ASSESSMENT OF THE LOAD BEARING CAPACIlY OF HISTORIC MULTIPLE LEAF MASONRY WALLS

Ralph Egermann1 and Claudia Neuwald-Burg2

1. SUMMARY

The aim ofthis research is to minimise the amount of strengthening and repair ofmultiple leaf masonry, by establ.i.shing a better understanding of its bearing and failure behaviour. The paper gives an introduction to the failure theory which is valid for selected loading and boundary conditions. Based on the behaviour ofparallel arranged composite systems under vertical loading, the theory has been used to analyse the stress relationships of multiple leaf masonry cross sections. The validity of the theory was proven by a series of experiments on quater and full seale masonry specirnens, as well as by finite element analysis. Additional full seale tests are described in detail , and a eomparison to the model tests is made. The full scale test results show a rcasonabIe eonsisteney with the findings on the quarter scale masonry. The bearing behaviour deterroined by the model e>'.'"j)eri­ments and the derived failure eriterion are well confumed by the tests on prototypes.

2. INTRODUCTION

When dealing with the preservation or restoration of historic buildings, the question of how to assess the residual strength ofthe existing masonry frequently arises. In order to evaluate the residual structural capaeity, the structural loading respoÍlse must be under­stood. Detailed knowledge of the structural behaviour only permits a static eheck; but together with testing of the building materiaIs, it allows the safety leveI of the structure to be assessed.

Keywords: Multiple leafwalls, Composite, Models, Historic masonry, Compression

I Dipl.-Ing., civil engineer at Wenzel, Frese, Poertner, Haller, Buero fuer Baukonstruktionen, Rudolfstr. 15, D-7613I Karlsruhe, FRG

2 Dipl.-Ing., research assistent at Forschungsgruppe Mauerwerk in the Institut fuer Tragkonstruktionen, University ofKarlsruhe, Hertzstr. 16, D-76187 Karlsruhe, FRG

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Historie masonry was eommonly built using multiple leaf walls eonsisting in general of two outer skins and a more or less heterogeneous infill; the total thiekness being not less than 50 em 1bis method ofbuilding is around 4000 years old and exists in a variety of forms. Therefore a detailed understanding of the behaviour of these struetures is essen­tia~ in order to reduce any intervention for the purpose of strengthening or repair to a minimum. Thus historie buildings can be maintained in as authentie a state as possible.

The foeus ofthis paper lies in the failure theory and its verification by full seale tests. It is to be pointed out that this researeh work is a step by step approach. Therefore the pre­sented results are only valid for the assurned boundary eonditions which are quite simpli­fied for the first steps. However, the findings will prepare the platform for further re­search whieh is currently I1IDlÚng at the SFB 315 (speeial researeh programme).

3. THEORY

3.1 Boundary conditions

It is presurned that the loading is vertical and uniform!y applied. Additional (eccentric) loads eaused by wind, hogging or sagging, shaking by traffic or earthquake as well as the influences oftemperature and moisture are the subject offurther researeh work.

For the deseription of the bearing and failure behaviour of multiple leaf masonry, me­ehanieal mode!s are needed. It has been shown that the silo mode! leads to an overesti­mation ofthe horizontalloading ofthe outer shells. !fthe design of strengthening follows the silo approach the monument will get more steel and grout than necessary. Enormous loss of substance and higher costs would be the consequence.

By the use of the multi-material mode! the mechanieal behaviour of multiple leaf masonry ean be deseribed sufficiently. The following conditions are presumed for the validity of the mode!:

- the system is formed by two parallel situated components (outer skins, infill), - the outer skins are of similar geometry and materiais, - a stiffloading platen distributes load to the components (uniform vertical strain:

Eo = E, = Ez ),

- the wall is restrained from rotation about the !ines of externai loading, - the wall is "long" (plain strain eonditions apply: Ex = O).

