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Engineering StructuresManuscript Draft
Manuscript Number: ENGSTRUCT-D-14-00490
Title: Laboratory testing and finite element simulation of the structural
response of an adobe masonry building under horizontal loading
Article Type: Research Paper
Keywords: Adobe masonry; horizontal loading; finite element model;damaged plasticity; non-linear analysis
Abstract: This paper is concerned with the calibration and validation ofa numerical modelling approach for adobe masonry buildings underhorizontal loading. The paper first reviews the state-of-the-art inexperimental and computational research of adobe structures and thenpresents results obtained from monotonic lateral loading laboratory testson a 1:2 scaled unreinforced adobe masonry building. Through the
experimental investigation conducted, useful conclusions concerning theinitiation and propagation of cracking failure are deduced. In addition,damage limit states at different levels of deformation are identified.Experimental results verify that the response of adobe structures tohorizontal loads is critically affected by weak bonding between themasonry units and mortar joints and by lack of effective diaphragmaticfunction at roof level. Based on experimental material data, a finiteelement continuum model is developed and calibrated to reproduce the teststructure's force-displacement response and mode of failure. An isotropicdamaged plasticity constitutive law is adopted for the numericalsimulation of adobe masonry and the use of appropriate modellingparameters is discussed. The analyses carried out reveal that the globalstructural behaviour is primarily influenced by the tensile response
assigned to the homogenized masonry medium. Results show that, despiteits generic limitations and simplifications, continuum macro-modellingcan approximate the structural behaviour of horizontally loaded adobemasonry construction with sufficient accuracy.
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Highlights
A 1:2 scaled adobe masonry building is tested in laboratory under horizontal
loading. Conclusions on the initiation and propagation of cracking failure are deduced. Damage limit states at different levels of deformation are identified. A non-linear finite element continuum model of the scaled building is developed. The FE model is calibrated to reproduce the structural response with sufficient
accuracy.
ghlights (for review)ck here to download Highlights (for review): highlights.docx
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ABSTRACT1
This paper is concerned with the calibration and validation of a numerical modelling2
approach for adobe masonry buildings under horizontal loading. The paper first3
reviews the state-of-the-art in experimental and computational research of adobe4
structures and then presents results obtained from monotonic lateral loading5
laboratory tests on a 1:2 scaled unreinforced adobe masonry building. Through the6
experimental investigation conducted, useful conclusions concerning the initiation and7
propagation of cracking failure are deduced. In addition, damage limit states at8
different levels of deformation are identified. Experimental results verify that the9
response of adobe structures to horizontal loads is critically affected by weak bonding10
between the masonry units and mortar joints and by lack of effective diaphragmatic11
function at roof level. Based on experimental material data, a finite element12
continuum model is developed and calibrated to reproduce the test structure’s force -13
displacement response and mode of failure. An isotropic damaged plasticity14
constitutive law is adopted for the numerical simulation of adobe masonry and the use15
of appropriate modelling parameters is discussed. The analyses carried out reveal that16
the global structural behaviour is primarily influenced by the tensile response assigned17
to the homogenized masonry medium. Results show that, despite its generic18
limitations and simplifications, continuum macro-modelling can approximate the19
structural behaviour of horizontally loaded adobe masonry construction with20
sufficient accuracy.21
KEYWORDS22
Adobe masonry, horizontal loading, finite element model, damaged plasticity, non-23
linear analysis24
stractk here to download Abstract: abstract.docx
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1. Introduction1
Adobe masonry structures are encountered in almost every region of the world2
and are considered to possess significant historic and cultural value. At the same time,3
unreinforced adobe masonry is quite susceptible to seismic damage [1]. The strong4
seismicity of areas where a considerable number of earthen buildings exists (i.e. wider5
Eastern Mediterranean region, South Asia, South America), renders the study of the6
behaviour of adobe structures under horizontal loads essential. The development of7
structural analysis methods that account for the specific characteristics of adobe8
masonry is also required to facilitate the implementation of rational engineering9
assessment/design.10
Up to date, several studies involving laboratory testing of full- and/or reduced-11
scale adobe structures have been conducted [2-19]. Emphasis has been primarily12
given on evaluating various repair/retrofitting techniques, rather than on providing13
extensive data which can be exploited for the calibration and validation of numerical14
analysis tools. Researchers who have developed numerical models of adobe masonry15
structures [20-29] have mainly performed conceptual analyses aiming to obtain16
qualitative information regarding the response of typical traditional earthen buildings.17
Detailed comparisons between simulation results and physically measured aspects of18
structural behaviour (i.e. deformation, load-resistance) are rather limited [23-25]. This19
indicates that there is a need for adopting a more integrated research approach that20
will combine experimental and computational work on adobe masonry buildings, in21
order to develop reliable assessment procedures and analysis methods.22
The present study aims to extend existing knowledge regarding the structural23
behaviour of adobe buildings by contributing towards the development of appropriate24
anuscriptck here to download Manuscript: text.docx Click here to view linked References
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assessment procedures and analysis methods. Hence, it utilizes the results of large-25
scale laboratory tests to develop a Finite Element (FE) continuum macro-model26
capable of simulating the response of a horizontally loaded unreinforced adobe27
masonry building with sufficient accuracy. More specifically, for the purpose of28
validating the FE model, a 1:2 scaled replica of an existing single-storey traditional29
adobe building was constructed and subjected to static monotonic lateral loading tests.30
Masonry failure mechanisms (i.e. initiation and propagation of cracking) were31
recorded during the experimental procedure, while damage limit states at different32
levels of deformation were identified. In the framework of the numerical33
investigation, a detailed 3D FE model of the scaled building was developed. This was34
used for performing non-linear analyses, aiming to macroscopically reproduce the35
