Modeling the Effects of Oyster Reefs and Breakwaters on Seagrass Growth

Seagrass beds have declined in Chesapeake Bay, USA as well as worldwide over the past century. Increased seston concentrations, which decrease light penetration, are likely one of the main causes of the decline in Chesapeake Bay. It has been hypothesized that dense populations of suspension-feeding bivalves, such as eastern oysters (Crassostrea virginica), may filter sufficient seston from the water to reduce light attenuation and enhance seagrass growth. Furthermore, eastern oyster populations can form large three-dimensional reef-like structures that may act like breakwaters by attenuating waves, thus decreasing sediment resuspension. We developed a quasi-three-dimensional Seagrass-Waves-Oysters-Light-Seston (SWOLS) model to investigate whether oyster reefs and breakwaters could improve seagrass growth by reducing seston concentrations. Seagrass growth potential (SGP), a parameter controlled by resuspension-induced turbidity, was calculated in simulations in which wave height, oyster abundance, and reef/breakwater configuration were varied. Wave height was the dominant factor influencing SGP, with higher waves increasing sediment resuspension and decreasing SGP. Submerged breakwaters parallel with the shoreline improved SGP in the presence of 0.2 and 0.4 m waves when sediment resuspension was dominated by wave action, while submerged groins perpendicular to the shoreline improved SGP under lower wave heights (0.05 and 0.1 m) when resuspension was dominated by along-shore tidal currents. Oyster-feeding activity did not affect SGP, due to the oysters’ distance from the seagrass bed and reduced oyster filtration rates under either low or high sediment concentrations. Although the current implementation of the SWOLS model has simplified geometry, the model does demonstrate that the interaction between oyster filtration and along-shore circulation, and between man-made structures and wave heights, should be considered when managing seagrass habitats, planning seagrass restoration projects, and choosing the most suitable methods to protect shorelines from erosion.     

Dynamic Model of Fracture Normal Behaviour and Application to Prediction of Stress Wave Attenuation Across Fractures

Summary.  The purpose of this paper is to establish a dynamic constitutive model of fracture normal behaviour, based on laboratory tests of artificial fractures cast by cement mortar. A series of tests are systematically carried out under quasi-static (10⁻¹ MPa/s) up to highly dynamic (10³ MPa/s) monotonic loading conditions. The normal stress-fracture closure response is measured at different loading rates. Based on the measured curves, a nonlinear (hyperbolic) dynamic model of fracture normal behaviour, termed as dynamic BB model, is proposed. The dynamic model is modified from the existing BB model of static normal behaviour of fractures by taking into account the loading-rate effect. Two important dynamic parameters of fractures, FSC _d (dynamic fracture stiffness constant, which describes the incremental ratio of dynamic initial stiffness) and FCC _d (dynamic fracture closure constant, which describes the decremental ratio of dynamic maximum allowable closure), are identified. They indicate the quantitative degree of loading-rate effect on fracture normal behaviour subjected to dynamic loads. For practical application, the new model is incorporated into the Universal Distinct Element Code (UDEC) and subsequently, UDEC modelling of normally incident P-wave transmission across single fractures with the dynamic BB model is conducted. Wave transmission coefficient is obtained for various combinations of fracture dynamic parameters, as well as different wave amplitudes and frequencies. The numerical results show that wave transmission coefficient for a fracture with the dynamic BB model is greater than that for a fracture with the static BB model. In addition, a fracture with higher values of FSC _d and FCC _d leads to higher transmission (lower attenuation). Author’s address: J. Zhao, Ecole Polytechnique Federale de Lausanne (EPFL), Rock Mechanics Laboratory, 1015 Lausanne, Switzerland     

A semianalytical solution for one-dimensional transient wave propagation in a saturated single-layer porous medium with a fluid surface layer

