Low dispersive modeling of Rayleigh waves on partly staggered grids

In elastic media, finite-difference (FD) implementations of free-surface (FS) boundary conditions on partly staggered grid (PSG) use the highly dispersive vacuum formulation (VPSG). The FS boundary is embedded into a “vacuum” grid layer (null Lame’s constants and negligible density values) where the discretized equations of motion allow computing surface displacements. We place a new set of compound (stress-displacement) nodes along a planar FS and use unilateral mimetic FD discretization of the zero-traction conditions for displacement computation (MPSG). At interior nodes, MPSG reduces to standard VPSG methods and applies fourth-order centered FD along cell diagonals for staggered differentiation combined with nodal second-order FD in time. We perform a dispersion analysis of these methods on a Lamb’s problem and estimate dispersion curves from the phase difference of windowed numerical Rayleigh pulses at two FS receivers. For a given grid sampling criterion (e.g., six or ten nodes per reference S wavelength λ ^S), MPSG dispersion errors are only a quarter of the VPSG method. We also quantify root-mean-square (RMS) misfits of numerical time series relative to analytical waveforms. MPSG RMS misfits barely exceed 10 % when nine nodes sample the minimum S wavelength $\lambda _{\text {MIN}}^{\mathrm {S}}$ in transit (along distances $\sim $ 145 $\lambda _{\text {MIN}}^{\mathrm {S}}$ ). In same tests, VPSG RMS misfits exceed 70 %. We additionally compare MPSG to a consistently fourth-order mimetic method designed on a standard staggered grid. The latter equates the former’s dispersion errors on grids twice denser and shows higher RMS precision only on grids with six or less nodes per $\lambda _{\text {MIN}}^{\mathrm {S}}$ .     

Twenty years of progresses in oceanic rogue waves: the role played by weakly nonlinear models

Here we discuss some of the progresses that have been made in the last 20 years in the field of oceanic rogue waves, focusing on the role played by leading order equations such as the nonlinear Schrödinger and the Korteweg-De Vries equations. For such equations, it is possible, as shown in Onorato et al. (Origin of heavy tail statistics in equations of the nonlinear Schrödinger type: an exact result, 2016. arXiv:1601.04317), to derive a very simple relation in which the variation of the third (for the KdV) and fourth (for the NLS) moment of the probability density function of the wave field can be related to the variation of the spectral bandwidth. These relations give some new perspectives on the formation of rogue waves in a random sea state.     

Self-similar focusing of rarefaction waves in relativistic collapsing clouds

The development of an inhomogeneous collapse of an initially homogeneous cloud in pressure equilibrium with an external medium is considered in a general-relativistic treatment. It is shown that a rarefaction wave propagating from the outer boundary toward the center of the cloud forms in the initial stage of the collapse. The rarefaction front moves through the collapsing gas at the sound speed, and separates the cloud material into an inner, uniform core and an outer, inhomogeneous envelope. Our analysis distinguishes two possible collapse regimes, depending on the ratio of the focusing time for the rarefaction wave and the free-fall time for the cloud. In massive clouds, the focusing time for the rarefaction wave exceeds the free-fall time, and the collapse of such clouds inevitably leads to the formation of an event horizon and black hole. In low-mass clouds, the focusing time is less than the free-fall time. After the focusing, the collapse of such clouds is fully inhomogeneous, and can be appreciably slowed by the pressure gradient. The compression of a cloud in a transitional regime separating these two scenarios is studied. In this case, a self-similar collapse regime is realized in the central part of the cloud near the focusing time for the rarefaction wave. The constructed self-similar solution describes both early stages in the compression up to the focusing of the rarefaction wave and later stages with the accretion of gas onto the black hole that is formed. Asymptotic distributions of quantities in the inhomogeneous region at large distances from the rarefaction front and in the accreting envelope are found. The structure of space-time in the vicinity of the black hole that is formed at the center of the cloud as a result of the focusing of the rarefaction wave is discussed.     

