Your SQL is just 1 query, so not sure what you're trying to nest. But try the following:
$em = \Zend_Registry::get('em');
$qb_1 = $em->createQueryBuilder();
$q_1 = $qb_1->select('link_req')
->from('\Entities\link_requests','link_req')
->where( 'link_req.is_confirmed = 1' )
->andWhere('link_req.link_requestsSenderUser=:user_id or link_req.link_requestsSenderUser=:user_id')
->andWhere('link_req.link_requestsReceiverUser=:user_id or link_req.link_requestsReceiverUser=:user_id');
$q_1->setParameter('user_id', $user1_id);
$query = $q_1->getQuery();
echo $query->getSql();
Notice how I removed the $
in front of link_requestsReceiverUser
. I also made a parameter from $user1_id
, this prevents SQL injections.