I am not sure if this is an aesthetic problem or not. I suspect that if I do not fix the damage properly the water will continue to infiltrate the cracks and it will create larger problems in the future.
Here are some pictures
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Water plays a major role when maintaining the surface of your driveway. It can have drastic effects on concrete surfaces. When it is absorbed or flows into a hardscape, water will start it's damage by an expansion and contraction cycle. This is accelerated in climates that are prone to freezing weather. Hot weather and exposure to direct sunlight (UV rays) will also degrade roadways. Asphalt, which doesn't have the inherent strength of concrete, needs more maintenance in order to increase its longevity and keep it aesthetically pleasing. From looking at your photos it would be wise to consider investing some repair time to your asphalt and concrete surfaces. For asphalt repair: 1) clean soil from cracks and fill with an asphalt filler. 2) After the filler is dry, squeegee the surface with a sealer specifically made for asphalt. The sealer flows into the porous gaps and fills fissures that allow water to penetrate. It also dries to a uniform black color which looks aesthetically pleasing. Depending on your climate, resealing should be between 2-4 years (+/-). Concrete, doesn't need as much care. It should be sealed with a sealer made for concrete (if it's less than 2 months old wait for full cure). If cracks develop (like those in your photo's): 1) chisel-out loose pieces and try to form an inverted "V"- shape in the crack to allow for a better mechanical bond. 2) flush remaining dust and dirt with a water stream. 3) Apply a bonding agent to the crack walls (this isn't critical, but it helps with repair adhesion). 3) mix up a batch of store bought concrete repair patch, either powdered or pre-mixed, and apply. If the total concrete surface needs sealing it may be necessary to power wash and remove impurities so as to allow complete absorption of the sealer. Also if water can be seen as being absorbed by the concrete it can be sealed.