Numerical simulation of ground flow caused by seismic liquefaction

Flow failure of sandy subsoil induced by seismic liquefaction is known to cause significant damage to structures. It is induced not only by the dynamic forces exerted by seismic acceleration but also by the static gravity force in consequence of the topography of the ground. The ground flow may sometimes continue after the end of the seismic loading and finally the ground is significantly deformed to cause a failure.This paper numerically predicts the magnitude of flow that could occur when soil liquefaction continues for a sufficiently long period. It is considered that liquefied soil behaves like a viscous liquid, and hence, ground flow is governed by the principle of minimum potential energy. In the calculation, liquefied sand is assumed to be a viscous liquid that deforms in undrained conditions with its volume remaining constant. To consider the non-linearity due to large displacement, the updated Lagrangian method is used to solve the equation of motion. The Newmark β method is employed to calculate the time history of the ground motion. Finally, a simulation using this calculation method shows that the proposed method gives reasonable results for the conditions indicated.     

Si diffusion in zircon

Self-diffusion of Si under anhydrous conditions at 1 atm has been measured in natural zircon. The source of diffusant for experiments was a mixture of ZrO₂ and ³⁰Si-enriched SiO₂ in 1:1 molar proportions; experiments were run in crimped Pt capsules in 1-atm furnaces. ³⁰Si profiles were measured with both Rutherford backscattering spectrometry (RBS) and nuclear reaction analysis with the resonant nuclear reaction ³⁰Si(p,γ)³¹P. For Si diffusion normal to c over the temperature range 1,350–1,550°C, we obtain an Arrhenius relation D = 5.8 exp(−702 ± 54 kJ mol⁻¹/RT) m² s⁻¹ for the NRA measurements, which agrees within uncertainty with an Arrhenius relation determined from the RBS measurements [62 exp(−738 ± 61 kJ mol⁻¹/RT) m² s⁻¹]. Diffusion of Si parallel to c appears slightly faster, but agrees within experimental uncertainty at most temperatures with diffusivities for Si normal to c. Diffusion of Si in zircon is similar to that of Ti, but about an order of magnitude faster than diffusion of Hf and two orders of magnitude faster than diffusion of U and Th. Si diffusion is, however, many orders of magnitude slower than oxygen diffusion under both dry and hydrothermal conditions, with the difference increasing with decreasing temperature because of the larger activation energy for Si diffusion. If we consider Hf as a proxy for Zr, given its similar charge and size, we can rank the diffusivities of the major constituents in zircon as follows: D _Zr < D _Si << D _{O, dry} < D _{O, ‘wet’}.     

Effect of spatial variability of cross‐correlated soil properties on bearing capacity of strip footing

Geotechnical engineering problems are characterized by many sources of uncertainty. Some of these sources are connected to the uncertainties of soil properties involved in the analysis. In this paper, a numerical procedure for a probabilistic analysis that considers the spatial variability of cross‐correlated soil properties is presented and applied to study the bearing capacity of spatially random soil with different autocorrelation distances in the vertical and horizontal directions. The approach integrates a commercial finite difference method and random field theory into the framework of a probabilistic analysis. Two‐dimensional cross‐correlated non‐Gaussian random fields are generated based on a Karhunen–Loève expansion in a manner consistent with a specified marginal distribution function, an autocorrelation function, and cross‐correlation coefficients. A Monte Carlo simulation is then used to determine the statistical response based on the random fields. A series of analyses was performed to study the effects of uncertainty due to the spatial heterogeneity on the bearing capacity of a rough strip footing. The simulations provide insight into the application of uncertainty treatment to geotechnical problems and show the importance of the spatial variability of soil properties with regard to the outcome of a probabilistic assessment. Copyright © 2009 John Wiley & Sons, Ltd.     

A stability analysis of a conduit flow model for lava dome eruptions

Periodic variations in magma discharge rate and ground deformation have been commonly observed during lava dome eruptions. We performed a stability analysis of a conduit flow model by Barmin et al. [Barmin, A., Melnik, O., Sparks, R.S.J., 2002. Periodic behavior in lava dome eruptions. Earth and Planetary Science Letters 199 (1-2), 173–184], in which the periodic variations in magma flow rate and chamber pressure are reproduced as a result of the temporal and spatial changes of the magma viscosity controlled by the kinetics of crystallization. The model is reduced to a dynamical system where the time derivatives of the magma flow rate (dQ/dt) and the chamber pressure (dP/dt) are functions of Q and P evaluated at a shifted time t − t_?. Here, the time delay t_? represents the time for the viscosity of fluid particle to increase in a conduit. The dynamical system with time delay is approximated by a simple two-dimensional dynamical system of Q and P where t_? is given as a parameter. The results of our linear stability analyses for these dynamical systems indicate that the transition from steady to periodic flow depends on nonlinearities in the steady state relation between Q and P. The steady state relation shows a sigmoidal curve in Q − P phase plane; its slope has negative values at intermediate flow rates. The steady state solutions become unstable, and hence P and Q oscillate periodically, when the negative slope of the steady state relation ([dP/dQ]_S) exceeds a critical value; that is [dP/dQ]_S < − t_?γ/(2V_ch), where V_ch is the chamber volume and γ is an elastic constant which is related to the rigidity of chamber wall. We also found that the period and the pattern of oscillation of the conduit flow primarily depend on a quantity defined by LV_ch/r⁴, where L is the conduit length and r is the conduit radius.     

