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.     

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.     

在各类天气系统影响下石臼港沿岸波浪场的分布

本文查阅了从１９７３－１９８５，１３年的历史资料，对石臼港沿岸波浪场进行了详细的分类、统计分析和计算，提出了各类较强天气系统影响石（即指石臼港）的极端区域，同时获得了石港沿岸各类天气系统影响下的波浪分布特点以及波高计算式，为保障石港的生产及港口建设为石港的波了提供了有益的分析数据和预报手段。     

Variations in wave direction estimated using first and second order Fourier coefficients

In most design applications such as alignment of the berthing structure and breakwater alignment, it becomes necessary to determine the direction of design wave. There are two different approaches to determine wave direction. One involves the use of first order Fourier coefficients (mean wave direction) while the other uses second order Fourier coefficients (principal wave direction). Both the average wave direction over the entire frequency range (0.03–0.58 Hz) and the direction corresponding to the peak frequency are used in practice. In the present study, comparison is made on wave directions estimated based on first and second order Fourier coefficients using data collected at four locations in the west and east coasts of India. Study shows that at all locations, the mean and principal wave directions for frequencies ranging from 0.07 to 0.25 Hz (±0.5 times peak frequency) co-vary with a correlation coefficient of 0.99 but at lower and higher frequencies, difference between the parameters is large. Average difference between the mean wave direction at peak frequency and the average over the frequency related to spectral energy more than 20% of maximum value is less, around 13°. Study shows that average difference in the sea and swell directions is around 39°.     

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。     

Effect of wave-directionality on second-order loads induced by the set-down

At first-order of approximation a sea-state may be considered as an infinite sum of Airy components with angular frequencies ω_i and wave-number vectors k_i. A second-order analysis shows the co-existence of long waves appearing at the difference frequencies ω_i—ω_j with wave-number vectors k_i—k_j. In shallow water they become appreciable in amplitudes and may induce slow-drift motion of moored structures.For small values of ω_i—ω_j,k_i—k_j may take all kinds of directions for an angular-spread wave system. Then it may be questioned how the in-line and transverse second-order accelerations compare to those obtained for a mono-directional wave-system.This analysis is carried out here by relating the spectra of the second-order horizontal accelerations to the directional wave-spectrum. Numerical applications are first performed for deep water. They show that at low frequencies, even for very narrowly spread wave systems, the transverse component is larger than the in-line component. In shallow water both components are dratically reduced as compared to the mono-directional case. As a consequence one may question the validity of model-testings or numerical models which take no account of the directionality of the wave-system.     

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%.