no such clear trend was found in the stations located along the backward direction. From the observed acceleration time histories at various locations, the rupture process of the 2008 Wenchuan appears to be more complicated than the focal mechanism interpreted from far-field seismic records. For example, the generation mechanism of the two distinct wave trains observed at Wolong and other stations need more detailed studies.
This paper derives an exact solution for the non-uniform stress and displacement fields within a ... more This paper derives an exact solution for the non-uniform stress and displacement fields within a finite, transversely isotropic, and linear elastic cylinder under compression with a kind of radial constraint induced by friction between the end surfaces of the cylinder and the loading platens. The main feature of the present work is the introduction of a general solution form for Lekhnitskii's stress function such that the governing equation and all end and curved boundary conditions of the cylinder are satisfied exactly. Two different solutions were obtained corresponding to the real or complex characteristic roots of the governing equation, depending on the combination of the elastic material constants. The solution by Watanabe [Watanabe, S., 1996. Elastic analysis of axi-symmetric finite cylinder constrained radial displacement on the loading end. Structural Engineering/Earthquake Engineering JSCE 13, 175s-185s] for isotropic cylinders under compression test can be recovered as a special case. Our numerical results show that both the non-uniform stress distribution and the difference between the apparent and the true Young's moduli of the cylinder are very sensitive to the anisotropy of Young's moduli, Poisson's ratios and shear moduli. A more distinct bulging shape of the cylinder is expected when anisotropy in shear modulus is strong, the cylinder is relatively short, and the end constraint is large. The bulging shape, however, does not depend strongly on anisotropy of either Poisson's ratio or Young's modulus.
In this paper, a soil-pile-structure model is tested on a shaking table subject to both a sinusoi... more In this paper, a soil-pile-structure model is tested on a shaking table subject to both a sinusoidal wave and the acceleration time history of the scaled 1940 El Centro earthquake. A medium-size river sand is compacted into a 1.7-m-high laminar rectangular tank to form a loose fill with a relative density of 15%. A single-storey steel structure of 2.54 ton is placed on a concrete pile cap, which is connected to the four end-bearing piles. A very distinct pounding phenomenon between soil and pile is observed; and, the acceleration response of the pile cap can be three times larger than that of the structural response. The pounding is due to the development of a gap separation between soil and pile, and the extraordinary large inertia force suffered at the top of the pile also induces cracking in the pile. To explain this observed phenomenon, nonlinear finite element method (FEM) analyses with a nonlinear gap element have been carried out. The spikes in the acceleration response of the pile cap caused by pounding can be modeled adequately by the FEM analyses. The present results suggest that one of the probable causes of pile damages is due to seismic pounding between the laterally compressed soil and the pile near the pile cap level.
Seismic torsional pounding between an asymmetric single-story tower and a neighboring barrier und... more Seismic torsional pounding between an asymmetric single-story tower and a neighboring barrier under harmonic ground excitation is modeled as the nonlinear Hertz contact in this paper. The governing equations of motion are numerically solved using the fourth-order Runge-Kutta method with an adaptive step size control. An analytical solution is obtained for the first time for a special case of periodic torsional pounding. Results of our numerical simulations reveal that torsional pounding tends to be much more complex and unpredictable than translational pounding, and most of them are either multiple or chaotic impacts. The maximum torsional impact velocity tends to be insensitive to the changes of separation distance and eccentricity as long as impact is developed. Although the analytical solution fails to predict the exact impact velocity of multiple torsional pounding, it does provide some useful insights into this complex phenomenon. The analytical solution succeeds in predicting the overall patterns as well as the abrupt jump of torsional impact velocity spectra.
