Khaled and I spend much of our time on site, joining fragments. The purpose of this is so that inscriptions are more easily read and frankly, so that these often small fragments do not become lost. In an outdoor environment, we need to use a durable adhesive. In this case, we use an epoxy with a barrier layer of a more reversable adhesive. Making joins that are perfect can be tough.
Often the surfaces are so eroded, there are not good clean areas to join. Also, getting the right balance, so that the pieces stay together while the adhesive cures can be a challenge. At least in Egypt, there is enough sand to make many sandboxes to assist in this effort.