Fig. 3. Simulation of critical and super-critical crack lengths normalized by the elastic length Λ as a function of the normalized slope angle.

A simulation is presented of critical (green squares) and super-critical (red circles) crack lengths normalized by the elastic length Λ as a function of the normalized slope angle $\left(\psi -{\varphi }^{*}\right)/\varphi$ (ϕ, friction angle; ${\varphi }^{*}$, effective friction angle). Solid and dashed lines correspond to theoretical curves for effective friction angles of ${\varphi }^{*}=\varphi$ and ${\varphi }^{*}=0.4$, respectively. The inset shows ${\varphi }^{*}/\varphi$ as a function of the collapse amplitude h normalized by weak-layer thickness D_wl (data points correspond to an average of several simulations and error bars represent the s.d.).