An Accurate Life Estimation Method for Existing Railway Bridges

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referred to as S-N or Wohler curve). However, the Miner's rule does not properly take account of loading sequence effect [6-8]. As a result, real fatigue life due to ...
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- V o l . XXXXI, N o . 02, p p . 7-16, 2008

© The Institution of Engineers, Sri Lanka

An Accurate Life Estimation Method for Existing Railway Bridges P. B. R. Dissanayake and S.C. Siriwardane Abstract: T h e p a p e r p r o p o s e s a n accurate m e t h o d o l o g y to estimate r e m a i n i n g fatigue lives of riveted railway bridges. T h e p r o p o s e d m e t h o d mainly consists of m e a s u r e d stress histories, recently d e v e l o p e d sequential l a w a n d fully k n o w n Wbhler curve. H e r e , it is essential to use the fully k n o w n W d h l e r curve as the related fatigue c u r v e . Therefore the technique, w h i c h utilizes to transfer the partially k n o w n W b h l e r c u r v e to fully k n o w n curve, is also discussed u n d e r this p a p e r . Since m o s t of the b r i d g e s d o not h a v e past strain m e a s u r e m e n t s , this m e t h o d describes reasonably accurate p r o c e d u r e to obtain the p a s t stress histories from p r e s e n t d a y m e a s u r e d stress histograms. Initially p a p e r describes the p r o p o s e d m e t h o d for r e m a i n i n g fatigue life estimation. Secondly r e m a i n i n g fatigue life of an existing railway b r i d g e is e s t i m a t e d b y p e r f o r m i n g a case s t u d y . Case s t u d y describes the details of the c o n s i d e r e d r a i l w a y b r i d g e a n d t h e a p p r a i s a l s r e l a t e d to c o n d i t i o n e v a l u a t i o n , FE a n a l y s i s , m a t e r i a l t e s t i n g , e x p e r i m e n t a l static a n d d y n a m i c l o a d t e s t i n g . T h e n t h e r e m a i n i n g f a t i g u e lives of e a c h critical c o m p o n e n t s of the b r i d g e are obtained. H e n c e validity a n d merits of p r o p o s e d m e t h o d is confirmed by c o m p a r i n g the results w i t h p r e v i o u s m e t h o d - b a s e d fatigue lives. Keywords: R e m a i n i n g life, Railway bridge, Sequential law, H e a l t h m o n i t o r i n g

1.

Introduction

h i s t o g r a m s u n d e r actual traffic load p r o v e s to be a m o r e a c c u r a t e a n d e f f i c i e n t m e t h o d for existing b r i d g e s [3,4]. M o s t of the p r e s e n t d a y fatigue a s s e s s m e n t a p p r o a c h e s used for r a i l w a y b r i d g e s are generally b a s e d o n c o m b i n a t i o n of m e a s u r e d stress histories, M i n e r ' s rule [5] a n d r a i l w a y c o d e p r o v i d e d fatigue c u r v e (also referred to as S-N or W o h l e r curve). H o w e v e r , the Miner's rule d o e s not p r o p e r l y take account of l o a d i n g sequence effect [6-8]. As a result, real fatigue life d u e to s a m e l o a d i n g p a t t e r n is higher than the Miner's expectation for increasing type loads a n d it is lower t h a n the Miner's expectation for d e c r e a s i n g t y p e l o a d s . R e c e n t l y , a n e w d a m a g e indicator-based sequential law [8] w a s o r i g i n a t e d to o v e r c o m e t h i s s h o r t c o m i n g of M i n e r ' s r u l e a n d it h a s b e e n p r o v e d t h a t sequential law gives m o r e realistic results than M i n e r ' s r u l e w h e n m a t e r i a l is s u b j e c t e d to variable a m p l i t u d e loading.

In p a s t t w o d e c a d e s , a significant a m o u n t of efforts h a v e b e e n d i r e c t e d t o w a r d s the d e v e l o p m e n t of s t r u c t u r a l h e a l t h m o n i t o r i n g a n d n o n - d e s t r u c t i v e a s s e s s m e n t m e t h o d s to m a n a g e civil structures m o r e efficiently [1]. At present, rail a u t h o r i t i e s all over the w o r l d are p a y i n g special a t t e n t i o n to e v a l u a t e the r e m a i n i n g fatigue life of riveted r a i l w a y bridges, since most of these b r i d g e s are n e a r i n g the e n d of their theoretical fatigue lives. F u r t h e r m o r e , the fatigue b e h a v i o u r of w r o u g h t i r o n a n d older s t e e l s , w h i c h w e r e c h i e f l y u s e d for t h e construction of these bridges, is not well k n o w n . T h e s e o b s e r v a t i o n s c o u p l e d w i t h t h e lack of information o n l o a d i n g history of these b r i d g e s raise question a b o u t their fatigue p e r f o r m a n c e [2]. As a r e s u l t , t h e a s s e s s m e n t of r e m a i n i n g f a t i g u e life of a r i v e t e d r a i l w a y b r i d g e for c o n t i n u i n g services h a s b e c o m e m o r e i m p o r t a n t than ever, especially w h e n decision m a k i n g regarding structure replacement, deck replacement or other major retrofits.

