If rainwater or any other water gathers in a ditch and is less than kur (there is a difference of opinion on what amount is exactly kur, and there are different ways of measuring it, according to Imam Khomeini, one way is that if the three dimensions of a container measure to be three and a half hand spans each, it is kurr), after it stops raining, if any nijasah (anything that is najis) comes in contact with the water, all of the water will become najis. Therefore, since dogs are najis, if they come in contact with the wet pavement after rain, only the sections they have come in contact with become najis and if one’s shoes or feet or anything else come in contact with those sections while they are wet, they will become najis too.
Of course, if the sun shines on the pavement that has become najis as a result of coming in contact with a dog, causing the wet pavement to dry, the pavement will become tahir (the opposite of najis, pure, clean). In this case, if one walks on the pavement his/her shoes will not become najis.
Also, walking on the ground makes ones shoes tahir without any need for washing with water, given that some conditions are observed which you can learn about by referring to the risalahs.