Preliminary Seismic Hazard Analyses for the Ugandan Region

Uganda is situated between the two seismically active branches of the East African Rift Valley System, which are characterized by high levels of seismicity. A probabilistic approach has been used to assess the seismic hazard for Uganda and the surrounding areas. A probabilistic seismic hazard analysis requires the availability of an earthquake catalog, relevant ground motion prediction equations, and an outline of how the hazard calculations will be conducted. Using online sources, an earthquake catalog for Uganda and the immediate areas around Uganda was compiled spanning 108 years, from 1912 to 2020. This catalog was homogenized to moment magnitude to match with the selected ground motion prediction equations from Toro and Idriss. A logic tree accounting for the two ground motion prediction equations and dividing the study region into four seismic zones was used for calculating the seismic hazard. As an example, the seismic hazard results at two sites close to each other showed how different seismic hazards can be. Results from the probabilistic seismic hazard analyses was expressed through seismic hazard maps for peak ground acceleration at 10% probability of exceedance in 5, 10, 20, 50, 100 and 500 years, corresponding to return periods of 50, 100, 200, 500, 1000 and 5000 years, respectively. The seismic hazard map for 10% probability of exceedance in 5 years calculated PGAs from 0.02 to 0.10 g and 0.10 to 0.27 g outside of and within the western branch of the East African Rift Valley System, respectively. The estimated PGAs from previous studies at a similar probability of exceedance level are within the range of these findings, although the ranges calculated herein are wider.

Updated Probabilistic Seismic Hazard Assessment of Pakistan

Probabilistic seismic hazard assessment of Pakistan is carried out to compute hazard in terms of peak ground acceleration (PGA) and spectral acceleration (SA) for 975 and 2475 years return periods. A composite earthquake catalogue consisting of 32,700 events has been compiled having a magnitude range of Mw 4.0-8.2 in this study and used in the analysis to make computations at a rectangular grid of 5 km in the OpenQuake plateform. Ground motion values have been obtained for flat rock reference seismic site conditions with shear wave velocity of 760 m/s. The epistemic uncertainties inherent in ground motion prediction equations and maximum magnitude potential of seismic sources are taken into account through logic tree. Ground motion prediction equations are assigned equal weights in the logic tree while different various weight are assigned to the maximum magnitude potential models. Results of the study are expressed as ground motion contour maps, mean uniform hazard spectra for important cities in Pakistan. PGA ranges from 0.16 to 0.54g for 10 % of probability of exceedance, 0.23 to 0.72g of probability of exceedance 0.32 to 1.02 g for 2 % of probability of exceedance in 50 years. Spectral acceleration at 0.2 s range from 0.67 to 2.19g for 2% chance of exceedance in 50 years, respectively. While spectral acceleration at 1.0 s values range from 0.09 to 0.52g 2% chance of exceedance in 50 years. Comparison of results of this study with other well regarded references of suggest that results of the study are rational and are reliable.

ON THE APPLICATION OF THE EXTREME VALUE THEORY IN SHIP’S STRENGTH CALCULATIONS

A procedure is proposed for application of the extreme value theory (EVT) approach considering not only the maximal value of the corresponding random variable but also its probability of exceedance. It substantially reduces the probability of exceedance of any given limit value used in the case when traditional EVT is applied. Examples are provided to illustrate its application when records of the random process are available.

Damage Equivalent Load Synthesis and Stochastic Extrapolation for Fatigue Life Validation

Present verification of the fatigue life margins on wind turbine structures utilizes damage equivalent load (DEL) computations over limited time duration. In this article, a procedure to determine long term fatigue damage and remaining life is presented as a combination of stochastic extrapolation of the 10-minute DEL to determine its probability of exceedance and through computationally fast synthesis of DELs using level-crossings of a Gaussian process. Both the synthesis of DELs and long-term stochastic extrapolation are validated using measured loads from a wind farm. The extrapolation for the blade root flap and tower base fore-aft damage equivalent moment is presented using a three-parameter Weibull distribution, whereby the long term damage equivalent load levels are forecast for both simulated and measured values. The damage equivalent load magnitude at a selected target probability of exceedance provides an indicator of the integrity of the structure for the next year. The extrapolated damage equivalent load over a year is validated using measured multi-year damage equivalent loads from a turbine in the Lillgrund wind farm, which is subject to wakes. The simulation of damage equivalent loads using the method of level crossings of a Gaussian process is shown to be able to reconstruct the damage equivalent load for both blade root and tower base moments. The prediction of the tower base fore-aft DEL is demonstrated to be feasible when using the Vanmarcke correction for very-narrow band processes. The combined method of fast damage equivalent load computations and stochastic extrapolation to the next year, allows a quick and accurate forecasting of structural integrity of operational wind turbines.

