Influence of Structural Non-Stationarity of Surface Roughness on Morphological Characterization and Mechanical Deformation of Rock Joints

Summary Structural non-stationarity of surface roughness affects accurate morphological characterization as well as mechanical behaviour of rock joints at the laboratory scale using samples with a size below the stationarity threshold. In this paper, the effect of structural non-stationarity of surface roughness is investigated by studying the scale dependence of surface roughness and mechanical behaviour of rock joints. The results show that the structural non-stationarity mainly affects the accurate characterization of the surface roughness of the fracture samples. It also controls the amount and location of the contact areas during shear tests, which in turn affects the mechanical properties and asperity degradation of the samples. It is concluded that for accurate determination of the morphological and mechanical properties of rock joints at laboratory and field scales, samples with size equal to or larger than the stationarity threshold are required. Author’s address: Nader Fardin, Rock Mechanics Group, Department of Mining Engineering, Faculty of Engineering, University of Tehran, P.O. Box: 11365/4563, Tehran, Iran     

Change of multifractal thermal characteristics in the western Philippine sea upper layer during internal wave-soliton propagation

The upper layer (above 140 m depth) temperature in the western Philippine Sea near Taiwan was sampled using a coastal monitoring buoy (CMB) with 15 attached thermistors during July 28–August 7, 2005. The data were collected every 10 min at 1, 3, 5, 10, 15, and 20 m using the CMB sensors, and every 15 sec at 15 different depths between 25 m and 140 m. Internal waves and solitons were identified from the time-depth plot of the temperature field. Without the internal waves and solitons, the power spectra, structure functions, and singular measures (representing the intermittency) of temperature field satisfy the power law with multi-scale characteristics at all depths. The internal waves do not change the basic characteristics of the multifractal structure. However, the internal solitons change the power exponent of the power spectra drastically, especially in the low wave number domain; they also break down the power law of the structure function and increase the intermittency parameter. The physical mechanisms causing these different effects need to be explored further.     

Statistical tests for regional seismic phase characterizations

In seismic analysis some assumptions are often made aboutthe data, e.g. stationarity and Gaussianity. This is not obvious for all realseismic data. Here, we use statistical tests for characterization of regionalseismic data. We apply tests for stationarity, symmetry, linearity, andtime-reversibility. In the analysis we use twelve regional seismic events inFennoscandia recorded with the seismic small-aperture arrays NORESS,ARCESS and FINESA at hypocentral distances in the range from 160 to1580 km. For the tests we use the regional phases Pn, secondary P, Sn and Lg-phases and the preceding noise. Two of the eventsare explosions, two are rockbursts and eight are earthquakes. Theperformance and possibilities of using statistical tests based on bispectra, asa complementary tool for conventional analysis of seismic phases isdemonstrated. The preceding noise recorded before the first onset of theP-wave for the twelve events is tested to be spatially stationarybetween each channel within each array and temporal stationary in 21consecutive time windows of 3.2 sec each. Also, the preceding noise issymmetric and linear. The seismic phases defined by the symmetry test asnon-Gaussian (not symmetric) are all linear. This means a linear model canbe used to characterize both the noise and the phases. The first P-phase for the two explosions is characterized as non-Gaussian at thethree arrays. For all 36 possibly first P-phase arrivals at the three arraystations, 23 are non-Gaussian. The second P-phase is non-Gaussian at13 of 36 data records, the S-phase at eleven of 36 and the Lg-phase at nine of 36. For all the four phases more than 32 of possible36 are time-reversible.     

