performance function

Sustainable management of Urban Drainage Systems (UDSs) is challenging since the hydraulic characteristics and pollutants discharged into catchment areas are constantly changing. Quantifying the resilience of UDSs is a crucial step towards long-term and sustainable management of these chatments in urban areas. This study was performed to evaluate the resilience of UDSs against flooding through combining hydraulic performance of stormwater drainage network with the system performance function. To conduct this performance evaluation extreme rainfall intensity values for different return year periods ranging from 2 to 100 years were used for catchment drained into the West Flood-Diversion (WFD) system in Tehran. Both hydraulic and hydrodynamic simulations were performed for these stormwater drainage system under two scenarios: with and without BMPs. To further evaluate the systems performance and resilience, additional simulation analysis was performed using one specific flooded node under extreme rainfalls with different return periods. The results showed that adding a vegetative swale to the drainage system would decrease the nodal flooding duration and the flood volume up to 15% and 47%, respectively. The results also shown that the resilience against flooding will increase from about 0.4% up to 6% under the above-mentioned conditions. From the results of this study, we can conclude that employing some types of BMP along with the existence low-impact development measures within the traditional urban drainage areas may be sufficient to increase the system resilience and sustainable control of flooding.

Underground tunnels, particularly, have distinct seismic behaviour due to their complete enclosure in soil or rock and their significant length. Therefore, seismic response of tunnel support systems warrant closer attention. The geological settings in which they are placed are often difficult to describe due to limited site investigation data and vast spatial variability. Therefore, the parameters which govern the design are many and their variabilities cannot be ignored. A solution to this issue is reliability based analysis and design. These real conditions of variability can only be addressed through a reliability based design.
The concepts of reliability has been less considered by the researchers in the engineering analysis and design of tunnels and underground spaces. Laso et. al (1995) studied the reliability in the designing of tunnel lining. Quing Lu et. al (2013) evaluated the reliability of the rock tunnels with respecting to several statuses of rupture mode. The studies conducted on the reliability of tunnels, mostly ignored the seismic design parameters as well as the consideration of reliability in the parameters of the surrounding tunnel soil.
Methodology and Approaches :In this research, response surface method (RSM), the reliability concept of Hasofer-Lind and finite element method (FEM) are composed in order to investigate the reliability of the lining of shallow underground tunnels. For this purpose, an underground tunnel with the height of 5m has been subjected to 7 earthquake records using finite element software ABAQUS. The random variables considered for surface response method are soil dynamic elasticity module, cohesion and internal friction angle of the soil. The reliability index has been approximated for axial force, flexural moment, shear force and displacement of tunnel by conducting trial and error tests on the three mentioned parameters.
Results and The results obtained in this research are briefly summarized as follows:The reliability index value is lower in the tunnel lining under seismic loads for all obtained responses, comparing to those under static loading. In the other words, the reliability of soil and tunnel systems are reduced concerning the random nature and criticality of loading as well as randomness of soil parameters .
The reliability index values are lower for the shear force response of the tunnel lining under Earthquake records, comparing to those of axial force and flexural moment. Consequently, it is recommended to retrofit the whole soil under earthquake loading against shear cracking.