One-dimensional transient wave propagation in a saturated single-layer porous medium with a fluid surface layer is studied in this paper. An analytical solution for a special case with a dynamic permeability coefficient k_f → ∞ and a semianalytical solution for a general case with an arbitrary dynamic permeability coefficient are presented. The eigenfunction expansion and precise time step integration methods are employed. The solution is presented in series form, and thus, the long-term dynamic responses of saturated porous media with small permeability coefficients can be easily computed. We first transform the nonhomogeneous boundary conditions into homogeneous boundary conditions, and then we obtain the eigenvalues and orthogonal eigenfunctions of the fluid–solid system. Finally, the solutions in the time domain are developed. As the model is one dimensional, geometric attenuation is absent, and only the attenuation in the saturated porous medium is considered. We can apply this model to analyse the influences of different seabed types on the propagation of acoustic waves in the fluid layer, which is very important in ocean acoustics and ocean seismic. This solution can also be employed to validate the accuracies of various numerical methods.     

Elastic waves at a corrugated interface between two dissimilar fibre‐reinforced elastic half‐spaces

The reflection and transmission phenomena of elastic waves incident at a corrugated interface between two dissimilar fibre‐reinforced elastic half‐spaces have been analysed. Using Rayleigh method of approximation, the expressions of the reflection and transmission coefficients are obtained in closed form for the plane interface as well as for the first order approximation of the periodic interface ζ = d cos px. All these reflection and transmission coefficients of regular and irregular waves are found to be the functions of angle of incidence and elastic parameters of the media. Moreover, the coefficients of irregularly reflected and transmitted waves are found to be proportional to the amplitude of the corrugated interface and are functions of the frequency of the incident wave. Numerical computations have been performed for a specific model to compute these coefficients and results obtained are shown graphically. The results of Singh and Singh (Sadhana 2004; 29 :249–257) and Ben‐Menahem and Singh (Seismic Waves and Sources. Springer: New York) have been derived from our analysis as particular cases. Copyright © 2006 John Wiley & Sons, Ltd.     

Application of wave transformation models for estimation of morphological changes at Vellar estuary,southeast coast of India

Assessment of the wave climate at near coast is vital for estimation of morphological changes, such as growth of sand spit and associated siltation of tidal inlets. Vellar (bar-built) estuary is one of the prominent estuaries along the southeast coast of India, located at 11°30′N and 79°46′E, less studied in terms of its morphological features. The inlet of Vellar is exposed to high energetic waves, inducing large sediment transport rates and shoreline changes. Local wave characteristics are not accurately defined and the available wave information at near coast is limited (point based observations). In the present study, three decoupled numerical models are employed to derive the monthly nearshore wave climate at Vellar by transforming waves from deep water to nearshore. These models are independently validated with buoy observations in deep water and wave gauge data at nearshore. Based on the nearshore wave data, littoral drift along the coast was estimated and compared with the spit growth at Vellar inlet. The estimated average littoral drift along this coast from February to October is 1.93 × 10⁶ m³ toward north and from November to January it is 1.52 × 10⁶ m³ toward south, resulting in a net northerly drift. Results indicated that increase in the wave energy during the period of July to September is responsible for the maximum growth of the sand spit observed in the field.     

Analytical solutions for dynamic pressures of coupling fluid–porous medium–solid due to SV wave incidence

This paper presents the results of theoretical investigation on the dynamic coupling of an ideal fluid‐porous medium‐elastic half‐space system subjected to SV waves to study the effect of sediment on the seismic response of dams for reservoirs that are deposited with a significant amount of sediment after a long period of operation. The effects of the porous medium and the incident wave angle on dynamic pressures in the overlying ideal fluid are analyzed, and the reflection and transmission coefficients of the wave at the material interfaces are derived using an analytical solution in terms of displacement potentials. The numerical test of modeling shows that the dynamic pressures significantly depend on the properties of porous medium. The fully saturated porous medium reduces the response peaks slightly, while the partially saturated porous medium causes a considerable increase in the resonance peaks. Copyright © 2009 John Wiley & Sons, Ltd.     

