Earthquake Influence on Bearing Capacity of Foundation Soil

Building codes uses intensity of earthquake for a designed area rather than earthquake magnitude. Depending on intensity of earthquake, different zones are created for a given region. For each zones there have a specified earthquake zone factor. Zone factors are derived from the risk categories of a region.
A bigger earthquake have a larger intensity associated with a greater earthquake co-efficient or seismic coefficient. At first lets discuss the basic equation for determining bearing capacity in static condition. The ultimate bearing capacity for a bearing stratum is determine by Nc, Nq, Nϒ, the angle of shearing resistance and cohesion of soil.
Earthquake foundation failure resulting tilted building
One thing is added in case of seismic bearing capacity is modification factors for bearing capacity which are depend on angle of shearing resistance of soil, φ.  The basic equation provided by Terzaghi for unit foundation length. At first we provide the parameter used in this expression:
capacity of soil
of soil
weight of soil
of foundation
Ultimate bearing capacity for a foundation soil according to Terzaghi
These factors used in bearing capacity expression may be modified using following table:

Modification factor for bearing capacity equation by Terzaghi
Earthquake induced foundation settlement Where k=0 in case of bearing capacity factors provided by Terzaghi.
As an example:
Let consider,
c=200 lb/ft2
B=5  ft
Df=3 ft
Qstatic=5(200X36 + 112X3X22 + 112X5X20)
=100960 lbs/ft of unit foundation length
If earthquake hazard provides k=0.2 then
Qearthqauke=5(200X17 + 112X3X7 + 112X5X4)
=34360 lbs/ft of unit foundation length
From this example we can conclude a considerable reduction in ultimate bearing capacity of foundation soil is occurred on account of earthquake event. 

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