Engineering Structures 80 (2014) 362–376

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Engineering Structures

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Laboratory testing and finite element simulation of the structuralresponse of an adobe masonry building under horizontal loading

http://dx.doi.org/10.1016/j.engstruct.2014.09.0080141-0296/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +357 22892202; fax: +357 22895322.E-mail address: charmpis@ucy.ac.cy (D.C. Charmpis).

Rogiros Illampas, Dimos C. Charmpis ⇑, Ioannis IoannouDepartment of Civil and Environmental Engineering, University of Cyprus, 75 Kallipoleos Str., P.O. Box 20537, 1678 Nicosia, Cyprus

a r t i c l e i n f o

Article history:Received 7 April 2014Revised 27 August 2014Accepted 1 September 2014Available online 29 September 2014

Keywords:Adobe masonryHorizontal loadingFinite element modelDamaged plasticityNon-linear analysis

a b s t r a c t

This paper is concerned with the calibration and validation of a numerical modelling approach for adobemasonry buildings under horizontal loading. The paper first reviews the state-of-the-art in experimentaland computational research of adobe structures and then presents results obtained from monotoniclateral loading laboratory tests on a 1:2 scaled unreinforced adobe masonry building. Through the exper-imental investigation conducted, useful conclusions concerning the initiation and propagation of crackingfailure are deduced. In addition, damage limit states at different levels of deformation are identified.Experimental results verify that the response of adobe structures to horizontal loads is critically affectedby weak bonding between the masonry units and mortar joints and by lack of effective diaphragmaticfunction at roof level. Based on experimental material data, a 3D finite element (FE) continuum modelis developed and calibrated to reproduce the test structure’s force–displacement response and mode offailure. An isotropic damaged plasticity constitutive law is adopted for the numerical simulation of adobemasonry and the use of appropriate modelling parameters is discussed. The FE analyses carried out revealthat the global structural behaviour is primarily influenced by the tensile response assigned to thehomogenized masonry medium. Results show that, despite its generic limitations and simplifications,FE continuum macro-modelling can approximate the structural behaviour of horizontally loaded adobemasonry construction with sufficient accuracy. In order to enrich the available information on the seismicbehaviour of adobe structures, the calibrated FE model is also subjected to time-history analysis using anaccelerogram recorded during a real earthquake.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Adobe masonry structures are encountered in almost everyregion of the world and are considered to possess significant his-toric and cultural value. At the same time, unreinforced adobemasonry is quite susceptible to seismic damage [1]. The strongseismicity of areas where a considerable number of earthen build-ings exists (i.e. wider Eastern Mediterranean region, South Asia,South America) renders the study of the behaviour of adobestructures under horizontal loads essential. The development ofstructural analysis methods that account for the specific character-istics of adobe masonry is also required to facilitate the implemen-tation of rational engineering assessment and design.

Up to date, several studies involving laboratory testing offull- and/or reduced-scale adobe structures have been conducted[2–19]. Emphasis has been primarily given on evaluating variousrepair/retrofitting techniques, rather than on providing extensive

data, which can be exploited for the calibration and validation ofnumerical analysis tools. Researchers who have developednumerical models of adobe masonry structures [20–29] havemainly performed conceptual analyses aiming to obtain qualitativeinformation regarding the response of typical traditional earthenbuildings. Detailed comparisons between simulation results andphysically measured aspects of structural behaviour (i.e. deforma-tion, load-resistance) are rather limited [23–25]. This indicates thatthere is a need for adopting a more integrated research approachthat will combine experimental and computational work on adobemasonry buildings, in order to develop reliable assessment proce-dures and analysis methods.

The present study aims to extend existing knowledge regardingthe structural behaviour of adobe buildings by contributingtowards the development of appropriate assessment proceduresand analysis methods. Hence, it utilizes the results of large-scalelaboratory tests to develop a finite element (FE) continuummacro-model capable of simulating the response of a horizontallyloaded unreinforced adobe masonry building with sufficientaccuracy. More specifically, for the purpose of validating the FE

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model, a 1:2 scaled replica of an existing single-storey traditionaladobe building was constructed and subjected to monotonic staticlateral loading tests. Masonry failure mechanisms (i.e. initiationand propagation of cracking) were recorded during the experimen-tal procedure, while damage limit states at different levels of defor-mation were identified.

In the framework of the numerical investigation, a detailed 3DFE model of the scaled building was developed. This was used forperforming non-linear analyses, aiming to macroscopically repro-duce the general response of the structure under test. For thenumerical representation of adobe masonry behaviour, a damagedplasticity constitutive law was adopted, while experimentallyderived material data were used as input parameters. The validityof the numerical results was verified both qualitatively and quan-titatively through comparisons with the experimental damage pat-terns and force–displacement curves. Numerical work did nothowever solely focus on the reproduction of the experimentalresults. A sensitivity analysis was also carried out to examinehow the various modelling parameters affect the simulation ofstructural response. The scope of the paper extends to the use ofthe calibrated FE model for performing non-linear dynamic analy-sis, thus acquiring useful information on the seismic behaviour ofadobe structures. Overall, this work represents a promising steptowards the numerical modelling of the seismic behaviour ofearthen constructions, while at the same time it identifies areaswhere further research is required.

2. Review of experimental and computational research onadobe structures

2.1. Experimental work

Most experimental data currently available regarding theresponse of adobe masonry construction has been obtained byexamining model structures before and after the implementationof repair/strengthening interventions.

Systematic testing of unreinforced adobe masonry structurestook place in the framework of various research projectsundertaken by the Pontifical Catholic University of Peru. Relevantexperimental work included static tilt tests on house modules[2], displacement-controlled cyclic tests on ‘I’-shaped wall config-urations [3] and shake table tests on single- [4–7] and two-storey[8] model buildings and vaulted structures [9,10]. In all cases, theresponse of unreinforced model structures was compared to thatof reinforced ones (i.e. structures incorporating timber ring beams,cane rods, steel wire meshes, geogrids, fibre-reinforced polymerstrips, tire straps, etc.).

Noticeable experimental research on the dynamic response ofunreinforced adobe masonry buildings was also carried out duringthe Getty Seismic Adobe Project. In the first phase of this project,1:5-scaled replicas of single-storey dwellings were subjected toimpact hammer and shake table tests before and after repairing/strengthening [11]. In the second phase of the same project [12],dynamic excitations based on real accelerograms were imposedon larger (1:2 scaled) models. At this phase, in addition to unrein-forced masonry structures, model buildings retrofitted with bondbeams, horizontal/vertical straps, local ties, centre-core rods andwooden roof diaphragms were also examined.

Dowling [13] conducted shake table tests on 1:2 scaled‘U’-shaped wall units and complete buildings to examine thedynamic behaviour of unreinforced adobe masonry construction.Along with plain unreinforced masonry structures, models incor-porating pilasters/buttresses, wire meshes, bamboo poles and tim-ber ring beams were also constructed and tested in this study. Theoutcomes obtained were used for proposing retrofitting solutions.

More recently, a real-scale ‘I’-shaped adobe wall was examinedat Aveiro University [14]. Following a number of cyclic lateral load-ing tests, the cracks formed in the masonry were injected with limemortar and a polymeric mesh was fixed on the surface of the wall.The repaired/retrofitted structure was subjected to further lateralloading tests.

