Setting up logback JMX for a web application requires a bit too many manual steps. It is not enough to simply add <jmxConfigurator /> to the configuration file. You should also set the context path but often you can't know that in advance. In addition you still need to write custom code to prevent memory leaks. These issues could all be addressed by a custom context listener.

<listener>
<listener-class>ch.qos.logback.classic.selector.servlet.JmxEnabler</listener-class>
</listener>

Code attached.