scholarly journals Copula-Based Method for Estimating the Minimum Void Ratio Parameters of Tailings Deposits

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hao Li ◽  
Yichuan Tang ◽  
Shibo Li ◽  
Jianquan Ma ◽  
Xiaojie Zhao
Keyword(s):  
Probability Distribution ◽  
Fine Particle ◽  
Void Ratio ◽  
Joint Probability ◽  
Copula Function ◽  
Distribution Model ◽  
Joint Probability Distribution ◽  
Particle Content ◽  
Edge Distribution ◽  
Guarantee Rate

The pore ratio is an important parameter affecting the stability and safety of tailings reservoirs; however, the relationship between the pore ratio and physical properties of tailings sand has not been researched in-depth. In this paper, using the tailings from a tungsten mine in southern Shaanxi as a case study, the correlation between the minimum void ratio and related parameters is analyzed, based on laboratory test data, and the optimal marginal distribution function of the parameters is determined. The Gumbel-Hougard copula function that best describes the correlation between parameters is identified, and it is used to establish the joint probability distribution model of the three parameters, and the guarantee rate α is introduced to estimate and analyze the minimum void ratio. The results show that the optimal edge distribution of the fine particle content and specific gravity follows a truncated normal distribution, and the optimal edge distribution of the minimum void ratio follows a logarithmic normal distribution. According to AIC criterion, the Gumbel-Hougard copula is the best three-dimensional copula function to fit the minimum void ratio and related parameters. When the guarantee rate α is 0.485, the joint probability distribution model achieves optimal performance in terms of estimating the minimum void ratio. The maximum error of the estimation is 1.99%, which is verified through data, and the estimation meets the requirements for practical engineering. The method proposed in this paper uses the existing measured data to establish a joint probability distribution model and combines the collected fine particle content and specific gravity data with the guarantee rate to estimate the minimum void ratio, providing a novel basis for the study of the physical properties of tailings.

scholarly journals The joint probability distribution of runoff and sediment and its change characteristics with multi-time scales

2014 ◽  
Vol 62 (3) ◽  
pp. 218-225 ◽  
Author(s):  
Jinping Zhang ◽  
Zhihong Ding ◽  
Jinjun You
Keyword(s):  
Probability Distribution ◽  
Time Scales ◽  
Joint Probability ◽  
Copula Function ◽  
Annual Runoff ◽  
Joint Probability Distribution ◽  
Mode Decomposition ◽  
Change Characteristics ◽  
Empirical Mode Decomposition Method ◽  
Statistical Analysis Method

Abstract River runoff and sediment transport are two related random hydrologic variables. The traditional statistical analysis method usually requires those two variables to be linearly correlated, and also have an identical marginal distribution. Therefore, it is difficult to know exactly the characteristics of the runoff and sediment in reality. For this reason, copulas are applied to construct the joint probability distribution of runoff and sediment in this article. The risk of synchronous-asynchronous encounter probability of annual rich-poor runoff and sediment is also studied. At last, the characteristics of annual runoff and sediment with multi-time scales in its joint probability distribution space are simulated by empirical mode decomposition method. The results show that the copula function can simulate the joint probability distribution of runoff and sediment of Huaxia hydrological station in Weihe River well, and that such joint probability distribution has very complex change characteristics at time scales.

scholarly journals Temporal Analysis and the Joint Probability Distribution of Rainfall Indexes in the Taihu Lake Basin, China

2021 ◽  
Author(s):  
Manqiu Hao ◽  
Cheng Gao ◽  
Jian Chen
Keyword(s):  
Probability Distribution ◽  
Taihu Lake ◽  
Three Dimensional ◽  
Joint Probability ◽  
Daily Rainfall ◽  
Copula Function ◽  
Joint Probability Distribution ◽  
Lake Basin ◽  
Goodness Of Fit Test ◽  
Taihu Lake Basin