Extensive literature on the response of strengthened/retrofittedadobe masonry buildings can also be found in [15–19], which pres-ent results from shake table tests and static horizontal loadingtests on 1:1.5 [15], 1:2.5 [16], 1:3 [18], 1:5 [15] and 1:10 [17,19]scaled model structures.

The main conclusion derived from the aforementioned tests isthat adobe masonry structures generally have limited capacity toresist horizontal loads. This is attributed to two factors: (a) poorbonding between the adobe bricks and the mortar joints, whichreduces the tensile strength of the masonry [4,11,14], and (b) lackof diaphragmatic function at roof level, which precludes effectivetransfer of loads among the load-bearing walls [11,12]. Under seis-mic action, out-of-plane failure, either due to extensive cracking ordue to detachment at cross-walls and overturning, prevails[4,11–13]. Integrated retrofitting systems can improve the poorseismic behaviour of unreinforced adobe masonry buildings, eitherby increasing their overall lateral resistance or by producing a con-finement effect, which reduces the risk of brittle collapse [12–19].

2.2. Numerical modelling and analysis

In contrast to experimental work, computational research onadobe masonry structures has not been as rigorous. Despite thefact that advanced analysis methods have been extensively usedfor the simulation of conventional masonry structures (i.e. struc-tures built with stone, fired clay bricks, concrete blocks, etc.), theapplication of numerical tools has not been meticulously studiedin the context of earthen construction.

Simulation of masonry structures can follow a macro- or amicro-approach. In the macro-approach, either distinct macro-elements are used to represent individual piers and spandrels, orthe masonry is treated as a fictitious homogeneous medium repre-sented by continuum finite elements. In the micro-approach, themasonry unit–mortar interfaces are considered as potentialcrack/slip planes, while the building blocks and the mortar areeither explicitly described (detailed micro-modelling) or repre-sented by repeated expanded cellular units interacting at theirboundaries (simplified micro-modelling).

Continuum FE models of adobe-wood buildings have beendeveloped by Che et al. [20]. These were subjected to elastic timedomain analysis, in order to examine their seismic response. Lineardynamic analyses by response spectra have also been conducted byGomes et al. [21] on 3D models of unreinforced and reinforcedadobe buildings.

Using experimental material data, Meyer [22] modified theHolmquist–Johnson–Cook model for concrete to capture the pres-sure and strain-rate-dependent non-linear behaviour of adobes.The formulated constitutive law was used for performing phys-ics-based penetration simulations on adobe targets.

Non-linear static and dynamic simulations on FE continuummodels composed of shell elements have been undertaken byTarque et al. [23–25]. These studies focused on approximatingthe macroscopic behaviour (mode of failure, displacements, etc.)of structures tested in the laboratory. Modelling parameters werecalibrated by matching numerical–experimental results. Bothorthotropic smeared cracking and isotropic damaged plasticityconstitutive laws were considered.

In addition to FE models of continua, Tarque et al. [23] exam-ined 3D micro-models of adobe walls loaded in-plane. The authorsassumed that the response of adobe bricks is elastic isotropic and

Fig. 1. (a) General view of the 1:2 scaled model structure tested at the StructuresLaboratory of the University of Cyprus. (b) A traditional monochoro makrynaridwelling located in Limassol, Cyprus. The model structure examined in this studyrepresents a building of this typology.

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assigned non-linear behaviour to the masonry joints via a com-bined crushing–shearing–cracking interface damage model.

A similar approach was adopted in [26,27] for performing a ser-ies of dynamic simulations with the purpose of developing seismicvulnerability functions. In these two studies, adobe masonry wasmodelled as an assemblage of rigid blocks connected by zero-thickness non-linear interfaces that could sustain tensile, shearor compressive damage.

Using non-linear anisotropic constitutive laws for the adobebricks and specially formulated viscoelastic elements for the joints,Cao and Watanabe [28] developed 3D models of a single-storeyadobe building. Through dynamic analyses, the above researchersinvestigated the earthquake response of adobe construction andverified the efficiency of wooden frame reinforcement.

Morales and Delgado [29] examined 2D models of single- andtwo-storey adobe walls. The models were composed of distinct ele-ments connected with springs and dashpots that acted as possiblefracture points. The seismic capacity of the simulated structureswas assessed by imposing reversing horizontal accelerations.

In light of the above, one can argue that research on the numer-ical simulation of adobe masonry has not been sufficiently system-atic and comprehensive, because it is usually not based onexperimental data and physical measurements. Although consider-able progress in this field has been recently achieved, further workis still required in order to develop valid analysis methods that canbe widely adopted in research-related and practice-orientedapplications.

The present paper aims to address this gap by specificallystudying the formulation of appropriate non-linear continuummodels based on the outcomes of laboratory tests. Motivated bythe lack of a complete and extensive experimental database onthe properties of adobe masonry constituents, large-scale staticlaboratory testing of a model building was undertaken in theframework of the present study, in order to calibrate the modellingparameters required for simulating the response of adobestructures to lateral loading. Unlike most relevant studies, whichconsider the use of shell element models of continua for thenon-linear representation of masonry, this paper discusses thedevelopment and analysis of 3D FE models composed ofhexahedral ’brick’ elements. This approach enables a more detailedexamination of the numerically predicted damage evolutionand allows for the identification of localized failure mechanismsdeveloping at the surface of the masonry and of cracks extendingthroughout the whole width of a wall.

3. Laboratory testing of an adobe model building

3.1. Construction of model building

For investigating the structural response of adobe masonrybuildings, a 1:2 scaled replica of a traditional Cypriot dwellingwas constructed and tested at the Structures Laboratory of theUniversity of Cyprus (Fig. 1a). The model structure represents amonochoro makrynari, which is the simplest and oldest typologyof vernacular architecture encountered on the island [30](Fig. 1b). Monochoro makrynari buildings are rectangular single-roomed structures with a longitudinal interior space that is usually7–15 m long. Their width is limited by the available length of theroof’s timber rafters and can vary from 2.5 m to 4.5 m.

The model structure’s walls were 220 mm thick and were builtwith adobe bricks measuring (height �width � length)30 � 150 � 220 mm3, which were obtained from a local producer.The bricks’ size implies a scaling-down from the original dimen-sions of local adobes (height �width � length = 50 � 300 �450 mm3) by a factor of approximately 2. For the production of

the scaled-down adobes, soil (composition: 78–91% silt and clay,8–18% sand, 1–4% gravel) and finely chopped straw fibres(3–25 mm in length; 20–40% per unit volume) were mixed withwater to plastic consistency in a planetary mixer [31]. The mixturewas left to ferment for 1–3 days and was then cast into moulds.The end-products were laid on a flat concrete surface and wereallowed to dry under the sun for at least 3 days before beingtransported to the laboratory.

For the construction of the model structure, earth mortar (com-position soil:straw:water � 200:6:100 w/w) prepared in the labo-ratory was also used. This was composed by the same rawmaterials as the adobe bricks and was allowed to ferment indoorsfor 2 days before being used. Following the island’s traditionalbuilding techniques, the masonry was built in a running bond pat-tern and the joint thickness was consistently kept below 10 mm.

