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This paper presents a stochastic analysis of the size effect on the nominal strength of quasibrittle structures with a large preexisting notch. This type of scaling behavior has been extensively studied within a deterministic framework. Little attention is paid to stochastic analysis, which is essential for reliability-based analysis and design of engineering structures. Stochastic finite element simulations are performed to study the failure of geometrically similar beams of different sizes. The numerical analysis uses a continuum damage model, in which the tensile strength and fracture energy are modeled by homogeneous random fields. Different correlation lengths are considered as a parametric study. The analysis yields the size effects on the mean and coefficient of variation (CoV) of the nominal structural strength. It is shown that the size effect on the mean strength agrees well with the Bazant size effect model. The simulation predicts a strong size effect on the CoV of the nominal strength. Small-, intermediate-, and large-size asymptotes are derived analytically for the scaling behavior of the strength CoV. Based on these asymptotes, an approximate scaling equation is proposed for the CoV of nominal strength. The effect of the correlation length on the simulated failure behavior is discussed. [ABSTRACT FROM AUTHOR]

This paper investigates the influence of time-dependent bond slip on the delayed failure of RC frames. The time-dependent model of bond slip is formulated based on the mechanism of subcritical damage accumulation along the steel–concrete interface. A kinetic model of the time dependence of slip under sustained loading is developed through numerical simulations. The model is incorporated into a recently developed reduced-order numerical model for simulations of the progressive collapse of RC frames. It is shown that the present model captures the essential deformation mechanisms of the frame under both monotonic loading and sustained loading, and that the time dependence of bond slip has a profound influence on the delayed failure of RC frames, especially under moderate sustained loading. This finding highlights the importance of understanding and accounting for the time dependence of bond slip for future study of the delayed progressive collapse of RC structures. [ABSTRACT FROM AUTHOR]

Recent disagreements on the mathematical modeling of fracture and size effect in concrete and other quasi-brittle materials are obstacles to improvements in design practice, and especially in design codes for concrete structures. In an attempt to overcome this impediment to progress, this paper compares the Hu-Duan boundary effect model (BEM) expounded since 2000 to the size-shape effect law (SEL) proposed at Northwestern University in 1984 and extended to the geometry (or shape) effects in 1990. It is found that within a rather limited part of the range of sizes and shapes, the fracture energy values identified by BEM and SEL from the test data on maximum loads are nearly the same. But in other parts of the range the BEM is either inferior or inapplicable. The material tensile strength values identified by BEM have a much larger error than those obtained from the SEL after calibration by the cohesive crack model. From the theoretical viewpoint, several hypotheses of BEM are shown to be unrealistic. CE Database subject headings: Cracking; Concrete; Structural failures; Data analysis; Size effect. Author keywords: Fracture scaling; Fracture energy; Concrete; Asymptotics of fracture; Cohesive cracks; Failure of structures; Evaluation of experimental data. DOI: 10.1061/(ASCE)EM.1943-7889.89

This paper presents a discrete element model for simulations of the compaction process of hot mixed asphalt (HMA). The model is anchored by the concept of a fine aggregate matrix (FAM), which consists of the binder and fine aggregates. In the simulation, the coarse aggregates are explicitly modeled as composite particles. Meanwhile, the FAM is considered as the thick coating of the coarse aggregates with complex constitutive laws. Interparticle interactions include influences of (1) particle properties via Hertz–Mindlin relations; and (2) FAM properties via lubrication relationships. The lubrication relationships include a variable for viscosity for which we derive normal and tangential rate-dependent forms using rheology theory of dense granular-fluid systems, verified reasonable for our systems with the discrete element simulations and experiments with FAM. We assimilate these elements into gyratory compaction simulations of HMA of different aggregate size distributions. We compare these with experiments and find that this model is capable of capturing the measured effects of grain size distribution on the overall compaction behavior of HMA. We conclude by highlighting the advantages of this discrete element model for HMA compaction problems. [ABSTRACT FROM AUTHOR]

Gyratory compaction has widely been used to evaluate the compactability of hot asphalt mixtures. Existing efforts on modeling of gyratory compaction have largely been devoted to sophisticated high-fidelity numerical simulations. This paper presents a one-dimensional nonlocal model for gyratory compaction. The model is anchored by the principle of mass conversation, in which the local densification rate is formulated as a function of the nonlocal packing fraction. The nonlocal model involves a material characteristic length scale, which is independent of the specimen size. The nonlocality gives rise to strong effects of the specimen height on the overall compaction curve as well as on the profile of the local packing fraction. A set of gyratory compaction experiments is performed on specimens of different heights. It is shown that the model is able to capture the measured size effect on the compaction curves. A parametric study is carried out to investigate the effects of nonlocality and model parameters on the predictions of compaction curve and profile of packing fraction. [ABSTRACT FROM AUTHOR]