Abstract Taking the Taihu Lake Basin as an example, in this study, the characteristics of the rainfall factors in the study area were analyzed using daily rainfall data from 1955 to 2018. Three factors, i.e., the contribution rate of the rainfall in the flood season, the rainfall frequency, and the maximum daily rainfall, were selected to determine the optimal probability distribution function for each single factor. Furthermore, the root mean square error (RMSE) goodness of fit test was used to determine the optimal copula function for the three-dimensional joint probability distribution characteristics of the rainfall factors. The research results show that the three-dimensional copula joint probability method contains much more information than the results of the single variable probability calculation. The copula function can be used to analyze the multi-dimensional joint distribution of rainfall factors, which can fill the gap in research on multiple rainfall factors.

scholarly journals Joint improvement of river water quality indicators based on a multivariate joint probability distribution of the discharge and water quality

2018 ◽  
Vol 49 (6) ◽  
pp. 1915-1928 ◽  
Author(s):  
Yang Liu ◽  
Shengle Cao ◽  
Xi Zhang ◽  
Fuzhen Li ◽  
Xitong Li
Keyword(s):  
Water Quality ◽  
Probability Distribution ◽  
River Water ◽  
Quality Indicators ◽  
Joint Probability ◽  
Copula Function ◽  
River Water Quality ◽  
Statistical Characteristics ◽  
Joint Probability Distribution ◽  
Water Quality Indicators

Abstract Based on the multivariate joint probability distribution of the discharge and water quality indicators, this paper analysed the occurrence probabilities and improvement probabilities of combinations of water quality indicators under different discharge conditions and then presented a method for calculating the optimal discharge to seek a balance between the discharge dispatch and water quality improvement. The method was used to construct the relationship curve between the discharge and joint improvement probability used by a copula function and then calculate the critical point on the curve. The proposed method was applied to the Yi River Basin above Gegou Station with data composed of the discharge and main pollution indicators (NH3-N and CODMn) from 1982 to 2015. The results showed that the trivariate joint probability distribution can more reasonably reveal the statistical characteristics of different combinations of discharge and water quality indicators. Furthermore, the optimal discharges and the corresponding improvement probabilities that improved NH3-N and CODMn to different grades were calculated. The calculation method took the interdependence of multiple water quality indicators into account, thereby providing a more reasonable method for using discharge dispatch data to improve the river water quality.

scholarly journals Stochastic Dynamic Response Analysis of the 3D Slopes of Rockfill Dams Based on the Coupling Randomness of Strength Parameters and Seismic Ground Motion

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3256
Author(s):  
Rui Pang ◽  
Laifu Song
Keyword(s):  
Slope Stability ◽  
Ground Motion ◽  
Joint Probability ◽  
Copula Function ◽  
Distribution Model ◽  
Joint Probability Distribution ◽  
Strength Parameters ◽  
Distribution Models ◽  
Dynamic Reliability ◽  
Seismic Ground Motion

Because rockfill strength and seismic ground motion are dominant factors affecting the slope stability of rockfill dams, it is very important to accurately characterize the distribution of rockfill strength parameters, develop a stochastic ground motion model suitable for rockfill dam engineering, and effectively couple strength parameters and seismic ground motion to precisely evaluate the dynamic reliability of the three-dimensional (3D) slope stability of rockfill dams. In this study, a joint probability distribution model for rockfill strength based on the copula function and a stochastic ground motion model based on the improved Clough-Penzien spectral model were built; the strength parameters and the seismic ground motion were coupled using the GF-discrepancy method, a method for the analysis of dynamic reliability of the 3D slope stability of rockfill dams was proposed based on the generalized probability density evolution method (GPDEM), and the effectiveness of the proposed method was verified. Moreover, the effect of different joint distribution models on the dynamic reliability of the slope stability of rockfill dams was revealed, the effect of the copula function type on the dynamic reliability of the slope stability was analysed, and the differences in the dynamic reliability of the slope stability under parameter randomness, seismic ground motion randomness, and coupling randomness of parameters and seismic ground motion were systematically determined. The results were as follows: the traditional joint distribution models ignored related nonnormal distribution characteristics of rockfill strength parameters, which led to excessively low calculated failure probabilities and overestimations of the reliability of the slope stability; in practice, we found that the optimal copula function should be selected to build the joint probability distribution model, and seismic ground motion randomness must be addressed in addition to parameter randomness.

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