Presenting several aspects of hydrogeological risk in mountain environments. The purposes are the knowledge of the theoretical issues, the capability to conceptualize a flood scenario and quantitatively represent it by integration and parameterization of several models. knowledge of theories for river modeling (Mallero).

1. Hydrological Risk in Mountain Area
Hydraulic Assessment

2. Contents
• General Overview of Case Study
• Clear Water Evaluation
• Sediment Mobility of Mallero River
• Morphological Evolution of Bed under 1987 Flood Wave (Fixed Bed)
• Case Study: Morphological Evolution & Flooding Hydrographs for 1987
Flood
• Case Study: River2D Modelling of Flood Propagation in Sondrio City

3. Overall Framework
𝑸 𝑸 𝒔
𝒛 𝒃𝒆𝒅
𝑸 𝒐𝒖𝒕
𝒉 𝑽

4. General Overview
• Mallero River with length 𝟗𝟒𝟖𝟎 𝒎 , 𝐶𝑆36 ~ 𝐶𝑆92

5. General Overview
• System of Partial Differential Equations in 1D Model:
𝜕𝑄
𝜕𝑠
+
𝜕𝐴
𝜕𝑡
= 0 𝐶𝑜𝑛𝑡𝑖𝑛𝑢𝑖𝑡𝑦 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛
𝜕𝑉
𝜕𝑡
+ 𝑉
𝜕𝑉
𝜕𝑠
+ 𝑔
𝜕𝑑
𝜕𝑠
= 𝑔 𝑆0 − 𝑆𝑓 𝑀𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛
𝜕𝑄 𝑠
𝜕𝑠
1
1−𝑃0
+
𝜕𝐴 𝑠
𝜕𝑡
= 𝑞 𝑠 𝐸𝑥𝑛𝑒𝑟 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛
𝑄𝑠 = 𝑓 𝜏∗
, 𝜏 𝑐
∗
𝐶𝑙𝑜𝑠𝑢𝑟𝑒 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑇𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦
+BC,IC
• River Reach:
Upstream:
• Higher
Slope
(~3%)
• Higher
roughness
Sondrio:
• Lower
Slope
(~1%)
• Lower
roughness

6. Clear Water Evaluation

7. 𝑻𝟏𝟎𝟎 Hydro – No Sediment
• 𝑇100 hydrograph
• Critical time (𝑡 = 28ℎ𝑟) with Maximum discharge (𝑄 = 640 𝑚3
𝑠) at Critical Section (𝐶𝑆74)
(Suspected to outflow)

8. Bankfull Discharge
• Suspected Cross Section  𝐶𝑆74
• Different constant discharges to evaluate 𝐶𝑆74 bankfull discharge (No Sed.)
• Outflow observed at 𝑪𝑺𝟕𝟒 with constant 𝑸 = 𝟕𝟕𝟓 𝒎 𝟑
𝒔 inflow with No
Sediment Input

9. Sediment Mobility

10. Critical Diameter – Different Discharges
• According to the Duration Curves, critical diameters has been evaluated for
– 𝑄 = 10 𝑚3
𝑠 corresponds to about 100 days a year discharge (Frequent discharge)
– 𝑄 = 35 𝑚3
𝑠 corresponds to 14 days a year discharge (Medium to strong discharge)
– 𝑄 = 100 𝑚3
𝑠 corresponds to 1 day a year discharge (Very strong discharge)
– 𝑄 = 640 𝑚3
𝑠 corresponds to peak discharge of 𝑇100 (Extreme, Once every 100 year)

11. Critical Diameter – Different Discharges
• Some Formulas and assumptions:
–
𝑑 𝑠 𝑐 =
𝜏
𝜌𝑔 𝑠−1 𝜏 𝑐
∗
𝜏 𝑐
∗
= 0.03 − 0.06
𝑎𝑠𝑠𝑢𝑚𝑒𝑑
𝜏 𝑐
∗
= 0.05
𝜏 = 𝜌𝑔𝑅 𝐻 𝑆𝑓
𝑅 𝐻 ≅ ℎ
𝑆𝑓 =
𝑛 𝑠𝑘𝑖𝑛
2
𝑉2
𝑅 𝐻
4
3
𝑜𝑟 𝑆𝑓 ≅ 𝑆0
𝑛 𝑠𝑘𝑖𝑛 =
𝑑90
1
6
26
• 𝑑 𝑠 𝑐 can be computed either by using:
– Shear stress obtained from basement (Accurate 𝜏 computed using correct 𝑅 𝐻)
– Shear stress, assuming 𝑅 𝐻 ≅ ℎ and 𝑆𝑓 ≅ 𝑆0
– Shear stress, assuming 𝑅 𝐻 ≅ ℎ and 𝑆𝑓 with assumed roughness