Spatial aggregation of time‐variant stream water ages in urbanizing catchments

We calibrated an integrated flow–tracer model to simulate spatially distributed isotope time series in stream water in a 7.9‐km² catchment with an urban area of 13%. The model used flux tracking to estimate the time‐varying age of stream water at the outlet and both urbanized (1.7 km²) and non‐urban (4.5 km²) sub‐catchments over a 2.5‐year period. This included extended wet and dry spells where precipitation equated to >10‐year return periods. Modelling indicated that stream water draining the most urbanized tributary was youngest with a mean transit time (MTT) of 171 days compared with 456 days in the non‐urban tributary. For the larger catchment, the MTT was 280 days. Here, the response of urban contributing areas dominated smaller and more moderate runoff events, but rural contributions dominated during the wettest periods, giving a bi‐modal distribution of water ages. Whilst the approach needs refining for sub‐daily time steps, it provides a basis for projecting the effects of urbanization on stream water transit times and their spatial aggregation. This offers a novel approach for understanding the cumulative impacts of urbanization on stream water quantity and quality, which can contribute to more sustainable management. Copyright © 2015 John Wiley & Sons, Ltd.     

Rainfall flood hazard at nuclear power plants in India

Flood hazard evaluation is an important input for Nuclear Power Plants external events safety studies. In the present study, flood hazard at various nuclear sites in India due to rainfall has been evaluated. Hazard estimation is a statistical procedure by which rainfall intensity versus occurrence frequency is estimated from historical records of rainfall data and extrapolated with asymptotic extreme value distribution. Rainfall data needed for flood hazard assessment are daily annual maximum rainfall (24?h data). The observed data points have been fitted using Gumbel, power law and exponential distribution, and return period has been estimated. To study the stationarity of rainfall data, a moving window estimate of the parameters has been performed. The rainfall pattern is stationary in both coastal and inland regions over the period of observation. The coastal regions show intense rainfall and higher variability than inland regions. Based on the plant layout, catchment area and drainage capacity, the prototype fast breeder reactor (PFBR) site is unlikely to be flooded.     

Fitting variogram models by weighted least squares

The method of weighted least squares is shown to be an appropriate way of fitting variogram models. The weighting scheme automatically gives most weight to early lags and down-weights those lags with a small number of pairs. Although weights are derived assuming the data are Gaussian (normal), they are shown to be still appropriate in the setting where data are a (smooth) transform of the Gaussian case. The method of (iterated) generalized least squares, which takes into account correlation between variogram estimators at different lags, offer more statistical efficiency at the price of more complexity. Weighted least squares for the robust estimator, based on square root differences, is less of a compromise.     

Non‐stationary seismic response of tanks with soil interaction by wavelets

A wavelet‐based random vibration theory has been developed for the non‐stationary seismic response of liquid storage tanks including soil interaction. The ground motion process has been characterized via estimates of statistical functionals of wavelet coefficients obtained from a single time history of ground accelerations. The tank–liquid–soil system has been modelled as a two‐degree‐of‐freedom (2‐DOF) system. The wavelet domain equations have been formulated and the wavelet coefficients of the required response state are obtained by solving two linear simultaneous algebraic equations. The explicit expression for the instantaneous power spectral density function (PSDF) in terms of the functionals of the input wavelet coefficients has been obtained. The moments of this PSDF are used to estimate the expected pseudo‐spectral acceleration (PSA) response of the tank. Parametric variations are carried out to study the effects of tank height, foundation natural frequency, shear wave velocity of soil and ratio of the mass of tank (including liquid) to the mass of foundation on the PSA responses of tanks. Copyright © 2001 John Wiley & Sons, Ltd.     

