P‐wave transmission across fractures with nonlinear deformational behaviour

Stress wave attenuation across fractured rock masses is a great concern of underground structure safety. When the wave amplitude is large, fractures experience nonlinear deformation during the wave propagation. This paper presents a study on normal transmission of P‐wave across parallel fractures with nonlinear deformational behaviour (static Barton–Bandis model). The results show that the magnitude of transmission coefficient is a function of incident wave amplitude, nondimensional fracture spacing and number of fractures. Two important indices of nondimensional fracture spacing are identified, and they divide the area of nondimensional fracture spacing into three parts (individual fracture area, transition area and small spacing area). In the different areas, the magnitude of transmission coefficient has different trends with nondimensional fracture spacing and number of fractures. In addition, the study reveals that under some circumstances, the magnitude of transmission coefficient increases with increasing number of fractures, and is larger than 1. Copyright © 2006 John Wiley & Sons, Ltd.     

The response of an elastic half‐space under a momentary shear line impulse

The response of an ideal elastic half‐space to a line‐concentrated impulsive vector shear force applied momentarily is obtained by an analytical–numerical computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. The shear force is concentrated along an infinite line, drawn on the surface of the half‐space, while being normal to that line as well as to the axis of symmetry of the half‐space. An exact loading model is introduced and built into the computational method for this shear force. With this model, a compatibility exists among the prescribed applied force, the geometric decay of the shear stress component at the precursor shear wave, and the boundary conditions of the half‐space; in this sense, the source configuration is exact. For the transient boundary‐value problem described above, a wave characteristics formulation is presented, where its differential equations are extended to allow for strong discontinuities which occur in the material motion of the half‐space. A numerical integration of these extended differential equations is then carried out in a three‐dimensional spatiotemporal wavegrid formed by the Cartesian bicharacteristic curves of the wave characteristics formulation. This work is devoted to the construction of the computational method and to the concepts involved therein, whereas the interpretation of the resultant transient deformation of the half‐space is presented in a subsequent paper. Copyright © 2003 John Wiley & Sons, Ltd.     

Survival,growth and shell deformities of copper- and cadmium-exposed mussels (Mytilus edulis L.) in brackish water

Mussels, Mytilus edulis L., were exposed to elevated concentrations of copper or cadmium in the laboratory, then placed in cages in the sea (salinity 7‰). One year later maximum lengths of the mussels were measured and shells screened for deformities. Growth was 0·6 cm year^?1 in the control cages and retarded in cages of exposed mussels. A total of 63% of cadmium-exposed and 46% of copper-exposed mussels had shell deformities. In the control cages 26% were deformed while in a natural population only 3% were deformed. The proportion of deformities to growth was inversely related. Low concentrations showed their injuriousness in this long-term test, probably due to the closing of the valves during exposure to high concentrations.     

Numerical prediction of blast‐induced stress wave from large‐scale underground explosion

This paper presents a numerical model for predicting the dynamic response of rock mass subjected to large‐scale underground explosion. The model is calibrated against data obtained from large‐scale field tests. The Hugoniot equation of state for rock mass is adopted to calculate the pressure as a function of mass density. A piecewise linear Drucker–Prager strength criterion including the strain rate effect is employed to model the rock mass behaviour subjected to blast loading. A double scalar damage model accounting for both the compression and tension damage is introduced to simulate the damage zone around the charge chamber caused by blast loading. The model is incorporated into Autodyn3D through its user subroutines. The numerical model is then used to predict the dynamic response of rock mass, in terms of the peak particle velocity (PPV) and peak particle acceleration (PPA) attenuation laws, the damage zone, the particle velocity time histories and their frequency contents for large‐scale underground explosion tests. The computed results are found in good agreement with the field measured data; hence, the proposed model is proven to be adequate for simulating the dynamic response of rock mass subjected to large‐scale underground explosion. Extended numerical analyses indicate that, apart from the charge loading density, the stress wave intensity is also affected, but to a lesser extent, by the charge weight and the charge chamber geometry for large‐scale underground explosions. Copyright © 2004 John Wiley & Sons, Ltd.     

Quick-look assessments to identify optimal CO2 EOR storage sites

A newly developed, multistage quick-look methodology allows for the efficient screening of an unmanageably large number of reservoirs to generate a workable set of sites that closely match the requirements for optimal CO₂ enhanced oil recovery (EOR) storage. The objective of the study is to quickly identify miscible CO₂ EOR candidates in areas that contain thousands of reservoirs and to estimate additional oil recovery and sequestration capacities of selected top options through dimensionless modeling and reservoir characterization. Quick-look assessments indicate that the CO₂ EOR resource potential along the US Gulf Coast is 4.7 billion barrels, and CO₂ sequestration capacity is 2.6 billion metric tons. In the first stage, oil reservoirs are screened and ranked in terms of technical and practical feasibility for miscible CO₂ EOR. The second stage provides quick estimates of CO₂ EOR potential and sequestration capacities. In the third stage, a dimensionless group model is applied to a selected set of sites to improve the estimates of oil recovery and storage potential using appropriate inputs for rock and fluid properties, disregarding reservoir architecture and sweep design. The fourth stage validates and refines the results by simulating flow in a model that describes the internal architecture and fluid distribution in the reservoir. The stated approach both saves time and allows more resources to be applied to the best candidate sites.     

