Display more than 10 posts on author.php file

when you use the loop the number of post displayed is choosen fron the option set in Settings->Reading in you backend. It affects all the standard loops, not only the author page.

To change only for author page you have to use pre_get_posts hook and set the wanted number of posts using posts_per_page argument:

add_action('pre_get_posts','change_numberposts_for_author');

function change_numberposts_for_author( $query ) {
  if ( ! is_admin() && $query->is_main_query() && is_author() ) {
    $query->set('posts_per_page', 30); // 30 is the number of posts
  }
}

See also is_author() on Codex