8. summary and conclusionsnicolatarque.weebly.com/uploads/1/2/6/9/12699783/... · during the...

8. SUMMARY AND CONCLUSIONS

This thesis deals with the analysis of adobe masonry with emphasis on the selection of its elastic and inelastic parameters. The gathered experimental data derives basically from static and dynamic tests carried out at the Pontificia Universidad Católica del Perú. The numerical results of an adobe wall and an adobe module, run in Midas FEA and Abaqus, show a strong agreement with the experimental results in terms of failure pattern and seismic capacity.

Peru, as many other countries, has a strong tradition in adobe construction. However, the good tradition is being lost; for example, new adobe houses located along the Peruvian coastline do not follow an acceptable geometrical configuration such as thicker walls with buttresses and small openings at the walls. The necessity of building with thinner walls is related to the small land size relatively available for low incomes families, which almost in all cases build without taking into account any seismic reinforcement or improvement. Therefore, the seismic vulnerability of adobe houses increases due to the lack of good construction practices.

The seismic behaviour of unreinforced adobe constructions seems to follow a common failure sequence: the roof is not rigid enough to guarantee a rigid diaphragm so the adobe walls behave independently and are very vulnerable to out of plane loads. During the earthquakes the walls separates from each other due to the large vertical cracks that appear at the wall intersections. Simultaneously, diagonal cracks start at the wall openings and cracks due to horizontal and vertical bending break the walls into small rigid blocks, followed by wall overturning if the movement continues. The roof collapses after the walls fall down. One way to reduce the high seismic risk is by understanding how adobe structures (considering different configurations and different uses, e.g. houses, churches, monuments) behave under different levels of ground motion. Considering the high cost of the experimental tests, the numerical modelling of adobe constructions is an option for understanding its seismic behaviour.

Little work has been published on modelling of adobe structures. It appears that the best approach is to use finite element models developed for other britlle materials, mainly concrete and masonry. Two general approaches were seen here: the micro-modelling and the macro-modelling. The first one related with the discontinuous or discrete approach and the second one with the continuum approach. The principal input for these

Sabino Nicola Tarque Ruíz

194

approaches are the constitutive laws in tension, compression and shear in the elastic and inelastic range. Information on mechanical properties is however scarce for adobe masonry. Micro-modelling is used for analysis of small masonry structures and especially for understanding the behaviour of the brick-mortar interface; while macro-modelling is used for representing large structures with distributed damage. Another approach for modelling masonry structures is by an equivalent frame method; which can be considered within a macro-modelling approach.

In this thesis the material parameters of adobe masonry are calibrated for the two finite element approaches previously mentioned and implemented into Midas FEA and Abaqus (standard and explicit). For the micro-modelling the composite model developed by Lourenço [1996] for fired brick masonry is used in Midas FEA. This model allows concentrating all the inelasticity (tension, compression and shear) at the mortar joints. Following this approach the adobe wall tested under cyclic loads by Blondet et al. [2005] is reproduced here in Midas FEA but considering only monotonic displacements. The numerical results match quiet well the failure pattern and seismic capacity of the experimental test until certain displacement level, but the analysis stops due to convergence problems. Although the material parameters seems to be correctly calibrated (see Table 6.3), it is recommended to elaborate a test campaign to obtain experimentally the constitutive laws for tension and shear at the mud mortar joints and compression tests of the composite (brick plus mortar). Since adobe is a brittle material, displacement controlled tests can be a good option for capturing the inelastic range. The author recommends using the data specified in Table 6.3 within a discrete approach.

For the macro-modelling two finite element models are used: the total-strain model implemented in Midas FEA and the concrete damaged plasticity model implemented in Abaqus (within a standard and explicit solution). Unlike fired clay masonry, the adobe masonry can be considered as a homogeneous and isotropic material due to the similarity in material properties between the adobe bricks and the mud mortar joints. Generally, the adobe bricks are fabricated and after some time they are used for construction, in this case the mud mortar has not the same age of the bricks and the dry process between mortar and bricks can generate weak zones at the bed and head contact zones.

Similarly to the work done with the discrete approach, the material properties of the adobe masonry in the macro-models are calibrated based on the cyclic test of an adobe wall. Special attention is paid to simulate the crack opening/closing due to tension. Again, the failure pattern and the seismic capacity is quiet well represented and it is concluded that the calibrated material parameters shown in Table 6.4 (for Midas FEA, total-strain model) and Table 6.5 (for Abaqus, concrete damaged plasticity model) can be used for analysis of other geometrical configurations of adobe structures. The adobe module dynamically tested by Blondet et al. [2006] was reproduced using Abaqus/Implicit

Numerical modelling of the seismic behaviour of adobe buildings

195

and Abaqus/Explicit. The acceleration record related to the displacement input used in the experimental tests was applied at the base of the numerical module. The results match well the displacement and acceleration responses measured at the adobe walls (see Appendix). However, the solution within an implicit approach has problems of convergence due to the formation of cracking in the walls, while the analysis with explicit solution does not have convergence problems.