general response of the structure under test. For the numerical representation of adobe36
masonry, a damaged plasticity constitutive law was adopted, while experimentally37
derived material data were used as input parameters. The validity of the numerical38
results was verified both qualitatively and quantitatively through comparisons with39
the experimental damage patterns and force-displacement curves. The numerical40
investigation conducted enabled the identification of the factors which critically affect41
the FE simulation of adobe structures. The results of this work represent a promising42
step towards the numerical modelling of the seismic behaviour of earthen43
constructions.44
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48
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2. Review of experimental and computational research on adobe structures49
2.1. Experimental work50
Most experimental data currently available regarding the response of adobe51
masonry construction has been obtained by examining model structures before and52
after the implementation of repair/strengthening interventions.53
Systematic testing of unreinforced adobe masonry structures took place in the54
framework of various research projects undertaken by the Pontifical Catholic55
University of Peru. Relevant experimental work included static tilt tests on house56
modules [2], displacement- controlled cyclic tests on „I‟ -shaped wall configurations57
[3] and shake table tests on single- [4-7] and two-storey [8] model buildings and58
vaulted structures [9, 10]. In all cases, the response of unreinforced model structures59
was compared to that of reinforced ones (i.e. structures incorporating timber ring60
beams, cane rods, steel wire meshes, geogrids, fibre-reinforced polymer strips, tire61
straps, etc.).62
Noticeable experimental research on the dynamic response of unreinforced63
adobe masonry buildings was also carried out during the Getty Seismic Adobe64
Project. In the first phase of this project, 1:5-scaled replicas of single-storey dwellings65
were subjected to impact hammer and shake table tests before and after66
repairing/strengthening [11]. In the second phase of the same project [12], dynamic67
excitations based on real accelerograms were imposed on larger (1:2 scaled) models.68
At this phase, in addition to unreinforced masonry structures, model buildings69
retrofitted with bond beams, horizontal/vertical straps, local ties, centre-core rods and70
wooden roof diaphragms were also examined.71
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Dowling [13] conducted s hake table tests on 1:2 scaled „U‟ -shaped wall units72
and complete buildings to examine the dynamic behaviour of unreinforced adobe73
masonry construction. Along with plain unreinforced masonry structures, models74
incorporating pilasters/buttresses, wire meshes, bamboo poles and timber ring beams75
were also constructed and tested in [13]. The outcomes obtained were used for76
proposing retrofitting solutions.77
More recently, a real- scale „I‟-shaped adobe wall was examined at Aveiro78
University [14]. Following a number of cyclic lateral loading tests, the cracks formed79
in the masonry were injected with lime mortar and a polymeric mesh was fixed on the80
surface of the wall. The repaired/retrofitted structure was subjected to further lateral81
loading tests.82
Extensive literature on the response of strengthened/retrofitted adobe masonry83
buildings can be also found in [15-19] which present results from shake table tests and84
static horizontal loading tests on 1:1.5 [15], 1:2.5 [16], 1:3 [18], 1:5 [15] and 1:10 [19]85
scaled model structures.86
The main conclusion derived from the aforementioned tests is that adobe87
masonry structures generally have limited capacity to resist horizontal loads. This is88
attributed to two factors: (a) poor bonding between the adobe bricks and the mortar89
joints which reduces the tensile strength of the masonry [4, 11, 14] and (b) lack of90
diaphragmatic function at roof level which precludes effective transfer of loads among91
the load-bearing walls [11, 12]. Under seismic action, out-of-plane failure, either due92
to extensive cracking or due to detachment at cross-walls and overturning, prevails [4,93
11-13]. Integrated retrofitting systems can improve the poor seismic behaviour of94
unreinforced adobe masonry buildings, either by increasing their overall lateral95
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resistance or by producing a confinement effect which reduces the risk of brittle96
collapse [12-19].97
2.2. Numerical modelling and analysis98
In contrast to experimental work, computational research on adobe masonry99
structures has not been as rigorous. Despite the fact that advanced analysis methods100
have been extensively used for the simulation of conventional masonry structures (i.e.101
structures built with stone, fired clay bricks, concrete blocks, etc.), the application of102
numerical tools has not been meticulously studied in the context of earthen103
construction.104
Simulation of masonry structures can follow a macro- or a micro-approach. In105
the macro-approach, either distinct macro-elements are used to represent individual106
piers and spandrels, or the masonry is treated as a fictitious homogeneous medium107
represented by continuum finite elements. In the micro-approach, the masonry unit-108
mortar interfaces are considered as potential crack/slip planes, while the building109
blocks and the mortar are either explicitly described (detailed micro-modelling) or110
represented by repeated expanded cellular units interacting at their boundaries111
(simplified micro-modelling).112
Continuum FE models of adobe-wood buildings have been developed by Che et113
al. [20]. These were subjected to elastic time domain analysis in order to examine114
their seismic response. Linear dynamic analyses by response spectra have been also115
conducted by Gomes et al. [21] on 3D models of unreinforced and reinforced adobe116
buildings.117
Using experimental material data, Meyer [22] modified the Holmquist-Johnson-118
Cook model for concrete to capture the pressure and strain-rate-dependent non-linear119
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Morales and Delgado [29] examined 2D models of single- and two-storey adobe142
walls. The models were composed of distinct elements connected with springs and143
dashpots that acted as possible fracture points. The seismic capacity of the simulated144
structures was assessed by imposing reversing horizontal accelerations.145
3. Laboratory testing of an adobe model building146
3.1. Construction of model building147
For investigating the structural response of adobe masonry buildings, a 1:2148
scaled replica of a traditional single-roomed Cypriot dwelling ( monochoro makrynari )149
[30] was constructed and tested at the Structures Laboratory of the University of150
Cyprus (Fig. 1).151
The model structure‟s walls were 220 mm thick and were built with scaled-152
down adobe bricks measuring (height x width x length) 30 x 150 x 220 mm 3. The153
bricks were obtained from a local producer and were laid with the application of earth154
mortar (composition soil:straw:water ≈ 200:6:100 w/w) prepared in the laboratory.155
Following the island‟s traditional building techniques, the masonry was constructed in156