G e n e r a l l y , r a i l w a y b r i d g e s a r e s u b j e c t e d to c h a n g e s of traffic l o a d a n d f r e q u e n c y of o p e r a t i o n s w i t h r a p i d d e v e l o p m e n t of t r a n s p o r t a t i o n facilities w h i c h is e n c o u n t e r e d w i t h in the p e r i o d of age. Therefore, m o s t of the

Experiences from engineering practices have indicated that fatigue analysis based on specification loads a n d distribution factors u s u a l l y u n d e r e s t i m a t e s t h e r e m a i n i n g fatigue life of existing b r i d g e s by overestimating the live load stress r a n g e s . In this c o n t e x t fatigue evaluation based o n field m e a s u r e d stress r a n g e

Eng. (Dr.) P.B. R. Dissanayake, B.Sc. Eng. (Hons) (Peradeniya), C. Eng., MlE(Sri Lanka), M.Eng., Dr. Eng. (Ehime), Senior Lecturer in Civil Engineering, Department of Civil Engineering, the University of Peradeniya. S. C. Siriwardane, B.Sc. Eng. (Hons) (Peradeniya), M.Phil (Peradeniya).

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railway bridges subjected to variable a m p l i t u d e loadings including both increment and d e c r e m e n t of live load. Since the M i n e r ' s rule p r o d u c e s i n a c c u r a t e p r e d i c t i o n s to t h e r e a l failure in variable a m p l i t u d e l o a d i n g [6-8], it is doubtful to use the M i n e r ' s r u l e for r e m a i n i n g fatigue life estimation of r a i l w a y bridges. But as for the a u t h o r s v i e w , r e l a t e d investigations to r e m o v e t h e u s a g e of M i n e r ' s r u l e a g a i n s t the s e q u e n t i a l l a w for r e m a i n i n g f a t i g u e life estimation of existing r a i l w a y b r i d g e s h a v e not been so far a t t e n d e d .

is d i s c u s s e d i n t h i s s e c t i o n . P a r t i c u l a r m e t h o d o l o g y follows three major steps s u c h as s t r e s s e v a l u a t i o n , d e t e r m i n a t i o n of W o h l e r curve a n d application of sequential law. 2.1 Structural appraisal and stress evaluation In o r d e r to a p p l y the uniaxial sequential law, it is e s s e n t i a l to d e t e r m i n e t h e p r i m a r y s t r e s s ranges generated b y the p a s s a g e of trains over the bridge. Therefore, it is r e q u i r e d to k n o w the stress cycles (stress histories) distributions of all the critical m e m b e r s for trains that are i n c l u d e d in p r e s e n t a n d p a s t t i m e t a b l e s . Since f a t i g u e evaluation b a s e d o n field-measured stress r a n g e h i s t o g r a m s u n d e r a c t u a l traffic l o a d s of t h e b r i d g e is a m o r e accurate a n d efficient m e t h o d for existing bridges [3,4], this section describes the e v a l u a t i o n m e t h o d o l o g y of real stresses in the b r i d g e related to the c u r r e n t state.

T h e r e f o r e m a j o r objective of this p a p e r is to check t h e significance a n d applicability of the sequential law to estimate the r e m a i n i n g fatigue life of a riveted railway b r i d g e by p r o p o s i n g a n e w m e t h o d b a s e d o n m e a s u r e d stress histories, r e c e n t l y d e v e l o p e d s e q u e n t i a l l a w [8], a n d Wohler curve. Railway code provided Wohler c u r v e o n l y d e s c r i b e s s t r e s s r a n g e s , w h i c h are c o r r e s p o n d i n g to m o r e t h a n ten t h o u s a n d s of failure cycles (usually called as partially k n o w n W o h l e r c u r v e ) . B u t f o r t h e a p p l i c a t i o n of sequential l a w to estimate the fatigue life, it is c o m p u l s o r y to h a v e fully k n o w n W o h l e r curve. Therefore the t e c h n i q u e , w h i c h utilizes to transfer the p a r t i a l l y k n o w n W o h l e r c u r v e to fully k n o w n curve, is also discussed u n d e r this paper. Further this paper describes the reasonably accurate p r o c e d u r e to obtain the past stress histories from present day m e a s u r e d stress h i s t o g r a m s . This is of extreme i m p o r t a n c e because m o s t of the b r i d g e s d o not h a v e the past strain m e a s u r e m e n t s .