This paper derives analytically the stress intensity factors (SIFs) of a frictional interfacial c... more This paper derives analytically the stress intensity factors (SIFs) of a frictional interfacial crack in a viscoleastic bimaterial subject to the action of a center of dilatation. The standard linear viscoelastic solid or ''three-parameter-viscoelastic-model" is adopted. Using the correspondence principle, the problem is formulated in Laplace transform space. The problem is decomposed into two Auxiliary Problems: (I) a bimaterial containing a center of dilatation; and (II) an interfacial crack in the bimaterial subject to tractions that cancel those induced by the Auxiliary Problem I. Schapery's direct method is used to obtain the inverse Laplace transform and, in turn, obtain the SIF as a function of time. Creeping tests for the Swiss Central Alps shales have been adopted for viscoelastic parameter calibration. When the bimaterial degenerates into a homogenous material, the SIFs are independent of time. If the medium containing the center of dilatation is stiffer, the long term SIF is larger than the instantaneous SIF; and if the medium containing the center of dilatation is softer, the long term SIF is smaller than the instantaneous SIF. Therefore, short term crack stability does not necessarily rule out long term crack propagation. If the overburden stress and the friction on crack surface are neglected, both modes I and II SIFs are induced at the crack tips. The mode II SIF is, in general, larger than that of mode I. When both friction and overburden pressure are included in the analysis, tensile cracking is unlikely whilst shear cracking remains possible. The maximum mode II SIF strongly depends on the orientation as well as the distance of the center of dilatation from the crack tip. Both overburden pressure and crack face friction decreases chance of crack propagation.
Direct shear tests on concrete specimens were conducted to investigate the shearing behaviour of ... more Direct shear tests on concrete specimens were conducted to investigate the shearing behaviour of the material under varying normal confining stresses. Test results were analyzed to quantify the mobilization of shear strength components derived from hydrated cement paste-aggregate adhesion, contact friction, shear dilation, and cement-aggregate interlock along the sheared surface under direct shearing. It was found that each component has its unique response in terms of mobilized shear stress and shear displacement. In addition, different modes of failure observed in uniaxial compression, splitting tension, and direct shear tests were identified to delineate the Mohr-Coulomb failure envelope for shear strength of concrete material.
Statistics of the mechanical and failure properties on the grain scale are often assumed to follo... more Statistics of the mechanical and failure properties on the grain scale are often assumed to follow the Weibull distribution in numerical simulations of failure and damage development. To investigate the microstructural basis for such a statistical model of compressive failure in a brittle rock, we consider the development of instability in a wing crack model and establish a methodology whereby the Weibull parameters can be inferred from microstructural data on microcrack density and length statistics for input into finite element simulations. Application of this methodology to six Yuen Long marble samples provides important insights into how different attributes of the microstructure may influence the progressive development of rock failure. The finite element simulations underscore the significant influence of microcrack length statistics, which has not been emphasized in continuum damage mechanics models that usually emphasize the roles of average crack size and crack density. The microstructural data indicate that strength heterogeneity increases with increasing grain size, and this plays a key role in lowering the uniaxial compressive strength, which contributes to the overall decrease of strength with increasing grain size.
For static compressions of spheres, a new stress analysis for isotropic elastic spheres compresse... more For static compressions of spheres, a new stress analysis for isotropic elastic spheres compressed between two¯at rigid platens is proposed by incorporating the Hertz contact stress. The predictions of the failure load for various sizes and strengths of spheres agree very well with our static experiments on a brittle plaster material. For dynamic compressions of spheres, a simple crushing analysis illustrates that the size of the contact zone can be estimated quite accurately in terms of the size of the sphere, the dynamic hardness, and the impact energy. Although the maximum contact force at failure is larger in the static case than that in the dynamic case, the energy required for fragmentation of the solid spheres is larger under dynamic test than under static test. Comparisons of the static and dynamic tests show that the impact energy required for fragmentation of a sphere can be approximated as 1.5 times of that for the static test. As expected, the impact energy for fragmentation increases monotonically with the size and strength of the spheres. The contact time at failure, however, does not exhibit a clear trend with the changes in size and strength of the spheres. Ó
This study presents a framework for numerical simulations based upon micromechanical parameters i... more This study presents a framework for numerical simulations based upon micromechanical parameters in modeling progressive failures of heterogeneous rock specimens under compression. In our numerical simulations, a Weibull distribution of the strength and elastic properties of the finite elements is assumed, and the associated Weibull parameters are estimated in terms of microstructural properties, such as crack size distribution and grain size, through microscopic observations of microcracks. The main uncertainty in this procedure lies on the fact that various ways can be used to formulate a ''microcrack size distribution'' in relating to the Weibull parameters. As one possible choice, the present study uses the number of counted cracks per unit scanned volume per grain size to formulate the crack distributions. Finally, as a tool, the Rock Failure Process Analysis code (RFPA 2D ) is adopted for simulating the progressive failure and microseismicity of heterogeneous rocks by using an elastic-damage finite-element approach. To verify our framework, compression tests on marble specimens are conducted, and the measured acoustic emissions (AE) are compared with those predicted by the numerical simulations. The mode of failure, compressive strength and AE pattern of our simulations basically agree with experimental observations. . Incorporation of AE or CT measurements with surface observations leads to a better understanding of the progressive failure of rocks under compression.
