Modelling bivariate rainfall distribution and generating bivariate correlated rainfall data in neighbouring meteorological subdivisions using copula

The rainfall patterns of neighbouring meteorological subdivisions of India are similar because of similar climatological and geographical characteristics. Analysing the rainfall pattern separately for these meteorological subdivisions may not always capture the correlation and tail dependence. Furthermore, generating the multivariate rainfall data separately may not preserve the correlation. In this study, copula method is used to derive the bivariate distribution of monsoon rainfall in neighbouring meteorological subdivisions. Different Archimedean copulas are used for this purpose and the best copula is selected based on nonparametric test and tail dependence coefficient. The fitted copula is then applied to derive the bivariate distribution, joint return period and conditional distribution. Bivariate rainfall data is generated with the fitted copula and it is observed with the increase of sample size, the generated data is able to capture the correlation as well as tail dependence. The methodology is demonstrated with the case study of two neighbouring meteorological subdivisions of North‐East India: Assam and Meghalaya meteorological subdivision and Nagaland, Manipur, Mizoram and Tripura meteorological subdivision. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic response of high-speed rail foundations using linear hysteretic damping and frequency domain substructuring

A proposed method for mitigating ground-borne vibration generated by high-speed trains is the usage of rubber-modified asphalt concrete as a ballast mat material. To gauge this material's influence in vibration control, a dynamic finite element code that models distinct damping properties in a large, nonhomogenous system was created. A linear hysteretic damping model is used to capture the dissipative mechanisms of each material; frequency domain substructuring is used for computational efficiency. Vibratory responses utilizing different ballast mat materials in a high-speed rail foundation are compared. It is shown that rubber-modified asphalt concrete results in a general reduction of motion, particularly in directions horizontally parallel and perpendicular to the train's passage. The described modeling procedure may be used for any dynamic analysis where the preservation of material damping characteristics is desired.     

Implicit structural inversion of gravity data using linear programming,a validation study*

In this study, a regional scale gravity data set has been inverted to infer the structure (topography) of the top of the basement underlying sub‐horizontal strata. We apply our method to this real data set for further proof of concept, validation and benchmarking against results from an earlier forward modelling done elsewhere. Our aim is to carry out implicit structural inversion, i.e., to obtain a geologically reasonable model, without specifically solving for structure. The 2.5D volume of interest is parametrized with homogeneous horizontal prisms and a two‐lithology medium is assumed. A possible regional linear trend and a general floating reference are also inverted for. Using a gridded parametrization, linear programming is used to minimize the L₁ ‐norm of the data misfit, relative to a floating reference. Given a known density contrast between the lithologies, an inversion using linear programming has the intrinsic advantage that a relatively sharp image of the sub‐surface is retrieved instead of a smooth one. The model recovered is almost bi‐modal and its general features seem to be robust with respect to several parametrization scenarios investigated. The floating reference and a linear trend in the data were also retrieved simultaneously. The inversion results, indicating two depressions in the basement, are robust and agree with those obtained earlier based upon detailed 2D forward modelling using many narrow, near‐vertical prisms.     

Evaluation of the structural response under seismic actions using non‐linear static methods

The paper investigates the degree of accuracy achievable when some non‐linear static procedures based on a pushover analysis are used to evaluate the seismic performance. In order to assess the significance of different sources of errors, three types of structural systems are analysed: (i) single‐degree‐of‐freedom (SDOF) systems with different hysteretic behaviour; (ii) shear‐type multi‐degree‐of‐freedom (MDOF) systems with elastic–perfect plastic (EPP) shear force–interstorey drift relationships; (iii) a steel moment‐resisting frame with rigid joints and EPP moment–curvature relationship. In SDOF systems, the source of approximation comes only from the calibration of the demand spectrum, while in MDOF systems some further errors are introduced by the schematization with an equivalent SDOF system. The non‐linear static procedures are compared with rigorous time‐history analyses carried out by considering ten generated earthquake ground motions compatible with the Eurocode 8 elastic spectra. It was found that SDOF systems with longer periods satisfy the equal displacement approximation regardless of the hysteretic model, while hysteresis loops with smaller energy dissipated indicate lower response for shorter periods. This is the opposite of what predicted by the ATC‐40 capacity spectrum method, which underestimates and overestimates, respectively, the actual response of low‐ and high‐ductility systems. Conversely, the inelastic spectrum method proposed by Vidic, Fajfar and Fischinger leads to the most accurate results for all types of structural systems. The analyses carried out on EPP shear‐type frames point out a large concentration of the ductility demand on some storeys. However, such a concentration markedly reduces when some hardening is accounted for. Copyright © 2006 John Wiley & Sons, Ltd.     

