Unlike mortared masonry system, the surface roughness at the bed joint in mortarless masonry systems plays a critical role. The contact behavior of a dry masonry joint is a complex phenomenon due to the high stress concentrations in the asperities, which cause local crushing at the bed surface. For example, as the vertical load applied on the dry-stacked units increases, the asperities are crushed and the gaps between the units gradually close, leading to the softening behavior or what is referred to as the “seating effect.” Computational modeling can be used to describe further this contact behavior between the units on mortarless structures under different load scenarios.
Finite element modeling has been widely used at various levels of sophistication to simulate the complex contact behavior in mortarless construction (Pei et al. 2005; Zhang et al. 2014). One modeling approach, to account for surface roughness at the bed joint, has
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involved modeling the asperities by considering their approximate geometric properties in a three-dimensional solid model (see Fig. 2-2). In Martinez at el. (2017), this approach was used to compare the compressive response of prisms using a ground (smooth) surface to prisms using an unground (rough) surface at the bed joint. In this study, contact elements were used at the bed joint to control for the sliding behavior in both surface treatments.
Fig. 2-2. Representative FE models for prisms with (a) ground and (b) unground units
[Source: Martínez et al. 2017, with permission].
Additionally, three-dimensional numerical simulations have also been used to model the effect of contact between the units on mortarless structures. To model this contact, another technique relies on the use of nonlinear spring elements that link nodes of the units’ bed surface mesh under vertical loads (as shown in Fig. 2-3). These spring elements are unidirectional elements in which a generalized force-displacement curve is needed to describe the nonlinear contact stiffness of the joint. Using such nonlinear link elements with eight-node solid elements to represent the masonry units, Oh (1994) described the response of mortarless prisms in terms of stresses and displacements under
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vertical loads. The response of this modeling technique has been evaluated, resulting within the 20% of the experimental data.
Fig. 2-3. Numerical model for three-unit mortarless prism using spring elements at the
dry joint.
Simplified models using three-node interface elements to simulate the dry joint have been employed to study the effect of the surface roughness on the mechanical behavior of masonry structures. One of these models uses two-dimensional eight-node isoparametric plane elements for the masonry units combined with interface elements for the dry joint. For example, Al-Wathaf (2006) developed a model to assess the effect of the surface roughness on the response of dry-stack structures subjected to vertical (see Fig. 2-4-a), in-plane (see Fig. 2-4-b), and out-of-plane loads (see Fig. 2-4-c). These models require a normal tangent and a shear stiffness of the joint to describe the nonlinear behavior of the closing deformation at the bed joint under vertical loads. Al-Wathaf modeled the joint he used in his research using a three-node interface element, but in furthering this research study using the joint with plate elements and six nodes, Hejazi was able to describe the mortarless behavior.
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Fig. 2-4. Numerical models of mortarless masonry (a) three-unit prism under vertical
load; (b) wall under vertical and lateral in-plane load; and (c) wall under vertical and lateral out-of-plane loads using zero-thickness elements at the dry joint.
Instead of Al-Wathaf’s three-node interface elements, the research conducted by Hejazi et al. (2016) used six-node isoparametric interface plane elements which were used to model the horizontal and vertical dry joints between the units as seen in Fig. 2-5. Hejazi et al. developed a two-dimensional wall model to simulate the behavior of dry-stack masonry walls under lateral in-plane seismic activity using eight-node isoparametric plane elements to model the masonry units. The behavior of the bed joints is described by properties in the interface elements such as the normal and tangent stiffness to account for the compressive and shear behavior. This technique has not widely been implemented, and thus requires rigorous validation with experimental data.
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Fig. 2-5. (a) Eight-node elements used for modeling of hollow units, (b) six-node
elements used for modeling the vertical interface, (c) six-node elements used for modeling the horizontal interface, (d) connection of two horizontal hollow units with
vertical interface, and (e) connection of two vertical hollow units with horizontal interface [Source: Hejazi et al. 2015, with permission].
Some of the aforementioned modeling techniques showed acceptable correlation to experimental data. Three-dimensional models are powerful to account with different unit geometries and design configurations in which the surface roughness is the key in these mortarless systems. These models allow for a precise prediction of the evolution of the stress distribution and failure modes along the masonry structure. On the other hand, simplified techniques can assess the effect of the surface roughness with limitations and assumptions in the behavior of mortarless masonry. In any case, experimental tests are necessary for the purpose of validating the simulations through rigorous test-analysis comparisons. Research on mortarless prisms and walls has been conducted using non- interlocking and interlocking units combined with alternatives to enhance the behavior through experimental tests, numerical models, or a combination of these.
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2.3 Knowledge-Base on Mortarless Masonry Systems with Non-Interlocking Units