A new constitutive model is proposed for the description of induced anisotropic damage in brittle... more A new constitutive model is proposed for the description of induced anisotropic damage in brittle rocks. The formulation of the model is based on relevant results from micromechanics consideration. The distribution of microcracks is approximated by a second-order damage tensor. The effective elastic properties of damaged material are derived from the free enthalpy function. The evolution of damage is directly related to the growth of microcracks in different space orientations. The volumetric dilatancy due to sliding crack opening is taken into account. The model is extended to the description of creep deformation in brittle rocks. The time dependent deformation is seen as a consequence of the sub-critical propagation of microcracks due to stress corrosion process. The proposed model is applied to a typical brittle rock, the Lac du Bonnet granite. A general good agreement is obtained between numerical simulations and experimental data. r
In this paper, a coupled constitutive model is proposed for anisotropic damage and permeability v... more In this paper, a coupled constitutive model is proposed for anisotropic damage and permeability variation in brittle rocks under deviatoric compressive stresses. The formulation of the model is based on experimental evidences and main physical mechanisms involved in the scale of microcracks are taken into account. The proposed model is expressed in the macroscopic framework and can be easily implemented for engineering application. The macroscopic free enthalpy of cracked solid is first determined by approximating crack distribution by a second-order damage tensor. The effective elastic properties of damaged material are then derived from the free enthalpy function. The damage evolution is related to the crack growth in multiple orientations. A pragmatic approach inspired from fracture mechanics is used for the formulation of the crack propagation criterion. Compressive stress induced crack opening is taken into account and leads to macroscopic volumetric dilatancy and permeability variation. The overall permeability tensor of cracked material is determined using a micro-macro averaging procedure. Darcy's law is used for fluid flow at the macroscopic scale whereas laminar flow is assumed at the microcrack scale. Hydraulic connectivity of cracks increases with crack growth. The proposed model is applied to the Lac du Bonnet granite. Generally, good agreement is observed between numerical simulations and experimental data.
Brittle solids, such as rock or concrete, may contain numerous randomly distributed micro-flaws (... more Brittle solids, such as rock or concrete, may contain numerous randomly distributed micro-flaws (e.g. cracks, pores or weak inclusions). When they are loaded in compression, cracks may nucleate from these flaws. These cracks then continue to grow in a stable manner with the increasing axial compression, curving toward an orientation parallel to the direction of axial compression. Their propagation and interaction may lead to the collapse of the solid in a splitting mode. With a newly developed numerical code, MFPA 2D (material failure process analysis), heterogeneous solids containing pre-existing single, triple and multi-pore-like flaws are numerically tested to study the mechanisms of compression-induced axial splitting. The interaction of growing cracks with the surfaces of the specimen and with each other in terms of stress field and failure modes is numerically analyzed in detail. Under uniaxial compressions, specimens containing holes in a diagonal array are more conducive to interaction than specimens containing holes arranged either in a horizontal or vertical array. Various parameters, such as hole diameter, specimen width, and the geometrical arrangement of hole locations, that characterize the growth process are quantified. Numerical results mimic the phenomena of experimentally observed splitting failure in brittle solids such as rocks in a realistic way.