The model structure was securely bolted on the laboratory con-crete floor. The structure’s external dimensions were (width �length) 1.75 � 3.60 m2. The height of the front elevation was1.50 m and that of the opposite rear wall was 1.65 m. A door mea-suring 1.10 m in height and 0.70 m in width was formed on thefaçade. Two openings with dimensions 0.55 � 0.55 m2 were alsocreated on the two side walls. A triangular notch 0.22 m wideand 0.18 m high was formed on the rear wall to simulate theventilation notches encountered in local vernacular buildings.

It was presumed that the stone masonry foundations of tradi-tional earthen structures preclude horizontal translation of thewalls at ground level, but allow bending. Therefore, the first layerof adobe bricks was simply set with the application of earth

Fig. 2. (a) Test set-up used for the implementation of monotonic lateral loading onthe 1:2 scaled adobe masonry building. (b) LVDT positions. The displacementresults presented in this paper refer to the monitoring points of LVDT1, LVDT3 andLVDT13.

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mortar. Horizontal displacements at this level were constrained bytimber elements installed along the structure’s perimeter. At thecross-walls, overlapping bricks were laid upon each other toachieve adequate interconnection.

Above all openings, lintels consisting of two jointed timberbeams, each with a cross-section of 85 � 85 mm2, were installed;these were set into the masonry using gypsum mortar. The roofstructure comprised of a 20 mm-thick wooden panel nailed uponnine timber rafters (45 � 90 mm2 in cross-section) that spannedthe space between the two opposite longitudinal walls. This woo-den panel represented the roof under-layer that in local vernacularbuildings consisted either of reed matting, timber planks nailedorthogonally to the rafters or even tightly packed dried twigs andshrubs. Above this, a series of ceramic tiles (pitched roofs) or alayer of compressed clay-straw mixture 100–200 mm thick (flatroofs) was usually set. In the model structure, the weight of theroof covering was simulated using uniformly placed adobes ontop of the roof panel. It should be noted that, although the roofstructure of the model building is itself more rigid compared tocertain forms of traditional construction, this could not signifi-cantly influence the results of the tests, because the transfer offorces between the walls and the roof members is solely dictatedby the properties at the rafters–masonry interfaces. In the testedstructure, the representation of the latter is an exact reproductionof the traditional building technique, with the roof rafters being setinto the masonry with gypsum mortar.

3.2. Test procedure and instrumentation

Load testing of the model building commenced nine weeks afterthe completion of its construction to ensure adequate curing of thejointing mortar and settling of the walls. The experimental proce-dure involved the application of monotonically increasing lateralforces at successive loading–unloading steps to record the gradualevolution of damage and to assess the maximum lateral resistanceof the structure. During each test cycle, the exerted load was pro-gressively increased up to the point where noticeable damage (i.e.severe cracking of the masonry walls) developed. Afterwards, theapplied force was completely removed, the remaining displace-ment was recorded and a new test cycle was initiated.

Loading was applied on the rear wall using a steel hydraulic jackwith 60 kN maximum capacity (Fig. 2a). The load imposition sys-tem was supported by a rigid steel reaction frame (see backgroundof Fig. 1a). To achieve a more even load distribution, a timber beamstrengthened at its centre was used along the rear wall (Fig. 2a).This timber loading beam was 45 mm thick and 3.80 m long. Thelength of the central strengthened section was 1.90 m, while itstotal thickness was 90 mm. It is worth mentioning that the hydrau-lic jack accommodated a swivel head that enabled it to stay in con-tact with the loading beam when out-of-plane bending wasinduced. Loading was applied at approximately 2/3 of the wall’sheight.

Linear Variable Displacement Transducers (LVDTs) (ran-ge ± 50.8 mm, accuracy ± 0.25%) were placed at 15 different posi-tions on the model structure to record displacements (Fig. 2b).Emphasis was given in monitoring the out-of-plane movement ofthe longitudinal walls and the in-plane bending of the side walls.Therefore, one of the side walls and the two adjacent halves ofthe longitudinal walls were instrumented. Indeed, during the testsit was confirmed that there was close analogy between theresponses of the half-structure’s sections examined and of theparts symmetric to them. LVDTs were also placed at the structure’sbase to verify that no translation or rotation took place. All mea-surements were recorded automatically via a data acquisition sys-tem. Digital cameras were also used for monitoring failureevolution and crack opening–closing.

A total of 10 monotonic loading–unloading cycles were imple-mented. The forces imposed on the structure during all loading–unloading cycles in relation to the cumulative displacements mea-sured at the upper sections of the rear wall (LVDT13), the façade(LVDT1) and the side wall (LVDT3) are given in Fig. 3. Cumulativedisplacement values were computed by adding to the recordings ofeach individual test cycle the permanent deformations noted afterthe completion of all previous cycles. The experimental procedurewas terminated when a significant reduction of the lateral resis-tance of the model structure was detected.

3.3. Experimental results and discussion

3.3.1. Crack patternsThe crack pattern recorded after the completion of the experi-

mental procedure is shown in Fig. 4. Damage modes were almostidentical during all tests, with most cracks developing during thefirst four load cycles. Subsequent load cycles led to re-opening ofpre-existing fissures and increased crack widths.

Damage was noted at the rear and the two side walls, but not atthe façade or at any of the timber members. Damage localizationreveals stress concentrations and implies that the load-bearingmembers of the model failed to react as a homogeneous assem-blage of structural elements (i.e. as a fully connected structuralsystem). In addition, it indicates lack of diaphragmatic functionat the roof level.

Out-of-plane bulging of the rear wall caused the formation of amajor horizontal crack at the interior of the structure, along the

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Fig. 3. Load and cumulative displacement data recorded at the upper sections of (a)the rear wall (LVDT13), (b) the façade (LVDT1) and (c) the side wall (LVDT3) duringsuccessive loading–unloading test cycles. Characteristic data points ( , , ),which correspond to the maximum force magnitudes recorded at different levels ofdeformation and which have been used to form the force–displacement envelopesshown in Fig. 6, are noted in the diagrams. (For interpretation of the references tocolour in this figure legend, the reader is referred to the web version of this article.)

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line of loading (Fig. 4a). Due to overstressing at the load impositionpoint, diagonal cracks extending from the centre of the walltowards its two lower sides were generated below the aforemen-tioned horizontal fissure. In addition, a ‘V’-shaped cracked sectionwas formed between the triangular ventilation notch and the fourcentral roof rafters.

At the exterior surface of the rear wall, a continuous horizontalcrack occurred between the 7th and 8th rows of adobe bricks(Fig. 4b). Towards the two sides, because of the restrain imposedby the side walls, this crack was inclined. Less severe crackingwas recorded below this zone. Furthermore, failure of the gypsummortar joints at the roof rafter abutments and subsequent slidingof the timber members were noted. As the rear wall was subjectedto significant out-of-plane deformations, stress concentrationswere generated at the areas where the masonry was in contactwith the much stiffer timber rafters. This led to horizontal crackingat the vicinity of the roof supports; cracking extended diagonallywhere restrain by the two side walls became effective.