a running bond pattern and the joint thickness was consistently kept below 10 mm.157
The model structure was securely bolted on the laboratory concrete floor. The158
structure‟s external dimensions were (width x length) 1.75 x 3.60 m 2. The height of159
the front elevation was 1.50 m and that of the opposite rear wall was 1.65 m. A door160
measuring 1.10 m in height and 0.70 m in width was formed on the façade. Two161
openings with dimensions 0.55 x 0.55 m 2 were also created on the two side walls. A162
triangular notch 0.22 m wide and 0.18 m high was formed on the rear wall to simulate163
the ventilation notches encountered in local vernacular buildings.164
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It was presumed that the stone masonry foundations of traditional earthen165
structures preclude horizontal translation of the walls at ground level, but allow166
bending. Therefore, the first layer of adobe bricks was simply set with the application167
of earth mortar. Horizontal displacements at this level were constrained by timber168
elements installed a long the structure‟s perimeter. At the cross-walls, overlapping169
bricks were laid upon each other to achieve adequate interconnection.170
Above all openings, lintels consisting of two jointed timber beams, each with a171
cross-section of 85 x 85 mm 2, were installed. The roof structure comprised of a 20172
mm-thick wooden panel nailed upon nine timber rafters (45 x 90 mm 2 in cross-173
section) that spanned the space between the two opposite longitudinal walls. On top of174
the panel, adobes were uniformly placed to represent the weight of roof tiles. All175
timber elements were set into the masonry with gypsum mortar.176
3.2. Test procedure and instrumentation177
The model building was tested nine weeks after its construction by applying178
monotonically increasing lateral forces until noticeable damage (i.e. severe cracking179
of the masonry walls) was observed. Loading was applied on the rear wall using a180
steel hydraulic jack with 60 kN maximum capacity (Fig. 2a). The load imposition181
system was supported by a rigid steel reaction frame (see background of Fig. 1). To182
achieve a more even load distribution a timber beam strengthened at its centre was183
used along the rear wall. The hydraulic jack accommodated a swivel head that184
enabled it to stay in contact with the loading beam when out-of-plane bending was185
induced. Loading was applied at approximately 2/3 of the model‟s height .186
Linear Variable Displacement Transducers (LVDTs) (range ± 50.8 mm,187
accuracy ± 0.25%) were placed at 15 different positions on the model structure to188
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record displacements (Fig. 2b). Emphasis was given in monitoring the out-of-plane189
movement of the longitudinal walls and the in-plane bending of the side walls.190
Therefore, one of the side walls and the two adjacent halves of the longitudinal walls191
were instrumented. Indeed, during the tests it was confirmed that there was close192
analogy between the responses of the half- structure‟s sections examined and of the193
parts symmetric to them. LVDTs were also placed at the structu re‟s base to verify that194
no translation or rotation took place. All measurements were recorded automatically195
via a data acquisition system. Digital cameras were also used for monitoring failure196
evolution and crack opening-closing.197
A total of 10 monotonic loading-unloading cycles were implemented. The198
experimental procedure was terminated when a significant reduction of the lateral199
resistance of the model structure was detected.200
3.3. Experimental results and discussion201
3.3.1. Crack patterns202
The crack pattern recorded after the completion of the experimental procedure is203
shown in Fig. 3. Damage modes were almost identical during all tests, with most204
cracks developing during the first four load cycles. Subsequent load cycles led to re-205
opening of pre-existing fissures and increased crack widths.206
Damage was noted at the rear and the two side walls, but not at the façade or at207
any of the timber members. Damage localization reveals stress concentrations and208
implies that the load-bearing members of the model failed to react as a homogeneous209
assemblage of structural elements (i.e. as a fully connected structural system). In210
addition, it indicates lack of diaphragmatic function at the roof level.211
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Out-of-plane bulging of the rear wall caused the formation of a major horizontal212
crack at the interior of the structure, along the line of loading (Fig. 3a). Due to213
overstressing at the load imposition point, diagonal cracks extending from the centre214
of the wall towards its two lower sides were generated below the aforementioned215
horizontal fissure. In addition, a „V‟ -shaped cracked section was formed between the216
triangular ventilation notch and the four central roof rafters.217
At the exterior surface of the rear wall, a continuous horizontal crack occurred218
between the 7th and 8th rows of adobe bricks (Fig. 3b). Towards the two sides,219
because of the restrain imposed by the side walls, this crack was inclined. Less severe220
cracking was recorded below this zone. Furthermore, failure of the gypsum mortar221
joints at the roof rafter abutments and subsequent sliding of the timber members were222
noted. As the rear wall was subjected to significant out-of-plane deformations, stress223
concentrations were generated at the areas where the masonry was in contact with the224
much stiffer timber rafters. This led to horizontal cracking at the vicinity of the roof225
supports; cracking extended diagonally where restrain by the two side walls became226
effective.227
The mode of failure sustained by the two side walls was mainly characterized228
by the formation of diagonally orientated shear cracks that radiated out of the two229
openings‟ corners and propagated through the brick joints in a stepped pattern (Fig.230
3c). These cracks extended throughout the whole width of the side walls. Damage at231
the upper section of the walls spread towards the intersection with the rear wall,232
eventually joining with the external rear wall cracks that formed just below the roof233
rafters. During the two final test cycles, out-of-plane torsional movement of the side234
walls‟ upper crac ked sections was also recorded.235
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In all cases, failure was characterized by loss of bonding between the masonry236
units; no damage of the adobe bricks was reported. This verifies that the failure237
mechanisms encountered in adobe structures are primarily a product of weak adhesion238
among the adobes [4, 11, 31, 32]. Crack opening was significant and ranged from 5 to239
20 mm (Fig. 4). Interestingly enough, when loading was removed, the fissures formed240
closed completely and no sign of damage was visible. However, cohesion between the241
masonry units at these areas had been lost and when load was exerted again, re-242
opening of the cracks was mobilized.243
Despite the fact that the experimental set-up enabled only the imposition of244
static forces, the recorded modes of damage correspond well to those observed in245
dynamic tests and to those sustained by adobe buildings during earthquakes. Crack246
