change base url adding string after /

Hi,
I’m moving a wp installation to another server and I’m trying to make it accessible through a url such as:
http://www.domain.com/string
I’m testing it without https for now, because normally I use varnish, so the ssl certification is not directly installed on the webserver, and I want to know exactly how the server itself reacts.
This my apache config:

<VirtualHost *:80>
        ServerName www.domain.com
        ServerAdmin my@email.com
        DocumentRoot /var/www/html/string
	<Directory /var/www/html/string>
	AllowOverride all
	Options -Indexes +FollowSymLinks +MultiViews
	</Directory>
        ErrorLog ${APACHE_LOG_DIR}/error.log
        CustomLog ${APACHE_LOG_DIR}/access.log combined
</VirtualHost>

Here is the .htaccess of the document root:

<IfModule mod_rewrite.c>
Options +FollowSymLinks
RewriteEngine On
RewriteBase /
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule .* /index.php/$0 [PT,L]
</IfModule>

As it is, I can access phpmyadmin after changing the alias to /string/phpmyadmin /usr/share/phpmyadmin. So I needed to add the “/string” part. That’s not an issue.
The problem is that I cannot access wp-admin using the domain.com/string/wp-admin url. It simply ignores the request and leads me back to domain.com/string. I’m not sure exactly what I’m doing wrong.
From wp-config.php:

define('WP_HOME','http://www.domain.com/string/');
define('WP_SITEURL','http://www.domain.com/string/');

Any ideas?
Thanks