An explicit analysis (Abaqus/Explicit) is adequate for dealing with dynamic problems with quasi-brittle material and contact problems. The integration scheme allows continuing computing the displacement field at the shell elements avoiding convergence problems due to progressive degradation and progressive loss of the material integrity.

The continuum models do not allow the physical separation of the rigid blocks produced by the movement, for this reason the rocking behaviour of the adobe walls are not perfectly captured by the model run in Abaqus, but it is still good enough to understand the cracking process and to identify the zones where the adobe masonry behaves inelastically. According to the non-linear dynamic analysis of the adobe module the numerical displacement response of the walls shows some dependency between the parallel and perpendicular walls; however, in the experimental model a physical separation (vertical cracks) was observed at the union of the walls allowing a rocking behaviour at the walls perpendicular to the movement and a quasi rigid movement at the parallel walls. When high relative displacements are read in the displacement history of the walls, the failure pattern should be controlled to check if vertical cracks are produced at the wall intersection zones.

According to section 6.2.1 it is shown that the governing material property in the adobe masonry is the tension strength and the tensile softening. Here a ft= 0.04 MPa with I

fG = 0.01 N/mm and h 140 mm is recommended for further analyses. The compression behaviour of the adobe masonry does not affect the seismic capacity of the walls. However, a lower bound of the compression strength fc = 0.30 MPa could be considered, with a ratio of c

f cG f/ = 0.344 mm. Analyses with fc= 0.7 MPa were also carried out and the results did not vary too much. Here it is recommended to use fc= 0.45 MPa maintaining the ratio c

f cG f/ = 0.344 mm. The elastic behaviour of the adobe masonry is greatly controlled by the elasticity modulus E, which is considered between 200 to 230 MPa. Lower values of E seem to underestimate the seismic capacity of the masonry. If the analysis requires a given shear retention factor, a value of 0.05 is suggested. Besides, a small dilatancy angle is considered, similarly to masonry structures [Lourenço 1996]. The material parameters shown in Table 6.5 are specified for numerical analysis of adobe structures with different configurations within an explicit solution.


196

Because of the importance of the roof on the seismic behavior of the adobe module, sSpecial attention was placed in understanding the interaction between the roof (formed by wooden beams) and the walls. Experimentally, the wooden beams were attached to the adobe walls through steel nails and mud mortar. During the first phase of the test (with maximum total displacement at the base of 30 mm) separation between the wooden beams and the walls were observed, especially at the wall corners. During the phase 2, which was analyzed in this work, this detachment is clearly seen at the walls perpendicular to the movement, causing the rocking behavior. The effect of partial connection between the wooden beams and the walls has been studied in the finite element models. The best solution was to simulate detachment of the wooden beams from the walls by removing some linear wooden elements close to the wall intersections. When dealing with the analysis of other structures, special attention should be placed to the roof simulation and to evaluate the possibilities of allowing vertical cracking at the wall intersections if they do not have any confining element.

The general conclusion of this thesis is the acceptability of micro and macro modelling for the analysis of adobe structures; besides, the author recommends to use the second approach (continuum model) since the adobe material is reasonable well modelled as a homogeneous material and its behaviour can be represented by a calibrated tension and compression behaviour. The calibrated material parameters for new analyses are given in Table 6.5. It is also recommended to follow when possible an explicit method. In this case the concrete damaged plasticity model should be used.

Although the results achieved in this research, further detailed work should be addressed, namely to:

characterize the mechanical behaviour of adobe material. In this case, an exhaustive experimental campaign should be developed to investigate the linear and the non-linear material properties of the adobe masonry. Since adobe is a brittle material, the testing setups to be adopted should capture the post maximum strength response, thus displacement controlled tests are suggested.

study the influence of roof-wall connections in the response of the constructions. It was seen that the roof system conformed by wooden beams are normally not properly connected to the adobe walls. Those are just attached with steel nails which were disconnected from the walls during the dynamic test. In the research developed in this thesis a simplification of the connection was assumed in the numerical models, reducing the wooden beam length and disconnecting them from the walls at the corners. However, simplified non-linear response of this interaction mechanism should be proposed and calibrated with experimental results.