patterns similar to the ones observed at the rear wall of the model building have been247
reported in [1, 3, 11, 12, 33, 34]. Diagonal shear cracking of adobe walls loaded in-248
plane has been noted in several other experimental [3, 11, 14] and field [1, 35] studies.249
However, due to the unilateral and monotonic load imposition process, separation250
between intersecting walls did not occur, although such a response of unreinforced251
adobe masonry to seismic loads is rather common [4, 16, 33, 35]. Moreover, the lack252
of diaphragmatic roof function, caused by the sliding failure of the rafter supports, did253
not enable the effective transfer of forces from the rear wall to the façade. Therefore,254
as opposed to a dynamic state where all sections perpendicular to the direction of the255
principal action would sustain reversing out-of-plane bending loads, in the tests256
conducted here, movement of the façade was dictated by the in-plane drift of the side257
walls and therefore no noticeable damage (i.e. cracking and/or detachment)258
developed.259
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3.3.2. Force-displacement response and limit states260
Force-displacement data envelopes obtained from the implementation of the 10261
test cycles are presented in Fig. 5. The diagrams show the variation of the cumulative262
displacements measured at the upper sections of the rear (LVDT13), the side263
(LVDT3) and the façade (LVDT1) walls in relation to the load imposed. Cumulative264
displacement values were computed by adding to the recordings of each individual265
test cycle the permanent deformations noted after the completion of all previous266
cycles.267
Based on the structural response recorded and the corresponding state of268
damage observed, four limit states (LS1-4) can be identified. Up to approximately 5%269
of its total displacement capacity and 75% (10.6 kN) of its maximum lateral resistance270
(LS1), the structure performed with no or negligible damage and the various load-271
bearing members maintained a consistent response to horizontal loading. The272
displacements recorded at the model structure‟s walls during this stage were rather273
uniformly distributed. They lied in the region of 1.8 mm and correspond to274
approximately 0.11% of drift (estimated as horizontal displacement divided by the275
monitoring point‟s vertical distance from the building‟s base) .276
Above the 10.6 kN threshold, stiffness degradation started to develop and277
cracking damage was initiated at the interior of the rear wall and at the two side walls.278The structure, however, could still function as a homogeneous structural system up to279
11% of its total displacement capacity and 85% (12 kN) of its maximum lateral280
resistance (LS2). A co-instantaneous movement of 4 mm and a lateral drift of 0.26%281
were recorded at the upper sections of the walls monitored. It should be noted that the282
first and second limit states were already reached by the end of the initial test cycle.283
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When the displacement induced exceeded 11% of the total displacement284
capacity, interaction among the s tructure‟s load -bearing members was effectively lost285
and differential movement of the masonry walls took place. This was accompanied by286
further cracking, permanent distortion and considerable reduction of the overall287
stiffness. Such highly non-linear response continued until the load exerted became288
equal to the maximum force the structure could withstand (14.2 kN) and the289
displacement induced was 26% of the total deformation capacity (LS3). During this290
stage, sliding failure of the roof rafters‟ supports and cracking of the rear wall‟s base291
were observed. Furthermore, the cracks previously formed on the rear wall‟s interior292
and on the two side walls extended in length. Cumulative displacements at the façade293
and the side wall were 7 and 7.7 mm, respectively. In terms of lateral drift, these294
values can be interpreted as 0.5%. Cumulative displacement at the centre of the rear295
wall was 21.6 mm and accounts for 1.4% lateral drift. The aforementioned data were296
obtained after the completion of the first four test cycles.297
After LS3 and up to the last limit state (LS4), the structure was characterized by298
depletion of its overall stiffness and by inability to sustain higher levels of loading.299
Relatively small augments of the imposed load led to large in- and out-of-plane drifts.300
Moreover, significant inelastic deformations were generated, while crack opening301
eventually attained its maximum value (≈ 20 mm) . At LS4, the cumulative horizontal302
translation of the side wall was 25.2 mm, while that of the façade was 23.8 mm. The303
lateral drift at these sections was estimated as 1.6%. The total movement of the rear304
wall was 84.9 mm and the lateral drift at its central section was 5.7%.305
After LS4, at the last loading cycle , an abrupt drop in the structure‟ s lateral306
resistance occurred. The sections of the two side walls above the diagonal shear307
cracks were isolated by cracking damage. As a result, the façade and the adjacent308
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triangular halves of the two side walls were detached from the rear part of the309
building. The load-bearing system was practically split into two independent parts that310
could only transfer forces between them through contact points. Under the application311
of load, the kinematic mechanism formed was mobilized causing rocking motion of312
the frontal part and reducing the effective resisting area. Although the overall strength313
fell to a residual value, total or partial collapse did not occur. Nevertheless, crack314
formation and/or growth at this state could have been critical, if the relative315
displacement induced across the planes of weakness had been larger.316
Using experimental results from cyclic load tests on full- scale „I‟-shaped adobe317
walls, Figueiredo et al. [14] and Tarque et al. [36] defined damage limit states similar318
to those reported in this study. The experimentally recorded maximum load resistance319
accounts for approximately 30% of the model building‟s self -weight. This is in total320
agreement with the data obtained by Benedetti et al. [37] from extended dynamic321
experiments on unreinforced masonry buildings constructed with fired clay bricks.322
However, it is lower than the 34-100% base shear force-to-weight ratios reported by323
researchers who performed shake table [4, 8, 38] and static tilt [39] tests on adobe324
model structures. Despite being rather conservative, the load-bearing capacity325
determined in the present work cannot be injudiciously adopted as a safe indicator for326
the seismic behaviour of unreinforced adobe masonry construction. This is because327
the monotonic imposition of forces during the testing procedure did not enable the328
development of certain failure mechanisms (e.g. detachment of intersecting walls) that329
would drastically reduce lateral resistance in the event of dynamic excitation. In330
addition, the application of reversing horizontal accelerations would have probably331
caused the out-of-plane failure of the longitudinal walls, either by detachment and332
