Structural Analysis of Historical Constructions - Modena, Lourenço & Roca (eds) © 2005 Taylor & Francis Group, London, ISBN 04 1536 379 9

The mechanical behaviour of mortars in triaxial compression

R. Hayen Arte Constructo, Schelle, Be/gium

K. Van Balen & D. Van Gemert Department ofCivil Engineering, K. U Leuven, Leuven, Be/gium

ABSTRACT: Most commonly the mechanical behaviour ofthe masonry composite is derived from the complex interaction in between the masonry units, stone and/or brick, and the mortar joint. While generally mortars are described by means of their mechanical properties in uni-axial compression, equilibrium within the masonry composite most often results in the presence of a horizontal confinement within the mortar joint. A series of tests on mortar samples in a state of triaxial compression evidences a clear change in mechanical behaviour and failure mechanism compared to the mechanical behaviour ofthe mortar in uni-axial compression. In order to describe the mechanical behaviour of the masonry composite from the individual materiaIs, an adequate modelling of the mechanical behaviour in triaxial compression of the mortar becomes necessary. This paper describes the mechanical behaviour of mortar in triaxial compression and the first step towards the modelling ofthe mechanical behaviour.

fNTRODUCTION

The main objective for the presented study is to under­stand the differences in material behaviour of the composite masonry constructed with different mor­tar types; e.g. putty lime, hydraulic lime, cement or lime-cement mortars. While lime mortars generally obtain a lower compressive strength than nowadays cement-based mortars, its influence on the overall strength of the masonry structure is minimal and the possibility of the former to adapt to settlements is extraordinary (Figure I) and still not understood, as mentioned amongst others by Sahlin (1971) and Van Balen (1991).

Masonry is a composite material, built up ofbrick or natural stone units and a mortar as binder matrix. 80th composing materiais are different in nature. 80th brick and natural stone can be considered as an elastic brittle material with a certain compressive strength and some tensile strength, which is often considered only one tenth of its compressive strength. Mortar is generally also considered an elastic brittle material , however, with a much higher deformability with regard to the brick or natural stone units. Due the composite nature of masonry and the important difference in deforma­bility of the composing materiais, the stresses and strains will be divided in a complex manner between the brick units and the mortar matrix . The commonly accepted linear elastic approach on the redistribution

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Figure I. Settlement af a histarical masanry structure withaut actual slructural failure af lhe structure.

Figure 2. Redistribution of the stresses in a masonry com­posite structure.

ofthe strains and stresses within a masonry composite structure was originally introduced by Francis et aI. (Hendry 1998). They put forward that the vertical loads, coming from the dead load on a load-bearing structure, result in a horizontal confinement on the mortar within the horizontal joint, as it tries to move out horizontally from between both bricks due to its elevated deformability. On the other hand, equi librium within the composite masonry structure results in the built-up of horizontal tensile stresses at the brick's contact surface with the mortar (Figure 2).

A linear elastic approach incorporates, inevitably, a constant value for the Young's modulus Ey and the coefficient of Poisson v for both the brick or natural stone unit and the mortar. Furthermore, an equal distri­bution of the confining stresses on the masonry units and the mortar over the total height of each element is considered. As such, a linear elastic approach implies the presence of a constant relationship in between the vertical load on the structure and the resulting confining stresses within the mortar joint. This rela­tionship ah/av, which shall be denoted as K for the following paragraphs, can be calculated analytically and is determined by means of equation (1) by Tassios (1988) :

(1)

where Eb, Em = Young's moduli of the brick and mortar, respectively; Vb, Vm = the coefficients of Poisson of the brick and mortar, respectively; and tb, tm = the heights of the brick unit and the mortar joint, respectively.

