This work presents a new damage criterion suitable for elastic, elastic-plastic/viscous or elastic-viscous-plastic materials involving rupture effects. Its derivation, made here within a thermodynamic framework, follows previous scalar-valued damage mechanics approaches. Such approaches are appropriate to many geophysical problems involving quasi-brittle materials for which there is no clear physical justification for the level of complexity of a tensorial damage variable. Distinction between the mechanical response to compressive and tensile stresses is therefore not introduced by the damage itself but via a special definition of the Helmholtz free energy. This scheme differs from previous ones in that it combines with an evolution of Poisson's ratio with the level of damage, which allows expressing the damage criterion in the principal stresses space. Moreover, there is no need to compute the stress eigensystem, which makes it simpler to implement than the Mohr-Coulomb damage criterion. Here we derive this damage criterion and compare it to observations of the variations of the bulk modulus in damaged geomaterials. We also compare it to in-situ stress measurements and find a good agreement in terms of the shape of the criterion in the stress space. We tentatively interpret the results in the context of previous studies of rock and ice mechanics.