Sampling analysis of concrete structures for creep and shrinkage with correlated random material parameters

The latin hypercube sampling method, which represents the most efficient way to determine the statistics of the creep and shrinkage response of structures, has previously been developed and used under the assumption that the random parameters of the creep and shrinkage prediction model are mutually independent. In reality they are correlated. On the basis of existing data, this paper establishes, by means of the method of maximum likelihood, the joint multivariate probability distribution of the random parameters involved, tests the hypothesis of mutual dependence of parameters on the basis of the χ²-distribution, and generalizes the latin hypercube sampling method to the case of correlated multinormal random parameters. The generalization is accomplished by an orthogonal matrix transformation of the random parameters based on the eigenvectors of the inverse of the covariance matrix. This yields a set of new random parameters which are uncorrelated (independent) and can be subjected to the ordinary latin hypercube sampling, with samples of equal probabilities. Numerical examples of statistical prediction of creep and shrinkage effects in structures confirm the practical feasibility of the method and reveal a good agreement with the scatter observed in some previous experiments.     

Size Effect on Strength of Floating Sea Ice under Vertical Line Load

The size effect on the nominal strength of a floating ice plate subjected to a vertical uniform line load is analyzed. The cracks produced by the load, which are parallel to the load line, are treated as softening inelastic hinges. The problem is one dimensional in the direction normal to the load line, equivalent to a beam on elastic foundation provided by buoyancy of ice in water. The softening moment-rotation diagram of inelastic hinges is simplified as linear and its dependence on structure size (ice thickness) is based on the energy dissipated by fracture. For thick enough plates, no two hinges (on one side of the line load) can soften simultaneously, in which case a simple analytical solution is possible. In that case, the load-deflection diagram has multiple peaks and troughs and consists of a sequence of spikes that get progressively sharper as the plate thickness increases. In terms of a dimensionless nominal strength, the effect of a finite fracture process zone at ice surface leads to an up-and-down size effect plot, such that each load peak decreases with the size at first but then asymptotically approaches a rising asymptote of the type (thickness)1/4 (which implies a reverse size effect, caused by buoyancy). The energy dissipation when the crack in the hinge gets deep causes a strong monotonic size effect, such that the dimensionless troughs between two spikes, in the case of thick enough plate, decrease asymptotically as (thickness)?1/2. For thin enough plates, more than one hinge soften simultaneously and, in the asymptotic case of vanishing ice thickness, the plasticity solution, which has no size effect, is approached. In the intermediate size range with hinges softening simultaneously, the exact solution is complicated and only approximate formulas for the size effect are possible. They are constructed by asymptotic matching.     

Improved prediction model for time-dependent deformations of concrete: Part 7—Short form of BP-KX model,statistics and extrapolation of short-time data

For structures that do not have a high sensitivity to creep or for preliminary design of any structures, practising engineers demand a short formula for predicting the material creep properties. Such a formula is given in the present addendum to a previous six-part paper. It is based on optimal fitting of the previously published log-double power law to the formulae of the BP-KX model. A simple formula giving directly the compliance function rate is also presented. Finally, a simple method of improving the predictions on the basis of short-time measurements is described, and tables giving the statistics of the deviations of the prediction formulas of the simplified model and its short form from the data in the literature are presented.     

Live TV subtitling through respeaking with remote cutting-edge technology

Multimedia Tools and Applications - This article presents an original system for live TV subtitling using respeaking and automatic speech recognition. Unlike several commercially available live...     

Effect of cracking in drying and shrinkage specimens

The significance of cracking and microcracking caused by nonuniform drying shrinkage of test specimens is analyzed. To assure that no cracks are produced by drying in load-free specimens, one must lower the environmental humidity gradually and sufficiently slowly, and use very thin specimens (about 1 mm thick). Graphs for the maximum admissible rate of change of environmental humidity, calculated from both linear and nonlinear diffusion theories, are provided. The spacing and width of parallel cracks due to drying are estimated from fracture mechanics considerations. In normal size specimens the drying cracks are usually too narrow to be visible. Drying leads to discontinuous microcracking rather than continuous macrocracks and is represented better as strain softening than as an abrupt stress drop. Shrinkage cracking can increase drying diffusivity by several orders of magnitude.     

Cohesive Crack with Rate-Dependent Opening and Viscoelasticity: I. Mathematical Model and Scaling

The time dependence of fracture has two sources: (1) the viscoelasticity of material behavior in the bulk of the structure, and (2) the rate process of the breakage of bonds in the fracture process zone which causes the softening law for the crack opening to be rate-dependent. The objective of this study is to clarify the differences between these two influences and their role in the size effect on the nominal strength of stucture. Previously developed theories of time-dependent cohesive crack growth in a viscoelastic material with or without aging are extended to a general compliance formulation of the cohesive crack model applicable to structures such as concrete structures, in which the fracture process zone (cohesive zone) is large, i.e., cannot be neglected in comparison to the structure dimensions. To deal with a large process zone interacting with the structure boundaries, a boundary integral formulation of the cohesive crack model in terms of the compliance functions for loads applied anywhere on the crack surfaces is introduced. Since an unopened cohesive crack (crack of zero width) transmits stresses and is equivalent to no crack at all, it is assumed that at the outset there exists such a crack, extending along the entire future crack path (which must be known). Thus it is unnecessary to deal mathematically with a moving crack tip, which keeps the formulation simple because the compliance functions for the surface points of such an imagined preexisting unopened crack do not change as the actual front of the opened part of the cohesive crack advances. First the compliance formulation of the cohesive crack model is generalized for aging viscoelastic material behavior, using the elastic-viscoelastic analog (correspondence principle). The formulation is then enriched by a rate-dependent softening law based on the activation energy theory for the rate process of bond ruptures on the atomic level, which was recently proposed and validated for concrete but is also applicable to polymers, rocks and ceramics, and can be applied to ice if the nonlinear creep of ice is approximated by linear viscoelasticity. Some implications for the characteristic length, scaling and size effect are also discussed. The problems of numerical algorithm, size effect, roles of the different sources of time dependence and rate effect, and experimental verification are left for a subsequent companion paper. This revised version was published online in July 2006 with corrections to the Cover Date.     

