Embed Size (px)
Citation preview
Int J Fract (2011) 172:193–200DOI 10.1007/s10704-011-9651-5 © Springer Science+Business Media B.V. 2011
123
AN EXPERIMENTAL STUDY ON DAMAGE EVOLUTION OF UNFIRED DRY EARTH UNDER COMPRESSION
Stefano Lenci*, Quintilio Piattoni*, Francesco Clementi*, Tomasz Sadowski**
*Department of Architecture, Buildings and Structures, Polytechnic University of Marche, via Brecce Bianche, I-60131 Ancona, Italy e-mail: [email protected]
**Lublin University of Technology, Faculty of Civil and Sanitary Engineering, 40 Nadbystrzycka St., 20-618 Lublin, Poland e-mail: [email protected]
Abstract. The damage behaviour of unfired dry earth is determined experimentally under compression by means of loading-unloading cyclic tests. The scalar damage parameter is determined and its evolution law is related to the applied strain - d ( ). Interpolating functions are determined, permitting to estimate how the damage depends on the deformation process of the considered material. Different aspect-ratios of the specimens are considered.
Keywords: Earth blocks, Compressive strength, Damage, Softening behaviour.
1. Introduction. Over the past seventy years the use of unfired earth block experiences a sort of revival, and they have been “re-discovered” and increasingly used. This trend call for a determination of the mechanical properties on earth blocks. Great attention has been paid to the experimental determination of the compressive strength (Walker, 1997; 2000) as it represents the most important parameter to evaluate the load-carrying capacity. The influence of different ages of seasoning on compression tests was reported by Lilley and Robinson (1995) and by Medjo Eko et al. (2006). The matter of how properly perform a compression test has been deeply analyzed and reviewed by Morel et al. (2007), where the influence of the block geometry, of the test procedure (including those proposed by international standards) and of the basic material properties (dry density, cement and moisture contents) have been discussed. The effect of reinforcing fibers, both natural (straw) and artificial (plastic and polystyrene) inserted in the earth block as a fabric layers are investigated by Binici et al. (2005-2007) while Yetgin et al. (2008) have shown that the addition of straw fibers decrease the compressive strength, a result which is confirmed by Bouhicha et al. (2005). In Yetgin et al. (2008) also tensile tests were performed. The effect of stabilization with added cement was also considered by Mattone (2001). On the contrary, up to the authors’ knowledge, less or no attention has been paid to other important characteristic, such as experimentally assessed the damage evolution law under compression, which constitutes the objectives of this paper. The damage evolutions during deformation processes are discussed with reference to two different specimens, compressed cubes and prisms, in order to investigate the effect of the aspect ratio. In particular compression tests, conducted with monotonic and cyclic load, are presented in the form of stress-strain diagrams. For cyclic load we have determine the scalar damage parameter d of the samples for different stages of the deformation processes.
123
194 S. Lenci et al.
2. Materials and preparation. The material used to realized the compressed earth block is made of three different constituents, having the following proportions: 1 volume of “earth,” 1/2 volume of “sandstone” and 1/2 volume of fibres straw. The geotechnical characteristics of the “earth” are reported in Fig. 1a (particle size distribution). According to the ASTM D2487 it can be classified as “lean clay with sand (CL).” The geotechnical characteristics of the “sandstone” are reported in Fig. 1b (particle size distribution). According to the ASTM D2487 it can be classified as “well graded sand (SW).” The fibres straw has a length which varies from 2 to 8 cm, with an average value of 5 cm.
0
20
40
60
80
100
1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02
Grain size [mm]
Pass
ing
[%]
0
20
40
60
80
100
1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02
Grain size [mm]Pa
ssin
g [%
]
(a) (b) Fig. 1 Grading curve for (a) the “earth” and (b) the “sandstone.”
