Showing papers by "Zdenek P. Bazant published in 2014"

Universal Size-Shape Effect Law Based on Comprehensive Concrete Fracture Tests

Abstract: The universal size-shape effect law is a law that describes the dependence of nominal strength of specimen or structure on both its size and the crack (or notch) length, over the entire range of interest, and exhibits the correct small-size and large-size asymptotic properties as required by the cohesive crack model (or crack band model). The main difficulty has been the transition of crack length from 0, in which case the size effect is Type 1, to deep cracks (or notches), in which case the size effect is Type 2 and is fundamentally different from Type 1, with different asymptotes. In this transition, the problem is not linearizable because the notch is not much larger than the fracture process zone. The previously proposed universal law could not be verified experimentally for the Type 1-Type 2 transition because sufficient test data were lacking. The current study is based on recently obtained comprehensive fracture test data for three-point bend beams cast from one batch of the same concrete and cured and tested under identical conditions. The test data reveal that the Type 1-Type 2 transition in the previous universal law has insufficient accuracy and cannot be captured by Taylor series expansion of the energy release rate function of linear elastic fracture mechanics. Instead, the size effect for a zero notch and for the transitional range is now characterized in terms of the strain gradient at the specimen surface, which is the main variable determining the degree of stress redistribution by the boundary layer of cracking. The new universal law is shown to fit the comprehensive data quite well, with a coefficient of variation of only 2.3%.

Theory of cyclic creep of concrete based on Paris law for fatigue growth of subcritical microcracks

Abstract: Recent investigations prompted by a disaster in Palau revealed that worldwide there are 69 long-span segmental prestressed-concrete box-girder bridges that suffered excessive multi-decade deflections, while many more surely exist. Although the excessive deflections were shown to be caused mainly by obsolescence of design recommendations or codes for static creep, some engineers suspect that cyclic creep might have been a significant additional cause. Many investigators explored the cyclic creep of concrete experimentally, but a rational mathematical model that would be anchored in the microstructure and would allow extrapolation to a 100-year lifetime is lacking. Here it is assumed that the cause of cyclic creep is the fatigue growth of pre-existing microcracks in hydrated cement. The resulting macroscopic strain is calculated by applying fracture mechanics to the microcracks considered as either tensile or, in the form of a crushing band, as compressive. This leads to a mathematical model for cyclic creep in compression, which is verified and calibrated by laboratory test data from the literature. The cyclic creep is shown to be proportional to the time average of stress and to the 4th power of the ratio of the stress amplitude to material strength. The power of 4 is supported by the recent finding that, on the atomistic scale, the Paris law should have the exponent of 2 and that the exponent must increase due to scale bridging. Exponent 4 implies that cyclic creep deflections are enormously sensitive to the relative amplitude of the applied cyclic stress. Calculations of the effects of cyclic creep in six segmental prestressed concrete box girders indicate that, because of self-weight dominance, the effect on deflections absolutely negligible for large spans ( > 150 m ) . For small spans ( 40 m ) the cyclic creep deflections are not negligible but do not matter since the static creep causes in such bridges upward deflections. However, the cyclic creep is shown to cause in bridges with medium and small spans ( 80 m ) a significant residual tensile strain which can produce deleterious tensile cracking at top or bottom face of the girder.

Why Fracking Works and How to Optimize It

Abstract: Although spectacular advances in hydraulic fracturing, aka fracking, have taken place and many aspects are well understood by now, the topology, geometry and evolution of the crack system hydraulically produced in the shale still remains an enigma. Expert opinions differ widely and fracture mechanicians must wonder why fracking works. Fracture mechanics of individual pressurized cracks has recently been clarified but the vital problem of stability of interacting hydraulic cracks escaped attention. Progress in this regard would likely allow optimization of fracking and reduction of environmental footprint. The present article first focuses on the classical solutions of the critical states of localization instability of a system of cooling or shrinkage cracks and shows that these solutions can be transferred to the system of hydraulic cracks. It is concluded that if the profile of hydraulic pressure along the cracks can be made almost uniform, with a steep pressure drop at the front, the localization instability can be avoided. To achieve this kind of profile the pumping rate (corrected for the leak rate) must not be too high. Subsequently, numerical solutions are presented to show that an idealized system of circular equidistant vertical cracks propagating from a horizontal borehole behaves similarly. It is pointed out that one important role of proppants, as well as acids that promote creation debris in the new cracks, is that they partially help to limit crack closings and thus localization. Based on the extremely low permeability of gas shale, one must imagine a hierarchical progressively refined crack systems in which the finest cracks have spacing in the sub-centimeter range. The overall conclusion is that what makes fracking work is the suppression or mitigation of localization instabilities of crack systems, which requires achieving uniform pressure profiles along the cracks.

Recalibration and uncertainty quantification of the B3 creep model for long term estimates using Bayesian methods

Abstract: Arecalibration of the B3 model for creep and shrinkage has become possible with the availability of a new expanded statistical database on creep and shrinkage at Northwestern University that now also covers high performance concretes with admixtures. The recently collected evidence on excessive multi-decade deflections of numerous pre-stressed long-span box-girder bridges shows that this recalibration is indeed necessary. Data containing precise information of concrete materials as well as curing and testing conditions are needed in order to update the model parameters.To accurately capture the long-termbehavior of a structure, the model must also be calibrated with long-term data.Yet, precise laboratory tests pertain mostly to durations <6 years and are not available on the time scale of many decades that engineers need to predict the behavior with desired lifetimes >50 years and often>100 years.To performthe required recalibration, two databases are used simultaneously— one for laboratory test data with accurate material information but unknown long-term behavior and another for long-term bridge deflections with unknown or uncertain material information and structural characteristics. A Bayesian approach to this problem is presented. First the parameters of the B3 model are recalibrated with the enlarged laboratory test database, which is regarded as the Bayesian prior information, see Figure 1. Then the model is updated in the Bayesian sense using the incomplete bridge deflection data to obtain the posterior information. The resulting model predicts the long-term structural behavior more accurately and provides the associated measures of uncertainty based on both sets of data.