Firstly you need to import JSON content to your application as a string what can be done with file_get_contents().
After that you have to decode--or "translate"--JSON format to PHP primitives via json_decode(). The result will be the expected array to be handled.
Then you may append a new item to that array using [] suffix eg. $a[] = $b;
These three steps are exemplified below.
// get raw json content
$json = file_get_contents('data.json');
// translate raw json to php array
$array = json_decode($json);
// insert a new item to the array
$array[] = array('2015-11-24 20:54:28', 177);
In order to update the original file you have to encode PHP primitives to JSON via json_encode() and can write the result to desired file via file_put_contents().
// translate php array to raw json
$json = json_encode($array);
// update file
file_put_contents('data.json', $json);