Initially a condition s u r v e y h a s to be carried out to assess the p r e s e n t g e o m e t r i c c o n d i t i o n a n d d a m a g e s . Generally, it consists of detailed visual e x a m i n a t i o n , i n - s i t u m e a s u r e m e n t s of e a c h c o m p o n e n t of the b r i d g e a n d n o n - d e s t r u c t i v e field e x a m i n a t i o n s . T h e n l a b o r a t o r y tests will need to be carried out to d e t e r m i n e the current s t a t e of m e c h a n i c a l p r o p e r t i e s a n d c h e m i c a l composition of the b r i d g e materials. T h e static a n d d y n a m i c load testing can b e r e c o m m e n d e d as next major step to s t u d y the real b e h a v i o r of the b r i d g e u n d e r v a r i o u s l o a d c o m b i n a t i o n s . The obtained results is u s e d to d e v e l o p a p r o p e r a n a l y t i c a l m o d e l a n d f u r t h e r assists in e v a l u a t i n g a c t u a l d y n a m i c f a c t o r s of e a c h structural c o m p o n e n t . Finally the b r i d g e will be subjected to finite e l e m e n t (FE) analysis u n d e r test a n d actual l o a d i n g s to d e t e r m i n e stresses a n d deflections, as well as variations of stresses u n d e r m o v i n g loads. Material p r o p e r t i e s w h i c h are obtained t h r o u g h laboratory tests and current geometric p r o p e r t i e s o b t a i n e d from c o n d i t i o n a s s e s s m e n t a r e a p p l i e d to t h e FE m o d e l for m o r e realistic o u t p u t s . The validation of t h e FE m o d e l h a s t o b e c a r r i e d o u t b y c o m p a r i n g the results from analysis w i t h those f r o m f i e l d - t e s t s . T h e FE m o d e l , w h i c h g i v e s b e t t e r c o m p a r i s o n to l o a d test r e s u l t s c a n b e n o m i n a t e d as " v a l i d a t e d a n a l y t i c a l m o d e l " . Hence, a v a l i d a t e d analytical m o d e l is u s e d to o b t a i n p a s t a n d p r e s e n t static s t r e s s h i s t o r i e s d u e to passage of trains specified by the o w n e r .

Initially p a p e r describes the p r o p o s e d m e t h o d for r e m a i n i n g fatigue life estimation. The details of case s t u d y r a i l w a y b r i d g e a n d the appraisals related to condition evaluation, material testing, field static a n d d y n a m i c load testing, structural analysis are mentioned. Then, the remaining fatigue life of e a c h critical c o m p o n e n t of t h e bridge is discussed. Finally c o m p a r i s o n s of the results are m a d e with Miner's rule-based previous estimation. Hence, validity and a p p l i c a b i l i t y of t h e p r o p o s e d a p p r o a c h is discussed.

2.

Proposed method for remaining fatigue life estimation

P r o p o s e d m e t h o d for r e m a i n i n g f a t i g u e life estimation of a n existing riveted railway b r i d g e

|88j8

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8

D u e to t h e d y n a m i c effect of m o v i n g trains, the

description of t h e sequential l a w is available in

actual w o r k i n g stresses s h o u l d b e h i g h e r t h a n

t h e c o r r e s p o n d i n g p a p e r [8]. H e r e o n l y t h e

the analytical static stress. Therefore,

c o n c e p t is s u m m a r i z e d w i t h a n a l g o r i t h m for

the

d y n a m i c f a c t o r s of e a c h m e m b e r , w h i c h a r e

u n d e r s t a n d i n g (see Fig. 2).

f o u n d e x p e r i m e n t a l l y , is u s e d to m u l t i p l y t h e static stress to get t h e service stresses. Finally, t h e s t r e s s h i s t o r i e s h a v e to b e c o n v e r t e d i n t o

A new damage indicator based sequential

stress r a n g e s b y u s i n g t h e r e s e r v o i r c o u n t i n g

r»i cycles at a i stress

m e t h o d (BS 5400 p a r t 10,1980). T h e d e s c r i b e d stress

evaluation

procedure

is

briefly

Ni failure cycles number at oi stress level (Wohler)

s u m m a r i z e d as s h o w n in p i g - 1 .

