Numerical Simulations of Soil Liquefaction using Stochastic Input Parameters

The influence of spatial variability of soil properties on the results of numerical simulations of dynamically induced pore water pressure is addressed. Random media of NSPT values are generated based on in situ test results. The soil geomechanical properties are evaluated at each location, function of the NSPT values, and finite element simulations of the behavior of a horizontally layered soil subjected to seismic loading are performed. The influence of : (1) assumed distribution of the underlying random variable, (2) scale of fluctuation, and (3) finite element mesh size are discussed in terms of predicted liquefaction index and excess pore pressure build-up

Variability and uncertainty in empirical ground-motion prediction for probabilistic hazard and risk analyses

© The Author(s) 2015.The terms aleatory variability and epistemic uncertainty mean different things to people who routinely use them within the fields of seismic hazard and risk analysis. This state is not helped by the repetition of loosely framed generic definitions that actually inaccurate. The present paper takes a closer look at the components of total uncertainty that contribute to ground-motion modelling in hazard and risk applications. The sources and nature of uncertainty are discussed and it is shown that the common approach to deciding what should be included within hazard and risk integrals and what should be pushed into logic tree formulations warrants reconsideration. In addition, it is shown that current approaches to the generation of random fields of ground motions for spatial risk analyses are incorrect and a more appropriate framework is presented

Bearing Capacity of Spatially Random Cohesive Soil Using Numerical Limit Analyses

This paper describes a probabilistic study of the two dimensional bearing capacity of a vertically loaded strip footing on spatially random, cohesive soil using Numerical Limit Analyses (NLA‐CD). The analyses uses a Cholesky Decomposition (CD) technique with mid‐point discretization to represent the spatial variation in undrained shear strength within finite element meshes for both upper and lower bound analyses, and assumes an isotropic correlation length. Monte Carlo simulations are then used to interpret the bearing capacity for selected ranges of the coefficient of variation in undrained shear strength and the ratio of correlation length to footing width. The results are compared directly with data from a very similar study by Griffiths et al. in which bearing capacity realizations were computed using a method of Local Average Subdivision (LAS) in a conventional displacement‐based Finite Element Method (FEM‐LAS). These comparisons show the same qualitative features, but suggest that the published FEM calculations tend to overestimate the probability of failure at large correlation lengths. The NLA method offers a more convenient and computationally efficient approach for evaluating effects of variability in soil strength properties in geotechnical stability calculations

On the Role of Global Warming on the Statistics of Record-Breaking Temperatures

We theoretically study long-term trends in the statistics of record-breaking daily temperatures and validate these predictions using Monte Carlo simulations and data from the city of Philadelphia, for which 126 years of daily temperature data is available. Using extreme statistics, we derive the number and the magnitude of record temperature events, based on the observed Gaussian daily temperatures distribution in Philadelphia, as a function of the number of elapsed years from the start of the data. We further consider the case of global warming, where the mean temperature systematically increases with time. We argue that the current warming rate is insufficient to measurably influence the frequency of record temperature events over the time range of the observations, a conclusion that is supported by numerical simulations and the Philadelphia temperature data.Comment: 11 pages, 6 figures, 2-column revtex4 format. For submission to Journal of Climate. Revised version has some new results and some errors corrected. Reformatted for Journal of Climate. Second revision has an added reference. In the third revision one sentence that explains the simulations is reworded for clarity. New revision 10/3/06 has considerable additions and new results. Revision on 11/8/06 contains a number of minor corrections and is the version that will appear in Phys. Rev.

Chord distribution functions of three-dimensional random media: Approximate first-passage times of Gaussian processes

The main result of this paper is a semi-analytic approximation for the chord distribution functions of three-dimensional models of microstructure derived from Gaussian random fields. In the simplest case the chord functions are equivalent to a standard first-passage time problem, i.e., the probability density governing the time taken by a Gaussian random process to first exceed a threshold. We obtain an approximation based on the assumption that successive chords are independent. The result is a generalization of the independent interval approximation recently used to determine the exponent of persistence time decay in coarsening. The approximation is easily extended to more general models based on the intersection and union sets of models generated from the iso-surfaces of random fields. The chord distribution functions play an important role in the characterization of random composite and porous materials. Our results are compared with experimental data obtained from a three-dimensional image of a porous Fontainebleau sandstone and a two-dimensional image of a tungsten-silver composite alloy.Comment: 12 pages, 11 figures. Submitted to Phys. Rev.

Nonstationary random acoustic and electromagnetic fields as wave diffusion processes

We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as an ideal incoherent and statistically homogeneous isotropic random scalar or vector field, respectively. A physical model is constructed showing that the field dynamics can be characterized as a generalized diffusion process. The Langevin--It\^{o} and Fokker--Planck equations are derived and their associated statistics and distributions for the complex analytic field, its magnitude and energy density are computed. The energy diffusion parameter is found to be proportional to the square of the ratio of the standard deviation of the source field to the characteristic time constant of the dynamic process, but is independent of the initial energy density, to first order. The energy drift vanishes in the asymptotic limit. The time-energy probability distribution is in general not separable, as a result of nonstationarity. A general solution of the Fokker--Planck equation is obtained in integral form, together with explicit closed-form solutions for several asymptotic cases. The findings extend known results on statistics and distributions of quasi-stationary ideal random fields (pure diffusions), which are retrieved as special cases.Comment: 54 pages, 8 figures, to appear in J. Phys. A: Math. Theo

Synthesis of accelerograms compatible with the Chinese GB 50011-2001 design spectrum via harmonic wavelets: artificial and historic records

A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum (EPS). Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average (ARMA) filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals’ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice