As a low-lying city, Shanghai faces threats from typhoon and spring tide under the condition of climate change and land subsidence. With high water level at the toe, the sea embankment is likely to be overtopped and breached, finally resulting in inundation inland.  The objective of this research is to study climate change and land subsidence effects on Shanghai inland inundation due to dike overtopping and breaching under extreme weather condition.  A hydrodynamic model and a wave model have been established by Delft3D-FM and Delft3D respectively. Through validations on historical events, the hydrodynamic model and wave model are proved to be valid. The water level and wave condition along the coast, which are concerned as the results of these two models, are also essential inputs for overtopping and breach discharge calculation. In overtopping and breach discharge calculation, the threshold of breaching is estimated as an overtopping rate of 0.1 m3/m/s. The resulting overtopping and breach discharge gives the boundary condition of the overland simulation. The inundation map over Shanghai area can then be achieved by the overland simulation. A sensitivity analysis of the breach widths is also done.   Ten hypothetical typhoon events are provided by the Met Office Hadley Center under past and future climate conditions. These cases are applied to the whole process to study the effects of climate change on coastal flooding in Shanghai. The relative sea level rise is also considered for both past and future climate conditions.   The results show that places with high water level and low sea dike elevation are more likely to get high overtopping that can finally result in breaching. For Shanghai city, such vulnerable places can be found along Hangzhou Bay, especially in Jinshan District and the south-east corner of Shanghai. Besides, the entrance of Shanghai Yangtze River Tunnel is also vulnerable due to land subsidence. For some extreme cases, the whole Shanghai coast is in danger.  For the past climate and land elevation around the year 2000 with the wind speed return period of 1.3 yr and the breach width assumed to be 300 m, it is simulated that the maximum inundation area in Shanghai can be 1,805 km2 (33.3% of the simulated area in Shanghai). In the future, given the challenge of climate change and land subsidence, the sea level is relatively rising. The intensity of typhoon will generally strengthen. For the future climate and land elevation around the year 2100 with the wind speed return period of 4.5 yr, it is simulated that the inundation area in Shanghai can be 3,388 km2 (62.4% of the simulated area in Shanghai), which is almost twice of the inundation area around the year 2000.  The breach width also affects the inundation situation. If the breach width becomes larger, the inundation situation will be worse. However, as the breach width grows, the increase of the inundation area decreases.

The safety level of a dike is expressed in terms of risk. Risk is defined as the product of the probability of inundation of a polder (after failure of a dike) and the expected damage (casualties, economic damage and damage to the infrastructure) caused by inundation. The rate of inundation determines the amount of casualties and depends heavily on the flow velocity through the breach and breach development in time. The flow velocity in a breach can become larger than 5 m/s. Due to these large flow velocities, the application of conventional sediment pick-up functions in breach growth models, leads to a significant overestimation of the breach growth and thus the rate of inundation.

Breaching is the most frequent form of embankment failure in the world. Due to overtopping, an embankment starts to breach when part of the embankment actually breaks away, leaving an opening for water to flood the land protected by the embankment. A breach can be a sudden or gradual failure that is caused by surface erosion and/or headcut erosion in the embankment. The magnitude and extent of the losses depend highly on the rate of breaching of the embankment, which determines the discharge through the breach and the speed and rate of inundation of the valley or polder. Therefore, modelling of the breach evolution in embankments is of significant interest for damage assessment and risk analysis. It is also important for the development of early warning systems for dike and dam failures and of evacuation plans for people at risk.
The breach flow plays an important role in the embankment breaching process, coupling the hydraulic process and the sediment transport process. During the breaching process, the flow overtops the entire embankment crest and generates the breach channel in the initial phase of the breach development. As the breach further develops, the breach flow goes only through the breach channel due to the decrease of the upstream water level. The breach flow can thus be classified as compound weir flow and weir flow, each having own special characteristics. In a breach, the helicoidal flow accelerates the sediment undermining at the toe of the breach slopes and widens the breach in the lateral direction of the embankment. A triangular hydraulic jump happens when the breach flow changes from supercritical flow into subcritical flow, with a triangular critical area at the toe of the breach. The triangular hydraulic jump works as a driving force to the headcut erosion in the breaching process and the scour hole development at the toe of embankment. According to the hydraulic energy loss in the breach, the discharge coefficients are deducted for both weir flow condition and compound weir flow condition. The resulting discharge coefficients can be used in the calculation of the breach discharge in a breach model.
In the present study, five runs of breach experiments were conducted in a relative large laboratory flume. The experimental results clearly expose the hydrodynamic process and the erosion process in the breaching of the cohesive embankment. The breaching starts with the initial erosion of the embankment surface washing away the embankment surface. Due to the surface erosion at the toe of the embankment, the headcut erosion is stimulated on the embankment slope. While headcut migration stimulates the breach to develop in longitudinal direction, the lateral erosion triggers the breach to widen in lateral direction. Three types of erosion (surface erosion, headcut erosion and lateral erosion) contribute to the breach erosion process in the embankment, however, the breach flow is the driving force for the erosion. Sediment deposition in the breaching process, generally ignored in the embankment breaching studies, is also of importance.
A mathematical model has been developed that couples weir flow and erosion (surface erosion, headcut erosion and lateral erosion). The breaching process is simplified into initial development, deepening development and widening development, corresponding with surface erosion, headcut erosion and lateral erosion, respectively. As the link between flow and embankment material, erosion plays a key role in the embankment breach model. Mathematical descriptions of the headcut migration and the lateral migration rate have been developed to simulate the breaching process in cohesive embankments. The headcut erosion and the lateral erosion are considered to occur in the form of clay blocks instead of in the form of individual clay particles.