How to split a path properly in PHP

Something like this maybe (if I got your intention right):

<?php
$str = 'dir1/dir2/dir3/dir4';

$output = array();
$chunks = explode('/', $str);
foreach ($chunks as $i => $chunk) {
    $output[] = sprintf(
        '<a href="#/%s">%s</a>',
        implode('/', array_slice($chunks, 0, $i + 1)),
        $chunk
    );
}

echo implode(' &gt;&gt; ', $output);

Output:

<a href="#/dir1">dir1</a> &gt;&gt; 
<a href="#/dir1/dir2">dir2</a> &gt;&gt;
<a href="#/dir1/dir2/dir3">dir3</a> &gt;&gt;
<a href="#/dir1/dir2/dir3/dir4">dir4</a>

I'd do it like this...

<?php

$path = 'dir1/dir2/dir3/dir4';
$dirs = explode('/', $path);

while (count($dirs) > 0) {
    $link = '/' . implode($dirs, '/');
    $text = array_pop($dirs);
    $breadcrumb = "<a href=\"$link\">$text</a>" . $breadcrumb;
    if (count($dirs) > 0) {
        $breadcrumb = ' &gt;&gt; ' . $breadcrumb;
    }
}

echo $breadcrumb;

If you are getting this path based on the URL you shouldn't need to use DIRECTORY_SEPARATOR because URLs should always use /. If it is derived from the filesystem path you would need to swap it in instead of '/' on line 4.

Var 1

<?php

    $str = '/dir1/dir2/dir3/dir4';
    $arr = array_filter(explode('/',$str));
    $out = array('/'.implode('/',$arr).'/');
    while((array_pop($arr) and !empty($arr))){
        $out[] = '/'.implode('/',$arr).'/';
    };

    print_r($out);

    /*
    Array(
       [0] => /dir1/dir2/dir3/dir4/
       [1] => /dir1/dir2/dir3/
       [2] => /dir1/dir2/
       [3] => /dir1/
    )
    */

?>

Var 2 ( Links )

<?php

    $str = '/dir1/dir2/dir3/dir4';
    $arr = array_filter(explode('/',$str));
    $out = array('<a href="/'.implode('/',$arr).'/">'.basename($str).'</a>');
    while((array_pop($arr) and !empty($arr))){
        $out[] = '<a href="/'.implode('/',$arr).'/">'.end($arr).'</a>';
    };

    print_r($out);

    /*
    Array
    (
        [0] => <a href="/dir1/dir2/dir3/dir4/">dir4</a>
        [1] => <a href="/dir1/dir2/dir3/">dir3</a>
        [2] => <a href="/dir1/dir2/">dir2</a>
        [3] => <a href="/dir1/">dir1</a>
    )
    */

?>