Normal-and high-strength concrete cylinders (designed compressive strengths of 30 and 90 MPa at 2... more Normal-and high-strength concrete cylinders (designed compressive strengths of 30 and 90 MPa at 28 days) were loaded uniaxially. Computer tomography (CT) scanning technique was used to examine the evolution of air voids inside the specimens at various loading states up to 85% of the ultimate compressive strength. The normal-strength concrete yielded a very different behaviour in changes of internal microstructure as compared to the high-strength concrete. There were significant instances of nucleation and growth in air voids in the normal-strength concrete specimen, while the increase in air voids in the high-strength concrete specimen was insignificant. In addition, CT images were used for mapping the aggregate spatial distributions within the specimens. No intrinsic anisotropy was detected from the fabric analysis. D
As over seventy percent of the land of Hong Kong is mountainous, rainfall-induced debris flows ar... more As over seventy percent of the land of Hong Kong is mountainous, rainfall-induced debris flows are not uncommon in Hong Kong. The objective of this study is to incorporate numerical simulations of debris flows with GIS to identify potential debris flow hazard areas. To illustrate this approach, the proposed methodology is applied to Leung King Estate in Tuen Mun. A Digital Elevation Model (DEM) of the terrain and the potential debris-flow sources were generated by using GIS to provide the required terrain and flow source data for the numerical simulations. A theoretical model by improved by incorporating a new erosion initiation criterion was used for simulating the runout distances of debris flows. The well-documented 1990 Tsing Shan debris flow, which occurred not too far from Leung King Estate, was used to calibrate most of the flow parameters needed for computer simulations. Based on the simulation results, a potential hazard zone was identified and presented by using GIS. Our proposed hazard map was thus determined by flow dynamics and a deposition mechanism through computer simulations without using any so-called expert opinions, which are bounded to be subjective and biased.
This paper studies experimentally the coalescence mechanism between two parallel three-dimensiona... more This paper studies experimentally the coalescence mechanism between two parallel three-dimensional (3-D) pre-existing surface cracks in granite specimen under uniaxial compression. The bridge angles between the two pre-existing cracks vary from 01 to 1351. The digital speckle correlation method (DSCM) is used to analyze the captured images producing strain fields during the cracking process, and thus reveals the mode of cracking (either tensile, shear or their combination). Petal crack that initiates from internal crack fronts of the pre-existing surface cracks plays an important role in crack initiation, propagation and coalescence. Microcracks underneath the specimen surface appear as white patches on the surface, which always appear preceding the appearance of surface macrocracks (either wing or antiwing cracks). Cracks, which grow in a direction opposite to that of wing cracks, were consistently observed before the appearance of wing cracks; and these cracks are therefore called "anti-wing cracks". In addition, DSCM results suggest that wing crack and anti-wing crack are tensile during initiation but may subsequently turn into mixed mode. The coalescence between the two 3-D pre-existing surface cracks takes place both on the specimen surface (through wing, anti-wing cracks or secondary cracks) and inside the specimen (through internal petal cracks). Depending on the bridge angle β between the two pre-existing cracks, there can be no crack coalescence, coalescence in forms of tensile cracks (tensile mode), coalescence by mixed mode cracks (mixed mode), and finally coalescence in forms of a secondary crack jointing an initiated wing or anti-wing crack, emanating from one tip, to the other tip (secondary crack mode).
This paper derives a new three-dimensional (3-D) analytical solution for the indirect tensile tes... more This paper derives a new three-dimensional (3-D) analytical solution for the indirect tensile tests standardized by ISRM (International Society for Rock Mechanics) for testing rocks, and by ASTM (American Society for Testing and Materials) for testing concretes. The present solution for solid circular cylinders of finite length can be considered as a 3-D counterpart of the classical two dimensional (2-D) solutions by Hertz in 1883 and by Hondros in 1959. The contacts between the two steel diametral loading platens and the curved surfaces of a cylindrical specimen of length H and diameter D are modeled as circular-tocircular Hertz contact and straight-to-circular Hertz contact for ISRM and ASTM standards respectively. The equilibrium equations of the linear elastic circular cylinder of finite length are first uncoupled by using displacement functions, which are then expressed in infinite series of some combinations of Bessel functions, hyperbolic functions, and trigonometric functions. The applied tractions are expanded in Fourier-Bessel series and boundary conditions are used to yield a system of simultaneous equations. For typical rock cylinders of 54 mm diameter subjected to ISRM indirect tensile tests, the contact width is in the order of 2 mm (or a contact angle of 4°) whereas for typical asphalt cylinders of 101.6 mm diameter subjected to ASTM indirect tensile tests the contact width is about 10 mm (or a contact angle of 12°). For such contact conditions, 50 terms in both Fourier and Fourier-Bessel series expansions are found sufficient in yielding converged solutions. The maximum hoop stress is always observed within the central portion on a circular section close to the flat end surfaces. The difference in the maximum hoop stress between the 2-D Hondros solution and the present 3-D solution increases with the aspect ratio H/D as well as Poisson's ratio m. When contact friction is neglected, the effect of loading platen stiffness on tensile stress in cylinders is found negligible. For the aspect ratio of H/D = 0.5 recommended by ISRM and ASTM, the error in tensile strength may be up to 15% for both typical rocks and asphalts, whereas for longer cylinders with H/D up to 2 the error ranges from 15% for highly compressible materials, and to 60% for nearly incompressible materials. The difference in compressive radial stress between the 2-D Hertz solution or 2-D Hondros solution and the present 3-D solution also increases with Poisson's ratio and aspect ratio H/D. In summary, the 2-D solution, in general, underestimates the maximum tensile stress and cannot predict the location of the maximum hoop stress which typically locates close to the end surfaces of the cylinder.
