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

Q) The width of outcrop of a lime stone bed on a sloping ground is 20 meters. The slope of the ground and the dip of the strata are in the same direction and their amounts are being 10⁰ and 25⁰ respectively. Calculate the thickness of the limestone

(Thanks to Chandrasekhar, ANU)

Solution:

Given that width of outcrop (W) = 20 m

Slope of the ground (i) = 10⁰

Dip of the strata ($\theta$) =25⁰

Thickness of the bed (d) =?

Case (1):

If the slope of the ground and dip of the strata are in the same direction, then

The thickness of the bed (d) = $ width(W) \times\sin(\theta-i)$

= $20 \times\sin(25-10)$

=$ 20 \times\sin(15)$

=$20\times0.2588$

=$5.17 m$

Case(2):

If the slope of the ground and dip of the strata are in the opposite direction, then

The thickness of the bed (d) = $ width(W) \times\sin(\theta+i)$

= $20 \times\sin(25+10)$

=$ 20 \times\sin(35)$

=$20\times0.5735$

=$11.47 m$

Reference : Principles of Engineering Geology by K.M. Bangar. (Pg No :415)