The query you need to use is not so complicated as you basically just what to get posts from only certain taxonomies. You are right that you should use the `tax_query`.

The first thing that you should do is collate all your category IDs in only one array as there is no need for multiple ones since you are only using the `IN` condition (that means posts that belong to at least one category in the list). It makes code error-prone and slow to have multiple tax queries when one would suffice.

The problem with your query is that you are using a `AND` relation that is never true in your case (ie. you don't have a post that is *at the same time* in categories 108 or 109, *and* in categories 112 or 113).

So I would suggest you use WP_Query args like so:

    $args = array(
    	'post_type' => 'post',
    	'tax_query' => array(
    		array(
    			'taxonomy' => 'category',
    			'field'    => 'term_id',
    			'terms'    => array( 108, 109, 112, 113, 114, 115, 116, 117, 118, 102, 103 ),
    			'operator' => 'IN',
    		),
    	),
    );

Or if the internal logic prevents you from doing this, one-level deep with OR relation:

    $args = array(
    	'post_type' => 'post',
    	'tax_query' => array(
    		'relation' => 'OR',
    		array(
    			'taxonomy' => 'category',
    			'field'    => 'term_id',
    			'terms'    => array( 108, 109 ),
    			'operator' => 'IN',
    		),
    		array(
    			'taxonomy' => 'category',
    			'field'    => 'term_id',
    			'terms'    => array( 112, 113 ),
    			'operator' => 'IN',
    		),
    		array(
    			'taxonomy' => 'category',
    			'field'    => 'term_id',
    			'terms'    => array( 114, 115, 116 ),
    			'operator' => 'IN',
    		),
    		array(
    			'taxonomy' => 'category',
    			'field'    => 'term_id',
    			'terms'    => array( 117, 118 ),
    			'operator' => 'IN',
    		),
    		array(
    			'taxonomy' => 'category',
    			'field'    => 'term_id',
    			'terms'    => array( 102, 103 ),
    			'operator' => 'IN',
    		),
    	),
    );

Let me know how this goes.