11th INTERNATIONAL BRICKJBLOCK MASONRY CONFERENCE

TONGJJ UNIVERSITY, SHANGHAI, CHINA, 14 - 16 OCTOBER 1997

ASSESSMENT OF DAMAGE ON MASONRY STRUCTURE

Tang Dai Xin1 and Liu Zhen1

1. ABSTRACT

Basing on the analysis of damage behavior on existing masonry structure, this

paper presents the general maths model of damage and introduces the

damagevalue concept to measure the damage on mosonry structure. Damage

Value is cIosely related to structural reliability, for example, the paper gives the

crack damage value formula of brick wall, the result of assessment is satisfacto-

ry.

2. INTRODUCTION

It is known that the macro-sopic damage on structure is direct1y related to the

structure reliability. In general, the assessment of structure damage is a typical

inverse problem. In many eases, structure determination is difficult, and so an

expert's experience is important. The assessment of damage on masonry struc­

ture is a meaningful task. At present, the general method is checking the mason­

ry structure strength, but this is not suitable for the masonry structure under

damage (crack. corrosion. decay. deformation).

Key words: masonry; damage assessment; damage value.

1. 2 Professor, Doctor, Department of structural Engineering, Harbin U niversity of Civil

Engineering and Architecture, 66 Dazhi street Harbin 150006 China.

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From the angle of reliability, damage will reduce the masonry structure

strength t(\ some extent and result the reduction of masonry structure

reliability, therefore the ultimate state formula of masonry structure is more

complexo Some scholars suggested that damage degree can be classified by reli­

ability index, but masonry structures are so complicated, that reliability index

of masonry structure is difficult to be caculated. In masonry fields, many ex­

perts have done . some experiments and accumulated a lot of experience, their

original knowledge is more valuable. This paper induce some expert's know­

ledge and presents damage value method of damage assessment, we has set up

an expert system software named DAMAGE on micro-computer with dam­

age value concept.

3_ BEARING CAPACITY DEGREE OF MASONRY ELEMENT

In some documents, R / "loS is used to measure the structure element bearing

capicity(l) ,where R, S, "lo is corresponding to resistant force of structure ele­

ment, load capacity and coefficient of structure safety. In general, "lo = I, (Pl = 3.7, P is the structure element reliability index here. The masonry element

can be classified for four leveis(\):

Levei A: completely satisfy the current masonry standard (R / S> O < = > P >Pmu. = 3.7).

LeveI B: slight1y low in the current masonry standard (0.92< R I S

< 1.0 < = > 3.45 = Pmid<P<Pmu.) LeveI C: Obviously low in the current masonry standard, the masonry

element is very dangerous and must. be repaired at once (0.87<

RI S<0.92< = >3.2=pmin <p<pmid).

LeveI D: The masonry element is extremely dangerous and may collapse at

any time (R I S < 0.87 < = > P < Pmin).

In fact, this classification judge the masonry element safety levei by reliability

index,that is to say, the safty leveI corresponds to the reliability indexo so one

hand, the determination of masonry structure is necessary, but on the other

hand, the determination is not easy and cost1y. We want to set up an easy

method to evaluate thc safety state of masonry structure approximately, this

new method judge the masonry state by damage pattern information.

4. SOME EXPERIENCES OF DAMAGE

By collecting a hundred example of brick building under damage, We find that

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the damage on masonry exist differences on time and space, and some typical

damage can be analysed below:

(!)crack by axial compressed load.

A typical piece of experience about crack by axial compressed load can be con­

cluded in table I. by experimento In fact, the practical load state of masonry

structure may be different from experiment circumstances, but the

experience between crack and safety can be gathered by consulting some do­

main experts. We find that crack width ,crack expanding speed, crack conti­

nuity are main factors for masonry safety by summing up investigation

and experinment recordo This conclusion is also applicable for crack by local

compressed load or partial compressed load.

Table 1 relation between crack and safety

Crack levei crack pattern hundred percent or lutimate load

LeveI A small crack on single brick -50%

LeveI B

LeveI C

LeveI D

crack on single brick begins to expand - 50% - 80%

crack expand for 4- 5 cákes of brick - 80% - 90%

crack expand quickly and divide the masonry > 90%

into many small columns.

®corrosion of bearing masonry

The corrosion reduce the thickness of masonry and result the reduction of

bearing capacity. Let h is the original thickness, X is the thickness of damage,

a compressed masonry can be formulated as N< cIlAf by current masonry

standand, where cIl is a coefficient, A is compressed area, f is the compressed

strength of masonry. Let R = cIlAf, load capacity s = h, let k = R / )loS =

cIlAf / N(let )lo = 1). When no damage, the thickness h\ = h, k\ =

)I\A\f / N; when damage, the thickness h2=h-x,k\ =cIl2Al / N . It is

approximately considered that f. N do not change from no damage to damage.

