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Experimental characterization of stone masonry in shear and compression
Construction and Building Materials 23 (2009) 3337–3345
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Experimental characterization of stone masonry in shear and compression G. Vasconcelos *, P.B. Lourenço ISISE, Department of Civil Engineering, University of Minho, Guimarães, Portugal
a r t i c l e
i n f o
Article history: Received 7 August 2008 Received in revised form 2 June 2009 Accepted 18 June 2009
Keywords: Granite Stone Shear Compression Bed joint Testing
a b s t r a c t Shear and compressive mechanical properties are needed for the evaluation of the strength of masonry shear walls by means of simplified methods or numerical analysis. This, in turn, allows to design or assess masonry buildings subjected to combined vertical and horizontal loading. Even if many results on the mechanical properties of modern brick and block masonry are available in the literature, only a few results exist for stone masonry. Here, the shear and compressive strength parameters of stone masonry using granite blocks are provided. In addition, a first aspect addressed is the shape of the shear stress–displacement diagrams under monotonic and cyclic loading. A second aspect addressed is the influence of the surface roughness and of the bed joint material on the compressive behavior of masonry. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Ancient masonry is a non-homogeneous material, composed by units and mortar, which can be of different types, with distinct mechanical properties. Often in monumental buildings, and if materials were available locally, bricks were used for vaults while stone was used in the construction of walls. The influence of mortar joints acting as a plan of weakness on the composite behavior of masonry is particularly relevant in case of strong unit–weak mortar joint combinations, which are characteristic of ancient stone masonry [1]. Two basic failure modes can occur at the level of the unit–mortar interface: tensile failure (mode I) associated to stresses acting normal to joints and leading to the separation of the interface, and shear failure (mode II) corresponding to a sliding mechanism of the units or shear failure of the mortar joint. In terms of the composite behavior of masonry, failure modes related to tensile splitting of the units and mortar crushing need to be taken into account [2]. The preponderance of one failure mode over another or the combination of various failure modes is essentially related to the orientation of the bed joints with respect to the principal stresses and to the ratio between the principal stresses [3]. Even if several results on the mechanical properties of brick and block masonry assemblages are available in the literature [4–7] scarce experimental data is available for stone masonry [8,9]. The present work deals firstly with the mechanical characterization
* Corresponding author. Tel.: +351 253 510200; fax: +351 253 510217. E-mail address: [email protected] (G. Vasconcelos). 0950-0618/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2009.06.045
of the masonry components: stone units and mortar, as well as with the shear behavior of dry and mortar masonry joints (cohesion, friction angle and dilatancy). Then, the compressive properties of the masonry composite (compressive strength and modulus of elasticity) are addressed. In order to attain such a goal, an experimental program was defined, including direct shear tests conducted on dry and mortar masonry joints and uniaxial compression tests carried out on a set of stone masonry prisms with distinct types of bed joints. Besides providing mechanical properties for numerical simulations of the in-plane behavior of stone masonry walls, the adopted testing program provides also the fundamental parameters required for the seismic assessment of masonry buildings based on simplified analytical models.
2. Shear behavior of stone masonry joints Although several experimental studies have been carried out on the bond shear strength of unit–mortar interfaces [4,5], limited research is available on the shear behavior of dry masonry joints [8]. On the other hand, the knowledge gathered on rock joints under shear behavior can be partly extended to dry masonry joints. The shear behavior of rock joints plays an important role in rock mechanics research, with several experimental and numerical studies pointing out the role of the surface roughness on the cyclic shear behavior of natural rock joints [9,10]. The relation between normal and shear stresses plays a major role in the shear behavior of masonry joints, actually governing its failure mode [11]. For pre-compression stresses above a certain level, the shear strength decreases and a combined shear-splitting
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failure or splitting of the units occur. In case of joint shear failure by slipping of the units, an increase of the normal stress leads to an increase of the shear strength. As has been widely reported [4,12], the shear strength of masonry under moderate normal stresses, for which the non-linear behavior of mortar is negligible and the friction resistance takes the central role, can be given by the Coulomb criterion:
s ¼ c þ lr
ð1Þ
where c is the shear strength at zero vertical load stress (usually denoted by cohesion) and l is the friction coefficient or tangent of the friction angle. For dry joints, the cohesion is obviously zero. 2.1. Test specimens and testing procedure Although triplet tests have been adopted as the European standard method [13] to perform shear tests in masonry joints, the strength properties of dry and mortar joints were obtained here by means of direct shear tests carried out on couplet specimens, see Fig. 1, [14]. In fact, the triplet test is rather complex to analyze and control after peak displacement due to the fact that two joints are tested simultaneously, see also [15]. The shear tests were carried out in a servocontrolled universal testing machine CS7400S composed by two independent hydraulic actuators used to transmit normal and shear loads, able to operate under force or displacement control. Both shear and normal stresses were measured and recorded by horizontal and vertical load cells of 22 kN capacity. Due to the limited space between steel platens the most suitable testing sample is composed by the two units with geometry and dimensions indicated in Fig. 1a, similarly to [6] and [16]. The surface of the dry stone masonry units is relatively smooth resulting from sawing, whereas the joint surface of the units of the mortar assemblages presents the typical handcoursed roughness to achieve realistic bond conditions. The granite used for the masonry units is a medium grained two-mica granite [17–19]. The shear specimens were placed between two thick steel plates and attached to the steel platens by steel bolts, so that shear force could be transmitted, see Fig. 1b. Thin steel sheets were attached to the steel plates to concentrate the shear load as close as possible of the bed joint, aiming at providing a more uniform shear stress distribution. In order to guarantee right angle surfaces, the dry specimens were suitably ground using a rectifying machine. The specimens were properly attached for load reversal by means of adjustable steel plates on both sides of the specimen.
a
The numerical assessment of test setup performed by Lourenço and Ramos [8] indicates the adequacy of the proposed approach. In order to simulate typical normal stresses existing in ancient masonry structures three distinct pre-compression stress levels were considered, r = 0.5 N/mm2, r = 0.75 N/mm2 and r = 1.0 N/ mm2. An additional pre-compression stress level equal to r = 1.25 N/mm2 was adopted for the monotonic tests in mortared assemblages. Three specimens were tested for each level of precompression, and for dry and mortared joints. In addition, the influence of the moisture content on the shear response of dry masonry joins was investigated by considering dry and saturated conditions. The relative horizontal displacement of the joint was measured by the horizontal LVDTs placed at each side of the specimen, see Fig. 1b. The vertical displacement of the joint was measured by the LVDTs placed at the opposite corners of the specimen, which enabled the assessment of possible dilatant behavior of the joints. The cyclic tests were carried out under displacement control following the time-displacement history used in [14]. 2.2. Monotonic behavior of masonry joints The shear load–displacement diagrams for distinct pre-compression stress levels resulting from the monotonic tests carried out on dry and saturated specimens are displayed in Fig. 2. The shear displacement is the result of averaging the measurements recorded by the LVDTs placed at each side of the specimen. The shear stress s and the normal stress r are obtained by dividing the shear
a
b
b
Fig. 1. Masonry specimens: (a) dry joints and mortar joints and (b) arrangement of the LVDTs for measuring the relative horizontal and vertical displacements. Dimensions are in mm.
Fig. 2. Shear stress–displacement diagrams in dry joints: (a) dry specimens and (b) saturated specimens.