Chau, K.T. (2013). Analytic Methods in Geomechanics. CRC Press, Boca Raton (457 pages)., Jan 2013
Bringing together a range of areas including tensor analysis, elasticity, plasticity, fracture me... more Bringing together a range of areas including tensor analysis, elasticity, plasticity, fracture mechanics and viscoelasticity, among others, this book is an indispensible guide to the fundamentals of geomechanics. It provides explanations of each subject area, using a step-by-step process with numerous worked examples. The more advanced material, such as complex variables in 2-D elasticity and application of J-integral to model slipping slopes then supplies a gateway into understanding the latest research results and applying them to practical problems. The book is suitable for undergraduate and graduate students as well as professionals and researchers.
The free-field strong ground motions recorded at 64 sites within 200 km from the ruptured Longmen... more The free-field strong ground motions recorded at 64 sites within 200 km from the ruptured Longmen Shan fault during the 12 May 2008 M w 7.9 Wenchuan earthquake were used to examine the near-source strong ground motioncharacteristics. The magnitude of vertical and horizontal peak ground accelerations (PGAs), frequency content, and duration of acceleration histories are analyzed. The observed peak ground accelerations at distances exceeding 60 km from the ruptured fault were significantly higher than those predicted by the Next Generation Attenuation (NGA) model, whereas, for periods of larger than 1 s, the spectral accelerations are much smaller than those of the NGA model. The same is also true for the observed peak ground velocities (PGVs). The duration of ground shaking is longer than for most earthquakes of comparable similar magnitude. For sites within 60 km from the ruptured fault, the accelerations observed on the hanging wall are larger than those observed on the footwall. The duration of ground shaking along the rupture direction (or the forward direction) is shorter than that opposite to the rupture direction (or the backward direction). There is also a systematic increase of PGA and PGV at sites located in the direction of the rupture propagation, whereas no such clear trend was found in the stations located along the backward direction. From the observed acceleration time histories at various locations, the rupture process of the 2008 Wenchuan appears to be more complicated than the focal mechanism interpreted from far-field seismic records. For example, the generation mechanism of the two distinct wave trains observed at Wolong and other stations need more detailed studies.
This paper derives an exact solution for the non-uniform stress and displacement fields within a ... more This paper derives an exact solution for the non-uniform stress and displacement fields within a finite, transversely isotropic, and linear elastic cylinder under compression with a kind of radial constraint induced by friction between the end surfaces of the cylinder and the loading platens. The main feature of the present work is the introduction of a general solution form for Lekhnitskii's stress function such that the governing equation and all end and curved boundary conditions of the cylinder are satisfied exactly. Two different solutions were obtained corresponding to the real or complex characteristic roots of the governing equation, depending on the combination of the elastic material constants. The solution by Watanabe [Watanabe, S., 1996. Elastic analysis of axi-symmetric finite cylinder constrained radial displacement on the loading end. Structural Engineering/Earthquake Engineering JSCE 13, 175s-185s] for isotropic cylinders under compression test can be recovered as a special case. Our numerical results show that both the non-uniform stress distribution and the difference between the apparent and the true Young's moduli of the cylinder are very sensitive to the anisotropy of Young's moduli, Poisson's ratios and shear moduli. A more distinct bulging shape of the cylinder is expected when anisotropy in shear modulus is strong, the cylinder is relatively short, and the end constraint is large. The bulging shape, however, does not depend strongly on anisotropy of either Poisson's ratio or Young's modulus.
