This document describes a risk assessment methodology for hydraulic overloading of urban drainage networks using fuzzy set theory. It presents a case study of a town in Bulgaria with a combined sewer system and reports on hydraulic modeling conducted. The modeling found some design issues but no surface flooding. The methodology defines membership functions to assess reliability and risk based on the response of the system to external loads from rainfall events of varying return periods. Maps can show the spatial distribution of reliability across the urban area before and after reconstruction. The methodology is proposed as an appropriate approach to adequately assess risk of overloading through simulations at different rainfall intensities.

1. Risk Assessment Methodology for
Hydraulic Overloading of Urban Drainage
Networks and Flooding of Urban Areas
T. IGNEVA-DANOVA
University of Architecture, Civil Engineering and Geodesy
Sofia, Bulgaria

2. CASE STUDY
• The town is situated in the middle north part of Bulgaria
• The climate in the region is typical continental – cold winters, springs
with intensive rainfalls and hot summers
• The town is built on relatively steep terrain with considerable
displacement between its upper and lower parts
• The drainage area is approximately 75 ha
• The urban area is drained by combined sewer system with total length
of nearly 8 km
• The total number of the population is approximately 4 000 people
• Existing sewer pipes and joints are in relatively good technical
condition
• Existing combined sewer system after rehabilitation is planned to be
exploited as storm system

3. RAINFALL INTENSITY AND RETURN
PERIOD
• Definitions for the term “intensive rainfall”
• Inability to accept universal border of intensity and duration of
these rains
• Standards for modelling hyetographs - “intensive rainfalls” are
accepted to be these with intensity more than 30 l/s.ha (0,18
mm/min) regardless to their duration.
• For the area of the town intensive rains with duration of 5
minutes (independently from its intensity) are 30 cases per a
year and these with duration from 10 to 17 minutes – 17 cases
per year. The number of heavy rains with duration of 30 minutes
is 5 to 6.
• The probability of occurring heavy rains with 60 minutes
duration is about 60-70% per year
• Return period P is considered in accordance with type of sewer
system

4. RAINFALL INTENSITY AND RETURN
PERIOD
• The existing combined sewer network is designed for 2 years
return period
• About 67% of the total drainage area is taken by yards
• On the territory of the two districts there are no underground
warehouses, stores and business buildings.
• Eventual flooding with waste waters in basements would not
cause so many damages in comparison with flooding in town
centre
• During the past 20 years no actual damages due to hydraulic
overloading of sewer network were recorded
• The design return period of the storm water system is
diminished to 1 year

5. HYDRAULIC MODELLING
• Exiting urban drainage network was performed by means of
MOUSE software, based on the available electronic cadastre
• Imperviousness is precisely defined in accordance with surface
type and information from the cadastre. The mean percentage
of imperviousness in the considered districts is 33%
• New storm water collectors
• The influence of these seven newly designed collectors on the
conveyance of the existing network is examined through the
computer model
• Two of the sewer overflows are planned to be used as dividing
chambers and the excess storm water is going to be discharged
to the river. The third sewer overflow will be reconstructed as a
manhole with no direct discharge to the river

6. HYDRAULIC MODELLING
• The hydraulic model comprises of:
• 241 manholes
• 236 pipes
• 67 catchments with total drainage area of 50,3 ha
• 2 outlets
• 2 dividing chambers
• The total length of the modelled network is 7740 m

7. HYDRAULIC MODELLING
manhole
pipe
weir Legend:
Diameters of pipes:
--- 0,3 – 0,5 m
--- 0,5 – 0,6 m
--- 0,6 – 0,8 m
--- 0,8 – 1,2 m
outlet Δ - outlet
 - weir
 - manhole

8. COMPUTER SIMULATIONS
Design rainfall
• Return period P=1 year
• Rainfall duration 30 minutes
• Rainfall intensity 100 l/s.ha

9. COMPUTER SIMULATIONS
• Depth of cover over sewer pipes lower than the minimum admissible
• Sewer pipes with steep slope followed by pipes with flat slope. Reducing
of velocity is precondition for backflow and pressure conditions in sewer
pipes.
• Higher velocity in secondary sewer collectors at the point of attachment to
main sewer than in the main collector. This non-compliance with design
criteria leads to backflows at three certain sewer sections.
• Pressurized sewer pipes - total length is 455 m or 6,2 % of the whole
sewer network.
• No surface flooding occurs during the simulated event.
• Despite the mentioned above design shortcomings, the existing sewer
network possesses relatively good hydraulic capacity and can be
exploited without serious problems.
• Pressurized regime in storm water sewers is not so dangerous because
there is no potential threat of basements’ flooding.