Previous analysis of progressive collapse showed that gravity alone suffices to explain the overall collapse of the World Trade Center Towers. However, it remains to be determined whether the recent allegations of controlled demolition have any scientific merit. The present analysis proves that they do not. The video record available for the first few seconds of collapse is shown to agree with the motion history calculated from the differential equation of progressive collapse but, despite uncertain values of some parameters, it is totally out of range of the free fall hypothesis, on which these allegations rest. It is shown that the observed size range (0.01-0.1 mm) of the dust particles of pulverized concrete is consistent with the theory of comminution caused by impact, and that less than 10% of the total gravitational energy, converted to kinetic energy, sufficed to produce this dust (whereas, more than 150 t of TNT per tower would have to be installed, into many small holes drilled into concrete, to produce the same pulverization). The air ejected from the building by gravitational collapse must have attained, near the ground, the speed of almost 500 miles per hour (or 223 m/s, or 803 km/h) on average, and fluctuations must have reached the speed of sound. This explains the loud booms and wide spreading of pulverized concrete and other fragments, and shows that the lower margin of the dust cloud could not have coincided with the crushing front. The resisting upward forces due to pulverization and to ejection of air, dust, and solid fragments, neglected in previous studies, are indeed found to be negligible during the first few seconds of collapse but not insignificant near the end of crush-down. The calculated crush-down duration is found to match a logical interpretation of seismic record, while the free fall duration grossly disagrees with this record. CE Database subject headings: Collapse; Structural dynamics; Buildings, high-rise; Towers; New York; New York City; Terrorism.

In shear failure, reinforced concrete (RC) beams always develop, in a stable manner, a finite length crack before the maximum load is reached. Thus, the crack tip location cannot sample a large volume of material with random strength because a small region in which the crack tip can lie is fixed by fracture mechanics. Consequently, the size effect on the mean strength cannot be statistical. It must be predominantly energetic or deterministic and, thus, must follow the Type-2 size effect law. What has not yet been clarified is the size effect on the coefficient of variation (CoV) of beam strength, which is important for anchoring the probability distribution of shear strength and choosing the safety factor. In this study, we run thousands of explicit finite element simulations using Abaqus-Explicit version 6.14 with microplane model M7, each with a random input of material strength and Young's modulus for each finite element in the structure. The CoV of beam strength is found to decrease with the structure size when geometrically similar beams are compared, although the CoV tends to a constant for large sizes. This size effect on the CoV is similar to that in ductile failure governed by a Gaussian distribution of strength and contrasts with that in brittle failures following the Weibull distribution, for which the CoV is size independent. To characterize the size dependence of the strength CoV, an analytical formula is developed based on the statistics of the sample quantiles of a series of random variables. [ABSTRACT FROM AUTHOR]

There has been ever-increasing interest over the past decade in improving understanding of the mechanisms responsible for the progressive collapse of structures. Existing design recommendations and analyses are largely limited to instantaneous (time-independent) collapse. However, recent experiments revealed that reinforced concrete (RC) structures may be susceptible to delayed collapse, prompting the consideration of time-dependent material behavior as part of progressive collapse analysis and design. A reduced-order computational model for delayed collapse behavior of RC structures is introduced here in which the potential damage zones that evolve within a structure are treated as cohesive elements. The constitutive model of the cohesive element accounts for viscoelastic deformation and time-dependent damage accumulation of the concrete and hardening plasticity of the steel reinforcement. The remaining part of the structure is treated as a viscoelastic continuum. The model is first applied to simulate a pushdown experiment on a RC frame subassemblage under displacement-controlled loading. The deformation and failure mechanisms are in good agreement with experimental observations. The model is then used to investigate the behavior of the subassemblage in a "static fatigue scenario" in which the load is monotonically increased to a prescribed level and is then held constant until ultimate structural failure resulting from the assumed time-dependent response of the concrete material. The corresponding timescale of the delayed failure is on the order of hours, a result that has important implications not only for the analysis and design of RC structures against progressive collapse but also for the safety of first responders who enter structures that may collapse within that period of time. [ABSTRACT FROM AUTHOR]

