drain design (proag)

8/13/2019 Drain Design (Proag)

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THE JOURNAL OF THE INSTITUTION OF ENGINEERS MAURITIUS

7

Abstract

Many areas in Mauritius get ooded regularly due

to

(a) sudden rain of unexpected magnitude

(b) building permits given on historically ood-

able land

(c) inadequate drains.

Rainfall frequency and intensity records can be

used to estimate the magnitude of rains and the en-

suing ood ows. There is a 26 % probability that

a 100 year rain will occur during the next 30 years

(a generation). Even if a higher return interval, e.g.

1,000 years is taken, it is found that there is 7.2 %

chance (not to be neglected as being small) that a1,000 year ood will occur during a 75 year span

a mans lifetime.

In a small country like Mauritius, it is difcult to

give ood warnings in advance that one can aban-

don house and move furniture. The ooding might

occur suddenly in the middle of the night, when

there has been a power cut.

The only solution to have dry feet would be to haveadequate drainage.

Is it acceptable for ones house to get ooded every

10 years? Or every 30 years? Or never at all during

ones lifetime? The three alternatives will require

drains of different sizes, with different costs.

Once the desired safety from oods has been ac-

cepted preferably through legislation it would

be easy todesign for the adequate drain capacity(1)

earmark the boundary of the reserved low lying(2)

areas reserved for extreme ood conditions.

This paper presents the relevant criteria to adopt for

drain design in Mauritius.

1. IntroductionThere are many places which receive heavy rains

without anybody being aware of the fact, simply

because no area gets ooded. In other places, how-

ever, there are many tell-tale signs, either during or

after the heavy rains. The signs noticed afterwards

indicate the levels to which the water levels rose

during the peak of the storm. If the existing drains

are unable to carry the ood peaks generated, then

people do notice the ooding of the surroundings,

sometimes with devastating results and loss of life

and material damage. A sudden heavy rainfall will

cause ooding if there is no drain to carry the water

away.

A low lying area will certainly be ooded because

all water will eventually accumulate there and it is

usually difcult to make drains which are at a still

lower level. The area nearby is also likely to be af-

fected in case the drain, if any, has an inadequate

carrying capacity.

Flooding seems to be a regular phenomenon which

occurs in many countries for several reasons,

namely: (a) building permits given on historically

oodable land (b) inadequate drains (c) sudden

rain of unexpected magnitude

It is therefore important that the catchment area of

the urban environment be studied for the low lying

areas and the natural draining channels. These areas

DRAIN DESIGN FOR DRY FEET

Virendra PROAG

University of Mauritius

[email protected]


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should in the rst instance be completely avoided

for building purposes.

2. Outline Planning Schemes

An outline planning scheme aims to dene zoneswhere different activities are allowed, including

housing. The main parameters that are considered

are environmental, but rarely do we nd drainage

being taken into account because of possible impacts

of its non existence.

If there were no oods during some 50 years in liv-

ing memory (or sometimes even during the last 40

years average service time of a building permit

ofcer), it is reasonably felt that there is no dangerof any big ood occurring in the area. Very often,

there are historical records which can conrm that

the given area had been ooded so many years ago

sometimes, 300 years or 500 years. Unfortunately,

it is not always easy to go through these records or

to check them.

Thus, building permits are very often given on land

which, according to historical records, is prone to

ooding.

Building lots have often been earmarked by the land

promoter within drainage channels low lying con-

tours. While these should be a constraint against

giving the building permit, political pressure or an

unwary building permit ofcer may come in the

way. At other times, a whole set of houses have been

built in a low lying area which could very well form

a lake if a regular means of feeding it with water was

available. In this case, it is usually difcult to makedrains which are at a lower level.

Very often, ooding occurs because the drain, if any,

has an inadequate carrying capacity, or has a carry-

ing capacity which has not been designed to take

sudden heavy rainfalls Sometimes, the drains are

permanently inadequate as one road engineer ex-

plained, he designed road drains to cater only for the

rainfall coming from the road. The drains coming

from the nearby building lots were not supposed todischarge into his road drain !!!.

While the above explains how building permits

wrongly given or drains with inadequate capacity

allow ooding to occur, it is judicious to examine

sudden rainfall. If intense rainfall magnitudes can

be estimated, this could help in designing the appro-

priate drains. Thus, before designing drains to carry

ood ows, it is necessary to determine the magni-

tude of the ood ows.