Effect of pore connectivity on reflection amplitudes of an inhomogeneous wave in a composite porous solid saturated by two immiscible fluids

Present paper aims to study the phenomenon of reflection and transmission when an inhomogeneous wave strikes some discontinuity in a composite porous medium saturated by two immiscible viscous fluids. The incident wave splits into six reflected and six transmitted waves at the interface. All reflected and transmitted waves are inhomogeneous in nature with different directions of propagation vector and attenuation vector. A dimensionless parameter \(\varsigma \in [0, 1]\) is introduced to represent the extent of connection among the pores at the interface. Expression of Umov–Poynting vector is derived to obtain energy flux vector. Continuity of energy flux vector at the interface gives the required boundary conditions for the system. Connecting parameter \(\varsigma \) is also employed in boundary conditions to model the partial connection of pores at the interstices of two media. For numerical discussion we consider a porous medium composed of sandstone and ice, saturated with oil and water. The effect of parameter \(\varsigma \) and angle of incidence is determined numerically on the amplitude and the energy ratios of reflected and transmitted waves.     

半圆型结构冰压力的物理模拟试验研究

利用DUT-1非冻结合成模型冰开展1:25冰对半圆型构件的物理模拟试验研究. 首先用简单的斜面构件的物理模拟试验检验了整体试验装置和技术设备的可靠性, 然后以同样比尺进行2种冰厚在5个不同水位条件的系列试验, 获得了模型冰排在半圆型构件前的破碎堆积现象和作用于构件上的水平和垂直作用力过程.结合实测模型冰物理和力学指标, 通过优化组合, 拟合出半圆型防波堤冰荷载的试验公式. 这些公式包含了冰对半圆型结构的弯曲破坏作用力、挤压破坏作用力及爬坡和堆积作用力.     

Wave Attenuation at a Salt Marsh Margin: A Case Study of an Exposed Coast on the Yangtze Estuary

To quantify wave attenuation by (introduced) Spartina alterniflora vegetation at an exposed macrotidal coast in the Yangtze Estuary, China, wave parameters and water depth were measured during 13 consecutive tides at nine locations ranging from 10 m seaward to 50 m landward of the low marsh edge. During this period, the incident wave height ranged from <0.1 to 1.5 m, the maximum of which is much higher than observed in other marsh areas around the world. Our measurements and calculations showed that the wave attenuation rate per unit distance was 1 to 2 magnitudes higher over the marsh than over an adjacent mudflat. Although the elevation gradient of the marsh margin was significantly higher than that of the adjacent mudflat, more than 80% of wave attenuation was ascribed to the presence of vegetation, suggesting that shoaling effects were of minor importance. On average, waves reaching the marsh were eliminated over a distance of ∼80 m, although a marsh distance of ≥100 m was needed before the maximum height waves were fully attenuated during high tides. These attenuation distances were longer than those previously found in American salt marshes, mainly due to the macrotidal and exposed conditions at the present site. The ratio of water depth to plant height showed an inverse correlation with wave attenuation rate, indicating that plant height is a crucial factor determining the efficiency of wave attenuation. Consequently, the tall shoots of the introduced S. alterniflora makes this species much more efficient at attenuating waves than the shorter, native pioneer species in the Yangtze Estuary, and should therefore be considered as a factor in coastal management during the present era of sea-level rise and global change. We also found that wave attenuation across the salt marsh can be predicted using published models when a suitable coefficient is incorporated to account for drag, which varies in place and time due to differences in plant characteristics and abiotic conditions (i.e., bed gradient, initial water depth, and wave action).     

P波在弹性介质与饱和冻土介质分界面上的透反射问题研究

基于弹性波在冻结饱和多孔介质与单相弹性介质中的传播理论,研究了平面P波在饱和冻土介质与单相弹性介质分界面上的透反射问题。利用Helmholtz矢量分解定理,根据分界面上的边界条件,获得了平面P波从单相弹性介质入射到饱和冻土介质分界面上透反射振幅比的理论表达式。通过数值计算,分析了在不同入射频率、胶结参数、孔隙率、饱和度和接触参数下,弹性波的透反射振幅比随入射角变化的关系。研究结果表明：P波从单相弹性介质垂直入射到饱和冻土介质分界面上时只有反射P波和3种透射P波产生,当掠入射时只产生反射而没有透射现象发生。入射频率、胶结参数、孔隙率、饱和度以及接触参数等参数对反射波和透射波的振幅比影响显著。     

