04/22/23 Asheesh 1

The Mathematical Model of the Rehabilitation

of The Water Pipes Network(Condition Index)

byMohamed Asheesh

Mohmaed.asheesh@oamk.fiFinland

04/22/23 Asheesh 2

The Mathematical Model of the Rehabilitation of the Water

Pipe Network(The Condition Index)

The condition of the water pipe network can be evaluated by different ways:•the mathematical model, the condition indexthe condition index is based on the probability, availability, reliability of the system, and the break frequency of the pipeline. Understanding the theory of Understanding the theory of damagebility. damagebility. •The cost analysis method•The risk analysis method•The classification method

04/22/23 Asheesh 3

The Condition Index of the Water Pipe Network

Previou s Breaks

B reak F req u en cyp /y/km

Mod u lu s of E lastic ity

Ag e

Materials

P ip eK p

Reg ression Coeffic ien t

B reak F req u en cyp /y/km

Ag e

Typ e

Join tKs

Reg ress ion Coefficien t

B reak F req u en cy

Ag e

Typ e

ValveKv

R eason of B reaks

E xtern al Ph ysical Factors

Leakag e

Fu n ction al In d ex

Stru ction al In d ex

Con d ition S itu ationKc

P ip e Typ e

S u p p lied Area

Reh ab ilitation

E xtern al F actors

E xtern al F actorsU l

S troke Pressu re

U sed P ressu re

P lan n ed Pressu re

P ressu reP

Con d ition Ind ex

04/22/23 Asheesh 4

The Data Base• pipe record number• street name• pipe segment origin and destination node• pipe diameter• pipe length• number of hydrants• year in which pipe was placed• pipe material• month and year in which pipe broke• type of break

• break location

04/22/23 Asheesh 5 Asheesh con

The Condition index

ULC+KKKK

PPP

kKI cvspo

iku

5

04/22/23 Asheesh 6 Asheesh con

Condition IndexIn which:

• Kp =Pipe Condition Index (material, age, durability, strength ).

• KS =Joint Condition Index (age,durability, strength, type )

• KV =Valve Condition Index • KC =Condition Situation• UL =External Factors• Cu =Classification of the External Factors

04/22/23 Asheesh 7 Asheesh con

The Contents of the Condition index

7

KI =Condition Index

k=Regression ( <value>)

PK =Fet pressure in the net work, depends on the position

( 100-700 kpa/cm)

Pi =Stroke pressure

P0 =Planned pressure, 1000 kpa/cm2

04/22/23 Asheesh 8

The Mathematical Model of the Condition Index

KI=Pk+Pi)/(P0)][Kp+Ks+kv+kc] + C.UL}in which: scaling coefficientPk=(100-700)kpa/cm2

P0= planned pressurePi = Pi stroke pressureKp=C1C2 e (t-k)

ks=Cse t

Kv=Cve t

Kc=(CT,FM, L * ).CC.UL

04/22/23 Asheesh 9

Pk=(100-700)kpa/cm2

P0= planned pressurePi = Pi stroke pressure

04/22/23 Asheesh 10

KUNT OINDEKSIKI={[(Pk+Pi)/P o ]x[Kp+Ks+Kv+Kc]+Cu xUL}

Raken teid en ku n toK p ,Ks,Kv,K c

MateriaaliK im m om od uu liIkäAikaisem m at vu od otVau riotih eys

KpP u tken ku n to

Materiaalin tyyp p iIkäVau riotih eysKerroin Cs

KsSau m ojen ku n to

Tyyp p iVau riotih eysKerroin Cv

K vVen ttiil ien ku n to

Ikä

S yy

Raken teell in en ku n toToim in n all in en ku n to

Vu otavu u s

Pain u m at

Vau riotih eys

KcK u n totilan n e

Vesijoh d on tyyp p iLiitty jätO losu h teet joh d on

yläp u olella

ULUlkoiset tekijät

Pain eolotP i,P k,

P 0

U lkoiset tek ijätCu x UL

04/22/23 Asheesh 11

The Condition Index

• Kp=C1p C2 p p e(t-k)

• KS=sCses (t-k)

• Kv=vev(t-k)

• Kc = c {Sr (RT+TM+V)}

04/22/23 Asheesh 12 Asheesh con

PIPE CONDITION INDEX

Kp=C1p C2 p p e(t-k)

04/22/23 Asheesh 13

C1p =Break frequency for a determined material with (no,one or more ) previous breaks/Overall break frequency for the same material

C2p =Break frequency for a determined material with diameter x / Overall break frequency for the same material with the same diameter

= Poisson number.

p = (0,2-0,17) exponential damage expansion(failure number)

= pipe damage expansion parameter pipe breakfrequency /time year/pipe length

t = timek = installation year

04/22/23 Asheesh 14

BREAK FREQUENCY

050

100150200250300350400450500

0 10 20 30 40 50

time

et

1

2

3

04/22/23 Asheesh 15

JOINT CONDITION INDEX

• KS=sCses (t-k)

s =joint number(1kpl/6m) divided by length multiplied by joint break frequency in which the materials were considerd

• Cs =pipe length s =damage expansion parametre, depends on material and

conditions• t =time

• k =installation year

04/22/23 Asheesh 16

VALVE CONDITION

• Kv = vev(t-k)

v = damage frequency(Mays 1986) (depends on valve type) v = damage expansion parameter, depends on valve break

frequency (valve number/valve break frequency in which the pressure was)

• t = time• k =installation year

04/22/23 Asheesh 17

EXTERNAL FACTORSEXTERNAL FACTORSKc =

c {Sr (RT+TM+V)}

In which

c = correction factor coefficient

Sr = the frequency of a certain reason of break = the frequency of the external physical pressure

RT = constructional condition

TM = functional condition = leakage coefficient

V = leakage

04/22/23 Asheesh 18

The Purpose of The Condition Index

Purpose: • Controlling the capability of the water pipe network• Investigating the water pipe net work• Integrating the rehabilitation methods and the future

water network plans • Finding a proper way to rehabilitate by determining

the condition of the pipes and the location of the area.

04/22/23 Asheesh 19

THANK YOU THAT IS ALL

BYE