That's what I suspected.
Your method is very similar to what I generally use for a temporary patch, until you can dig up, cut out the broken section and splice in a new piece.
However I would add a few steps and this is best done when everything is dry.
- Clean the pipe surfaces with a wire brush.
- Make a tin cover that overlaps the hole, take time to make it well fitting and extending a couple of inches beyond the hole. Apple juice cans often provide a good source of material.
- Apply a good quality outdoor caulking around the hole and press the tin patch in place.
- Before covering the whole thing with a layer of concrete I would paint the entire area with a coating of concrete bonding agent, available at HomeDepot. Or you could use a 1/2 inch layer of Top and Bond cement, (it has bonding agent already in it, but can only be applied in thin layers).
- When that cures apply a healthy layer of concrete over the whole patch area extending a foot in both directions.
good luck
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