A numerical procedure for obtaining the mean solution and variance of the two-dimensional stochastic convection equation

Under certain conditions the concentration of a substance moving in a stochastic flow field is described by the stochastic convection equation. A numerical method yielding the mean solution and variance of the two-dimensional problem is described here. First, the differential operator is replaced by a discrete linear operator based on finite differences. The resulting system of stochastic equations is then replaced by a system of equations whose solution is the mean concentration. The variance of the concentration can then be calculated. In addition, and example is given for which an approximate analytical solution and its variance is known. The numerical method is applied to the example and results compared to the approximate analytical solution and variance.     

Implementation of a second‐order paraxial boundary condition for a water‐saturated layered half‐space in plane strain

A half‐space finite element and a transmitting boundary are developed for a water‐saturated layered half‐space using a paraxial boundary condition. The exact dynamic stiffness of a half‐space in plane strain is derived and a second‐order paraxial approximation of the stiffness is obtained. A half‐space finite element and a transmitting boundary are then formulated. The development is verified by comparison of the dynamic stiffness of impermeable and permeable rigid strip foundations with other published results. The advantage of using the paraxial boundary condition in comparison with the rigid boundary condition is examined. It is shown that the paraxial boundary condition offers significant gain and the resulting half‐space finite element and transmitting boundary can represent the effects of a water‐saturated layered half‐space with good accuracy and efficiency. In addition, the numerical method described herein maintains the strengths and advantages of the finite element method and can be easily applied to demanding problems of soil–structure interaction in a water‐saturated layered half‐space. Copyright © 2010 John Wiley & Sons, Ltd.     

一种基于逾渗模型的裂隙岩石渗透系数确定方法

针对裂隙岩体提出了一种基于双重逾渗模型的渗流系数分析方法。通过变参数研究,考察了岩体中渗流和孔压分布的不均匀;根据裂隙长度的不同将岩体分为孔隙控制渗流模式和裂隙控制渗流模式。这种模型不仅能够同时考虑孔隙和裂隙的作用,而且在模拟大规模裂隙网络时更加快捷简便。     

A three‐dimensional transmitting boundary formulated in Cartesian co‐ordinate system for the dynamics of non‐axisymmetric foundations

A three‐dimensional transmitting boundary is formulated in the Cartesian co‐ordinate system. It is developed for the dynamic soil–structure interaction problems of arbitrary shape foundations in laterally heterogeneous strata overlying rigid bedrock. Dynamics of a rectangular rigid surface foundation on a homogeneous stratum is analysed by a hybrid approach in which the finite region including foundation is modelled by the conventional finite element method and the surrounding infinite region by the newly developed transmitting boundary. To demonstrate its strength, the present method is applied to a rectangular foundation in a horizontally heterogeneous ground consisting of two distinct regions divided by and welded along a vertical plane. Copyright © 2000 John Wiley & Sons, Ltd.     

Noise suppression for microseismic data by non‐subsampled shearlet transform based on singular value decomposition

The existence of strong random noise in surface microseismic data may decrease the utility of these data. Non‐subsampled shearlet transform can effectively suppress noise by properly setting a threshold to the non‐subsampled shearlet transform coefficients. However, when the signal‐to‐noise ratio of data is low, the coefficients related to the noise are very close to the coefficients associated with signals in the non‐subsampled shearlet transform domain that the coefficients related to the noise will be retained and be treated as signals. Therefore, we need to minimise the overlapping coefficients before thresholding. In this paper, a singular value decomposition algorithm is introduced to the non‐subsampled shearlet transform coefficients, and low‐rank approximation reconstructs each non‐subsampled shearlet transform coefficient matrix in the singular value decomposition domain. The non‐subsampled shearlet transform coefficients of signals have bigger singular values than those of the random noise, which implies that the non‐subsampled shearlet transform coefficients can be well estimated by taking only a few largest singular values. Therefore, those properties of singular value decomposition may significantly help minimise overlapping of noise and signals coefficients in the non‐subsampled shearlet transform domain. Finally, the denoised microseismic data are obtained easily by giving a simple threshold to the reconstructed coefficient matrix. The performance of the proposed method is evaluated on both synthetic and field microseismic data. The experimental results illustrate that the proposed method can eliminate random noise and preserve signals of interest more effectively.     