A Probabilistic Model for Maximum Rainfall Frequency Analysis

As determining the probability of the exceedance of maximum precipitation over a specified duration is critical to hydrotechnical design, particularly in the context of climate change, a model was developed to perform a frequency analysis of maximum precipitation of a specified duration. The PMAXΤP model (Precipitation MAXimum Time (duration) Probability) harbors a pair of computational modules fulfilling different roles: (i) statistical analysis of precipitation series, and (ii) estimation of maximum precipitation for a specified duration and its probability of exceedance. The input data consist of homogeneous 30-element series of precipitation values for 16 different durations: 5, 10, 15, 30, 45, 60, 90, 120, 180, 360, 720, 1080, 1440, 2160, 2880, and 4320 min, obtained through Annual Maximum Precipitation (AMP) and Peaks-Over-Threshold (POT) approaches. The statistical analysis of the precipitation series includes: (i) detecting outliers using the Grubbs–Beck test; (ii) checking for the random variable’s independence using the Wald–Wolfowitz test and the Anderson serial correlation coefficient test; (iii) checking the random variable’s stationarity using nonparametric tests, e.g., the Kruskal–Wallis test and Spearman rank correlation coefficient test for trends of mean and variance; (iv) identifying the trend of the random variables using correlation and regression analysis, including an evaluation of the form of the trend function; and (v) checking for the internal correlation of the random variables using the Anderson autocorrelation coefficient test. To estimate maximum precipitations of a specified duration and with a specified probability of exceedance, three-parameter theoretical probability distributions were used: a shifted gamma distribution (Pearson type III), a log-normal distribution, a Weibull distribution (Fisher–Tippett type III), a log-gamma distribution, as well as a two-parameter Gumbel distribution. The best distribution was selected by: (i) maximum likelihood estimation of parameters; (ii) tests of the hypothesis of goodness of fit of the theoretical probability distribution function with the empirical distribution using Pearson’s χ2 test; (iii) selection of the best-fitting function within each type according to the criterion of minimum Kolmogorov distance; (iv) selection of the most credible probability distribution function from the set of various types of best-fitting functions according to the Akaike information criterion; and (v) verification of the most credible function using single-dimensional tests of goodness of fit: the Kolmogorov–Smirnov test, the Anderson–Darling test, the Liao–Shimokawa test, and Kuiper’s test. The PMAXTP model was tested on data from two meteorological stations in northern Poland (Chojnice and Bialystok) drawn from a digital database of high-resolution precipitation records for the period of 1986 to 2015, available for 100 stations in Poland (i.e., the Polish Atlas of Rainfall Intensities (PANDa)). Values of maximum precipitation with a specified probability of exceedance obtained from the PMAXTP model were compared with values obtained from the probabilistic Bogdanowicz–Stachý model. The comparative analysis was based on the standard error of fit, graphs of the density function for the probability of exceedance, and estimated quantile errors. The errors of fit were lower for the PMAXTP compared to the Bogdanowicz–Stachý model. For both stations, the smallest errors were obtained for the quantiles determined on the basis of maximum precipitation POT using PMAXTP.