197

study other type of adobe structures. The macro-modelling approach suggested in this research work can be extended to the analysis of other adobe structures with different configurations, especially for the evaluation of the seismic vulnerability of historic structures as houses, churches and convents, frequently found in Latin-American countries. With this, the weak zones of adobe structures can be identified and based on these results retrofitting solutions may be proposed.

study retrofitting solutions for adobe constructions. The efficiency of different strengthening solutions (invasive and non-invasive) can be numerically assessed, estimating the benefits in terms of post-elastic behaviour of the retrofitted adobe structures, namely ductility and energy dissipation capacity.

page intentionally left blank.

REFERENCES

Abaqus 6.9 SIMULIA. [2009] “Abaqus/CAE Extended Funcionality EF2,” Manual, Dassault Systemss Corporation, Providence, RI, USA.

Ali, S. S., and Page, A. W. [1987] “Finite Element Model for Masonry Subjected to Concentrated Loads,” Journal of Structural Engineering, Vol. 114, No.8, p. 1761.

Amadei, B., Sture, S., Saeb, S., and Atkinson, R. H. [1989] “An evaluation of masonry joint shear strength in existing buildings,” Report, Dept. Civ., Envir., and Arch. Engrg., University of Colorado, Boulder, Colorado, USA.

Arya, S. K., and Hegemier, G. A. [1978] “On nonlinear response prediction of concrete masonry assemblies,” Proceedings of North American Masonry Conference, Boulder, Colorado, USA, pp. 19.1-19.24.

Attard, M. M., Nappi, A., and Tin-Loi, F. [2007] “Modeling Fracture in Masonry,” Journal of Structural Engineering, Vol. 133, No.10, p. 1385.

Attard, M. M., and Tin-Loi, F. [1999] “Fracture simulation using a discrete triangular element,” Proceedings of Mechanics of Structures and Materials, M. Bradford and R. Q. Bridge, eds., A. A. Balkema, Sydney, Australia.

Attard, M. M., and Tin-Loi, F. [2005] “Numerical simulation of quasibrittle fracture in concrete,” Engineering Fracture Mechanics, Vol. 72, No.3, pp. 387-411.

Bažant, Zden k P., and Oh, B. H. [1983] “Crack band theory for fracture of concrete,” Matériaux et Constructions, Vol. 16, No.3, pp. 155-177.

Behbahanifard, M. R., Grondin, G. Y., and Elwi, A. E. [2004] “Analysis of steel plate shear walls using explicti finite element method,” Proceedings of 13th World Conference on Earthquake Engineering, Vancouver, Canada.

Blind, N., and Östlund, R. [2009] “Analysis of an engine frame subjected to large imbalance loads,” Master Thesis, Luleá University of Technology, Porsön, Sweden.


200

Blondet, M., Ginocchio, F., Marsh, C., Ottazzi, G., Villa-García, G., and Yep, J. [1988] “Shaking table test of improved adobe masonry houses,” Proceedings of 9th World Conference on Earthquake Engineering, Tokyo-Kyoto, Japan.

Blondet, M., Madueño, I., Torrealva, D., Villa-García, G., and Ginocchio, F. [2005] “Using industrial materials for the construction of safe adobe houses in seismic areas,” Proceedings of Earth Build 2005 Conference, Sydney, Australia.

Blondet, M., Torrealva, D., Vargas, J., Tarque, N., and Velásquez, J. [2006] “Seismic reinforcement of adobe houses,” Proceedings of 1st European Conference on Earthquake Engineering and Seismology, Geneva, Switzerland.

Blondet, M., Vargas, J., Velásquez, J., and Tarque, N. [2006] “Experimental Study of Synthetic Mesh Reinforcement of Historical Adobe Buildings,” Proceedings of Structural Analysis of Historical Constructions, P. B. Lourenço, P. Roca, C. Modena, and Agrawal. S., eds., New Delhi, India, pp. 1-8.

Blondet, M., Vargas, J., Villa-García, G., Torrealva, D., and Tarque Ruíz, N. [2005] “Refuerzo de construcciones de adobe con elementos producidos industrialmente: Ensayos de simulación sísmica,” Report, Division of Civil Enginering, Pontificia Universidad Católica del Perú, Lima, Peru.

Blondet, M., Vargas, J., and Tarque, N. [2008a] “Observed behaviour of earthen structures during the Pisco earthquake (Peru),” Proceedings of 14th World Conference on Earthquake Engineering, Beijing, China.

Blondet, M., Vargas, J., and Tarque, N. [2008b] “Ava lable low-cost technolog es to mprove the se sm c performance of earthen houses n se sm c areas,” Proceedings of Kerpic08 - Learning from earthquake architecture in climate change., Lefkosa, Northen Cyprus.

Blondet, M., Vargas, J., and Villa-García, G. [2008] “Reparación de grietas en construcciones históricas de tierra en áreas sísmicas. Parte IV: aplicación y desarrollo de nuevos métodos de inyección,” Report, Division of Civil Engineering, Pontifcia Universidad Católica del Perú, Lima, Peru.