overturning or by diagonal and vertical cracking [33], at significantly lower levels of333
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deformation. Hence, it may be argued that the maximum lateral translation measured334
during the tests is overestimated and does not realistically represent the displacement335
capacity of unreinforced adobe masonry structures when these are subjected to336
seismic action.337
4. Numerical simulation of the response of the adobe model building338
4.1. Finite element modelling and analysis339
For simulating the response of the tested structure, a full 3D FE model was340
developed in Abaqus/CAE (Fig. 6) [40]. The various parts comprising the341
experimental set-up were modelled as individual bodies interacting with each other.342
Hence, the FE model included different representations for the adobe masonry walls,343
the openings‟ lintels, the roof and the timber loading-beam. Since the test344
configuration is symmetric, only half the structure was numerically examined. All345
bodies were discretized using 8-noded 3D linear brick elements (C3D8) with sides 40346± 4 mm long. The mesh generated consisted of 47,808 elements and 68,139 nodes347
resulting in 169,515 degrees of freedom.348
Adobe masonry was numerically handled in the context of a macro-modelling349
strategy. It was thus treated as a fictitious homogeneous continuum and no distinction350
between masonry units and mortar joints was made. For simulating its behaviour, the351concrete damaged plasticity constitutive model [40-42] was adopted. This is a352
continuum, plasticity-based, isotropic damage model that assumes two main failure353
mechanisms: tensile cracking and compressive crushing. The material admissible354
stress field is bounded by a yield surface that is controlled by hardening variables355
linked to cracking and crushing strains.356
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Most parameter values used for the application of the damaged plasticity357
constitutive law were based on experimental data. The density of adobe masonry was358
set as ρ = 670 kg/m 3. This was estimated following simple gravimetric measurements359
on the adobes used to construct the model structure. Poisson‟s ratio (ν = 0.3) was360
evaluated from the deformations recorded during the compressive strength testing of a361
stack-bonded adobe masonry prism, as the ratio of transverse to axial strains.362
Compressive stress-strain response was described using the polynomial relation363
developed by Illampas et al. [43] for adobe bricks (Fig. 7a). The Young‟s modulus364
was computed from the assigned stress-strain response as a secant modulus up to the365
yielding point; E = 18 MPa. Compressive strength ( f c = 1.2 MPa) and strain at peak366
compressive stress ( ε cu = 0.1 mm/mm) were defined from the average results of367
laboratory tests on stack-bonded prisms [44]. Considering that adobes possess a368
granular structure and thus have limited elastic response to compression [22], material369
non-linearity was assumed after 5% of the compressive strength.370
In tension, linear behaviour up to the maximum allowable stress and post-peak371
softening were assumed (Fig. 7b). Inelastic tensile stress-strain response was372
described using the exponential function developed by Lourenço [45] :373
exp ck t
t t t f
hf f G
(1)
In the above, f t is the tensile strength of masonry, G f is the tensile fracture energy,
ck t
374
is the tensile cracking strain and h is the characteristic crack length.375
Tensile strength was set as f t = 0.04 MPa, following the diagonal tension testing376
of an adobe wallette. Regarding the tensile fracture energy G f of the homogenized377
masonry, direct tension tests on adobe couplets in [46] yielded a mean value of G f =378
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4.5 N/m. The average tensile strength of the specimens examined in [46] was 0.01379
MPa; assuming a linear analogy between the bearing capacity and the fracture energy,380
the value of G f = 18 N/m was adopted for f t = 0.04 MPa.381
The characteristic crack length h was defined as [47, 48]:382
3 x y z h h h h (2)
In the above equation h x, h y and h z are the element‟s lengths along the x, y and z axes.383
The element size during meshing was selected to satisfy the energy criterion given in384
equation 3:385
2
f
t
G E h
f (3)
Theoretically, through the definition of the characteristic crack length, mesh-386
dependency of numerical results was treated. However, the use of this parameter387
implies that, in non-structured meshes, the elements with larger aspect ratios will tend388to have rather different behaviour, depending on the direction in which they crack.389
This effect may have introduced some mesh sensitivity to the results presented in this390
study, despite making efforts to use elements with aspect ratios close to one,391
especially in areas where tensile damage was expected.392
For the rate at which the hyperbolic flow potential approaches its asymptote ( e =3930.1) and the ratio between the initial equibiaxial and the initial uniaxial compressive394
yield stresses ( σ b0/σ c0 = 1.16), the default values suggested in [40] were adopted. The395
plasticity parameter which relates the second stress invariant on the tensile meridian396
to the equivalent invariant on the compressive meridian was set as K c = 0.8, in line397
with the recommendations of [40] for soils modelled with a Drucker-Prager yield398
function. Based on [25] and [49], a very low dilation angle ψ = 1 o was selected.399
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Since no damage or considerable deformation was observed during the400
experimental procedure in any of the timber members (i.e. lintels, rafters, loading-401
beam, roof panel), these were all modelled using linear elasticity constitutive laws. In402
addition, it was assumed that the mechanical properties of timber are isotropic. The403
material parameters used were drawn from the literature [50, 51] as follows: (a) wood404
panel – density, ρ = 380 kg/m 3; Young‟s modulus , E = 8000 MPa; Poisson‟s ratio , ν =405
0.2 and (b) timber lintels, rafters and loading-beam – density, ρ = 670 kg/m 3; Young‟s406
modulus, E = 7000 MPa; Poisson‟s ratio ν = 0.3.407
At the areas where the masonry was in contact with the timber members, contact408
pairs were formed and surface to surface interactions were defined via master-slave409
associations. When under compression, interacting surfaces were assumed to remain410
in contact; thus, any pressure could be transmitted across the interfaces. When the411
contact pressure reduced to zero, separation of the surfaces took place and no transfer412
of tensile stresses across interfaces was allowed. To simulate the behaviour hereby413
described, a “hard” contact pressure -overclosure relationship [40] was defined in the414
normal direction.415
In the tangential direction, a finite-sliding formulation [40] based on the416
Coulomb friction theory was used. The Coulomb friction model available in417
Abaqus/CAE cannot account for cohesion among interacting surfaces and computes418
the shear stress at which sliding initiates ( τ crit ) simply as a function of the contact419
pressure ( p) and the coefficient of friction ( μ ) between the surfaces:420
τ crit = μp (4)
At the interfaces between the masonry and the opening lintels and the masonry and421
