Investigation of motions of catamarans in regular waves—II

By extending the linear frequency domain theory, a quasi-non-linear time-domain technique has been developed to investigate the large amplitude motions of catamarans in regular waves. The non-linearity of hydrodynamic forces included in this practical method comes from variations of a ship's submerged portion. These forces are obtained from a database generated by the linear frequency domain method at each time step. The coupled equations, heave and pitch, are solved in the time domain by using the Runge-Kutta method with proper initial values. In order to investigate the non-linear effects of large amplitude motions of the V-1 catamaran in the head-sea condition, numerical results obtained from the linear and non-linear strip methods have been compared with those obtained from a series of experiments carried out in the towing tank of the Hydrodynamics Laboratory at the University of Glasgow. Based on the comparative studies, the numerical results obtained from the time-domain program can provide better predictions for the large amplitude motions of catamarans than the linear frequency domain method. It is concluded that the non-linear effects are significant when the model speeds and wave amplitudes increase. The peak values of large amplitude motions around the resonance frequencies, as obtained from the non-linear time-domain predictions as well as from measurements, are smaller than those obtained from the linear theory.     

Segmentation along Strike-Slip Faults Revisited

Fault segmentation and fault steps and their evolution are relevant to the dynamics and size of earthquake ruptures, the distribution of fault damage zones and the capacity of fault seal. Furthermore, segment interactions and coalescence are the fundamental processes for fault growth. To contribute to this end, we investigated the architecture of strike-slip faults by combining field observations in the Valley of Fire State Park, Nevada, and the published data sets. First, we studied the trace complexity for 49 faults with offsets ranging from 12 m to 460 km. We established that the number of fault steps (hence fault segments) per unit length is correlated to the maximum fault offset by a negative power law. The faults have longer segments and fewer steps when their offsets increase, indicating the progressive growth, smoothening and simplification of the fault traces as a function of the offset, as proposed by previous investigators. Second, we studied the dimensions of the segments and steps composing ~20 of the previous fault systems. The mean segment length, mean step length and mean step width are all correlated to the maximum fault offset by positive power laws over four orders of magnitude of the offset. In addition, the segment length distributions of four of the faults with offsets ranging from 80 m to 100 km are all lognormal, with most of the segment lengths falling in the range of one to five times the maximum offset of the faults. Finally, the fault steps have an approximately constant length-to-width ratio indicating that, regardless of their environment, strike-slip faults have a remarkable self-similar architecture probably due to the mechanical processes responsible for fault growth. Our data sets can be used as tools to better predict the geometrical attributes of strike-slip fault systems with important consequences for earthquake ruptures, the distribution and properties of fault damage zones, and fault sealing potential.     

Quasi‐static analysis of elastic behavior for some systems having higher fracture densities

Elastic behavior of geomechanical systems with interacting (but not intersecting) fractures is treated using generalizations of the Backus and the Schoenberg–Muir methods for analyzing layered systems whose layers are intrinsically anisotropic due to locally aligned fractures. By permitting the axis of symmetry of the locally anisotropic compliance matrix for individual layers to differ from that of the layering direction, we derive analytical formulas for interacting fractured regions with arbitrary orientations to each other. This procedure provides a systematic tool for studying how contiguous, but not yet intersecting, fractured domains interact, and provides a direct (though approximate) means of predicting when and how such interactions lead to more dramatic weakening effects and ultimately to failure of these complicated systems. The method permits decomposition of the system elastic behavior into specific eigenmodes that can all be analyzed, and provides a better understanding about which of these specific modes are expected to be most important to the evolving failure process. Copyright © 2009 John Wiley & Sons, Ltd.     

Interaction of multiple cracks and formation of echelon crack arrays

Fracturing of rock under compression is a product of a series of processes, including nucleation, growth, interaction and coalescence of multiple microcracks. The formation of echelon arrays of microcracks and macrocracks is one of the crucial rings in the processes. We use a superposition and asymptotic approximation technique to analyse the interaction of multiple cracks with various geometrical configurations. It is shown that crack geometry has a strong influence on crack interaction. Echelon crack arrays produce the strongest interaction and are the preferred geometrical configuration for multiple cracks prior to the formation of through-going shear fractures. This technique provides parameter-dependent global behaviour, and is more efficient and easier to use.     

Evaluation of parameters affecting earthquake damage by decision tree techniques

Earthquake damages are assessed based on a holistic approach using structural as well as non-structural factors to model earthquake damage distributions with Decision Tree Techniques, using the Answer Tree program and the damage data from recent major earthquakes in Turkey. The damage dataset consists of approximately 9,400 buildings that were surveyed to evaluate the factors affecting building damage after Erzincan [1992], Dinar [1995], and Kocaeli [1999] earthquakes. The earthquake damage is defined as the dependent variable, while earthquake magnitude (M), intensity (I) in the city, peak ground acceleration (PGA) in each city, epicenter distance (ED), building types (BT), number of storeys (NS), presence of soft storey (SS), building position (BP) on the site, and site conditions (SC) are independent variables in the proposed model. The damage level (DL) was classified with respect to red, yellow, and green codes. The main purpose was (1) to identify the factors controlling building damage during earthquakes; (b) to determine the most significant factor; (c) to evaluate the effects of different factors for different earthquakes; (d) to develop damage distribution models for different subgroups based on the Decision Tree Techniques.