Freely floating-body simulation by a 2D fully nonlinear numerical wave tank

Nonlinear interactions between large waves and freely floating bodies are investigated by a 2D fully nonlinear numerical wave tank (NWT). The fully nonlinear 2D NWT is developed based on the potential theory, MEL/material-node time-marching approach, and boundary element method (BEM). A robust and stable 4th-order Runge–Kutta fully updated time-integration scheme is used with regriding (every time step) and smoothing (every five steps). A special φ_n-η type numerical beach on the free surface is developed to minimize wave reflection from end-wall and wave maker. The acceleration-potential formulation and direct mode-decomposition method are used for calculating the time derivative of velocity potential. The indirect mode-decomposition method is also independently developed for cross-checking. The present fully nonlinear simulations for a 2D freely floating barge are compared with the corresponding linear results, Nojiri and Murayama’s (Trans. West-Jpn. Soc. Nav. Archit. 51 (1975)) experimental results, and Tanizawa and Minami’s (Abstract for the 6th Symposium on Nonlinear and Free-surface Flow, 1998) fully nonlinear simulation results. It is shown that the fully nonlinear results converge to the corresponding linear results as incident wave heights decrease. A noticeable discrepancy between linear and fully nonlinear simulations is observed near the resonance area, where the second and third harmonic sway forces are even bigger than the first harmonic component causing highly nonlinear features in sway time series. The surprisingly large second harmonic heave forces in short waves are also successfully reproduced. The fully updated time-marching scheme is found to be much more robust than the frozen-coefficient method in fully nonlinear simulations with floating bodies. To compare the role of free-surface and body-surface nonlinearities, the body-nonlinear-only case with linearized free-surface condition was separately developed and simulated.     

Modelling of periodic wave transformation in the inner surf zone

In this paper, we analyse the ability of the nonlinear shallow-water (NSW) equations to predict wave distortion and energy dissipation of periodic broken waves in the inner surf zone. This analysis is based on the weak-solution theory for conservative equations. We derive a new one-way model, which applies to the transformation of non-reflective periodic broken waves on gently sloping beaches. This model can be useful to develop breaking-wave parameterizations (in particular broken-wave celerity expression) in both time-averaged wave models and time-dependent Boussinesq-type models. We also derive a new wave set-up equation which provides a simple and explicit relation between wave set-up and energy dissipation. Finally, we compare numerical simulations of both, the NSW model and the simplified one-way model, with spilling wave breaking experiments and we find a good agreement.     

规则波和不规则波作用下消波建筑物前的波高分析

消波建筑物在国内外已得到广泛应用。本文采用近似方法分析了明基床上直立式消波建筑物前的波高及消波室内的波高，从而确定建筑物的消波效果。并在规则波的基础上将成果推广至不规则波作用下的情况。     

On the recovery of surface wave by pressure transfer function

Except the commonly selected pressure transfer function derived from the linear wave theory, a previous study on the pressure transfer function for recovering surface wave from underwater pressure transducer suggested that the pressure transfer function is a function of frequency parameter only. With careful analysis, this study showed that the pressure transfer function should include a transducer submergence parameter as that given by the linear theory. It was found that the previously suggested empirical formula should be restricted to measurements with the pressure transducer close to the surface; otherwise overestimation of wave height would result. Field measurements were carried out with an acoustic wave gauge and a synchronized pressure transducer located at various depths with submergence parameter close to 1 (near the sea floor). It was shown that the previous one-parameter empirical formula might overestimate the significant wave height by more than 30%. This study found that with deep-water wave bursts excluded, the transfer function based on the linear wave theory provided a fairly good estimation on the significant wave heights, with an average deviation of 3.6%.     

The Nonlinear Wave Force on a Circular Cylinder in Shallow Water

Based on the 1st order cnoidal wave theory, the nonlinear wave diffraction around a circular cylinder in shallow water is studied in this paper. The equation of the wave surface around the cylinder is formulated and by using this formula the wave surface elevation on the cylinder surface can be obtained. In this paper, the formula for calculating the cnoidal wave force on a circular cylinder is also derived. For the wave conditions which are often encountered in practical engineering designs, the ratios of the nonlinear wave forces to the linear wave forces are calculated, and the results are plotted in this paper for design purposes. In order to verify the theoretical results, model tests are conducted. After comparing the test results with the theoretical ones, it is concluded that, in shallow water, for the case of T g / d~(1/2) > 8-10 and H / d > 0.3, the cnoidal wave theory should be used to calculate the wave action on a cylindrical pier.