12. Critical Diameter – Different Discharges
• In general
– For Large Discharge 𝑄  Large Velocity 𝑉 & Shear Stress 𝜏  High 𝑑 𝑠 𝑐
– For Large 𝑆0 & Narrow 𝐵  High Velocity 𝑉 & Shear Stress 𝜏  High 𝑑 𝑠 𝑐
• Results from different methods (𝑄 = 10 𝑚3
𝑠):
– High variability in 𝑆0 & Larger 𝑅 𝐻 (ℎ)  more variable and larger 𝑑 𝑠 𝑐 wrt Basement
– Same velocity 𝑉 as Basement but smaller roughness & larger 𝑅 𝐻 Same trend but smaller
𝑑 𝑠 𝑐

13. Critical Diameter – Different Discharges
• Smoothed results for different discharges (Basement 𝜏):
– Same trend but with increase of 𝑄  increase of 𝑑 𝑠 𝑐
– Higher slope in upstream wrt to downstream  Larger 𝑑 𝑠 𝑐 & visible 𝑑 𝑠 in upstream wrt Sondrio
– For 𝑄 = 10 𝑚3
𝑠 as being frequent  𝑑50,𝑢𝑝𝑠𝑡. = 15𝑐𝑚 (lower than measured) & 𝑑50,𝑑𝑜𝑤𝑛𝑠𝑡. = 5𝑐𝑚
– For 𝑄 = 100 𝑚3
𝑠 less frequent  largest visible  𝑑90,𝑢𝑝𝑠𝑡. = 45𝑐𝑚 & 𝑑90,𝑑𝑜𝑤𝑛𝑠𝑡. = 15𝑐𝑚 (armored)
– For 𝑄 = 640 𝑚3
𝑠 (extreme)  Big flood can transport 𝑑 𝑠 = 1𝑚 upstream & 𝑑 𝑠 = 45𝑐𝑚 in Sondrio
– 𝑄 = 495 𝑚3
𝑠 (Flood 1987) used in our assessment

14. Critical Diameter – Different Discharges
• Critical diameters for 𝑄 = 495 𝑚3
𝑠 (Flood 1987) used in our assessment:
– Upstream  𝑑 𝑠 𝑐 = 90𝑐𝑚
– Intermediate  𝑑 𝑠 𝑐 = 70𝑐𝑚
– Sondrio,1 ( 𝐶𝑆68~𝐶𝑆83) 𝑑 𝑠 𝑐 = 40𝑐𝑚
– Sondrio,2 ( 𝐶𝑆83~𝐶𝑆92) 𝑑 𝑠 𝑐 = 15𝑐𝑚

15. Morphological Evolution of
Bed

16. Different Sediment Volume Input
• 1987 flood hydrograph
• Non-erodible bed, monogranular sediment size of 𝑑 𝑠 = 10𝑐𝑚
• Different total sediment volumes of 50,000m3
, 300,000m3
& 500,000m3
with the
same trend as hydrograph is assumed:

17. Different Sediment Volume Input
• Evolution of bed at final time (𝑡 = 60ℎ𝑟):

18. Different Sediment Volume Input
– Small volume of Sed. (50,000𝑚3
)  No tangible evolution, both upstream & downstream
– Large volume (500,000𝑚3
)  Significant deposition in the reach, more in downstream
– In general, higher deposition in downstream due to high inflow discharge (1987 flood) &
higher transport capacity of upstream for 𝑑 𝑠 = 10𝑐𝑚 than downstream
– 𝑑 𝑠 𝑐 for Sondrio, varies from 40𝑐𝑚 for 𝑄 = 495 𝑚3
𝑠 to 5𝑐𝑚 for 𝑄 = 10 𝑚3
𝑠

19. Different Sediment Grain Size
• Sediment Grain Size  important factor in sediment distribution
• Different sediment grain sizes of 2𝑐𝑚, 10𝑐𝑚 & 30𝑐𝑚 has been considered
• Total sediment volume of 500,000𝑚3
is fixed
• Evolution of bed at final time (𝑡 = 60ℎ𝑟):

20. Different Sediment Grain Size
• Interpretation:
– Small sediment size (2𝑐𝑚)  more aggradation in Sondrio
𝑑𝑢𝑒 𝑡𝑜
small Sed. w.r.t.
𝑑 𝑠 𝑐 & higher transport capacity in upstream
– Intermediate sediment size (10𝑐𝑚)  distributes more/less equally along the reach
– Large sediment size (30𝑐𝑚)  more aggradation in upstream
𝑑𝑢𝑒 𝑡𝑜
going towards
downstream sections, capacity to transport large grains decreases
– 𝑑 𝑠 𝑐 for Sondrio, varies from 40𝑐𝑚 for 𝑄 = 495 𝑚3
𝑠 to 15𝑐𝑚 for 𝑄 = 100 𝑚3
𝑠 to
5𝑐𝑚 for 𝑄 = 10 𝑚3
𝑠  30𝑐𝑚 grain size is not able to be transported most of the time
– No sediment of 30𝑐𝑚 transported in 𝐶𝑆83~𝐶𝑆92  𝑑 𝑠 𝑐 = 15𝑐𝑚 for 𝑄 = 495 𝑚3
𝑠

