Fragility Curve

Fragility curves used in the Methodology to estimate the probability of Slight, Moderate, Extensive and Complete damage to general building stocks.

So far we have learnt to find the capacity curve of different types of building with different types of vulnerabilities.

For an example consider C3L type building. In this particular C3L type building can behave differently due to the existence of different vulnerabilities.

We know the capacity curve of 1 storey building will be different than that of 2 storey building or 3 storey building. Again if there presents any vulnerable factors in the building , capacity curve will be different than that of the same height building which do not have any vulnerable factors. For better understanding see the following figures.

Fig 1: C3L buildings of different storey height.

All of the buildings shown above are C3L but resistance capacity of earthquake will be different.

Fig 2: 2 and 3 storey C3L buildings with soft storey

Resistance capacity of C3L building in Fig 2 will be different than that of Fig 1 because there presents a vulnerability factor (Soft Story).

Fig 3: C3L buildings with soft storey and heavy overhang.

Resistance capacity of C3L buildings in Fig 3 will be different than that of in Fig 1 and Fig 2 because there presents 2 vulnerable factors (Soft storey & heavy overhang) though all of them are C3L buildings.

Though all of the buildings in Fig 1 , Fig 2 & Fig 3 are C3L, capacity curve will be different for each building. Here I have shown 3 possibilities but there may be other possibilities like C3L with short column, C3L with short column and heavy overhang etc. 

To represent these variation in single type of building, fragility curve need to be developed. 

Let us consider the C3L building parameters to be modeled.

Model name and the corresponding building figures are shown in fig1, 2 and 3. 

After modeling all these building, we will find different capacity curves for each type of building. If we plot these capacity curves of C3L building, it will look like as below.

Fig 4: Individual capacity spectrum of the generic building models for C3L structure type

Now from the above analysis we can easily find the spectral displacement (Sd) of each modeled building for which that building experiences slight, moderated, extensive and complete damage state. For better clarification please see the Capacity Curve page.

Fig 5: Threshold spectral displacements for C3L general building models.

This is the tabular form of the above graphical representation. From these table we can easily say that for C3L1A type building, whenever it will expose 0.22 inch spectral displacement, it will slightly damaged. Again when it will expose 0.54 inch displacement, it will moderately damaged and so on.

To interpret the variation, now just consider only the slight or minor damage state. 

From your survey find out how many of different types of building you models like C3L1A, C3L2A , C3L3D you have in your study area.

From our study,

Fig 6: Relative frequencies of C3L buildings with different combinations of seismic vulnerability factors

For example, if we just consider only minor damage state, We can say from Fig 5 and 6 that if spectral displacement , Sd is 0.22 inch , 3.68 % C3L building of the study area will experience slight damage. If Sd is 0.29 inch 19.54% C3L building of that are will experience slight damage. As 0.29 exceeds 0.22 inch so C3L1A will also experience slight damage in addition with C3L1C. So total slight damage building percent will be (3.68+15.86 ) 19.54 of total C3L building. Plotting all value and making it best fit, we can find the following curve.

Fig 7: Statistical distributions and log-normal fits of threshold spectral displacement for minor damage state of C3L buildings in the study area.

Now considering all other damage states we can find the following graph.

Fig 8: Comparison between the newly developed set of fragility functions for C3L buildings in Dhaka and those provided by HAZUS.