Erik H. Vanmarcke

Random fields and stochastic finite elements

Abstract This state of the art paper identifies as the distinguishing feature of stochastic finite element analysis that it involves the discretization of the parameter space of a random field of material properties and / or loads. This discretization implies that the stochastic input consists of a vector of random variables whose covariance matrix depends on the finite element mesh. The paper provides an overview of basic concepts underlying random field theory, describes specific analytical tools to convey first- and second-order information about homogeneous random fields, and surveys available information on the space-time variation of random loads and material properties encountered in structural engineering. Stochastic finite element formulations covering a wide range of applications to both static and dynamic problems in structural engineering are examined, and a parallel approach to stochastic finite difference analysis is outlined.

Risk assessment of hurricane storm surge for New York City

[1] Hurricane storm surge presents a major hazard for the United States. We apply a model‐based risk assessment methodology to investigate hurricane storm surge risk for New York City (NYC). We couple a statistical/deterministic hurricane model with the hydrodynamic model SLOSH (sea, lake, and overland surges from hurricanes) to generate a large number of synthetic surge events; the SLOSH model simulations are compared to advanced circulation model simulations. Statistical analysis is carried out on the empirical data. It is observed that the probability distribution of hurricane surge heights at the Battery, NYC, exhibited a heavy tail, which essentially determines the risk of New York City being struck by a catastrophic coastal flood event. The peaks‐over‐threshold method with the generalized Pareto distribution is applied to estimate the upper tail of the surge heights. The resulting return periods of surge heights are consistent with those of other studies for the New York area. This storm surge risk assessment methodology may be applied to other coastal areas and can be extended to consider the effect of future climate change.

Matrix formulation of reliability analysis and reliability-based design☆

Abstract To further the application of reliability concepts in structural design, considerable improvement is needed in the methods to evaluate structural safety. The exact evaluation of the reliability, or the probability of survival, of structural systems having several statistically inter-dependent failure modes, requires lengthy numerical integration. Commonly used approximations of system reliability are based either on the assumption of probabilistic independence of the mode failure events, or on that of their complete statistical dependence. For large systems, the resulting upper and lower bounds may be widely different, however. In this paper, a matrix formulation of the reliability analysis and reliability-based design of structures is developed. This approach seems necessary if reliability computations are to become practical for full-scale structures. The correlation between failure modes is conservatively accounted for by using a newly developed approximation which incorporates the effect of the dependence between any two modes through the coefficient of correlation between their modal safety margins (i.e. modal resistance minus modal load effect). The paper also outlines a method to design structural systems for minimum weight based on reliability constraint. Its principal feature is that at each stage of the design process a feasible upper bound and an unfeasible lower bound to the minimum weight are generated. One may, at any time, decide to terminate the procedure if these bounds are sufficiently close. Upper and lower bounds can be calculated relatively inexpensively; it involves the selection, from the set of possible failure modes, of a subset of ‘basic’ failure modes. If one selects those modes that actually dominate or govern the design as the basic ones, then close upper and lower bounds will result. Otherwise it is necessary to reassess the decomposition of the modes by choosing a new set of basic failure modes. The entire design procedure can be linded to any existing structural analysis program. The above described method allows safety and performance considerations to enter into design decisions in a quantitative way, and can be used by designers (i) to choose among alternative designs that satisfy all existing code regulations, (ii) to design systems in the absence of formal code regulations, e.g. when new structural systems or materials are introduced, and (iii) to serve as a mechanism for detecting inconsistencies in various existing codes and resolving conflicts between them. Through a feedback process, widespread use of probabilistic design schemes to supplement deterministic code requirements, can lead to relatively rapid improvement of deterministic design codes.

Probabilistic stability analysis of earth slopes

Abstract A method of probabilistic analysis of three-dimensional limit equilibrium stability of long earth slopes is presented and its application to earth embankment design is discussed. The method accounts for the spatial variability of the shear strength. It is in principle capable of accommodating frictional and cohesive components of shear strength as well as a spectrum of drainage conditions. The probabilistic model predicts that slope failure events involving very long or very short widths of the failure zone are highly improbable. The paper evaluates the probability of a sliding failure at a specific location, as well as the risk that a failure will occur anywhere along a slope of given total length.

Methods of stochastic structural dynamics

Abstract A concise review is given of the analytical methods of stochastic structural dynamics which deals with structural systems under time-varying random excitation. Included in the review are both linear and nonlinear structures and both parametric and non-parametric random excitations. Mathematically, parametric excitations appear in the coefficients for the unknowns in the equations of motion, whereas non-parametric excitations appear as inhomogeneous terms on the right hand side. Physically, random parametric excitations represent the variation of structural properties with time; therefore, they can affect the stability of structural response. Approximate methods are described for those cases for which exact solutions are presently not available.

Hurricane Damage and Loss Estimation Using an Integrated Vulnerability Model

An integrated vulnerability model is presented to estimate structural damage and related economic losses in clusters of residential buildings resulting from hurricane winds. The model accounts for the occurrence of a possible “chain reaction” of events involving wind-pressure damage and wind-borne debris damage, amplifying overall losses. Different approximate damage and loss prediction methods are compared, and three numerical examples are provided.

Stochastic finite elements and experimental measurements

Abstract Basic concepts and methods of random field theory, needed to characterize “distributed disordered systems”, are reviewed, extended and applied. Linking stochastic finite element analysis to experimental measurements enables updating of response and performance predictions and optimizing data acquisition. The case studies involve analysis and measurement of seepage through randomly permeable strata below a dam and through the body of an earth dam.

Estimation of lags for a seismograph array: wave propagation and composite correlation

Abstract This article describes a method to estimate the time lags between stations of a dense strong-motion seismograph array and to obtain composite (as opposed to frequency-dependent) spatial correlation functions. The main features of the proposed procedure are the closure property, expressing the need for internal consistency in the pattern of lags, and the use of relative maxima of cross-correlation functions, yielding multiple estimates of each lag and the associated correlation coefficient. Results obtained by processing 12 events recorded by the SMART1 array provide insight into the propagation of seismic waves across a dense-array site, enabling the development of a regression model for the lags. The simplest model assumes plane waves traveling at constant velocity in the epicentral direction, and the lag estimation yields both the local-mean propagation velocity and a set of inferred deviations from this local mean. Results are also presented for the spatial correlation of the horizontal components of the ‘aligned accelerations’ for the 12 SMART1 events, and the decay of composite correlation with distance is tentatively interpreted in terms of the frequency content of the ground motions.

Spatial correlation of earthquake ground motion: non-parametric estimation

Abstract A non-parametric method, called multidimensional correlation mapping (MCM), is used to describe the local spatial correlation of different components of earthquake ground acceleration. The method estimates spatial correlation without presuming homogeneity or isotropy of the phase-aligned local ground motion fields. For selected events recorded by the SMART1 accelerograph array, we obtain contour plots of equal correlation of ground acceleration, with respect to the center of the array. Displacement time-histories are also computed from the accelerograms and the spatial correlation of the displacements is estimated for comparison with that of the accelerations.

Infrastructure Risk Management Processes: Natural, Accidental, and Deliberate Hazards

Prepared by the Risk and Vulnerability Committee of the Council on Disaster Risk Management of ASCE