Materials’ behaviour

i) Masonry

The main characteristics of masonry are its heterogeneity, anisotropy, high compressive strength and reduced tensile strength.

The masonry found in arch bridges, particularly in Portugal, is usually comprised by natural stone blocks with interfaces in between them, which can be mortared or dry (without mortar), thus constituting a heterogeneous and anisotropic, with discontinuities and complex behaviour. From the point of view of its mechanical behaviour, the masonry is controlled by the mechanical properties of its constituents, blocks, mortar and interfaces. The interfaces constitute discontinuity planes of weakness in the masonry, where opening/closing and sliding can occur. The presence of mortar joints in a masonry structure can provide strength to tensile stress, which is markedly less than the material compressive strength. When subjected to very low stress levels, masonry behaves approximately in a linear elastic manner, but it becomes increasingly non-linear after the formation of cracks and the subsequent redistribution of stresses through the uncracked material as the structure approaches collapse (Sarhosis et al., 2015).

Depending on the magnitude and direction of shear and normal stresses applied to masonry, different failure modes can occur, as shown in Figure 3.1, for a basic association of two blocks with mortar in between them.

Figure 3.1 – Failure modes in masonry (Lourenço & Rots, 1997).

When subjected to tensile stresses, the masonry structures exhibit quasi-brittle behaviour with very low tensile strength. The characterization of masonry samples is difficult to carry out given the low resistance they exhibit in this domain. In Van der Pluijm (1999), direct tensile tests were performed in masonry samples, constituted by stone blocks and mortared interfaces. The characterization of each masonry component separately and using stone and mortar tests is simpler than the characterization of samples involving interfaces, and that is the reason why these types of tests are more frequent.

For the stone material, the tensile behaviour can be observed in a direct tensile experimental test, by displacement control, resulting in a diagram illustrated in Figure 3.2a. The diagram starts with a linear elastic part until the tensile strength is reached and the first cracking occurs. After that point softening takes place, which is indicated by a decrease in the stiffness of the material and also a decrease in the load applied to the material sample. The total fracture energy can be derived from the diagram by integrating the stress-displacement curve. The material is considered completely failed when the strength and stiffness are equal to zero. Some experiments regarding the tensile behaviour of granite stone were performed by Vasconcelos et al. (2008), where tensile strengths ranging from 1.6 MPa to 8.1

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behaviour Figure 3.2b, also starts with a linear elastic part until the first micro-cracks appear. At that moment the hardening starts, which means that the stiffness of the material starts to decrease but the load can still increase. This goes on until the point where multiple micro-cracks connect and result in bigger macro cracks. Then the softening part of the stress-strain diagram starts, where the size and number of cracks increases. The final stage is a plateau because in compression a small amount of strength remains regardless of the number of cracks that have developed.

a) b)

Figure 3.2 – a) Tensile and b) compressive behaviour of stone-like materials (Lourenço, 1998).

The shear behaviour of masonry depends essentially on the shear strength of its interfaces. Given the distinction between the various types of joints commonly found in masonry structures and arch bridges in particular, it is usual to differentiate the behaviour of dry joints and mortared joints. Some experiments were carried out by Costa (2009) and reported in Arêde et al. (2019) regarding the shear behaviour of stone-to-stone granite joint samples considering different normal stress levels.

In the case of mortared joints, its evolution, shown in Figure 3.3a, is characterized by a rapid increase of stress until shear strength is reached (peak resistance), which corresponds to the sum of shear strength by the interface mortar between the two blocks mobilized for their separation (usually called cohesion) and the friction resistance between the contact surfaces mobilized in shear (horizontal) displacement (γ).

After the peak value, the curve exhibits a softening branch until reaching the zero level or a residual value. By recording the peak and residual values of shear strength for different values of normal compression and adjusting these values to a linear regression, two lines are obtained as represented in Figure 3.3b. This relationship between the peak values of the shear strength τ and the normal stress σ can be represented by a Mohr-Coulomb envelope which depends on the parameters c and ϕ which are, respectively, the cohesion and the friction angle of the joint.

a) b)

Figure 3.3 – Shear test in mortared joints: a) Evolution for different normal stresses and b) Mohr-Coulomb envelope (Costa, 2009).

In the case of dry joints, the evolution in shear stress vs shear displacement, shown in Figure 3.4a, depends only on the friction mobilized by the joint. Its representation exhibits an hardening phase followed by a branch with a constant value. On the other hand, the Mohr-Coulomb criterion suited for this type of joint, represents the residual friction angle corresponding to the value at shear peak strength, Figure 3.4b.

a) b)

Figure 3.4 – Shear test in dry joints: a) Evolution for different normal compression values and b) Mohr-Coulomb envelope (Costa, 2009).

The compressive behaviour of the masonry is very diverse and, as described below, depends on the properties of the materials, stone blocks and mortar, the opening and closing conditions and the roughness of the interfaces. The compressive failure mode of masonry, as previously seen in Figure 3.1 (e), is prominently characterized by the existence of cracking parallel to the direction of the applied stress in the blocks and mortar due to the Poisson effect.

For the characterization of the uniaxial compression behaviour in masonry prisms, Vasconcelos and Lourenço (2009) carried out a campaign of monotonic and cyclic compression tests on prisms of granite stone blocks interposed with and without mortared joints with different block surface conditions, where the obtained behaviour curves are presented in Figure 3.5. The shape of the stress–strain curve is characterized by an initial upward concavity due to the initial setting of the bed joints, then followed by a linear behaviour until a compressive stress close to the peak strength and after the peak load is reached the majority failed in a brittle manner. In cyclic tests, it is observed that significant higher stiffness in the reloading cycles in the pre-peak regime are recorded comparatively to the stiffness of the virgin branch. The conclusions drawn from this study pointed out that the material and surface condition (smooth or rough) of the bed joints influences considerably the failure mode and the compressive strength of stone masonry.

a) b)

Figure 3.5 – Typical stress-strain diagrams for compression tests: a) monotonic and b) cyclic (Vasconcelos &

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ii) Infill

In masonry arch bridges, the materials used as infill can be diverse. For roadway bridges, solutions of granular materials with spread granulometry (tout-venant type) with gravel or soil, are normally adopted.

On the other hand, in railway bridges, it is more frequent to find solutions in which the bridge is filled with irregular stones and cement mortar, winding up as a more mortared material similar to plain concrete. This material has more strength than a regular tout-venant or soil mixture.

The behaviour expressed by this type of infill material is similar to masonry, in terms of the relation between stress and strain. In this context, the shear strength could be expressed by a Mohr-Coulomb yield surface, which represents the dependence between the shear stress and the normal stress as a function of the friction angle and cohesion, and the evolution of the plastic yield is translated by appropriate constitutive behaviour laws.