1 Nw=Ni-nf. Residual life a (ijfrf: Damage stress for Nm cycles (Wohler curve)

Condition Survey

I Material Testing

A=

1 Field Load Testing

1 Development of validated analytical model

i Stress Evaluation (Past and Present) Figure 1. Flow of stress evaluation procedure 2.2 Determination of Wbhler curve

n/ cycles at oi stress level

Fatigue failure

Damage transformationfromprevious step to next step

T o c a p t u r e t h e f a t i g u e d a m a g e d u e to t h e s e c o n d a r y stresses n e a r the r i v e t e d connection or d i s c o n t i n u i t i e s , d e t a i l c l a s s [9] of r i v e t e d connection b a s e d W o h l e r c u r v e s are considered

a l(i)ed associated number of cycles N^R (Wohler curve)

for life estimation. T h e detail class is d e t e r m i n e d by c o n s i d e r i n g t h e q u a l i t y of t h e w o r k m a n s h i p

/

N(,)R =N (i)R-n : i

a n d c u r r e n t c o n d i t i o n of the riveted connection. Generally, t h e S-N c u r v e , w h i c h is m e n t i o n e d u n d e r the U K r a i l w a y a s s e s s m e n t c o d e [10], is considered as the suitable fatigue curve for this

I a

: Damage stress for N ^ cycles (Wohler)

I

e v a l u a t i o n . But, c h o s e n fatigue c u r v e only describes stress ranges, w h i c h are c o r r e s p o n d i n g to m o r e t h a n t e n t h o u s a n d s of failure cycles (usually called as partially k n o w n

Wbhler

c u r v e ) . In t h e c a s e of s e q u e n t i a l l a w it is e s s e n t i a l to k n o w t h e W b h l e r c u r v e for full r a n g e of t h e n u m b e r of cycles. Therefore, t h e chosen partially k n o w n W b h l e r curve, w h i c h is mentioned u n d e r the UK railway assessment code [10], h a s to b e transferred to fully k n o w n Wbhler curve by u s i n g K o h o u t a n d Vechet Wbhler c u r v e m o d e l i n g t e c h n i q u e [11].

i=>i+l Figure 2. Flow chart for damage stress based sequential law The h y p o t h e s i s b e h i n d t h e m o d e l is that if the p h y s i c a l s t a t e of d a m a g e is t h e s a m e , t h e n fatigue life d e p e n d s only o n l o a d i n g condition. T h e r e f o r e , t h e life c a n b e a s s e s s e d u s i n g t h e W b h l e r c u r v e for n e w structures, w h i c h are still free of d a m a g e . At load level i, a certain stress a m p l i t u d e a is a p p l i e d for a n u m b e r of cycles n .

2.3 Application of sequential l a w

H e r e t h e n u m b e r of cycles to failure from t h e W b h l e r c u r v e for a is N.. T h u s , after n. a p p l i e d

A n e w d a m a g e indicator b a s e d sequential l a w in

cycles, the r e s i d u a l life is c o n s i d e r e d as

{N.-n)

8

m u l t i a x i a l f a t i g u e ) , is u s e d to o b t a i n a m o r e

for load level i. F r o m t h e W b h l e r curve, a,.. , is

realistic fatigue life for t h e b r i d g e . A d e t a i l e d

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(3)

'{:+\)ed

w h e r e a' is d a m a g e equivalent stress at the level i+l. T h u s , t h e c o r r e s p o n d i n g e q u i v a l e n t n u m b e r of c y c l e s t o f a i l u r e , N ' . can be o b t a i n e d from the W o h l e r c u r v e as s h o w n in Fig. 3. T h e o ' . is t h e m a g n i t u d e of a p p l i e d stress a n d it is subjected to n. n u m b e r of cycles at the level i+l. Then the c o r r e s p o n d i n g residual life at the load level i+l, N ' is calculated as, iH)ed

+I

+]

(4)

(i+l)

Figure 3. Schematic representation of parameters in Wohler curve

Hence the d a m a g e stress o , which c o r r e s p o n d s to N . at l o a d i n g level i+l, can be obtained from the W o h l e r c u r v e as s h o w n in Fig. 3. Then the c u m u l a t i v e d a m a g e at l o a d i n g level i+l is defined as, ed

th

said to be z level d a m a g e stress (otherwise can be i n t r o d u c e d as stress relevant to the residual life) which c o r r e s p o n d s to the failure life (Ni-ni), (see Fig. 3). H e n c e , t h e d a m a g e s t r e s s , Di is defined as,

R

a

(i+\)ed

M

(5)

cr„ - ai+l

(1)

D, =

a

The s a m e p r o c e d u r e is followed until the failure w h e r e o is the m a g n i t u d e of u l t i m a t e stress. T h e stress field can b e c o n s i d e r e d in t e r m s of equivalent v o n Mises stress a n d in this w a y the model can be applied to the multiaxial fatigue. In the case of uniaxial l o a d i n g c o n d i t i o n , the s t r e s s field c a n b e c o n s i d e r e d i n t e r m s of c o r r e s p o n d i n g stress values. The a is equal to o, at first cycle w h e n d a m a g e indicator D=0 a n d a is equal to a at the last cycle w h e n D=l. Therefore, the d a m a g e indicator is n o r m a l i z e d to 1 at the failure of material.

of material, that is, w h e n d a m a g e indicator D.=l.

u

(j)ed

3.