The mode of failure sustained by the two side walls was mainlycharacterized by the formation of diagonally orientated shear

cracks that radiated out of the two openings’ corners and propa-gated through the brick joints in a stepped pattern (Fig. 4c). Thesecracks extended throughout the whole width of the side walls.Damage at the upper section of the walls spread towards the inter-section with the rear wall, eventually joining with the external rearwall cracks that formed just below the roof rafters. During the twofinal test cycles, out-of-plane torsional movement of the side walls’upper cracked sections was also recorded.

In all cases, failure was characterized by loss of bondingbetween the masonry units; no damage of the adobe bricks wasreported. During the loading process, as the opening of the cracksincreased, fragments of mortar fell from the joints (e.g. see close-up of cracked adobe masonry in Fig. 5). This indicates that theproperties of the unit–mortar interface pose a critical effect onstructural behaviour and verifies that the failure mechanismsencountered in adobe structures are primarily a product of weakadhesion among the adobes [4,11,32,33]. Crack opening was signif-icant and ranged from 5 to 20 mm (Fig. 5). Interestingly enough,when loading was removed, the fissures formed closed almostcompletely and very limited signs of damage were visible. How-ever, cohesion between the masonry units at these areas had beenlost and when load was exerted again, re-opening of the cracks wasmobilized.

Despite the fact that the experimental set-up enabled only theimposition of static forces, the recorded modes of damage corre-spond well to those observed in dynamic tests and to those sus-tained by adobe buildings during earthquakes. Crack patternssimilar to the ones observed at the rear wall of the model buildinghave been reported in [1,3,11,12,34,35]. Diagonal shear cracking ofadobe walls loaded in-plane has been noted in several other exper-imental [3,11,14] and field [1,36] studies. However, due to the uni-lateral and monotonic load imposition process, separation betweenintersecting walls did not occur, although such a response of unre-inforced adobe masonry to seismic loads is rather common[4,16,34,36]. Moreover, the lack of diaphragmatic roof function,caused by the sliding failure of the rafter supports, did not enablethe effective transfer of forces from the rear wall to the façade.Therefore, as opposed to a dynamic state where all sections per-pendicular to the direction of the principal action would sustainreversing out-of-plane bending loads, in the tests conducted here,movement of the façade was dictated by the in-plane drift of theside walls and therefore no noticeable damage (i.e. cracking and/or detachment) developed.

3.3.2. Force–displacement response and limit statesForce versus cumulative displacement data envelopes obtained

from the implementation of the 10 test cycles are presented inFig. 6. The envelopes were formed using characteristic data points,which correspond to the maximum force magnitudes recorded atdifferent levels of deformation (Fig. 3).

Based on the structural response recorded and the correspond-ing state of damage observed, four limit states (LS1-4) can be iden-tified. Up to approximately 5% of its total displacement capacityand 75% (10.6 kN) of its maximum lateral resistance (LS1), thestructure performed with no or negligible damage and the variousload-bearing members maintained a consistent response to hori-zontal loading. The displacements recorded at the model struc-ture’s walls during this stage were rather uniformly distributed.They lied in the region of 1.8 mm and correspond to approximately0.11% of drift (estimated as horizontal displacement divided by themonitoring point’s vertical distance from the building’s base).

Above the 10.6 kN threshold, stiffness degradation started todevelop and cracking damage was initiated at the interior of the rearwall and at the two side walls. The structure, however, could stillfunction as a homogeneous structural system up to 11% of its totaldisplacement capacity and 85% (12 kN) of its maximum lateral

Fig. 4. Crack pattern recorded after subjecting the model structure to monotonously increasing horizontal loading tests: (a) rear wall interior surface, (b) rear wall exteriorsurface and (c) side walls.

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resistance (LS2). A co-instantaneous movement of 4 mm and alateral drift of 0.26% were recorded at the upper sections of thewalls monitored. It should be noted that the first and second limitstates were already reached by the end of the initial test cycle.

When the displacement induced exceeded 11% of the total dis-placement capacity, interaction among the structure’s load-bearingmembers was effectively lost and differential movement of themasonry walls took place. This was accompanied by further crack-ing, permanent distortion and considerable reduction of the overallstiffness. Such highly non-linear response continued until the loadexerted became equal to the maximum force the structure couldwithstand (14.2 kN) and the displacement induced was 26% ofthe total deformation capacity (LS3). During this stage, sliding fail-ure of the roof rafters’ supports and cracking of the rear wall’s basewere observed. Furthermore, the cracks previously formed on the

rear wall’s interior and on the two side walls extended in length.Cumulative displacements at the façade and the side wall were7 and 7.7 mm, respectively. In terms of lateral drift, these valuescan be interpreted as 0.5%. Cumulative displacement at the centreof the rear wall was 21.5 mm and accounts for 1.4% lateral drift.The aforementioned data were obtained after the completion ofthe first four test cycles.

After LS3 and up to the last limit state (LS4), the structure wascharacterized by depletion of its overall stiffness and by inability tosustain higher levels of loading. Relatively small augments of theimposed load led to large in- and out-of-plane drifts. Moreover,significant inelastic deformations were generated, while crackopening eventually attained its maximum value (�20 mm). AtLS4, the cumulative horizontal translation of the side wall was25.2 mm, while that of the façade was 23.8 mm. The lateral drift

Fig. 5. Characteristic crack opening recorded: (a) at the centre of the rear wall’sexterior surface near the structure’s base and (b) at the exterior surface of the sidewall’s upper section at the vicinity of the opening’s timber lintel.

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at these sections was estimated as 1.6%. The total movement of therear wall was 84.9 mm and the lateral drift at its central sectionwas 5.7%.

After LS4, at the last loading cycle, an abrupt drop in the struc-ture’s lateral resistance occurred. The sections of the two side wallsabove the diagonal shear cracks were isolated by cracking damage.As a result, the façade and the adjacent triangular halves of the twoside walls were detached from the rear part of the building. Theload-bearing system was practically split into two independentparts that could only transfer forces between them through contactpoints. Under the application of load, the kinematic mechanismformed was mobilized causing rocking motion of the frontal partand reducing the effective resisting area. Although the overallstrength fell to a residual value, total or partial collapse did notoccur. Nevertheless, crack formation and/or growth at this statecould have been critical, if the relative displacement inducedacross the planes of weakness had been larger.

Using experimental results from cyclic load tests on full-scale‘I’-shaped adobe walls, Figueiredo et al. [14] and Tarque et al.

[37] defined damage limit states similar to those reported in thisstudy. The experimentally recorded maximum load resistanceaccounts for approximately 30% of the model building’s self-weight. This is in total agreement with the data obtained by Bened-etti et al. [38] from extended dynamic experiments on unrein-forced masonry buildings constructed with fired clay bricks.However, it is lower than the 34–100% base shear force-to-weightratios reported by researchers who performed shake table [4,8,39]and static tilt [40] tests on adobe model structures.