A general framework for analyzing the failure probability of concrete specimens with the mean strength sampled from a large database is presented. The framework explicitly takes into account the level of uncertainty of the existing strength database involving different concretes tested in different labs. This uncertainty strongly influences the probability distribution of the nominal strength of each structure. The energetic (nonstatistical) size effect on structural strength is also incorporated into the analysis. The proposed framework is demonstrated by analyzing the reliability of reinforced concrete beams against diagonal shear failure. The analysis considers four different levels of uncertainty of the mean strength database, with coefficients of variation 5%, 10%, 25%, and 40%. It is shown that the overall failure probability strongly depends on the structure size, and that this size effect is also influenced by the uncertainty level of the database. In addition, an approximate solution procedure is developed for calculating the failure probability in the spirit of the first-order reliability method. Compared to the existing procedure, the proposed model is shown to yield a more realistic estimate of the structural failure risk and to lead to an analytical solution of the safety factor that can be used for reliability-based structural design. [ABSTRACT FROM AUTHOR]

Anchored by the theory of extreme value statistics, Weibull distribution is the most widely used mathematical model for strength distribution of brittle structures. In a series of recent studies, a finite weakest-link model was developed for strength distribution of quasi-brittle structures, and the classical Weibull distribution was shown to represent the large-size asymptote of the model. By employing a length scale, the finite weakest-link model is capable of capturing correctly the size effects on both the probability distribution and the mean value of structural strength. However, the connection of this length scale with the basic material properties is still missing. This study investigates the relationship between the length scale of the finite weakest-link model and the material length scales by analyzing the size effect on the mean structural strength. The mathematical form of this relationship is derived through dimensional analysis. To validate the model, a set of mean size effect curves is obtained through stochastic simulations, which use a nonlinear constitutive model involving both the Irwin characteristic length and the crack band width. The internal length scale of the weakest-link model is determined by optimum fitting of the benchmark size effect curves in the small-size range. Furthermore, the effect of stress field on this internal length scale is studied by considering three different loading configurations. The present analysis reveals the importance of the mean size effect analysis for the calibration of finite weakest-link model. [ABSTRACT FROM AUTHOR]

Previous analysis of progressive collapse showed that gravity alone suffices to explain the overall collapse of the World Trade Center Towers. However, it remains to be determined whether the recent allegations of controlled demolition have any scientific merit. The present analysis proves that they do not. The video record available for the first few seconds of collapse is shown to agree with the motion history calculated from the differential equation of progressive collapse but, despite uncertain values of some parameters, it is totally out of range of the free fall hypothesis, on which these allegations rest. It is shown that the observed size range (0.01–0.1 mm) of the dust particles of pulverized concrete is consistent with the theory of comminution caused by impact, and that less than 10% of the total gravitational energy, converted to kinetic energy, sufficed to produce this dust (whereas, more than 150 t of TNT per tower would have to be installed, into many small holes drilled into concrete, to produce the same pulverization). The air ejected from the building by gravitational collapse must have attained, near the ground, the speed of almost 500 miles per hour (or 223 m/s, or 803 km/h) on average, and fluctuations must have reached the speed of sound. This explains the loud booms and wide spreading of pulverized concrete and other fragments, and shows that the lower margin of the dust cloud could not have coincided with the crushing front. The resisting upward forces due to pulverization and to ejection of air, dust, and solid fragments, neglected in previous studies, are indeed found to be negligible during the first few seconds of collapse but not insignificant near the end of crush-down. The calculated crush-down duration is found to match a logical interpretation of seismic record, while the free fall duration grossly disagrees with this record. [ABSTRACT FROM AUTHOR]

The collapse of the World Trade Center towers was initiated by the impact of the upper falling part onto the underlying intact story. At the moment of impact, the velocity of the upper part must have decreased. The fact that no velocity decrease can be discerned in the videos of the early motion of the tower top has been recently exploited to claim that the collapse explanation generally accepted within the structural mechanics community was invalid. This claim is here shown to be groundless. Calculations show that the velocity drop is far too small to be perceptible in amateur video records and is much smaller than the inevitable error of such video records. [ABSTRACT FROM AUTHOR]

In this article, the authors present their views in response to a comment on their article related to the claims against the scientific basis for gravity-driven progressive collapse occurred in the towers of the World Trade Center (WTC) in New York City. As per them, the claims include violation of momentum conservation principles and sustained column heating. They state that structural mechanics without standard simplifying hypothesis made structural analysis feasible.