3. Determination of Flood Flows

One approach to the problem is as follows:

Walk over survey of the area

Obtain local historical ooding levels from

the residents

Collect data

Analysis of collected data to estimate ood

ows

Estimate size of channel sections under the

bridge

4. Walk Over Survey

Site visits undertaken on the existing or nearby re-

gions will enable meeting people, sometimes old,who recollect what they (or their grandparents) saw

during ood conditions - the ood levels observed.

A backow analysis may help in crosschecking the

present ood estimates.

These are certainly of use, as a check, during design

work.

5. Data Collection

5.1 General Approach

How often have promoters accepted a consultants

offer to design drains capable of carrying ow with

a return period of 2 years?

Many codes of practice indicate a good guideline to

design drains, etc with a return period of 50 years.

This section refers to the catchment parameterswhich will enable determining some further factors


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needed for the calculation of oods. In a rst stage, the catchment area, slope (= elevation difference/stream

length) are required to nd the time of concentration.

The peak ood ow is given by the relation Qp= CiA, adjusted (for the units given) to

Qp= 0.278 C i A

Where C = runoff coefcient

i = rainfall intensity (mm/hr)

A = drainage catchment area (km2)

Qp= Design Discharge (m3/s)

The runoff coefcient is a function of the vegetation, urbanisation and other factors of the catchment. The

rainfall intensity to be used depends on the time it takes the whole catchment to contribute to the ow in the

drainage channel.

These parameters are discussed below.

Figure 1 shows the process of rainfall, wherein rainfall (or precipitation when it includes hail, snow, etc) is

the sum of the ensuing evaporation, inltration and runoff.

The lands surface always has a slope, however small it might be, which determines the direction of ow

(here, the runoff).

Figure 2 indicates how the ridge at the top of a valley slope will divide rainfall, which will run along slopes

of either side of the ridge. The area enclosed by a given ridge determines a catchment area. Depending on

the point of interest, the catchment area will vary. Point X determines a smaller catchment area than point

Y, and it turn area at point Y is smaller than that governed by point Z. Eventually, the estuary governs aneven bigger area.

Figure 1 : How rainfall is shared among different components


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So, this diagram illustrates how rain from the valley will run to a low point. Therefore, unless a drain

has been specically designed to take this rainwater, it will run into the drain besides the road, even if

the engineer wrongly believed that only water from his road would run into the road drained he designed

to take water, just from the road. And, if there are no road drains, the road itself will act as a well-

designed drain. The recent heavy rainfalls in Port Louis and in other places bear good testimony to this

phenomenon.

Figure 2: The catchment area gets bigger downstream of the valley

Figure 3: The estuary is the lowest and nal exit drainage point


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Therefore, one rst rule to avoid ooding is to

make sure that the catchment area of the drain

being designed is not underestimated. Not rocket

science, but how often ignored by engineers and

planners!

Figure 3 gives an overall picture of a valley (with

smaller valleys inside) and indicates how everything

discharges into the lowest point which happens to be

the estuary.

In this connection, there is a parallel with trafc

ow. Unless the conveying capacity QOUT

is greater

than the incoming ow of trafc QIN

, there is going

to be a trafc jam. While this results in a halt or

lower speed in case of vehicles, unfortunately with

water, this higher inow leads to non-stopping ow

which results in overtopping the drain and ooding

the sides.

Therefore, another rule to avoid ooding would

be to make sure that the carrying capacityCOUT

of the channel drain exceeds the peak discharge

Qp.

COUT

Qp

Simple logic, but how often ignored!

5.2 Runoff Coefficient Value

The runoff coefcient C represents the ratio of a peak

ow and rainfall rate of selected duration determined

or the same average recurrence interval from

frequency analysis of ood peaks and rainfalls.

There are various factors affecting the runoff

coefcient which must be considered. In

consideration of these, the Institution of Engineers,

Australia (Abbey, 1999) recommends that the runoff

coefcient C be taken as

C = Fy(0.45 + 0.20 f

i)

Where

fi = impervious factor, taken as 1 as a worst

case.

Fy = frequency factor

= 1.20 for a 100-year return period.

The runoff coefcient thus works out (for this return

period) to beC = 1.2 (0.45 + 0.20 x 1) = 0.78

Different authors give other formulae or tabulated

values, depending on soil cover.