Size effect on buckling strength of eccentrically compressed column with fixed or propagating transverse crack

The strength and size effect of a slender eccentrically compressed column with a transverse pre-existing traction-free edge crack or notch is analyzed. Rice and Levy’s spring model is applied to simulate the effect of a crack or notch. An approximate, though accurate, formula is proposed for the buckling strength of the column of variable size. Depending on the eccentricity, the crack at maximum load can be fully opened, partially opened or closed. The size effects in these three situations are shown to be different. The exponent of the power-law for the large-size asymptotic behavior can be −1/2 or −1/4, depending on the relative eccentricity of the compression load. Whether the maximum load occurs at initiation of fracture growth, or only after a certain stable crack extension, is found to depend not only on the column geometry but also on its size. This means that the definition of positive or negative structural geometry (as a geometry for which the energy release rate at constant load increases or decreases with the crack length) cannot be extended to stability problems or geometrically nonlinear behavior. Comparison is made with a previous simplified solution by Okamura and coworkers. The analytical results show good agreement with the available experimental data.     

Stability and post-critical growth of a system of cooling or shrinkage cracks

When a system of parallel equidistant cooling cracks propagates into an elastic halfspace, it reaches at a certain depth of the cracks a critical point of instability, and the equilibrium path of the system bifurcates. Further extension of equally long cracks is unstable and impossible. The stable post-critical path consists of extension of every other crack upon further cooling, initially with a crack jump at constant temperature, while the intermediate cracks stop growing and gradually diminish their stress intensity factor until it becomes zero. This represents a second critical state at which these intermediate cracks suddenly close over a finite length at no change in temperature and at constant length of the leading cracks. Subsequently, as the cooling front further advances, the leading cracks grow at equal length until they again reach a critical state, at which every other crack stops growing, and the process in which the crack spacing doubles is repeated. In this manner, the spacing of the opened cooling cracks fluctuates around roughly the one-half value of the cooling penetration depth.The instability is determined by the sign of the second variation of the work needed to create the cracks, which leads to positive definiteness conditions for a matrix consisting of partial derivatives of the stress intensity factors with regard to crack lengths, subjected to admissibility conditions for the eigenvector of crack length increments. The first initial state of crack arrest is characterized by the vanishing of the diagonal element of the matrix, while the second critical state of crack closing is characterized by the vanishing of the determinant of this matrix.The critical states and the postcritical crack growth are calculated numerically by finite elements. The solution is applied to the cooling of a hot granite mass, the cracking of which is important for one recently proposed geothermal heat extraction scheme. The solution is also of interest for drying shrinkage cracks, especially in concrete.

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Résumé Lorsque un système de fissures équidistantes parallèles survenant lors d'un refroidissement se propage dans un demi espace élastique, il atteint à une certaine profondeur de fissuration un état critique d'instabilité et le chemin d'équilibre du système bifurque. Une extension ultérieure de fissures de longueurs égales se présente comme instable est impossible. Le chemin post-critique stable correspondra à une extension de toute autre fissure correspondant à un refroidissement ultérieur, et ce à l'origine avec un resaut de la fissure à temperature constante, tandis que les fissures intermédiaires cessent leur croissance et voient leur facteur d'intensité de contrainte graduellement diminuer jusqu'à la valeur nulle. Ceci correspond à un deuxième état critique pour lequel les fissures intermédiaires se ferment brusquement sur une longueur finie sans que ne se produise un changement de température, et à longueur constante des fissures principales. Par après lorsque le front de refroidissement continue d'avancer, les fissures principales croissent d'une longueur égale jusqu'à ce qu'elles atteignent à nouveau un état critique, état pour lequel les autres fissures cessent de croître et pour lequel le processus d'espacement des fissures est répété. De cette manière, l'espacement de fissures s'ouvrant lors du refroidissement fluctue autour d'une valeur correspondant sensiblement à la moitié de la valeur de la pénétration de refroidissement.L'instabilité est déterminée par le signe de la deuxième variation du travail nécessaire pour créer les fissures, ce qui conduit à des conditions positives non définies pour une matrice comportant les dérivées partielles des facteurs d'intensité d'entaille par rapport aux longueurs de la fissure, l'ensemble étant sujet aux conditions d'admissibilité de l'eigenvector pour des accroissement de longueurs de la fissures. Le premier état initial de l'arrêt de la fissure est caractérisé par la disparition de l'élément diagonal de la matrice tandis que le deuxième état critique de fermeture de la fissure est caractérisé par la disparition du déterminant de cette matrice.Les états critiques et la croissance post-critique de la fissure sont calculés de façon numérique par des éléments finis. La solution est appliquée au refroidissement d'une masse granitique à haute température dont la fissuration est importante, dans le cadre d'un schéma d'extraction de la chaleur géothermique proposé récemment. La solution est également intéressante à appliquer dans le cas de fissures procédant d'une contraction due au séchage, et ce en particulier dans le cas du béton.