RELIABILITY-BASED CAPACITY ASSESSMENT OF WATER STORAGE SYSTEM MOHAMMAD MUZAMMIL Professor JAVED ALAM 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. Probability of Failure/Risk Limit State Function Reliability Index (Co-variance matrix) Reliability Index (Correlation Coefficient )

Table 1 Statistical data of the various parameters Basic parameters (x) Distribution Mean COV Water demand Normal 3.00 0.25 Capacity 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 1.598 0.055 Lognormal Distribution 1.546 0.061 FORM on Spread Sheet 1.600

Table 3 Relation of the reliability index (β) and the failure probability with safety factor S.N. FS β Pf 1 0.700 2.51756E-08 0.5000 11 1.667 1.600595117 0.054733 2 0.800 12 1.700 1.658693261 0.048589 3 0.900 1.74414E-07 13 1.800 1.82526659 0.03398 4 1.000 1.68391E-08 14 1.900 1.978619406 0.023929 5 1.100 0.300285407 0.38198 15 2.000 2.119995759 0.017003 6 1.200 0.577109857 0.281933 16 2.200 2.371245155 0.008864 7 1.300 0.83173046 0.202781 17 2.500 2.683281573 0.003645 8 1.400 1.065625231 0.143297 18 2.700 2.856840263 0.002139 9 1.500 1.2803688 0.100208 19 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 Index (βT) Safety Factor (SF) Risk/Failure Probability (%) 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 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.  

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