Blondet, M., Villa-García, G., and Brzev, S. [2003] “Earthquake-Resistant Construction of Adobe Buildings: A Tutorial,” (M. Greene, ed.), Report, EERI/IAEE World Housing Enciclopedy, Okland, California, USA.

Blondet, M., and Vargas, J. [1978] “Investigación sobre vivienda rural,” Report, Division of Civil Engineering, Pontificia Universidad Católica del Perú, Lima, Peru.


201

de Borst, René. [1991] “Computational methods in non-linear solid mechanics. Part 2: physical non-linearity,” Report, Delft University of Technology, Delft, The Netherlands.

de Borst, René, and Nauta, P. [1985] “Non-orthogonal cracks in a smeared finite element model,” Report, Delft University of Technology, Delft, The Netherlands.

Brignola, A., Frumento, S., Lagomarsino, Sergio, and Podestà, S. [2008] “Identification of Shear Parameters of Masonry Panels Through the In-Situ Diagonal Compression Test,” International Journal of Architectural Heritage, Vol. 3, No.1, pp. 52-73.

CENAPRED. [2003] Reinforcement methods for self-construction of rural housing (in Spanish), Mexico City, Mexico.

CTAR/COPASA, GTZ, PUCP, and SENCICO. [2002] Terremoto? ¡Mi casa sí resiste! – Manual de construcción para viviendas sismo resistentes en adobe, Lima, Peru.

CUR. [1997] Structural masonry: a experimental/numerical basis for practical design rules (in Dutch), (J. G. Rots, ed.), A. A. Balkema/Rotterdam/Brookfield, Gouda, The Netherlands.

Calderini, C., Cattari, S., and Lagomarsino, S. [2009] “In plane seismic response of unreifnorced masonry walls: comparison between detailed and equivalent frame models,” ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, M. Papadrakakis, N. D. Lagaros, and M. Fragiadakis, eds., Rhodes, Greece.

Cao, Z., and Watanabe, H. [2004] “Earthquake response predication and retroftiing techniques of adobe structures,” Proceedings of 13th World Conference on Earthquake Engineering, Vancouver, Canada.

Chen, W.-F., and Han, D.-J. [1988] Plasticity for structural engineers, Springer-Verlag, New York, USA, p. 606.

Cope, R. J., Rao, P. V., Clark, L. A., and Norris, P. [1980] “Modelling of reinforced concrete behaviour for finite element analysis of bridge slabs,” International Conference: Numerical methods for non-linear problems, Pineridge Press, Swansea, Wales, United Kindom, pp. 457-470.

Cruz, J. S., Barros, J., and Azevedo, Á. [2004] “Elasto-plastic multi-fixed smeared crack model for concrete,” Report 04-DEC/E-05, University of Minho, Minho, Portugal.

Cundall, P. A. [1971] “A computer model for simulating progressive large scale movements in blocky rock systems,” Proceedings of Symposium on Rock Fracture (ISRM), Nancy, France.


202

Van Der Pluijm, R. [1993] “Shear behaviour of bed joints,” Proceedings of 6th North American Masonry Conference, A. A. Hamid and H. G. Harris, eds., Drexel University, Philadelphia, Pennsylvania, USA, pp. 125-136.

Dowling, D. [2004] “Adobe housing in El Salvador: Earthquake performance and seismic improvement,” Geological Society of America Special Papers, I. Rose, J. J. Bommer, D. L. López, M. J. Carr, and J. J. Major, eds., pp. 281-300.

Easton, D. [2007] The Rammed Earth House, (J. Barstow, ed.), Chelsea Publishing Company, Vertmon, USA, p. 266.

Elsaigh, W. A. M. H. [2007] “Modelling the behaviour of steel fibre reinforced concrete pavements,” Ph.D. Thesis, University of Petroria, Petroria, South Africa.

Feenstra, P. H. [1993] “Computational aspects of biaxial stress in plain and reinforced concrete,” Ph. D. Thesis, Delft University of Technology, Delft, The Netherlands.

Feenstra, P. H., and de Borst, Rene. [1992] “The use of various crack models in F.E. analysis of reinforced concrete panels,” Proceedings of First International Conference on Fracture Mechanics of Concrete Structures: FraMCoS1, Zdenek P. Bažant, ed., Taylor and Francis, Breckenridge, Colorado, USA.

Feenstra, P. H., and Rots, J. G. [2001] “Comparison of Concrete Models for Cyclic Loading,” Modelling of Inelastic Behaviour of RC Structures under Seismis Loads, P. Benson Shing and T.-aki Tanabe, eds., American Society of Civil Engineers, USA, pp. 38-55.

