In general, soil pumping is an expression of locallized, excess pore water pressure. Please note that the soils do not have to be entirely saturated but, subjected to heavy and changing loads. A wet near surface or surface layer 'squishes' from beneath the load. Or, water can be literally 'pumped up' from depth, I have seen over 8 feet.

The soil type will have a large influence on the amount and appearance of 'pumping'. Some soils, such as silt, very fine sands and silty clays are very sensitive and can be quickly overworked. Sometimes these soils have a nearby watertable, the soils have been overworked and just require no compactive effort for a period of time and will 'heal'. In this case of a nearby watertable, immediate reworking the upper soils will not result in any improvement.

Proof Rolling always requires 'local calibration' and several 'knowns'. The location of the water table will determine whether large amounts of subgrade rolling (pumping) are due to deeper subgrade problems or to a wet, near surface layer. Each situation may require very different responses.

Actual rutting during the final stages of fill placement is generally not acceptable but, the final use will govern how much instability can be tolerated. I often times use a preliminary proof rolling to recommend the amount of soil improvement (Structural Fill Thickness, use of Geofabrics and/or Geogrids). Final proofrolling oftentimes results in deflections and sometimes very minor rutting of less than 1/2 inch. I have been on some projects, with very high ground water tables, in which rutting up to 1-1/2 inches was still acceptable.

I am sure that others in this forum will have more to add, based upon a wide range of experiences.

We use proofrolling to detect near surface zones of bad fill materials, or soft clays or clayey sands.  We normally recommend use of a loaded dump truck for proofrolling.  Areas where the soil ruts permanently are identified by the proofrolling operations.  One can then perform shallow manual auger borings or manual cone penetrometer soundings to determine the depth to and the thickness of the weak soil.  These borings/soundings can also be performed in areas that did not rut in order to calibrate the cone data.  Pumping occurs due to  vibrations in saturated or near-saturated soil profiles.  Pore pressures will dissipate with time if the vibrations are stopped. Clean sandy fill can be compacted using a dozer if pumping becomes a real problem.

I am a firm believer in quantifying everything, including proofrolling. Proofrolling basically measures stiffness. I don't mean to sound commercial, but Humboldt Mfg. Co. Norridge, IL manufactures a device that measures both the structural stiffness and soil modulus. Worth checking out.

As both Emmgjld and KAM stated, proofrolling is a localized, site-relative issue.  It is mostly subjective and not easily quantifiable, nor is it usually necessary to quantify.  As Emmgjld stated, the manifestation is local...surface yielding or pumping under load.  This has to be compared to the areas around the yielding in a subjective manner (for instance, is this spot deflecting greatly as compared to this other spot over here that has been subjected to the same loading).  For this reason, heavy rubber-tire vehicles are often more effective for proofrolling than compaction equipment.