The current research was implemented to monitor and rehabilitate the structural health of Masjed-E-Soleyman dam (MESD). With a height of 177 m, the MESD is one of the highest rockfill dams in Iran, and suffers from extensive and unpredictable settlements and related cracks. To investigate the non-homogeneous (conglomerate) rockfill's brittle behaviour in before–after and during triaxial tests, a series of laboratory tests under conventional stress paths were carried out using a large-scale triaxial apparatus. A numerical time-dependent model was used to find a relationship between particle breakage and the time-dependent settlement of the embankment dam. The core aim of this work was to investigate particle breakage of the conglomerate material in the MESD and to identify the non-homogeneous relative particle breakage index (RPBI) by establishing a relationship between the RPBI for this material and plastic work. The research was divided into three significant steps. The breakage index (before–after tests) was calculated in the first step. The relationship between the breakage index and plastic work (during tests) was then introduced. Finally, the future crest settlement of the MESD was predicted using a numerical viscoelastic Burgers model that was calibrated using accurate monitoring data of the dam.