How to use $variables from theme setting in main menu
You can't use name suggestions with double underscore in preprocess function names.

You have to replace this with an if statement in code:

function saka_theme_preprocess_menu(&amp;$variables) {
  if ($variables['menu_name'] == 'main') {
    $variables['social_url_fb'] = theme_get_setting('social_url_fb','saka_theme');
  }
}