Despite being rather conservative, the load-bearing capacitydetermined in the present work cannot be injudiciously adoptedas a safe indicator for the seismic behaviour of unreinforced adobemasonry construction. This is because the monotonic imposition offorces during the testing procedure did not enable the develop-ment of certain failure mechanisms (e.g. detachment of intersect-ing walls) that would drastically reduce lateral resistance in theevent of dynamic excitation. In addition, the application of revers-ing horizontal accelerations could cause the out-of-plane failure ofthe longitudinal walls, either by detachment and overturning or bydiagonal and vertical cracking [34], at significantly lower levels ofdeformation. Hence, it may be argued that the maximum lateraltranslation measured during the tests is overestimated and doesnot realistically represent the displacement capacity of unrein-forced adobe masonry structures when these are subjected to

R. Illampas et al. / Engineering Structures 80 (2014) 362–376 369

seismic action. Nevertheless, the main purpose of the experimentalprocedure was not to assess the structure’s seismic capacity, but toobtain results that could be exploited for the calibration and vali-dation of FE models.

4. Numerical simulation of the response of the adobe modelbuilding

4.1. Finite element modelling and analysis

For simulating the response of the tested structure, a 3D FEmodel was developed in Abaqus/CAE (Fig. 7) [41]. The various partscomprising the experimental set-up were modelled as individualbodies interacting with each other. Hence, the FE model includeddifferent representations for the adobe masonry walls, the open-ings’ lintels, the roof and the timber loading-beam. Since the testconfiguration is symmetric, only half the structure was numeri-cally examined. All bodies were discretized using 8-noded 3D lin-ear brick elements (C3D8); for masonry elements, the sides were40 ± 4 mm long. In total, the mesh generated consisted of 47,808

Fig. 7. 3D FE model developed for simulating the structural response of the scaledadobe building subjected to lateral loading laboratory tests.

elements and 68,139 nodes, resulting in 169,515 degrees offreedom.

Adobe masonry was numerically handled in the context of amacro-modelling strategy. It was thus treated as a fictitious homo-geneous continuum and no distinction between masonry units andmortar joints was made. For simulating its behaviour, the concretedamaged plasticity constitutive model [41–43] was adopted. Thisis a continuum, plasticity-based, isotropic damage model thatassumes two main failure mechanisms: tensile cracking and com-pressive crushing. The material admissible stress field is boundedby a yield surface that is controlled by hardening variables linkedto cracking and crushing strains.

Most parameter values used for the application of the damagedplasticity constitutive law were based on experimental data. Thedensity of adobe masonry was set as q = 1300 kg/m3. This was esti-mated following simple gravimetric measurements on the adobesused to construct the model structure. Poisson’s ratio (m = 0.3)was evaluated from the deformations recorded during the com-pressive strength testing of a stack-bonded adobe masonry prism,as the ratio of transverse to axial strains.

Compressive stress–strain response was described using thepolynomial relation developed by Illampas et al. [31] for adobebricks (Fig. 8a). The Young’s modulus was computed from theassigned stress–strain response as a secant modulus up to the

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.00 0.10 0.20 0.30 0.40 0.50

Stre

ss (M

Pa)

Strain (mm/mm)

0.00

0.01

0.02

0.03

0.04

0.05

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Stre

ss (M

Pa)

Strain (mm/mm)

(a)

(b)

Fig. 8. Compressive (a) and tensile (b) stress–strain response assigned to thehomogenized adobe masonry medium.

370 R. Illampas et al. / Engineering Structures 80 (2014) 362–376

yielding point; E = 18 MPa. Compressive strength (fc = 1.2 MPa) andstrain at peak compressive stress (ecu = 0.1 mm/mm) were definedfrom the average results of laboratory tests on stack-bondedprisms [44]. Considering that adobes possess a granular structureand thus have limited elastic response to compression [22], mate-rial non-linearity was assumed after 5% of the compressivestrength.

In tension, linear behaviour up to the maximum allowablestress and post-peak softening were assumed (Fig. 8b). Inelastictensile stress–strain response was described using the exponentialfunction developed by Lourenço [45]:

rt ¼ f t exp �hft

Gfeck

t

� �: ð1Þ

In the above equation, ft is the tensile strength of masonry, Gf is thetensile fracture energy, eck

t is the tensile cracking strain and h is thecharacteristic crack length.

Tensile strength was set as ft = 0.04 MPa, following the diagonaltension testing of an adobe wallette. Regarding the tensile fractureenergy Gf of the homogenized masonry, direct tension tests onadobe couplets in [46] yielded a mean value of Gf = 4.5 N/m. Theaverage tensile strength of the specimens examined in [46] was0.01 MPa; assuming a linear analogy between the bearing capacityand the fracture energy, the value of Gf = 18 N/m was adopted forft = 0.04 MPa.

The characteristic crack length h was defined as [47,48]:

h ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffihxhyhz

3q

: ð2Þ

In the above equation, hx, hy and hz are the element’s lengths alongthe x, y and z axes. The element size during meshing was selected tosatisfy the energy criterion given by:

h 6Gf E

f 2t

: ð3Þ

Theoretically, through the definition of the characteristic cracklength, mesh-dependency of numerical results was treated. How-ever, the use of this parameter implies that, in non-structuredmeshes, the elements with larger aspect ratios will tend to haverather different behaviour, depending on the direction in whichthey crack. This effect may have introduced some mesh sensitivityto the results presented in this study, despite making efforts touse elements with aspect ratios close to one, especially in areaswhere tensile damage was expected.

For the rate at which the hyperbolic flow potential approachesits asymptote (e = 0.1) and the ratio between the initial equibiaxialand the initial uniaxial compressive yield stresses (rb0/rc0 = 1.16),the default values suggested in [41] were adopted. The plasticityparameter, which relates the second stress invariant on the tensilemeridian to the equivalent invariant on the compressive meridian,was set as Kc = 0.8, in line with the recommendations of [41] forsoils modelled with a Drucker–Prager yield function. Based on[25] and [49], a very low dilation angle w = 1� was selected.

Since no damage or considerable deformation was observedduring the experimental procedure in any of the timber members(i.e. lintels, rafters, loading-beam, roof panel), these were all mod-elled using linear elasticity constitutive laws. In addition, it wasassumed that the mechanical properties of timber are isotropic.The material parameters used were drawn from the literature[50,51] as follows: (a) wood panel – density, q = 380 kg/m3;Young’s modulus, E = 8000 MPa; Poisson’s ratio, m = 0.2 and (b)timber lintels, rafters and loading-beam – density, q = 670 kg/m3;Young’s modulus, E = 7000 MPa; Poisson’s ratio m = 0.3.

At the areas where the masonry was in contact with the timbermembers, contact pairs were formed and surface to surface inter-actions were defined via master–slave associations. In any contact

pair, the master surface was chosen to be the one of the timber ele-ment, as this belonged to a structural component that is stifferthan the masonry walls. When under compression, interacting sur-faces were assumed to remain in contact; thus, any pressure couldbe transmitted across the interfaces. When the contact pressurereduced to zero, separation of the surfaces took place and no trans-fer of tensile stresses across interfaces was allowed. To simulatethe behaviour hereby described, a ‘‘hard’’ contact pressure–over-closure relationship [41] was defined in the normal direction.