A probabilistic performance‐based approach for mitigating the seismic pounding risk between adjacent buildings

Existing design procedures for determining the separation distance between adjacent buildings subjected to seismic pounding risk are based on approximations of the buildings' peak relative displacement. These procedures are characterized by unknown safety levels and thus are not suitable for use within a performance‐based earthquake engineering framework. This paper introduces an innovative reliability‐based methodology for the design of the separation distance between adjacent buildings. The proposed methodology, which is naturally integrated into modern performance‐based design procedures, provides the value of the separation distance corresponding to a target probability of pounding during the design life of the buildings. It recasts the inverse reliability problem of the determination of the design separation distance as a zero‐finding problem and involves the use of analytical techniques in order to evaluate the statistics of the dynamic response of the buildings. Both uncertainty in the seismic intensity and record‐to‐record variability are taken into account. The proposed methodology is applied to several different buildings modeled as linear elastic single‐degree‐of‐freedom (SDOF) and multi‐degree‐of‐freedom (MDOF) systems, as well as SDOF nonlinear hysteretic systems. The design separation distances obtained are compared with the corresponding estimates that are based on several response combination rules suggested in the seismic design codes and in the literature. In contrast to current seismic code design procedures, the newly proposed methodology provides consistent safety levels for different building properties and different seismic hazard conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Estimating the seismic displacement of friction pendulum isolators based on non‐linear response history analysis

A procedure for developing equations that estimate the isolator displacement due to strong ground motion is applied to buildings isolated with the friction pendulum system. The resulting design equations, based on rigorous non‐linear analysis, offer an alternative to the iterative equivalent‐linear methods used by current U.S. building codes. The governing equations of the system are reduced to a form such that the median normalized displacement of the system due to an ensemble of ground motions is found to depend on only the isolation period—a function of the curvature of the isolator—and the friction force at incipient slip normalized by peak ground velocity. The normalization is effective in minimizing the dispersion of the normalized displacement for an ensemble of ground motions, implying that the median normalized displacement is a reliable estimate of response. The design equations reflect the significant (20 to 38%) increase in displacement when the excitation includes two lateral components of ground motion instead of just one component. Equivalent‐linear methods are shown to underestimate by up to 30% the exact median displacement determined by non‐linear response history analysis for one component of ground motion, and building codes include at most a 4.4% increase for a second component. Copyright © 2003 John Wiley & Sons, Ltd.     

Investigations on the influence of pore‐space geometry on concentration patterns and transportation properties of dissolved oxygen in a bioactive sandy sediment by a lattice Boltzmann automaton model

A lattice Boltzmann automaton (LBA) is used as a modelling approach to investigate the influence of pore‐space geometry on intrinsic processes and component distributions in recent tidal sediments. The simulations are performed on real pore‐space structures obtained from scanning electron photomicrographs, which document the mesoscopic geometry of bioactive sandy surface sediments. The discrete transport–reaction model for dissolved oxygen shows that in advective controlled systems oxygen concentration properties can be clearly related to the pore‐space geometry. Variability of measured high‐resolution concentration gradients can therefore can be attributed to the structural heterogeneity of pore‐space geometry. Copyright © 2001 John Wiley & Sons, Ltd.     

A study on the seismic performance of steel‐reinforced concrete frame‐concrete core wall high‐rise mixed structure by large‐scale shaking table tests and numerical simulations

This paper reports a study for the seismic performance of one large‐scaled (1/15) model of 30‐story steel‐reinforced concrete frame‐concrete core wall mixed structure. The study was implemented by both shaking table tests, in which the similarity ratio for lateral and gravitational accelerations was kept to 1:1, and numerical nonlinear dynamic analysis. The test observations presented herein include story displacement, interstory drift, natural vibration periods, and final failure mode. The numerical analysis was performed to simulate the shaking table test procedure, and the numerically obtained responses were verified by the test results. On the basis of the numerical results, the progressions of structural stiffness, base shear, and overturning moment were investigated, and the distributions of base shear and overturning moment between frame and core wall were also discussed. The test demonstrates the seismic performance of the steel‐reinforced concrete frame‐core wall mixed structure and reveals the potential overturning failure mode for high rise structures. The nonlinear analysis results indicate that the peripheral frames could take more shear forces after core wall damaged under severe earthquakes. Copyright © 2013 John Wiley & Sons, Ltd.     

