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1 Structural Analysis of Historical Constructions Jerzy Jasieńko (ed) 212 DWE, Wrocław, Poland, ISSN , ISBN DIAGONAL STRENGTH OF ADOBE BRICK WALL sincenzo diamundo 1, dian miero iignola 2, Andrea mrota 3, daetano Manfredi 4 ABSTRACT Previous experimental studies showed that the ratio between mortar and brick mechanical properties (i.e. strength, stiffness and Young modulus) influences not only the design approaches (in terms of basic assumptions and analytical models e.g. homogenization) but also the global response of the masonry walls in term of strength and ductility. A specific analysis is herein presented in the case of earth bricks or adobe constructions, highlighting main issues and variability in the behavior of seismic resisting walls varying the properties (i.e. soil composition, curing) of the materials used for the adobe production. heywords: Adobe, Masonry walls, cinite element method, konlinear analysis, peismic vulnerability 1. INTRODUCTION Earth is one of the oldest and most widespread construction material used in the construction of buildings for thousands of years. Earth can be considered as the cheapest material readily available for construction. It has been used extensively for wall constructions around the world. The popularity of adobe is also related to the low level of skill and technology required for the production of the bricks and constructions and inherent properties of earth that is an efficient heat and sound insulating material. Adobe earth construction was copious in the ancient world and examples in many different places have been discovered so that preservation of historic, or even archeological, structures is nowadays a rising awareness. Despite the numerous advantages, adobe constructions are prone to damage under seismic actions. Unfortunately research on the structural behavior of adobe buildings is inadequate so far. The seismic behavior of adobe masonry walls is related to the in-plane shear behavior. The typical failure mode is the (diagonal) cracking mode. This occurs when the principal tensile stresses developed in the wall under a combination of vertical and horizontal loads exceed the tensile strength of the adobe material. The seismic characterization of the masonry structural element is generally carried out through direct shear tests or diagonal compression tests. The diagonal compression test is a research test method that covers determination of the diagonal tensile or shear strength of masonry assemblages by loading them in compression along one diagonal, thus causing a diagonal tension failure with the specimen splitting apart parallel to the direction of load [1]. This test allows evaluating the effects of variables such as type of masonry unit, mortar, workmanship, etc. [2]. 2. SUMMARY OF EXPERIMENTAL OUTCOMES 2.1. Test setup Experimental diagonal compression tests on adobe wall panels are presented by Turanly and Saritas 211 [3]. All the tested panels were subjected to diagonal compressive loads (compressive edge load) acting in the plane of wall and forming a 45 angle with the direction of the mortar bed joints; geometry of a tested panel is reproduced in (Fig. 1). The specimens were built with the global size (8 8 cm 2 ) and bricks size ( cm 3 ) as shown in (Fig. 1) but with different adobe 1 Ph.D. Student, Univ. of Naples Federico II, Dept. of Structural Engineering, vincenzo.giamundo@unina.it 2 Assistant Professor, Univ. of Naples Federico II, Dept. of Structural Engineering, glignola@unina.it 3 Associate Professor, Univ. of Naples Federico II, Dept. of Structural Engineering, aprota@unina.it 4 Full Professor, Univ. of Naples Federico II, Dept. of Structural Engineering, gamanfre@unina.it 1827

2 soil composition and curing for both the bricks and the mortar. The mortar height and width are respectively 1 cm and 11.5 cm for all the specimens. 8 1,5 1,5 1,5 1,5 1,5 1,5 1, ,5 8 Fig. 1 Tested panel geometry 2.2. Material characterization The mechanical properties are in part given by [1] and in part achieved by fitting numerical global experimental data. Tensile and compressive strengths for different curing times were computed by interpolation starting from the values suggested in [4], while the Young Modulus, E, of the adobe soil was achieved by fitting global response curve, because such mechanical characterization was lacking [1]. The trend of compression and tensile strength with curing time is shown in (Fig. 2), based on tests [4]. Such tests provide data from days to 28 days curing, both for plain soil and soil plus 1% straw content. For both materials, the strength almost doubled. 1, Strength ratio,75,5,25 Plain Straw, Curing days Fig. 2 Strength trend varying curing time Similarly, the trend of Young modulus, E, varying the straw content was given in ref. [5]. The experimental trend is given by dots in (Fig. 3) and a exponential trend is interpolated in dashed line. The main outcome is a descending trend with straw content; in particular the ratio between the Young modulus for adobe soil without straw and with 1% of straw content is about E (Mpa) Straw (%) Fig. 3 Adobe soil Young modulus trend varying straw content 1828