3.2 Derivation ofthe vertical stresses in the composite system

Ifthe influenee oflateral strain is negleeted, the multi-material model ean be simplified to the spring model p]. The mechanieal behaviour of the components can be described by different springs so that the stresses of outer skins (azz, o) and infill (a:z, ,) only depend on the ratios of stiffuess (E) and geometry (t, A):

(I)

p (5 - - . - ---;,,-'7'"

xx. i - ~ 1 + 2 Ea . ta (2)

E,· t,

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The modulus ofelasticity ofthe multiple leafwali (Em') can be derived by the modulus of elasticity of the components (Ea, E) and their are a ratios. Because of the same compo­nent lengths the are a ratios onJy are influenced by the thicknesses:

Aa = ~ (3) A 2ta +ti

A; __ ti _ (4)

A 2ta +ti

E I=~.E + __ 1;_. m 2to+1; o 210 +1;

E; (5)

Equation (5) forms the basis of predicting the ultimate strength. The condition of com­patibility requires the same vertical strains in ali components and with the knowledge of the stress-strain behaviour ofthe components the actual stress ofthe system can be gen­erally derived from the component stresses and their area or thickness ratios:

(6)

The maximum composite strength is reached if the ultimate strains (eJ of the compo­nents are equal. In that case the crushing strengths of the components (fa ' /;) determine the system strength (Im')

2t li maxj, = __ 0_ j, + __ j, (7) ml 210 +1, o 210 +1, '

Normaly the ultimate strength of the system depends on the crushing strength of the component with the lower peak strain , and the relating stress levei ofthe remainder.

3.3 Stress-strain curves of the components outside and inside ofthe composite system

cr 33 multiple leaf ma somy specimens with three different tlllckness and five

la different stiffuess ratios of outeI' sbells outer shell

. __ ' multlple leal speclmen I _._- -. ---

-- E

Fig. I Stress-strain curves of the components outside and inside of the composite system

were analysed in separate compression tests.

and in.fill were tested under vertical loading. During the compression tests the vertical and horizontal deforma­tions of the quarter scale specimens were measured, as well as the load dis­tribution within the outer and inuer layers at the base of the walls. This enabled the description of tbe load de­pending normal stresses in the compo­nents during tbe testo TI1e stress-strain bebaviour of botb . outer skins and in­filI, outside of the composite system.

Fig. I shows an overlay of the stress-strain curves of the components. outside of the composite system, with the corresponding curve of the multiple leaf masonry wallet. In

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this example the infill consisted of a mix of sand, lime and cement, with the binder con­tent being very low. It was obvious that inside ofthe composite system, the vertical ulti­mate strain ofthe infill is higher than its uniaxial ultimate strain (Eu.J An outer shell of the same mechanical properties and the same geometry as in the multiple leaf wallet shows a higher ultimate strain (Eu o) than in the composite system. That means that the crushing strength ofthe outer shells is reduced by the composite system, but the uniaxial ultimate strength of the infill increases inside of a multiple leaf masonry wall. In case of a sti.ff in.fill the same phenomenon was found .

3.4 Stress relationships inside ofthe composite system

Fig.2 Stress relationships in a vertIcal loaded multlple leafmasonry cross section ana­lysed by tinite elements

Linear and non-linear finite elemellt analyses were made to study the influ­ence of the mechanical properties of the components on their stress state inside the composite system. Fig. 2 describes the results. Near the wall crest and the base of the wall, outer shells and in.fill are in a triaxial compressive stress state be­cause of the hindered lateral deforma­tiOllS. Half way up , ouly a biaxial com­pressive state of the components was found . In the outer shells the lateral stresses along the wall (x-direction) are around seven times smaller than in the load direction (z). The vertical stress dis­tribution is not uniform. That refers to bending moments.

In the infill, the stress ratio GJ Goo varies between 0,15 and O) in the linear elastic

analysis, and amounts 0,78 in the plastic state. The lateral G}y-stresses call be lleglected because ofthe separatioll ofthe outer skins from the infill at a specialloading phase. We call the load phase before the separation phase J and afterwards phase JJ

It can be summarised that the outer shells are stressed by a biaxial compressive loading and bending moments. The in.fill is under the defined loading and sUPPOrt conditions in a biaxial compressive state.

3.5 Behaviour ofthe in.fill under biaxial compressive stress

In a first approach the biaxial compressive behaviour ofthe infill material is similar to the behaviour ofconcrete. To get an idea ofthe increase ofthe uniaxial compressive strength in case of an additional horizontal stress, the failure criterion of Ottosen [2] was used . For the calculated stress state of GJ crzo = 0,78 figo 3 gives a 33 % increase ofthe uniax­ial compressive strength (f'i)'

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-1~ -12 -10 -0.8 -Q6 .1J. ~ -0.2 O °2.1/ Iem

I I

o nllem 1 i/ I 03.1// ° 121 I

: ~ _~o,, : -02

-0.1. ) 1 l/ /

- 0.6

1.--/

---- " " - "- " __ o.

""" -0.8

I / I1 /

I -lO \ 1// ~ j -12 / / f'-- -V -11.

em

Fig.3 Strength of concrete under biaxial stresses (2]

c,

1.< I 1.'

