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RELIABILITY-BASED CAPACITY ASSESSMENT OF
WATER STORAGE SYSTEM
MOHAMMAD MUZAMMIL
JAVED ALAM
Professor
Associate Professor
Department of Civil Engineering
ALIGARH MUSLIM UNIVERSITY,
ALIGARH, INDIA
OBJECTIVE
 A reliability-based assessment of the capacity
for a water storage system is of paramount
importance in examining the relationship
between safety factor and reliability

A methodology for the reliability assessment
of the reservoir capacity has been presented
using First Order Reliability Method (FORM).
 To
achieve desirable safety level in the design
of the structure foundation reliability based
safety factors have also been proposed.
INTRODUCTION
 Conventional
hydraulic
design
is
deterministic, i.e. it does not account for
possible variations of the parameters
 Composite
risk analysis is a method of
accounting for the risk resulting from the
various sources of uncertainty to produce an
overall risk assessment for a particular
design

The concept of demand and capacity are
central to this analysis.
INTRODUCTION
 The
demand placed on the system is the
measure of the impact of external events.

The demand for water supply is determined
by the people who use the water.
 The
capacity is the measure of the ability of
the system to meet the demand.
LITERATURE
Johnson 1992, Johnson and Ayyub 1992,
Chang et al. 1994, Johnson and Dock
1998, Ghosn and Johnson 2000, Johnson
and Niezgoda 2004
 Yanmaz and Cicekdag 2001, Yanmaz
and Ustun 2001, Yanmaz 2002, Yannmaz
and Celebi 2004
 Siddiqui et al. 2004, Muzzammil et al.
2006, Muzzammil et al. 2008, Muzzammil
et al. 2009a,b,

RELIABILITY BASED CAPACITY ASSESSMENT OF
WATER STORAGE SYSTEM
The
reliability assessment of any
engineering system is concerned with
the calculation and prediction of its
probability of limit state violation at any
stage during its entire life.
The
limit state violation is the exceeding
the maximum demand from the capacity
of the water storage system.
The demand placed on the system is the
measure of the impact of external events. The
demand for water supply is determined by the
people who use the water. The capacity is the
measure of the ability of the system to with
stand the loading or meet the demand.
Pf  P[ g ( x)  0]
Probability of Failure/Risk
g ( x)  C  D
Limit State Function
Reliability Index
(Co-variance matrix)
Reliability Index
(Correlation Coefficient )
  min
xF
  min (
xF
(x  μ)T CM  1 (x  μ)
xi  i

)T R 1 (
xi  i
i
)
Table 1 Statistical data of the various parameters
Basic parameters (x)
Distribution
Mean
COV
Water demand
Normal
3.00
0.25
Capacity
Normal
5.00
0.20
Table 2 A Comparative Study of various methods of reliability
Methods of Reliability
Distribution
β
Pf
Numerical Integration
Normal Distribution
1.626 0.052
Analytical Method
Normal Distribution
Lognormal
Distribution
1.598 0.055
Normal Distribution
1.600 0.055
FORM on Spread Sheet
1.546 0.061
Table 3 Relation of the reliability index (β) and the failure probability with
safety factor
S.N.
S.N. FS
FS
β
Pf
β
Pf
1
11
0.700 2.51756E-08 0.5000
1.667 1.600595117 0.054733
2
12
0.800 2.51756E-08 0.5000
1.700 1.658693261 0.048589
3
13
0.900 1.74414E-07 0.5000
1.800 1.82526659 0.03398
4
14
1.000 1.68391E-08 0.5000
1.900 1.978619406 0.023929
5
15
1.100 0.300285407 0.38198
2.000 2.119995759 0.017003
6
16
1.200 0.577109857 0.281933
2.200 2.371245155 0.008864
7
17
1.300 0.83173046 0.202781
2.500 2.683281573 0.003645
8
18
1.400 1.065625231 0.143297
2.700 2.856840263 0.002139
9
19
1.500
1.2803688 0.100208
3.000 3.076923078 0.001046
10
1.600 1.477545701 0.069765
A RELIABILITY BASED SAFETY FACTORS
 Safety
factors are widely used to incorporate
uncertainties involved in the various stages
of designing and construction of the
structures
 Regression
analysis was used to get a
relation of safety factor in terms of reliability
index with coefficient of determination (R2) as
0.99
 One
can find out an appropriate value of
safety factor for desired reliability.
A RELIABILITY BASED SAFETY FACTORS
 But
safety factors obtained from the above
equations cannot be recommended for general
use
 Because these are based on only a limited set
of data and assumed values of uncertainties
 Other important issues such as cost issue,
issue of consequences of failure etc. are not
given the due consideration in the derivation of
above equations
 However, Eq. 5 or Table 4 can provide some
strong basis in the decision of appropriate
values of safety factor
Table 4 Relationship of Taget reliability with Safety factor and Risk
Target Reliability
Risk/Failure Probability
Index (βT)
Safety Factor (SF)
(%)
1.0
1.34
15.87
1.2
1.43
11.55
1.4
1.54
8.08
1.6
1.66
5.5
1.8
1.79
3.6
2.0
1.94
2.3
2.2
2.09
1.4
2.4
2.26
0.82
2.6
2.44
0.47
2.8
2.64
0.26
3.0
2.84
0.14
CONCLUSIONS
A methodology for a reliability-based
capacity assessment of water storage
system has been presented using First
Order Reliability Method on spreadsheet.
 The formulation of the reliability analysis
was employed for the numerical data to
illustrate the basic steps of the reliability
analysis.
 A comparative study of various methods of
reliability indicates that Integration method,
analytical method and the First Order
Reliability Method (FORM) provide almost
the same results with normal distribution
for the data.

CONCLUSIONS

It were further found that as the factor
of safety increases, the probability of
failure decreases while reliability index
increases.

A reliability-based safety factor has
also been developed in terms of the
reliability index in the present study.