If I may offer a small bit of advice. While it doesn't necessarily address the repair itself, I have seen similar issues. Once you do find a suitable method of repair and you've excavated the outer perimiter, I would suggest backfilling with clay and only adding a couple inches of topsoil for grass. The combination of repair and a 8-12" clay cap should ensure you never have another problem. Just be sure to hand tamp (every 2-3") and not use a plate tamper or jumping jack as it could damage both your repair and the foundation.
Best of luck!