So:

1 h-x

K 2 / K\ =cIl 2 A 2 /cIl\A\ =-h-

cIl = h 2 / (h 2 + 12(e -f:~i)2)

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• cIl 2

cIl\ (1)

Considered approximately that e)+ejJ = e2+ei2 and so:

h-x 3 k 2 h-x (-. -) <-<--

h KI h (2)

let k) Values from 1.0 to 0.87 and get the domain of k2 in table 2, We can con­

clude that when the thickness of damage is near to hundred percent of twenty

then the bearing capacity is very weak.

Table 2 K2 value domain and safety leveI

KI LeveI a leveI b leve! C leveld

x/h 1.0-1.3 0.92-1.0 0.87-0.92 0.6-0.87 0.94-1.27 0.87-0.98 0.82-0.90 0.56-0.85

1/50 a.a-. b b.c b c.d

0.93-1.27 0.86-0.98 0.8-0.896 0.55-0.84 1/40 -a.a-.b b.c C.C c.d

0.91-1.26 0.85-0.97 0.79-0.89 0.55-0.84 1/35 -a.a-.b.b- b.c C.C c.d

0.9-1.26 0.81-0.96 0.76-0.888 0.54-0.84 1/30 - -a.a-. b. b- b.c.c c.c c.d

0.87-1.24 0.8-0.95 0.76-0.874 0.52-0.82 1/20

a. b. b- c-.d d d 0.73-1.17 0.67-0.9 0.63-0.83 0.44-0.78

1/10 a. b. c.c - c.d c-.d d

0.512-1.04 0.47-0.8 0.45-0.74 0.3-0.7 1/5

a. b.c.d d d d 0.421-0.98 0.38-0.75 0.37-0.69 0.25-0.65

1/4 b.c.d d d d

@deformation of bearing masonry

The deformation of bearing masonry include sloping. bending. twisting. The

deformation limit is less discussed in current reliability determination

standard except sloping(l). In fact,the assessment of deformation includes both

safety factor and sensible factor. So the investigation of deformation is very

important. We have collected some example of deformation and deduce some

knowledge in software DAMAGE.

@Iocal construction of masonry

Construction directiy relates to masonry safety, let P is the ratio of height to

thickness and Po is the permissible Iimit of P in masonry standard, the safety

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leveI of masonry can be classified below:

LeveI A: construction is safe, P<Po; LeveI B: construction is slightly dangerous, I <P / Po< 1.1;

LeveI C: construction is dangerous, 1.1 < P / Po< 1.2;

LeveI D: construction is extremely dangerous, P/ Po> 1.2.

5. CONNECTION AMONG DAMAGE SCACLES

Many investigations show that damage scacles beco me larger at the same time.

For cxample, erack by axial compressed load with increasing in width, depth,

length in the meantime. In general, assessment of damage is a multi-dimen­

sion problem which can be transform to a single-dimension problem. For ex­

ample, the assessment of crack can be considered only by crack width or crack

length. and so the experience collection becomes easier. We delivered some in­

vestigation cards to many experts and gather knowledge between single dam­

age scale and masonry safety.

6. DAMAGE V ALUE CONCEPT

A local damage of kind p can be expressed by a vector r P)

(p) (p) (p). • = (x I ,·····,x ~ ), x i (I = I,·· ... ,n) correspond .to damage scacles. Wlth the

increase of xfp), the safety state is difTerent. Let a real number w and a

function cI> express a damage, that is w = cI>(rP». As a damage owns two limit:

absolute safe or dangerous with corresponding value m or M, as w E [m.M],

and so, (w-m) / (M-m) E [0,1], let wj=cI>(XfP) )E [0,1]( i= 1,.·····,n), a dam-=:-(p) -age vector X transform to vector Y = (wl,·····.wn).damage Value is a func-

tion from damage vector to safety and can be expressed below:

t(w I······,w ~) .... [0,1]

The damage ievel can be devided by damage value f:

(3)

LeveI A: no damage or small damage, the masonry safety is good

enough, f E [O,fmin ];

LeveI B: damage with middle scale, the masonry safety is enough. re­

pair is not necessary,fE [fmin,fmid ];

LeveI C: damage with larger scale, local bearing capacity is not enough.

repair is necessary at once. f E [ fmid, fmax ];

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LeveI D: dangerous damage, structure capacity is low enough, collapse

wi1l appear at any time, f E [fmu' 1].