Investigation of motions of catamarans in regular waves—I

In this paper an analytical technique based on the two-dimensional Green function method associated with a cross-flow approach for taking viscous effects into account to estimate the motion response of catamarans in the frequency domain is presented. In order to validate this method, the numerical results are compared with experimental values obtained for two different catamarans (ASR5061 [Wahab, R., Pritchett, C. and Ruth, L.C. 1971. On the behaviour of the ASR catamaran in waves. Marine Technology, 8, 334–360] and Marintek [Faltinsen, O., Hoff, J.R., Kvalsvold, J. and Zhao, R. 1992. Global loads on high speed catamarans. 5th Int. Symp. on Practical Design of Ships and Mobile Units, University of Newcastle-upon-Tyne, 1.360–1.373]).In the second part of the paper the tests carried out with a third catamaran configuration at the Hydrodynamics Laboratory of the University of Glasgow are presented to evaluate the non-linear effects. These test results cover different speeds and wave heights at a wide range of wave frequencies. The paper concludes that the two-dimensional method correlates very well with measurements of small amplitude motions. For large amplitude motion tests, the non-linear effects become significant when the model speed and wave amplitudes increase. The peak values of heave and pitch motions measured around the resonance frequency are smaller than those obtained from the linear theory.     

Artificial neural networks and their application to assessment of ultimate strength of plates with pitting corrosion

The potential for the structural capability degrading effects of both corrosion and fatigue induced cracks are of profound importance and must be both fully understood and reflected in vessel's inspection and maintenance programme. Corrosion has been studied and quantified by many researchers, however its effect on structural integrity is still subject to uncertainty, particularly with regards to localized corrosion. The present study is focused on assessing the effects of localized pitting corrosion on the ultimate strength of unstiffened plates. Over 265 non-linear finite-element analyses of panels with various locations and sizes of pitting corrosion have been carried out. The results indicate that the length, breadth and depth of pit corrosion have weakening effects on the ultimate strength of the plates while plate slenderness has only marginal effect on strength reduction. Transverse location of pit corrosion is also an important factor determining the amount of strength reduction. When corrosion spreads transversely on both edges, it has the most deteriorating effect on strength. In addition, artificial neural network (ANN) method is applied to derive a formula to predict ultimate strength reduction of locally corroded plates. It is found out that the proposed formulae can accurately predict the ultimate strength of locally corroded plates under uniaxial in-plane compression.     

Use of joint-growth directions and rock textures to infer thermal regimes during solidification of basaltic lava flows

Thermal contraction joints form in the upper and lower solidifying crusts of basaltic lava flows and grow toward the interior as the crusts thicken. Lava flows are thus divided by vertical joints that, by changes in joint spacing and form, define horizontal intraflow layers known as tiers. Entablatures are tiers with joint spacings less than about 40 cm, whereas colonnades have larger joint spacings. We use structural and petrographic methods to infer heat-transfer processes and to constrain environmental conditions that produce these contrasting tiers. Joint-surface morphology indicates overall joint-growth direction and thus identifies the level in a flow where the upper and lower crusts met. Rock texture provides information on relative cooling rates in the tiers of a flow. Lava flows without entablature have textures that develop by relatively slow cooling, and two joint sets that usually meet near their middles, which indicate mostly conductive cooling. Entablature-bearing flows have two main joint sets that meet well below their middles, and textures that indicate fast cooling of entablatures and slow cooling of colonnades. Entablatures always occur in the upper joint sets and sometimes alternate several times with colonnades. Solidification times of entablature-bearing flows, constrained by lower joint-set thicknesses, are much less than those predicted by a purely conductive cooling model. These results are best explained by a cooling model based on conductive heat transfer near a flow base and water-steam convection in the upper part of an entablature-bearing flow. Calculated solidification rates in the upper parts of such flows exceed that of the upper crust of Kilauea Iki lava lake, where water-steam convection is documented. Use of the solidification rates in an available model of water-steam convection yields permeability values that agree with measured values for fractured crystalline rock. We conclude, therefore, that an entablature forms when part of a flow cools very rapidly by water-steam convection. Flooding of the flow top by surface drainage most likely induces the convection. Colonnades form under conditions of slower cooling by conductive heat transfer in the absence of water.     

Permeability upscaling of fault zones in the Aztec Sandstone,Valley of Fire State Park,Nevada, with a focus on slip surfaces and slip bands

The effect of open and filled slip surfaces on the upscaled permeability of two fault zones with 6 and 14 m strike-slip in an eolian Aztec Sandstone, Nevada, USA is evaluated. Each fault zone is composed of several fault components: a fault core, bounded by filled through-going slip surfaces referred to as slip bands, and a surrounding damage zone that contains joints and deformation bands. Slip band geometry, composition, and petrophysical properties are characterized. Measurements and modeling show that slip band permeabilities can vary over 12 orders of magnitude depending on the degree of fill within the slip bands. The slip bands along with other fault zone components are represented in finite volume numerical calculations and the impact of various slip-band representations on upscaled fault zone permeability is tested. The results show 2 orders of magnitude variation in upscaled fault zone permeability in the fault-normal direction and a factor of 2 variation in the fault-parallel direction. The numerical results presented here are compared to the earlier numerical results in which structured Cartesian grids were used for the numerical simulations, and are in qualitative agreement with earlier calculations but use about a factor of 250–400 fewer numerical cells.