 Solution

Retain $a={\varphi }_1$, ${\varphi }_2=2a$ and the three settling shock speeds. A triple-shock sedimentation point requires the meeting of $V_2$ with $V_3$ to coincide with the meeting of $V_1$ with $V_2$. HenceSolving, and using the deposit-front position $2u_{s}at$, givesThe common height also equals $a(H+z_m)$, independently checking mass conservation. The second panel of the compression-shock diagram shows $V_1,V_2,V_3$ meeting at this point. For $t>t_c$ the suspension is exhausted: deposit below $h_c$ and clear fluid above it are separated by a stationary shock, with zero flux on both sides.