In high-altitude cold and arid regions, underground rock masses are subjected to long-term cyclic effects such as wet-dry alternation, freeze-thaw cycles and other combined environmental factors leading to the propagation of existing fractures or the initiation of new ones. Meanwhile, overburden weight and engineering disturbances further exacerbate rocks failure. To simulate the deformation and fracture process of rocks under the combined action of multi-environmental factors cycles and loading, a generalized damage model for rocks based on residual strength characteristics was proposed by introducing statistical damage theory. A theoretical calculation method for the generalized composite damage variable was derived, a damage constitutive model suitable for arbitrary multi-factors cycles-loading conditions was subsequently established, and the methods for determining the model parameters were given. Validation results demonstrated that the proposed model accurately described the deformation and fracture behavior of rocks under wet-dry cycles (WDCs), freeze-thaw cycles (FTCs) and wetdry-freeze-thaw cycles (WDFTCs), outperforming existing models in predictive capability. The influence of multienvironmental factors cycles on the load damage evolution was revealed. This model provides theoretical support for enhancing the design reliability and long-term operational safety of underground engineering in highaltitude cold and arid areas.