Estimating probability curves of rock variables using orthogonal polynomials and sample moments

A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. Orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve.

System reliability analysis of seismic pseudo-static stability of rock wedge based on nonlinear Barton–Bandis criterion

Based on the nonlinear Barton–Bandis(B–B)failure criterion,this study considers the system reliability of rock wedge stability under the pseudo-static seismic load.The failure probability(Pf)of the system is calculated based on the Monte−Carlo method when considering parameter correlation and variability.Parameter analysis and sensitivity analysis are carried out to explore the influence of parameters on reliability.The relationships among the failure probability,safety factor(Fs),and variation coefficient are explored,and then stability probability curves of the rock wedge under the pseudo-static seismic load are drawn.The results show that the parameter correlation of the B–B failure criterion has a significant influence on the failure probability,but correlation increases system reliability or decreases system reliability affected by other parameters.Under the pseudo-static seismic action,sliding on both planes is the main failure mode of wedge system.In addition,the parameters with relatively high sensitivity are two angles related to the joint dip.When the coefficient of variation is consistent,the probability of system failure is a function of the safety factor.

Ecological risk assessment of heavy metals in surface seawater and sediment near the outlet of a zinc factory in Huludao City, Liaoning Province, China

At present, the methods widely applied to assess ecological risk of heavy metals are essentially single-point estimates in which exposure and toxicity data cannot be fully used and probabilities of adverse biological effects cannot be achieved. In this study, based on investigation of concentrations of six heavy metals(As, Hg, Pb, Cd, Cu, and Zn) in the surface seawater and sediment near the outlet of a zinc factory, located in Huludao City, Liaoning Province, China, a tiered approach consisting of several probabilistic options was used to refi ne ecological risk assessment for the individuals. A mixture of various heavy metals was detected in the surface seawater, and potential ecological risk index(PERI) was adopted to assess the potential ecological risk of heavy metals in the surface sediment. The results from all levels of aquatic ecological risk assessment in the tiered framework, ranging from comparison of single effects and exposure values to the use of distribution-based Hazard Quotient obtained through Monte Carlo simulation, are consistent with each other. Briefl y, aquatic Zn and Cu posed a clear ecological risk, while Cd, Pb, Hg, and As in the water column posed potential risk. As expected, combined ecological risk of heavy metal mixture in the surface seawater was proved signifi cantly higher than the risk caused by any individual heavy metal, calculated using the concept of total equivalent concentration. According to PERI, the severity of pollution by the six heavy metals in the surface sediment decreased in the following sequence: Cd>Hg>As>Pb>Cu>Zn, and the total heavy metals in the sediment posed a very high risk to the marine environment. This study provides a useful mathematical framework for ecological risk assessment of heavy metals.

10Be Exposure Ages Obtained From Quaternary Glacial Landforms on the Tibetan Plateau and in the Surrounding Area

In situ terrestrial cosmogenic nuclide （TCN） exposure dating using 10Be is one of the most successful techniques used to determine the ages of Quaternary deposits and yields data that enable the reconstruction of the Quaternary glacial history of the Tibetan Plateau and the surrounding mountain ranges. Statistical analysis of TCN 10Be exposure ages, helps to reconstruct the history of glacial fluctuations and past climate changes on the Tibetan Plateau, differences in the timing of glacier advances among different regions. However, different versions of the Cosmic-Ray-prOduced NUclide Systematics on Earth （CRONUS-Earth） online calculator, which calculates and corrects the TCN ages of Quaternary glacial landforms, yield different results. For convenience in establishing contrasts among regions, in this paper, we recalculate 1848 10Be exposure ages from the Tibetan Plateau that were published from 1999 to 2017 using version 2.3 of the CRONUS-Earth calculator. We also compare the results obtained for 1594 10Be exposure ages using different versions （2.2, 2.3 and 3.0） of the CRONUS- Earth calculator. The results are as follows. （1） Approximately 97% of the exposure ages are less than 200 ka. A probability density curve of the exposure ages suggests that greater numbers of oscillations emerge during the Holocene, and the peaks correspond to the Little Ice Age, the 8.2 ka and 9.3 ka cold events; the main peak covers the period between 12 and 18 ka. （2） In most areas, the newer versions of the calculator produce older 10Be exposure ages. When different versions of the CRONUS-Earth calculator are used, approximately 29% of the 10Be exposure ages display maximum differences greater than 10 ka, and the maximum age difference for a single sample is 181.1 ka.

Probabilistic ecological risk assessment for three chlorophenols in surface waters of China

Individual and combined assessment of risks of adverse effects to aquatic ecosystems of three chlorophenols（CPs）,including 2,4dichlorophenol（2,4-DCP）,2,4,6-trichlorophenol（2,4,6-TCP） and pentachlorophenol（PCP）,were conducted.A probabilistic approach based on the concentrations of CPs in surface waters of China was used to determine the likelihood of adverse effects.The potential risk of CPs in surface waters of China was determined to be of concern,especially PCP and mixtures of CPs.The risks of adverse effects were examined as the joint probabilities of exposure and response.The joint probability for PCP was 0.271 in the worst case and 0.111 in the median case,respectively.Based on the cumulative probability,5% of aquatic organisms included in the assessment would be affected 21.36% of the time in the worst case and 5.99% of the time in median case,respectively.For the mixtures of CPs,the joint probability were 0.171 in the worst case and 0.503 in median case,respectively and 5% of species would be affected 49.83% of the time for the worst case and 12.72% in the median case,respectively.Risks of effects of the individual CPs,2,4-DCP and 2,4,6-TCP were deemed to be acceptable with a overlapping probability of 0.1 with 5% of species being affected less than 4% of the time.

A Proposal of Hyperbolic Fitting Method by Applying the Properties of Functions for Plateau Surface Analysis in ISO 13565-3

ISO 13565-3 provides an evaluation method for plateau structure surfaces used as sliding surfaces in machine tools and automobile engines.The evaluation method for plateau structure surfaces of ISO 13565-3 has problems,such as the processing procedure has an ambiguous basis,and the calculation method is not specified.The existing evaluation method that solves these problems requires the implementation of a difficult algorithm.In subsequent evaluation methods,these problems were resolved,and the implementation of complicated calculation algorithms became unnecessary.However,these methods use algorithms that do not conform to the evaluation method of ISO 13565-3.This lack of adherence to the ISO standard may hinder their application in the industrial world.Therefore,in this study,a new method that conforms to the evaluation method of ISO 13565-3 with a more concise algorithm was developed.We concluded that this proposed method can contribute to the formation of plateau surfaces and production control in the industrial world.