A comparison of several wave spectra for the random wave diffraction by a semi-infinite breakwater

A comparison of the diffraction of multidirectional random waves using several selected wave spectrum models is presented in this paper. Six wave spectrum models, Bretschneider, Pierson–Moskowitz, ISSC, ITTC, Mitsuyasu, and JONSWAP spectrum, are considered. A discrete form for each of the given spectrum models is used to specify the incident wave conditions. Analytical solutions based on both the Fresnel integrals and polynomial approximations of the Fresnel integrals and numerical solutions of a boundary integral approach have been used to obtain the two-dimensional wave diffraction by a semi-infinite breakwater at uniform water depth. The diffraction of random waves is based on the cumulative superposition of linear diffraction solution. The results of predicted random wave diffraction for each of the given spectrum models are compared with those of the published physical model presented by Briggs et al. [1995. Wave diffraction around breakwater. Journal of Waterway, Port, Coastal and Ocean Engineering—ASCE 121(1), 23–35]. Reasonable agreement is obtained in all cases. The effect of the directional spreading function is also examined from the results of the random wave diffraction. Based on these comparisons, the present model for the analysis of various wave spectra is found to be an accurate and efficient tool for predicting the random wave field around a semi-infinite breakwater or inside a harbor of arbitrary geometry in practical applications.     

Thermoelastic stress due to a rectangular heat source in a semi-infinite medium. Presentation of an analytical solution

The thermoelastic response due to a time-dependent rectangular heat source in a semi-infinite medium is analyzed. The problem originates from studies of nuclear waste repositories in rock. Canisters containing heat-emitting nuclear waste are deposited over a large rectangular area deep below the ground surface. The solution for a time-dependent heat source is obtained from the corresponding instantaneous heat source by superposition. The thermoelastic problem for the instantaneous rectangular heat source in a infinite surrounding is solved exactly. An important step is the introduction of so-called quadrantal heat sources. The solution for the rectangle is obtained from four quadrantal solutions. The solution for the quadrantal heat source depends on the three dimelasionless coordinates only. Time occurs in the scale factors only. The condition of zero normal and shear stresses at the ground surface is fulfilled by using a mirror heat source and a boundary solution. The boundary solution accounts for the residual normal stress at the ground surface. Using a Hertzian potential, a surprisingly simple solution is obtained. The final analytical solution is quite tractable considering the complexity of the initial problem. The solution may be used to test numerical models for coupled thermoelastic processes. It may also be used in more detailed numerical simulations of the process near the heat sources as boundary conditions to account for the three-dimensional global process.     

2021年青海玛多Mw7.5地震的同震变形及断层滑动模型研究

2021年5月22日,中国青海玛多县发生了M_W7.5地震.针对此次地震,国内外多家机构发布的震源机制解和有限断层滑动模型结果大都是基于半无限空间地球模型的位错理论反演得到的,未考虑地球曲率和层状效应的影响.该影响的量级以及其是否可以忽略目前仍是一个未知问题,值得研究.为此,本文利用美国地质调查局(USGS)、中国科学院青藏高原研究所以及中国地震局地球物理研究所提供的三个断层模型,基于弹性半无限空间、均质球、PREM三种地球模型的位错理论,分别计算了地表同震位移场和应变场,并对比分析了这些结果的差异.我们发现基于PREM位错理论的同震位移场与半无限空间模型的对应值差异约为3~28 cm,占PREM位错理论值的10%~30%,应变场差异更大,表明地球曲率和层状效应的影响不可忽略.此外,理论同震形变结果与GNSS和InSAR形变观测数据对比发现,基于PREM模型的理论位移场最接近于观测值.利用InSAR数据和三种地球模型反演得到的有限断层滑动模型存在差异,说明了地球模型的选择对断层模型的反演具有一定影响.本文的结果为今后对此次地震的观测数据物理解释和断层滑动反演提供了理论参考.     

Application of perfectly matched layers in the transient analysis of dam–reservoir systems

The transient analysis of dam–reservoir systems by employing perfectly matched layers has been investigated. In previous studies, boundary conditions of the PML region in the reservoir have been neglected. In this paper, they are incorporated completely in the formulation. Moreover, a technique is introduced to involve the effect of incident waves caused by vertical ground motions at the reservoir bottom in the analysis. Performing several numerical experiments indicates that applying boundary conditions of the PML domain and utilizing the proposed method for vertical excitation cases reduce the computational cost significantly and make the PML method a very efficient approach for the transient analysis of dam–reservoir systems.     