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force H and the normal force N, recorded in vertical and horizontal actuators, by the cross section of the joint A. It is observed that no significant differences were detected between dry and saturated specimens, apart from the slighter decrease on the peak stress in saturated specimens. Besides, higher scatter was found when the maximum pre-compression level (r = 1.0 N/mm2) was applied. Three stages can be considered to describe the shear-displacement diagrams. The pre-peak behavior is characterized by a linear stretch for low levels of shear stress and by a clear non-linear stretch before peak stress. A plateau is found after peak stress, representing the considerable plastic deformations associated to inelastic sliding. Similarly to what has been reported in the literature [10,20] no shear softening was recorded after peak stress, unlike rough rock joints that exhibit remarkable lowering of the shear resistance as the plastic shear displacement increases. The shear stress–displacement diagrams of mortared joints are shown in Fig. 3a. The general shape of the shear stress–shear displacement is characterized by a sharp initial linear stretch. The peak load is rapidly attained for very small shear displacements. Similarly to what was reported for dry masonry joints, non-linear deformations develop in the pre-peak regime. After peak load is attained there is a softening branch corresponding to progressive reduction of the cohesion, until reaching a constant dry-friction value. This stabilization is followed by the development of large plastic deformations. The evolution of the vertical displacement with the shear displacement is displayed in Fig. 3b, where in the majority of the tests two distinct phases can be distinguished. Firstly, the uplift of the joint is expressed by increasing positive vertical dis-
a
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placement. It is observed that the non-linear evolution of the vertical displacement provides variable dilatancy assuming decreasing values as the shear displacement increases up to the shear displacement corresponding to the stabilization of the shear stress. During the subsequent regime of pure friction the vertical displacement remains constant or progressively decreases, particularly when the level of pre-compression increases. The vertical displacement exhibits even negative values in some specimens submitted to pre-compression levels of r = 0.875, 1.00 and 1.25 N/mm2). The dilatant behavior reflects, to great extent, the distinct shear failure modes obtained in the specimens submitted to different normal stresses. For low to intermediate levels of pre-compression, shear failure occurs at the unit–mortar interface along one unit face, or divided between two unit faces. For the larger normal stress level (r = 1.25 N/mm2), failure is localized in the mortar. 2.3. Cyclic behavior of dry masonry joints The typical shear stress–displacement diagrams obtained in direct cyclic shear tests conducted in dry masonry joints, using dry and saturated specimens, are displayed in Fig. 4 for the level of pre-compression r = 0.75 N/mm2. Apart from the small difference of the peak shear stress, no significant differences in the shape of the diagrams were found. Minor differences were found in the shear strength during the reversal cycles, see Fig. 5a, despite wearing of the surface and degradation of rock forming minerals with the accumulation of degraded material, similarly to what has been pointed out by Lee et al. [9]. A very minor trend for compaction can be seen from the normal displacement–shear displacement diagrams indicated in Fig. 5b. A maximum value of vertical
a
b
Fig. 3. Shear behavior of mortared joints: (a) shear stress–displacement diagram and (b) relation between vertical displacement and shear displacement.
b
Fig. 4. Shear stress–displacement diagrams for dry joints under cyclic loading (r = 0.75 N/mm2): (a) dry specimens and (b) saturated specimens.
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a
Fig. 6. Correction of the measured shear displacement for a saturated specimen submitted to a normal stress r = 1.0 N/mm2.
b
Fig. 5. Characteristic aspects of the shear behavior of dry joints: (a) evolution of the shear stress–displacement diagrams between the first and the last cycle of reversal loading and (b) compaction due to the wearing of the joint surface.
displacement of ±0.06 mm was measured for the dry and saturated tested specimens, indicating that dry granitic joints are non-dilatant, which is in agreement with the findings of Lourenço and Ramos [8] for sandstone dry joints and of Homand et al. [21] for hammered granitic joints. Other relevant aspect in the discussion is the comparison between the loading–reloading stiffness. The stiffness of the unloading branches exhibits always higher stiffness than the stiffness obtained in the reloading cycles. The effect of the elastic deformation of stone unit is assessed by removing the elastic deformation of the unit:
ujoint ¼ umeas
s ku
ð2Þ
where umeas is the shear displacement given by the horizontal LVDTs, s is the shear stress for a given displacement and ku is the stiffness calculated in the unloading branches. It is possible to confirm that the elastic deformation of the units has a minor role in the total shear displacement of dry joint, see Fig. 6. Finally, it is observed that the shear cyclic behavior of dry joints is characterized by non-linear deformations in the pre-peak stage and perfect plastic deformations after peak stress resulting from the characteristic sliding failure mode. 2.4. Shear strength parameters Fig. 7 shows the linear relationships between the values of the shear strength obtained in the monotonic tests and in the first cycle of the cyclic tests for dry and saturated conditions and the
values of the normal stress, which confirm the assumption that the shear strength is well described by Coulomb’s friction law. The slight decrease in the shear strength obtained on saturated specimens is reflected by a decrease of 5% on the friction coefficient in saturated joints, being of 0.65 in dry joints and of 0.6 in saturated joints. A range for the friction angle between 10° and 22.4° for mudstone was pointed out by Geerstsema [22]. The friction coefficient of dry granitic joints is similar to the values found by Lourenço and Ramos [8] for sandstone units (l = 0.63), and by Lee et al. [9] for granitic joints (l = 0.69). The narrow range of values found for the friction angle seems to indicate that no significant differences are expected among distinct types of natural stone under similar roughness surface conditions (sawn-cut surfaces). It is observed that, particularly in the case of dry specimens, there is a small increase of the frictional coefficient with wearing. Significant linear correlation coefficients between normal and peak and residual shear stresses were also found in case of mortared masonry joints with coefficients of correlation of r2 = 0.88, and r2 = 0.81, respectively. A value of cohesion about 0.36 N/mm2 and the tangent of the friction angle, tan /, equal to 0.63, corresponding to a friction angle of 32.2°, were attained for the peak strength. The residual shear strength can be calculated with reasonable accuracy from a friction coefficient of 0.78. Table 1 summarizes selected results published in the literature referring to the shear strength properties, where very different values of the cohesion and friction angle are pointed out for distinct unit–mortar assemblages. The shear strength parameters are greatly dependent on the moisture content, porosity of the units, on the strength and composition of mortar and on the nature of the interface [23]. From the results of direct shear tests carried out by Pluijm [6], the coefficient of internal friction ranges between 0.61 and 1.17, whereas cohesion varies from 0.28 up to 4.76, depending on different types of units and mortar. It is seen that the values of the shear strength parameters obtained for assemblages of granitic stone and lime mortar presented in this study are of the same order of the shear parameters pointed out for assemblages of lime mortar and old bricks [4]. 3. Compressive behavior of stone masonry Several experimental, numerical and simplified analytical studies have been carried out in order to increase the knowledge about the compressive behavior of masonry [7,27,28]. Being masonry a composite material usually made of units and mortar, it has been largely accepted that its failure mechanism is governed by the interaction between the components.