_~_c,

t 12 c,

0,0 0.2 O." 0 ,6 0 ,8 1,0 1,2 1." 1.G

Flg 4 Fatlure surface for bnckwork under blax­lal compression [3]

For our own experiments the compres­sive strength (/;) was tested 00 prisms made up from the infilI matena!. Using form-factors, the result was converted into the uniaxial compressive strength (j'J

3.6 Behaviour ofthe outer shells under biaxial compression

With the help of biaxial tests on masonry panels, Page [3] has found a failure SUI­

face for brickwork loaded under different bed joint angles. Fig. 4 shows the failure surface of a parallel and vertically loaded pane!. For the calculated stress ratios in the multiple leaf cross sectioo, a low in­crease of the uniaxial compressive strength of 14 % can be derived.

Flg 5 Axial load-moment mteraction c urves for ddferent stress-stralll relatlOnshlps [4]

TIle compressive strengths of the outer skins were tested 00 specimens or the same ma­terial and the same geometry as in the composite system. The resulting characteri stica l compressive strengths (ja .k) include the influence of slendemess and suppon conditions.

3.7 8ehaviour of the outer shells under axialload and bending moments

An ioteraction curve is used to describe the decrease or the axial load, dependiog 00 the actiog bending moments, and the stress-strain relationsrups or the masonry (fig. 5). 1l1e so ca lled mamem maglllfier method is described in detail in [4] .

The finite elemeot analysis and the observation of the eX']Jerimen ts enabled the assump­tion that the ecceotriciry is smaUer th an 1/ 6. At lhat limit value the venical load is applied

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at the end of the middle third (M/Mk = 1). In case of an unrealistic linear e1astic behav­iour the ratio P/P o will be 0,5. For a parabolic curve, a value of 0,65 is to be expected. Consequently the bending moments cause a maximum reduction of the bearing load of around 33 %.

3.8 Correction factors

The ratio ofthe component compressive strength inside ofthe composite system and the uniaxial compressive strength is so called correction jactor (e):

(J (J e =~ and e=~ a I" 'j'

Ja,k i

(8)

According to the paragraphs 3.5 - 3.7 the correction factors for the in.fill and the outer shells can be theoretically derived as:

Si = 1,33

ea = 1,14' 0,67 = 0)6

With the help of as load cells acting 'Ioad bars' at the base of the multiple leaf masonry specimens, the ultimate compressive strength of the components «(Ju.a' (Ju, ,) were deter­mined. Together with the results ofthe component compression tests, the correction fac­tors could be calculated. They are reported in table 1:

correction factor of the correction factor ofthe infill infill outer shells

n 8, cv n 8a cv [%] [%]

mortar of a high binder content 3 1,23 21,2 2 0,64

mortar of a extremely low binder 7 1,41 21 ,8 6 0,76 14,8 content

sandwich pattem: layers of mor-2 1,84 5 0,81 2 1,3

tar followed layers of gravei

rnix'ture of crushed bricks and 7 1,86 34,6 11 0,82 11 ,7

morta r

Table I Measured correction factors of infill and outer shells

The correction factor ei is mostly influenced by the biaxial compressivc behaviour of the infill material and its structure. It can be recognised that the more homogeneous the infill, the lower is the correction factor. The theoretically deduced value lies near to the ex­perimentai findings on the homogeneous infills and therefore marks the lower limito

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The correction factor ea is influenced by the flexural rigidity, the support conditions, the bending moments and the biaxial compressive behaviour. The theoretical correction fac­tor suiE.ciently confirms the measured mean value.

Thus on the basis of equation (7) the compressive strength of a multiple leaf masonry wall can be calculated as

(9)

4. EXPERIMENTAL VERIFICATION: FULL SCALE TESTS

The derived formula for the assessment of the load bearing capacity (9) still had to be proven on full scaIe walls. The high costs of the experiments allowed only one series of three speeimens to be tested. Looking at the model tests previously deseribed, it was appropiate to ehoose a series of walls with a rather ineohesive infill. The foeus of the tests was not to imitate a historie wall seetion, but to prove the validity of the small scale tests. In-situ tests on existing historie walls are premature beeause the influenees of some important eharaeteristies, sueh as the indentation, the roughness of the eontact surface between outer leaves and infill, different grades of slendemess e. t. c. had not yet been in­vestigated in the first step of this researeh. These influences will be studied in a seeond step .

