How to filter table from some rows without flattening it?

Consider the following table:

a1[x_] = If[x < 1.1, 3, Pi/2]
tabb = ParallelTable[{x, y, z, a1[x]}, {x, 1, 2, 0.1}, {y, 
   0.5, 1, 0.1}, {z, 1, 3, 1}]

Here, a1[x] is some function that mimics some realistic functions; in reality, they may depend on other parameters except for x, and change in a different manner than just with x $>1.1$.

The output looks like {{{row,row,…},{row,row,…}},…},…}:

{{{{1., 0.5, 1, 3}, {1., 0.5, 2, 3}, {1., 0.5, 3, 3}}, {{1., 0.6, 1, 
    3}, {1., 0.6, 2, 3}, {1., 0.6, 3, 3}}, {{1., 0.7, 1, 3}, {1., 0.7,
     2, 3}, {1., 0.7, 3, 3}}, {{1., 0.8, 1, 3}, {1., 0.8, 2, 3}, {1., 
    0.8, 3, 3}}, {{1., 0.9, 1, 3}, {1., 0.9, 2, 3}, {1., 0.9, 3, 
    3}}, {{1., 1., 1, 3}, {1., 1., 2, 3}, {1., 1., 3, 3}}}, {{{1.1, 
    0.5, 1, 3}, {1.1, 0.5, 2, 3}, {1.1, 0.5, 3, 3}}, {{1.1, 0.6, 
    1, [Pi]/2}, {1.1, 0.6, 2, [Pi]/2}, {1.1, 0.6, 3, [Pi]/
    2}}, {{1.1, 0.7, 1, [Pi]/2}, {1.1, 0.7, 2, [Pi]/2}, {1.1, 0.7, 
    3, [Pi]/2}}, {{1.1, 0.8, 1, [Pi]/2}, {1.1, 0.8, 2, [Pi]/
    2}, {1.1, 0.8, 3, [Pi]/2}}, {{1.1, 0.9, 1, [Pi]/2}, {1.1, 0.9, 
    2, [Pi]/2}, {1.1, 0.9, 3, [Pi]/2}}, {{1.1, 1., 1, [Pi]/
    2}, {1.1, 1., 2, [Pi]/2}, {1.1, 1., 3, [Pi]/2}}},...}

It has a block-like structure. I would like to exclude rows for which a1 = $pi/2$. I may easily do this using Flatten[tabb,{1,2,3}], but the structure of the table would be destroyed (in general, the table may be much more complicated). Is it possible to remove such rows without destroying the structure of the table?

DeleteCases[t, {_, _, _, Pi/2}, {3}] /. {} -> Nothing