Investigations into the benefits of base isolation for non‐symmetric rigid blocks

In this paper the influence of base isolation on the behaviour of a work of art has been analysed. To make things more realistic, the work of art has been modelled with a non‐symmetrical rigid body, sitting on a base that is connected to a visco‐elastic device, which represents the passive control system. To prevent the breaking of the isolation device, security stops have been introduced to limit the displacement of the oscillating base to a maximum safety value. All analyses have been carried out comparing the behaviour of the non‐isolated and the isolated non‐symmetric rigid body subject to impulsive and seismic excitations. The analysis is particularly focused on the effects of the eccentricity of the rigid body and on the presence of the security stops. Generally, base isolation improves the behaviour of the system while the presence of an eccentricity makes the performance of the system worse with respect to the symmetric rigid body. Moreover the security stops, although they preserve the isolator devices, cause a worsening in the performance of the systems. Copyright © 2008 John Wiley & Sons, Ltd.     

A BME solution of the inverse problem for saturated groundwater flow

In most real-world hydrogeologic situations, natural heterogeneity and measurement errors introduce major sources of uncertainty in the solution of the inverse problem. The Bayesian Maximum Entropy (BME) method of modern geostatistics offers an efficient solution to the inverse problem by first assimilating various physical knowledge bases (hydrologic laws, water table elevation data, uncertain hydraulic resistivity measurements, etc.) and then producing robust estimates of the subsurface variables across space. We present specific methods for implementing the BME conceptual framework to solve an inverse problem involving Darcys law for subsurface flow. We illustrate one of these methods in the case of a synthetic one-dimensional case study concerned with the estimation of hydraulic resistivity conditioned on soft data and hydraulic head measurements. The BME framework processes the physical knowledge contained in Darcys law and generates accurate estimates of hydraulic resistivity across space. The optimal distribution of hard and soft data needed to minimize the associated estimation error at a specified sampling cost is determined. This work was supported by grants from the National Institute of Environmental Health Sciences (Grant no. 5 P42 ES05948 and P30ES10126), the National Aeronautics and Space Administration (Grant no. 60-00RFQ041), the Army Research Office (Grant no. DAAG55-98-1-0289), and the National Science Foundation under Agreement No. DMS-0112069.     

A phenomenological contact‐element model considering slight non‐uniform contact for pounding analysis of highway bridges under seismic excitations

Impact stiffness is an important parameter of the contact‐element models for the analysis and prediction of the pounding responses of highway bridges subjected to seismic excitations. This paper presents a pounding experiment to investigate the inconsistencies between the theoretical and experimental values of the impact stiffness both for the linear impact model and Kelvin impact model presented in literature. The analysis of the impact acceleration and acoustic emission signals indicates that accelerometer performance and the non‐uniform pounding are two important factors that affect the pounding responses. Based on this observation, a phenomenological contact‐element model is proposed based on the actual contact state of highway bridges during the impact. To evaluate the effectiveness of the proposed impact model, a numerical simulation is subsequently conducted. A comparison of the results indicates that the proposed impact model can effectively predict the pounding responses of highway bridges. Copyright © 2015 John Wiley & Sons, Ltd.     

Influence of bed clusters and size gradation on operational time distribution for non‐uniform bed‐load transport