Modelling non‐linear ground response of non‐liquefiable soils

A non‐linear finite element (FE) model is presented to account for soil column effects on strong ground motion. A three‐dimensional bounding surface plasticity model with a vanishing elastic region, appropriate for non‐liquefiable soils, is formulated to accommodate the effects of plastic deformation right at the onset of loading. The elasto‐plastic constitutive model is cast within the framework of a FE soil column model, and is used to re‐analyse the downhole motion recorded by an array at a Large‐Scale Seismic Test (LSST) site in Lotung, Taiwan, during the earthquake of 20 May 1986; as well as the ground motion recorded at Gilroy 2 reference site during the Loma Prieta earthquake of 17 October 1989. Results of the analysis show maximum permanent shearing strains experienced by the soil column in the order of 0.15 per cent for the Lotung event and 0.8 per cent for the Loma Prieta earthquake, which correspond to modulus reduction factors of about 30 and 10 per cent respectively, implying strong non‐linear response of the soil deposit at the two sites. Copyright © 2000 John Wiley & Sons, Ltd.     

Lateral force distributions for the linear static analysis of base-isolated buildings

This paper presents a new approach for the evaluation of accurate lateral force distributions for the Linear Static Analysis (LSA) of Base Isolated (BI-) buildings. In essence, the proposed lateral force distributions depend on a factor measuring the degree of non- linearity of the Isolation System (IS) and on the ratio between the effective period of the BI-structure (T_is) and the fundamental period of the Fixed Based (FB-) structure (T_fb). The proposed approach is fully compatible with the Direct Displacement-Based Design (DDBD) method, recently developed by Priestley and co-workers. The proposed lateral force distributions have been derived from the results of a large number of Nonlinear Time-History Analyses (NTHA), carried out on six numerical models of multi-storey buildings, differing in storey number (3, 5 and 8, respectively) and fundamental period of vibration (from 0.25 to 0.8 s) in the fixed-base configuration. A great variety of Isolation Systems (ISs), characterised by either Elasto-Plastic with Hardening (EPH) or Flag-Shaped (FS) force-displacement behaviour, have been considered in the NTHA. The numerical parameters of the IS models have been varied in such a way as to reproduce the actual mechanical behaviour of the main currently used ISs, including: (i) Lead Rubber Bearings (LRB), (ii) High-Damping Rubber Bearings (HDRB), (iii) Friction Pendulum Bearings (FPB), (iv) combinations of flat Sliding Bearings (SB) and Low-Damping Rubber Bearings (LDRB) and (v) Combinations of flat SB and re-centring devices based on Shape Memory Alloys (SMA). Comparisons between the storey shear forces derived with the proposed method and those obtained from NTHA clearly show the great improvements in the accuracy of LSA predictions, when using the proposed lateral force distributions.     

Identification of linear structural systems using earthquake-induced vibration data

This paper addresses the issue of system identification for linear structural systems using earthquake induced time histories of the structural response. The proposed methodology is based on the Eigensystem Realization Algorithm (ERA) and on the Observer/Kalman filter IDentification (OKID) approach to perform identification of structural systems using general input–output data via Markov parameters. The efficiency of the proposed technique is shown by numerical examples for the case of eight-storey building finite element models subjected to earthquake excitation and by the analysis of the data from the dynamic response of the Vincent-Thomas cable suspension bridge (Long Beach, CA) recorded during the Whittier and the Northridge earthquakes. The effects of noise in the measurements and of inadequate instrumentation are investigated. It is shown that the identified models show excellent agreement with the real systems in predicting the structural response time histories when subjected to earthquake-induced ground motion. Copyright © 1999 John Wiley & Sons, Ltd.     

Modelling road surface sediment production using a vector geographic information system

Field investigations indicate that unpaved roads are the largest sediment source on St John, US Virgin Islands. Cross-sectional measurements of eroded road surfaces were used to establish an empirical relationship to predict annual road surface erosion as a function of road gradient and contributing drainage area. A model (ROADMOD) for estimating and mapping average annual sediment production from a road network was developed by combining this empirical relationship with a series of network algorithms to analyse road data stored in a vector geographic information system. ROADMOD was used to estimate road surface erosion in two St John catchments with very different road densities but similar land cover, topography and soils. Unpaved roads were found to increase sediment production in the more densely roaded catchment by a factor of three to eight, and in the less-roaded catchment by a factor of 1·3–2·0. Turbidity measurements in the receiving bays of these two catchments are consistent with model predictions and observed sediment delivery processes. Although this model was developed specifically for St John, it can easily be adapted to other locations by substituting a locally derived predictive equation for road erosion. Model assumptions, limitations and potential improvements are discussed. © 1998 John Wiley & Sons, Ltd.     

