diff --git a/core/includes/batch.inc b/core/includes/batch.inc
index 2eddb0f..8e06a3a 100644
--- a/core/includes/batch.inc
+++ b/core/includes/batch.inc
@@ -280,12 +280,12 @@ function _batch_process() {
     $queue = _batch_queue($current_set);
 
     if ($batch['progressive']) {
-      if (drupal_valid_test_ua()) {
+      if (defined('DRUPAL_TEST_MEMORY_USAGE_TRIGGER')) {
         // Limit maximum memory when we're under test to the same value as
         // \Drupal\simpletest\WebTestBase::$memoryUsageTrigger to ensure that
         // Drupal works under that limit.
         // @see \Drupal\simpletest\WebTestBase::curlHeaderCallback
-        $maximum_memory = \Drupal::SIMPLETEST_MAXIMUM_MEMORY_USAGE;
+        $maximum_memory = DRUPAL_TEST_MEMORY_USAGE_TRIGGER;
       }
       else {
         $maximum_memory = ini_get('memory_limit');
diff --git a/core/includes/bootstrap.inc b/core/includes/bootstrap.inc
index ce872d4..f259c6d 100644
--- a/core/includes/bootstrap.inc
+++ b/core/includes/bootstrap.inc
@@ -618,8 +618,11 @@ function drupal_valid_test_ua($new_prefix = NULL) {
   // string.
   $http_user_agent = isset($_SERVER['HTTP_USER_AGENT']) ? $_SERVER['HTTP_USER_AGENT'] : NULL;
   $user_agent = isset($_COOKIE['SIMPLETEST_USER_AGENT']) ? $_COOKIE['SIMPLETEST_USER_AGENT'] : $http_user_agent;
-  if (isset($user_agent) && preg_match("/^(simpletest\d+);(.+);(.+);(.+)$/", $user_agent, $matches)) {
-    list(, $prefix, $time, $salt, $hmac) = $matches;
+  if (isset($user_agent) && preg_match("/^(simpletest\d+);(.+);(.+);(.+);(.+)$/", $user_agent, $matches)) {
+    list(, $prefix, $time, $salt, $hmac, $memory_usage_trigger) = $matches;
+    if ($memory_usage_trigger !== '0') {
+      define('DRUPAL_TEST_MEMORY_USAGE_TRIGGER', $memory_usage_trigger);
+    }
     $check_string =  $prefix . ';' . $time . ';' . $salt;
     // Read the hash salt prepared by drupal_generate_test_ua().
     // This function is called before settings.php is read and Drupal's error
@@ -648,7 +651,7 @@ function drupal_valid_test_ua($new_prefix = NULL) {
 /**
  * Generates a user agent string with a HMAC and timestamp for simpletest.
  */
-function drupal_generate_test_ua($prefix) {
+function drupal_generate_test_ua($prefix, $memory_usage_trigger = '64M') {
   static $key, $last_prefix;
 
   if (!isset($key) || $last_prefix != $prefix) {
@@ -678,7 +681,10 @@ function drupal_generate_test_ua($prefix) {
   // Generate a moderately secure HMAC based on the database credentials.
   $salt = uniqid('', TRUE);
   $check_string = $prefix . ';' . time() . ';' . $salt;
-  return $check_string . ';' . Crypt::hmacBase64($check_string, $key);
+  if ($memory_usage_trigger === FALSE) {
+    $memory_usage_trigger = '0';
+  }
+  return $check_string . ';' . Crypt::hmacBase64($check_string, $key) . ';' . $memory_usage_trigger;
 }
 
 /**
diff --git a/core/lib/Drupal.php b/core/lib/Drupal.php
index 9bd2ee2..ad525dd 100644
--- a/core/lib/Drupal.php
+++ b/core/lib/Drupal.php
@@ -94,14 +94,6 @@ class Drupal {
   const CORE_MINIMUM_SCHEMA_VERSION = 8000;
 
   /**
-   * Simpletest maximum target memory usage.
-   *
-   * This is defined here because it is used by child sites which do not have
-   * Simpletest installed.
-   */
-  const SIMPLETEST_MAXIMUM_MEMORY_USAGE = '64M';
-
-  /**
    * The currently active container object, or NULL if not initialized yet.
    *
    * @var \Symfony\Component\DependencyInjection\ContainerInterface|null
diff --git a/core/modules/simpletest/src/BrowserTestBase.php b/core/modules/simpletest/src/BrowserTestBase.php
index ed64f08..7b659ef 100644
--- a/core/modules/simpletest/src/BrowserTestBase.php
+++ b/core/modules/simpletest/src/BrowserTestBase.php
@@ -217,6 +217,20 @@
   protected $mink;
 
   /**
+   * The maximum memory usage to allow on the child site, in MB.
+   *
+   * The minimum amount of memory Drupal expects to have available is defined by
+   * DRUPAL_MINIMUM_PHP_MEMORY_LIMIT. This default value on the base class
+   * should be less than or equal to DRUPAL_MINIMUM_PHP_MEMORY_LIMIT. If a
+   * module requires more memory than this limit, the module should add a
+   * check to its hook_requirements() and use the higher value in its tests.
+   * The check can be disabled for a specific test by setting it to FALSE.
+   *
+   * @var string|FALSE
+   */
+  protected $memoryUsageTrigger = '64M';
+
+  /**
    * Initializes Mink sessions.
    */
   protected function initMink() {
@@ -449,7 +463,7 @@ public function assertSession($name = NULL) {
    */
   protected function prepareRequest() {
     $session = $this->getSession();
-    $session->setCookie('SIMPLETEST_USER_AGENT', drupal_generate_test_ua($this->databasePrefix));
+    $session->setCookie('SIMPLETEST_USER_AGENT', drupal_generate_test_ua($this->databasePrefix, $this->memoryUsageTrigger));
   }
 
   /**
diff --git a/core/modules/simpletest/src/WebTestBase.php b/core/modules/simpletest/src/WebTestBase.php
index 1d29493..e05b86c 100644
--- a/core/modules/simpletest/src/WebTestBase.php
+++ b/core/modules/simpletest/src/WebTestBase.php
@@ -76,7 +76,7 @@
    *
    * @var string|FALSE
    */
-  protected $memoryUsageTrigger = \Drupal::SIMPLETEST_MAXIMUM_MEMORY_USAGE;
+  protected $memoryUsageTrigger = '64M';
 
   /**
    * The handle of the current cURL connection.
@@ -1311,7 +1311,7 @@ protected function curlInitialize() {
     // We set the user agent header on each request so as to use the current
     // time and a new uniqid.
     if (preg_match('/simpletest\d+/', $this->databasePrefix, $matches)) {
-      curl_setopt($this->curlHandle, CURLOPT_USERAGENT, drupal_generate_test_ua($matches[0]));
+      curl_setopt($this->curlHandle, CURLOPT_USERAGENT, drupal_generate_test_ua($matches[0], $this->memoryUsageTrigger));
     }
   }