10. 5.11.2009 г. 12:30:10
COMPUTER SIMULATIONS

11. Methodology for Risk Assessment of Hydraulic
Overloading and Flooding of Urban Drainage
System Based on the Fuzzy Set Approach
Fuzzy Set Theory
• Zadeh – 1965
• Application in physically controlled systems, different
engineering problems, statistics, medicine, biology
• No information for application of this theory in risk
assessment for hydraulic overloading of urban drainage
networks is available for author’s best knowledge

12. Methodology for Risk Assessment of Hydraulic
Overloading and Flooding of Urban Drainage
System Based on the Fuzzy Set Approach
1. Area of absolutely safety (normal performance of the sewer
pipe) ►
2. Area of decreasing safety (increasing risk – the sewer pipe
is pressurized) ►
3. Area of absolute risk (the water level is above the terrain -
flooding) ►
4. Area of external load to the sewer pipe (rain with a definite
return period – P, at witch in this example the water level
rises up to 2 m above the sewer pipe invert) ► ►

13. Methodology for Risk Assessment of
Hydraulic Overloading and Flooding of Urban
Drainage System Based on the Fuzzy Set
Approach
► ► ►

14. Methodology for Risk Assessment of
Hydraulic Overloading and Flooding of Urban
Drainage System Based on the Fuzzy Set
Approach
1. External Load of the system - L
Its membership function µL is changing in the interval (0,1) at
maximum µL = 1 at a head/depth of 2 m, for this example
►
2. Response of the system – R
µR – increasing the pipe depth from D to terrain surface, the
membership function is changing from 1 to 0 linearly ►

15. Methodology for Risk Assessment of
Hydraulic Overloading and Flooding of Urban
Drainage System Based on the Fuzzy Set
Approach
_ _ _
Reliability measure M = R− L
∫µ
h >0
M
_ (m)dm
Reliability of the system Re =
∫µ
h
_
M
(m)dm

16. Methodology for Risk Assessment of
Hydraulic Overloading and Flooding of Urban
Drainage System Based on the Fuzzy Set
Approach
Dependence between Risk and Reliability
Re + Ri = 1
Ri = 1 - Re

17. Risk
R
1
0
1
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
R 30
1
R 31
1
R 57
1
R 77
3
R 22
3
R 31
4
R 32
4
R 33
4
R 34
4
R 35
4
R 36
4
R 37
4
R 38
4
R 39
4
R 40
R R441
43 4
3- 42
W
R eir
4
R 44
4
R 45
4
R 46
4
R 47
4
R 48
4
R 49
4
R 50
4
R 51
4
R 52
4
R 53
4
R 54
4
R 55
4
R 56
4
R 57
4
R 58
O 45
ut 9
le
t2
R
46
R 0
4
Manhole ID
R 61
4
R 62
4
R 63
4
R 64
on return period P
4
R 65
4
R 66
4
R 67
4
R 68
Risk of hydraulic overloading and flooding
O 46
ut 9
le
t1
R
60
R 6
4
R 70
4
R 71
4
W 72
P=5 years
P=2 years
e
P=40 years
P=30 years
P=20 years
P=10 years
R i r1
47
R 4
4
R 75
4
R 76
4
R 77
4
R 78
4
R 79
4
Based on the Fuzzy Set Approach
R 80
4
R 81
Risk of overloading and flooding of the sewer network depending
4
R 82
4
R 83
4
R 84
4
R 85
4
R 86
4
R 87
48
8
Methodology for Risk Assessment of Hydraulic
Overloading and Flooding of Urban Drainage System

18. Methodology for Risk Assessment of Hydraulic
[m]
0.0 Overloading and Flooding of Urban Drainage System
Diameters
0.0 Based on the Fuzzy Set Approach
0.0
Map of risk - spatial distribution of reliability over the territory of the
0.0 town of Novi Iskar before and after the reconstruction
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Legend:
0.0  Ri 0 – 0,25
 Ri 0,25 – 0,5
0.0  Ri 0,5-0,75
 Ri 0,75 - 1
0.0
0.0

19. CONCLUSIONS
Risk/reliability of hydraulic overloading of the urban
drainage networks can be adequately assessed only by
applying the appropriate approaches, models and software
In our view the most appropriate approach for assessment
of the hydraulic overloading/flooding of the sewer network
should be one, based on the Fuzzy Set Theory
The proper assessment of the hydraulic capacity of sewer
networks includes not only simulations with design rainfall,
but also giving quantitative assessment of risk for different
rain events

20. THANK YOU FOR YOUR
ATTENTION!