21. Case Study:
Morphological Evolution of
Bed for 1987 Hydrograph

22. Introduction
• Worst and Reasonable scenario threatening Sondrio  maximum volume of
sediment deposited in city reach  higher outflows in critical sections
• Three different factors are assessed:
1. Influence of time of arrival of sediment (Same time, Uniform, Anticipated, Postponed)
2. Influence sediment grain sizes (5𝑐𝑚 & 15𝑐𝑚)
3. Influence of total volume of sediment (550 𝑇𝑚3
(10years return period), 800 𝑇𝑚3
, 1 𝑀𝑚3
& 2 𝑀𝑚3
(40years return period))
• Non-erodible bed assumed
• 1987 flood hydrograph:

23. Time of Arrival of Sediments (EXTRA)
• Fixed monogranular 𝒅 𝒔 = 𝟏𝟓𝒄𝒎 , fixed total volume 𝟏 𝑴𝒎 𝟑
• Different time of arrival of sediments, same shape as hydrograph assumed:

24. Time of Arrival of Sediments (EXTRA)
• Morphological evolution  sensitive to time of arrival of sediments
• Evolution of bed at final time (𝑡 = 60ℎ𝑟):

25. Time of Arrival of Sediments (EXTRA)
– Postponed:
• Low sed. transport capacity of flow for large vol. of sed. recently entered  highest
deposition in first sections of upstream & least deposition in Sondrio  less interesting
– Uniform:
• Same constant sed. input & low sed. transport capacity at final hours  High deposition
in first sections upstream, but lower in next sections wrt “Anticipated” & “On Time”
– Anticipated: (Most Severe case)
• Most of sed. volume already entered by peak of inflow 𝑄 = 495 with high transport
capacity & time  Least accumulation in first sections & highest accumulation in
Sondrio  more interesting
– Ontime & Uniform:
• More/Less same accumulation in downstream

26. Sediment Grain Size
• Morphological evolution  highly sensitive to sediment size
• Fixed time of arrival of sediment “Anticipated” , fixed total volume 𝟏 𝑴𝒎 𝟑
• Evolution of bed at final time (𝑡 = 60ℎ𝑟) for two monogranular size of 𝟓𝒄𝒎 &
𝟏𝟓𝒄𝒎:

27. Sediment Grain Size
– 5𝑐𝑚 Sediment:
• No limitation in transport regarding sediment size ( 𝑑 𝑠 𝑐 > 5𝑐𝑚 for 𝑄 > 10)  sediment
can be transported total time  deposited less in upstream, more in Sondrio
– 15𝑐𝑚 Sediment:
• For 𝑄 < 100  in Sondrio 𝑑 𝑠 𝑐 < 15𝑐𝑚  limited time for transporting sediments to
Sondrio  deposited less in Sondrio, more in upstream
• The case with 5𝑐𝑚 grain size is more severe, in reality mixture of different sizes

28. Total Sediment Volume
• Maximum volume of sediment available from geological
– 550 𝑇𝑚3
for critical event with 𝑇 = 10𝑦𝑒𝑎𝑟𝑠
– 2 𝑀𝑚3
for critical event with 𝑇 = 40𝑦𝑒𝑎𝑟𝑠
• Fixed time of arrival of sediment “Anticipated” , monogranular sediment 5𝑐𝑚
• Evolution of bed at final time (𝑡 = 60ℎ𝑟) for four Total Sediment Volumes of
550 𝑇𝑚3, 800 𝑇𝑚3, 1 𝑀𝑚3 & 2 𝑀𝑚3:

29. Total Sediment Volume
– 2 𝑀𝑚3
:
• Huge difference in upstream wrt other volumes (40𝑚 deposition in 𝐶𝑆36)  unreasonable!
• Visible difference in Sondrio (not so much in 𝐶𝑆74)
𝑏𝑢𝑡
most of Sed. not transported!  low
transport capacity
– 1 𝑀𝑚3
:
• Deposition of 4.5𝑚 in 𝐶𝑆36  discussable (next slide)
• More/less same deposition in downstream (a bit more)
– 550 𝑇𝑚3
, 800 𝑇𝑚3
, 1 𝑀𝑚3
:
• Increasing the total volume  more/less same volume transported to downstream 
limited transport capacity
• The difference much more visible in very upstream sections