基于FLUENT的二维滑坡涌浪数值模拟

本文从N-S方程出发,建立了二维滑坡涌浪控制方程,使用二维非定常分离隐式PISO算法求解方程。通过UDF(User-Defined Function)编程,采用动网格技术控制滑体的运动,结合RNGk-ε湍流模型并采用VOF方法跟踪非线性自由表面流场,基于流体计算软件FLUENT模拟滑体下滑所引起的水的速度、自由表面高度变化以及流动过程,并将数值计算结果与Monaghan和Kos的试验数据进行比较。算例表明:本模型能很好地模拟出滑体下滑过程中孤立波的产生和传播以及涡流的形成。在此基础上,本文还研究了滑体速度对水体自由表面变形的影响。     

Solutions of pore pressure build up due to progressive waves

The analytical solution of soil pore pressure accumulations due to a progressive wave is examined in detail. First of all, the errors contained in a published analytical solution for wave‐induced pore pressure accumulation are addressed, and the correct solution is presented in a more general form. The behaviour of the solution under different soil conditions is then investigated. It is found that the solution for deep soil conditions is sensitive to the soil shear stress in the top thin layer of the soil. However the solution is significantly influenced by the shear stress in the thin layer of soil near the impermeable base, for shallow and finite depth soil conditions. It is also found that a small error in the soil shear stress can lead to a large error in the accumulated pore pressure. An error analysis reveals the relationships between the accuracy of the pore pressure accumulation and the accuracy of the soil shear stress. A numerical solution to the simplified Biot consolidation equation is also developed. It is shown that the error analysis is of significant value for the numerical modelling of pore pressure buildup in marine soils. Both analytical and numerical examples are given to validate the error estimation method proposed in the present paper. Copyright © 2001 John Wiley & Sons, Ltd.     

水库滑坡涌浪传播有限元数值模拟

库岸滑坡涌浪危害巨大,正确预测库区可能的滑坡涌浪非常重要,是工程可行性论证的重要内容之一。将浅水控制方程应用于滑坡涌浪数值模拟,控制方程采用简便且具有较高精度的两步Taylor-Galerkin方法进行求解。通过算例对数值模型的应用进行验证,结果表明,涌浪产生后将以入水点为源点迅速向四周推进并不断衰减,且随传播距离的增加浪高降幅逐渐减小。计算的涌浪高度及水位变化规律与实测资料吻合得很好,并将滑坡涌浪的沿程传播过程可视化。研究结果表明,文中方法模拟滑坡涌浪传播是有效可行的,可用于滑坡涌浪灾害的预测和防治。     

The impact of pyrite variability, dispersive transport and precipitation of secondary phases on the sulphate release due to pyrite weathering

The objective of this study was to investigate the impact of flow, transport and geochemical parameters in the unsaturated and saturated zones on the release of SO₄ from overburden lignite spoil piles into the adjacent lake. A vertical one-dimensional model was set up using the reactive transport simulator SULFIDOX in order to account for the unsaturated zone. The SULFIDOX model was calibrated for effective diffusion using measured O₂ in the gas phase and SO₄ concentrations in the liquid phase from the unsaturated zone of the heap. The results show high sensitivity to O₂ supply and initially present gypsum, but the inclusion of secondary mineral precipitation in equilibrium is of minor importance for the results. To account for the transport of released SO₄ from the saturated zone into the surface water, scenarios were performed by using SULFIDOX results as input concentration for a two-dimensional vertical model set up with PROCESSING MODFLOW and MT3D. These scenarios indicate a rising discharge of SO₄ into the adjacent lake due to continued pyrite weathering for 80 a. Results are highly sensitive to dispersivity, whereas the spatial variability of pyrite distribution did not show any influence on the results. The consideration of initially present gypsum shows a major effect on the modelled SO₄ release.     