Material preparation and mixing was carried out manually. 1/3 (on average) volume of water was added to guarantee normal consistency and manual operations. The mixture was manually pressed into formworks of wood of the dimensions of 32×46×13 cm. After removing the boxes, the blocks were cured under stationary thermo-hygrometric conditions (temperature 23-26 °C; relative humidity 45-55%). After about five months, the blocks were cut by saw to obtain the desired specimens. At the end of the tests, it was verified that the moisture contents was less than 3-4%, so we have actually tested a dry material.
3. Compression tests. As the compressive strength depends on the dimension of the specimen, and because this matter is still under investigation and it is not well understood the influence of the aspect ratio, see Morel et al. (2007), we decide to perform compression tests on cubic (Fig. 2a) and on prismatic (Fig. 2b) specimens.
(a) (b)
Fig. 2 The specimens for the compression tests. (a) cubic 50×50×50 cm and (b) prismatic 45×58×112 cm.
The procedure adopted is that of national standards and codes of practice for fired clay and concrete blocks. Specimens are capped and tested directly between steel plates.
123
An experimental study on damage evolution 195
Blocks surface are always sufficiently flat and parallel that only thin layer of sand capping is necessary. In order to detect the softening branch, we have applied a controlled displacement and measured the force, i.e. a soft device was used. For each specimen dimension, we have performed two tests. The first one is monotonic and is aimed at capturing the general overall behaviour, including the determination of the Young modulus E, of the maximum stress max and of the ultimate strain u. The second one is cyclic, and from this case we detected the damage behaviour of the material.
3.1. Cubic samples. The result of the monotonic compression tests are reported in Fig. 3. The maximum stress max=1.57 MPa and the Young modulus E=148.08 MPa are in agreement with the results of other studies (see, e.g., Yetgin et al. (2008)). Also the values of the strain in correspondence of max are comparable with that obtained by other authors (Yetgin et al. (2008)). What was not reported in other papers is the long softening branch, which highlights the very large deformation sustained before collapse, which is of course a consequence of the presence of the fibres of straw. Note that the ultimate strain u =20.8 % is comparable to that of steel. This sort of “ductility” is very important in terms of new trends for computing the seismic resistance of buildings.
00.20.40.60.81
1.21.41.61.8
0 0.05 0.1 0.15 0.2 0.25
Stre
ss
[MPa
]
Strain
max=1.57MPa; u=0.208; E=148.08MPa
Fig. 3 Stress-strain relation for the monotonic compression test on cubic specimen.
The cyclic test permits evaluating the damage evolution law of the material. The relation between the stress and the strain (Fig. 4) shows that the compressive strength, the overall shape of the curve and the initial Young modulus are comparable with that of the monotonic test, but the final strain is approximately halved. Thus, the damage has not only an influence on the reducing the elastic modulus, but also on reducing the “ductility.”
00.20.40.60.81
1.21.41.61.8
0 0.05 0.1 0.15 0.2 0.25
Stre
ss
[MPa
]
Strain
max=1.55MPa; u=0.118
Fig. 4 Stress-strain relation for the cyclic compression test on cubic specimen.
123
196 S. Lenci et al.
Table 1 shows the values of the Young’s modulus for each load step. It is evident how the first step of compression causes a compacting of the sample, so that initially the elastic modulus increases considerably. It becomes 4 time larger at the end of the linear elastic range, where we have performed the first unload-reload cycle. In subsequent cycles the current damage value of the specimen entails the reduction of the Young’s modulus, which is evident both in Fig. 4 and in Table 1.
Table 1 Young’s modulus and damage parameter for each load step. Cubic specimen.
No step Young’s modulus (MPa) d res [%]
1 132.33 / 0.00 2 = initial 606.52 0.00 0.88
3 493.16 0.19 2.02 4 413.24 0.32 3.18 5 260.28 0.57 4.10 6 124.41 0.79 5.09 7 79.88 0.87 6.12 8 67.26 0.89 7.42 9 45.94 0.92 8.61
The damage behaviour of the material is estimated as the scalar damage parameter, e.g. Lemaitre and Chaboche (1978), Sadowski (1994), Lemaitre (1996)
d = 1 – (Ea/Ei), (1)
where Ea is the elastic modulus of the current load step and Ei is the initial elastic modulus, which is reported in Table 1, where we have disregarded the E of the virgin state and have considered the “initial” value of E that after the compacting.