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a
b
c
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3.1. Experimental details The present experimental program aims at obtaining data on masonry compression for dry and low strength mortar, being the latter more representative of ancient masonry structures. In addition, the tests aim also at providing insight about the influence of the surface roughness and bed joint material on the compressive strength and deformation characteristics of masonry. With respect to dry masonry, both sawn (PR_S) and rough surface (PR_SR) joints are considered. The rough surface is obtained by sand-blasting. For mortared specimens, two types of interlayer material representative of ancient buildings are adopted, namely low strength lime mortar (PR_SM) and dry clay from sieving granitic soil (PR_SS). The compressive strength of masonry prisms is known to be affected by several factors, such as size, height and end conditions [30–32]. In order to reduce the platens confining effect, a height to length ratio of three was adopted according to ASTM E447 [33], see Fig. 8. The masonry prisms were made with three cubic stone units of 150 mm length and two bed joint courses, as shown in Fig. 8. The thickness of mortar or granitic soil placed in the bed joints was 10 mm. The dry stacked masonry prisms, PR_S and PR_SR, were built at the testing location by simply laying the second and third unit on top of the bottom unit in order to obtain vertical alignment of the specimen. The contact dry bed joints were properly selected so that maximum contact area between units could be attained. When mortar bed joints were considered, the stone units were carefully cleaned and wet to provide enough adhesion between units and mortar. The testing equipment consisted of the three-dimensional stiff steel frame used in [19]. Besides the large load capacity of the actuator, its remarkable stiffness is useful when stable displacement controlled failure is required. In order to induce uniform load distribution, a thick steel plate connected to a steel spherical seat was located at the top of the specimen. The deformation of the specimen during the test was recorded by means of four LVDTs located between steel platens at each side of the specimen. The vertical displacement of masonry prisms is defined by averaging the displacements measured by the LVDTs. In a first stage, two specimens of each masonry type were submitted to monotonic compression under displacement control. In a second stage more five specimens were tested under loading control and for cyclic conditions in the pre-peak regime at three different load stages of 25%, 55% and 75% of the average compressive strength obtained in the two previous monotonic tests. After this, the test control was switched to displacement control at a rate of 3 lm/s. The adoption of this velocity aimed to follow the possible stable failure of the masonry specimens and to obtain and characterize the post-peak behavior of stone masonry under uniaxial compression. 3.2. Experimental results
Fig. 7. Relationship between normal and shear stress: (a) dry specimens, (b) saturated specimens and (c) mortared joints.
The experimental characterization of masonry under compression requires representative wallets, with geometry and dimensions described in, e.g. the European Standard EN1052-1 [29], including at least one head joint and three masonry courses. Due to the very high strength of granite and the maximum capacity of actuators available for testing, the compressive features of stone masonry were obtained using prisms. According to Page and Shrive [30], the prisms are adequate masonry assemblages that include simultaneously the effect of bedding type, unit–mortar interaction and workmanship.
3.2.1. Failure modes The failure pattern of dry masonry prisms was difficult to monitor due to the encasing added to avoid injuries. Given its brittle behavior, most of the failures of the specimens PR_S were abrupt and explosive, see Fig. 9a. No signs of micro-cracks were recorded in the pre-peak regime. Micro-cracks become visible only after peak load has been reached. For dry masonry specimens, failure cracks usually develop along continuous shear bands that cross the joints, with some specimens exhibiting even double shear cracks. This suggests that after the initial adjustment of dry bed joints, the prism behavior is homogeneous and appears to be mostly determined by the compressive behavior of the granitic units. No differences were introduced in the failure modes by increasing the roughness of the bed joint surface. Abrupt failure occurred also in two specimens of rough dry masonry prisms tested
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Table 1 Shear strength properties for different unit–mortar assemblages. Source
Units
Mortar
c (N/mm2)
l
Atkinson et al. [4]
Old clay units Old clay units New clay units
1:2:9 (13) 1:2:9 (7) 1:1.5:4.5
0.127 0.213 0.811
0.695 0.640 0.745
Amadio and Rajgeli [23]
Solid bricks
Cement mortar Lime–cement mortar
0.65
0.723
Magenes [24]
Solid bricks
Hydraulic lime mortar Lime mortar
0.206 0.081
0.813 0.652
Binda et al. [25]
Sandstone Calcareous stone
Hydraulic lime mortar Hydraulic lime mortar
0.33 0.58
0.74 0.58
Roberti et al. [26] Lourenço et al. [15] This study
Bricks Hollow bricks Granitic units
Hydraulic lime mortar Micro-concrete Lime mortar
0.23 1.39 0.359
0.57 1.03 0.630
Fig. 8. Typical geometry of the masonry specimens. Dimentions are in mm.
under monotonic compressive loading. For the remaining five dry rough specimens, typical failures as the one exhibited in Fig. 9b developed. The failure of mortared masonry prisms was characterized by vertical splitting cracks appearing firstly in the central unit and extended to the other stones as the compressive stress increases, see Fig. 9c. This failure mode is mostly due to the lateral tensile stresses of the granitic units induced by the composite behavior of units and mortar with different elastic mechanical properties. Similar results have been reported by several authors [34]. On the other hand, the failure of the specimens PR_SS with granitic soil in the bed joints is more similar to the crack patterns exhibited by the dry masonry specimens. This can be explained by the peculiar trend for compaction exhibited by the granitic soil joints in contrast with the expansion of mortar [14]. 3.2.2. Stress–strain relationship For each specimen the corresponding value of the compressive stress was obtained by dividing the compressive load by the average cross section. The deformation at a given stress level, e, was calculated by dividing the vertical displacement by the height of the specimen, since the vertical displacement was taken as the average of the displacements recorded by the four vertical LVDTs. For a comparative analysis, all stress–strain diagrams obtained under monotonic loading are depicted in Fig. 10. The shape of the stress–strain diagrams of sawn dry joint prisms PR_S is characterized by an initial upward concavity. Although sawn surfaces are rather smooth and good adjustment of the stones was achieved during the construction of the masonry prisms, the upward concavity is in part due to the initial setting of the bed joints. After full contact of the bed joints upon increasing compressive stress, the behavior of masonry prisms depends mostly on the behavior of the stone. All prisms exhibit reasonable linear behavior until a compressive stress close to the peak strength. After the peak load is reached, it is still possible to record a considerable stretch of the
descending branch of the stress–strain diagrams in some specimens, even if most of them failed in a brittle manner. The stress– strain diagrams of rough dry joint prisms PR_SR show also an upward concavity for low stress level but over a larger part of the curve, leading to higher levels of deformation at peak load. As the compressive load increases, the roughness of the contact surface tends to break, leading progressively to partial leveling of the bed joint and to the improvement of the surface contact. In this case, the total deformation is the result of the deformation of the units and the local deformation at the bed joints. On the contrary, lime mortared masonry prisms PR_SM exhibit an initial stretch with downward concavity due to the composite behavior of units and mortar since early stages of loading. The role of the bed joint material on the deformational behavior of the masonry prism is further confirmed by the stress–strain diagrams obtained for the soil mortared specimens PR_SS. These diagrams are characterized by a large extent of the upward concavity from low to medium stress levels. The large initial deformation is related to the compaction of the granitic clay at the bed joints. The bed joints with an initial thickness of nearly 10 mm is at the end of the test a thin layer of compacted soil. 3.2.3. Pre-peak cyclic behavior It is observed that significant higher stiffness in the reloading cycles in the pre-peak regime was recorded comparatively to the stiffness of the virgin stretch for dry masonry prisms PR_S and PR_SR, see Fig. 11. This feature can be attributed to the fact that the stiffness of the unloading–reloading branches involves permanent deformations corresponding to a given stress level. This behavior is also found in the compressive behavior of rocks [35]. Besides, higher permanent deformations are recorded in rough specimens PR_SR with respect to the sawn prisms PR_S. This distinct behavior is the result of the continuous wearing of the higher asperities during the loading process. For lime mortared prisms PR_SM, unrecoverable deformations corresponding to the unloading–reloading are even more remarkable than deformations of dry rough specimens PR_SR, which should be attributed to the mortar deformability, see Fig. 12. Unlike dry masonry prisms, significant permanent deformations were recorded in the pre-peak unloading–reloading cycles in soil mortared prisms PR_SS, due to the compaction nature of the interlayer material [14]. 3.2.4. Compressive strength parameters A summary of average compressive parameters derived from the stress–strain diagrams, namely the compressive strength, fc, and the modulus of elasticity, Ec, is indicated in Table 2. Similarly to what was indicated by Binda et al. [5], the modulus of elasticity, Ec, was determined as the secant modulus in the range of 30% and 60% of the ultimate compressive strength in the ascending branch of the stress–strain diagram.
