Impact or thermal ignition of high explosives (HE) results in deformation that can lead to damage. Fractures or defects, combined with sufficient pressure, dramatically increase the available surface area and potentially changes even the mode of combustion. Recent impact and cookoff experiments on PBX 9501, (HMX, octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine, with a plasticized, Estane-based binder), have shown complex cracking patterns caused by impact or pressurization, Fast reactive waves have been observed to propagate through the cracks at hundreds of meters per second. We present experiments that examine the combustion of mechanically and thermally damaged samples of PBX 9501. Mechanically damaged samples, damaged by quasi-static compression, exhibit large, similar to200 mum stress fracture accompanied by extensive rubblization. Combustion experiments determine a 1.4 +/- 0.6 MPa critical pressure for the onset of violent convective combustion, consistent with connected porosity of 25 mum. Thermally damaged samples, damaged by heating in a 180 degreesC oven for 30 min, exhibit 2-20 mum cracks distributed throughout the sample. Combustion experiments indicate a 9.2 +/- 0.4 MPa critical pressure for the onset of violent convective combustion in the thermally damaged sample, consistent with connected porosity of 4 mum. Below the critical pressure, the burn rate and pressure exponent of thermally damaged PBX 9501 are close to those of the pristine material.