Demarcation of inland vessels’ limit off Mormugao port region,India: a pilot study for the safety of inland vessels using wave modelling

The Ministry of Shipping desires to revise the inland vessels’ limit (IVL) notification based on scientific rationale to improve the safety of vessels and onboard personnel. The Mormugao port region extending up to the Panaji was considered for this pilot study. Measured winds and wave parameters (AWS and moored buoy) as well as NCEP re-analysis and NCMRWF winds were used for the analysis and input to regional and local models. The results of wave model were validated with measured significant wave heights (SWHs) and the comparison shows a good match. The analysis indicates that SWHs do not exceed 2.0 m during non-monsoon months, and in monsoon months exceed 5.0 m, and even 7.0 m, especially during extreme events. In order to draw IVL contours for Goa coastal region, local model was set up and nearshore waves were simulated for the period May 2004–May 2005. Based on the nearshore SWH distribution, IVL contours have been fixed for the Mormugao port and Panaji coastal regions.     

Effect of dry sandiness parameter and initial stress on the scattering of plane SH wave

The present paper is incorporated into a mathematical model of transmission and reflection of shear waves through the initially stressed dry sandy medium sandwiched between two initially stressed distinct orthotropic half-spaces. The formulae of transmission and reflection coefficients have been deduced for the propagation of SH waves in the described model subjected to certain boundary conditions applying Snell’s law and Cramer’s method. These coefficients are observed as a function of wave number, phase velocity, initial stress, rigidity, and dry sandiness coefficients. The concepts of energy partition, phase shift, conservation of energy, critical angle, and slowness section are introduced. Graphical approach has been carried out to accomplish a relation between reflection/refraction coefficient, phase shift, and energy ratio with an angle of incidence and wave number on the propagation of shear wave. The study reveals that sandiness parameter, initial stress, and wave number have a cogent respond to the scattering of shear wave that has been illustrated graphically.     

Damage risk assessment of breakwaters under tsunami attack

Turkey was struck by two major events on 17 August and 12 November 1999, named Izmit (M _w = 7.4) and Düzce (M _w = 7.2) earthquakes, respectively. Rubble mound breakwaters in Izmit Bay experienced little damage, as forecasted by the new risk assessment model in which tsunami occurrence risk was included in the damage estimations. In order to determine the occurrence probability of structural damage under design conditions, including the environmental loading parameters of tsunami and storm waves, tidal range and storm surge, the Conditional Expections Monte Carlo simulation was applied in the risk assessment model developed in this study for the Esenköy Fishery Harbour, Turkey. A tsunami was not the key design parameter when compared to storm waves for the main breakwater of the harbour, however, in places with great seismic activity, the tsunami risk should be important depending on the occurrence probability and magnitude of the tsunami.     

A study on reflection pattern of swells from the shoreline of peninsular India

Information on reflected surface gravity waves from the shoreline is required for understanding the coastal hydrodynamics. We have quantified the reflected swells (frequency band 0.045–0.12 Hz) from the west and east coast of India based on the spectral wave data derived from the directional waverider buoys. Reflection coefficient, ratio of the reflected and incident spectral energy, was used to quantify the reflected waves. Influence of the seasons, cyclone, relative depth, land/sea breeze, tides and tidal current on the reflected waves were examined. For the locations off the west coast of India, seasons have large impact on the reflection coefficient and were relatively less during the monsoon season due to the increase in incident wave energy. Locations off the east coast of India show almost the same reflection coefficient throughout the year and have no significant seasonal variations. The reflection coefficient off Puducherry was higher than that for other locations due to the low incident wave energy. The reflection coefficient was low during the cyclone period, but the reflected energy during cyclone was higher than that during the normal condition due to the high incident wave energy. High-energy reflected waves show large variation with tide due to the trapping and dissipation of reflected wave by bottom friction and this effect cause low reflection in deep water location than shallow water location. The reflection coefficient decreases with increase in relative depth off west coast of India.     