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Fig. 10. Stress–strain diagrams for monotonic tests.
a
b
Fig. 9. Typical failure patterns of dry masonry prisms: (a) sawn dry joint specimen PR_S, (b) rough dry joint specimen PR_SR and (c) mortared joint specimen PR_SM.
Dry masonry prisms exhibit the highest compressive strength and modulus of elasticity and the lowest deformation at peak stress, being the compressive strength similar to the compressive strength of the units, which is equal to 69.2 N/m2 according to Vasconcelos [14]. According to Hendry [36], the strength of stone masonry built from dimensioned blocks with thin joints would be close to stone strength, irrespectively of the mortar strength, which is not clearly confirmed in the present study. The compres-
Fig. 11. Typical stress–strain diagrams for cyclic tests: (a) specimen PR_S10 and (b) specimen PR_SR7.
sive strength of rough prisms PR_SR undergoes a reduction of approximately 29% with respect to prisms PR_S, whereas the modulus of elasticity is 46% lower. Since the units are of the same granite of specimen PR_S, the increase of vertical strain at peak stress of approximately 27% is directly connected to the lower stiffness of the bed joints. The higher scatter found in sawn prisms PR_SR is attributed to the variability of the distribution of the roughness at the bed joint surfaces.
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a
b
Fig. 12. Typical stress–strain diagrams for cyclic tests: (a) specimen PR_SM7 and (b) specimen PR_SS3. Table 2 Mean values of the mechanical compressive properties of masonry prisms (seven specimens). Coefficient of variation is indicated inside brackets (%). Masonry prism
fc (N/mm2)
Ec (N/mm2)
PR_S (sawn) PR_SR (rough) PR_SM (lime mortar) PR_SS (soil mortar)
73.0 51.9 37.0 64.2
14,722 7934 4629 8920
(9.1) (16.2) (11.8) (13.5)
(19.0) (37.1) (17.5) (12.6)
The reduction on the compressive mechanical properties with respect to the reference masonry specimens (PR_S) is even more significant in mortared specimens (PR_SM), with a reduction of nearly 50% and 70% in the compressive strength and in the modulus of elasticity, respectively. The reduction of the compressive strength can be attributed to composite behavior of masonry with the development of a compression–tension–tension triaxial stress state for the units and a triaxial compression state for the mortar [24,37]. The introduction of granitic soil instead of mortar in the bed joints leads to an increase of 73% on the compressive strength and an increase of 92% on the modulus of elasticity concerning mortared prisms PR_SM. This is due to the compaction of the granitic soil and dilation of the mortar. 4. Conclusions Aiming at obtaining reliable insight on the shear and compressive strength properties of stone masonry an experimental campaign for the characterization of stone masonry under shear
and compressive loading is addressed, namely with respect to the shear behavior of dry and mortar masonry joints and to the uniaxial compressive behavior of masonry prisms with distinct bed joint materials and joint surfaces. It should be stressed that the shear strength of the mortar–stone interface as well as the compressive strength of masonry stone are basic mechanical properties when design or numerical modeling of stone shear walls is required. Concerning shear behavior of masonry joints, it is observed that: (a) an elastic perfectly plastic shear stress–shear-displacement diagram was found to characterize the monotonic and the cyclic envelope of dry masonry joints, whereas post-peak strength degradation and a consequent stabilization characterizes the monotonic behavior of mortar joints; (b) the moisture condition on the joints, from dry to saturated, seems to have a negligible effect on the friction coefficient; (c) no dilatancy was found to characterize the shear behavior of dry masonry joints, whereas dilatant behavior was found on mortared joints and (d) the shear strength properties of masonry joints enables the assessment of the inplane lateral strength of masonry walls under in-plane loading. With respect the compressive behavior of masonry it was observed that: (a) the surface condition (smooth or rough) influences the composite behavior of masonry under compression, mostly with respect to the compressive strength, modulus of elasticity and deformation at peak stress; (b) the material of the bed joints (lime mortar or clay material) influences considerably the failure mode and the compressive strength of stone masonry. The different bed joint materials lead to clear distinct pre-peak regime (stress–strain diagrams) resulting in very different modulus of elasticity, compressive strength and permanent deformations after loading-reloading cycles. The materials of the bed joints play a central role on the deformation behavior of stone masonry under compressive loading. (c) as the shear strength properties of masonry joints, also the compressive strength of stone masonry represents a valuable property for the assessment of the in-plane and outof-plane strength of masonry walls. Finally, it should be stressed that the experimental results and mechanical data on stone masonry pointed out in this work contribute for the improvement of the knowledge on the mechanics of stone masonry.
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G. Vasconcelos, P.B. Lourenço / Construction and Building Materials 23 (2009) 3337–3345 [13] EN 1052-3. Methods of test for masonry: part 3 – determination of initial shear strength; 2002. [14] Vasconcelos G. Experimental investigations on the mechanics of stone masonry: characterization of granites and behavior of ancient masonry shear walls. PhD thesis, University of Minho; 2005.. [15] Lourenço PB, Barros JO, Oliveira JT. Shear testing of stack bonded masonry. Construct Build Mater 2004;18:125–32. [16] Hansen KF. Bending and shear tests with masonry. SBI Bulletin 123, Danish Building Research Institute; 1999. p. 36. [17] Vasconcelos G, Lourenço PB, Alves CA, Pamplona J. Analysis of weathering and internal texture on the engineering properties of granites preservation. In: Proceedings of 11th international congress of the international society of rock mechanics. Workshop W3 of natural stone and rock weathering; 2007. p. 75– 83. [18] Vasconcelos G, Lourenço PB, Alves CA, Pamplona J. Experimental characterization of the tensile behavior of granites. Int J Rock Mech Min Sci 2008;45(2):268–77. [19] Vasconcelos G, Lourenço PB, Alves CA, Pamplona J. Ultrasonic evaluation of the physical and mechanical properties of granites. Ultrasonics 2008;48(5):453–66. [20] Misra A. Effect of the asperity damage on shear behavior of single fracture. Eng Fract Mech 2002;69:1997–2014. [21] Homand F, Belem T, Souley M. Friction and degradation of rock joint surfaces under shear loads. Int J Numer Anal Methods Geomech 2001;25:973–99. [22] Geerstsema AJ. The shear strength of planar joints in mudstone. Int J Rock Mech Min Sci 2002;39:1045–9. [23] Amadio C, Rajgelj S. Shear behavior of brick–mortar joints. Mason Int 1991;5(1):19–22. [24] Magenes G. Seismic behavior of brick masonry: strength and failure mechanisms. PhD thesis, Department of Structural Mechanics, University of Pavia; 1992 (in Italian).