Crytic period analysis model of hydrological process and its application

It is difficult to analyse the crytic period of the hydrological process, because hydrological time series is probably characterized by heteroscedasticity. To find out the crytic period, a model is constructed as follows: (1) after using zero‐mean transformation for the data, to do Augmented Dickey–Fuller stationary test for the sequence, to build the corresponding AR(p) model and then to do ARCH effects test and white noise test for residual series; (2) for those time series that cannot pass through ARCH test, using logarithm transformation to reduce the heteroscedasticity, and then to redo step (1) until they pass through ARCH test and stationary test; (3) using periodogram analysis to determine all the possible the prime periods and further to put forward three kinds of tests to determine significance level of those prime periods. As examples, the hydrological processes of streamflow from 1784 to 1997 for the gauging stations of Alaer and Xinquman along Tarim River are analysed. After reducing their heteroscedasticity, AR(4) and AR(2) models are developed, respectively. Our results show that the streamflows from the two gauging stations have the same cryptic period of 42·7 years. Furthermore, the reliability for the crytic period model is testified by variance analysis, which shows that the crytic period model is useful and reliable. Copyright © 2009 John Wiley & Sons, Ltd.     

Analysis of stochastic characteristics of the Benue River flow process

Stochastic characteristics of the Benue River streamflow process are examined under conditions of data austerity. The streamflow process is investigated for trend, non-stationarity and seasonality for a time period of 26 years. Results of trend analyses with Mann-Kendall test show that there is no trend in the annual mean discharges. Monthly flow series examined with seasonal Kendall test indicate the presence of positive change in the trend for some months, especially the months of August, January, and February. For the stationarity test, daily and monthly flow series appear to be stationary whereas at 1%, 5%, and 10% significant levels, the stationarity alternative hypothesis is rejected for the annual flow series. Though monthly flow appears to be stationary going by this test, because of high seasonality, it could be said to exhibit periodic stationarity based on the seasonality analysis. The following conclusions are drawn： （1） There is seasonality in both the mean and variance with unimodal distribution. （2） Days with high mean also have high variance. （3） Skewness coefficients for the months within the dry season period are greater than those of the wet season period, and seasonal autocorrelations for streamflow during dry season are generally larger than those of the wet season. Precisely, they are significantly different for most of the months. （4） The autocorrelation functions estimated ＂over time＂ are greater in the absolute value for data that have not been deseasonalised but were initially normalised by logarithmic transformation only, while autocorrelation functions for i = 1, 2 365 estimated ＂over realisations＂ have their coefficients significantly different from other coefficients.     

The effect of El Niño Southern Oscillation cycles on the decadal scale suspended sediment behavior of a coastal dry‐summer subtropical catchment

Rivers display temporal dependence in suspended sediment–water discharge relationships. Although most work has focused on multi‐decadal trends, river sediment behavior often displays sub‐decadal scale fluctuations that have received little attention. The objectives of this study were to identify inter‐annual to decadal scale fluctuations in the suspended sediment–discharge relationship of a dry‐summer subtropical river, infer the mechanisms behind these fluctuations, and examine the role of El Niño Southern Oscillation climate cycles. The Salinas River (California) is a moderate sized (11 000 km²), coastal dry‐summer subtropical catchment with a mean discharge (Q_mean) of 11.6 m³ s^?1. This watershed is located at the northern most extent of the Pacific coastal North America region that experiences increased storm frequency during El Niño years. Event to inter‐annual scale suspended sediment behavior in this system was known to be influenced by antecedent hydrologic conditions, whereby previous hydrologic activity regulates the suspended sediment concentration–water discharge relationship. Fine and sand suspended sediment in the lower Salinas River exhibited persistent, decadal scale periods of positive and negative discharge corrected concentrations. The decadal scale variability in suspended sediment behavior was influenced by inter‐annual to decadal scale fluctuations in hydrologic characteristics, including: elapsed time since small (~0.1 × Q_mean), and moderate (~10 × Q_mean) threshold discharge values, the number of preceding days that low/no flow occurred, and annual water yield. El Niño climatic activity was found to have little effect on decadal‐scale fluctuations in the fine suspended sediment–discharge relationship due to low or no effect on the frequency of moderate to low discharge magnitudes, annual precipitation, and water yield. However, sand concentrations generally increased in El Niño years due to the increased frequency of moderate to high magnitude discharge events, which generally increase sand supply. Copyright © 2014 John Wiley & Sons, Ltd.