Mechanical development of vein structures due to the passage of earthquake waves through poorly-consolidated sediments

Vein structures are typically the earliest expression of brittle deformation within sediments. These mud-filled veins, which characteristically occur regularly spaced within bed-parallel arrays, form in sediments that possess a strong interlocking particle framework. Downslope creep has been proposed to explain the origins of vein structures, however, a recent suggestion that they are generated by the passage of earthquake shear waves through sediments explains aspects of their morphology, and their dominant occurrence at active convergent margins. Their coexistence with less disruptive “ghost veins” in Peru margin sediments, and their almost normal attitude to bedding, however, suggests that vein structures were formed by processes more complex than downslope creep, or seismically induced shearing alone.

Experimental earthquake simulation was undertaken by laterally shaking a box containing crushed diatomite. Fractures were induced almost normal to the horizontal shaking direction, and to a lesser extent as antithetic Riedel shears, both of which closely resembled vein structures. The fracturing process during shaking may be viewed as a progressive fragmentation of the diatomite, in which new fractures form half-way between pre-existing ones. Thus fracture spacings are progressively halved. Shear zones oriented at a low angle to the shaking direction were also generated, combining with the high-angle fractures to form structures very similar to those observed in Peru margin sediments. When shaken, fines added to the diatomite segregated into planar zones that resembled ghost veins, half-way between fractures. The alternating pattern of fractures and fines indicated that a standing pressure wave had been created within the box during shaking. The fractures were created by alternating compression and extension at the antinodes, while the fines concentrated in zones of minimum grain movement around the nodal planes. This suggests that vein structures are initiated by the combined action of shear and pressure waves within a sediment. The strain waves may be seismic in origin, or may also form in downslope movement system.     

基于Levenberg-Marquardt算法的填埋场中降解产热参数反演研究

填埋场中垃圾降解产热参数是研究填埋场温度变化及热资源利用的基础。基于室内试验得到的峰值产热模型、填埋场中热传导理论以及Levenberg-Marquardt(LM)算法,提出了填埋场中降解产热参数的反演分析方法。结合填埋场实际工况,建立了填埋场热传导一维模型并得到了温度的解析解。基于某一深度的温度数据,采用LM算法反演得到了填埋场的降解产热参数,采用反演得到的降解产热参数可以计算填埋场任意深度的温度。基于产热参数可以计算得到填埋场的峰值产热速率、峰值产热时间和总产热量。以中国无锡桃花山填埋场和美国密歇根填埋场为例,分别反演得到了降解产热参数,采用反演得到的降解产热参数计算反演点之外测点的温度并与实测值进行对比,验证了反演模型的合理性和适用性。对比发现,与实际填埋场相比,室内试验的降解产热峰值更大,且峰值时间更短。与密歇根填埋场相比,无锡桃花山填埋场的前期产热速率更大,到达降解产热峰值的时间更短。     

Computational dynamic homogenization for the analysis of dispersive waves in layered rock masses with periodic fractures

The analysis of the wave propagation in layered rocks masses with periodic fractures is tackled via a two-scale approach in order to consider shape and size of the rock inhomogeneities. To match the displacement fields at the two scales, an approximation of the micro-displacement field is assumed that depends on the first and second gradients of the macro-displacement through micro-fluctuation displacement functions obtained by the finite element solution of cell problems derived by the classical asymptotic homogenization. The resulting equations of motion of the equivalent continuum at the macro-scale result to be not local in space, thus a dispersive wave propagation is obtained from the model. The simplifying hypotheses assumed in the multi-scale kinematics limit the validity of the model to the first dispersive branch in the frequency spectrum corresponding to the lowest modes.Although the homogenization procedure is developed to study the macro-scale wave propagation in rock masses with bounded domain, the reliability of the proposed method has been evaluated in the examples by considering unbounded rock masses and by comparing the dispersion curves provided by the rigorous process of Floquet–Bloch with those obtained by the method presented. The accuracy of the method is analyzed for compressional and shear waves propagating in the intact-layered rocks along the orthotropic axes. Therefore, the influence of crack density in the layered rock mass has been analyzed. Vertical cracks have been considered, periodically located in the stiffer layer, and two different crack densities have been analyzed, which are differentiated in the crack spacing. A good agreement is obtained in case of compressional waves travelling along the layering direction and in case of both shear and compressional waves normal to the layering. The comparison between two crack systems with different spacing has shown this aspect to have a remarkable effect on waves travelling along the direction of layering, and limited in the case of waves propagating normal to the layers.The equivalent continuous model obtained through the dynamic homogenization technique here presented may be applied to the computational analysis of non-stationary wave propagation in rock masses of finite size, also consisting of sub-domains with different macro-mechanical characteristics. This avoids the use of computational models represented at the scale of the heterogeneities, which may be too burdensome or even unfeasible.     