If Figure 1 is examined again, several observations

may be made:

The equation,

Rainfall = Evaporation + Inltration + Runoff

while holding true in all cases, does not indicate that

runoff or any of the other parameters are constant,

though they may be taken to be taken as an average

over the year and so on.

For example, during a hot sunny day, imagine that

some rain falls. As the rain drops touch the ground

(soil or road surface) water vapour can be seen torise in the air. Evaporation is actually occurring!

If it is a light rain, the ground surface will be seen

to dry up quickly. Either all rain water evaporates

on the road or some of the rain is absorbed into the

earth : inltration is taking place.

The end result is, however: there is NO runoff!

At the other end of the scale, even under the samesunny conditions, if there is a heavy rain, there will

a substantial runoff towards a low point (drain, river,

pond), because the soil has reached its inltration

capacity. The soil is momentarily saturated.

The ratio of this runoff to the measured rainfall is

the runoff coefcient.

Again, this runoff coefcient may be measured as an

average over a period of time, or at every instant orover very short intervals.


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Typically, it is usual to give the average over a

long interval of time for the runoff coefcient.

However, for those people who have experienced

cyclonic conditions, the situation is different.

When there are heavy rains, in fact, rain might be

falling continuously/on and off, during several days.

The soil is now saturated over a longer period, and

this can be felt even outside cyclonic conditions.

Imagine now a sudden, heavy rainfall under these

conditions. This will just be runoff. There will be

NO inltration (saturated soil) and little evaporation

(the air is saturated with water vapour).

So now, the runoff coefcient C = 1, taken as 1 is a

worst case, that needs to be considered.

Although this might be difcult to swallow, it is

judicious to examine the situation in the light of

actual experience. Mauritius is a tropical island with

tropical heavy rains, not a desert where it rains 20

mm per year !!

If, on top of that (as in Port Louis), the ground

surface consists of clayey soil or is mostly paved,

again the runoff coefcient is going to be C = 1.

This is the third rule to consider: In tropical

countries, take C = 1

This factor will increase the design ow to be

considered, for sure. However, though the engineersjob is to do an economical design, he should not

underestimate the loading conditions (here, the

possibility that the rain will not inltrate at all, nor

evaporate, is real. It does happen.). Furthermore,

the drain is expected to be effective under extreme

conditions, not only when it rains slightly.

5.3 Intense Rainfalls

Normal rainfalls do not cause ooding to occur. So

a serious study of ooding needs to consider intense

rainfalls.

The worlds greatest recorded rainfalls, according to

the World Meteorological Organisation are approxi-

mated by the equation

P = 422475.0

dT

Where

P = the rainfall (precipitation) depth in

millimetres

Td= the duration in hours

The equation was obtained by tting data from

observed extreme rainfalls at many locations for

durations ranging from one minute to several

months. This equation is an estimate of the

precipitation depths that could occur under very

extreme circumstances.

If Td

is taken as 1 hour, the rainfall is 422 millimetres.

Something to think about!

Fortunately, the rainfall records in Mauritius do

not indicate such extremes in Mauritius, but heavy

rains with 100 mm/hr over an hour or so are not

uncommon (89 mm at Dubreuil on 22ndDecember

1979 over 1 hour , 310 mm at La Brasserie over 150

minutes on 6th February 1992 and more recently 91

mm at Line Barracks, Port Louis, between 2 and 3

p.m, on 30thMarch 2013. The rainfall collected over

the rst half hour was 50 mm which amounts to an

intensity of 100 mm/hour)

5.4 Rainfall Intensity and Frequency

To introduce the subject, a 100 m sprinter runs at

a speed of 36 km/h on a 10 second race, but theaverage speed is much lower (22 km/h) when another

Table 1: Typical Rainfall Intensities (mm/h)

Duration (mins)

T = 100 yearsSeychelles Mauritius

30 mins 150 120

60 120 100

Duration (mins)

T = 50 years

30 140 110

60 105 90


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runner (or the same person) undertakes a 10,000 m

marathon.

Similarly, though a rainfall may last several hours

(long distance race), the critical condition to observe

in drain design is the highest rain intensity (highestspeed over a short distance race).

The rainfall intensity i is the average rate of

precipitation in mm/hr from a storm having a

duration equal to the time of concentration.

It is assumed that runoff due to a heavy rainfall will

reach a peak at the time of concentration when the

whole catchment is contributing to ow. Then, the

duration of the design storm is equal to the time ofconcentration.