In the tangential direction, a finite-sliding formulation [41]based on the Coulomb friction theory was used. The Coulomb fric-tion model available in Abaqus/CAE cannot account for cohesionamong interacting surfaces and computes the shear stress at whichsliding initiates (scrit) simply as a function of the contact pressure(p) and the coefficient of friction (l) between the surfaces:

scrit ¼ lp: ð4Þ

At the interfaces between the masonry and the opening lintels andthe masonry and the roof rafters, a friction coefficient l = 0.5 wasspecified. This value was based on the data reported in [33], which,however, do not refer to the frictional properties of timber elementsembedded in adobe masonry, but to the friction developed betweenthe masonry units and joints of adobe walls. Frictionless sliding(l = 0) was assumed to take place between the masonry and theloading-beam and the masonry and the roof panel.

All nodes at the base of the walls were considered to be pinned.Horizontal kinematic constraints were imposed at the perimeternodes affected by the timber elements, which were installed inthe actual structure to retain lateral movement at the base. Atthe area where the hydraulic jack was in contact with the timberloading-beam, constraints precluding translation along the x andz axes were imposed. Movement in the x direction and rotationsaround the y and z axes were not allowed along the plane ofsymmetry.

The weight of the adobes placed on the roof was evenly distrib-uted to the roof panel as an additional body force. Horizontal loadswere applied in the form of lateral displacements at the nodes ofthe timber loading-beam in contact with the jack. The amplitudeof the lateral displacements was formulated according to thecumulative displacement data recorded during the laboratorytests.

The numerical solution process was completed in two succes-sive steps. At the initial step, the dead loads were incrementallyimposed. At the second step, the lateral displacements at thejack-loading beam interface were incrementally enforced at timeintervals ranging from 1 � 10�19 to 1 � 10�4 s over the 1 s analysisperiod. In both cases, a general non-linear static procedurewith automatic stabilization was implemented, adopting the fullNewton solution scheme. The effect of geometric non-linearitywas accounted for in all numerical steps.

4.2. Comparison between experimental–numerical results

Fig. 9 shows contour representations of the displacements com-puted in the y-direction. Results show that the FE model captureswell the deformed shape of the structure. As expected, the maxi-mum lateral displacement occurs at the rear wall, at the levelwhere loading was applied. In line with the experimental observa-tions, the out-of-plane movement of the façade is dictated by thein-plane drift of the side wall. Furthermore, displacements alongthe height of the façade display a linear increase towards the wall’stop. The backwards movement predicted at the rear central part ofthe side wall is verified by experimental measurements and isattributed to out-of-plane bending and subsequent torsion of thissection.

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

Fig. 9. Plots of deformed mesh (deformation scale � 1) with contour representations of the lateral (along the y-axis) displacement distribution.

R. Illampas et al. / Engineering Structures 80 (2014) 362–376 371

In order to obtain the graphical visualization of the numericallypredicted damage pattern of Fig. 10, it was assumed that the direc-tion of the vectors normal to the crack planes is parallel to thedirection of the maximum principal plastic strains [41,42]. TheFE model adequately captured the structure’s mode of failure, bothin terms of damage distribution and in terms of crack initiation andpropagation.

The onset of tensile failure during the simulation occurred atthe upper central section of the rear wall’s interior side. The plasticstrain magnitude at this point eventually attained the highest com-puted value, coinciding with the location where the maximumcrack opening of approximately 20 mm was observed during thelaboratory tests. Crack propagation was rapid, with plastic strainsspreading across a horizontal band, parallel to the loading beam.Almost co-instantaneously, tensile failure was initiated at thetwo opposite corners of the side wall’s window opening. The con-centration of significantly high tensile stresses in this area pro-duced a diagonal distribution of plastic strains, similar to thecrack pattern observed on the tested building.

The gradual increase of the imposed load led to the formation ofplastic strains that followed inclined paths on the interior surfaceof the rear wall. As in the case of the actual model building, damageextended from the principal horizontal line of failure towards theupper and lower sections of the wall. Furthermore, horizontaland diagonal cracking at the exterior base of the rear wall andpropagation of basal damage to the side wall were wellreproduced.

The development of horizontal cracks at the vicinity of the roofrafter supports was also adequately approximated. However,unlike experimental observations, plastic strains in this area didnot extend to the side wall and did not intersect with the crackappearing above the window’s lintel. Instead, a near-vertical crackoccurred at the upper rear section of the side wall. This inconsis-tency is attributed to overestimation of the side wall’s out-of-planetorsional displacement by the FE analysis.

Fig. 11 compares the outcomes of the FE analysis with theexperimentally derived force–displacement data envelopes forthe upper sections of the rear wall, the façade and the side wall.

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

Fig. 10. Contour diagrams with the maximum principal plastic strains computed.

372 R. Illampas et al. / Engineering Structures 80 (2014) 362–376

Numerical load data were estimated as the sum of all lateral con-tact forces generated at the interface nodes of the timber load-ing-beam with the rear adobe wall.

Reasonable agreement is found between the experimental andnumerical capacity curves, as in both cases the same trends aregenerally observed. The FE model successfully predicted the occur-rence of a post-yield plateau and a gradual reduction of the load-bearing capacity. However, the abrupt drop in load resistance,observed in the final loading cycle of the test, was not captured.This is likely due to the fact that the kinematic mechanisms form-ing at large deformation levels could not be accurately simulatedthough the use of a homogenized continuum. Such an approachdoes not allow the discrete modelling of units and joints and there-fore it cannot capture the rocking motion of the façade and the tri-angular halves of the side walls that were detached from the rearpart of the structure after LS4 due to cracking.

Table 1 presents the experimental and numerical force anddisplacement values recorded at all monitoring points for the

previously identified damage limit states (LS1-4) and the near-fail-ure condition reached after the completion of the horizontal load-ing tests. Striking correspondence is found between thenumerically derived lateral resistance and the maximum forcemeasured on the actual structure. The ultimate displacement com-puted at the rear wall’s control nodal point practically coincideswith the one recorded during the laboratory tests. The out-of-planetranslation of the façade and the in-plane translation of the sidewall were slightly miscomputed: 25.2 mm instead of the actual26.6 mm for the façade; 28.0 mm instead of the actual 27.1 mmfor the side wall.

The underestimation of forces and overestimation of displace-ments at the ascending branches of the diagrams can be attrib-uted to the isotropic fracture criterion adopted. Tension andshear tests conducted on mud brick specimens and masonryprisms revealed that the tensile strength of adobe itself and thefrictional resistance along the joints can be at least an order ofmagnitude higher than the bonding strength [46]. Given that

0

2

4

6

8

10

12

14

16

0 10 20 30 40 50 60 70 80 90 100

Load

(kN

)

Cumulative Displacement (mm)

Experimental

Numerical

0

2

4

6

8

10

12

14

16

0 3 6 9 12 15 18 21 24 27 30

Load

(kN

)

Cumulative Displacement (mm)

Experimental

Numerical

0

2

4

6

8

10

12

14

16

0 3 6 9 12 15 18 21 24 27 30

Load

(kN

)

Cumulative Displacement (mm)

Experimental

Numerical

(a)

(b)

(c)

Fig. 11. Comparison between the experimental force–displacement data envelopesand the corresponding FE results for the upper sections of (a) the rear wall, (b) thefaçade and (c) the side wall. The data points corresponding to limit states LS1-4 arenoted on both the experimental and numerical curves.