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[25] Binda L, Fontana A, Mirabella G. Mechanical behavior and stress distribution in multiple-leaf stone walls. In: Proceedings of 10th international brick block masonry conference, Calgary, Canada; 1994. p. 51–9. [26] Roberti GM, Binda L, Cardani G. Numerical modeling of shear bond tests on small brick–masonry assemblages. In: Computer methods in structural masonry – 4, Florence, Italy; 1997. p. 145–52. [27] Naguib EMF, Suter GT. Stresses in a running bond brick masonry 3-D finite element model under axial compression. Mason Int 1991;5(2): 48–54. [28] Vermeltfoort A Th. Compression properties of masonry and its components. In: Proceedings of 10th international brick block masonry conference, Calgary, Canada; 1994. p. 1433–42. [29] EN 1052-1. Methods of test for masonry: part 1 – determination of compressive strength; 1999. [30] Page AW, Shrive NG. A critical assessment of compression tests for hollow block masonry. Mason Int 1988;5(2):64–70. [31] Kingsley GR, Atkinson RH, Noland JL, Hart GC. The effect of height on stress– strain measurements on grouted concrete masonry prisms. In: Proceedings of 5th Canadian masonry symposium, Vancouver, Canada; 1989. p. 587– 695. [32] Khalaf FM, Hendry AW, Fairbairn DR. Study of the compressive strength of blockwork masonry. ACI Struct J 1994;91(4):367–74. [33] ASTM E447. Standard test methods for compressive strength of masonry prisms. American Society for Testing Materials; 1992. [34] Andreaus U, Ceradini G. Failure modes of solid brick masonry under in-plane loading. Mason Int 1992;6(1):1–8. [35] Goodman R. Introduction to rock mechanics. 2nd ed. New York: John Wiley & Sons; 1989. [36] Hendry AW. Structural masonry. 2nd ed. MacMillian Press Ltd.; 1998. [37] McNary WS, Abrams DP. Mechanics of masonry compression. J Struct Eng 1985;111(4):857–70.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Experimental characterization of stone masonry in shear and compression G. Vasconcelos *, P.B. Lourenço ISISE, Department of Civil Engineering, University of Minho, Guimarães, Portugal
a r t i c l e
i n f o
Article history: Received 7 August 2008 Received in revised form 2 June 2009 Accepted 18 June 2009
Keywords: Granite Stone Shear Compression Bed joint Testing
a b s t r a c t Shear and compressive mechanical properties are needed for the evaluation of the strength of masonry shear walls by means of simplified methods or numerical analysis. This, in turn, allows to design or assess masonry buildings subjected to combined vertical and horizontal loading. Even if many results on the mechanical properties of modern brick and block masonry are available in the literature, only a few results exist for stone masonry. Here, the shear and compressive strength parameters of stone masonry using granite blocks are provided. In addition, a first aspect addressed is the shape of the shear stress–displacement diagrams under monotonic and cyclic loading. A second aspect addressed is the influence of the surface roughness and of the bed joint material on the compressive behavior of masonry. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Ancient masonry is a non-homogeneous material, composed by units and mortar, which can be of different types, with distinct mechanical properties. Often in monumental buildings, and if materials were available locally, bricks were used for vaults while stone was used in the construction of walls. The influence of mortar joints acting as a plan of weakness on the composite behavior of masonry is particularly relevant in case of strong unit–weak mortar joint combinations, which are characteristic of ancient stone masonry [1]. Two basic failure modes can occur at the level of the unit–mortar interface: tensile failure (mode I) associated to stresses acting normal to joints and leading to the separation of the interface, and shear failure (mode II) corresponding to a sliding mechanism of the units or shear failure of the mortar joint. In terms of the composite behavior of masonry, failure modes related to tensile splitting of the units and mortar crushing need to be taken into account [2]. The preponderance of one failure mode over another or the combination of various failure modes is essentially related to the orientation of the bed joints with respect to the principal stresses and to the ratio between the principal stresses [3]. Even if several results on the mechanical properties of brick and block masonry assemblages are available in the literature [4–7] scarce experimental data is available for stone masonry [8,9]. The present work deals firstly with the mechanical characterization
* Corresponding author. Tel.: +351 253 510200; fax: +351 253 510217. E-mail address: [email protected] (G. Vasconcelos). 0950-0618/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2009.06.045
of the masonry components: stone units and mortar, as well as with the shear behavior of dry and mortar masonry joints (cohesion, friction angle and dilatancy). Then, the compressive properties of the masonry composite (compressive strength and modulus of elasticity) are addressed. In order to attain such a goal, an experimental program was defined, including direct shear tests conducted on dry and mortar masonry joints and uniaxial compression tests carried out on a set of stone masonry prisms with distinct types of bed joints. Besides providing mechanical properties for numerical simulations of the in-plane behavior of stone masonry walls, the adopted testing program provides also the fundamental parameters required for the seismic assessment of masonry buildings based on simplified analytical models.
2. Shear behavior of stone masonry joints Although several experimental studies have been carried out on the bond shear strength of unit–mortar interfaces [4,5], limited research is available on the shear behavior of dry masonry joints [8]. On the other hand, the knowledge gathered on rock joints under shear behavior can be partly extended to dry masonry joints. The shear behavior of rock joints plays an important role in rock mechanics research, with several experimental and numerical studies pointing out the role of the surface roughness on the cyclic shear behavior of natural rock joints [9,10]. The relation between normal and shear stresses plays a major role in the shear behavior of masonry joints, actually governing its failure mode [11]. For pre-compression stresses above a certain level, the shear strength decreases and a combined shear-splitting
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failure or splitting of the units occur. In case of joint shear failure by slipping of the units, an increase of the normal stress leads to an increase of the shear strength. As has been widely reported [4,12], the shear strength of masonry under moderate normal stresses, for which the non-linear behavior of mortar is negligible and the friction resistance takes the central role, can be given by the Coulomb criterion:
s ¼ c þ lr
ð1Þ
where c is the shear strength at zero vertical load stress (usually denoted by cohesion) and l is the friction coefficient or tangent of the friction angle. For dry joints, the cohesion is obviously zero. 2.1. Test specimens and testing procedure Although triplet tests have been adopted as the European standard method [13] to perform shear tests in masonry joints, the strength properties of dry and mortar joints were obtained here by means of direct shear tests carried out on couplet specimens, see Fig. 1, [14]. In fact, the triplet test is rather complex to analyze and control after peak displacement due to the fact that two joints are tested simultaneously, see also [15]. The shear tests were carried out in a servocontrolled universal testing machine CS7400S composed by two independent hydraulic actuators used to transmit normal and shear loads, able to operate under force or displacement control. Both shear and normal stresses were measured and recorded by horizontal and vertical load cells of 22 kN capacity. Due to the limited space between steel platens the most suitable testing sample is composed by the two units with geometry and dimensions indicated in Fig. 1a, similarly to [6] and [16]. The surface of the dry stone masonry units is relatively smooth resulting from sawing, whereas the joint surface of the units of the mortar assemblages presents the typical handcoursed roughness to achieve realistic bond conditions. The granite used for the masonry units is a medium grained two-mica granite [17–19]. The shear specimens were placed between two thick steel plates and attached to the steel platens by steel bolts, so that shear force could be transmitted, see Fig. 1b. Thin steel sheets were attached to the steel plates to concentrate the shear load as close as possible of the bed joint, aiming at providing a more uniform shear stress distribution. In order to guarantee right angle surfaces, the dry specimens were suitably ground using a rectifying machine. The specimens were properly attached for load reversal by means of adjustable steel plates on both sides of the specimen.