4.1 MateriaIs

It has been shown that it is almost impossible to produce bricks and mortar of the same mechauical properties in different seales, beeause the raw material cannot be scaled. The pore system of the model brick is quile similar to that of a full scale brick. The strength can be diminished by a weaker buming of the elay, which means lhat the mineralogical composition will nol be the same. Similar problems occur for lhe mortar. It s hardening process, for example, depends on the water- and air diffusion , and thereby on the pore structure ofthe bricks.

In order to avoid these diffieulties, it had not been tried to copy the materiais used for the model specimens in the full scale tests. Similar materiais have been employed in order to make the comparison easier. The materiais did not necessarily have to be the same, be­cause the failure criterion should be valid for any case.

According to the sma]] scale tests, the outer leaves have been built in solid bricks iu stretching bond Thus, there was only mortar bouding between leaves and iufill . This type of inuer conneetion was assumed to mark the lower bound of the load bearing capacity of multiple leaf walls. Modem bricks tend to be very strong. Even if the weakest avail­able briek was chosen, its mean compressive strength has been of 35 N /mm2 (lested ac­cording to lhe Gerrnan Standard DIN 105).

A commercial cement-lime-mortar was used. The mass-ratio of sand :binder:water have been 7: I : 1,5. The mortar was almost the same as that used for the smaU scale specimen, apart from the grading ofthe sand, which was coarser in the fuU scale mortar.

The 'worst' kind of infilI material in historic masonry is supposed to be a deteriorated lime mortar made from earth or sand and very little amounts of lime. Such a material

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A commercial cement-lime-mortar was used. The mass-ratio of sand:binder:water have been 7: 1: 1,5. The mortar was almost the same as that used for the small scale specimen, apart from the grading of the sand, which was coarser in the full scale mortar.

The 'worst' kind of infill material in historic masonry is supposed to be a deteriorated lime mortar made from earth or sand and very little amounts of lime. Such a material hardly has any cohesion. The experiments were therefore run using a sand-mortar-mix in the ratio of 17:1:2,5. This mix had the two qualities ofbeing rather weak and compact enough not to settle too much. Thus, the infill might exert a horizontal loading on the outer leaves already under a low vertical pressure.

j , ..... -! r .1.'

• 1 ~'--'. t . I \ •

Fig.6 Muliple leafmasoruy specimen after the compression test

4.2 Geometry

The geometry of the specimen was deter­mined by the dimensions ofthe quarter scale mo deis. Consequently the length of the walls was 1,25 Dl, their height 1,56 m The thickness of the leaves was fi.xed by the width of a standard brick, i.e. about 12 cm For the choice of the infill thickness the results of former investigations were taken into account. The quarter scale specimens had had thickness ratios (tl ta) of 1, 3 and 5 . Quantity surveys on ruin walls had shown that in medieval buildings a ratio tl ta = 5 is rarely exceeded. The most common ratio was found to be 3. For that reason, a medium ratio of tl ta = 3 has been adopted for the tests.

4.3 Manufacture

Three specimens have been built in the labo­ratory, using a falsework system for the outer leaves, which guaranteed vertical ac-curacy and a constant bed joint thickness of

the walls. The front surfaces of the specimens were closed by wooden panels, 50 as to avoid a loss of material during the filling. The wall crest was finished by a cement mortar cap o

The masonry was covered by wet cloth, in order to prevent the hydraulic binder from drying out. At the same time, samples of maSOnry mortar have been taken, in order to control the homogeneity of the walls. Prisms were produced and cured according to the German testing standard for mortars.

Moreover, six five-high stack bonded piers have been produced to assess the uniaxial compressive strength of the outer leaves.

Three days afier building the outer leaves, the infill was casted in successive layers, each of which was compacted by punning. The leaves had been fortified by a shuttering which compensated for the hydrostatic pressure ofthe fresh infill-mortar. Again, the walls were

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4.4 Testing equipment

Aluminium bars load dlstflbutlon plate

=~ ~ steal plates

Fig.7 Measuring unit at the walJ crest to deter­mine the nonnaJ stress distribution in the components

The wa11s were tested by means of a hy­draulic 15 MN test machine. Nine trans­ducers on each side measured the hori­zontal deformations during the loading. The longitudinal deformations were measured on the two she11s, as we11 as between the machine table. A special measuring ce11 had been designed for the assessment ofthe load distribution across the wa11 section, consisting of steal plates and aluminium bars. The strain distribu-tion could thus be measured, using strain

gauges, because of the low stiffuess of the aluminium bars. From this distribution, the stresses of the components (outer and inner leaf) could be calculated. Fig. 7 gives a se c­tion of this measuring unit. The loading was applied in 100 kN steps until a third of the expected crushing strength was reached. Thereafter, the load was applied to achieve a deformation rate of 0,7 mm/s. A data logger and a computer stored a11 the load and de­formation measurements at constant intervals.