R. Illampas et al. / Engineering Structures 80 (2014) 362–376 373

the adopted tensile strength ft = 0.04 MPa actually refers to resis-tance against de-bonding of the masonry units, the bearing capac-ity implicitly assumed for the masonry medium in the directionparallel to the bed joints (where the response is governed by fric-tion) is most probably underestimated. However, the formulationof the damaged plasticity constitutive law does not allow for thedefinition of separate tensile strengths along each direction.Another factor which may have influenced the simulatedresponse is that no bonding strength (cohesion) was assigned tothe roof rafter–brick interfaces. Consequently, the effective trans-fer of forces among opposite longitudinal walls at low levels ofdeformation was precluded.

4.3. General discussion of numerical results

The numerical results obtained can be deemed as sufficientlyaccurate. Of particular importance is the adequacy of the devel-oped FE model to predict the failure mechanisms sustained bythe tested structure. Considering the inhomogeneous and randomnature of earthen materials, the correlation between the numericaland experimental load–displacement data is also satisfactory.

Besides, perfect agreement between the results of simulationsand the outcomes of laboratory tests is usually regarded as a coin-cidence and should not be the mere objective of numerical model-ling [52]. This is because experimental data possess inherentvariability. In addition, despite applying an energy-based regulari-zation of the masonry medium’s tensile response, a slight meshdependency of the FE analysis procedure possibly still existed,affecting, albeit to a limited degree, the simulation results.

In the process of model calibration, a number of simulationsusing each time a different set of material properties (i.e. Young’smodulus, Poisson’s ratio, plasticity characteristics, tensile andcompressive strengths, friction coefficient at the timber–masonryinterface) were conducted as a kind of sensitivity analysis to deter-mine which modelling parameters are more critical. In each ofthese simulations, a single parameter was modified, while all otherparameters retained the values given in Section 4.1.

The masonry’s Young’s modulus was varied within the range15 < E < 70 MPa by specifying different strains at peak compressivestress to change the secant modulus of the compressive stress–strain curve up to the yielding point. As the magnitude of theYoung’s modulus determines the stiffness of the walls, a significanteffect on the computed displacements and deformations was notedwhen varying E. Damage initiation was also affected due to the factthat the Young’s modulus is used in the definition of the tensilecracking strain (the higher the Young’s modulus the lower the ten-sile cracking strain). Consequently, adopting values of E > 35 MPadid not improve the prediction of displacements up to LS2. Instead,premature tensile cracking of the side walls occurred and the over-all deformation capacity of the structure was significantlyunderestimated.

On the other hand, the masonry’s Poisson’s ratio and plasticitycharacteristics proved to have very limited influence on the FEresults. For these parameters, the following sets of values wereconsidered: Poisson’s ratio v = 0.1 and 0.3; dilation angle w = 1�and 13�; eccentricity e = 0.1 and 0.2; ratio rb0/rc0 = 1.16 and1.25; parameter Kc = 0.667 and 0.800.

No significant alteration of the results was observed whendifferent compressive strength values in the range 1 < fc < 2.2 MPawere assumed. However, convergence difficulties were encounteredwhen the compressive yielding stress fell below 0.05 MPa.Analyses with tensile strength values in the range 0.01 < ft < 0.1 MParevealed that the employed tensile stress–strain relation (Fig. 8b)is the most crucial aspect of the simulation, since it dictates theoverall lateral resistance and displacement capacity predicted.The increase of the masonry’s tensile strength from 0.04 to0.1 MPa (along with an analogous increase of the tensile fractureenergy) led to over-prediction of the structure’s load bearingcapacity by approximately 95%. When the tensile strength wasset as 0.01 MPa and the tensile fracture energy was decreasedaccordingly, the maximum lateral resistance and the displace-ments computed at LS4 were 50% and 210% respectively lowerthan the corresponding experimental values. It is worth noting thatanalogous conclusions concerning the sensitivity of numericalresults to compression and tension parameters have been derivedby Tarque et al. [23], who simulated adobe walls using the samedamaged plasticity constitutive law.

Various friction coefficients 0.5 < l < 1.35 were used for model-ling mechanical contact at the masonry–timber interfaces. The out-comes of the simulations verified that this parameter controls thetransfer of forces between the two opposite longitudinal walls anddetermines whether shear sliding of the roof rafters will occur.Consequently, it also affects to some extent the displacementscomputed. Adopting values of l > 0.65, in particular, establishesan unrealistic effective transfer of stresses at the brick–timberinterfaces, causing underestimation of the deformations inducedby lateral loading.

Table 1Experimental and numerical displacement values recorded at the rear, façade and side walls’ monitoring points and force magnitudes measured when the different limit states(LS1-4) and the near-failure condition were reached. Numerical limit state values were defined by correlating key points of the experimental force–displacement curves with thecorresponding data obtained from the simulation.

Measurement Monitoring point Process Limit-state

LS1 LS2 LS3 LS4 Near-failure

Force (kN) Load-imposition point Experimental 10.6 12.0 14.2 13.1 9.1Numerical 9.1 12.0 14.1 10.9 10.3

Displacement (mm) Rear wall Experimental 1.4 4.1 21.5 84.9 96.0Numerical 4.3 11.6 22.5 84.8 96.0

Façade wall Experimental 1.9 3.9 7.0 23.8 26.6Numerical 3.7 6.3 7.7 23.0 25.2

Side wall Experimental 1.8 3.8 7.7 25.2 27.1Numerical 3.8 5.5 8.4 25.6 28.0

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0 4 8 12 16 20 24

Acc

eler

atio

n (g

)

Time (s)

Fig. 12. Accelerogram of the lateral component of the 1999 August 11thEarthquake that was recorded at Limassol’s Water Treatment Plant.

-15

-10

-5

0

5

10

15

0 2 4 6 8 10 12 14 16 18 20 22 24

Rel

ativ

e di

spla

cem

ent (

mm

)

Time (s)

Fig. 13. Time history of the relative displacement computed along the direction ofthe seismic action (y) for the rear wall’s central topmost nodal point.

374 R. Illampas et al. / Engineering Structures 80 (2014) 362–376

5. Dynamic FE analysis of the adobe model building

The experimental investigation conducted in the framework ofthis study aimed at the calibration of a valid numerical modelcapable of capturing the general behaviour of adobe masonrystructures under static horizontal loading. The conditions consid-ered did not resemble those of a seismic event, as they involvedimposition of monotonic forces instead of load reversals. Thisaffected the damage mechanisms generated and the lateral resis-tance developed. Thus, in terms of seismic performance, the exper-imental results obtained are most probably optimistic and cannotbe injudiciously associated with the actual dynamic behaviour ofadobe masonry. In order to have some indications of what isexpected to happen when an adobe structure is struck by a realearthquake, a dynamic FE simulation based on the damaged plas-ticity constitutive law hereby calibrated was performed. For thederivation of comparable numerical results, the same FE modelused in the static simulation of Section 4 was subjected to time-history analysis imposing only the lateral component of an earth-quake recorded in Cyprus.