Furukawa, A., and Ohta, Y. [2009] “Failure process of masonry buildings during earthquake and associated casualty risk evaluation,” Natural Hazards, pp. 25-51.

Galasco, Alessandro, Lagomarsino, Sergio, Penna, Andrea, and Resemini, S. [2004] “Non-linear seismic analysis of masonry structures,” Proceedings of 13th World Conference on Earthquake Engineering, Vancouver, Canada.

Gambarotta, L., and Lagomarsino, S. [1997a] “Damage models for the seismic response of brick masonry shear walls. Part I: The mortar joint and its applications,” Earthquake Engineering & Structural Dynamics, Vol. 26, No.4, pp. 423-439.

Gambarotta, L., and Lagomarsino, S. [1997b] “Damage models for the seismic response of brick masonry shear walls. Part II: The continuum model and its applications,” Earthquake Engineering & Structural Dynamics, Vol. 26, No.4, pp. 441-462.


203

Gascón, M., and Fernández, E. [2001] “Terremotos y sismos en la evolución urbana de Hispanoamèrica. Ejemplos coloniales y estudio de caso,” Report, Mendoza, Argentina.

Gavrilovic, P., Sendova, V., Ginell, W. S., and Tolles, L. [1998] “Behaviour of adobe structures during shaking table tests and earthquakes,” Proceedings of 11th European Conference on Earthquake Engineering, P. Bisch, P. Labbé, and A. Pecker, eds., Rotterdam, The Netherlands.

Guinea, G., Hussein, G., Elices, M., and Planas, J. [2000] “Micromechanical modeling of brick-masonry fracture,” Cement and Concrete Research, Vol. 30, No.5, pp. 731-737.

Harewood, F. J., and McHugh, P. E. [2007] “Comparison of the implicit and explicit finite element methods using crystal plasticity,” Computational Materials Science, Vol. 39, No.2, pp. 481-494.

Hernández, O., Meli, R., Padilla, M., and Valencia, E. [1981] “Refuerzo de vivienda rural en zonas sísmicas: Estudios experimentales,” Report, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City, Mexico.

Hilber, H. M., Hughes, T. J. R., and Taylor, Robert L. [1977] “Improved numerical dissipation for time integration algorithms in structural dynamics,” Earthquake Engineering & Structural Dynamics, Vol. 5, No.3, pp. 283-292.

Hodge, P. G. [1957] “Discussion of [Prager 1956],” Journal of Applied Mechanics, Vol. 23, pp. 482-484.

Houben, H., and Guillard, H. [1994] Earth Construction: A Comprehensive Guide, Practical Action, London, United Kindom, p. 372.

INEI. [2008] “Census 2007: XI de Población y VI de Vivienda,” Report, National Institute of Statistics and Informatics, Lima, Peru.

Jirasek, M., and Bažant, Zdenek P. [2002] Inelastic Analysis of Structures, John Wiley and Sons Ltd, New York, USA, p. 734.

Jurina, L., and Righetti, M. [2008] “Traditional building in Peru,” Report, ICOMOS.

Kappos, A. J., Penelis, G. G., and Drakopoulos, C. G. [2002] “Evaluation of Simplified Models for Lateral Load Analysis of Unreinforced Masonry Buildings,” Journal of Structural Engineering, Vol. 128, No.7, p. 890.


204

Karapitta, L., Mouzakis, H., and Carydis, P. [2011] “Explicit finite-element analysis for the in-plane cyclic behavior of unreinforced masonry structures,” Earthquake Engineering & Structural Dynamics, Vol. 40, No.2, pp. 175-193.

Koiter, W. T. [1960] “General theorems for elastic-plastic solids,” Progress in Solid Mechanics, I. N. Sneddon and R. Hill, eds., North Holland Publishing Company, pp. 165-221.

Lagomarsino, S, Galasco, A, and Penna, A. [2007] “Non-linear macro-element dynamic analysis of masonry buildings,” Proceedings of ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rethymno, Crete, Greece.

Lee, J., and Fenves, G. L. [1998] “Plastic-Damage Model for Cyclic Loading of Concrete Structures,” Journal of Engineering Mechanics, Vol. 124, No.8, pp. 892-900.

Liberatore, D., Spera, G., Mucciarelli, M., Gallipoli, M. R., Masini, N., Racina, V., Capriuoli, A., Cividini, A., and Tedeschi, C. [2006] “Typological and Experimental Investigation on the Adobe Buildings of Aliano ( Basilicata , Italy ),” Proceedings of Structural Analysis of Historical Constructions, P. B. Lourenço, Pere Roca, and S. Agrawal, eds., New Delhi, India, p. 8.

Lotfi, H. R., and Shing, P. Benson. [1994] “Interface Model Applied to fracture of masonry Structures,” ASCE, Vol. 120, No.1, pp. 63-80.