In this paper, a soil-pile-structure model is tested on a shaking table subject to both a sinusoi... more In this paper, a soil-pile-structure model is tested on a shaking table subject to both a sinusoidal wave and the acceleration time history of the scaled 1940 El Centro earthquake. A medium-size river sand is compacted into a 1.7-m-high laminar rectangular tank to form a loose fill with a relative density of 15%. A single-storey steel structure of 2.54 ton is placed on a concrete pile cap, which is connected to the four end-bearing piles. A very distinct pounding phenomenon between soil and pile is observed; and, the acceleration response of the pile cap can be three times larger than that of the structural response. The pounding is due to the development of a gap separation between soil and pile, and the extraordinary large inertia force suffered at the top of the pile also induces cracking in the pile. To explain this observed phenomenon, nonlinear finite element method (FEM) analyses with a nonlinear gap element have been carried out. The spikes in the acceleration response of the pile cap caused by pounding can be modeled adequately by the FEM analyses. The present results suggest that one of the probable causes of pile damages is due to seismic pounding between the laterally compressed soil and the pile near the pile cap level.
Seismic torsional pounding between an asymmetric single-story tower and a neighboring barrier und... more Seismic torsional pounding between an asymmetric single-story tower and a neighboring barrier under harmonic ground excitation is modeled as the nonlinear Hertz contact in this paper. The governing equations of motion are numerically solved using the fourth-order Runge-Kutta method with an adaptive step size control. An analytical solution is obtained for the first time for a special case of periodic torsional pounding. Results of our numerical simulations reveal that torsional pounding tends to be much more complex and unpredictable than translational pounding, and most of them are either multiple or chaotic impacts. The maximum torsional impact velocity tends to be insensitive to the changes of separation distance and eccentricity as long as impact is developed. Although the analytical solution fails to predict the exact impact velocity of multiple torsional pounding, it does provide some useful insights into this complex phenomenon. The analytical solution succeeds in predicting the overall patterns as well as the abrupt jump of torsional impact velocity spectra.
This paper derives analytically the stress intensity factors (SIFs) of a frictional interfacial c... more This paper derives analytically the stress intensity factors (SIFs) of a frictional interfacial crack in a viscoleastic bimaterial subject to the action of a center of dilatation. The standard linear viscoelastic solid or ''three-parameter-viscoelastic-model" is adopted. Using the correspondence principle, the problem is formulated in Laplace transform space. The problem is decomposed into two Auxiliary Problems: (I) a bimaterial containing a center of dilatation; and (II) an interfacial crack in the bimaterial subject to tractions that cancel those induced by the Auxiliary Problem I. Schapery's direct method is used to obtain the inverse Laplace transform and, in turn, obtain the SIF as a function of time. Creeping tests for the Swiss Central Alps shales have been adopted for viscoelastic parameter calibration. When the bimaterial degenerates into a homogenous material, the SIFs are independent of time. If the medium containing the center of dilatation is stiffer, the long term SIF is larger than the instantaneous SIF; and if the medium containing the center of dilatation is softer, the long term SIF is smaller than the instantaneous SIF. Therefore, short term crack stability does not necessarily rule out long term crack propagation. If the overburden stress and the friction on crack surface are neglected, both modes I and II SIFs are induced at the crack tips. The mode II SIF is, in general, larger than that of mode I. When both friction and overburden pressure are included in the analysis, tensile cracking is unlikely whilst shear cracking remains possible. The maximum mode II SIF strongly depends on the orientation as well as the distance of the center of dilatation from the crack tip. Both overburden pressure and crack face friction decreases chance of crack propagation.
Direct shear tests on concrete specimens were conducted to investigate the shearing behaviour of ... more Direct shear tests on concrete specimens were conducted to investigate the shearing behaviour of the material under varying normal confining stresses. Test results were analyzed to quantify the mobilization of shear strength components derived from hydrated cement paste-aggregate adhesion, contact friction, shear dilation, and cement-aggregate interlock along the sheared surface under direct shearing. It was found that each component has its unique response in terms of mobilized shear stress and shear displacement. In addition, different modes of failure observed in uniaxial compression, splitting tension, and direct shear tests were identified to delineate the Mohr-Coulomb failure envelope for shear strength of concrete material.
