Advanced computational modelling can provide a powerful tool for material investigation and characterisation. For concrete materials, appropriate description of the heterogeneity and realisation of complex fractures are two challenging aspects in high fidelity numerical simulations. This paper presents a new mesoscale model for concrete with the ability of simulating natural evolution of fracture at the interface between the aggregates and mortar matrix and without restriction to the loading conditions. To this end, a combined cohesive and contact interface approach is employed. The contact-friction process at a fractured interface is treated as an independent process that complements the general cohesive law, thus allowing the closure of cracked surfaces and the development of residual shear resistance in a realistic manner. Parametrisation is conducted to examine the effects of pertinent interface parameters on the macroscopic behaviour of concrete. The modelling approach is demonstrated to be capable of simulating the behaviour of concrete under a variety of loading conditions, including confined and dynamic compression. The new mesoscale model provides a comprehensive numerical means for investigating into the micro-mesoscale mechanisms underlying the macroscopic behaviour of concrete.