the roof rafters, a friction coefficient of μ = 0.5 was specified. This value was based422
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on the data reported in [32] which, however, do not refer to the frictional properties of423
timber elements embedded in adobe masonry, but to the friction developed between424
the masonry units and joints of adobe walls. Frictionless sliding ( μ = 0) was assumed425
to take place between the masonry and the loading-beam and the masonry and the426
roof panel.427
All nodes at the base of the walls were considered to be pinned. Horizontal428
kinematic constrains were imposed at the perimeter nodes affected by the timber429
elements, which were installed in the actual structure to retain lateral movement at the430
base. At the area where the hydraulic jack was in contact with the timber loading-431
beam, constraints precluding translation along the x and z axes were imposed.432
Movement in the x direction and rotations around the y and z axes were not allowed433
along the plane of symmetry.434
The weight of the adobes placed on the roof was evenly distributed to the roof435
panel as an additional body force. Horizontal loads were applied in the form of lateral436
displacements at the nodes of the timber loading-beam in contact with the jack. The437
amplitude of the lateral displacements was formulated according to the cumulative438
displacement data recorded during the laboratory tests.439
The numerical solution process was completed in two successive steps. At the440
initial step, the dead loads were incrementally imposed. At the second step, the lateral441
displacements at the jack-loading beam interface were incrementally enforced at time442
intervals ranging from 1x10 -19 to 1x10 -4 s over the 1 s analysis period. In both cases, a443
general non-linear static procedure with automatic stabilization was implemented,444
adopting the full Newton solution scheme. The effect of geometric non-linearity was445
accounted for in all numerical steps.446
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4.2. Comparison between experimental-numerical results447
Fig. 8 shows contour representations of the displacements computed in the y-448
direction. Results show that the FE model captures well the deformed shape of the449
structure. As expected, the maximum lateral displacement occurs at the rear wall, at450
the level where loading was applied. In line with the experimental observations, the451
out-of-plane movement of the façade is dictated by the in-plane drift of the side wall.452
Furthermore, displacements along the height of the façade display a linear increase453
towards the wall‟s top. The backwards movement predicted at the rear central part of454
the side wall is verified by experimental measurements and is attributed to out-of-455
plane bending and subsequent torsion of this section.456
In order to obtain the graphical visualization of the numerically predicted457
damage pattern of Fig. 9, it was assumed that the direction of the vectors normal to458
the crack planes is parallel to the direction of the maximum principal plastic strains459
[40, 41]. The FE model adequately captured the structure‟s mode of failure, both in460
terms of damage distribution and in terms of crack initiation and propagation.461
The onset of tensile failure during the simulation occurred at the upper central462
section of the rear wall‟s interior side. The plastic strain magnitude at this point463
eventually attained the highest computed value, coinciding with the location where464
the maximum crack opening of approximately 20 mm was observed during the465
laboratory tests. Crack propagation was rapid, with plastic strains spreading across a466
horizontal band, parallel to the loading beam. Almost co-instantaneously, tensile467
failure was initiated at the two opposite corners of the side wall‟s window opening.468
The concentration of significantly high tensile stresses in this area produced a469
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diagonal distribution of plastic strains, similar to the crack pattern observed on the470
tested building.471
The gradual increase of the imposed load led to the formation of plastic strains472
that followed inclined paths on the interior surface of the rear wall. As in the case of473
the actual model building, damage extended from the principal horizontal line of474
failure towards the upper and lower sections of the wall. Furthermore, horizontal and475
diagonal cracking at the exterior base of the rear wall and propagation of basal476
damage to the side wall were well reproduced.477
The development of horizontal cracks at the vicinity of the roof rafter supports478
was also adequately approximated. However, unlike experimental observations,479
plastic strains in this area did not extend to the side wall and did not intersect with the480
crack appe aring above the window‟s lintel . Instead, a near-vertical crack occurred at481
the upper rear section of the side wall. This inconsistency is attributed to482
overestimation of the side wall‟s out -of-plane torsional displacement by the FE483
analysis.484
Fig. 10 compares the outcomes of the FE analysis with the experimentally485
derived force-displacement data envelopes for the upper sections of the rear wall, the486
façade and the side wall. Numerical load data were estimated as the sum of all lateral487
contact forces generated at the interface nodes of the timber loading-beam with the488
rear adobe wall.489
Reasonable agreement is found between the experimental and numerical490
capacity curves, as in both cases the same trends are generally observed. The FE491
model successfully predicted the occurrence of a post-yield plateau and a gradual492
reduction of the load-bearing capacity. However, the abrupt drop in load resistance,493
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observed in the final loading cycle of the test, was not captured. This is likely due to494
the fact that the kinematic mechanisms forming at large deformation levels could not495
be accurately simulated though the use of a homogenized continuum. Such an496
approach does not allow the discrete modelling of units and joints and therefore it497
cannot capture the rocking motion of the façade and the triangular halves of the side498
walls that were detached from the rear part of the structure after LS4 due to cracking.499
Striking correspondence is found between the numerically derived lateral500
resistance and the maximum force measured on the actual structure. The ultimate501
displacement computed at the rear wall‟s control nodal point practically coincides502
with the one recorded during the laboratory tests. The out-of-plane translation of the503
façade and the in-plane translation of the side wall were slightly miscomputed: 24.7504
mm instead of the actual 26.6 mm for the façade; 28.0 mm instead of the actual 27.1505
mm for the side wall.506
The underestimation of forces at the ascending branches of the diagrams can be507
attributed to the isotropic fracture criterion adopted. Tension and shear tests508
conducted on mud brick specimens and masonry prisms revealed that the tensile509
strength of adobe itself and the frictional resistance along the joints can be at least an510
order of magnitude higher than the bonding strength [46]. Given that the adopted511
