In this paper, we analyze column density and temperature maps derived from Herschel dust continuum observations of a sample of prominent, massive infrared dark clouds (G11.11-0.12, G18.82-0.28, G28.37+0.07,G28.53-0.25). We disentangle the velocity structure of the clouds using 13CO 1-0 and 12CO 3-2 data, showing that these IRDCs are the densest regions in massive GMCs and not isolated features. The probability distribution function (PDF) of column densities for all clouds have a power-law distribution over all (high) column densities, regardless of the evolutionary stage of the cloud. This is in contrast to the purely lognormal PDFs reported for near/mid-IR extinction maps. Only if we perform PDFs of the column density maps of the whole GMC, in which the IRDCs are embedded, we find a lognormal distribution for lower column densities. By comparing the PDF slope and the radial column density profile for three of our clouds, we attribute the power law to the effect of large-scale gravitational collapse and to local free-fall collapse of pre- and protostellar cores. A significant impact on the cloud properties from radiative feedback is unlikely because the clouds are mostly devoid of star formation. Independently from the PDF analysis, we find infall signatures in the spectral profiles of 12CO for G28.37+0.07 and G11.11-0.12, supporting the scenario of gravitational collapse. At least some of them are probably the same features as ridges(high-column density regions with N>10^23 cm^-2 over small areas) that were defined for nearby IR-bright GMCs. Because IRDCs are only confined to the densest (gravity dominated) cloud regions, the PDF constructed from such a clipped image does not represent the (turbulence dominated) low column density regime of the cloud.