From the linear elastic approach it is c1ear that the determination of the elastic properties, the Young's

moduli and the coefficients of Poisson, are utterly important in order to evaluate the occurrence and the importance of the confining stresses within the mor­tar joint in the first place, without even considering any effect of a non linear deformation of the individ­uai materiais. While in general the Young's moduli are determined experimentally, the coefficient of Poisson is most often approached from literature data assum­ing a mean coefficient of Poisson, in the case of the mortar, of about 0.20.

2 ANALYSIS OF THE MATERIAL BEHAVIOUR IN COMPLEX LOADING CONDITIONS

2.1 Introduction

The following paragraphs outline the change in mate­rial behaviour and failure mechanism of a mortar upon triaxial loading. It is important to note that, apart from the actual values of compressive strength and the associated deformations, no important differences are found for different mortar types upon their overall mechanical behaviour in triaxial compression, as has been described in Schueremans (1999), Hayen (200 I) and Hayen (2003). The analysis ofthe influence ofthe triaxial loading condition on the material behaviour is therefore valid for mortar in general, independent of the type and composition of the morta r (e.g. putty lime, hydraulic lime, cement or lime-cement mortar).

2.2 From brittle to elasto-plastic deformation

Upon triaxial loading an evident change in material behaviour can be discemed, as is demonstrated in Figure 3, where the deformations of a putty lime mor­tar are represented in both uni-axial and triaxialload­ing conditions. From the analysis of the development of the stress- strain relationship with an increasing K-value the following observations can be deduced:

• a change in material behaviour is observed from brittle in a uni-axialloading condition to a combined elastic and plastic behaviour in triaxialloading con­ditions, from rather low confining pressures up to hydrostatic compression. From K as low as 0.15 the influence ofthe rather limited confining pressure is important, resulting initially in some post-peak plas­tic behaviour and gradually, as K increases, altering the mechanical behaviour to an elasto-plastic mate­rial. A similar change in material behaviour has been recorded for several other materiais as e.g. porous chalk, porous sandstone and concrete by Homand (2000), Wong (1997) and van Mier (1986), respectively .

• while in general in a linear elastic approach a cer­tain value for the coefficient of Poisson is assumed, the results ofthe mechanical behaviour in uni-axial

612

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Radial strain [mS] Vertical strain [mS]

Figure 3. Vertical and horizontal deformations in uni-axial and triaxial loading conditions. The legend represents K in hundredths of a unit.

as well as in triaxial loading conditions yield no 0,5

\ evidence for such an approach . On the contrary, the initiallack in horizontal deformation does evidence 0,4

1\ the absence of an actual coefficient of Poisson. The instantaneous relationship in between the

vertical and horizontal displacements, being rep­resented in Figure 4 in the case of the uni-axial compression test on a putty lime mortar sample, clearly evidences the initial absence ofany horizon­tal deformation in the mortar. Only as the vertical compression on the mortar sample approaches the compressive strength of the material the horizontal deformations do occur quite suddenly in uni-axial compression. In a state of triaxial compression the horizontal deformations become more and more plastic in nature as the influence of the horizon­tal confining pressure on the overall mechanical behaviour of the mortar increases.

• a tendency towards an increase in deformability in the elastic region at higher K-values. The collected data is however rather limited and toa scattered in order to formulate a relationship between the change in modulus of elasticity Ey and K.

• an important increase in strength is observed with onlya slight increase in the contribution ofthe hor­izontal confining pressure on the overall loading condition. This is fairly evident in the graphi­cal representation of the corresponding horizon­tal and vertical loading conditions at failure, the

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Figure 4. Evolution of the Poisson ratio in function of the applied uni-axial load in lhe case of a putty lime morta r.

triaxial yield criterion in the alI = alIl = ah plane, in Figure 5.

2.3 From shear failure to pore collapse

Analysis of the volumetric deformation upon triax­ial loading, represented in Figure 6 for a moderately hydraulic lime mortar, evidences a change in failure mechanism at values of K above 0.25 (at K equal to 0.25 both failure mechanisms have been observed for the different morta r types).

613

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Figure 5. Triaxial yield criterion in the a Jl = a l Jl = a h plane.

