GATE-2018 (24) :Wyllie – Time average equation

116) An earthquake occurring at every 100 years leads to a displacement of 2m over a 40 km long fault. The corresponding shear strain accumulation rate is _____

(Thank to Chandrasekhar, ANU)
 

Solution:

Given that time = 100 years

Displacement = 2 m 

 

Fault length = 40 km = 40,000 m

Shear strain =?

$Shear strain =\frac{change in length}{original length}$

$Change in length (Velocity) =\frac{Displacement}{time}$

                   = $\frac{2 meters}{100 year}$

                                                          = $0.02 meter/ year$

$Shear stain =\frac{change in length}{original length}$

$Shear stain =\frac{0.02 meter/year}{40000 meter}$

$ shear strain =0.0000005 / year$

$ shear strain = 0.5 \times 10 ^{-6}/ year$