复杂地表条件下基于线性插值和窄带技术的地震波走时计算

为了在复杂地表条件下实现地震波走时计算,提出了一种基于线性插值和窄带技术的走时计算新方法.其中,线性插值用于局部走时计算,窄带技术用于局部波前捕获和追踪.为了逼近起伏地表,采用三角网和矩形网相结合的方法对速度模型进行剖分.为了得到局部走时计算公式,利用费马（Fermat）原理和关于入射点位置的限定条件.有关编程实践和数值试验表明：新方法不仅可以有效、灵活地处理地表高程的剧烈变化,而且还具有很好的适应性和稳定性,得到的计算结果满足波前传播规律.     

非比例阻尼线性体系地震反应计算的振型分解反应谱法

以非比例阻尼线性体系地震反应计算实数形式的一般解答为基础,推导得到了非比例阻尼线性体系水平地震作用计算的多种形式,建立了非比例阻尼线性体系地震反应计算振型分解反应谱法的基本过程与步骤。最后,以一个五层剪切型结构为例,通过与各种常用直接积分方法计算结果的比较,证实了本文非比例阻尼线性体系地震反应计算实数形式的一般解答的高精度与可靠性。通过对多种形式地震作用所得地震效应的比较,证实了非比例阻尼线性体系地震反应振型分解反应谱方法的可靠性及可行性。     

Monthly spatial rainfall correlation functions and interpretations for Turkey

Abstract

Monthly spatial rainfall distribution features and their effects on spatial correlation patterns are significant in any regional study. In this paper, first a number of statistical terms and properties are explained with reference to the spatial correlation functions (SCFs). This is followed by the analysis of a theoretical spatial correlation model and its parameter estimation. Monthly empirical SCFs are examined in relation to spatial rainfall characteristics. In order to obtain a definite pattern, the SCF values are averaged in successive equal-distance groups. This average spatial correlation function shows a decreasing pattern with distance. Some interpretations of these spatial correlation functions are given for Turkey with discussion of the results obtained.     

Approximation of Sahelian rainfall fields with meta-Gaussian random functions

For the purpose of numerically studying sahelian storm rainfields, a family of random functions is described with a characterization of its finite dimensional law. Some problems appearing when fitting its functional parameters are put forward and two solutions to bypass those problems are provided, according to the regularity properties of the marginal cumulative distribution function. An illustration of this method is implemented on a set of sahelian rainfields of event accumulation displaying a strong spatial intermittency.     

Nonlinear response estimates of RC frames using linear analysis of SDOF systems

An approximate‐simple method for nonlinear response estimates of reinforced concrete frames subjected to near‐field and far‐field records is presented in this paper. The approximate method is based on equivalent single‐degree‐of‐freedom and linear multi‐degree‐of‐freedom models. In this procedure, the nonlinear maximum roof displacement is estimated using an effective period factor and elastic response spectrum with an equivalent damping. The effective period factor was proposed for far‐field and near‐field ground motion records. For regions of high seismicity, the maximum roof displacement can be estimated by applying an effective period factor of 2.3 and 2.1 for near‐field and far‐field records, respectively, and 9% damped displacement response spectrum. For regions of moderate seismicity, a lower effective period factor of 1.9 and 1.8, for near‐field and far‐field records, respectively, can be applied to estimate the maximum roof displacement. A relationship between linear and nonlinear response of multi‐degree‐of‐freedom systems was also proposed to obtain estimates of the maximum inter‐story drift of nonlinear responding reinforced concrete frames. In addition, the effects of number of ground motion records used in the analyses on the scatters of results were investigated. The required number of ground motions to produce a reliable response was proposed. Copyright © 2013 John Wiley & Sons, Ltd.     

Stochastic analysis of the linear equivalent response of bridge piers with aseismic devices

The dynamic response of bridge piers with aseismic devices to earthquake excitation is evaluated by the stochastic equivalent linearization technique. The seismic acceleration is schematized through a Gaussian stationary random process. The pier is considered linear elastic, the span is idealized as a rigid mass, the restoring force of the device is represented through a non-linear differential model. The study of the complex modes of the linearized system gives an interpretation of the mechanical behaviour, leads to a formally elementary solution and highlights some phenomena which are typical of the hysteretic systems, particularly of those marked by weak hardening. Even though the solution is limited to the stationary field, it brings out several noteworthy considerations about the effective non stationary behaviour of the structure. Copyright © 1999 John Wiley & Sons, Ltd.     

