I wonder whether C, phi, and Ka or Ko are the right model to use. I have heretofore assumed that CLSM pressures (prior to curing) had to be treated as if it were a fluid (>110 pcf?), especially if gets a little vibration. Is that not correct?
Once it sets, it would seem to me that it's out of the range of typical soil mechanics, and would not need any lateral confinement to keep it in place (unless the fill is so high that its shear strength comes into play, or the CLSM wants to swell against rigid boundaries). Either way, the flowable stage would, I believe, govern the lateral support requirements.
How would you test that? Maybe start by assuming an unconfined compressive strength of what, 100 psi? This gives a shear strength of roughly 50 psi or 7200 psf (conservatively assuming a flat strength envelope). If you were to analyzed a vertical cut in material with that strength, you would probably find that it's stable to a pretty good height. If it is, then the lateral pressure would be pretty small, unless the CLSM tries to swell against rigid boundaries, or something like that.
Bon chance!
DRG