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Reliability?
  • “BEST bus services are very reliable”
  • “BMC water supply is not very reliable”
  • “In Mumbai, Western Railway’s service is more reliable than that of the Central Railway”
What is reliability, in technical terms?
  • How do we measure it?
  • Why is not a system fully reliable?
Civil Engineering Systems
  • Structural (Buildings, Bridges, Dams, Fly-overs)
  • Transportation (Road systems, Railways, Air traffic)
  • Water (Water supply networks, Waste water networks)
Each system is designed differently, but there is a common philosophy
How to Design
Requirement
Provision
Demand
apacity/Supply
Load
Resistance
x million liter/day of
x million liter/day of
water for IITB
water for IITB
residents
Residents
Basic Design Philosophy
Capacity should be more than demand
C ? D
Example: Provide at least x million liter/day of water to a colony residents
How much more than the demand?
  • Theoretically, just more
  • However, designers provide a lot more
  • Why? ->Because of uncertainty
Uncertainty
We are not certain about the values of the parameters that we use in design specifications Sources/reasons of uncertainty:
  • Errors/faults/discrepancies in measurement (for demand) or manufacturing (for capacity)
  • Approximations/idealizations/assumptions in modeling
  • Inherent uncertainty — “Aleatory”
  • Lack of knowledge — “Epistemic”
Measurement and Manufacturing Errors
  • Strength of concrete is not same at each part of a column or a beam in a building system
  • the depth of a steel girder is not exactly same (and not as specified) at each section (Errors in estimating demand/capacity?)
clip_image002
  • Weight of concrete is not same at each part of a column or a beam in a building system (Error in estimating demand/capacity?)
  • Wheels of an aircraft hit the runway at different speeds for different flights
Moral of the story:
Repeat a measurement/estimate/experiment several times and we do not get exactly the same result each time
IDEALIZATIONS IN MODELING
  • Every real system is analyzed through its “model”
  • Idealizations/simplifications are used in achieving this model
Example: (modeling live load on a classroom floor)
  • Live loads are from non-permanent “occupants”; such as people, movable furnishers, etc.
  • We assume live load to be uniform on a classroom (unit?)
  • [We also assume the floor concrete to be “homogeneous” (that is, having same properties, such as strength, throughout)]
  • Therefore our analysis results are different from the real situation
Example: (modeling friction in water systems)
  • Friction between water and inner surface of a pipeline reduces flow
  • We assume a constant friction factor for a given pipe material
  • In reality, the amount of friction changes if you have joints, bends and valves in a pipe
  • If we need to consider these effects, the analysis procedure will be very complicated
  • However, we should remember that there is difference between the behaviors of model and the real system
clip_image004
Epistemic and Aleatory Uncertainties
Epistemic
  • Due to lack of understanding
  • Not knowing how a system really works
  • These uncertainties can be reduced over time (enhanced knowledge, more observation) Aleatory
  • Due to inherent variability of the parameter
  • Unpredictability in estimating a future event
  • These uncertainties can be reduced as well, with more observations
The Case of Earthquakes
  • Structures have to be designed to withstand earthquake effects
  • Earthquakes that a structure is going to face during its life-span are unpredictable
  • We do not know when, how big (magnitude), how damaging (intensity)
  • This is due to the unpredictability inherent in the physical nature of earthquakes
Aleatory uncertainty
How Earthquakes Occur
clip_image006
Plate Tectonics
clip_image008
Elastic Rebound Theory
clip_image010
AD = Fault line (along which one side of earth slides with respect to the other)
A = Focus of the earthquake (where the slip occurs and energy is released)
C = Epicenter of the earthquake (point on earth surface directly above the focus)
B = Site (location for the structure)
Earthquake waves travel from A to B (body waves) and C to B (surface waves)
Earthquake waves travel from epicenter to the site (site= where the structure is located)

  • The shock-wave characteristics are changed by the media it is traveling through
  • The earthquake force that is coming to the base of a structure is also determined by the soil underneath
  • We need to know accurately these processes by which the ground motion is affected
  • Any lack of knowledge in these regards will lead to: Epistemic uncertainty
Effects of Uncertainty
  • Analysis results are not exactly accurate (that is, not same as in real life)
  • Estimation of demand and capacity parameters is faulty
  • We may not really satisfy the C ? D equation
  • However, we will not know this
  • Solution: apply a factor of safety (F)
C ? FD or C/F ? D
  • This factor takes care of the unforeseen errors due to uncertainty
If C ? 2.5D, then even in real situation, it should be C ? D
Deterministic Design: Factor of Safety
  • This is the traditional design philosophy
  • A deterministic design procedure assumes that all parameters can be accurately measured (determined)
  • Thus, there is no uncertainty in estimating either C or D
  • So, if we satisfy a design equation, we make the system “ 100% safe” . It cannot fail.
  • In addition, we add a factor of safety to account for unforeseen errors
  • This factor of safety is specified based on experience and engineering judgement
  • The value of the safety factor varies for different cases
Example:
clip_image012
0.447 fcAc + 0.8 fsAs ? P
  • This is the design specification for a reinforced concrete column (RC = concrete reinforced with steel bars)
  • fc = strength of concrete, fs = strength of steel
  • Ac = area of concrete, As = area of steel bars
  • 0.447 and 0.8 are for safety factors
  • P = Force acting on the column (demand)
Reliability-Based Design
  • This is the newly developed design philosophy
  • Here, we accept the uncertainties in both demand and capacity parameters
  • However, all these uncertainties are properly accounted for
  • Uncertainty in estimating each parameter is quantified
  • The C ? D equation does not provide a full-proof design
  • The design guideline specifies a probability of failure due to those uncertainties
  • Load and resistance factors are used in stead of a single factor of safety
  • These factors are based on analysis, not on judgement
Old vs. New
Deterministic
Reliability-Based
100% safe
Less than 100% safe
No uncertainty
Uncertainties are properly accounted for
Factor of safety is based on judgement
Factors are calculated from uncertainty
Simple, but claims are not realistic
More scientific in all aspects, but complex
Reliability-Based Design
  • Reliability-based design equation:
clip_image014
  • clip_image016 = Resistance/Capacity Factor
  • clip_image018 = Load/Demand Factor
  • This equation assigns a probability of failure (Pf) for the design
  • This Pf is based on the load and resistance factors (also known as “ partial safety factors” )
  • Real systems always have some probability of failure (even though deterministic design does not recognize)
Uncertainties are unavoidable; it exists in natural systems and the way we measure and manufacture
  • It is not wise to ignore them
  • The best way to deal with uncertainties is to quantify them properly (using statistics and probability)
  • Reliability-based design accounts for uncertainties scientifically (whereas, deterministic design does not)
  • RBD assigns a specific reliability on a design through Pf (probability of failure)
  • It is not bad for a system to have probability of failure, but bad not to know how much
  • RBD tries to keep Pf within a target level

About Gopal MishraVerified

Gopal Mishra is a Civil Engineer from NIT Calicut and has more than 10 years of experience in Civil Engineering and Construction. He is the founder of The Constructor.