Obtain path to wp-admin directory in WordPress.

get-admin-path.php

<?php
/**
 * Obtain the path to the admin directory.
 *
 * @return string
 */
function my_plugin_get_admin_path() {
	// Replace the site base URL with the absolute path to its installation directory. 
	$blogUrl = preg_replace("(^https?://)", "", get_bloginfo( 'url' ));
	$adminUrl = preg_replace("(^https?://)", "", get_admin_url());

	$admin_path = str_replace( $blogUrl . '/', ABSPATH,  $adminUrl);

	// Make it filterable, so other plugins can hook into it.
	$admin_path = apply_filters( 'my_plugin_get_admin_path', $admin_path );

	return $admin_path;
}

Modified so that if url's contain a mix of http and https, function still works.

And you can use trailingslashit(ABSPATH)