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A simple analytical model is developed to predict the average crack spacing and crack depth in highway pavements due to thermal loading. The pavement is modeled as a beam on a Winkler elastic foundation. The effect of cracks on the pavement is considered on the basis of compliance functions. A simple method is introduced to describe the behavior of the pavement material according to nonlinear fracture mechanics. It is shown that the material length in the fracture model should be defined by the total fracture energy, rather than the effective fracture energy. The effect of nonlinearity in the distribution of thermal stress across the pavement depth is also analyzed. The foundation of the pavement is found to have little importance. The theoretical predictions are shown to compare well with field observations on asphalt pavements.

The problem of static penetration of an object through a sea ice plate is studied as a two‐dimensional fracture problem using linear elastic fracture mechanics. The ice sheet floating on water is modeled as a thin elastic plate resting on Winkler's elastic foundation. The equilibrium equations are established by minimizing the potential energy approximated by finite differences in terms of nodal deflections. The growth of radial cracks is analyzed using the plate bending theory. The fracture process zone is assumed to be a point in the plane of plate. The maximum load is found to occur when circumferential cracks begin to form, which is governed by a strength criterion. As a refinement and extension of a previous idea, a theory of initial crack spacing is proposed to estimate the number of radial cracks formed during penetration. This theory can also explain the change of the failure mechanism, from failure by formation of circumferential cracks to failure by a conic crack. Particular attention is paid to...

Vertical penetration of an object through a floating elastic‐brittle plate from the bottom up or the top down is studied. Based on field observations, it is assumed that many symmetric cracks grow radially from a small loaded area, and the maximum load is achieved at the initiation of circumferential cracks. Nevel's approximation, in which the plate wedges between the radial cracks are analyzed as narrow floating beams of linearly varying width, is adopted. This makes an analytical solution possible. The rate of energy release due to the radial crack growth is calculated according to linear elastic fracture mechanics and the theory of thin plates. This yields the dependence of the radial crack length on the load, which is considered to be uniformly distributed along a small circle. It is confirmed that there is a size effect such that the nominal stress (load divided by ice thickness squared) that causes similar cracks to grow is proportional to (icethickness)-3/8 or, equivalently, to (flexuralwavelengths...

A boundary element program based on a fictitious crack‐model (FCM) was used to study the size effect in concrete during mode‐I nonlinear fracturing. Series of numerical parametric studies were performed to examine the effects of specimen size, loading configuration (three‐point beam and double cantilever beam), and initial notch size on the nonlinear fracture characteristics. The results of numerical simulations confirmed the curve‐fitting procedure proposed by Bažant and his coworkers in their size‐effect law method. However, two notable exceptions were observed: (1) Small size specimens where bending strengthening may be pronounced; and (2) specimens with small initial notch. In addition to examining the range of applicability of Bažant's size‐effect law method, this paper provides empirical equations for determination of the maximum process‐zone length under three‐point bending or double cantilever beam (DCB) loading condition. Finally, the normalized R‐curves expressed in terms of the energy release r...

A simple analytical model has been developed for prediction of size‐dependent maximum loads of concrete‐beam specimens subjected to mode‐I rupture. The analytical model is cast within a framework of a fictitious crack model, but incorporating the following simplifying assumptions: (1) The tension‐softening law is linear; (2) the crack‐opening profile remains linear throughout the fracture process; (3) the resultant cohesive force is acted at an approximate, yet constant, location; (4) the stress distribution in the ligament of the beam specimens is described by a quadratic function; and (5) a simplified compliance equation is adopted to relate the crack opening to the applied loads. The model requires input of four material properties: Young's modulus, Poisson’s ratio, threshold separation, and tensile strength. Model predictions were compared with experimental data as well as numerical simulations. The favorable comparisons suggest that, instead of a number of simplifying assumptions made in the formulat...