a
The numerical assessment of test setup performed by Lourenço and Ramos [8] indicates the adequacy of the proposed approach. In order to simulate typical normal stresses existing in ancient masonry structures three distinct pre-compression stress levels were considered, r = 0.5 N/mm2, r = 0.75 N/mm2 and r = 1.0 N/ mm2. An additional pre-compression stress level equal to r = 1.25 N/mm2 was adopted for the monotonic tests in mortared assemblages. Three specimens were tested for each level of precompression, and for dry and mortared joints. In addition, the influence of the moisture content on the shear response of dry masonry joins was investigated by considering dry and saturated conditions. The relative horizontal displacement of the joint was measured by the horizontal LVDTs placed at each side of the specimen, see Fig. 1b. The vertical displacement of the joint was measured by the LVDTs placed at the opposite corners of the specimen, which enabled the assessment of possible dilatant behavior of the joints. The cyclic tests were carried out under displacement control following the time-displacement history used in [14]. 2.2. Monotonic behavior of masonry joints The shear load–displacement diagrams for distinct pre-compression stress levels resulting from the monotonic tests carried out on dry and saturated specimens are displayed in Fig. 2. The shear displacement is the result of averaging the measurements recorded by the LVDTs placed at each side of the specimen. The shear stress s and the normal stress r are obtained by dividing the shear
a
b
b
Fig. 1. Masonry specimens: (a) dry joints and mortar joints and (b) arrangement of the LVDTs for measuring the relative horizontal and vertical displacements. Dimensions are in mm.
Fig. 2. Shear stress–displacement diagrams in dry joints: (a) dry specimens and (b) saturated specimens.
G. Vasconcelos, P.B. Lourenço / Construction and Building Materials 23 (2009) 3337–3345
force H and the normal force N, recorded in vertical and horizontal actuators, by the cross section of the joint A. It is observed that no significant differences were detected between dry and saturated specimens, apart from the slighter decrease on the peak stress in saturated specimens. Besides, higher scatter was found when the maximum pre-compression level (r = 1.0 N/mm2) was applied. Three stages can be considered to describe the shear-displacement diagrams. The pre-peak behavior is characterized by a linear stretch for low levels of shear stress and by a clear non-linear stretch before peak stress. A plateau is found after peak stress, representing the considerable plastic deformations associated to inelastic sliding. Similarly to what has been reported in the literature [10,20] no shear softening was recorded after peak stress, unlike rough rock joints that exhibit remarkable lowering of the shear resistance as the plastic shear displacement increases. The shear stress–displacement diagrams of mortared joints are shown in Fig. 3a. The general shape of the shear stress–shear displacement is characterized by a sharp initial linear stretch. The peak load is rapidly attained for very small shear displacements. Similarly to what was reported for dry masonry joints, non-linear deformations develop in the pre-peak regime. After peak load is attained there is a softening branch corresponding to progressive reduction of the cohesion, until reaching a constant dry-friction value. This stabilization is followed by the development of large plastic deformations. The evolution of the vertical displacement with the shear displacement is displayed in Fig. 3b, where in the majority of the tests two distinct phases can be distinguished. Firstly, the uplift of the joint is expressed by increasing positive vertical dis-
a
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placement. It is observed that the non-linear evolution of the vertical displacement provides variable dilatancy assuming decreasing values as the shear displacement increases up to the shear displacement corresponding to the stabilization of the shear stress. During the subsequent regime of pure friction the vertical displacement remains constant or progressively decreases, particularly when the level of pre-compression increases. The vertical displacement exhibits even negative values in some specimens submitted to pre-compression levels of r = 0.875, 1.00 and 1.25 N/mm2). The dilatant behavior reflects, to great extent, the distinct shear failure modes obtained in the specimens submitted to different normal stresses. For low to intermediate levels of pre-compression, shear failure occurs at the unit–mortar interface along one unit face, or divided between two unit faces. For the larger normal stress level (r = 1.25 N/mm2), failure is localized in the mortar. 2.3. Cyclic behavior of dry masonry joints The typical shear stress–displacement diagrams obtained in direct cyclic shear tests conducted in dry masonry joints, using dry and saturated specimens, are displayed in Fig. 4 for the level of pre-compression r = 0.75 N/mm2. Apart from the small difference of the peak shear stress, no significant differences in the shape of the diagrams were found. Minor differences were found in the shear strength during the reversal cycles, see Fig. 5a, despite wearing of the surface and degradation of rock forming minerals with the accumulation of degraded material, similarly to what has been pointed out by Lee et al. [9]. A very minor trend for compaction can be seen from the normal displacement–shear displacement diagrams indicated in Fig. 5b. A maximum value of vertical
a
b
Fig. 3. Shear behavior of mortared joints: (a) shear stress–displacement diagram and (b) relation between vertical displacement and shear displacement.
b
Fig. 4. Shear stress–displacement diagrams for dry joints under cyclic loading (r = 0.75 N/mm2): (a) dry specimens and (b) saturated specimens.
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a
Fig. 6. Correction of the measured shear displacement for a saturated specimen submitted to a normal stress r = 1.0 N/mm2.
b
Fig. 5. Characteristic aspects of the shear behavior of dry joints: (a) evolution of the shear stress–displacement diagrams between the first and the last cycle of reversal loading and (b) compaction due to the wearing of the joint surface.
displacement of ±0.06 mm was measured for the dry and saturated tested specimens, indicating that dry granitic joints are non-dilatant, which is in agreement with the findings of Lourenço and Ramos [8] for sandstone dry joints and of Homand et al. [21] for hammered granitic joints. Other relevant aspect in the discussion is the comparison between the loading–reloading stiffness. The stiffness of the unloading branches exhibits always higher stiffness than the stiffness obtained in the reloading cycles. The effect of the elastic deformation of stone unit is assessed by removing the elastic deformation of the unit:
ujoint ¼ umeas
s ku
ð2Þ
where umeas is the shear displacement given by the horizontal LVDTs, s is the shear stress for a given displacement and ku is the stiffness calculated in the unloading branches. It is possible to confirm that the elastic deformation of the units has a minor role in the total shear displacement of dry joint, see Fig. 6. Finally, it is observed that the shear cyclic behavior of dry joints is characterized by non-linear deformations in the pre-peak stage and perfect plastic deformations after peak stress resulting from the characteristic sliding failure mode. 2.4. Shear strength parameters Fig. 7 shows the linear relationships between the values of the shear strength obtained in the monotonic tests and in the first cycle of the cyclic tests for dry and saturated conditions and the
values of the normal stress, which confirm the assumption that the shear strength is well described by Coulomb’s friction law. The slight decrease in the shear strength obtained on saturated specimens is reflected by a decrease of 5% on the friction coefficient in saturated joints, being of 0.65 in dry joints and of 0.6 in saturated joints. A range for the friction angle between 10° and 22.4° for mudstone was pointed out by Geerstsema [22]. The friction coefficient of dry granitic joints is similar to the values found by Lourenço and Ramos [8] for sandstone units (l = 0.63), and by Lee et al. [9] for granitic joints (l = 0.69). The narrow range of values found for the friction angle seems to indicate that no significant differences are expected among distinct types of natural stone under similar roughness surface conditions (sawn-cut surfaces). It is observed that, particularly in the case of dry specimens, there is a small increase of the frictional coefficient with wearing. Significant linear correlation coefficients between normal and peak and residual shear stresses were also found in case of mortared masonry joints with coefficients of correlation of r2 = 0.88, and r2 = 0.81, respectively. A value of cohesion about 0.36 N/mm2 and the tangent of the friction angle, tan /, equal to 0.63, corresponding to a friction angle of 32.2°, were attained for the peak strength. The residual shear strength can be calculated with reasonable accuracy from a friction coefficient of 0.78. Table 1 summarizes selected results published in the literature referring to the shear strength properties, where very different values of the cohesion and friction angle are pointed out for distinct unit–mortar assemblages. The shear strength parameters are greatly dependent on the moisture content, porosity of the units, on the strength and composition of mortar and on the nature of the interface [23]. From the results of direct shear tests carried out by Pluijm [6], the coefficient of internal friction ranges between 0.61 and 1.17, whereas cohesion varies from 0.28 up to 4.76, depending on different types of units and mortar. It is seen that the values of the shear strength parameters obtained for assemblages of granitic stone and lime mortar presented in this study are of the same order of the shear parameters pointed out for assemblages of lime mortar and old bricks [4]. 3. Compressive behavior of stone masonry Several experimental, numerical and simplified analytical studies have been carried out in order to increase the knowledge about the compressive behavior of masonry [7,27,28]. Being masonry a composite material usually made of units and mortar, it has been largely accepted that its failure mechanism is governed by the interaction between the components.
