Safety factors and the probability distribution of soil strength

1970 ◽  
Vol 7 (3) ◽  
pp. 225-242 ◽  
Author(s):  
Peter Lumb
Keyword(s):  
Probability Distribution ◽  
Beta Distribution ◽  
Probability Distributions ◽  
Earth Dams ◽  
Safety Factors ◽  
Independent Variables ◽  
Long Term Stability ◽  
Undrained Strength ◽  
Partial Safety Factors

For soils exhibiting both cohesive and frictional components of strength, the natural variabilities of the components are compared for soil in the undisturbed state and as compacted in earth dams. The probability distributions of the components are shown to agree more closely with a theoretical beta distribution than with the commonly assumed normal distribution.The cohesive and frictional components can be regarded as independent variables and the design safety factor interpreted in terms of probabilities. Assuming equal probabilities for each component leads to the use of partial safety factors which are larger for the cohesive part than for the frictional part. For long-term stability problems limiting partial safety factors corresponding to zero probability can be obtained.The undrained strength of clays also agrees with a beta distribution but in this case there are no limiting safety factors, and some non-zero probability must be associated with the design.

Three-dimensional stability charts for slopes based on limit analysis methods

2010 ◽  
Vol 47 (12) ◽  
pp. 1316-1334 ◽  
Author(s):  
A. J. Li ◽  
R. S. Merifield ◽  
A. V. Lyamin
Keyword(s):  
Limit Analysis ◽  
Three Dimensional ◽  
Preliminary Design ◽  
Safety Factors ◽  
Long Term Stability ◽  
Slip Surfaces ◽  
Short And Long Term ◽  
Lower Bound Limit Analysis ◽  
Natural Slopes

This paper uses finite element upper and lower bound limit analysis to produce chart solutions for three-dimensional (3D) natural slopes for both short- and long-term stability. The presented chart solutions are convenient tools that can be used for preliminary design purposes. The rigorous limit analysis results in this paper were found to bracket the true factor of safety within ±10% or better, which can be used as a benchmark for the solutions from other methods. The depth of the slip surfaces is observed to be generally shallow for most analyzed cases, particularly for the long-term slope stability problem. In addition, it was found that using a two-dimensional (2D) analysis may lead to significant differences in estimating safety factors, which can differ by 2%–60% depending on the slope geometry and soil properties. Therefore, great care and judgement are required when applying 2D analyses to 3D slope problems.

scholarly journals RELIABILITY ANALYSIS OF THE LATERAL TORSIONAL BUCKLING RESISTANCE AND THE ULTIMATE LIMIT STATE OF STEEL BEAMS WITH RANDOM IMPERFECTIONS

2015 ◽  
Vol 21 (7) ◽  
pp. 902-911 ◽  
Author(s):  
Zdeněk Kala
Keyword(s):  
Failure Probability ◽  
Limit State ◽  
Ultimate Limit State ◽  
Safety Factors ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Random Variability ◽  
Partial Safety Factors ◽  
Ultimate Limit

The paper deals with the analysis of reliability of a hot-rolled steel IPE-beam designed according to Eurocodes. A beam at its ultimate limit state is considered. The load acting on the beam consists of permanent and long-term single variation actions. The beam is loaded with end bending moments about the major principal axis. The beam is susceptible to lateral torsional buckling between the end supports. Reliability of the beam is assessed using probabilistic analysis based on the Monte Carlo method. Failure probability is a function of the random variability of the loadcarrying capacity and the random variability of load effects. The variability of the load-carrying capacity is influenced by the variability of initial imperfections. Imperfections are considered according to experimental research. Numerical studies showed that the failure probability is significantly misaligned. High values of failure probability were obtained for slender beams, for beams loaded only by permanent load action, and for beams loaded only by long-term single variation load. In further studies the values of partial safety factors of load and resistance were calibrated so that the failure probability had a target value of 7.2E–5. Relatively high values of partial safety factors were obtained especially for beams with high slenderness.

scholarly journals The probability distribution of daily streamflow in the conterminous United States

2016 ◽  
Author(s):  
Annalise G. Blum ◽  
Richard M. Vogel ◽  
Stacey A. Archfield
Keyword(s):  
United States ◽  
Probability Distribution ◽  
Regression Models ◽  
Probability Distributions ◽  
Practical Method ◽  
Daily Streamflow ◽  
Flow Duration ◽  
Generalized Pareto ◽  
Flow Duration Curves