0
0.2
0.4
0.6
0.8
1
0 0.03 0.06 0.09 0.12 0.15
d
Strain Fig. 5 The scalar damage parameter as a function of the strain (thick line), and the interpolating curve (thin line) for
the cubic specimen.
Following the deformation damage theory (Sadowski, 1991) the damage evolution law can be a function of the residual strain at the end of the unload process (see Table 1), Fig. 5
d ( ) = 0.0007 4 – 0.0161 3 + 0.1104 2 – 0.0891 , (2)
which gives R2 = 0.9898 and therefore it is very accurate. From Fig. 5 it is seen that the
123
An experimental study on damage evolution 197
damage increases rapidly in the softening path of the stress-strain curve (compare Figs. 4 and 5), and that it quickly tends to the completely damage state (d = 1). For example, for = 0.05, i.e. when the stress in still about 80% of the maximum stress (Fig. 4), that
damage is about 0.8 (Fig. 5), i.e. the material is almost completely damaged while still having a good stress resistance.
3.2. Prismatic samples. The experimental stress-strain relation for the monotonic test on the prismatic sample is reported in Fig. 6, where the corresponding curve of the cubic sample (Fig. 3) is also reported for comparison. We see that with the prismatic sample we have a slightly higher maximum stress, and the “same” Young modulus. The main differences, both qualitative and quantitative, are in the softening branch, that of prismatic sample being much more (approximately one half) shorter. Thus, the “ductility” is lost by the prismatic sample. This can be explained by the different breaking mechanism observed in the two cases. In fact, for the cubic specimen we have a spread cracking (Fig. 7a), so that a lot of energy is spent to break the material, while for the prismatic specimen we have seen only one diagonal main crack (Fig. 7b), i.e. a localized rupture requiring less energy and thus developing in an easier way and for lower values of the strain. This is a noteworthy “size effect” observed in our tests.
Fig. 6 Stress-strain relation for the monotonic compression test on prismatic (gray) and cubic (black) specimens.
(a) (b)
Fig. 7 The breaking of (a) the cubic and (b) the prismatic specimens.
The result of the cyclic compression test is reported in Fig. 9. We have that the maximum stress has been reduced with respect to the monotonic test ( max=1.31 MPa vs max=1.70
123
198 S. Lenci et al.
MPa), while the initial Young modulus is unchanged (E=129.32 MPa vs E=130.22 MPa). As in the case of cubic specimen, there is an initial compacting phase, where the elastic modulus strongly increases (see Fig. 8 and Table 2) before undergoing damage. The overall softening branch has not been strongly modified in the cyclic test.
00.20.40.60.81
1.21.41.61.8
0.00 0.05 0.10 0.15 0.20 0.25
Stre
ss
[MPa
]
Strain
max=1.31MPa; u=0.063
Fig. 8 Stress-strain relation for the cyclic compression test on prismatic specimen.
The damage characteristics are reported in Table 2 and in Fig. 9, whereas the damage evolution law can be taken as the following interpolating curve
d ( )= 0.0012 4 – 0.0231 3 + 0.1254 2 – 0.1132 (3)
with R2 = 0.9733. When compared with Fig. 5, the Fig. 9 shows that for the prismatic test the development of damage is minor, and it tends to the final value of d = 0.4, which means that at the rupture the damage is less than one-half. Thus, the loss of “ductility” is balanced by the increment of the undamaged features at breaking. This agrees with the localized damage observed at breaking (Fig. 7b).
Table 2 Young’s modulus and damage parameter for each load step. Prismatic specimen.