The selected b r i d g e to e v a l u a t e the r e m a i n i n g fatigue life is one of the longest r a i l w a y bridges in Sri Lanka h a v i n g a length of 160 m (Fig.4). It is a six s p a n riveted b r i d g e w i t h d o u b l e lane rail tracks h a v i n g w a r r e n t y p e semi t h r o u g h trusses, s u p p o r t e d on cylindrical piers. The b r i d g e deck is m a d e of w r o u g h t iron a n d the piers are m a d e of cast iron casings w i t h infilled concrete. The bridge has constructed in 1885. Details of trains c a r r i e d by the b r i d g e at p r e s e n t a n d their frequencies illustrate that the b r i d g e is subjected to variable a m p l i t u d e loading.

u

Same d a m a g e is t h e n t r a n s f o r m e d to load level i+1 a n d hence d a m a g e equivalent stress at level i+l is calculated w i t h the relation,

D, =

'(i+\)ed

'i+l

Case study: Remaining life estimation of a riveted railway bridge

(2)

'i+l

Further simplification of Eq. (2),

il

f

v

y

• i

Figure 4. General vieivs of the riveted bridge

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10

Figure 5. Some of photos to show the corrosion of the bridge

Ml 1

MCI \

MCI

MC2

J

DT2

MC2

MC2

MC3

J

v DT4

If!

MC3 ^ ITTS

S'l

, / \ K

ST

J1

t(N/

M

S T

/

/uci\ MT1

MT1

MTl

MT2

4

\

MT2

/

/bcs\ MT2

MT3

ST

k

(a)

R

3

/

1

CG ST

/

V _

ST

CG

ST

\ B

EB2 EB1 EB4

ST

ST ST

MT3

| ^

CG

CG ST

n

ST

S T \

/ S T

, ! i < ;

1\ \

ST

x

(b) Figure 6. Member set categorization (a) Main truss girder (b) Horizontal bridge deck

3.1 S t r u c t u r a l a p p r a i s a l a n d stress e v a l u a t i o n

Table 1: Mechanical properties of super structure material

Extensive condition s u r v e y , laboratory testing, field-testing, and analytical work were p e r f o r m e d to o b t a i n m o r e realistic stresses of critical c o m p o n e n t s of the b r i d g e [12,13]. 3.1.1

Condition survey

The condition s u r v e y revealed that s o m e places of t h e b r i d g e h a v e b e e n s u b j e c t e d t o m i l d corrosion d u e to the absence of anti corrosive c o a t i n g (see F i g . 5 ) . N o v i s u a l c r a c k s w e r e o b s e r v e d in a n y c o m p o n e n t of t h e s u p e r s t r u c t u r e . In s i t u m e a s u r e m e n t s of m e m b e r sizes, connections a n d s u p p o r t bearings verified t h e fact t h a t t h e e x i s t i n g d r a w i n g s w e r e applicable a n d only few significant v a r i a t i o n s w e r e observed. F u r t h e r the b r i d g e c o m p o n e n t s h a v e been categorized to several g r o u p s entitled " m e m b e r set" by considering similar cross sectional p r o p e r t i e s as s h o w n in Fig.6. Finally it can be said that c o m p a r a t i v e m a i n t e n a n c e w o r k carried out on the b r i d g e t h u s far is satisfactory. 3.1.2

Property

Values

Density Yield Strength in tension Ultimate tensile strength Elastic modulus Fatigue limit

7600 k g / m 240 MPa 383 MPa 195 GPa 155 MPa

3

obtained mechanical p r o p e r t i e s of the w r o u g h t iron is s h o w n in Table 1. 3.1.3

Field load testing

Static a n d d y n a m i c load testings w e r e p e r f o r m e d to s t u d y t h e real b e h a v i o r of t h e bridge u n d e r v a r i o u s load combinations. The in situ m e a s u r e m e n t s w e r e p e r f o r m e d u s i n g t w o M8 engines, each w e i g h t i n g 1120 k N , w h i c h is the heaviest rail traffic in c u r r e n t operation. The bridge was i n s t r u m e n t e d with strain gauges placed at selected locations to m e a s u r e n o r m a l strains. In addition, the triaxial vibrations w e r e recorded at several locations using a c c e l e r o m e t e r s . In o r d e r to m e a s u r e free vibration, accelerations w e r e recorded after the M8 engines had crossed the bridge. Displacement t r a n s d u c e r s w e r e u s e d to m e a s u r e s v e r t i c a l deflection at three places a r o u n d the m i d s p a n area of the bridge.