Statistics of the mechanical and failure properties on the grain scale are often assumed to follo... more Statistics of the mechanical and failure properties on the grain scale are often assumed to follow the Weibull distribution in numerical simulations of failure and damage development. To investigate the microstructural basis for such a statistical model of compressive failure in a brittle rock, we consider the development of instability in a wing crack model and establish a methodology whereby the Weibull parameters can be inferred from microstructural data on microcrack density and length statistics for input into finite element simulations. Application of this methodology to six Yuen Long marble samples provides important insights into how different attributes of the microstructure may influence the progressive development of rock failure. The finite element simulations underscore the significant influence of microcrack length statistics, which has not been emphasized in continuum damage mechanics models that usually emphasize the roles of average crack size and crack density. The microstructural data indicate that strength heterogeneity increases with increasing grain size, and this plays a key role in lowering the uniaxial compressive strength, which contributes to the overall decrease of strength with increasing grain size.
For static compressions of spheres, a new stress analysis for isotropic elastic spheres compresse... more For static compressions of spheres, a new stress analysis for isotropic elastic spheres compressed between two¯at rigid platens is proposed by incorporating the Hertz contact stress. The predictions of the failure load for various sizes and strengths of spheres agree very well with our static experiments on a brittle plaster material. For dynamic compressions of spheres, a simple crushing analysis illustrates that the size of the contact zone can be estimated quite accurately in terms of the size of the sphere, the dynamic hardness, and the impact energy. Although the maximum contact force at failure is larger in the static case than that in the dynamic case, the energy required for fragmentation of the solid spheres is larger under dynamic test than under static test. Comparisons of the static and dynamic tests show that the impact energy required for fragmentation of a sphere can be approximated as 1.5 times of that for the static test. As expected, the impact energy for fragmentation increases monotonically with the size and strength of the spheres. The contact time at failure, however, does not exhibit a clear trend with the changes in size and strength of the spheres. Ó
This study presents a framework for numerical simulations based upon micromechanical parameters i... more This study presents a framework for numerical simulations based upon micromechanical parameters in modeling progressive failures of heterogeneous rock specimens under compression. In our numerical simulations, a Weibull distribution of the strength and elastic properties of the finite elements is assumed, and the associated Weibull parameters are estimated in terms of microstructural properties, such as crack size distribution and grain size, through microscopic observations of microcracks. The main uncertainty in this procedure lies on the fact that various ways can be used to formulate a ''microcrack size distribution'' in relating to the Weibull parameters. As one possible choice, the present study uses the number of counted cracks per unit scanned volume per grain size to formulate the crack distributions. Finally, as a tool, the Rock Failure Process Analysis code (RFPA 2D ) is adopted for simulating the progressive failure and microseismicity of heterogeneous rocks by using an elastic-damage finite-element approach. To verify our framework, compression tests on marble specimens are conducted, and the measured acoustic emissions (AE) are compared with those predicted by the numerical simulations. The mode of failure, compressive strength and AE pattern of our simulations basically agree with experimental observations. . Incorporation of AE or CT measurements with surface observations leads to a better understanding of the progressive failure of rocks under compression.
