First I will give a disclaimer. If you have high flow through amounts of water, that in my opinion is going to be a lot harder repair than if you only had occasional low amounts of overflow. Having gotten that out of the way, will give you some general tips I have picked over the years. They will not answer your specific questions, but might be helpful in formulating your own solutions.
There are several tricks you can do with equipment to get it to give you more compaction than would normally be associated with that piece of equipment.
A regular tractor or TLB can give you a lot of compaction by using the front tires to compact with the front end loader bucket full of dirt. The small tire with a heavy load on it will exert a lot of pressure on the ground and the lugged portion even more. I have used this to advantage packing in clay around pipes by running the tire width repeatedly along the side of the pipe, moving over the width of the tire, and repeating. Then split the middle on the next compaction pass. This is slow. You would not want to do a whole pond bottom this way. But it is an effective way to compact a small area fairly well. Ag tread tires works better than industrial tread in this application because the lugs are narrower and deeper and tend to knead the soil better, but either will work. Make sure soil moisture levels are conducive to good compaction. Add water if needed or let things dry some between packings if it is too wet.
A dozer can be operated in such a manner to compact better than the advertised PSI per square inch loading would indicate. Again, this is good only for specific small areas and not suitable for compacting large areas. First of all, the grouser bars exert a lot more pressure than the overall track. So repeated passes. Many, many passes allow the grouser bars to compact more than what would happen in only a single pass. Multiple angles also help. Another trick on something like a pond dam is to compact cross wise to the dam direction. By climbing over the top of the dam if the front and rear idlers are off the ground you can up to double the pressure on the grouser portion that is touching in the middle. Small dam doable, huge dam get the proper equipment. It is a work around, not the general correct way to do something.
As far as patching a hole in a dam, this is the way I would approach it. It may or may not be the correct way. Water is going to try and follow the path left where the old part of the dam follows the new dirt. So try to make that transition as long as possible. One way would be to use a back hoe and trench lengthwise the dam on both sides of the break. This lets your dam repair take on a "Tee" formation instead of just plugging the original break. Also take this "tee" down below the grade of the original break. Make that water have to follow a longer path to get through to the other side, instead of just the distance of the width of the dam. Here is a good place where the front end tire of a tractor with a load of dirt in the loader bucked for weight can be used to compact this "Teed" portion of the dam repair. It goes without saying have the proper material to repair area. Clay is good but actually a mix of clay and topsoil, completely mixed, is better. Straight clay can crack with wetting and drying. Having a certain mix of topsoil helps out with this. According to our local NRCS guy most of our topsoils alone will seal adequately for a pond dam because our clay content is high enough to do so. But he also said to put the best clay material in the center portion of the dam and not rely on the lower content topsoil. Always put your best sealing material in the middle of the dam.
That is what little I think I know. Use it at your own risk. I'm not a contractor. I'm not a professional. I'm a flunky farmer with some construction equipment, but I have been running equipment for well over 40 years so I do have at least some practical experience.
