More grout might not have saved Teton Dam.
1. The site geology was very bad, with huge open contraction joints in the volcanic rock (some you could walk into).
2. They did not adequately protect the narrow cutoff trench in bedrock from joints on its downstream side (no filter, no slush grout at the surface) and there were some very high gradients through the cutoff and over the grout cap. Furthermore, the narrow, steep-sided cutoff trench in the right abutment likely caused arching which could have made the confining stress lower than the pore pressure.
3. They were filling faster than their first-fill criteria allowed, and without adequate instrumentation to track seepage conditions. The river outlet was not yet functional.
4. The fill was borrowed mostly from ML aeolian silt, with low resistance to erosion.
Nobody knows exactly how it failed, so take your pick of several possible mechanisms.
Surprisingly (to me anyway), there are still farmers in the area who want Reclamation to go back and finish the dam.
If ever in eastern Idaho, take a side trip to the site, just outside of Rexburg, north of Idaho Falls on US 20. It's sobering.
(BTW, I'm no relation to the Mary Gillette who died in the flood.)