An expansion joint for use between a turbine duct and a diffuser duct includes a first flange coupled to the turbine duct, a second flange coupled to the diffuser duct, and a flexible element positioned between and coupled to the first flange of the turbine duct and the second flange of the diffuser duct. The flexible element defines a trough for receiving a liquid therein. The trough includes a drain pipe configured to channel the liquid away from the trough.