Limited heights of vertical cliffs and mountain walls linked to fracturing in deep tunnels - Q-slope application if jointed slopes

Intact brittle rock can fail in tension even when all principal stresses are compressive.This is due to lateral expansion and extension strain when near to a free surface, caused by Poisson's ratio.Exceeding tensile strength due to stress anisotropy and Poisson's ratio are the fracture-initiating conditions around deep tunnels, not the increasing mobilization of compressive strength, commonly beyond 0.4 x UCS.In a related discovery, the limiting height of vertical cliffs and near-vertical mountain walls can also be explained using extension strain theory.The range of limiting heights of approximately 20m for cliffs in porous tuff to record 1,300m high mountain walls in granite are thereby explained.Tensile strength is the weakest link behind cliffs and ultrasteep mountain walls.Sheeting joints can also be explained by extension strain theory.Maximum shear strength is the weakest link when stress levels are ultra-high, or when there is jointing and maximum slope angles is the issue.Here one can use Q-slope.The world's highest mountains are limited to 8 to 9km.This is due to non-linear critical state rock mechanics.It is not due to UCS.