Flood-risk vulnerabilities of sanitation facilities in urban informal settlements: Lessons from Kisumu City, Kenya

Flood disasters have increased in frequency and severity over the recent decades causing untold destruction to vulnerable physical infrastructure such as sanitation facilities. Factors including construction quality, design, siting, and users’ behaviour further exacerbate the vulnerability of facilities. Despite this reality, very little has been done to document the extent of flood risk facing such facilities in the pro-poor urban informal settlements in developing countries. This study assessed the flood risks of vulnerable sanitation facilities in the urban informal settlements of Kisumu city, Kenya. The methodology involved assessment of sanitation facilities’ flood vulnerabilities and assessment of flood risk models. Flood risk was assessed by estimating runoff from yearly rainfall totals and also by calculating storm return period and probability of exceedance. Vulnerability assessment for each sanitation facility was done by scoring against flood risk indicators ordered by weighted rank. The study observed that majority sanitation facilities in the urban informal settlements were considered “highly vulnerable” (57%). Flood risk analysis predicted growing vulnerability due to shorter storm return periods, especially under the RCP 8.5 scenario. It was established that over 20% of all rainfall events in the 50-year timeline had a higher than 80% probability of exceedance rainfall, signifying higher storm risks. Additionally, the study showed that between 44% of rainfall received in the study area could translate to runoff, in the near future, further compounding flood risk predictions. With key informal settlements such as Nyalenda and Manyatta facing stronger future flood risks, general public health may be threatened, leading to increased social and economic instability on families and households. The study recommends adherence to improved toilet standards of construction and toilet-raising as methods of improving flood risk resilience and adaptation.

Exceedance and Return Period of High Temperature in the African Region

Several studies have indicated that the social, economic and other impacts of global warming can be linked with changes in the frequency and intensity of extreme weather/climate events. Developing countries, particularly in the African region, are highly affected by extreme events such as high temperature, usually followed/accompanied by drought. Therefore, studying the probability of occurrence and return period of extreme temperatures, and possible change in these parameters, is of high importance for climate-related policy making and preparedness works in the region. This study aims to address these issues by assessing probability of exceedance and return period of extremes in annual maximum and annual mean temperatures. The analyses of historical data in this study showed that extremes in both annual maximum and mean temperature are highly likely to be exceeded more often in the future compared to the past. For the extreme event marker (threshold) defined in this study, probability of 3 exceedances in the following 19 years (for instance), at any gridpoint, is estimated to be at least 10% for extremes in annual maxima and at least 15% for those in annual means. Most places in the region, however, have much higher (up to 20%) probability of exceedance. The estimated probability of exceedance has shown increasing tendency with time. Return period, based on the most recent data, of extremes in annual maximum temperature is found to be less than 6.5 years at about 48% of the gridpoints in the region. Similarly, return period of extremes in annual mean temperature is estimated to be less than 5.5 years at about 82% of places in the region. These estimates have also shown a strong tendency of getting shorter as time goes on. On average, extremes in annual mean temperature were found to have shorter return periods (4–7 years) compared to those in annual maximum temperature (6–10 years), at 95% confidence. The empirical results presented in this study are generally in agreement with IPCC’s projections of increased warming trend. This data-driven, robust method is used in the present study and the results can also be considered as an alternative approach for detecting changes in climate via estimating and assessing possible changes in frequency of extreme events with time.

Probabilistic Assessment of Roof Snow Load and the Calibration of Shape Coefficients in the Eurocodes

In modern structural codes, the reference value of the snow load on roofs is commonly given as the product of the characteristic value of the ground snow load at the construction site multiplied by the shape coefficient. The shape coefficient is a conversion factor which depends on the roof geometry, its wind exposure, and its thermal properties. In the Eurocodes, the characteristic roof snow load is either defined as the value corresponding to an annual probability of exceedance of 0.02 or as a nominal value. In this paper, an improved methodology to evaluate the roof snow load characterized by a given probability of exceedance (e.g., p=0.02 in one year) is presented based on appropriate probability density functions for ground snow loads and shape coefficients, duly taking into account the influence of the roof’s geometry and its exposure to wind. In that context, the curves for the design values of the shape coefficients are provided as a function of the coefficient of variation (COVg) of the yearly maxima of the snow load on the ground expected at a given site, considering three relevant wind exposure conditions: sheltered or non-exposed, semi-sheltered or normal, and windswept or exposed. The design shape coefficients for flat and pitched roofs, obtained considering roof snow load measurements collected in Europe during the European Snow Load Research Project (ESLRP) and in Norway, are finally compared with the roof snow load provisions given in the relevant existing Eurocode EN1991-1-3:2003 and in the new version being developed (prEN1991-1-3:2020) for the “second generation” of the Eurocodes.