2014 Laboratory Testing and FEM Analysis Adobe ENGSTRUCT-D-14-00490

8/18/2019 2014 Laboratory Testing and FEM Analysis Adobe ENGSTRUCT-D-14-00490

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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.

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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

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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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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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21

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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22

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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23

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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24

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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25

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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26

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

References599

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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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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

http://ees.elsevier.com/engstruct/download.aspx?id=492686&guid=28babbde-f919-4830-a0a3-22fd039886c9&scheme=1http://ees.elsevier.com/engstruct/download.aspx?id=492686&guid=28babbde-f919-4830-a0a3-22fd039886c9&scheme=1


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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

http://ees.elsevier.com/engstruct/download.aspx?id=492687&guid=5cb4e988-8389-4df2-bddd-0e0a37462577&scheme=1http://ees.elsevier.com/engstruct/download.aspx?id=492687&guid=5cb4e988-8389-4df2-bddd-0e0a37462577&scheme=1


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Fig. 6


http://ees.elsevier.com/engstruct/download.aspx?id=492691&guid=37348b4a-1453-4177-bc79-54b06a331a9c&scheme=1http://ees.elsevier.com/engstruct/download.aspx?id=492691&guid=37348b4a-1453-4177-bc79-54b06a331a9c&scheme=1


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Fig. 7

(a)

(b)


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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

http://ees.elsevier.com/engstruct/download.aspx?id=492693&guid=8338ca8a-1049-446c-8ff0-e08870fe6746&scheme=1http://ees.elsevier.com/engstruct/download.aspx?id=492693&guid=8338ca8a-1049-446c-8ff0-e08870fe6746&scheme=1


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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)

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2014 Laboratory Testing and FEM Analysis Adobe ENGSTRUCT-D-14-00490

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