双相介质AVO方程及参数简化研究

基于2种双相介质分界面的反射系数和透射系数方程组,推导出了单相/双相分界面(储层顶界面)、双相/单相分界面(储层底界面)和单相/单相分界面(两种致密岩层分界面)3种类型分界面的反射系数和透射系数方程组,形成了从单相介质到双相介质较全面的AVO方程组;推导出了双相介质参数（A,N,Q,R,ρ11,ρ12,ρ22,）与纵波速度、横波速度、密度、孔隙度以及流体类型（油、气、水）之间的关系式,为双相介质AVO理论走向实用进行了有益的探索。设计了3种类型的岩性分界面,分别用双相介质AVO方程和Zeoppritz方程计算了各类界面的快纵波反射系数曲线,证实了Zoeppritz方程是双相介质AVO方程的一个特例。     

Shear wave velocity and attenuation structure for the shallow crust of the southern Korean peninsula from short period Rayleigh waves

We analyzed the short period Rayleigh waves from the first crustal-scale seismic refraction experiment in the Korean peninsula, KCRUST2002, to determine the shear wave velocity and attenuation structure of the uppermost 1 km of the crust in different tectonic zones of the Korean peninsula and to examine if this can be related to the surface geology of the study area. The experiment was conducted with two large explosive sources along a 300-km long profile in 2002. The seismic traces, recorded on 170 vertical-component, 2-Hz portable seismometers, show distinct Rayleigh waves in the period range between 0.2 s and 1.2 s, which are easily recognizable up to 30–60 km from the sources. The seismic profiles, which traverse three tectonic regions (Gyeonggi massif, Okcheon fold belt and Yeongnam massif), were divided into five subsections based on tectonic boundaries as well as lithology. Group and phase velocities for the five subsections obtained by a continuous wavelet transform method and a slant stack method, respectively, were inverted for the shear wave models. We obtained shear wave velocity models up to a depth of 1.0 km. Overall, the shear wave velocity of the Okcheon fold belt is lower than that of the Gyeonggi and Yeongnam massifs by  0.4 km/s in the shallowmost 0.2 km and by 0.2 km/s at depths below 0.2 km. Attenuation coefficients, determined from the decay of the fundamental mode Rayleigh waves, were used to obtain the shear wave attenuation structures for three subsections (one for each of the three different tectonic regions). We obtained an average value of Q_β^− 1 in the upper 0.5 km for each subsection. Q_β^− 1 for the Okcheon fold belt ( 0.026) is approximately three times larger than Q_β^− 1 for the massif areas ( 0.008). The low shear wave velocity in the Okcheon fold belt is consistent with the high attenuation in this region.     

Mud dispersal across a Cretaceous prodelta: Storm‐generated,wave‐enhanced sediment gravity flows inferred from mudstone microtexture and microfacies