3 3. NONLINEAR NUMERICAL ANALYSES 3.1. Finite-element method To understand the influence of the different constituent materials (i.e. local properties of soil, composition, curing) on the global shear mechanical properties and, in general, on the structural behavior, a Finite Element Method (FEM) model has been used as a theoretical tool. The FEM model has been validated through the comparison of the experimental data [3] and numerical FEM outcomes. Micromodeling was adopted and some parametric analyses were conducted. Numerical two-dimensional analyses have been performed under plane-stress assumption. This assumption is based on the fact that the width of the panel is much lower than the other two dimensions and in plane load were applied. The analyses were performed varying the mechanical parameters for both the bricks and the mortar and different strength values, according also to curing time, are reported in (Tab.1). Different values are provided for plain adobe soil at different curing days. They represent different aging of materials at time of testing [3] and in particular, bricks at testing time were 28 days old, while mortar was almost fresh. Similarly different compositions were tested for the brick, namely with the addition of fly ash or straw. For comparison purpose, lacking of experimental counterpart, numerical simulations were performed applying a better mortar, namely mortar B instead of plain fresh mortar, and considering for both mortar and bricks the same properties due to long curing, namely longer than 28 days. The analyses have been performed by means of the TNO DIANA v9.4.3 code. The simulated panel (Fig. 4) is constituted by more than 13 eight-node quadrilateral isoparametric plane stress elements. This element is based on quadratic interpolation and Gauss integration. Properties Table 1 Material mechanical properties Plain soil Plain soil Plain soil Fly Ash addition 1% Straw content Mortar B Curing days 28 > Tensile Strength [kpa] Compressive Strength [MPa] Fig. 4 Test setup: a) experimental, b) Finite element model (with mesh) Mortar and bricks are modeled individually without interface elements between them, according to total strain model coupled with the rotating crack stress-strain relationship approach. Neglecting interface elements is mainly due to the lack of experimental properties however it was already successfully employed in previous studies [2, 6]. In the total strain approach the constitutive model describes the stress as a function of the strain. In the rotating crack approach stress-strain relationships are evaluated in the principal directions of the strain vector [7]. Few data were available for constituent materials, especially for the nonlinear post peak phase, so that plasticity was assumed 1829

