A Discontinuous Cellular Automaton Method for Modeling Rock Fracture Propagation and Coalescence Under Fluid Pressurization Without Remeshing

We present a formulation of a discontinuous cellular automaton method for modeling of rock fluid pressure induced fracture propagation and coalescence without the need for remeshing. Using this method, modelers discretize a discontinuous rock-mass domain into a system composed of cell elements in which the numerical grid and crack geometry are independent of each other. The level set method, which defines the relationship between cracks and the numerical grid, is used for tracking the crack location and its propagation path. As a result, no explicit meshing for crack surfaces and no remeshing for crack growth are needed. Discontinuous displacement functions, i.e., the Heaviside functions for crack surfaces and asymptotic crack-tip displacement fields, are introduced to represent complex discontinuities. When two cracks intersect, the tip enrichment of the approaching crack is annihilated and is replaced by a Heaviside enrichment. We use the “partition of unity” concept to improve the integral precision for elements, including crack surfaces and crack tips. From this, we develop a cellular automaton updating rule to calculate the stress field induced by fluid pressure. Then, the stress is substituted into a mixed-mode fracture criterion. The cracking direction is determined from the stress analysis around the crack tips, where fracture fluid is assumed to penetrate into the newly developed crack, leading to a continuous crack propagation. Finally, we performed verification against independent numerical models and analytic solutions and conducted a number of simulations with different crack geometries and crack arrangements to show the robustness and applicability of this method.     

A preliminary archaeological and environmental study of pre‐Columbian burial towers at Huachacalla,Bolivian Altiplano

Chullpas are pre‐Columbian burial towers built by indigenous Aymaras on the Bolivian Altiplano. Bolivian chullpas date back to the Late Intermediate Period (A.D. 1000–1476) and the Late Horizon (A.D. 1476–1532). We recorded 228 chullpas among 84 sites in the Huachacalla region of west‐central Bolivia. In our study area, the chullpas are on debris flows and coarse alluvium in the proximal and medial segments of alluvial fans at the foot of two volcanoes. Grain‐size, element, and mineralogical analysis of chullpa wall material and local sediment revealed that the burial towers are composed of calcareous sand that is readily available in alluvial fan deposits near the sites. Our data suggest that the Aymaras considered environmental factors, such as drainage and stability of the soil, when they selected the locations of chullpas, whereas cultural factors played a significant role in chullpa architecture. © 2002 Wiley Periodicals, Inc.