While I understand that new concrete won't stick to old concrete, and that the purpose of the Bondfast suggested in the previous post is to physically glue the new concrete to the old, a better choice would be a concrete bonding agent, like this one:
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available from Home Depot and other stores.
A white wood glue like Bondfast, Weldbond or Elmer's Wood glue will re-emulsify (that is; dissolve in water, kinda) if it gets wet and stays wet for a long period of time. Furniture makers use wood glue for their furniture joints because it's strong AND because the joints can be taken apart to repair broken furniture by keeping the joints wet to dissolve (kinda) the glue in them.
Different concrete bonding agents work differently. Some use a resin (either PVA or acrylic) that gradually crosslinks with it's neighbors after the glue dries. That crosslinking turns the glue into one great big molecule which is too large to "dissolve" in water and is therefore no longer affected by moisture the way a white wood glue would be. Others have a chemical reaction that kicks in anywhere from a few hours to a few days after painting the bonding agent onto the concrete. The moisture from the fresh concrete re-activates the concrete bonding agent if it's dried up, and that re-activated bonding agent glues the new concrete to the old. However once that chemical reaction kicks in after the time window passes, the concrete bonding agent becomes unaffected by moisture, so that continuous contact with ground water won't affect it in any way.
Since rain storms only last a coupla days at most, you can generally get away with using white wood glue instead of a concrete bonding agent. However, if you're going to do any concrete repairs below grade or where the concrete can stay wet for long periods of time, then it would be better to use a concrete bonding agent instead of a white wood glue. Using a concrete bonding agent will ensure that any concrete repairs you do won't come apart if the concrete stays wet for a long time.
PS: You don't need to know the rest... Re-emulsifying is different than dissolving. When sugar dissolves in water, the result is individual sugar molecules suspended in water, and so there is no solid phase present. When white wood glue re-emulsifies in water, you have polyvinyl acetate resins suspended in water. Each of those resins is a microscopically small particle of solid plastic, and therefore you do have a solid phase present. Incident light will reflect and refract at a solid/liquid interface because there's a difference in the refractive index of the two media. This is why white wood glue is white in colour while it's in the jug, dries to a clear colourless solid, and then turns the water milky white again as it re-emulsifies again in water. The solid resins suspended in water make the slurry look white for the same reason that clowds and snowbanks and the head on a beer is white; it's because incident light reflects and refracts at each phase boundary and your eye sees the resulting mixture of different frequencies of light as the colour "white". If white wood glue DISSOLVED in water, the water solution would be clear just like ordinary water because there wouldn't be any solid plastic present to reflect and refract light.
In fact, all the milky white liquids you buy that turn clear as they dry (like grout sealers, floor "waxes", white wood glue, etc.) behave that way because they contain solid particles that reflect and refract light. As the liquid evaporates, those solid particles fuse together, thereby eliminating the liquid/solid interfaces where that reflection and refraction occured, and that eliminate the white colour. The reason why latex paints darken as they dry is because they contain plastic resins as well, and as the paint dries, you no longer get the white colour being produced by reflection and refraction, and as that white discolouration disappears, the colour of the latex paint appears to darken.