A thermodynamically consistent damage model for concrete is proposed, which accounts for the anisotropy induced by damage, and for the unilateral effects upon transition from tension to compression. The main features of the model are: (i) limited number of parameters: 5 material parameters in addition to elastic constants; (ii) two damage variables: a second order symmetric tensor pertaining to damage created in tension and a scalar pertaining to damage created in compression; (iii) an activation criterion that couples the evolution of both damage variables; (iv) a strain-dependent threshold that accounts for the asymmetry between tension and compression and for the confinement effect. The model fits within the framework of standard generalised materials, as defined by Halphen and Nguyen (1975). Numerical simulations exhibit satisfactory model predictions when compared to experimental tests.