Practical reliability analysis and design by Monte Carlo Simulation in spreadsheet - Risk and Reliability in Geotechnical Engineering - page 328

L i i ith subset of sample space of x k

m Highest Subset Simulation level

m φ Mean effective friction angle of soil

MCMC Markov chain Monte Carlo

MCS Monte Carlo Simulation

MRFD Multiple resistance factor design

n Ω i Number of failure samples in Ω i

Number of failure samples in Ω i with a combination of B and D

n iBD

Ω ,

n B , n D Number of possible discrete values for B and D

n f Number of failure samples in the simulation

n i Number of failure samples at the simulation level ' i '

n j Number of simulation samples where failure occurs and the x k

value falls into bin j

n ji Number of failure samples at the simulation level ' i ' with the x k

value falling into bin j

n min Minimum MCS sample number

n t Total number of samples in the MCS

N Number of samples per Subset Simulation level

N γ , N q Bearing capacity factors

N B , N D Number of possible values for B and D

p () Probability density function

p (|) Conditional probability density function

p 0 Conditional probability adopted in Subset Simulation

p f ULS , p f SLS Failure probability for ULS and SLS

p T Target failure probability

P () Probability

P (|) Conditional probability

PDF Probability density function

Q side , Q tip Side resistance and tip resistance

Q uls , Q sls ULS and SLS capacity

RBD Reliability-based design

SLS Serviceability limit state

SORM Second-order reliability method

S uM , S uL Undrained shear strength of the marine clay and the lacustrine clay

T cr , T L Thickness of the clay crust and the lacustrine clay

ULS Ultimate limit state

UPSS Uncertainty propagation using Subset Simulation

V Variable needed to be recorded during Subset Simulation

VBA Visual Basic for Applications

w Standard Gaussian variable

W Effective shaft weight

x A , y A x and y coordinates of point A

x k Value of random variable X k

X Uncertain parameter vector

X k Random variable

Y Driving variable

y Value of the driving variable

y m m th intermediate threshold value during Subset Simulation

y a Allowable displacement

Z H Hypothesis testing statistic