4 in compression, while in tension two limit cases were considered, namely plasticity and failure. All the analyses were performed under displacement control measuring in-plane deformations and evolution of reacting stresses. The diagonal compressive axial load has been applied, as a displacement load, through two wooden supports. The supports have been modeled at the two opposite corners of the panel (Fig. 4) according to experimental test setup [1]. These wooden supports have been also modeled by means of eight-node quadrilateral isoparametric plane stress element. As a boundary condition the bases were fixed Numerical test program Parametric FEM analyses were compared to experimental tests [1]. Variable parameters were the mechanical properties of the soil and the softening model in tension. In particular five cases were considered, each one including both an tensile plastic behavior and a tensile failure, namely: plain tested: the wall is made of plain adobe bricks 28 dd. curing and fresh plain mortar (i.e. dd. curing), Young modulus for both materials is 2 MPa based on experimental data fitting; straw tested: the wall is made of adobe bricks 28 dd. curing with 1% straw content and fresh plain mortar (i.e. dd. curing), Young modulus for brick is 1 MPa while for mortar is 2 MPa, it is based on experimental data fitting accounting for the ratio.5 due to straw content (see Fig. 2); fly ash tested: the wall is made of adobe bricks 28 dd. curing with 1% fly ash content and fresh plain mortar (i.e. dd. curing), Young modulus for both materials is 5 MPa based on experimental data fitting; long term: this wall, not tested in reality, is made of plain adobe bricks and plain mortar after long curing time (i.e. curing time higher than about 28 dd.); Young moduli were the same as the first case, for comparison purpose; mortar B: this wall, not tested in reality, is considered for comparison only purpose with plain tested wall; the wall is made of plain adobe bricks 28 dd. curing and a better mortar compared to plain soil; Young moduli were the same as the first case, for comparison purpose. 4. EXPERIMENTAL-THEORETICAL COMPARISON The behavior of adobe wall panel was analyzed (varying softening models and mechanical parameters) in terms of load-displacement curve, shear stress-average diagonal strain curve, shear stress-average shear strain curve, Poisson ratio-displacement and Shear modulus-displacement curves. According to ASTM E [1] standard method, the shear stress, τ, has been obtained as τ =.77 V/A n, were V = diagonal load and A n = net section area of the uncracked section of the panel (A n =.92 m 2 in the present case). The average vertical and horizontal strains, ε v and ε h have been computed as the average displacement along the compressive and tensile diagonals, respectively, over the same gauge length (4 mm). The shear strain, γ, according to ASTM E [1], is γ = ε v +ε h. The Shear modulus, G, and the Poisson ratio, ν, were computed according to the well-known solid mechanics relationship, respectively as ν = -ε h /ε v and G = τ/γ, where E is the Young Modulus. Fig. 5 Experimental failure mode (plain adobe soil) 183

5 For each analysis, the failure modes were also checked by means of the crack patterns. Experimental failure mode mainly involved cracking and detachment of lateral corners of the panel, outside the compressed strut between the two wooden loading supports, as shown in (Fig. 5). Numerical tests mainly reproduced the same cracking pattern, but the spreading of cracks (smeared crack strain field in numerical simulations), depends mainly on post peak tensile behavior of soil. In next figures solid signs represent experimental data, while continuous and dashed lines represent and post peak tensile behavior, respectively. A small cross remarks the failure point for material FEM model: plain tested The plain tested panel is almost homogeneous panel, in the sense that mortar and bricks are made of the same material. However, different curing times differentiate the two materials: mortar is almost fresh, while bricks are cured for 28 dd., so that their strength, both in tension and compression was higher. According to (Fig. 6) crack pattern almost involved vertical lines connecting the wooden supports. Global response in terms of Force/Displacement highlights an almost linear behavior, and material seems to better catch experimental failure, both in terms of crack pattern and of failure load. 5 Crack pattern ( in tension) Crack pattern ( in tension).4 Force [kn] curve experimental x failure eh [mm/mm] ev [mm/mm] G [MPa] n [-] Fig. 6 Experimental-theoretical comparison (plain adobe soil) 4.2. FEM model: straw tested The straw tested panel, conversely, is not homogeneous panel: mortar and bricks have different stiffness. Mortar has no straw content, so, according to (Fig. 2), its Young modulus is almost doubled if compared to bricks, having 1% straw content. Fitting of experimental elastic global curve leads to a Young modulus of bricks about 5 times higher compared to previous test. However, the modulus of bricks smaller than mortar produces a wider crack pattern (see Fig. 7) compared to previous test. Global response in terms of Force/Displacement highlights an almost linear behavior, and 1831