30. Maximum Sediment Volume (EXTRA)
• Some assumptions:
– Rectangular cross sections  simplicity
– Same bed width before 𝐶𝑆36  safe side
– Same bed slope before 𝐶𝑆36  not varying a lot
– Same deposited elevation before 𝐶𝑆36  safe side
– Maximum deposition of 10 𝑇𝑚3
considered negligible before 𝐶𝑆36
• For sediment volume 𝟏 𝑴𝒎 𝟑:
– With deposition elevation 4.5𝑚  𝑣𝑜𝑙𝑢𝑚𝑒 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑒𝑑 ≅ 8.5𝑇𝑚3
< 10𝑇𝑚3
 Acceptable
– Can be considered maximum reasonable sediment volume input for our reach with
anticipated time of arrival for sediment size 𝟓𝒄𝒎
• Different sed. size & time of arrival  changes maximum transportable volume

31. Our Scenario for Outflow & Water
Propagation in Sondrio
• For our scenario (Worst & Reasonable):
– Total Sediment Volume Input: 1,000,000 𝑚3
– Monogranular Sediment Size: 5 𝑐𝑚
– Time of Arrival of Sediments: 𝐴𝑛𝑡𝑖𝑐𝑖𝑝𝑎𝑡𝑒𝑑 𝐻𝑦𝑑𝑟𝑜𝑔𝑟𝑎𝑝ℎ 𝑆ℎ𝑎𝑝𝑒𝑑
– Fixed Bed assumed

32. Case Study:
Outflows, Clearance
Thresholds & Flood
Propagation in Sondrio

33. • River evolution for our scenario at different times:
t=28 hrt=37 hrt=60 hr
Outflows in Critical Sections of Sondrio
• At “Peak Inflow” time, outflow started already in 𝐶𝑆74
• At “Peak Outflow” time, outflow extends to 𝐶𝑆70, 𝐶𝑆71, 𝐶𝑆72 & 𝐶𝑆73
• Proceeding final time, water depth decreases (wrt new bed)  still outflow

34. Outflows in Critical Sections of Sondrio
• Upstream outflows neglected  water goes back to river (Valley)
• Outflows in Sondrio computed using “Weir Equation”:
– 𝑄 𝑜𝑢𝑡𝑓𝑙𝑜𝑤 = 𝐶 𝑤 𝐿ℎ 2𝑔ℎ
"Cw", 𝑓𝑜𝑟 𝑖𝑟𝑟𝑒𝑔𝑢𝑙𝑎𝑟 𝑠ℎ𝑎𝑝𝑒 → 𝐶 𝑤 = 0.3
"h", 𝑜𝑣𝑒𝑟𝑏𝑎𝑛𝑘𝑖𝑛𝑔 ℎ𝑒𝑖𝑔ℎ𝑡 → 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑑 𝑤𝑖𝑡ℎ 𝑠𝑎𝑚𝑒 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑎𝑟𝑒𝑎
"L", 𝑤𝑒𝑖𝑟 𝑤𝑖𝑑𝑡ℎ → 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑑 𝑏𝑦 𝑊. 𝑆. 𝐸 𝑐𝑟𝑜𝑠𝑠𝑖𝑛𝑔 𝑏𝑎𝑛𝑘𝑠
• Outflows are summed at each instant  unique outflow needed for River2D
• Outflow exceeds inflow after peak  uncoupled modelling  inflow discharge
chosen for outflow

35. Clearance & Thresholds
• Outflow begins from 𝐶𝑆74 (bridge in “Via de Simoni”)  Chosen for Clearance
• Thresholds for “Pre-alarm”, “Alarm” & “Emergency” phases:
– “Emergency” as we have outflow  𝑡 = 27ℎ𝑟
– “Pre-alarm” as minimum clearance we can stay in “Peace”  model with peak 𝑄
= 150 𝑚3
𝑠 (less than once a year), maximum bed evolution at 𝐶𝑆74 𝑐 = 2.5𝑚
– “Alarm” phase minimum duration 3ℎ𝑟𝑠 assumed

36. Clearance & Thresholds
• Clearances & Duration of Each Attention Phase:
– “Pre-alarm” Duration: 8 hours Clearance: 1 < 𝑐 ≤ 2.5
– “Alarm” Duration: 3 hours Clearance: 0 < 𝑐 ≤ 1
– “Emergency” Duration: 33 hours Clearance: 𝑐 = 0

37. • Total outflow hydrograph implemented in River2D
• Transmissivity  0.1
• Storativity  0.001  minimizing elevation of underground water
• Ran until peak of outflow (10ℎ𝑟𝑠)
• Water Depth results:
30 Minutes2 hours4 hours6 hours8 hours10 hours (Peak)
Water Depth
Flood Propagation in Sondrio

38. • Water Velocity results:
30 Minutes2 hours4 hours6 hours8 hours10 hours (Peak)
Water Velocity
Flood Propagation in Sondrio
• Using these maps, we are now able to proceed with “Emergency Planning”.

39. Thank you for your Attention