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The crack and ridge extend in a direction 140° East of North (roughly SE-NW). The general slope of the surface in this area is slightly downhill in the SE direction, and the SE terminus of the ridge and crack are at the edge of a marshy area, while the NW terminus is in a clearing in a relatively low area (by about 20 ft) between higher land on which some homes are situated, and the county road. Most of the crack and ridge are in a wooded area that slopes gently to the marsh or swamp (figure 7).
A double tree, with two trunks growing from one root ball, had fallen a couple of days after a strong windstorm about a week or ten days prior to the loud noise accompanying the formation of the crack and ridge. The tree was located about 25 feet from the crack near the uphill (NW) end. The two trunks fell in opposite directions, and had been salvaged in place for firewood (in fact, it was the person logging the fallen tree who first discovered the crack and ridge). The root balls, now exposed, seem too large to fit back in the hole from which they came (figure 8); it is unclear if this appearance is real and associated with the formation of the crack and ridge, or simply coincidental.
This paper presents a new crack band model (CBM) for probabilistic analysis of quasibrittle fracture. The model is anchored by a probabilistic treatment of damage initiation, localization, and propagation. This model regularizes the energy dissipation of a single material element for the transition between damage initiation and localization. Meanwhile, the model also takes into account the probabilistic onset of damage localization inside the finite element (FE) for the case where the element size is larger than the crack band width. The random location of the localization band is related to the random material strength, whose statistics is described by a finite weakest link model. The present model is applied to simulate the probability distributions of the nominal strength of different quasibrittle structures. It is shown that for quasibrittle structures direct application of the conventional CBM for stochastic FE simulations would lead to mesh-sensitive results. To mitigate such mesh dependence, it is essential to incorporate the strain localization mechanism into the formulation of the sampling distribution functions of material constitutive parameters.
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