P波作用下饱和土中输流管道动力响应

根据Biot波动理论,采用复变函数与多级坐标法,求解了P波作用下饱和土体中地下输流管道的波动散射方程,分析了管道中流体介质性质、入射波角度及管道埋深等对地下输流管道周边动应力集中系数及孔压集中系数分布的影响。计算结果表明：在低频弹性波入射时,管道周边动应力集中系数及孔压集中系数分布相对均匀,而随入射频率的增加,其分布变得复杂化,但其峰值有所减小;中低频波入射作用下,管道内为水、石油介质时,动应力集中系数和孔压集中系数较空气介质时小,而在高频波作用时情况相反;对于管道内流体介质为水时,随着入射角度的变化,应力集中分布也沿一定角度的方向发生转动,入射波自管道下方垂直入射时,管道周边动应力集中系数峰值相对较大;随埋深的增加,动应力集中系数和孔压集中系数均呈震荡减小的趋势。     

A new approximation for pore pressure accumulation in marine sediment due to water waves

The residual mechanism of wave‐induced pore water pressure accumulation in marine sediments is re‐examined. An analytical approximation is derived using a linear relation for pore pressure generation in cyclic loading, and mistakes in previous solutions (Int. J. Numer. Anal. Methods Geomech. 2001; 25 :885–907; J. Offshore Mech. Arctic Eng. (ASME) 1989; 111 (1):1–11) are corrected. A numerical scheme is then employed to solve the case with a non‐linear relation for pore pressure generation. Both analytical and numerical solutions are verified with experimental data (Laboratory and field investigation of wave– sediment interaction. Joseph H. Defrees Hydraulics Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY, 1983), and provide a better prediction of pore pressure accumulation than the previous solution (J. Offshore Mech. Arctic Eng. (ASME) 1989; 111 (1):1–11). The parametric study concludes that the pore pressure accumulation and use of full non‐linear relation of pore pressure become more important under the following conditions: (1) large wave amplitude, (2) longer wave period, (3) shallow water, (4) shallow soil and (5) softer soils with a low consolidation coefficient. Copyright © 2006 John Wiley & Sons, Ltd.     

Time-domain analysis of velocity waves in a pipe pile due to a transient point load

The propagation of stress waves in a pipe pile subjected to a transient point load cannot be expressed using traditional one-dimensional (1D) wave theory. This paper presents an analytical solution used to investigate the wave propagation in a pipe pile under an axial point load. The soil resistance is simulated using the Winkler model, and the excitation force is simulated with a semi-sinusoidal impulse. A time-domain analytical solution for the three-dimensional wave equation is derived using the separation of variables and variation of constants methods. The solution is verified with a frequency domain analytical solution in which the time-domain response is calculated by numerical Fourier inverse transformation. Furthermore, the solution proposed in this paper is compared with the results of model testing and 3D FEM analysis. The comparisons show that the analytical solution proposed in this study agrees well with the results of previous studies. The proposed solution is subsequently applied in case studies. The vertical velocity responses in the circumferential and axial directions are analyzed to reveal the propagation characteristics of transient waves in the pipe pile. Moreover, the effects of the location and period of the excitation force, the side and tip resistances and high-order modes are studied in detail.     