半空间饱和介质内圆形洞室对平面P1波的散射

考虑土颗粒和孔隙流体的压缩性以及孔隙流体与土骨架之间的粘性耦合作用,采用修正的Biot模型,假定半空间表面不透水,得到了平面P1波(快压缩波)在半空间表面的反射P1波、P2波(慢压缩波)和SV波(剪切波)的幅值.采用大圆弧假定将半空间内圆形洞室的散射问题转化为大圆弧和圆形洞室的多重散射问题,运用波函数展开法将入射波、反射波以及半空间表面和洞室的散射波的势函数展开成Fourier-Bessel函数的无穷级数形式,由Graf加法定理得到同一坐标系下的势函数的表达式,根据半空间表面和洞室完全自由的边界条件得到了待定复系数的理论解.通过数值计算,着重分析了平面P1波垂直向上入射时无量纲入射频率和洞室埋藏深度等对洞室的动应力集中因子和半空间表面的归一化水平和竖向位移的影响.     

Direct time-domain soil profile reconstruction for one-dimensional semi-infinite domains

We discuss the inverse medium problem associated with the reconstruction of the heterogeneous material profile of a semi-infinite (layered) soil medium, directly in the time domain, based on the complete waveform response of the medium to interrogating waves. To tackle the inversion process, we use a partial-differential-equation-constrained optimization approach, supplemented with a time-dependent regularization scheme. We introduce an absorbing boundary to truncate the semi-infinite extent of the physical domain, and propose two schemes to refine the reconstructed profiles: the first is based on iteratively re-positioning the truncation boundary until convergence, and the second is based on optimizing the observation period, so as to exclude records with information beyond the truncation boundary. We present numerical results that attest to the efficacy of the proposed schemes in reconstructing sharp profiles of semi-infinite soil domains using both noise-free and noisy data, while in the presence of absorbing boundaries.     

A method for nonlinear dynamic response analysis of semi-infinite foundation soil

This paper presents development of a special finite difference method for the nonlinear dynamic response analysis of semi-infinite foundation soil. Semi-infinite domain is mapped into the finite domain using special mapping. For the region of engineering interest, mapping is isometrical, and for far field, shrink mapping which transforms an infinite interval into a finite interval is adopted. Using linear and nonlinear constitutive models, the responses of semi-infinite foundation soil are computed using a proposed method with a small mesh model and an extensive mesh model. Surface loadings or incident earthquake waves are applied to the models in the computations. Good agreements were obtained among the theoretical and computed results of the two models and the effectiveness of the proposed method was demonstrated.     

ISMISIP: an inexact stochastic mixed integer linear semi-infinite programming approach for solid waste management and planning under uncertainty

An inexact stochastic mixed integer linear semi-infinite programming (ISMISIP) model is developed for municipal solid waste (MSW) management under uncertainty. By incorporating stochastic programming (SP), integer programming and interval semi-infinite programming (ISIP) within a general waste management problem, the model can simultaneously handle programming problems with coefficients expressed as probability distribution functions, intervals and functional intervals. Compared with those inexact programming models without introducing functional interval coefficients, the ISMISIP model has the following advantages that: (1) since parameters are represented as functional intervals, the parameter’s dynamic feature (i.e., the constraint should be satisfied under all possible levels within its range) can be reflected, and (2) it is applicable to practical problems as the solution method does not generate more complicated intermediate models (He and Huang, Technical Report, 2004; He et al. J Air Waste Manage Assoc, 2007). Moreover, the ISMISIP model is proposed upon the previous inexact mixed integer linear semi-infinite programming (IMISIP) model by assuming capacities of the landfill, WTE and composting facilities to be stochastic. Thus it has the improved capabilities in (1) identifying schemes regarding to the waste allocation and facility expansions with a minimized system cost and (2) addressing tradeoffs among environmental, economic and system reliability level.     

Spectral methods for coastal-trapped waves

This note describes efficient and accurate spectral numerical schemes to compute both propagating and evanescent free baroclinic coastal-trapped waves over general depth profiles for arbitrary vertical density profiles in horizontally semi-infinite domains. The general problem is recast into a linear eigenvalue problem for the along-shore wavenumber k, which can be solved directly, without initial guesses or searching, using any standard linear eigenvalue package to find real and complex eigenmodes simultaneously. An equivalent recasting gives the linearised eigenvalue problem for the frequency ω. A novel, nonlinear, boundary condition is derived that is particularly effective for modes whose offshore decay is weak, as in the long-wave limit. The resulting nonlinear eigenvalue problem is solved by a highly efficient Newton-Kantorovich algorithm.