Correlation study between ground motion intensity measure parameters and deformation demands for bilinear SDOF systems

The correlation between ground motion intensity measures （IM） and single-degree-of-freedom （SDOF） deformation demands is described in this study. Peak ground acceleration （APG）, peak ground velocity （VPG）, peak ground displacement （DPG）, spectral acceleration at the first-mode period of vibration [As（T1）] and ratio of VPG to APG are used as IM parameters, and the correlation is characterized by correlation coefficients p. The numerical results obtained by nonlinear dynamic analyses have shown good correlation between As（T1） or VPG and deformation demands. Furthermore, the effect of As（T1） and VPG as IM on the dispersion of the mean value of deformation demands is also investigated for SDOF systems with three different periods T=0.3 s, 1.0 s, 3.0 s respectively.     

历史文献中气候信息的评价

本文对我国史料中所载气候信息进行了评价。结论是:①对于史料所载的某一气候事件,我们将其状态分辨取越细,所获取的信息越少;②在分析过程中,对误差要求低些,所获取的信息反而高些;③就已记录的气候事件而言,官方组织的记载所提供的气候信息最多,私人笔札次之,方志类书最次。     

Uncertainty assessment for watershed water quality modeling: A Probabilistic Collocation Method based approach

Watershed water quality models are increasingly used in management. However, simulations by such complex models often involve significant uncertainty, especially those for non-conventional pollutants which are often poorly monitored. This study first proposed an integrated framework for watershed water quality modeling. Within this framework, Probabilistic Collocation Method (PCM) was then applied to a WARMF model of diazinon pollution to assess the modeling uncertainty. Based on PCM, a global sensitivity analysis method named PCM-VD (VD stands for variance decomposition) was also developed, which quantifies variance contribution of all uncertain parameters. The study results validated the applicability of PCM and PCM-VD to the WARMF model. The PCM-based approach is much more efficient, regarding computational time, than conventional Monte Carlo methods. It has also been demonstrated that analysis using the PCM-based approach could provide insights into data collection, model structure improvement and management practices. It was concluded that the PCM-based approach could play an important role in watershed water quality modeling, as an alternative to conventional Monte Carlo methods to account for parametric uncertainty and uncertainty propagation.     

Geostatistical Simulation of Regionalized Pore-Size Distributions Using Min/Max Autocorrelation Factors

In many fields of the Earth Sciences, one is interested in the distribution of particle or void sizes within samples. Like many other geological attributes, size distributions exhibit spatial variability, and it is convenient to view them within a geostatistical framework, as regionalized functions or curves. Since they rarely conform to simple parametric models, size distributions are best characterized using their raw spectrum as determined experimentally in the form of a series of abundance measures corresponding to a series of discrete size classes. However, the number of classes may be large and the class abundances may be highly cross-correlated. In order to model the spatial variations of discretized size distributions using current geostatistical simulation methods, it is necessary to reduce the number of variables considered and to render them uncorrelated among one another. This is achieved using a principal components-based approach known as Min/Max Autocorrelation Factors (MAF). For a two-structure linear model of coregionalization, the approach has the attractive feature of producing orthogonal factors ranked in order of increasing spatial correlation. Factors consisting largely of noise and exhibiting pure nugget–effect correlation structures are isolated in the lower rankings, and these need not be simulated. The factors to be simulated are those capturing most of the spatial correlation in the data, and they are isolated in the highest rankings. Following a review of MAF theory, the approach is applied to the modeling of pore-size distributions in partially welded tuff. Results of the case study confirm the usefulness of the MAF approach for the simulation of large numbers of coregionalized variables.     

General elastic analysis of piles and pile groups

This paper describes the development of a boundary element analysis for the behaviour of single piles and pile groups subjected to general three‐dimensional loading and to vertical and lateral ground movements. Each pile is discretized into a series of cylindrical elements, each of which is divided into several sub‐elements. Compatibility of vertical, lateral and rotational movements is imposed in order to obtain the necessary equations for the pile response. Via hierarchical structures, 12 non‐zero sub‐matrices in a global matrix are derived for the basic influence factors. Solutions are presented for a series of cases involving single piles and pile groups. In each case, the solutions are compared with those from more simplified existing pile analyses such as those developed by Randolph and by Poulos. It is shown that for direct loading effects (e.g. the settlement of piles due to vertical loading), the simplified analyses work well. However, for ‘off‐line’ response (such as the lateral movement due to vertical loading) the differences are greater, and it is believed that the present analysis gives more reliable estimates. Copyright © 2000 John Wiley & Sons, Ltd.     

Approximate incremental dynamic analysis using the modal pushover analysis procedure

Incremental dynamic analysis (IDA)—a procedure developed for accurate estimation of seismic demand and capacity of structures—requires non‐linear response history analysis of the structure for an ensemble of ground motions, each scaled to many intensity levels, selected to cover the entire range of structural response—all the way from elastic behaviour to global dynamic instability. Recognizing that IDA of practical structures is computationally extremely demanding, an approximate procedure based on the modal pushover analysis procedure is developed. Presented are the IDA curves and limit state capacities for the SAC‐Los Angeles 3‐, 9‐, and 20‐storey buildings computed by the exact and approximate procedures for an ensemble of 20 ground motions. These results demonstrate that the MPA‐based approximate procedure reduces the computational effort by a factor of 30 (for the 9‐storey building), at the same time providing results to a useful degree of accuracy over the entire range of responses—all the way from elastic behaviour to global dynamic instability—provided a proper hysteretic model is selected for modal SDF systems. The accuracy of the approximate procedure does not deteriorate for 9‐ and 20‐storey buildings, although their dynamics is more complex, involving several ‘modes’ of vibration. For all three buildings, the accuracy of the MPA‐based approximate procedure is also satisfactory for estimating the structural capacities for the limit states of immediate occupancy, collapse prevention, and global dynamic instability. Copyright © 2006 John Wiley & Sons, Ltd.