6 material failure matches experimental yielding point. The second less stiff branch is almost related to a global damage, as highlighted by sharp change in shear modulus, G, and Poisson ratio, ν, behavior. The scatter after 6 mm displacement is mainly due to the behavior in compression of materials, while a softening behavior in compression can be expected; however the limited knowledge in terms of experimental characterization of basic materials does not allow to better fit the curve up to failure. In any case the main difference, compared to previous test, is the Young modulus (while strength of bricks and mortar is the same), and the global effect is not only an increase of shear stiffness (about 5 times higher as the increase of Young Modulus of bricks), but also an increase of shear strength, about 3%. This increase in global shear strength is not related to any increase of strength of constituent materials, but only to an increase of Young Modulus. Force [kn] Crack pattern ( in tension) curve experimental Crack pattern ( in tension).5.25 x failure eh [mm/mm] ev [mm/mm] G [MPa] n [-] Fig. 7 Experimental-theoretical comparison (bricks having 1% straw content) 4.3. FEM model: fly ash tested The fly ash tested panel is again almost a homogeneous panel as the first plain one, in the sense that mortar and bricks have the same Young Modulus. However, a different strength differentiates the two materials: mortar is the same as in previous tests, almost fresh, while bricks cured for 28 dd., so that their strength, both in tension and compression was much higher (not only due to 28 dd. curing, but also due to fly ash addition). Fitting of experimental elastic global curve leads to a Young modulus of bricks about 2.5 times higher compared to first test. The crack pattern (see Fig. 8) is similar to first plain soil test. In this case the second less stiff branch starts before major cracking (and before material failure) and the scatter after about 3 mm displacement is mainly due to the behavior in compression of materials. In any case the main difference, compared to first test, is the higher Young 1832

modulus (about 2.5 times higher) and the higher strength of bricks (about 5% higher), and the global effect is not only an increase of shear stiffness, G, (about 2.

7 modulus (about 2.5 times higher) and the higher strength of bricks (about 5% higher), and the global effect is not only an increase of shear stiffness, G, (about 2.5 times higher), but also an increase of shear strength, being almost 7% higher. In this case, the global effect of shear strength increase (about 7% compared to first case), is almost comparable to the increase of brick strength (about 5%) emphasized by the increase of Young modulus of materials (as in previous case the increase of Young modulus alone was able to slightly increase the strength); the mortar is always the same in last three analyses. Force [kn] G [MPa] n [-] Crack pattern ( in tension) 6 5 curve exprerimental Crack pattern ( in tension).6.4 x failure eh [mm/mm] ev [mm/mm] Fig. 8 Experimental-theoretical comparison (bricks having 1% fly ash content) 4.4. FEM model: long term curing The long term curing panel was not experimentally tested, but it is analyzed to assess the influence of strength of materials on global behavior of the masonry panel. It is again almost an homogeneous panel as the first plain one, in a general sense that mortar and bricks have identical mechanical properties. The strength of the two materials is the same, corresponding to more than 28 dd. curing and it is about 25% higher, compared to plain soil bricks (28 dd. curing) and 2.5 times higher than plain soil mortar ( dd. curing). The crack pattern is almost similar (see Fig. 9a) compared to previous test, but the panel presents a higher strength. The global response in terms of Force/Displacement is almost linear up to failure point being the shear strength almost doubled if compared to first test (for this reason the crack pattern only is shown). In any case the main difference, compared to first test, is the strength of materials, and the global effect is an increase of shear strength, being comparable to the increase of mortar strength FEM model: mortar B The panel with a better mortar (compared to first test), was not tested in reality, but it is analyzed to assess the influence of strength of materials on global behavior of the masonry panel. It is again almost 1833