Lotfi, V., and Espandar, R. [2004] “Seismic analysis of concrete arch dams by combined discrete crack and non-orthogonal smeared crack technique,” Engineering Structures, Vol. 26, No.1, pp. 27-37.

Lourenco, P. B., and Rots, J. G. [1997] “Multisurface Interface Model for Analysis of Masonry Structures,” Journal of Engineering Mechanics, Vol. 123, No.7, p. 660.

Lourenço, P. B. [1994] “Analysis of masonry structures with interface elements: Theory and Applications,” Report, Delft University, Delft, The Netherlands.

Lourenço, P. B. [1996] “Computational strategies for masonry structures,” Ph.D. Thesis, Delft University, Delft, The Netherlands.

Lourenço, P. B. [1998] “Experimental and numerical issues in the modelling of the mechanical behaviour of masonry,” Proceedings of Structural Analysis of Historical Constructions II, Barcelona, Spain.


205

Lourenço, P. B., Rots, J. G., and Pluijm, R. V. D. [1999] “Understanding the tensile behaviour of masonry under tension parallel to the bed joints,” Masonry International, Vol. 12, No.3, pp. 96-103.

Lowman, P. D., and Montgomery, B. C. [1998] “Preliminary determination of epicenters of 358,214 events between 1963 and 1998,” <http://denali.gsfc.nasa.gov/dtam/seismic/> (Jun. 2011).

Lubliner, Jacob. [2006] Plasticity theory, University of California at Berkeley, Berkeley, California, USA.

Lubliner, J., Oliver, J., Oller, S., and Oñate, E. [1989] “A plastic-damage model for concrete,” International Journal of Solids and Structures, Vol. 25, No.3, pp. 299-326.

Magenes, G., and Della Fontana, A. [1998] “Simplified non-linear seismic analysis of masonry buildings,” Proceedings of Fifth International Masonry Conference, British Masonry Society, London, England.

Malm, R. [2009] “Predicting shear type crack initiation and growth in concrete with non-linear finite element method,” Ph.D. Thesis, Royal Institute of technology, Stockholm, Sweden.

Mehrabi, A. B., Shing, P. Benson, Schuller, M. P., and Noland, J. L. [1994] “Performance of masonry-infilled R/C frames under in-plane lateral loads,” Report, University of Colorado, Boulder, Colorado, USA.

Meli, Roberto, Hernández, Oscar, and Padilla, Marciano. [1980] “Strengthening of adobe houses for seismic actions,” Proceedings of 7th World Conference on Earthquake Engineering, Turkish National Committee on Earthquake Engineering, Istanbul, Turkey, pp. (4) 465-472.

Memari, A. M., and Kauffman, A. [2005] “Review of Existing Seismic Retrofit Methodologies for Adobe Dwellings and Introduction of a New Concept,” Proceedings of SismoAdobe2005, Pontificia Universidad Católica del Perú, Lima, Peru, p. 15.

Midas FEA v2.9.6. [2009] Nonlinear and detail FE Analysis System for civil structures. Manual: Analysis and Algorithm, CSP FEA.

Minke, G. [2005] Manual de construcción para viviendas antisísmicas de tierra, Kassel, Germany, p. 52.

NMX-C-085-ONNCCE. [2002] Industria de la construcción -Cementos Hidráulicos- Método estándar para el mezclado de pastas y morteros de cementantes hidráulico, Organismo Nacional de Normalización y Certificación de la Construcción y Edificación, S. C., Mexico D.F.


206

Ngo, D., and Scordelis, A. C. [1967] “Finite Element Analysis of Reinforced Concrete Beams,” American Concrete Institute, Vol. 64, No.3, pp. 152-163.

Noghabai, K. [1999] “Discrete versus smeared versus element-embedded crack models on ring problem,” Journal of Engineering Mechanics, Vol. 125, No.March, pp. 307-315.

Odqvist, F. K. G. [1933] “Die verfestigung von flusseisenahnlichen korpen. Ein beitrag zur plastizitiitstheorie,” Zeit. Angew. Math. Und Mech., Vol. 13, pp. 360-363.

Ohmenhauser, F., Weihe, S., and Kroplin, B. [1998] “Classification and algorithmic implementation of smeared crack models,” Proceedings of Computational Modelling of Concrete Structures, René De Borst, N. Bicanic, H. Mang, and G. Meschke, eds., A. A. Balkema, Badgastein, Austria, p. 577.

Oliveira, D. [2003] “Experimental and numerical analysis of blocky masonry structures under cyclic loading,” Ph.D. Thesis, University of Minho, Minho, Portugal.

