The damage mechanics challenge (DMC) represents a critical step in predicting the damage evolution and failure in rock-like materials displaying brittle/quasi-brittle characteristics. The phase-field fracture (PFF) model is a type of damage mechanics model that is thermodynamically consistent and is well suited for capturing complex crack patterns and interactions in 3D. However, there are two main shortcomings: (1) the definition of the crack driving force function and calibration of model parameters give rise to uncertainty in predictions of load–displacement curves; and (2) the finite element implementation of the PFF model generally necessitates the use of fine meshes, leading to higher computational costs. This study presents a novel numerical methodology that employs h-adaptive algorithms in combination with the stress-based PFF model, and demonstrates its validity against experimental data, as required by the DMC. The core strength of our methodology lies in its computational efficiency derived from dynamically-adaptive local mesh refinement. The potential of our methodology is further demonstrated through calibration, verification, and validation studies. Our 2D and 3D simulation results show good agreement with the benchmark laboratory data from three-point bending experiments, within the bounds of data uncertainty. Our blind prediction of the 3D crack geometry for the final challenge shows good agreement with the corresponding experimental data. We find that the stress-based PFF model simplifies the parameter calibration process to a single critical stress parameter, which reduces uncertainty.