G. Vasconcelos, P.B. Lourenço / Construction and Building Materials 23 (2009) 3337–3345
a
b
c
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3.1. Experimental details The present experimental program aims at obtaining data on masonry compression for dry and low strength mortar, being the latter more representative of ancient masonry structures. In addition, the tests aim also at providing insight about the influence of the surface roughness and bed joint material on the compressive strength and deformation characteristics of masonry. With respect to dry masonry, both sawn (PR_S) and rough surface (PR_SR) joints are considered. The rough surface is obtained by sand-blasting. For mortared specimens, two types of interlayer material representative of ancient buildings are adopted, namely low strength lime mortar (PR_SM) and dry clay from sieving granitic soil (PR_SS). The compressive strength of masonry prisms is known to be affected by several factors, such as size, height and end conditions [30–32]. In order to reduce the platens confining effect, a height to length ratio of three was adopted according to ASTM E447 [33], see Fig. 8. The masonry prisms were made with three cubic stone units of 150 mm length and two bed joint courses, as shown in Fig. 8. The thickness of mortar or granitic soil placed in the bed joints was 10 mm. The dry stacked masonry prisms, PR_S and PR_SR, were built at the testing location by simply laying the second and third unit on top of the bottom unit in order to obtain vertical alignment of the specimen. The contact dry bed joints were properly selected so that maximum contact area between units could be attained. When mortar bed joints were considered, the stone units were carefully cleaned and wet to provide enough adhesion between units and mortar. The testing equipment consisted of the three-dimensional stiff steel frame used in [19]. Besides the large load capacity of the actuator, its remarkable stiffness is useful when stable displacement controlled failure is required. In order to induce uniform load distribution, a thick steel plate connected to a steel spherical seat was located at the top of the specimen. The deformation of the specimen during the test was recorded by means of four LVDTs located between steel platens at each side of the specimen. The vertical displacement of masonry prisms is defined by averaging the displacements measured by the LVDTs. In a first stage, two specimens of each masonry type were submitted to monotonic compression under displacement control. In a second stage more five specimens were tested under loading control and for cyclic conditions in the pre-peak regime at three different load stages of 25%, 55% and 75% of the average compressive strength obtained in the two previous monotonic tests. After this, the test control was switched to displacement control at a rate of 3 lm/s. The adoption of this velocity aimed to follow the possible stable failure of the masonry specimens and to obtain and characterize the post-peak behavior of stone masonry under uniaxial compression. 3.2. Experimental results
Fig. 7. Relationship between normal and shear stress: (a) dry specimens, (b) saturated specimens and (c) mortared joints.
The experimental characterization of masonry under compression requires representative wallets, with geometry and dimensions described in, e.g. the European Standard EN1052-1 [29], including at least one head joint and three masonry courses. Due to the very high strength of granite and the maximum capacity of actuators available for testing, the compressive features of stone masonry were obtained using prisms. According to Page and Shrive [30], the prisms are adequate masonry assemblages that include simultaneously the effect of bedding type, unit–mortar interaction and workmanship.
3.2.1. Failure modes The failure pattern of dry masonry prisms was difficult to monitor due to the encasing added to avoid injuries. Given its brittle behavior, most of the failures of the specimens PR_S were abrupt and explosive, see Fig. 9a. No signs of micro-cracks were recorded in the pre-peak regime. Micro-cracks become visible only after peak load has been reached. For dry masonry specimens, failure cracks usually develop along continuous shear bands that cross the joints, with some specimens exhibiting even double shear cracks. This suggests that after the initial adjustment of dry bed joints, the prism behavior is homogeneous and appears to be mostly determined by the compressive behavior of the granitic units. No differences were introduced in the failure modes by increasing the roughness of the bed joint surface. Abrupt failure occurred also in two specimens of rough dry masonry prisms tested
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Table 1 Shear strength properties for different unit–mortar assemblages. Source
Units
Mortar
c (N/mm2)
l
Atkinson et al. [4]
Old clay units Old clay units New clay units
1:2:9 (13) 1:2:9 (7) 1:1.5:4.5
0.127 0.213 0.811
0.695 0.640 0.745
Amadio and Rajgeli [23]
Solid bricks
Cement mortar Lime–cement mortar
0.65
0.723
Magenes [24]
Solid bricks
Hydraulic lime mortar Lime mortar
0.206 0.081
0.813 0.652
Binda et al. [25]
Sandstone Calcareous stone
Hydraulic lime mortar Hydraulic lime mortar
0.33 0.58
0.74 0.58
Roberti et al. [26] Lourenço et al. [15] This study
Bricks Hollow bricks Granitic units
Hydraulic lime mortar Micro-concrete Lime mortar
0.23 1.39 0.359
0.57 1.03 0.630
Fig. 8. Typical geometry of the masonry specimens. Dimentions are in mm.
