Vacuum out the gap between the porch and the house with shop vac, leaving no fragments of concrete inside the crack.
Combine 3 parts masonry sand with 1 part Portland cement in a wheelbarrow and mix thoroughly with a masonry hoe.
Wet the dry sand/cement mixture with a garden hose and continue to mix but do not saturate the dry ingredients. Too much water will turn the mixture into what brick layers call "soup." It should have a mud-like consistency.
Open a can of concrete bonding agent and pour it into the separation crack, lining the crack with the liquid bonding agent.
Tilt the wheelbarrow up immediately, pouring the wet concrete into the separation crack until it is full. Smooth the wet "mud" with a trowel and let it dry and harden for 24 hours before walking on it.