Material testing

The sampling of m a t e r i a l s , specimen preparation and testing were carried out according to the ASTM s t a n d a r d s . The chemical a n a l y s e s as well as m i c r o s c o p i c e x a m i n a t i o n s led to conclusion that the b r i d g e s u p e r structure m a t e r i a l is w r o u g h t i r o n . A s u m m a r y of t h e

11

ENGINEER

Time (sec)

(d)

Time ( ) sec

(e)

Time (sec)

(f)

Figure 7. Field measurements of the bridge due to heaviest load (a) Stresses at bottom chord of the main girder (b) Stresses at diagonal members which are usually subjecetd to tensile stress (c) Stresses at stringers (d) Stresses at secondry cross girders (e) Vertical displacemnt at midspan (f) Vertical acceleration at midspan.

To a c q u i r e s t a t i c a n d d y n a m i c r e s p o n s e s of strains, displacements and accelerations, sophisticated static a n d d y n a m i c d a t a loggers w e r e used. To obtain the different t y p e of load c o m b i n a t i o n s , w h i c h are critical to the b r i d g e , t h e t w o t e s t - e n g i n e s w e r e p l a c e d as w e l l as m o v e d u n d e r different s p e e d s . The considered t h r e e static l o a d c o m b i n a t i o n s are d e f i n e d as static load case (SLC) 1,2 a n d 3 by c o n s i d e r i n g criteria of m a x i m u m s h e a r effect, m a x i m u m b e n d i n g effect ( m a x i m u m d e f l e c t i o n ) a n d m a x i m u m t o r s i o n effect to t h e b r i d g e d e c k respectively. The criteria, which were c o n s i d e r e d for d y n a m i c l o a d c o m b i n a t i o n s , b a s i c a l l y i l l u s t r a t e t h a t i m p a c t effect t o t h e b r i d g e w i t h d i f f e r e n t l e v e l s of s p e e d a n d t r a c t i o n force effect. A p a r t f r o m t h e a b o v e m e n t i o n e d formal field load testing, the b r i d g e w a s subjected to a t w o d a y s c o n t i n u o u s field m e a s u r e m e n t p r o g r a m u n d e r p r e s e n t d a y actual traffic. E v e n t h o u g h u n d e r this i n v e s t i g a t i o n m a n y t y p e s of l o a d c o m b i n a t i o n s w e r e considered, only the combinations, w h i c h w e r e

ENGINEER

u s e d to e v a l u a t e the fatigue life of the b r i d g e , are s h o w n in this p a p e r . W h e n t h e b r i d g e is affected b y m a x i m u m load d u e to t h e p r e s e n t d a y heaviest train passage, the obtained s a m p l e m e a s u r e m e n t s are s h o w n in Fig. 7. M a x i m u m values of r e s p o n s e s w h i c h w e r e m e a s u r e d while m o v i n g the test-engine w i t h different s p e e d s , are plotted against the s p e e d of the train (Some of p l o t s a r e i l l u s t r a t e d in pig- 8). Finally t h e d y n a m i c factors w e r e o b t a i n e d as 1.3,1.4 a n d 1.4 for m a i n truss girders, s e c o n d a r y cross girders by the ratio of m a x i m u m d y n a m i c r e s p o n s e to static response. 3.1.4

Development of validated analytical model

The Bridge girder w a s a n a l y z e d u s i n g the finite e l e m e n t (FE) m e t h o d e m p l o y i n g t h e g e n e r a l p u r p o s e p a c k a g e S A P 2000. A t h r e e dimensional (3D) m o d e l (Fig- 9) of o n e c o m p l e t e m i d d l e s p a n of the b r i d g e w a s a n a l y z e d u n d e r test loadings a n d actual loadings to d e t e r m i n e stresses in m e m b e r s a n d deflections, as well as variations of stresses u n d e r m o v i n g loads. The

12

0

10

20 30 40 50 Train speed (km/h)

10

(a)

20 30 40 50 Train speed (km/h)

0

10

20 30 40 50 Train speed (km/h)

(c)

(b)

Fig. 8. Dynamic factor determination curves (Maxitnutn responds variation with speed) (a) Main truss girder (b) Secondary cross girders (c) Stringers

