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Investigation of statistical scaling in localization-induced failures dates back to da Vinci's speculation on the length effect on the rope strength in 1500s. The early mathematical description of statistical scaling stems from the birth of the extreme value statistics. The most commonly known mathematical model for statistical scaling is the Weibull size effect, a direct consequence of the infinite weakest-link model. However, abundant experimental observations on different localization-induced failures showed that the Weibull size effect is inadequate. Over the last two decades, two mathematical models were developed to describe the statistical size effect on localization-induced failures. One is the finite weakest-link model, in which the random structural resistance is expressed as the minimum of a set of discrete independent random variables, and the other is the level excursion model, a continuum description of the finite weakest-link model, in which the structural failure probability is calculated as the probability of the upcrossing of a random field over a barrier. This paper reviews the mathematical formulation of these two models, and their applications to various engineering problems including the strength distributions of quasibrittle structures, failure statistics of micro-electro-mechanical systems (MEMS) devices, breakdown statistics of highk gate dielectrics, and probability distribution of buckling pressure of spherical shells containing random geometric imperfections. The implications of statistical scaling for the stochastic finite element simulations and the reliability-based structural design are discussed. In particular, the recent development of the size-dependent safety factors is reviewed.

This paper proposes a methodology to construct logs of rock strength from the cutting force signal recorded in scratch tests conducted in the ductile regime. The approach, which is based on the application of discrete wavelet transforms, recognizes the existence of two length scales ℓcand ℓr. The strength length scale ℓcrepresents the length over which it is meaningful to measure strength, while the repeatability length scale ℓris related to the resolution at which the force signal must be observed to become insensitive to the stochastic micro-failure events triggered by the motion of the cutter. It is postulated that the original cutting force signal, assumed to be sampled at a high enough frequency, can be decomposed into a deterministic signal intrinsic to the rock and a stochastic one resulting from discrete rock failure events. The technique of multiresolution analysis based on the maximal overlap discrete wavelet transform is applied as a low-pass filter to the original cutting force signals so as to wipe out the high-frequency components associated with the stochastic rock failure events. A criterion to determine the optimum cutoff frequency of the low-pass filter and the corresponding repeatability length scale is discussed in terms of the correlation coefficients between different filtered signals. It is shown that the low-pass filtered signals obtained at the optimum cutoff frequency have two salient features: (i) repeatability over different tests conducted at the same depth of cut on the same sample, and (ii) variability along the cutting distance. The excellent repeatability reveals that the deterministic background trend of the original force signals is relevant to the rock strength property, and the variability of the background trend captures the spatial variation of the rock strength.

This proof of concept study investigates the electrical conductivity and damage healing capability of graphite nano-platelet (GNP)-taconite modified asphalt materials. Different combinations of GNP and taconite concentrate are added to an asphalt binder, and the electrical conductivity is measured by a four-probe conductivity test. Similar combinations of GNP and taconite concentrate are used to prepare asphalt mixture specimens to investigate the healing capability. Semi-circular bend (SCB) tests are performed at low temperature in two stages. First, specimens are damaged by loading them into the post peak region using crack mouth opening displacement (CMOD) control. The specimens are then subjected to microwave heating, after which they reloaded to measure the strength capacity. It is shown that the addition of GNP and taconite concentrate could effectively enhance the electrical conductivity of asphalt binders. The results also demonstrate the influence of humidity on the measured conductivity. The SCB fracture tests show that the application of microwave energy to the pre-damaged specimens restores their original load capacity, a clear indication of damage healing.

Compaction of asphalt mixtures is a critical component of the construction process of asphalt pavements. The quality of compaction has a significant consequence for the durability of asphalt pavements. Compaction of asphalt mixtures is a complex physical process, which has not been fully understood. In this study, we investigate the physical mechanisms of compaction, based on which we propose a new method to evaluate the compactability of asphalt mixtures. Two mesoscopic physical mechanisms are introduced. One is related to the jamming of aggregates, which governs the densification process of the mixture. The other is related to the binder-aggregate interaction, which is responsible for the change of shear resistance of mixtures during compaction. Based on these mechanisms, different indices are proposed to characterise the compactability of asphalt mixtures. The model is applied to analyse seven asphalt mixtures that were used to construct test sections at MnROAD research facility. Statistical analysis is performed to identify correlations between the compactability indices and material compositions, such as gradation and binder content. Based on the most significant correlations, multiple linear regression models are developed, which can be used to design more compactable mixtures.

This paper presents an experimental investigation of the properties of asphalt binders and mixtures modified with graphite nanoplatelets (GNPs). The focus is on studying the effects of GNP addition on low-temperature rheological and fracture properties of asphalt binders and mixtures and on compaction effort of asphalt mixtures. This is the first time that these effects are investigated and significant findings are reported. The study considers three types of GNP materials, including graphite nanoplatelets and sub-microscale graphite flakes. The cost of these materials is reasonably low, which makes them suitable for large-scale applications, unlike other types of graphite and graphene materials. The experimental results indicate that the addition of GNPs leads to considerable improvements of low-temperature strength and fracture properties of asphalt binders and mixtures. While the properties of asphalt binders at intermediate temperatures are minimally affected, for some combinations of binders and GNPs the increase in low-temperature strength is over 100%. A similar effect is observed for some of the asphalt mixtures investigated, in which the low-temperature fracture energy almost doubles. The laboratory compaction experiments show that the number of gyrations required for achieving a target density can be reduced by as much as 20–40% by adding a small percentage of GNPs into asphalt binders. The results of this experimental study indicate that GNP-modified asphalt binders and mixtures have significant potential for increasing the durability of asphalt pavements in cold regions, by reducing the compaction effort and improving the low-temperature strength and fracture properties of asphalt materials.

This paper presents a simple formulation to predict the size effect curve of mean structural strength of the asphalt mixture from the strength histogram obtained on single-size beam specimens under three-point bend tests. This method is based on the weakest link model (WLM), which relates the mean structural strength to the size dependence of the probability distribution of the material strength. The proposed formulation is verified by an extensive experimental work consisting of strength histogram and mean size effect tests on the asphalt mixture at low temperature. The mean strength size effect curve obtained from the WLM is found to be in very good agreement with the experimental mean strength results obtained on the asphalt mixture specimens of different sizes and geometries, providing evidence of the ductile to brittle transition (Type I size effect) of the asphalt mixture strength.

The Semi-Circular Bending (SCB) fracture test is commonly used to evaluate the low temperature fracture properties of asphalt mixtures. The present work investigates the presence of a size effect in SCB fracture testing of asphalt mixtures. Un-notched and notched geometrically similar SCB specimens of various sizes are tested at−24°C loaded by crack-mouth opening displacement (CMOD). The effect of specimen size on the nominal strength is investigated through the well-established size effect theories and conclusions are drawn regarding the fracture behaviour of mixtures at low temperature.