Abstract. One of the most commonly used tools in hydrology, empirical flow duration curves (FDCs) characterize the frequency with which streamflows are equaled or exceeded. Finding a suitable probability distribution to approximate a FDC enables regionalization and prediction of FDCs in basins that lack streamflow measurements. FDCs constructed from daily streamflow observations can be computed as the period-of-record FDC (POR-FDC) to represent long-term streamflow conditions or as the median annual FDC (MA-FDC) to represent streamflows in a typical year. The goal of this study is to identify suitable probability distributions for both POR-FDCs and MA-FDCs of daily streamflow for unregulated and perennial streams. Comparisons of modeled and empirical FDCs at over 400 unregulated stream gages across the conterminous United States reveal that both the four-parameter kappa (KAP) and three-parameter generalized Pareto (GPA3) distributions can provide reasonable approximations to MA-FDCs; however, even four and five-parameter distributions are unable to capture the complexity of the POR-FDC behavior for which flows often range over five or more orders of magnitude. Regional regression models developed for the mid-Atlantic and Missouri regions as case studies present a simple and practical method to predict MA-FDCs at ungaged sites, which can be accurately predicted more consistently compared to POR-FDCs.

scholarly journals Noise-induced mixing and multimodality in reaction networks

2018 ◽  
Vol 30 (5) ◽  
pp. 887-911 ◽  
Author(s):  
TOMISLAV PLESA ◽  
RADEK ERBAN ◽  
HANS G. OTHMER
Keyword(s):  
Probability Distribution ◽  
Regulatory Networks ◽  
Probability Distributions ◽  
Mass Action ◽  
Reaction Networks ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Gene Products ◽  
Mass Action Kinetics

We analyse a class of chemical reaction networks under mass-action kinetics involving multiple time scales, whose deterministic and stochastic models display qualitative differences. The networks are inspired by gene-regulatory networks and consist of a slow subnetwork, describing conversions among the different gene states, and fast subnetworks, describing biochemical interactions involving the gene products. We show that the long-term dynamics of such networks can consist of a unique attractor at the deterministic level (unistability), while the long-term probability distribution at the stochastic level may display multiple maxima (multimodality). The dynamical differences stem from a phenomenon we call noise-induced mixing, whereby the probability distribution of the gene products is a linear combination of the probability distributions of the fast subnetworks which are ‘mixed’ by the slow subnetworks. The results are applied in the context of systems biology, where noise-induced mixing is shown to play a biochemically important role, producing phenomena such as stochastic multimodality and oscillations.

CONSTRUCTION METHOD AND STABILITY OF EMBANKMENTS ON MUSKEG

1969 ◽  
Vol 6 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Gerald P Raymond
Keyword(s):  
Factor Of Safety ◽  
Soil Mechanics ◽  
Strength Analysis ◽  
Term Stability ◽  
Long Term Stability ◽  
Safety Consideration ◽  
Undrained Strength ◽  
Mechanics Concepts

A method for the design and construction of relatively thick highway embankments across muskeg deposits is described. Using theoretical soil-mechanics concepts it is predicted that the long-term stability of the muskeg necessitates the use of berms despite the fact that an undrained strength analysis based on in situ vane tests may predict a reasonable factor of safety. Consideration of both theoretical soil-mechanics concepts and practical considerations suggested that the interaction between the soil and the berm dictates that berm construction should be from the outer limits towards the center and should be placed prior to the central fill.Several case records are presented to support the conclusions drawn and furthermore suggest that the width of the berms should be [Formula: see text] to 2 times the thickness of the muskeg (peat plus lake marl).

scholarly journals The similarity about the probability distributions of variables in the Bayesian regression model and application

2021 ◽  
Vol 5 (1) ◽  
pp. 1325-1339
Author(s):  
Hoa Thanh Le ◽  
Uyen Hoang Pham ◽  
An Thị Đỗ Nguyễn ◽  
Bao The Pham
Keyword(s):  
Probability Distribution ◽  
Regression Model ◽  
Normal Distribution ◽  
Stock Price ◽  
Probability Distributions ◽  
Random Variable ◽  
Bayesian Regression ◽  
Independent Variables ◽  
Classical Statistics ◽  
The Mean