Let p=L(f), PE [Pmm,Pmu]. One hand p=Pmuthen f=fmm ,On the Other hand P = Pminthen f= fma". The rc:lation between P and f is approximately lineal

and let P = af+b, so:

P",,,",, - P",jN a ~ ,

f",Ut - f",dJt (4)

As a < O then P is the decrease function of f, and fmin, fmax can be determined by consulting experts. In general cases, human estimate one thing by four

leveIs, and so fmin is near to 0.25 while fmax is near to 0.85. Some characters

of damage value can be shown below: Character 1. a)f(O," •• 0 ,0) = O,f(1 ," •• 0 , I) = 1; b) f is the monotonous func­

tion ofai

Character 2. Awi>O= >Aw;>O(i::;é:j );

Character 3. damage value formula can be composed by experience and practi-

cal examples.

A specific damage value formula should be composed with easy principIe, be­

cause the assessment of damage inc1ude probability and fuzzy factors. In many

cases, we suggest that the formula of f can be expressed as:

f= 1..1; :: L À. j W j( L À. j = 1,À. j ~ O) (5) l_I I_I 1.1

~ .À.i is coefficient of W i and changeable, if a certain important damage scale is

larger, then the formula of f can be expressed below:

f= maxw . I

I-I

7. SOME NOTES OF DAMAGE V ALUE

(6)

@ The danger degree of damage on masonry have relation not only with dam­

age scales, but also with damage position, so the formula of damage value

should include this factor.

® Some deformation damage such as bending is difficult to make analysis for­

mula of damage value. In this case, damage can be devided into some leveIs

which correspond to a real humber (or fuzzy number) and can be judged by site

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examiner.

crJ Local damage value is the damage value in a local region (such as a piece of

brick waIl). The bearing system damage value is dxetermined by local damage

value, the caculation step is omitted here.

@ Many practical examples of damage lack the fixed quantity infonnation, so

neural net is difficult to use in composition of damage value formula which has

relation with specific region to some extent.

8. APPLICATION

We has set up a multimedia expert system softeware C2l which can estimate

the safety of masonry structure under dainage. Table 3 is the damage formula

of crack by compressed load in Software DAMAGE.

Table 3 damage formula of crack by compressed load

Wj expression

crack on a single brick crack with connection

1 (d>4mm) 1 (d>1.5mm)

w1 w1= w1=

(d-O.l) 13.9 (d<4mm) (d-O.l) I 1.4 (d< l.5mm) 1 (La/L>O.S) 1 (La I L>0.4)

w2 w2= W2=

La/O.SL (Lal L<O.S) La I O.4L (La I L < 0.4) I (n>lO) 1 (n>3)

w) w)= w)=

n 1 10 (nIO) n/3 (n<3) 1 (V>O.OS) 1 (V>0.01)

w. w.= w.=

V I 0.05 (V < 0.05) V 1 0.01 (V < 0.01) 1 below beam or column

w, = 0.7 conjuction wall or top or w,= 1 w,

window door

0.4 other

general Àl = 0.s,À2 = 0.05)) = 0.05, IFmax(w1,w.) >0.85 ormin (W2

r À. = 0.3S,À, = 0.05 w3,w,»0.8S

f= À1Wl+À2W2+ÀlW)+À.W.+À,w, f=max(w 1,w2'W),w.,w,)

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note. 1 wj correspond tó crack fuzzy function of width, length, density, speed

, location ; À j is coefficient, d is crack width, La / L is larger of the

ratio of crack longitudul length to wall length or crack height to wall

height.

2 n is crack number on IOm2area.

3 V is the increment of width in 10 days, when V is not examined and

crack expands quickly, let V = d.nax / 18t, t is the time from original

crack to current (in general V = dmax / 36t).

Example: A brick building built in 1961 in Harbin was examined in 1991, a

piece of site record is: there were two crack on the inner bearing wall which wos

near to door, the width of crack is abOl~t 3.5mm, the length of crack is near to

1/3 of wall height between two floors. We can use damage value concept to

estimate the damage danger degree. From table 3, V = dmax / 36t, w I = 1,

w2 =O.33/0.4,wJ =2/3,w4 =V/O.Ol=O.32,ws=l, f=l, and the crack is

extreme1y dangerous.

9. CONCLUSION

This paper presents an approximate maths model to estimate the macro-sopic

damage, the damage value concept express fuzziness on assessment of damage.

The larger the damage value is, the less reliability index of masonry becomes.

The damage value method is easily used and tested by some practical examples.

REFERENCE

1 YB-88, The Standard on Reliability Assessment of Steel Built

Industry Construction. Beijng: Architecture Industrial Publishing

House ofPeople/s Republic of China, 1991.

2 Liu Zhen , A first exploration of Human-Computer- realm

intelligent multimedia methodology for structure enginnering, doctors

thesis, Library of Harbin Universituy of Architecture and Engineerong

,1996.

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