Context: Planetary embryos can continue to grow by pebble accretion until they become giant planet cores. Simultaneously, these embryos mutually interact and also migrate due to torques arising from the protoplanetary disk. Aims: Our aim is to investigate how pebble accretion alters the orbital evolution of embryos undergoing the Type-I migration. In particular, we study whether they establish resonant chains, whether these chains are prone to instabilities and if giant planet cores form

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... embryo merging, thus occurring more rapidly than by pebble accretion alone. Methods: For the first time, we perform self-consistent global-scale radiative hydrodynamic simulations of a two-fluid protoplanetary disk consisting of gas and pebbles, the latter being accreted by embedded embryos. Accretion heating, along with other radiative processes, is accounted for to correctly model the Type-I migration. Results: We track the evolution of four super-Earth-like embryos, initially located in a region where the disk structure allows for a convergent migration. Generally, embryo merging is facilitated by rapidly increasing embryo masses and breaks the otherwise oligarchic growth. Moreover, we find that the orbital eccentricity of each embryo is considerably excited (≃0.03) due to the presence of an asymmetric underdense lobe of gas, a so-called 'hot trail', produced by accretion heating of the embryo's vicinity. Eccentric orbits lead the embryos to frequent close encounters and make resonant locking more difficult. Conclusions: Embryo merging typically produces one massive core (≳ 10 M_E) in our simulations, orbiting near 10 AU. Pebble accretion is naturally accompanied by occurrence of eccentric orbits which should be considered in future efforts to explain the structure of exoplanetary systems.