Ottazzi, G., Yep, J., Blondet, M., Villa-García, G., and Ginocchio, F. [1989] “Ensayos de simulación sísmica de viviendas de adobe,” Report, Division of Civil Engineering, Pontificia Universidad Católica del Perú, Lima, Peru.

Page, A. W. [1978] “Finite element model for masonry,” Journal of Structural Engineering, Vol. 104, No.8, pp. 1267-1285.

Pande, G. N., Beer, G., and Williams, J. R. [1990] Numerical methods in rock mechanics, John Wiley and Sons Ltd, Chichester, England.

Paulay, T., and Priestley, M. J. N. [1992] Seismic design of reinforced concrete and masonry buildings, John Wiley & Sons, New York, USA.

Pelà, L. [2008] “Continuum damage model for nonlinear analysis of masonry sructures,” Ph.D. Thesis, Università degli Studi di Ferrara, Ferrara, Italy.

Prager, W. [1955] “The theory of plasticity: a survey of recent achievements,” ARCHIVE: Proceedings of the Institution of Mechanical Engineers 1847-1982 (vols 1-196), London, England, Vol. 169, No.1955, pp. 41-57.

Prager, W. [1956] “A new Method in Analyzing Stresses and Strains in Work-Hardening Plastic Solids,” Journal of Applied Mechanics, Vol. 23, pp. 493-496.


207

Raijmakers, T. M. J., and Vermeltfoort, A. T. [1992] “Deformation controlled tests in masonry shear walls (in Dutch),” Report B-92- 1156, Delft University of Technology, Eindhoven, The Netherlands.

Roca, Pere, Cervera, M., Gariup, G., and Pela’, L. [2010] “Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches,” Archives of Computational Methods in Engineering, Vol. 17, No.3, pp. 299-325.

Rosell, L. A. [2010] “Explicit / Implicit Nonlinear Soil Structure Interaction Study of the Bell Tower of Santa Maria Maggiore , Guardiagrele,” Master Thesis, ROSE School, Istituto di Studi Superiori di Pavia IUSS, Pavia, Italy.

Rots, J. G. [1988] “Computational modeling of concrete fracture,” Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands.

Rots, J. G. [1991] “Numerical simulation of cracking in structural masonry,” Heron, Vol. 36, No.2, pp. 49-63.

Rots, J. G. [2002] “Comparative study of crack models,” Proceedings of Third DIANA World Conference, M. A. N. Hendriks and J. G. Rots, eds., A. A. Balkema, Tokyo, Japan, pp. 17-28.

Saouma, V. E. [2000] Fracture mechanics, Dept. of Civil Environmental and Architectural Engineering, University of Colorado, Boulder, Colorado, USA, p. 446.

De Sensi, B. [2003] “Terracruda, la diffusione dell’architettura di terra,” www.terracruda.com/architetturadiffusione.htm, http://www.terracruda.com/architetturadiffusione.htm, <www.terracruda.com/architetturadiffusione.htm>.

Silveira, D., Varum, H., and Costa, A. [2007] “Rehabilitation of an important cultural and architectural heritage: the traditional adobe constructions in Aveiro district,” Proceedings of Sustainable Development and Planning III, WIT Press, Southampton, UK, pp. 705-714.

Stavridis, A., and Shing, P . B. [2010] “Finite Element Modeling of Nonlinear Behavior of Masonry-Infilled RC Frames,” Journal of Structural Engineering, ASCE, 136(3), 285-296., Vol. 3, No.136, pp. 285-296.

Sui, C., and Rafiq, M. Y. [2009] “Laterally loaded masonry wall panels: a review of numerical models,” Journal of the International Masonry Society, Vol. 22, No.2, pp. 47-52.


208

Taylor, R. L. [2007] “FEAP - A finite element analysis program, version 8.1,” University of California at Berkeley, Berkeley, California, USA.

Tolles, L., and Krawinkler, H. [1990] “Seismic studies on small-scale models on adobe houses,” Engineering, Report CEE-8311150, Department of Civil Engineering, Stanford University, Stanford, USA.

Vargas, J., Blondet, M., Ginocchio, F., and Villa-García, G. [2005] “35 años de investigaciones en sismo adobe: La tierra armada,” Report, Division of Civil Engineering, Pontificia Universidad Católica del Perú, Lima, Peru.

Vargas, J., Blondet, M., and Tarque, N. [2006] “The Peruvian Building Code for Earthen Buildings,” Proceedings of Getty Seismic Adobe Project 2006 Colloquium, M. Hardy, C. Cancino, and G. Ostergren, eds., Los Angeles, California, USA, pp. 45-51.

Vargas, J., and Ottazzi, G. [1981] “Investigaciones en adobe,” Report, Division of Civil Engineering, Pontificia Universidad Católica del Perú, Lima, Peru.

