Geomechanics and Ground Control · Geomechanics · 2 marks · Numerical answer
A 100 mm high rock specimen with one horizontal joint is loaded vertically at 20 MPa as shown. Rock elastic modulus is 10 GPa and joint normal stiffness is 5 GPa/m. With one-dimensional elastic behaviour, find loading-surface displacement in mm, to one decimal.
Rock compression is σL/E = (20/10000)×100 = 0.2 mm. Joint closure is σ/kn = 20×10⁶/(5×10⁹) = 0.004 m = 4.0 mm. These series displacements add, giving 4.2 mm. Joint stiffness is per unit opening displacement, unlike the rock modulus.
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