Round Up kills by contact with the green parts of a plant, won't damage roots by washing. You can rake the weeds out of the gravel, pull them out one by one or use Round Up.

Over the years that this gravel has been down dust from the air and bits of organic matter have filtered in between the stones and those weeds you are seeing are germinating and growing in that soil. Spraying with a plant poison is simply attacking the symptom of a problem, plants growing where there is soil. The long term control here would be to remove the stone (gravel) and wash the soil out, and then replace the stone. Spraying with some plant poison will kill those "weeds" and the dead plant material will, eventually, filter down between the stones adding more material for plants to grow in causing you to have to buy more plant poison to control the plants growing in that soil that is being created there.

ortho ground clear will stop the problem for several years if applied correctly, but as kimmsr pointed out above the only real way to stop it is remove the gravel and redo it. if you use the ortho, be careful as it WILL sterilze all soil it contacts. best to use RU and repaet as necessary.

at our tower sites we put down a layer of THICK fabric before the gravel goes down. this stops the gravel settling in and keeps weeds at bay for years. even so, after several year they start to grow and the only thing to do then is spray them or redo the gravel.

Thank everyone very much. I have printed out the suggestions and will follow-thru!