The time of concentration tcis thus the time taken

for water to travel from the catchment boundary to

the point of interest (Points X, Y or Z or estuary) in

Figure 2).

For small, steep areas, (e.g. Mauritius, Seychelles),

the Kirpich formula has been found to give reasonable

estimates for tc. In this formula,

tc= 0.01947 L0.77S -0.385

where

tc = time of concentration in minutes

L = maximum length of travel of water (m)

and

S = slope of catchment = H/L in which

H = difference in elevation between the most

remote point on the catchment and the outlet.

Mays (2004), Reddy (2008) and Rmniras (1986)

give other similar formulae, applicable in different

conditions.

Rainfall intensity-frequency-duration curves are

usually derived by the countrys Meteorological

Services. The rainfall intensity (mm/ or mm/min)

gures are available for different periods of time,

such as 5, 10, 15, 20, 30, 60 and 120 minutes. Table 1

shows examples of rainfall intensities for Seychelles

and Mauritius.

The time of concentration rarely falls exactly on the

duration time for which gures have been provided

by the Meteorological Services. A judicious

interpolation helps.

As previously indicated, a 50 year return period is

a good guideline, but sometimes the designer might

feel that a 100 year return period might be better.

For example, a bridge (Bindra, 1975) is a structure

that is expected to be in operation during a very long

period. In this context, it is natural to consider events

with a return period of 50 years or even more. There

are so many bridges in the world which have been

standing for more than 50 years.

A 100-year rainfall has a 1% chance of occurring in

any single year. This issue will be discussed below.

6. Is a Return Period of 50 years Acceptable?

The results obtained from the above calculations

can prove to be very important in the design of hy-

drological structures such as bridge culverts and

channels to drain the area under consideration and

prevent ooding. Every structure is designed for a

certain design life and it must be ensured that this

structure serves for its purpose without endangering

any life and property.

The risk that failure of such a structure occurring

during its design life has been explained by Mays

(2004) as follows:

Let P be the probability of the occurrence of an

event,

1 P = probability that the event will not

occur

(1 P)(1 P) = probability that the event will notoccur in two successive years.

(1 P)(1 P)(1 P) = probability that the event will

not occur in three successive years.

(1 P) N = probability that the event will not

occur during a span of N successive years.

Hence, the risk, R or the probability that the event

will occur during a span of N years is given by,

R = 1 (1 - P)N

The probability P is given by P = 1/Tr. Table 2 shows,for return periods T

rand various spans of years N,


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the risk Rthat a ood with certain return period will

be equalled or exceeded during periods of span N

years.

Rainfall frequency and intensity records can be used

to estimate the magnitude of rains and the ensuing

ood ows. In this respect, it is important to notethat there is a 26 % probability that a 100 year rain

will occur during the next 30 years (a generation).

In practical terms, this means that each generation

has a 1 in 4 chance of experiencing ooding, even

if an exceptional (?) rainfall intensity of 100 year

has been considered. Over a 75 year lifetime, the

likelihood rises to 0.53, i.e., the average person has

a 1 in 2 chance of experiencing ooding during

his lifetime.

Is the population ready to accept this?

Even if a higher return interval (e.g. 1,000 years) is

taken, it is found that there is 7.2 % chance (not to be

neglected as being small) that a 1,000 year ood will

occur during a 75 year span a mans lifetime.

It can be noticed that the risk that an event is reached

or exceeded for a certain span of time, decreaseswith an increase in return period. This result is of-

ten used in the design of huge structures. There is

also an increase in cost by considering the design of

a structure for a long return period. However, this

should be done to be safe from calamities causing

loss of life and property.

Many Codes of Practice indicate that one of the

reasons for choosing a return period of 50 years has

been that the average lifetime of most buildings and

structures is near 50 years.

This may have been true at one time. There

are, however, other factors which need to be

considered:

(1) the use of better materials has increased the

lifetime of the buildings and structures. Similarly,the corresponding drains or bridge culverts will

have a longer life.

(2) why should any owner, demolish his building

after 50 years, if it is still serviceable? The Eiffel

Tower was built in 1889, to be demolished just after

the Universal Paris Exhibition. It is still standing and

being regularly maintained. We have not yet seen

any drain being demolished to be enlarged, except

when they have really been shown to be inadequate.

Even if a local authority tried to do so, it very likelythat adjoining structures would prevent this.

