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Adobe constructions were widespread in the ancient world, and earth was one of the most used construction materials in ancient times. Therefore, the preservation of adobe structures, especially against seismic events, is nowadays an important structural issue. Previous experimental tests have shown that the ratio between mortar and brick mechanical properties (

Earth is one of the oldest and most widespread construction material used in the construction of buildings and has been used for thousands of years. Earth can be considered the cheapest material readily available for construction. It has been extensively used for masonry 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 construction. Furthermore, due to its inherent properties, earth is an efficient heat and sound insulating material [

Experimental diagonal compression tests on adobe wall panels (unreinforced and reinforced with plaster fiberglass mesh) presented in [

The specimens were built with the global size of 80 × 80 cm^{2}. The brick unit size was 11.5 × 10.5 × 21.5 cm^{3}. The mortar thickness was 10 mm, while the width (the third out-of-plane dimension) was 11.5 cm for both bricks and mortar. Different adobe soil curing for both the bricks and the mortar were used for each specimen. The reinforced panels were built placing a plaster reinforcement fiberglass mesh (with equal spacing of 5 mm × 5 mm) inside the horizontal mortar joint of the adobe blocks. This sort of mesh fiber reinforcement is very cheap and commonly used for reinforced plaster coatings, usually applied on the exterior and interior faces of walls by the construction industry.

Tested panel geometry.

An essential mechanical characterization of the material is provided in [

Compressive and tensile strength trends when varying the curing time.

The influence of the different constituent materials (^{2}, density 2.5 g/cm^{3}, elastic modulus 20 GPa and strength 1000 N/50 mm. Lacking an experimental counterpart, for comparison purposes, numerical simulations were performed considering two more cases: the first one applying a mortar having higher performances compared to plain fresh mortar, namely, “mortar B”; the second one considering for both mortar and bricks the same properties, due to the long time of the curing (

Material mechanical properties.

Properties | Fresh plain soil | Plain soil | Plain soil | Mortar B |
---|---|---|---|---|

Curing time (days) | 0 | 28 | >28 | 0 |

Tensile strength (kPa) | 39.2 | 78.4 | 98 | 98 |

Compressive strength (MPa) | 3.32 | 6.64 | 8.30 | 8.30 |

The FEM model used is constituted of more than 13,000 eight-node quadrilateral isoparametric plane stress elements based on quadratic interpolation and Gauss integration (

All the analyses have been performed by means of the TNO DIANA v9.4.4 code. In the FEM model, bricks and mortar are modeled individually, without interface elements between them, according to the total strain model coupled with the rotating crack stress-strain relationship approach. In particular, 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, as reported in [

Test setup: (

Few data were available for constituent materials, especially for the nonlinear post peak phase; therefore, ideal plasticity was assumed in compression. This assumption is acceptable, since the compressive strength has never been reached during the analyses, remarking that the tensile behavior governs the problem. Therefore, in tension, two limit cases were considered, namely “ideal plasticity” and “brittle failure”. The “brittle failure” represents the worst case, which is the more realistic, as well. This case has been modeled by means of an elastic-brittle model. Whereas the “ideal plasticity”, which represents the upper bound, has been modeled by means of an elastic-perfectly plastic model. These two cases have been considered in order to define the boundaries between which the real behavior has to be. All the analyses were performed under displacement control, measuring in-plane deformations and the 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, according to the experimental test setup [

The results of FEM analyses were validated through a comparison between experimental and numerical outcomes. In particular, three main cases were considered, each one including both the tensile plasticity models introduced in the previous section (

Plain tested: the wall is made of plain adobe bricks, 28 days curing and fresh plain mortar (

Long-term curing (LTC): this wall, not tested in reality, is made of plain adobe bricks and plain mortar after a long curing time (

Mortar B (MB): this wall, not tested in reality, is considered only for comparison purposes with the plain tested wall; the wall is made of plain adobe bricks, 28 days curing and a better mortar compared to plain soil; elastic moduli were the same as the first case, for comparison purposes.

The masonry material properties used in the FEM analyses are listed in the following

Material parameters used for the finite element method (FEM) analyses. LTC, long-term curing; MB, Mortar B.