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Figure 6. Volumetric deformations in uni-axial and triaxial loading conditions. The legend represents K in hundredths of a unit.

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Under uni-axial loading or triaxial loading con­ditions with a relative limited horizontal component (K < 0.25), the recorded volumetric deformations, as well as the evolution of the Poisson 's ratio through­out the test, evidence the existence of a shear failure mechanism. After an initial decrease in volume, proba­bly due to the closing of existing cracks and anomalies within the mortar structure, an increase in volume is rather soon observed as a network of very fine verti­cal cracks starts to grow and shear bands develop . The mortar sample finaJly coJlapses along diagonal shear bands accompanied by a substantial increase in vol­ume over the middle section of the cylindrical mortar sample.

For triaxial loading conditions with an important horizontal confining pressure (K > 0.25), failure ofthe morta r no longer coincides with an increase in volume. Hence, no shear failure mechanism is observed. In stead a rather constant decrease in volume is observed right to the end of the triaxial test, setting forward the possibility of a pore coJlapse mechanism. The exis­tence of such a pore coJlapse mechanism has been demonstrated by Vlado (1996) and Bésuelle (2000) in the case opporous rocks. In most cases the tri­axial tests were however broken off before the actual failure ofthe mortar was observed, due to the limited measurement range ofthe triaxial test apparatus (these points are referred to as non broken in Figure 3), at least if failure is defined as a decrease in bearing capac­ity of the mortar sample. Careful study of the mortar samples after the triaxial tests proved that, although the bearing capacity of the mortar was unaffected, the internai structure of the morta r was almost com­pletely destroyed and the mortar internaJly was turned to powder. Failure itself, therefore, was not observed as a decrease in bearing capacity, but rather by the coJlapse of the internai structure of the mortar. If and how the bearing capacity ofthe mortar finaJly wiJl fade away, could not be derived from the current study.

2.4 Evidence for a pore collapse mechanism

The study of the internai pore structure of very weak lime mortars, let alone the study ofa deteriorated lime mortar after triaxial compression, is a problem on its own which faces a lot ofproblems regarding the valid­ity of the test results. The most important issue is the influence ofthe test conditions on the pore structure of the weak sample. In order to at least put forward some evidence of a pore coJlapse mechanism severa I tests were explored and combined; the determination ofthe total pore volume through vacuum submersion and the analysis of the pore structure by means of mercury intrusion and scanning electron microscopy.

The results obtained are represented in Figure 7a, for the total porosity by vacuum submersion in the case ofan hydraulic lime mortar, and Figure 7b, for the pore

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Figure 7. (a) Total pore volume by vacuum submersion. (b) Pore size distribution by mercury intrusion. The legend represents k in hundredths of a unit.

size distribution by mercury intrusion in the case of a putty lime mortar. Both studies show some evidence for the alteration of the internai pore structure of the morta r upon triaxial loading conditions for K above 0.50. For the hydraulic lime mortar the decrease in total porosity, even considering a normal variation in material properties of the material, is substantial. The study ofthe pore structure by mercury intrusion on the other hand shows that the internai structure ofthe putty lime mortar undergoes an important transformation. The triaxial loading condition, again in the case of the presence of an important horizontal component, is responsible for the formation of both a network of fine to large cracks and the closing ofthe medium sized pores. This was also recorded by means of the SEM­images, where indeed the formation of a network of fine cracks from grain to grain was confirmed.