tensile strength of f t = 0.04 MPa actually refers to resistance against de-bonding of the512
masonry units, the bearing capacity implicitly assumed for the masonry medium in513
the direction parallel to the bed joints (where the response is governed by friction) is514
most probably underestimated. However, the formulation of the damaged plasticity515
constitutive law does not allow for the definition of separate tensile strengths along516
each direction. Another factor which may have influenced the simulated response is517
that no bonding strength (cohesion) was assigned to the roof rafter-brick interfaces.518
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Consequently, the effective transfer of forces among opposite longitudinal walls at519
low levels of deformation was precluded.520
4.3. General discussion of numerical results521
The numerical results obtained can be deemed as sufficiently accurate. Of522
particular importance is the adequacy of the developed FE model to predict the failure523
mechanisms sustained by the tested structure. Considering the inhomogeneous and524
random nature of earthen materials, the correlation between the numerical and525
experimental load-displacement data is also satisfactory. Besides, perfect agreement526
between the results of simulations and the outcomes of laboratory tests is usually527
regarded as a coincidence and should not be the mere objective of numerical528
modelling [52]. This is because experimental data possess inherent variability. In529
addition, despite applying an energy-based regularization of the masonry medium‟s530
tensile response, a slight mesh dependency of the FE analysis procedure possibly still531
existed, affecting, albeit to a limited degree, the simulation results.532
A number of simulations conducted in the process of model calibration, using533
different material properties (i.e. Young‟s modulus, Poisson‟s ratio, plasticity534
characteristics, tensile and compressive strengths, friction coefficient at the timber-535
masonry interface), revealed which modelling parameters are more critical. The536
Young‟s modulus assigned to adobe masonry determines the stiffness of the walls and537
defines the tensile cracking strain (the higher the Young‟s modulus the lower t he538
tensile cracking strain), thus affecting damage initiation. On the other hand, the539
masonry‟s Poisson‟s ratio and plasticity characteristics (i.e. dilation angle, flow540
potential eccentricity, ratio of initial equibiaxial compressive yield stress to initial541
uniaxial compressive yield stress, relation between second stress invariant on the542
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tensile meridian to that on the compressive meridian) have very limited influence on543
the FE results.544
No significant alteration of the results was observed when different compressive545
strength values in the range 1 < f c < 2.2 MPa were assumed. However, convergence546
difficulties were encountered when the compressive yielding stress fell below 0.05547
MPa. Analyses revealed that tensile response is the most crucial aspect of the548
simulation, since it dictates the lateral resistance and the displacement capacity549
predicted. It is worth noting that analogous conclusions concerning the sensitivity of550
numerical results to compression and tension parameters have been derived by Tarque551
et al. [23], who simulated adobe walls using the same damaged plasticity constitutive552
law. The friction coefficient assigned to the timber-masonry interface controls the553
transfer of forces between the two opposite longitudinal walls and determines whether554
shear sliding of the roof rafters will occur. Consequently, it also affects to some extent555
the displacements computed.556
5. Conclusions557
Laboratory testing of a 1:2 scaled model building revealed that, under lateral558
loading, damage in unreinforced adobe structures is primarily concentrated at the559
masonry walls, whereas stiffer load-bearing members (i.e. timber elements) remain560
practically intact. The prevalent failure mechanism that occurs is cracking due to561
inadequate bonding between the bricks and the mortar. Damage initiation can be562
influenced by stress augmentation at the corners of openings and at the abutments of563
timber members.564
Upon load removal, the cracks formed on adobe masonry walls close almost565
completely, leaving little indication of damage. Cracked sections act as planes of566
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weakness and crack re-opening is mobilized when load is re-applied. This highlights567
the cumulative effect that pre-existing damage poses on the structural behaviour of568
adobe buildings. It also indicates that particular attention should be paid during the in-569
situ inspection of earthen structures after seismic events.570
Experimental force-displacement data show that adobe masonry structures571
possess limited stiffness and can thus develop considerable deformations. Results also572
show that homogeneous structural response is lost as soon as stiffness degradation573
occurs and differential movement of the walls takes place. This verifies that absence574
of a stiff diaphragm configuration at roof level and insufficient interaction between575
the various load-bearing members pose a negative effect on the structural behaviour576
of masonry buildings.577
The damaged plasticity constitutive law adopted in this study has proven to be578
adequate for modelling adobe masonry as an idealized homogenized continuum.579
Provided that appropriate material data is used and that proper calibration is580
undertaken, FE models can capture the force-displacement response and the failure581
mode of adobe structures. The generic limitations of continuum modelling and the582
assumption of isotropic damage may introduce some inconsistencies to the outcomes583
of simulations, but do not preclude sufficient macroscopic approximation of the584
global structural behaviour.585
The sensitivity of numerical results to certain modelling parameters indicates586
that a more detailed database of information on the properties of adobe masonry is587
required. In particular, further experimental investigation should be undertaken to588
assess the stiffness characteristics of adobe masonry and to thoroughly examine its589
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response to tensile loads. The frictional and bonding properties at the interfaces590
between adobes and timber elements embedded in masonry should also be evaluated.591
Acknowledgements592
The funding granted by the University of Cyprus in the framework of research593
program „Experimental and Computational Investigation of the Structural response of594
Adobe Buildings‟ , as well as the financial support provided by the European Regional595
Development Fund and the Republic of Cyprus through the Cyprus Research596
Promotion Foundation in the framework of research program597
„ΕΠΙΧΕΙΡΗ ΕΙ /ΠΡΟΙΟΝ/0609/41‟ are gratefully acknowledged.598
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[50] Green DW, Winandy JE, Kretschman DE. Mechanical properties of wood. In: Wood
handbook: Wood as an engineering materia. General Technical Report FPL-GTR-113,
Madison WI: U.S. Department of Agriculture, Forest Service, Forest Products
Laboratory; 1999.