under monotonic compressive loading. For the remaining five dry rough specimens, typical failures as the one exhibited in Fig. 9b developed. The failure of mortared masonry prisms was characterized by vertical splitting cracks appearing firstly in the central unit and extended to the other stones as the compressive stress increases, see Fig. 9c. This failure mode is mostly due to the lateral tensile stresses of the granitic units induced by the composite behavior of units and mortar with different elastic mechanical properties. Similar results have been reported by several authors [34]. On the other hand, the failure of the specimens PR_SS with granitic soil in the bed joints is more similar to the crack patterns exhibited by the dry masonry specimens. This can be explained by the peculiar trend for compaction exhibited by the granitic soil joints in contrast with the expansion of mortar [14]. 3.2.2. Stress–strain relationship For each specimen the corresponding value of the compressive stress was obtained by dividing the compressive load by the average cross section. The deformation at a given stress level, e, was calculated by dividing the vertical displacement by the height of the specimen, since the vertical displacement was taken as the average of the displacements recorded by the four vertical LVDTs. For a comparative analysis, all stress–strain diagrams obtained under monotonic loading are depicted in Fig. 10. The shape of the stress–strain diagrams of sawn dry joint prisms PR_S is characterized by an initial upward concavity. Although sawn surfaces are rather smooth and good adjustment of the stones was achieved during the construction of the masonry prisms, the upward concavity is in part due to the initial setting of the bed joints. After full contact of the bed joints upon increasing compressive stress, the behavior of masonry prisms depends mostly on the behavior of the stone. All prisms exhibit reasonable linear behavior until a compressive stress close to the peak strength. After the peak load is reached, it is still possible to record a considerable stretch of the
descending branch of the stress–strain diagrams in some specimens, even if most of them failed in a brittle manner. The stress– strain diagrams of rough dry joint prisms PR_SR show also an upward concavity for low stress level but over a larger part of the curve, leading to higher levels of deformation at peak load. As the compressive load increases, the roughness of the contact surface tends to break, leading progressively to partial leveling of the bed joint and to the improvement of the surface contact. In this case, the total deformation is the result of the deformation of the units and the local deformation at the bed joints. On the contrary, lime mortared masonry prisms PR_SM exhibit an initial stretch with downward concavity due to the composite behavior of units and mortar since early stages of loading. The role of the bed joint material on the deformational behavior of the masonry prism is further confirmed by the stress–strain diagrams obtained for the soil mortared specimens PR_SS. These diagrams are characterized by a large extent of the upward concavity from low to medium stress levels. The large initial deformation is related to the compaction of the granitic clay at the bed joints. The bed joints with an initial thickness of nearly 10 mm is at the end of the test a thin layer of compacted soil. 3.2.3. Pre-peak cyclic behavior It is observed that significant higher stiffness in the reloading cycles in the pre-peak regime was recorded comparatively to the stiffness of the virgin stretch for dry masonry prisms PR_S and PR_SR, see Fig. 11. This feature can be attributed to the fact that the stiffness of the unloading–reloading branches involves permanent deformations corresponding to a given stress level. This behavior is also found in the compressive behavior of rocks [35]. Besides, higher permanent deformations are recorded in rough specimens PR_SR with respect to the sawn prisms PR_S. This distinct behavior is the result of the continuous wearing of the higher asperities during the loading process. For lime mortared prisms PR_SM, unrecoverable deformations corresponding to the unloading–reloading are even more remarkable than deformations of dry rough specimens PR_SR, which should be attributed to the mortar deformability, see Fig. 12. Unlike dry masonry prisms, significant permanent deformations were recorded in the pre-peak unloading–reloading cycles in soil mortared prisms PR_SS, due to the compaction nature of the interlayer material [14]. 3.2.4. Compressive strength parameters A summary of average compressive parameters derived from the stress–strain diagrams, namely the compressive strength, fc, and the modulus of elasticity, Ec, is indicated in Table 2. Similarly to what was indicated by Binda et al. [5], the modulus of elasticity, Ec, was determined as the secant modulus in the range of 30% and 60% of the ultimate compressive strength in the ascending branch of the stress–strain diagram.
G. Vasconcelos, P.B. Lourenço / Construction and Building Materials 23 (2009) 3337–3345
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Fig. 10. Stress–strain diagrams for monotonic tests.
a
b
Fig. 9. Typical failure patterns of dry masonry prisms: (a) sawn dry joint specimen PR_S, (b) rough dry joint specimen PR_SR and (c) mortared joint specimen PR_SM.
Dry masonry prisms exhibit the highest compressive strength and modulus of elasticity and the lowest deformation at peak stress, being the compressive strength similar to the compressive strength of the units, which is equal to 69.2 N/m2 according to Vasconcelos [14]. According to Hendry [36], the strength of stone masonry built from dimensioned blocks with thin joints would be close to stone strength, irrespectively of the mortar strength, which is not clearly confirmed in the present study. The compres-
Fig. 11. Typical stress–strain diagrams for cyclic tests: (a) specimen PR_S10 and (b) specimen PR_SR7.
sive strength of rough prisms PR_SR undergoes a reduction of approximately 29% with respect to prisms PR_S, whereas the modulus of elasticity is 46% lower. Since the units are of the same granite of specimen PR_S, the increase of vertical strain at peak stress of approximately 27% is directly connected to the lower stiffness of the bed joints. The higher scatter found in sawn prisms PR_SR is attributed to the variability of the distribution of the roughness at the bed joint surfaces.
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G. Vasconcelos, P.B. Lourenço / Construction and Building Materials 23 (2009) 3337–3345
a
b
Fig. 12. Typical stress–strain diagrams for cyclic tests: (a) specimen PR_SM7 and (b) specimen PR_SS3. Table 2 Mean values of the mechanical compressive properties of masonry prisms (seven specimens). Coefficient of variation is indicated inside brackets (%). Masonry prism
fc (N/mm2)
Ec (N/mm2)
PR_S (sawn) PR_SR (rough) PR_SM (lime mortar) PR_SS (soil mortar)
73.0 51.9 37.0 64.2
14,722 7934 4629 8920
(9.1) (16.2) (11.8) (13.5)
(19.0) (37.1) (17.5) (12.6)
The reduction on the compressive mechanical properties with respect to the reference masonry specimens (PR_S) is even more significant in mortared specimens (PR_SM), with a reduction of nearly 50% and 70% in the compressive strength and in the modulus of elasticity, respectively. The reduction of the compressive strength can be attributed to composite behavior of masonry with the development of a compression–tension–tension triaxial stress state for the units and a triaxial compression state for the mortar [24,37]. The introduction of granitic soil instead of mortar in the bed joints leads to an increase of 73% on the compressive strength and an increase of 92% on the modulus of elasticity concerning mortared prisms PR_SM. This is due to the compaction of the granitic soil and dilation of the mortar. 4. Conclusions Aiming at obtaining reliable insight on the shear and compressive strength properties of stone masonry an experimental campaign for the characterization of stone masonry under shear
and compressive loading is addressed, namely with respect to the shear behavior of dry and mortar masonry joints and to the uniaxial compressive behavior of masonry prisms with distinct bed joint materials and joint surfaces. It should be stressed that the shear strength of the mortar–stone interface as well as the compressive strength of masonry stone are basic mechanical properties when design or numerical modeling of stone shear walls is required. Concerning shear behavior of masonry joints, it is observed that: (a) an elastic perfectly plastic shear stress–shear-displacement diagram was found to characterize the monotonic and the cyclic envelope of dry masonry joints, whereas post-peak strength degradation and a consequent stabilization characterizes the monotonic behavior of mortar joints; (b) the moisture condition on the joints, from dry to saturated, seems to have a negligible effect on the friction coefficient; (c) no dilatancy was found to characterize the shear behavior of dry masonry joints, whereas dilatant behavior was found on mortared joints and (d) the shear strength properties of masonry joints enables the assessment of the inplane lateral strength of masonry walls under in-plane loading. With respect the compressive behavior of masonry it was observed that: (a) the surface condition (smooth or rough) influences the composite behavior of masonry under compression, mostly with respect to the compressive strength, modulus of elasticity and deformation at peak stress; (b) the material of the bed joints (lime mortar or clay material) influences considerably the failure mode and the compressive strength of stone masonry. The different bed joint materials lead to clear distinct pre-peak regime (stress–strain diagrams) resulting in very different modulus of elasticity, compressive strength and permanent deformations after loading-reloading cycles. The materials of the bed joints play a central role on the deformation behavior of stone masonry under compressive loading. (c) as the shear strength properties of masonry joints, also the compressive strength of stone masonry represents a valuable property for the assessment of the in-plane and outof-plane strength of masonry walls. Finally, it should be stressed that the experimental results and mechanical data on stone masonry pointed out in this work contribute for the improvement of the knowledge on the mechanics of stone masonry.
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