The linear regression model as well as the time series model is applied in many fields, in which the mean of the dependent variable is one function of the mean of the independent variables. However, to consider the regression model following in the Classical Statistics (the Frequent Statistics), it means that the parameters are the constants, in many situations, the regression model does not describe the fluctuation of both the dependent variable and the independent variables. Therefore, we need to modify the parameters following the random variable form, not the constant form, like as the regression in Bayesian Statistics. The other side, when the parameters considered as the random variables, computations in the regression model becomes very complex, because we need to compute the product of the probability distributions. So, we must evaluate about to vary of the variables' probability distributions not only the normal distribution, the Student distribution t, the Poisson distribution, the binomial distribution… In this paper, we estimated the dependent variable's probability distribution form through the simple Bayesian regression model in cases having many the probability distribution forms of the independent variable. In addition, we apply the results to real stock price data, proving that the most appropriate probability distribution with the data is a mixture of probability distributions, not a single normal distribution.

Stability and Change in Emotional Intelligence: Exploring the Transition to Young Adulthood

2005 ◽  
Vol 26 (2) ◽  
pp. 100-106 ◽  
Author(s):  
James D.A. Parker ◽  
Donald H. Saklofske ◽  
Laura M. Wood ◽  
Jennifer M. Eastabrook ◽  
Robyn N. Taylor
Keyword(s):  
High School ◽  
Emotional Intelligence ◽  
Postsecondary Education ◽  
Life Transition ◽  
Full Time ◽  
Major Life ◽  
Long Term Stability ◽  
Time Period ◽  
Transition From High School

Abstract. The concept of emotional intelligence (EI) has attracted growing interest from researchers working in various fields. The present study examined the long-term stability (32 months) of EI-related abilities over the course of a major life transition (the transition from high school to university). During the first week of full-time study, a large group of undergraduates completed the EQ-i:Short; 32 months later a random subset of these students (N = 238), who had started their postsecondary education within 24 months of graduating from high school, completed the measures for a second time. The study found EI scores to be relatively stable over the 32-month time period. EI scores were also found to be significantly higher at Time 2; the overall pattern of change in EI-levels was more than can be attributed to the increased age of the participants.

Multi-Center Calibration of the Second Reference Material for Thromboplastin, Rabbit, Plain, Coded CRM 149R

1991 ◽  
Vol 65 (03) ◽  
pp. 263-267 ◽  
Author(s):  
A M H P van den Besselaar ◽  
R M Bertina
Keyword(s):  
Reference Material ◽  
Standard Error ◽  
Standard Errors ◽  
Sensitivity Index ◽  
Long Term Stability ◽  
Significant Bias ◽  
The Mean ◽  
The Relationship ◽  
International Sensitivity Index

SummaryIn a collaborative trial of eleven laboratories which was performed mainly within the framework of the European Community Bureau of Reference (BCR), a second reference material for thromboplastin, rabbit, plain, was calibrated against its predecessor RBT/79. This second reference material (coded CRM 149R) has a mean International Sensitivity Index (ISI) of 1.343 with a standard error of the mean of 0.035. The standard error of the ISI was determined by combination of the standard errors of the ISI of RBT/79 and the slope of the calibration line in this trial.The BCR reference material for thromboplastin, human, plain (coded BCT/099) was also included in this trial for assessment of the long-term stability of the relationship with RBT/79. The results indicated that this relationship has not changed over a period of 8 years. The interlaboratory variation of the slope of the relationship between CRM 149R and RBT/79 was significantly lower than the variation of the slope of the relationship between BCT/099 and RBT/79. In addition to the manual technique, a semi-automatic coagulometer according to Schnitger & Gross was used to determine prothrombin times with CRM 149R. The mean ISI of CRM 149R was not affected by replacement of the manual technique by this particular coagulometer.Two lyophilized plasmas were included in this trial. The mean slope of relationship between RBT/79 and CRM 149R based on the two lyophilized plasmas was the same as the corresponding slope based on fresh plasmas. Tlowever, the mean slope of relationship between RBT/79 and BCT/099 based on the two lyophilized plasmas was 4.9% higher than the mean slope based on fresh plasmas. Thus, the use of these lyophilized plasmas induced a small but significant bias in the slope of relationship between these thromboplastins of different species.

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