Evaluating reliability in geotechnical engineering - Risk and Reliability in Geotechnical Engineering - page 164

assumptions of the Simplified Hasofer Lind method has on the result. It can be seen that the
results of the Simplified Hasofer Lind method are very similar to the results obtained with
the Monte Carlo Simulation method.

3.8.1 Summary of the hasofer lind method

1. Estimate the standard deviations of the parameters that involve uncertainty, using the
methods discussed in this chapter.

2. Compute the reliability index that gives a factor of safety equal to one. This is an itera-
tive process where a trial value of the reliability index (β) is assumed, and values of the
variables ( x i ) are calculated using Equation 3.24 for normal distributions of variable
or Equation 3.25 for lognormal distributions.

x i =− βσ µ * +

(3.24) xi xi

σ
µ

2
2

1 2

(* − βζ λ + ) xi

xi

2
* ζ xi

xe
i

= where ζ = ln 1 + and λ = ln() µ − (3.25)

xi xi

xi xi xi

3. Determine the change in the factor of safety for a 10% change in each of the variables.
If the variables are related to capacity, increase the value by 10%, if the variables are
related to demand, decrease the variable by 10%.

4. Calculate gradients using Equations 3.26 and 3.27

∆
∆

F
x

dg

(3.26)

=

dx

′ i

i

x − µ

i xi

x ′ = (3.27)

i

σ

xi

5. Repeat step 2 to find a new value of β by repeated trials, this time calculating the vari-
ables by using values of α i calculated using Equation 3.28 a nd values of x i calculated
using Equations 3.29 or 3.30

)

dg

dx

′

i

α i = (3.28)

)

2

dg

∑

dx ′

i

x i

′ =−

αβ σµ * +

(3.29) i xi xi

σ
µ

2
2

− 1 2 xe

i

=

( − αβζλ * + )

where ζ = ln 1 +

xi
xi

and λ = ln( µ ) *

2
ζ xi

(3.30)

i i i

xi xi xi

The value of β is correct when the factor of safety calculated using the values of x i is
equal to 1.00.

6. Calculate the probability of failure using Equation 3.8 .

(3.8)

p f = 1 − NORMSDIST (β)