In this work, a computational framework to simulate crack propagation in a heterogeneous material under drying conditions is proposed. The numerical approach is based on a finite strain phase field formulation, devised to reproduce experimentally determined crack paths and deformation patterns(under given boundary conditions). The effects of geometry, mechanical parameters and uncertainties are first discussed by using parametric analyses. The modeling effort is next complemented by the development of specific experiments on wet clay samples, filled with solid stiff inclusions. The experimental data thus obtained are finally used to identify model parameters and assess the relevance of the framework.