[51] Katsaragakis ES. Timber construction [In Greek]. Athens: NTUA Academic
Publications; 2000.
[52] Lourenço PB, Rots J, Blaauwendraad J. Continuum model for masonry: Parameter
estimation and validation. Journal of Structural Engineering. 1998;124(6):642-652.
600
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Figure Captions601
Fig. 1. General view of the 1:2 scaled model structure tested at the Structures602
Laboratory of the University of Cyprus.603
Fig. 2. (a) Test set-up used for the implementation of monotonic lateral loading on the604
1:2 scaled adobe masonry building. (b) LVDT positions. The displacement results605
presented in this paper refer to the monitoring points of LVDT1, LVDT3 and606
LVDT13.607
Fig. 3. Crack pattern recorded after subjecting the model structure to monotonously608
increasing horizontal loading tests: (a) rear wall interior surface, (b) rear wall exterior609
surface and (c) side walls.610
Fig. 4. Characteristic crack opening recorded: (a) at the centre of the rear wall‟s611
exterior surface near the structure‟s base and (b) at the exterior surface of the side612
wall‟s upper section at the vicinity of the opening‟s timber lintel. 613
Fig. 5. Load versus cumulative displacement data envelopes recorded at the upper614
sections of (a) the rear wall (LVDT13) and (b) the façade (LVDT1) and side615
(LVDT3) walls. Four limit states (LS1-4) are identified at different levels of616
deformation. The cracking damage recorded at the interior (upper inset diagram) and617
exterior (lower inset diagram) surface of the rear wall (a) and at the side wall (b) is618
presented for each limit state.619
Fig. 6. 3D FE model developed for simulating the structural response of the scaled620
adobe building subjected to lateral loading laboratory tests.621
Fig. 7. Compressive (a) and tensile (b) stress-strain response assigned to the622
homogenized adobe masonry medium.623
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33
Fig. 8. Plots of deformed mesh (deformation scale x 1) with contour representations624
of the lateral (along the y axis) displacement distribution.625
Fig. 9. Contour diagrams with the maximum principal plastic strains computed.626
Fig. 10. Comparison between the experimental force-displacement data envelopes and627
the corresponding FE results for the upper sections of (a) the rear wall, (b) the façade628
and (c) the side wall.629
630
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Fig. 1
ure 1-4ck here to download Figure: figs1_4.docx
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Fig. 2
(a)
(b)
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Fig. 3
(a)
(b)
(c)
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Fig. 4
(a)
(b)
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Fig. 5
LS2LS3
LS4
(a)
LS1
LS3
LS2
LS4
(b)
ure 5ck here to download Figure: fig5.docx
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Fig. 6
ure 6ck here to download Figure: fig6.docx
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Fig. 7
(a)
(b)
ure 7ck here to download Figure: fig7.docx
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Fig. 8
U, U2 (mm)+ 95.97+ 89.31
+ 82.65+ 75.98+ 69.32+ 62.66+ 55.99+ 49.33+ 42.66+ 36.00+ 29.34+ 22.67+ 16.01+ 9.346+ 2.682- 3.982- 10.65
U, U2 (mm)
+ 95.97+ 89.31+ 82.65+ 75.98+ 69.32+ 62.66+ 55.99+ 49.33+ 42.66+ 36.00+ 29.34+ 22.67+ 16.01
+ 9.346+ 2.682- 3.982- 10.65
ures 8-9ck here to download Figure: figs8_9.docx
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Fig. 9
PE Max. Principal(Avg: 75%)
+ 4.237e-02+ 3.972e-02+ 3.707e-02+ 3.443e-02+ 3.178e-02+ 2.913e-02+ 2.648e-02+ 2.383e-02+ 2.119e-02+ 1.854e-02+ 1.589e-02+ 1.324e-02+ 1.059e-02+ 7.954e-03+ 5.296e-03
+ 2.248e-03+ 0.000e+00
PE Max. Principal(Avg: 75%)
+ 4.237e-02+ 3.972e-02+ 3.707e-02+ 3.443e-02+ 3.178e-02+ 2.913e-02+ 2.648e-02+ 2.383e-02+ 2.119e-02+ 1.854e-02+ 1.589e-02+ 1.324e-02+ 1.059e-02
+ 7.954e-03+ 5.296e-03+ 2.248e-03+ 0.000e+00
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Fig. 10
(a)
(b)
(c)
ure 10ck here to download Figure: fig10.docx
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