Vecchio, F. J., and Collins, M. P. [1986] “The modified compression field theory for reinforced concrete elements subjected to shear,” ACI Journal, Vol. 22, pp. 219-231.

Wawrzynek, A., and Cincio, A. [2005] “Plastic-damage macro-model for non-linear masonry structures subjected to cyclic or dynamic loads,” Proceedings of Conf. Analytical Models and New Concepts in Concrete and Masonry Structures, AMCM’2005, Gliwice, Poland.

Webster, F., and Tolles, L. [2000] “Earthquake damage to historic and older adobe buildings during the 1994 Northridge, California Earthquake,” Proceedings of 12th World Conference on Earthquake Engineering, Auckland, New Zealand.

Yamin, L., Rodríguez, A., Fonseca, L., Reyes, J., and Phillips, C. [2004] “Seismic behaviour and retrofit alternatives for adobe and rammed earth buildings,” Proceedings of 13th World Conference on Earthquake Engineering, Vancouver, Canada.

Yi, T. [2004] “Experimental investigation and numerical simulation of an unreinforced masonry structure with flexible diaphragms,” Ph.D. Thesis, Civil and Enviromental Engineering, Georgia Institute of Techonology, Georgia, USA.

Yi, T., Moon, F. L., Leon, R. T., and Kahn, L. F. [2006] “Analyses of a Two-Story Unreinforced Masonry Building,” Journal of Structural Engineering, Vol. 132, No.5, p. 653.


209

Zegarra, L., Quiun, D., San Bartolomé, A., and Giesecke, A. [1997] “Reforzamiento de viviendas de adobe existentes, 2da parte: Ensayo sísmico de módulos,” Proceedings of XI National Congress of Civil Engineering, Trujillo, Peru.

Zegarra, L., Quiun, D., San Bartolomé, A., and Giesecke, A. [2001] “Comportamiento ante el terremoto del 23-06-2001 de las viviendas de adobe reforzadas en Moquegua, Tacna y Arica,” Proceedings of XIII National Congress of Civil Engineering, Puno, Peru.

APPENDIX A. Comparison of the experimental and

numerical relative displacement response of the adobe

module. Implicit analysis.


212

A.1. Relative displacement history. Model 1.

Right Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)

ExperimentalNumerical

Left Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Front Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Rear Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)



213


Right Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Left Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Front Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Rear Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)



214


Right Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Left Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Front Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Rear Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)



215


Right Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Left Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Front Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Rear Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)



216


Right Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Left Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Front Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Rear Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)



217


Right Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Left Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Front Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Rear Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)



218


Right Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Left Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Front Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Rear Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)



219


Right Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Left Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Front Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Rear Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


APPENDIX B. Comparison of the experimental and

numerical total acceleration response of the adobe module.

Implicit analysis.


222

B.1. Total acceleration history. Model 1.

Right Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)

NumericalExperimental

Left Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Front Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Rear Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

) NumericalExperimental


223


Right Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Left Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Front Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Rear Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g



224


Right Wall

-1-0.5

00.5

11.5

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Left Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Front Wall

-3-2-10123

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Rear Wall

-1.5-1

-0.50

0.51

1.52

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

) ExperimentalNumerical


225


Right Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Left Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Front Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Rear Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g



226


Right Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Left Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Front Wall

-4

-2

0

2

4

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Rear Wall

-4

-2

0

2

4

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g



227


Right Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Left Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Front Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Rear Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g



228


Right Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Left Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Front Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Rear Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g



229


Right Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Left Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Front Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Rear Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


APPENDIX C. Comparison of the experimental and

numerical relative displacement response of the adobe

module. Explicit analysis.


232

C.1. Relative displacement history. Model 9.

Right Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Left Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Front Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Rear Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)



233


Right Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Left Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Front Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Rear Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)



234


Right Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Left Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Front Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Rear Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)



235


Right Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Left Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Front Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Rear Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)



236


Right Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Left Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Front Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


Rear Wall

-50-25

0255075

100

0 5 10 15 20 25 30

Time (s)

Dis

plac

emen

t (m

m)


APPENDIX D. Comparison of the experimental and

numerical total acceleration response of the adobe module.

Explicit analysis.


238

D.1. Total acceleration history. Model 9.

Right Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


Left Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Front Wall

-4

-2

0

2

4

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Rear Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g



239


Right Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


Left Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


Front Wall

-4

-2

0

2

4

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


Rear Wall

-4

-2

0

2

4

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g



240


Right Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


Left Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


Front Wall

-4

-2

0

2

4

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


Rear Wall

-4

-2

0

2

4

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g



241


Right Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


Left Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


Front Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


Rear Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g



242


Right Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g

)


Left Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


Front Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


Rear Wall

-2

-1

0

1

2

0 5 10 15 20 25 30

Time (s)

Acc

eler

atio

n (g


8. summary and conclusionsnicolatarque.weebly.com/uploads/1/2/6/9/12699783/... · during the...

Documents