The need of sustainable resilient structures and infrastructures push towards the use of cementitious materials able to heal micro-cracks and defects. For real structural application under service loading the time-dependent behavior is of the utmost importance, especially in presence of cracks which can lead to a nonlinear creep behavior that might cause the structural failure. Now the new challenge is to study and quantify the effect of crack-healing on the nonlinear creep behavior. This study aims at the following goals: 1) to characterize with experimental investigations the effect of the healing in tests in which the specimens, along the exposure time and under controlled environmental conditions, are under sustained load, the expected service load, determined as a fraction of the pre-cracking load; 2) develop a comprehensive numerical framework for the interpretation and simulation of the experimentally observed results. To this purpose an experimental investigation is currently ongoing at Politecnico di Milano with reference to an Ultra High-Performance Concrete developed in the framework of the H2020 ReSHEALience project for exposure to extremely aggressive environments. The numerical framework is based on the recent developments of the multiphysics lattice particle model