Figure 9. 3D frame element model for single span (a) Deflected shape for SLC 2 (b) Axial force diagram atSLC2 (c) Bending moment diagram at SLC 2 bridge deck w a s m o d e l e d with 3D frame elements and the riveted connections are a s s u m e d to b e fully-fixed [2]. Even t h o u g h the cross girders are ideally s u p p o r t e d o n b o t t o m chord of the m a i n truss girder, t h e a s s u m p t i o n of r o t a t i o n a l s t i f f n e s s b e h a v i o r w i t h s m a l l m a g n i t u d e for r e p r e s e n t a t i v e c o n n e c t i o n of cross girder to truss w e r e found to be in better a g r e e m e n t w i t h field m e a s u r e m e n t s t h a n t h e p i n n e d c o n n e c t i o n a s s u m p t i o n . Every r i v e t e d connections of cross girders w i t h b o t h stringers a n d bracings w e r e a s s u m e d to b e fixed.

several periods. According to the past and p r e s e n t t i m e t a b l e s of t h e b r i d g e , it c o u l d b e a s s u m e d t h a t t h e traffic s e q u e n c e is a l m o s t constant d u r i n g a single w e e k of each p e r i o d of age. T h e n t h e v a l i d a t e d analytical m o d e l w a s used to obtain the static stress histories of each critical m e m b e r d u r i n g a single w e e k of e a c h p e r i o d . D u e to the d y n a m i c effect of m o v i n g trains, the actual w o r k i n g stresses should be higher than the analytical static stress. Therefore, the d y n a m i c factor of each m e m b e r , w h i c h w a s found experimentally, w a s u s e d to m u l t i p l y the static stress to get the service stresses. Then the stress histories were converted into stress ranges by using the reservoir c o u n t i n g m e t h o d [9].

The validation of FE m o d e l w a s carried o u t by c o m p a r i n g the results from analysis w i t h those from field-tests as s h o w n in Table 2. From the results of static l o a d cases it w a s seen that there is a g o o d a g r e e m e n t a m o n g analytical results of the FE m o d e l a n d the m e a s u r e m e n t of the actual bridge. Therefore, the c o n s i d e r e d 3D frame element m o d e l w a s defined as ivalidated analytical m o d e l . 3.1.5

3.2 Determination of W o h l e r curve Field i n v e s t i g a t i o n s reveal that the r i v e t e d c o n n e c t i o n s of the b r i d g e r e p r e s e n t l a p p e d or spliced connection behavior with normal c l a m p i n g force. Therefore, riveted connections w e r e c l a s s i f i e d a s c l a s s W r o u g h t - i r o n (WI), w h i c h is p r o p o s e d b y t h e U K r a i l w a y a s s e s s m e n t c o d e [10]. H e n c e t h e S-N c u r v e , w h i c h is m e n t i o n e d u n d e r t h e U K r a i l w a y

Stress evaluation

Since the t y p e s of trains u s e d are c h a n g e d w i t h age of the bridge, the age h a d to be d i v i d e d in to

13

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Table 2. Comparison of FE analytical results with load test results Static load case

Displacement (mm) Location of measurement Load test

Stress (MPa) FEM

Location of measurement

Load test FEM

SLC1

Main girder mid span

19.4

21.0

Critical member of DC3 Critical member of DT3 Critical member of MT3

-40.2 51.4 47.3

-40.6 57.3 48.2

SLC2

Main girder mid span

21.3

22.5

Critical member of DC3 Critical member of DT3 Critical member of MT3

-37.8 44.5 53.5

-37.7 43.6 53.9

SLC 3

Main girder mid span

-

19.1

Critical member of DC3 Critical member of DT3 Critical member of MT3

-39.5 35.2 39.0

-39.9 41.5 44.7

4.

assessment c o d e for WI detail class connection [10], w a s t r a n s f e r r e d to fully k n o w n W o h l e r c u r v e by u s i n g K o h o u t a n d Vechet W o h l e r c u r v e m o d e l i n g t e c h n i q u e [11]. T h e o b t a i n e d f u n c t i o n a n d t h e g e o m e t r i c a l s h a p e of n e w fatigue c u r v e , w h i c h c o r r e s p o n d s to class WI riveted connection, are illustrated in Fig.10.