3 THEORETICAL BACKGROUND FOR THE CHANGE IN FAILURE MECHANISM

The occurrence of intersecting diagonal shear bands in uniaxial vertical compression is generaJly attributed to the formation of a network of interacting vertical cracks (Van de Steen 2001), which are induced by the

615

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I I I I I I I I : I A \ , I 1\ \ I I 1\ \ I I I \ 1

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-s Figure 8. Stress distribution and the onset of crack for­mation fo r a circular hole in an infin ite plate in uniaxial compression.

stress concentrations occurring around pores, anoma­lies or existing flaws within the internaI structure of the mortar upon compression (Figure 8). The analyt­ical solution for the 2-dimensional stress distribution surrounding a circular hole in an infinite plate is well known. The structural discontinuity ofthe hole leads to the occurrence ofboth compressive and tensile stress concentrations at its edge. In uniaxial compression a compressive stress, 3 times the applied uniaxial stress, appears at the holes' edges in a direction perpendicular to the externally applied stress, while tensile stresses, in absolute value equal to the applied stress, occur at the holes' edges parallel to the loading direction. The occurrence of such tensile stresses in a low tensile strength materialleads gradually, as the externalloads increase, to the formation of an increasing number of cracks parallel to the applied load at pores, anoma­lies and existing flaws within the mortar structure. The mechanical interaction of these individual cracks finally leads to the occurrence of diagonal shear bands, inducing failure of the mortar sample.

In the case of a triaxial loading condition, the horizontal confinement will of course counteract the horizontal tensile stresses induced by the ma in 'vertical' load. Returning to the analytical solution of the stress distribution around a hole, one can deter­mine that at a kappa value of 0.25 the maximum tensile stress at the holes ' edge has already dimin­ished considerably. In order for a crack to form and the adhered shear band to develop, the main 'vertical' load has to increase accordingly. At a kappa value of lI3, the tensile stresses within the holes' neighborhood even disappear completely (Figure 9). Hence, failure along shear bands becomes by definition impossible. Regarding the fact that the internaI structure of a mate­rial always presents at least some tensile strength, the formation of shear bands wiU practically be already inhibited at a somewhat earlier stage. The observation

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.~ 0.5 .... ....................... .. .... .. ..................... .

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Figure 9. The maximum tension stress around a circular hole in an infinite plate in function of the applied state of triaxial compression (K-value).

ofthe disappearance ofthe failure phenomenon along shear bands at a K-value ofO.25 is therefore confirmed.

4 CONCLUSIONS AND FURTHER RESEARCH

The change in mechanical behaviour of morta r from a brittle material in simple uniaxial compression to a elasto-plastic structure in triaxial compression has been demonstrated experimenlally. Additionally, the adhering change offailure mechanism from the occur­rence of diagonal shear bands, attributed to the forma­tion of a large number of interacting vertical cracks forming the shear bands, lo a mere pore collapse of the internaI structure is observed as well. A theoretical approach, based upon the initiation of lhe nelwork of vertical cracks within the shear bands, tends to con­firm the observed value of K at which the change in failure mechanism is observed experimentally.

The initial presence of a shear failure mechanism puts forward the use of a non-associated Mohr­Coulomb or Drucker-Prager failure criterion, while the changes in pore structure could probably be mod­elled with an alteralion of the parameters, due lo an increase in damage, of the description of the mortar as a cohesive-frictional material (Lubarda 1996). The elaboration of such a material mo dei is foreseen in the near future.

On the leveI of the modelling of the masonry composite, lhe initial absence ofany horizontal defor­mation upon uni-axialloading conditions does already question the validity of the linear elastic approach in order to describe accurately it's mechanical behaviour. Apparently, the horizontal confinement within the mortar joint does only initiate at the moment that the

616

mortar reaches its uniaxial compressive strength. Only then the confinement of the surrounding bricks can be addressed as the mortar, within the mortar joint, starts to crack internally. From that moment on the mechanical behaviour of the mortar as well as of the overall composite structure changes dramatically from an almost linear material to a elasto-plastic material.

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Hayen R. , Van Balen K. & Van Gemert D. 2003. Meehan­ieal behaviour of mortars in triaxial eompression. In EH. Wittmann, A. Gerdes & R. Nuesch (eds .), Plvceed­ings of lhe 61h Inlernalional Conference on Materiais Science and Resloralion, Karlsruhe 2003: pp. 295- 302.

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