块系岩体间黏弹性性质对摆型波传播的影响

基于深部非连续自应力等级块系岩体构造理论,研究冲击载荷在块系岩体中以摆型波形式传播时岩块间黏弹性性质对摆型波传播的影响。当岩块间具有五种不同黏弹性性质时,通过对块系岩体的始端和末端区域中间岩块加速度响应计算及各岩块加速度正负摆幅幅值分析可知：岩块间黏性变化时,对岩块加速度衰减周期没有影响,但黏性增大时各岩块正负摆幅下降幅度比黏性周期增大时大;岩块间弹性变化时岩块加速度衰减周期均发生变化,但弹性减小时正负摆幅值向平衡位置平移,弹性周期减小时块系岩体的前半部分岩块正负摆幅曲线均出现波动且负摆波动较大,岩块间弹性梯级增大时,岩块加速度迅速衰减,同时各岩块加速度的正负摆幅曲线在初始端区域出现波动。     

空隙特征对砂岩水致劣化规律的影响

针对南京秦淮东河开挖后的稳定性问题,选取黄马青组（T2h）砂岩为研究对象,对砂岩在吸水-干燥循环条件下的单轴抗压、抗拉特性进行试验研究。考虑到未来边坡运营过程中水的影响,试验时分别考虑自然吸水和饱和吸水两种情况。根据试验结果对所研究砂岩的空隙特征、水致劣化特征和劣化机制进行了详细分析。随着吸水-干燥循环次数增加,岩石的抗压、抗拉强度和凝聚力均呈劣化趋势,说明循环次数的增加对岩石的损伤有累积作用。岩石自然吸水条件下（小开空隙未进水时）强度和弹性模量下降速度较慢,而饱和吸水条件下（开空隙被水充满时）强度和弹性模量下降速度较快,表明岩石中小开空隙对岩石的劣化效果显著。微观结构分析结果表明,随着吸水-干燥循环次数增加,岩石中空隙率增大。结合抗剪强度特征分析认为,干-湿循环导致岩石的黏结强度不断下降,而摩擦强度变化较小,表明黏结强度劣化是岩石水致劣化的主要原因,干-湿循环导致水-岩反应,岩石颗粒胶结物发生松散,边缘发生开裂,宏观上表现为岩石劣化。该研究成果对于新开挖河道边坡稳定性分析具有较大的参考价值,为河岸边坡的长期稳定性分析提供了依据。     

Effect of translate speed of typhoon on wind waves

Natural Hazards - Quantitative assessments on the effect of translate speed of typhoons on wind waves were carried out. A WRF-SWAN coupled model that used observed meteorological data was applied...     

地下洞室群对地面运动影响问题的级数解答:SH波入射

采用波函数展开法给出平面SH波入射下半空间中洞室群对地面运动影响问题的一个级数解答，并分析了入射波频率和入射角以及两洞室之间距离等参数对地面运动的影响。数值结果表明，地下洞室群对沿线地面运动具有显著的放大作用：两个洞室情况地面运动可以达到单个洞室情况的1．6倍、无洞室情况的3．5倍以上。建议地铁等地下工程在设计和规划时应考虑工程建设后对沿线设计地震动的影响。     

滑坡体散体化对涌浪波动特征的影响

岩质滑坡在下滑过程中会发生散体化,进而分解成形状及大小各异的块体。已有滑坡体兴波方面的研究多采用单一刚性块体或均匀散体颗粒对滑坡体进行模拟,较少关注滑坡体散体化对涌浪的影响机制。本研究通过开展三维水池物理模型试验,初步探索滑坡体的散体化过程对涌浪波动特性的影响作用。结果表明：初生涌浪的最大波幅和最大波高随滑坡体散体化指标的增大而减小;第一波峰幅值和第一波高的沿程衰减规律符合孤立波理论,且其衰减速率分别依赖于涌浪的最大波幅和最大波高;三维水池试验中第一波峰幅值和第一波高的沿程衰减速度较二维水槽中更快。     

北京延庆地区地热开发对水文地质条件的影响

本文结合延庆盆地地热地质条件,从地热尾水的回灌、地面沉降原因、地震发生的机理等方面,全面、客观地分析了地热开发不会造成地表环境污染,也不会诱发地面沉降、地震等一系列的地质灾害问题,解除了人们对地热开发的顾虑,坚定了延庆地区利用地热供暖替代燃煤供暖的决心,为建立延庆生态模范县寻找到一种可利用的新能源.