The operational time distribution (OTD) defines the time for bed‐load sediment spent in motion, which is needed to characterize the random nature of sediment transport. This study explores the influence of bed clusters and size gradation on OTD for non‐uniform bed‐loads. First, both static and mobile bed armouring experiments were conducted in laboratorial flumes to monitor the transport of mixed sand/gravel sediments. Only in the mobile armouring experiment did apparent bed clusters develop, because of stable feeding and a longer transport period. Second, a generalized subordinated advection (GSA) model was applied to quantify the observed dynamics of tracer particles. Results show that for the static armour layer (without sediment feed), the best‐fit OTD assigns more weight to the large displacement of small particles, likely because of the size‐selective entrainment process. The capacity coefficient in the GSA model, which affects the width of the OTD, is space dependent only for small particles whose dynamics can be significantly affected by larger particles and whose distribution is more likely to be space dependent in a mixed sand and gravel system. However, the OTD for the mobile armour layer (with sediment recirculation) exhibited longer tails for larger particles. This is because the trailing edge of larger particles is more resistant to erosion, and their leading front may not be easily trapped by self‐organized bed clusters. The strong interaction between particle–bed may cause the capacity coefficient to be space‐dependent for bed‐load transport along mobile armour layers. Therefore, the combined laboratory experiments and stochastic model analysis show that the OTD may be affected more by particle–bed interactions (such as clusters) than by particle–particle interactions (e.g. hiding and exposing), and that the GSA model can quantify mixed‐size sand/gravel transport along river beds within either static or mobile armour layers. Copyright © 2016 John Wiley & Sons, Ltd.     

A new technique for non‐destructive field measurement of rock‐surface strength: an application of the Equotip hardness tester to weathering studies

Tafone‐like depressions have developed on the Aoshima sandstone blocks used for a masonry bridge pier in the coastal spray zone. A thin layer of partial granular disintegration was found on the surface in depressions. To evaluate quantitatively the strength of the thin weathered layer, the hardness was measured at the surface of the sandstone blocks using both an Equotip hardness tester and an L‐type Schmidt hammer. Comparison of the two testing results indicates that the Equotip hardness value is more sensitive in evaluating the strength of a thin layer of weathered surface rock than the Schmidt hardness value. By applying two methods, i.e. both the repeated impact method and the single impact method, the Equotip tester can evaluate the strengths of fresh internal and weathered surficial portions of rocks having a thin weathering layer. Comparison of the two strengths enables evaluation of strength reduction due to weathering. Copyright © 2007 John Wiley & Sons, Ltd.     

Performance‐based grouping methods of bridge classes for regional seismic risk assessment: Application of ANOVA,ANCOVA, and non‐parametric approaches

One of the key tasks to enable a regional risk assessment is to group structures with similar seismic performances and generate fragility curves representative of the grouped structures. The grouping has been traditionally performed based primarily on engineering judgment and prior experience. This paper (i) presents an overview of various statistical techniques such as analysis of variance, analysis of covariance, and Kruskal–Wallis test for grouping the bridges of similar performance; (ii) compares the groupings that emerge from the various grouping techniques; and (iii) identifies the method that has more statistical power in creating bridge sub‐classes of distinct structural performance. The grouping is achieved by comparing the structural responses of bridge classes obtained from the non‐linear time history analysis of bridges. The relative merits of these grouping techniques are discussed with the case study of box‐girder bridges in California. Copyright © 2017 John Wiley & Sons, Ltd.     

A web‐based methodology for the prediction of approximate IDA curves

A web‐based methodology for the prediction of approximate IDA curves, which consists of two independent processes, is proposed. The result of the first process is a response database of the SDOF model, whereas the second process involves the prediction of approximate IDA curves from the response database by using n‐dimensional linear interpolation. Such an approach enables user‐friendly prediction of the seismic response parameters with high accuracy. In order to demonstrate the capabilities of the proposed methodology, a web application for the prediction of the approximate 16th, 50th and 84th fractile responses of an RC structure was developed. For the presented case study, the response database was computed for a set of 30 ground motion records and the discrete values of six structural parameters. Very good agreement between the computed and the approximated IDA curves of the four‐storey RC building was observed. Copyright © 2012 John Wiley & Sons, Ltd.     