O b t a i n e d r e m a i n i n g fatigue lives for the critical m e m b e r s of each m e m b e r sets w e r e c o m p a r e d with the Mineris rule-based estimations (previously used m e t h o d ) as s h o w n in Table 3. Even t h o u g h the p r e d i c t e d lives from the t w o a p p r o a c h e s i l l u s t r a t e s s o m e a m o u n t of d e v i a t i o n from each other, it can b e said that b o t h a p p r o a c h e s h a v e h i g h l i g h t e d that the cross g i r d e r s b e c o m e s the m o s t critical m e m b e r s to fatigue failure. Further it reveals that in the case of truss m e m b e r s of m a i n girder, the sequential l a w - b a s e d r e m a i n i n g fatigue life gives h i g h e r values than Mineris rule-based values. H o w e v e r , it is t h e o p p o s i t e for b r i d g e d e c k m e m b e r s . Since Mineris rule e s t i m a t i o n p r o d u c e s p e s s i m i s t i c r e s u l t s w i t h i n c r e a s e of loads and optimistic results with decreases l o a d s [8], it can b e s a i d t h a t in c a s e of t r u s s m e m b e r s , the global i n c r e m e n t of live l o a d of trains w i t h each p e r i o d of age h a s greater effect on fatigue d a m a g e t h a n local variation (increase a n d d e c r e a s e of l o a d i n g d u r i n g a w e e k ) of loading in each week. Similarly, it can be seen that in the case of b r i d g e deck m e m b e r s (cross girders, s t r i n g e r s a n d bracings), the local v a r i a t i o n of l o a d i n g h a s a g r e a t e r effect o n f a t i g u e d a m a g e t h a n g l o b a l i n c r e m e n t of loading. A l t h o u g h these t y p e s of conclusions are p a r t i c u l a r to this t y p e of a b r i d g e a n d fatigue criticality of structure could v a r y from b r i d g e to bridge.

3.3 Application of sequential l a w T h e n e w d a m a g e i n d i c a t o r ( p r e s e n t Di value) w a s c a l c u l a t e d f r o m t h e d a t e of b r i d g e c o n s t r u c t i o n to the p r e s e n t by c o n s i d e r i n g the s e q u e n c e of s t r e s s r a n g e s of e a c h c r i t i c a l m e m b e r . A s s u m i n g t h a t f u t u r e s e q u e n c e of passage is similar to that of the p r e s e n t day, the time taken to r e a c h the p r e s e n t d a y ' s values to o n e ( w h e n D . = l is c o n s i d e r e d as f a t i g u e failure) w a s c o n s i d e r e d as the r e m a i n i n g fatigue life for e a c h critical m e m b e r . T h e c a l c u l a t e d r e m a i n i n g fatigue lives for critical m e m b e r s of e a c h m e m b e r set a r e s h o w n in T a b l e 3. T h e critical m e m b e r s of w h i c h the s t r e s s r a n g e is e n t i r e l y in c o m p r e s s i o n z o n e , t h e effect of fatigue d a m a g e w e r e i g n o r e d [9].

I.E-HW

l£*G2

l.E+04

l£405

I.EWK

l.E+07

1.E+A8

1E^»

Comparisons of remaining fatigue lives

5.

1£*10

Conclusions

Number of Cycln N

Figure 10. Predicted Wohler curve for wrought iron material

1«|S

ENGINEER

Condition evaluation of the b r i d g e exhibits that t h e o v e r a l l m a i n t e n a n c e of t h e c o n s i d e r e d b r i d g e is s a t i s f a c t o r y . H o w e v e r , t h e r e a r e localized mild corrosion at few places, a n d these

14

Table 3. Summary of remaining fatigue lives for critical members in member sets Member set

Bridge component

Remaining Fatigue life from today (years) Sequential Law

Miner's Rule MT1 MT2 MT3 CG ST DTI DT2 DT3 DT4

Main girder bottom chord Main girder bottom chord Main girder bottom chord Cross girders Stringers Truss diagonal (tension member) Truss diagonal (tension member) Truss diagonal (tension member) Truss diagonal (tension member)

323 165 169 12 13 191 171 138 162

305 156 157 20 24 179 168 131 152

n e e d i m m e d i a t e attention. It is found that, t h e

s u p p o r t given by t h e Sri L a n k a Railways (SLR)

l o w e s t r e m a i n i n g life d u e t o f a t i g u e for a

is also appreciated.

m e m b e r is 12 y e a r s , u n d e r c u r r e n t l o a d i n g s ,

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a n o t h e r 12 y e a r s p r o v i d e d t h a t t h e s p e e d , f r e q u e n c y , a n d w e i g h t of t h e t r a i n s a r e n o t

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2.

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Acknowledgement

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The a u t h o r s wish to express their sincere g r a t i t u d e t o S e n i o r Professor M . P R a n a w e e r a a n d other t e a m of e x p e r t s w h o w o r k in t h e Sri Lankan Railway Bridge project. The kind

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^Slg

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kelani river, EDC, University of Peradeniya, Sri Lanka, 2002. 13. Siriwardane, S.A.S.C, Fatigue life prediction of existing railway bridges, MPhil Thesis, University of Peradeniya, Sri Lanka, 2004.

IMS

ENGINEER

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