Table 2: Risk R, that a ood of a given return period will be equalled or exceeded during

periods of various lengths.

Return

Period

Tr (years)

Risk R for various spans of N years

5 10 30 50 75 100 200 500

1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

5 0.67 0.89 1.0 1.0 1.0 1.0 1.0 1.0

10 0.41 0.65 0.96 0.995 1.0 1.0 1.0 1.0

50 0.10 0.18 0.45 0.64 0.78 0.87 0.98 1.0

100 0.05 0.10 0.26 0.40 0.53 0.63 0.87 0.99

500 0.01 0.020 0.058 0.095 0.14 0.18 0.33 0.63

1,000 0.005 0.010 0.03 0.049 0.072 0.095 0.18 0.39

5,000 0.001 0.002 0.006 0.010 0.015 0.020 0.039 0.095

10,000 0.0005 0.001 0.003 0.005 0.0075 0.0099 0.020 0.049


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There so many cathedrals and nearby bridges built

in the eighteenth century in Mauritius (thirteenth

century in Europe) still standing today. Would any

present day designer still consider a 50 years lifetime

for such monuments?

(3) the cost of demolition becomes so high that the

owner is likely to push the time limit before he has

to really bring down the structure..

If these factors are considered, what return period

should be considered?

In dam hydrology, the notion of maximum possible

ood (return period of 10,000 to 50,000 years,

depending on authors) has made its appearance, for

exactly the same reasons the possible danger to

human life.

It might be argued that with only some 100 years

data or, in most cases, even less, it is difcult to

make predictions (or wild guesses) about 10,000

years recurrence intervals. But, if a bridge culvert or

drainage channel is needed now nobody will wait

to collect another 50 years of rainfall data.

7. Estimation of the Peak Design

DischargeAt this stage, the peak design discharge may be

calculated and hence used to design the drain or

bridge culvert as the case may be.

Once the design ow has been established, channel

hydraulics may be used to design the channel or

culvert. One typical carrying capacity formula is

that of Manning

where

COUT

= ow in channel (m3/s)

A = wetted area (m2)

R = hydraulic radius (m) = wetted area/wetted

perimeter (m)

S = channel slope

n = Mannings roughness coefcient

= 0.010 smooth, cement lining = 0.013 good brickwork

= 0.030 rivers in good condition

Design constraints are usually channel or river

width and slopes, but the designer should try to see

if other accompanying measures need to be taken.

The choice is likely to be governed by minimumheadway clearances under the bridge due (1) to the

possibility of branches and trees being carried away

and (2) other facilities passing under or by the side

of the bridge.

Some river training works might be necessary just

upstream or downstream of the bridge.

In this context, this formula is enlightening. The

same channel will have different carrying or

discharge capacities if any of the variables changes.

A bigger cross sectional area will increase the

channel capacity, but the effect will be attenuated

if the roughness changes from a smooth, cement

lining to a river in badcondition.

8. The Case for Port Louis

The motorway was ooded at Caudan between

Rogers House and the waterfront on 11thFebruary

2013, without much damage. There was a worse

incident on 30thMarch 2013, with loss of life.

The rainfall recorded, on 30thMarch 2013, at Line

Barracks (less than 100 mm in 1 hour) would

indicate, from Table 1, a return period of some 50-

100 years. However, the fact that there was a similar

ooding at Place dArmes/Caudan (apparently

without the underground pedestrian pathways

getting submerged) on 11thApril 2003 (Wright A.,

Moonien V., 2013) conrms the values of Table 2.

A 50 year ood does not occur every 50 years! It

will certainly occur during a period of 500 years, but

may also occur within the next 10 years !!

In the light of the above discussion, it is judicious

to ask whether ooding can occur again, and how

soon?

The motorway from Montebello towards Port Louis

is lined, practically on both sides with concrete

borders or walls, which are supposed to be very


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effective against cars trying to rub into them. The

walls are also provided, at regular distances, with

weep holes, which are expected to evacuate water

into the side drains.

While these weep holes can be very effective inevacuating low ows, their small size (some 30 x 10

cm to 40 x 15 cm) becomes inadequate when heavy

rains and winds bring in their loads of gravel, leaves,

and mud. When these weep holes are blocked, the

bituminous motorway becomes a very well designed,

bitumen lined channel, which was well evidenced

during the heavy rains of 30th March 2013. The

motorway was conveying water which was supposed

to be evacuated into the side drains.