No step Young’s modulus (MPa) d res [%]
1 129.33 / 0.00 2 = initial 434.45 0.00 0.41
3 430.26 0.01 1.12 4 412.20 0.05 1.92 5 331.71 0.24 2.72 6 280.08 0.36 3.56 7 272.53 0.37 4.44 8 255.09 0.41 5.28
123
An experimental study on damage evolution 199
0
0.2
0.4
0.6
0.8
1
0 0.02 0.04 0.06 0.08 0.1
d
Strain Fig. 9 The scalar damage parameter as a function of the strain (thick line), and the interpolating curve (thin line) for
the prismatic specimen.
4. Conclusions. The damage of the unfired dry earth has been investigated by different experimental tests. Both monotonic and cyclic applied displacements were considered, as well as two different aspect ratio. The monotonic tests were used to determine the Young’s modulus and compressive strength, which are seen to be comparable to those reported in the literature. The cyclic tests are used to determine the scalar damage parameter d of the samples and further the damage evolution law - d ( ), for both cubic and prismatic specimens, which have been shown to have the same qualitative behaviour but a quite different quantitative behaviour. We have highlighted the long softening branches experienced by all the specimens, which shows the very large deformation sustained before collapse. These properties, which are not reported in the literature, are a consequence of the straw fibres inside the material, and they are very important from a building design point of view. The compression tests have shown that the increment of the aspect ratio reduces the ultimate strain, i.e. it makes the specimen less “ductile.”
Acknowledgements The research leading to these results has received funding from the European Union Seventh
Framework Programme (FP7/2007 – 2013), FP7 - REGPOT – 2009 – 1, under grant agreement No: 245479; CEMCAST.
The support by Polish Ministry of Science and Higher Education - Grant No 1471-1/7.PR UE/2010/7 - is also acknowledged.
References
Binici H, Aksogan O, Shah T (2005) Investigation of fibre reinforced mud brick as a building material. Construction and Building Materials 19:313-8
Binici H, Aksogan O, Nuri Bodur M, Akca E, Kapur S (2007) Thermal isolation and mechanical properties of fibre reinforced mud bricks as wall materials. Construction and Building Materials 21: 901-6
Bouhicha M, Aouissi F, Kenai S (2005) Performance of composite soil reinforced with barley straw. Cement and Concrete Composites 27:617-21
Lemaitre J and Chaboche JL (1978) Aspect phenomenologiques de la rupture par endommagement. Jour. de Mech. Appl. 2:317-365
Lilley DM, Robinson J (1995) Ultimate strength of rammed earth walls with openings. In: Proc. Instn Civ. Engrs & Bldgs 110:278-87.
Mattone R (2001) Unfired earth, traditions and innovations. L’industria dei Laterizi 71:313-20 Medjo Eko R, Mpele M, Dtawagap Doumtsop M, Seba Minsili L, Wouatong AS (2006) Some hydraulic, mechanical,
and physical characteristics of three types of compressed earth blocks. Agricultural Engineering International: the CIGR Ejournal, VIII: Manuscript BC 06 007
Sadowski T (1991) Deformation damage theory of materials and ist application to the analysis of the deformation process of square plates. Arch. Appl. Mech. 61:449-461
Sadowski T (1994) Modelling of semi-brittle MgO ceramics behavior under compression. Mech. Materials 18:1-16 Walker P (1997) Characteristics of pressed earth blocks in compression. In: Proc. of the 11th international brick/block
masonry conference, Shangai, China, 14-16 October, 1-10
123
200 S. Lenci et al.
Walker P (2000) Strength and durability testing of earth blocks. In: Proc. of the 6th international seminar on structural masonry for developing countries, 111-18
Morel JC, Pkla A (2002) A model to measure compressive strength of compressed earth blocks with the ‘3 points bending test’. Constr. Build. Mat. 16:303-310
Morel JC, Pkla A, Walker P (2007) Compressive strength testing of compressed earth blocks. Constr. Build. Mat. 21: 303-309
Yetgin S, Cavdar O, Cavdar A (2008) The effects of the fiber contents on the mechanic properties of the adobes. Constr. Build. Mat. 22, 222-227