A new constitutive model is proposed for the description of induced anisotropic damage in brittle... more A new constitutive model is proposed for the description of induced anisotropic damage in brittle rocks. The formulation of the model is based on relevant results from micromechanics consideration. The distribution of microcracks is approximated by a second-order damage tensor. The effective elastic properties of damaged material are derived from the free enthalpy function. The evolution of damage is directly related to the growth of microcracks in different space orientations. The volumetric dilatancy due to sliding crack opening is taken into account. The model is extended to the description of creep deformation in brittle rocks. The time dependent deformation is seen as a consequence of the sub-critical propagation of microcracks due to stress corrosion process. The proposed model is applied to a typical brittle rock, the Lac du Bonnet granite. A general good agreement is obtained between numerical simulations and experimental data. r
In this paper, a coupled constitutive model is proposed for anisotropic damage and permeability v... more In this paper, a coupled constitutive model is proposed for anisotropic damage and permeability variation in brittle rocks under deviatoric compressive stresses. The formulation of the model is based on experimental evidences and main physical mechanisms involved in the scale of microcracks are taken into account. The proposed model is expressed in the macroscopic framework and can be easily implemented for engineering application. The macroscopic free enthalpy of cracked solid is first determined by approximating crack distribution by a second-order damage tensor. The effective elastic properties of damaged material are then derived from the free enthalpy function. The damage evolution is related to the crack growth in multiple orientations. A pragmatic approach inspired from fracture mechanics is used for the formulation of the crack propagation criterion. Compressive stress induced crack opening is taken into account and leads to macroscopic volumetric dilatancy and permeability variation. The overall permeability tensor of cracked material is determined using a micro-macro averaging procedure. Darcy's law is used for fluid flow at the macroscopic scale whereas laminar flow is assumed at the microcrack scale. Hydraulic connectivity of cracks increases with crack growth. The proposed model is applied to the Lac du Bonnet granite. Generally, good agreement is observed between numerical simulations and experimental data.
Brittle solids, such as rock or concrete, may contain numerous randomly distributed micro-flaws (... more Brittle solids, such as rock or concrete, may contain numerous randomly distributed micro-flaws (e.g. cracks, pores or weak inclusions). When they are loaded in compression, cracks may nucleate from these flaws. These cracks then continue to grow in a stable manner with the increasing axial compression, curving toward an orientation parallel to the direction of axial compression. Their propagation and interaction may lead to the collapse of the solid in a splitting mode. With a newly developed numerical code, MFPA 2D (material failure process analysis), heterogeneous solids containing pre-existing single, triple and multi-pore-like flaws are numerically tested to study the mechanisms of compression-induced axial splitting. The interaction of growing cracks with the surfaces of the specimen and with each other in terms of stress field and failure modes is numerically analyzed in detail. Under uniaxial compressions, specimens containing holes in a diagonal array are more conducive to interaction than specimens containing holes arranged either in a horizontal or vertical array. Various parameters, such as hole diameter, specimen width, and the geometrical arrangement of hole locations, that characterize the growth process are quantified. Numerical results mimic the phenomena of experimentally observed splitting failure in brittle solids such as rocks in a realistic way.
Normal-and high-strength concrete cylinders (designed compressive strengths of 30 and 90 MPa at 2... more Normal-and high-strength concrete cylinders (designed compressive strengths of 30 and 90 MPa at 28 days) were loaded uniaxially. Computer tomography (CT) scanning technique was used to examine the evolution of air voids inside the specimens at various loading states up to 85% of the ultimate compressive strength. The normal-strength concrete yielded a very different behaviour in changes of internal microstructure as compared to the high-strength concrete. There were significant instances of nucleation and growth in air voids in the normal-strength concrete specimen, while the increase in air voids in the high-strength concrete specimen was insignificant. In addition, CT images were used for mapping the aggregate spatial distributions within the specimens. No intrinsic anisotropy was detected from the fabric analysis. D
As over seventy percent of the land of Hong Kong is mountainous, rainfall-induced debris flows ar... more As over seventy percent of the land of Hong Kong is mountainous, rainfall-induced debris flows are not uncommon in Hong Kong. The objective of this study is to incorporate numerical simulations of debris flows with GIS to identify potential debris flow hazard areas. To illustrate this approach, the proposed methodology is applied to Leung King Estate in Tuen Mun. A Digital Elevation Model (DEM) of the terrain and the potential debris-flow sources were generated by using GIS to provide the required terrain and flow source data for the numerical simulations. A theoretical model by improved by incorporating a new erosion initiation criterion was used for simulating the runout distances of debris flows. The well-documented 1990 Tsing Shan debris flow, which occurred not too far from Leung King Estate, was used to calibrate most of the flow parameters needed for computer simulations. Based on the simulation results, a potential hazard zone was identified and presented by using GIS. Our proposed hazard map was thus determined by flow dynamics and a deposition mechanism through computer simulations without using any so-called expert opinions, which are bounded to be subjective and biased.
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Papers by Chau K.T.