At end of July 2013, the weep holes are still of the

same size!

Between Edith Cavell street and the Government

House, the lowest points in Port Louis occur along

the La Poudrire street. Rightly so, the two channels

Le Pouce stream and La Butte Thonnier canal are

located on both sides of this road. The ground also

has a downstream slope towards the sea. This means

that any rainfall will be channelled towards these two

canals/channels and towards the sea.

The only problem is that at the level of the Harbour

Front and Place dArmes, there is an uprising obstacle

(Photos 1 and2) in the form of the motorway and the

Caudan Esplanade. This now implies, that should the

peak discharge ow from heavy rainfall exceed the

discharge capacity of the channels, the ood waters

will not go directly towards the sea, unless and until

they have overtopped the motorway and the Caudan

waterfront Esplanade. Of course, with a consequential

ponding of the area between the Port Louis museum

and the Place dArmes. Again, this is simple logic,

borne out by the events of 11thApril 2003 and 30th

March 2013.

Even assuming that the motorway constitutes a

roadblock in the evacuation of rainwater from Place

dArmes, historical records (Chelin 1989) show

that oods have occurred several times, prior to

the construction of the motorway. This implies that

the existing canals/streams are not enough or are

inadequate to evacuate the water reaching Place

dArmes in case of heavy rainfall.

So, knowing that a rainfall of intensity 100 mm/

hr is not uncommon (see examples and valuesMeteorological Services Table 1), have we proposed

any new canals to evacuate more water?

9. Conclusion

This study has proposed an approach to be adopted

prior to the approval of planning or zoning schemes

with respect to possible ooding.

Rule 1: Do not underestimate the catchment to be

drained, particularly when designing roads. The area,A, is much bigger than the road itself.

Rule 2: In a tropical country like Mauritius, take C

= 1, to cater for extreme conditions when the soil is

saturated.

Rule 3: Determine the rainfall intensity, i, using

the proper and adequate return period, which is

commensurate with what the population expects from

engineers for leading a comfortable life.

Rule 4: Determine the peak discharge Qp fromthe equation Q

p= 0.278 C i A. The size (width and

height) of the channel must consider the possibility of

avoiding blockage by shrubs, leaves and trees during

cyclones.

Rule 5: Design the drain carrying capacity

Rule 6: Check that COUT

Qp

It has been argued that a 50 year return period is prob-

ably too low and higher return periods should be tak-

en, given the relatively high probability of occurrence

during a mans lifetime.

Once the desired safety from oods has been accepted

preferably through legislation it would be easy to

earmark the boundary of the reserved low lying areas reserved for extreme ood conditions. This should


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ensure that houses do not get ooded regularly.

It is essential that such guidelines and low lying

boundaries be properly adhered to, particularly when

establishing planning zones.

A discussion of the ooding occurrences in Port Lou-

is, before and after the construction of the motorway

in the 1970s, tends to highlight a possible inadequacy

of the existing drainage exits into the sea.

References

Abbey, P. 1999, Storm Water Drainage Design

Guidelines, report for Government of Seychelles,

Ministry of Environment and Transport.

Bindra S. P. 1975, Principles and Practice of Bridge

Engineering. Dhanpat Rai, New Delhi.

Chelin A. 1989, Maurice : Une le et son pass.

Editions du CRI, Ile de la Runion.

Mays L. W. 2004, Water Resources Engineering.

John Wiley, USA.

Moonien V. 2013, Inondations: Port Louis dj sous

leau 2003. LExpress, 11thAugust 2013, p. 20.

Parker D. J. 1998, Warnings for Torrential Rain and

Floodings in Mauritius. Recommendations for the

Government of Mauritius.

Proag V. 1995, The Geology and Water Resources of

Mauritius. Mahatma Gandhi Institute, Mauritius.

Reddy P. J. R. 2008, A Textbook of Hydrology.

University Science Press, New Delhi.

Rmniras G. 1986, Lhydrologie de lingnieur.

Eyrolles, Paris.Ven Te Chow., Maidment D.R., and Mays L. W. 1988,

Applied Hydrology. McGrawHill, New York.

Wilson E. M. 1990, Engineering Hydrology.

Macmillan, England.

Wright A . 2013, Rien na chang pour les autorits

. LExpress, 10thAugust 2013, p. 9.

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