Radial pressure gradient as a function of the orbital distance for discs with a viscosity of α = 5 × 10⁻³. Left panel: radial pressure gradients that originate from the discs displayed in Fig. 3. Middle panel: pressure gradient of discs that feature a transition in the dust fragmentation velocity for different water abundances (Fig. 4a). Right panel: pressure gradient of discs with a transition in the dust fragmentation velocity to 5 m s⁻¹ and different dust-to-gas ratios, as well as a disc featuring a transition in the dust fragmentation velocity from 1 to 10 m s⁻¹ and a dust-to-gas ratio of 1% (Fig. 4b). The coloured bars in Figs. 6b and 6c indicate the position of the ice line and are displayed in the colour of their respective disc parameters.