Monitoring surface change on a Namib linear dune

In tackling the apparently intractable problem of linear dune initiation and maintenance there has been a move away from large-scale deductive models to smaller-scale field studies of individual dunes. This paper reports a study of surface change on a large, complex linear dune in the Namib Desert, southern Africa. The dune surface responds to a markedly seasonal wind regime. In summer westerly winds erode sand from the west flank of the dune and deposit it on the easterly lee side of the dune crest. In winter this pattern is reversed. Easterly winds erode sand from the east slope and deposit it on the west slope. The crest therefore moves back and forth some 15 m each year returning at the end of a year's cycle to its position at the beginning. The position of the base of the dune appears to remain fixed, even though sand is moving throughout the dune system. The dune does extend northward along some resultant of the westerly and easterly winds. Despite relatively high levels of activity, especially at the dune crest, there is no evidence of the breakdown of the linear dune form. The conclusion must therefore be that linear dunes can be maintained in bimodal wind regimes and are not necessarily related to unidirectional parallel regimes as others have suggested.     

Earthquake response of hysteretic mass-column using non-Gaussian closure

A non-Gaussian closure scheme based on the Edgeworth expansion of the probability density function is used to study the response of a hysteretic structure under random parametric excitation. The system considered consists of a weightless mass supporting a concentrated mass and it is subjected to the vertical and horizontal components of the ground acceleration modeled as nonstationary Gaussian white noise processes. The material of the structure exhibits bilinear hysteretic behaviour. The equation governing the motion of the system is transformed into an Itô stochastic differential equation. A set of ordinary differential equations governing the response statistics are obtained. These form an infinite hierarchy of equations which must be truncated in order to solve for moments of any order. The Edgeworth expansion of the joint density is used to truncate this infinite hierarchy. Such a closure scheme appears desirable since for hysteretic systems an explicit expression of the probability density is required. A frequently used closure scheme based on Gaussian assumption underestimates the response. The non-Gaussian density can be used in reliability studies.     

Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Earthquake response

Investigated are earthquake responses of one‐way symmetric‐plan, one‐storey systems with non‐linear fluid viscous dampers (FVDs) attached in series to a linear brace (i.e. Chevron or inverted V‐shape braces).Thus, the non‐linear damper is viscous when the brace is considered rigid or viscoelastic (VE) when the brace is flexible. The energy dissipation capacity of a non‐linear FVD is characterized by an amplitude‐dependent damping ratio for an energy‐equivalent linear FVD, which is determined assuming the damper undergoes harmonic motion. Although this formulation is shown to be advantageous for single‐degree‐of‐freedom (SDF) systems, it is difficult to extend its application to multi‐degree‐of‐freedom (MDF) systems for two reasons: (1) the assumption that dampers undergo harmonic motion in parameterizing the non‐linear damper is not valid for its earthquake‐induced motion of an MDF system; and (2) ensuring simultaneous convergence of all unknown amplitudes of dampers is difficult in an iterative solution of the non‐linear system. To date, these limitations have precluded the parametric study of the dynamics of MDF systems with non‐linear viscous or VE dampers. However, they are overcome in this investigation using concepts of modal analysis because the system is weakly non‐linear due to supplemental damping. It is found that structural response is only weakly affected by damper non‐linearity and is increased by a small amount due to bracing flexibility. Thus, the effectiveness of supplemental damping in reducing structural responses and its dependence on the planwise distribution of non‐linear VE dampers were found to be similar to that of linear FVDs documented elsewhere. As expected, non‐linear viscous and VE dampers achieve essentially the same reduction in response but with much smaller damper force compared to linear dampers. Finally, the findings in this investigation indicate that the earthquake response of the asymmetric systems with non‐linear viscous or VE dampers can be estimated with sufficient accuracy for design applications by analysing the same asymmetric systems with all non‐linear dampers replaced by energy‐equivalent linear viscous dampers. Copyright © 2003 John Wiley & Sons, Ltd.     

Predicting rainfall intensity using a genetic algorithm approach

A genetic algorithm rainfall intensity (GARI) model has been developed and used to predict the intensities for given return period. It is a one‐step solution procedure that may not require any mathematical transformation. The problem formulation is given and the genetic algorithm solution of the problem is presented. The results show that the proposed GARI model can be used to solve the rainfall intensity–duration–frequency relations with lowest mean‐squared error between measured and predicted intensities. Predicted intensities are in good agreement between measured and predicted values for given return periods. Copyright © 2006 John Wiley & Sons, Ltd.