FEM model | Brick tensile strength (kPa) | Mortar tensile strength (kPa) | Brick compressive strength (MPa) | Mortar compressive strength (MPa) |
---|---|---|---|---|

Plain | 78.4 | 39.2 | 6.64 | 3.32 |

LTC | 98.0 | 98.0 | 8.30 | 8.30 |

MB | 78.4 | 98.0 | 6.64 | 8.3 |

The behavior of adobe wall panels (unreinforced and reinforced with fiberglass mesh) was analyzed (when varying tension softening models) in terms of the force/displacement curve, shear stress-average diagonal strain curve, shear stress-average shear strain curve, Poisson ratio-displacement and Shear modulus-displacement curves. According to [_{n}, where _{n} = the net section area of the uncracked section of the panel (in the considered case, _{n} = 0.092 m^{2}). 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 (400 mm). The shear strain, γ, according to [_{v} + ε_{h}. The shear modulus, _{h}/ε_{v} and

The FEM model has been validated both in the cases of unreinforced and reinforced plain panels. In both the cases, mortar and bricks are made of the same material. However, different curing times differentiate the two materials. In particular, the mortar is almost fresh, while bricks are cured for 28 days. Therefore, the strength of the brick is higher in both tension and compression.

The main outcomes of the numerical analyses and a comparison between the numerical and experimental force/displacement curves are presented in

Experimental-theoretical comparison (unreinforced plain adobe soil).

According to the results shown in

Detail of the experimental crack pattern (unreinforced plain adobe soil) (reprinted with permission from [

The global response of the reinforced panel in terms of force/displacement highlights, as well as the unreinforced panel is an almost linear behavior (see

Experimental-theoretical comparison (reinforced plain soil panel).

The brittle material model catches the experimental failure better, both in terms of crack pattern and failure load. In the case of the brittle material, the shear modulus,

The LTC panels were not experimentally tested, but they are analyzed to assess the influence of curing time (

In the case of reinforced LTC panel (

Numerical experimentation (unreinforced LTC panel).

Numerical experimentation (reinforced LTC panel).

The panels modeled with a better mortar, as well as the previous LTC panels were not tested in reality. However, this case has been analyzed to assess the influence of the strength of the mortar on the global behavior of the masonry panels. The MB panels are still almost homogeneous panels (having identical elastic moduli). However, the strength of the mortar is about 2.5 times higher, compared to plain soil mortar (0 day curing), while the brick properties are the same as the plain panels case. In the case of the unreinforced panel, both the crack pattern and the global response in terms of force/displacement are almost similar compared to the unreinforced plain panel (

In the reinforced MB panel, the global response in terms of force/displacement and crack pattern is almost similar to the previous case of the long-term curing panel reinforced with mesh (

Numerical experimentation (unreinforced MB panel).

Numerical experimentation (reinforced MB panel).

Adobe earth constructions were copious in the ancient world. Furthermore, earth is still diffuse as a construction material, especially for its cheapness. Many historic structures, built for thousands of years, are now in need of conservation. In spite of their diffusion, only a few experimental tests are available. Actually, the variability of soil mechanic properties due to aging and composition strongly influence the seismic performance of adobe constructions. Plaster fiberglass mesh reinforcement represents a valid seismic reinforcement system for adobe building. The basic concept of this reinforcement is to improve the frictional resistance at the horizontal mortar joint location. In fact, the link between the brick units is the weakest section in the structural behavior of adobe walls. Numerical experimentation is a feasible way to deepen the knowledge of the seismic behavior of such structures. After validating the numerical model, FEM simulations can be used as a tool to increase the knowledge of the effect of fiberglass mesh reinforcement, when varying the constituent materials, on global structural performances. The main scope of the present study is to highlight the influence of different mortar and brick compositions and aging combined with a fiberglass mesh reinforcement on the in-plane shear performance of adobe walls. A literature survey clarified the effect of curing time on the strength of the soil material, namely an increase of strength both in tension and in compression. Then, numerical analyses allowed for us to remark on the following effects. The crack pattern is directly affected by an increase of the mortar strength; in fact, a stronger mortar is able to spread the smeared cracking strain field. In

The main numerical outcomes (the ratios are related to the unreinforced plain panel).

FEM model | Material level (input data) | Global level (outcomes) | |||
---|---|---|---|---|---|

Brick strength ratio | Mortar strength ratio | G (MPa) | τ (MPa) | τ ratio | |

Plain (unreinforced) | 1 | 1 | 9.17 | 0.15 | 1.00 |

Plain (reinforced) | 1 | 1 | 8.14 | 0.19 | 1.26 |

LTC (unreinforced) | 1.25 | 2.5 | 9.17 | 0.32 | 2.20 |

LTC (reinforced) | 1.25 | 2.5 | 8.14 | 0.35 | 2.31 |

MB (unreinforced) | 1 | 2.5 | 9.17 | 0.25 | 1.70 |

MB (reinforced) | 1 | 2.5 | 8.14 | 0.34 | 2.31 |

The analyses were developed within the activities of Rete dei Laboratori Universitari di Ingegneria Sismica—ReLUIS for the research program funded by the Dipartimento di Protezione Civile—Progetto Esecutivo 2010–2013.

The authors declare no conflict of interest.