Adding a parameter to a Split URL variation while transferring the query parameters.

To add a parameter to a Split URL variation you should configure the Split URL parameters in the following way:

Original URL

http://www.domain.com/([^\?]+)?\?{0,1}(.*)$

Variation 1 URL 
http://www.domain.com/$1?name=value&$2

Make sure you exclude URLs in the Site Area with name=value parameter.