A two-step numerical solution process was again implementedtaking into account geometric non-linearity effects. Initially, thestructure was analyzed under dead loads using a general staticsolution procedure. At the second step, the seismic load wasimposed adopting a dynamic implicit procedure with direct inte-gration and a full Newton equation solver scheme [41]. Upon thetransition from the static to the dynamic step, the pinned boundaryconditions at the walls’ base were modified, removing the transla-tional constraint along the y-axis and enforcing a ground accelera-tion along the same direction. The total time period of the dynamicstep and the amplitude of the acceleration boundary conditionwere defined in accordance with the accelerogram of the lateralcomponent of the 1999 August 11th Earthquake recorded atLimassol’s Water Treatment Plant (Fig. 12). The duration of theselected seismic event is 22.61 s, while the peak groundacceleration is 0.167g and occurs at 4.9 s. It is worth noting thatthis is the highest seismic acceleration recorded in Cyprusduring the decade 1990–2000. The minimum and maximum loadimposition time increments for the dynamic step were set as1 � 10�15 s and 0.005 s, respectively.

The application of reversing seismic accelerations resulted to adamage pattern similar to the one observed at the side walls of thetested structure. Tensile cracking initiated at the corners of thewindow opening and propagated diagonally towards the upperand lower sections of the side wall. These inclined cracks wereactually formed when the maximum seismic accelerations wereimposed and rapidly extended throughout the whole width ofthe side wall. The final distribution of tensile plastic strains atthe cracked areas of the side wall is almost identical to that shownin Fig. 10. However, seismic damage was localized only around the

side wall’s window and no other cracks were generated at the faç-ade and rear walls.

Fig. 13 presents the time history of the relative out-of-plane dis-placement recorded at the rear wall’s central upper section. Rela-tive displacement data were computed by subtracting thetranslation of the rear wall’s central base node along the y-axisfrom the total out-of-plane displacement of the correspondingnodal point at the top of the wall. According to the resultsobtained, the maximum deflection induced is 11.4 mm and occursat 4.9 s, when the seismic acceleration attains its peak value. Fromthis point onwards, the rear wall oscillates around a new equilib-rium position at approximately �1.5 mm, indicating residualinelastic deformation.

The variation of the total base shear force in relation to the rel-ative displacement along the y-axis, measured at the rear wall’s

-15

-10

-5

0

5

10

15

-12 -9 -6 -3 0 3 6 9 12

Bas

e sh

ear

forc

e (k

N)

Relative displacement (mm)

Fig. 14. Total base shear force versus relative displacement in the y-direction forthe rear wall’s central topmost nodal point.

R. Illampas et al. / Engineering Structures 80 (2014) 362–376 375

highest point, is given in Fig. 14. Numerical results indicate thatstiffness degradation under dynamic excitation starts to developwhen the relative out-of-plane displacement induced exceeds5 mm. At this point, the shear force that develops at the base ofthe structure is of the order of 9 kN. The maximum load sustainedby the structure during the seismic event is about 11 kN, while themaximum relative displacement recorded for the rear wall isbelow 12 mm.

The aforementioned magnitudes of base shear force are quiteclose to the 10.6 and 12 kN lateral loads recorded at LS1 and LS2during the static laboratory tests. Furthermore, the predicted modeof damage is in line with the experimentally observed crack pat-tern at LS2 (Fig. 6b). Collapse mechanisms, such as detachmentbetween orthogonal walls or overturning of extensively crackedmasonry sections, were not activated due to the fact that the dis-placements induced at the levels of the seismic action imposedwere small. Nevertheless, the numerical results imply that, evenat moderate levels of seismic action, an unreinforced adobe struc-ture can lose a significant portion of its overall stiffness and maydevelop forms of damage that require prompt interventions andrepairs. Considering that the imposed dynamic acceleration mar-ginally exceeds the minimum design value of 0.15g prescribed inthe Cyprus National Annex to Eurocode 8 [53], concerns are raisedregarding the seismic vulnerability of the island’s unreinforcedearthen structures.

6. Conclusions

Laboratory testing of a 1:2 scaled model building revealed that,under lateral loading, damage in unreinforced adobe structures isprimarily concentrated at the masonry walls, whereas stifferload-bearing members (i.e. timber elements) remain practicallyintact. The prevalent failure mechanism that occurs is crackingdue to inadequate bonding between the bricks and the mortar.Damage initiation can be influenced by stress augmentation atthe corners of openings and at the abutments of timber members.

Upon load removal, the cracks formed on adobe masonry wallsclose almost completely, leaving little indication of damage.Cracked sections, however, act as planes of weakness and crackre-opening is mobilized when load is re-applied. This highlightsthe cumulative effect that pre-existing damage poses on the struc-tural behaviour of adobe buildings. It also indicates that particularattention should be paid during the in-situ inspection of earthenstructures after seismic events.

In terms of structural behaviour, the aspects that distinguishadobe masonry structures from stone or fired clay brick structuresare their inherent non-linear response and their rather limitedstiffness. Highly non-linear response occurs both at the level ofthe material itself and at the global behaviour of the structural sys-tem. Due to the granular soil structure of adobe bricks and earth-based mortars, elasticity in the case of adobe masonry can havelimited physical basis, since inelastic deformation of the masonryconstituents may develop even under vertical static loads.Moreover, the extremely weak adhesion among the masonry unitspractically precludes linear response of adobe structural membersto loads, when tensile stresses are generated. Experimental datashow that, unlike other types of masonry structures which are usu-ally quite rigid and present a very brittle global behaviour withlimited plastic displacement capacity, adobe masonry structurestend to develop considerable deformations when subjected to hor-izontal thrusts. Such deformations become even greater in theabsence of a stiff diaphragm configuration at roof level, which isnot uncommon in traditional adobe buildings. As a result of thisintense deformability, differential movement among the variousload-bearing members occurs at low levels of loading and homoge-neous structural response is lost soon after the global yieldingpoint.

The damaged plasticity constitutive law adopted in this studyhas proven to be adequate for modelling adobe masonry as anidealized homogenized continuum. Provided that appropriatematerial data is used and that proper calibration is undertaken,FE models can capture the force–displacement response and thefailure mode of adobe structures. The generic limitations of contin-uum modelling and the assumption of isotropic damage may intro-duce some inconsistencies to the outcomes of simulations, but donot preclude sufficient macroscopic approximation of the globalstructural behaviour.

The sensitivity of numerical results to certain modelling param-eters indicates that a more detailed database of information on theproperties of adobe masonry is required. In particular, furtherexperimental investigation should be undertaken to assess thestiffness characteristics of adobe masonry and to thoroughly exam-ine its response to tensile loads. The frictional and bonding proper-ties at the interfaces between adobes and timber elementsembedded in masonry should also be evaluated. Considering thatthe damaged plasticity model has the potential to simulate mate-rials subjected to cyclic/dynamic actions, future research shouldalso study phenomena such as stiffness reduction and recoveryupon load reversals to enhance the seismic numerical analysis ofadobe structures.

Acknowledgements

The funding granted by the University of Cyprus in the frame-work of research program ‘Experimental and ComputationalInvestigation of the Structural Response of Adobe Buildings’, aswell as the financial support provided by the European RegionalDevelopment Fund and the Republic of Cyprus through the CyprusResearch Promotion Foundation (Project EPIXEIPHREIR/PPOION/0609/41) are gratefully acknowledged. The Cyprus GeologicalSurvey Department is also acknowledged for providing the acceler-ogram used in the dynamic simulation.

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