8 a homogeneous panel as the first plain one (having identical Young Moduli only), but the strength of the mortar is about 2.5 times higher, compared to plain soil mortar ( dd. curing) brick are the same. The crack pattern is almost similar (see Fig. 9b) compared to first test, but the panel presents a higher strength, and also the global response in terms of Force/Displacement is similar (for this reason the crack pattern only is shown). The comparison with the first test allows to find, in general, a spreading of crack pattern and higher global performances, however an easier and more direct comparison can be made with previous test. In fact the main difference, compared to previous test, is the strength of brick, and the global effect is a reduction of shear strength (almost 2% smaller), being comparable to the reduction of strength of the bricks. Crack pattern ( in tension) Crack pattern ( in tension) Crack pattern ( in tension) Crack pattern ( in tension) a).4.4 b) Fig. 9 Theoretical crack pattern and τ-γ curves: a) plain adobe soil having long term curing; b) mortar having higher strength 5. CONCLUSIONS Earth is still diffused as construction material for many adobe constructions worldwide, especially for its cheapness. Also many historic structures, built for thousands of years, are now in the need of conservation. Despite their diffusion, only few experimental tests are available, hence numerical experimentation is seen as a feasible way to deepen knowledge on seismic behavior of such constructions. After validating the numerical model, FEM simulations can be used as a tool to increase the knowledge on the effect of constituent materials on global performances. In fact, both the intrinsic variability of soil material, and the variability due to aging and composition, jeopardize seriously the seismic performance of adobe constructions. Scope of present study is to highlight the influence of mortar and brick composition and aging on the shear performance of in-plane walls, after validating the model based on experimental tests. A literature survey clarified the effect of curing time on the strength of soil material, namely an increase of strength both in tension and in compression, and the effect of straw additions on Young modulus and of fly ash on strength. Then numerical analyses allowed to highlight the following effects. In (Tab. 2) ratios are evaluated with respect to plain soil test. Young modulus of bricks is the driving parameter for the shear stiffness of the panel, in fact the increase of stiffness of bricks (e.g. 1% straw test) directly reflects into a proportional increase of global stiffness, while the increase of mortar stiffness has no comparable effect. However the crack pattern is directly affected by an increase of mortar stiffness, in fact stiffer mortar is able to spread the smeared cracking strain field. The increase of stiffness is related to an increase of global shear strength, even if there is no increase of strength of basic materials. This is confirmed when increasing the brick strength only (e.g. 1% fly ash test), the global shear strength increase is more than proportional if attributed also to the increase of stiffness. 1834

9 The increase of mortar strength (e.g. equal for both long term curing and better mortar simulations), yet having the same stiffness of basic materials, leads to an increase of global shear strength. However the increase, at global level (about 2.5 times), is nearly proportional to the mortar strength increase, at local level (about 2.5 times), but it is mitigated by the reduction of brick strength, in fact a reduction of brick strength of about 2% corresponds almost proportionally to a 2% reduction of global shear strength. FEM Model Brick Strength Ratio Material Level (input data) Mortar Brick Strength Stiffness Ratio Ratio Table 2 Main results of FEM Mortar Stiffness Ratio G [MPa] Global Level Results τ [MPa] G Ratio τ Ratio Plain Straw 1% Fly Ash 1% Long Curing Mortar B REFERENCES [1] American Society for Testing Materials (ASTM). (1981) ptandard test method for diagonal tension EshearF in masonry assemblages. ApTM b [2] Lignola G.P., Prota A., Manfredi G. (29) Nonlinear analyses of tuff masonry walls strengthened with cementitious matrix-grid composites gournal of Composites for Construction ApCb, 13(4), pp [3] Turanli L., Saritas A. (211) Strengthening the structural behavior of adobe walls through the use of plaster reinforcement mesh. Construction and Building Materials, 25(4), pp [4] Turanli L., (1985) bvaluation of some physical and mechanical properties of plain and stabilized adobe blocks. Master thesis in civil engineering. Middle East Technical University, Ankara, Turkey. [5] Quagliarini E., Lenci S. (21) The influence of natural stabilizers and natural fibres on the mechanical properties of ancient roman adobe bricks. gournal of Cultural eeritage, 11(3), pp [6] Lignola G.P., Prota A., Manfredi G. (212) Numerical investigation on the influence of FRP retrofit layout and geometry on the in-plane behavior of masonry walls. gournal of Composites for Construction ApCb, In press, doi: 1.161/(ASCE)CC [7] Manie J., Kikstra W.P. (21) DIANA Finite Element Analysis. rser s Manual release VK4KPK blement iibrary, TNO DIANA bv, Delft, The Netherlands. 1835

Chapter 7. Finite Elements Model and Results

Chapter 7. Finite Elements Model and Results Chapter 7 Finite Elements Model and Results 7.1 Introduction In this chapter, a three dimensional model was presented. The analytical model was developed by using the finite elements method to simulate