A probabilistic framework for estimating the residual drift of idealized SDOF systems of non‐degrading conventional and damped structures

This paper presents a general framework for predicting the residual drift of idealized SDOF systems that can be used to represent non‐degrading structures, including those with supplemental dampers. The framework first uses post‐peak oscillation analysis to predict the maximum ratio of residual displacement to the peak transient displacement in a random sample. Then, residual displacement ratios obtained from nonlinear time‐history analyses using both farfield and near‐fault‐pulse records were examined to identify trends, which were explained using the oscillation mechanics of SDOF systems. It is shown that large errors can result in existing probability models that do not capture the influence of key parameters on the residual displacement. Building on the observations that were made, a general probability distribution for the ratio of residual displacement to the peak transient displacement that more accurately reflects the physical bounds obtained from post‐peak oscillation analysis is proposed for capturing the probabilistic residual displacement response of these systems. The proposed distribution is shown to be more accurate when compared with previously proposed distributions in the literature due to its explicit account of dynamic and damping properties, which have a significant impact on the residual displacement. This study provides a rational basis for further development of a residual drift prediction tool for the performance‐based design and analysis of more complex multi‐degree‐of‐freedom systems.     

A method of calculating the non‐linear seismic response of a building braced with viscoelastic dampers

Buildings are continually subject to dynamic loads, such as wind load, seismic ground motion, and even the load from internal utility machines. The recent trend of constructing more flexible high‐rise buildings underscores the importance of including viscoelastic dampers in building designs. Viscoelastic dampers are used to control the dynamic response of a building. If the seismic design is based only on the linear response spectrum, considerable error may occur when calculating the seismic response of a building; rubber viscoelastic dampers show non‐linear hysteretic damping that is quite different from viscous damping. This study generated a non‐linear response spectrum using a non‐linear oscillator model to simulate a building with viscoelastic dampers installed. The parameters used in the non‐linear damper model were obtained experimentally from dynamic loading tests. The results show that viscoelastic dampers effectively reduce the seismic displacement response of a structure, but transmit more seismic force to the structure, which essentially increases its seismic acceleration response. Copyright © 2003 John Wiley & Sons, Ltd.     

Landform‐oriented flow‐routing algorithm for the dual‐structure loess terrain based on digital elevation models

The loess landform in the Loess Plateau of China is with typical dual structure, namely, the upper smooth positive terrain and the lower cliffy negative terrain (P–N terrain for short). Obvious differences in their morphological feature, geomorphological mechanism, and hydrological process could be found in the both areas. Based on the differences, a flow‐routing algorithm that separately addresses the dual‐structure terrain would be necessary to encompass this spatial variation in their hydrological behaviour. This paper proposes a mixed flow‐routing algorithm to address aforementioned problems. First, the loess landform surface is divided into P–N terrains based on digital elevation models. Then, specific catchment area is calculated with the new algorithm to simulate the water flows in both positive and negative terrain areas. The mixed algorithm consists of the multiple flow‐routing algorithm (multiple‐flow direction) for positive areas and the D8 algorithm for negative areas, respectively. The approach is validated in two typical geomorphologic areas with low hills and dense gullies in the northern Shaanxi Loess Plateau. Four indices are used to examine the results, which show that the new algorithm is more suitable for loess terrain in simulating the spatial distribution of water accumulation, as well as in modeling the flow characteristics of the true surface by considering the morphological structures of the terrain. Copyright © 2013 John Wiley & Sons, Ltd.     

IM‐based and EDP‐based decision models for the verification of the seismic collapse safety of buildings

Decision models for the verification of seismic collapse safety of buildings are introduced. The derivations are based on the concept of the acceptable (target) annual probability of collapse, whereas the decision making involves comparisons between seismic demand and capacity, which is familiar to engineering practitioners. Seismic demand, which corresponds to the design seismic action associated with a selected return period, can be expressed either in terms of an intensity measure (IM) or an engineering demand parameter (EDP). Seismic capacity, on the other hand, is defined by dividing the near‐collapse limit‐state IM or EDP by an appropriate risk‐targeted safety factor (γ _im or γ _edp ), which is the only safety factor used in the proposed decision model. Consequently, the seismic performance assessment of a building should be based on the best possible estimate. For a case study, it is shown that if the target collapse risk is set to 10^?4 (0.5% over a period of 50 years), and if the seismic demand corresponds to a return period of 475 years (10% over a period of 50 years), then it can be demonstrated that γ _im is approximately equal to 2.5 for very stiff buildings, whereas for buildings with long periods the value of γ _im can increase up to a value of approximately 5. The model using γ _edp is equal to that using γ _im only if it can be assumed that displacements, with consideration of nonlinear behavior, are equal to displacements from linear elastic analysis.