The strengths ofthe components had been assessed by testing the stack bonded piers and prisms ofinfill immediately before the wa11 tests.

4.5 Results

1.0 ----

I 0.8 ----- ,

--.--1 I

~~ - ' fU~~I~ , ~j I L: ' . quarter scale _,~ I

O .O_--+---';---~--~---i

0 .0 0 .2 0.4 0.6 0 .8 1.0

f./f"

Non-rumensIOnalized stress-strain curves of a fulJ and quarter scale multipl e leaf masonry specimen measured at the exter­nai surfaces of the two outer shell s

The mean compressive slrength of the masonry piers has fOWld to be Ic.p = 13 ,7 N /mm2 Experimenls had shoWll that the characteristical compressive strength (fa k) is around 16 % lower lhan the pier stréngth (fc.p)

la.k = 0,84 . 13 ,7 = I 1.5 N /mm2

The prisms of the infill monar showed a uniaxial compressive strength (f',) of 0,26 N /mm2 Thus, the crushing strength of the composite section can be calcu­lated (eq . (9» , using lhe correcting fa c­tors determined in lhe quarter scale tests for a similar infill (see table I, 2nd row) :

2 3 cal j, ! = - 064 11.5 + - 1,4 1 0,26

m 5 ' 5

= 3) N/rnm 2

In comparison, the compressive strengtlJs of lhe three full scale wa11s were:

Im!. I = 4,07 N /mm' Im! .:! =3,4 N /mm' Iml.S = 3,7 N/rnm 2

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Thus, the average of the experimental findings is only 15 % higher than the related model resuIts. In respect ofthe masonry-usual variations the difference is in a reasonable range. The theory therefore can be considered as coufinned.

Fig. 8 shows a comparison of the stress-strain behaviour of the quarter and full scale walls. The irreguIarities in the stress-strain-curves are caused by a more accentuated transition from phase 1 to phase 11. Since the stiffuess ratio of the full scale walls was rather high, the transition can hardly be seen from the deformation ofthe outer shells.

P [kN ]

1r---r--,--,---r---r-,---,-----, 4000

If---° ... "' .... ~Sh"' .. ,_S 1---l-_-+_+_--j--,-,;nCCffil1+---j 3000 ~ :. i

f----+--+-....... -t~;;:f---t--1--·+t _ -+2000 .......

............. 1000

-200 -150 -100 -50 strain [10 - 6]

Fig.9 Average vertical strain in the Al-bars as a degree ofthe normal stress distribution in the components depending ofthe load (P)

Nevertheless, the clear distinction of two phases in the load bearing behaviour of multiple leaf walls could be proved even for tbis case. Fig. 9 reports the average strain of the aluminium bars. Since these bars were allowed to move independ­ently, the difference of the measured strains ofthe outer bars compared to the inner ones gives a qualitatÍve idea of the load distribution across the section. The gradient change of the outer shell's PIE.­curve marks the start ofthe phase lI.

5. OUTLOOK

The next step of the research will be to investigate the influence of an indentation or of the roughness of the interface between outer and inner leaves, as well as different de­grees of slenderness. Moreover other types of loading have to be studied.

Further research is needed to develop low-destructive tests to assess the parameters needed for the evaluation of the residual strength of a multiple Ieaf wall. In particular the compressive strength of the in.fill can not be determined without heavily damaging the structure using current methods.

REFERENCES

[I] Binda, L. ; Fontana, A. and Anti, L. , "Load transfer in multiple Ieaf masonry walls." Proceedings of the 9th lnternational BrickIBlock Masonry Conference, Berlin, 1991 , pp . 1488- 1497

[2] Ottosen, N.S. , "A failure eriterion for concrete.", Journal ofthe Engineering Me­chanies Division, ASCE, Vol. 103 , No. EM4, August 1977

[3] Page, A. W , "The biaxial compressive strength of brick masonry.", Proceedings ofthe lnstitution ofCivil Engineers, Part 2, VoI 71 , 1981, pp 893-906

[4] Turkstra , C. ; Ojinaga, 1. , "The moment magnifier method applied to brick walls." Proceedings of the Fourth lntemational Brick Masonry Conference, BTÜgge, 1976, paper 4.b.3

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