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With regards to the installation below, I am assuming that you are installing the MGS as a strong post median barrier system. This has been approved by FHWA with 12” blocks, and was subsequently tested at TTI using 8” blocks.

Installation of the strong guardrail posts in asphalt can be problematic as it limits the ability of the post to rotate in the soil and absorb energy. MwRSF and TTI have both conducted research related to this issue in the past.

http://mwrsf.unl.edu/researchhub/files/Report246/TRP-03-119-03.pdf

http://tti.tamu.edu/documents/0-4162-2.pdf

In the MwRSF research, the researchers designed an evaluated a system for installation of guardrail posts in rock where full embedment was not possible and backfilled cavities were placed in the rock to allow for post rotation. As part of this effort, MwRSF also made recommendations regarding the placement of posts in road paving. If guardrail posts are to be installed in pavement, such as in shoulders alongside the roadway, it was recommended to blockout a portion of the pavement so that the post would have room to rotate backwards. This could be done for both W6x9 steel and 6-in. x 8-in. timber posts. The size of the blocked out portion of the pavement for the post was recommended by assuming the post would rotate around a point two-thirds the depth of full embedment, and the post would be allowed to deflect backwards 18 in. at the rail midpoint height before contact with the pavement. The figure below shows possible geometries for blockout portions of pavement. Backfill with confined compression properties similar to ASTM C33 coarse aggregate, size no. 57, would possibly be acceptable for this application, but it was noted that further testing should likely be conducted. Thus, based on this research a 18” wide portions of roadway would be recommended for a roadside system (with the post located 1” from the front of the removed pavement). If you have median traffic and impacts, the post would need to rotate both ways, so the blocked out pavement would need to be 28” wide to allow for the same motion of the post in both directions with the post in the center of the removed pavement.

Subsequent research at TTI looked at grout filled leavouts for mow strips. Both steel and wood post systems were tested with 18 in. × 18 in. square leave-outs. It was noted that a 18 in. diameter round leave-out provides approximately the same area of leave-out material around the post and was considered to be an acceptable alternative to the square leave-out. Without further testing, these were considered to be the minimum acceptable dimensions for the leave-outs.  The material used to backfill the leave-outs was a standard two-sack grout mixture. Tests indicated a maximum 28-day compressive strength of 0.85 MPa (120 psi) for this material. Other leave-out backfill materials (e.g. foams) may be accepted as alternatives to the two-sack grout provided their compressive strength does not exceed that of the grout.

Thus, the TTI work came to a very similar conclusion regarding the size of pavement removed. Thus, we would likely recommend a 28” wide pavement removal with the posts installed in soil in the middle. If you wanted to use a leaveout backfill material in that area, the TTI recommendations for that material should be followed.

Let me know if that answers your question or if you need further information.