Determining sediment transport direction in ancient mudrocks is difficult. In order to determine both process and direction of mud transport, a portion of a well‐mapped Cretaceous delta system was studied. Oriented samples from outcrop represent prodelta environments from ca 10 to 120 km offshore. Oriented thin sections of mudstone, cut in three planes, allowed bed microstructure and palaeoflow directions to be determined. Clay mineral platelets are packaged in equant, face‐face aggregates 2 to 5 μm in diameter that have a random orientation; these aggregates may have formed through flocculation in fluid mud. Cohesive mud was eroded by storms to make intraclastic aggregates 5 to 20 μm in diameter. Mudstone beds are millimetre‐scale, and four microfacies are recognized: Well‐sorted siltstone forms millimetre‐scale combined‐flow ripples overlying scoured surfaces; deposition was from turbulent combined flow. Silt‐streaked claystone comprises parallel, sub‐millimetre laminae of siliceous silt and clay aggregates sorted by shear in the boundary layer beneath a wave‐supported gravity flow of fluid mud. Silty claystone comprises fine siliceous silt grains floating in a matrix of clay and was deposited by vertical settling as fluid mud gelled under minimal current shear. Homogeneous clay‐rich mudstone has little silt and may represent late‐stage settling of fluid mud, or settling from wave‐dissipated fluid mud. It is difficult or impossible to correlate millimetre‐scale beds between thin sections from the same sample, spaced only ca 20 mm apart, due to lateral facies change and localized scour and fill. Combined‐flow ripples in siltstone show strong preferred migration directly down the regional prodelta slope, estimated at ca 1 : 1000. Ripple migration was effected by drag exerted by an overlying layer of downslope‐flowing, wave‐supported fluid mud. In the upper part of the studied section, centimetre‐scale interbeds of very fine to fine‐grained sandstone show wave ripple crests trending shore normal, whereas combined‐flow ripples migrated obliquely alongshore and offshore. Storm winds blowing from the north‐east drove shore‐oblique geostrophic sand transport whereas simultaneously, wave‐supported flows of fluid mud travelled downslope under the influence of gravity. Effective wave base for sand, estimated at ca 40 m, intersected the prodelta surface ca 80 km offshore whereas wave base for mud was at ca 70 m and lay ca 120 km offshore. Small‐scale bioturbation of mud beds co‐occurs with interbedded sandstone but stratigraphically lower, sand‐free mudstone has few or no signs of benthic fauna. It is likely that a combination of soupground substrate, frequent storm emplacement of fluid mud, low nutrient availability and possibly reduced bottom‐water oxygen content collectively inhibited benthic fauna in the distal prodelta.     

Poroelastic model for pile–soil interaction in a half‐space porous medium due to seismic waves

In this paper, frequency domain dynamic response of a pile embedded in a half‐space porous medium and subjected to P, SV seismic waves is investigated. According to the fictitious pile methodology, the problem is decomposed into an extended poroelastic half‐space and a fictitious pile. The extended porous half‐space is described by Biot's theory, while the fictitious pile is treated as a bar and a beam and described by the conventional 1‐D structure vibration theory. Using the Hankel transformation method, the fundamental solutions for a half‐space porous medium subjected to a vertical or a horizontal circular patch load are established. Based on the obtained fundamental solutions and free wave fields, the second kind of Fredholm integral equations describing the vertical and the horizontal interaction between the pile and the poroelastic half‐space are established. Solution of the integral equations yields the dynamic response of the pile to plane P, SV waves. Numerical results show the parameters of the porous medium, the pile and incident waves have direct influences on the dynamic response of the pile–half‐space system. Significant differences between conventional single‐phase elastic model and the poroelastic model for the surrounding medium of the pile are found. Copyright © 2007 John Wiley & Sons, Ltd.     

基于离散颗粒模型的岩体结构面动-静态刚度系数对比的数值模拟研究

岩体工程计算分析中结构面刚度系数是至关重要的力学参数,计算分析的精度和可靠程度与这个参数密不可分,结构面刚度系数取值仍然是一个难点.岩体中应力波传播至结构面处将会发生反射和透射现象,利用应力波透射系数可反演结构面动态刚度系数.本文从细观力学角度运用颗粒离散元方法,开发分段线性接触模型及应力波吸收边界模型,开展宏观岩体中...     

不同饱和度土层分界面上剪切波的反射与透射

基于多相孔隙介质弹性理论,给出了非饱和土中不同弹性波的传播方程。根据分界面上的边界条件,建立了各势函数波幅值之间的关系式,讨论了入射剪切波在不同饱和度土层分界面上的反射与透射问题。在无限空间非饱和土体中存在3种压缩波和1种剪切波,因此,当剪切波传播到不同饱和度的非饱和土层分界面上将分别在上、下土层激发产生4种反射波和4种透射波。推导出不同反射波和透射波的振幅比例系数和能量比例系数的理论表达式,并且在此基础上进行数值分析。在数值算例中分别研究了各反射波与透射波的能量比例系数（即能量反射率和能量透射率）受入射频率、入射角度以及上、下土层土体饱和度变化的影响情况。计算结果表明：各能量反射率和能量透射率不仅与入射角和入射频率有关,而且其受上、下土层饱和度变化的影响也同样不能忽视。