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Laboratory experiments of water seepage in smooth and rough-walled, inclined fracture models were performed and the monitoring data analyzed for evidence of chaos. One fracture model consisted of smooth, parallel glass plates separated by 0.36 mm. The second model was made with textured glass plates. The fracture model was inclined 60{sup o} from the horizontal. Water was delivered to the fracture model through a capillary tube in contact with the top fracture edge at constant flow rates. Three types of capillary tubes were used: (1) a stainless steel blunt needle of 0.18 mm ID for flow rates of 0.25 to 4 mL/hr, (2) a nylon tube of 0.8 mm ID for flow rates of 0.25 to 10 mL/hr, and (3) a glass tube of 0.75 mm ID for flow rates of 0.5 to 20 mL/hr. Liquid pressure was monitored upstream of the capillary tube. Visual observations showed that water seeped through the fracture models in discrete channels that underwent cycles of snapping and reforming. Observations also showed that liquid segments, or drips, detached at different points along the water channel. The measured liquid pressure responded to the growth and detachment of drips. Separate experiments were carried out to measure pressure time-trends for dripping into open air to compare these data with those obtained in fracture models. Analysis of the pressure time-trends included determination of the time lag from the minimum of the average mutual information function, the local and global embedding dimensions, Lyapunov exponents and the Lyapunov dimension, the Hurst exponent and the entropy as a function of the embedding dimension for each data set. Most of the water pressure data contain oscillations exhibiting chaotic behavior, with local embedding dimensions ranging from 3 to 10, and global embedding dimensions one to two units higher. The higher dimensionality of some of the data sets indicates either the presence of high-dimensional chaos or a significant random component. It was determined that the flow rate, which affects seepage behavior and is reflected in the pressure measurements, is inversely correlated with the Hurst exponent. This supports the hypothesis that at higher flow rates, the random component of seepage behavior (as represented by liquid pressure) increases. However, there was no simple, consistent correlation between the trends for the other diagnostic parameters of chaos and flow rate. Three-dimensional plots of selected data sets in pseudo-phase space exhibit definite structures with some scattering of data points on the attractor. All the analyses confirm that the pressure time trends that describe flow behavior are mostly characterized by low-dimensional, deterministic chaotic dynamics with some random component

Experiments and evaluation of chaotic behavior of dripping waterin fracture models