Editorial for the Special Issue “Mortarless and Interlocking Structures: Towards Environmentally Friendly Construction”

1. Introduction

Traditional construction methods use considerable amounts of cement, and its production involves CO₂ emission. Another environmental impact is related to the production of waste during structural repairs, especially at the demolition stage at the end of the structure life cycle: recycling the waste presents a serios problem. One of the ways to mitigate these environmental impacts and turn traditional construction into an environmentally friendly construction method is to use mortarless interlocking structures, firstly through the use of topological interlocking structures whose building blocks have specially engineered contact surfaces to maintain structural integrity. An important feature of the interlocking structures is that they are demountable such that after the repair or demolition some blocks can be reused to minimize the waste. The main advantage of topological interlocking structures is the absence of stress concentrators such as keys or connectors which are detrimental to structural integrity and longevity. That is why construction based on topological interlocking is a preferred method of erecting mortarless and demountable structures.

Topological interlocking structures are structures assembled from elements or blocks (solid or hollow) which are not glued together but rather held in place by the geometry of their shapes. These shapes introduce kinematic constraints, where no block (element) can be removed from the assembly without disturbing (pushing away or elbowing) their neighbors. In the presence of a peripheral constraint (an external frame or post-tensioning cables running through the structure) which resists the movement of the neighboring blocks, the block cannot be removed from the assembly. This ensures that the topological interlocking assembly maintains its integrity. The interlocking property of such elements is independent of their dimensions and does not change with up- and downscaling. The shapes are designed in such a way that the elbowing occurs when the block moves in any allowable direction. When the topological interlocking structure is deformed each block can have both translational and rotational degrees of freedom: the elbowing can be related to each of them.

The absence of a binder in the blocks ensures elevated fracture resistance and energy absorption and considerably reduces the stiffness of the structures, making them flexible. The high flexibility and elevated fracture resistance and energy damping are important in engineering and attract attention to topological interlocking. Furthermore, the TI structures are demountable, which gives flexibility in repairing and altering the structures. It is important that the blocks from dismounted structures can be reused thus reducing the waste, cost, and CO₂ emissions associated with manufacturing the new blocks. This makes the topological interlocking construction environmentally friendly. Last but not least, the topological interlocking structures have an appealing appearance, which attracts interest from architects.

Since the initiation of the field of topological interlocking in 2001, it has progressed in the following two main directions: (1) development of new topological interlocking geometries interesting from mechanical, architectural and even educational points of view; (2) determination (experimental, numerical, and/or analytical) of the mechanical and acoustic properties of topological interlocking assemblies. These trends are reflected in the papers presented to this Special Issue.

2. Development of the New TI Geometries

Development of the topological interlocking shapes and assemblies is essentially a mathematical and geometrical endeavor. For planar assemblies of topological interlocking elements/blocks, the design process starts with nominating a suitable tessellation of a plane. This is what was performed at the beginning of the development of the field. The next step is to extend the tessellation elements into prisms and then incline their surfaces in such a way that they constrain the vertical movement (in both directions) of each prism, thus enabling topological interlocking. If a non-planar (e.g., spherical) assembly is required, the planar topological interlocking assembly is suggested to be deformed to the required geometry. In this case, each topological interlocking element will deform such that the initially equal elements may now assume different shapes.

Papers in this issue devise the method of designing non-planar topological interlocking assemblies without the necessity to deform an initial planar assembly.

Akpanya et al. (contribution 1) proposed a design method based on modifying the initial simple periodic tessellations by employing an Esher-like method. This method can produce a wide range of shapes of regular and semi-regular tessellations, including tiles with sharp angles. (While the sharp angles are not desirable from an engineering point of view, they are associated with the shapes having interesting visual features.) The 3D blocks are obtained by tessellating two parallel planes and forming the walls of the blocks by interpolating between the tiles of the opposite tessellated planes. A modification of the Esher-like method is developed that allows constructing the interlocking shapes assembled parallel to non-planar surfaces (sphere is used as an example). The developed methods contribute to understanding the geometry of TI assemblies and the interlocking process in general.

Bejarano and Moran (contribution 2) concentrated on a given tessellation of a plane into convex tiles each with an even number of sides and devised a method of evolution of a tile into a corresponding topological interlocking polyhedron. They proposed a generalization of the mid-section evolution concept, which provides a tool for designing blocks with topological interlocking properties. The proposed method introduces height parameters to generate topological interlocking elements suitable even for non-planar structures. Furthermore, the method avoids multiple iterations typical of the traditional method thus reducing the design procedure to a number of parametric evolution steps. In particular, the Evolution Steps method can realize single-direction and double-direction polygon–polyhedron evolutions. The method can generate topological interlocking assemblies with elements in the shape of truncated platonic solids, clipped solids, concave solids, and mixed solids. The assemblies can be both planar and non-planar. An additional benefit of the proposed methodology is its capacity to design topological interlocking elements or blocks that fit with minimal gaps, thus reducing material waste in the process of manufacturing interlocking blocks as the need for cutting and trimming is minimized.

Topological interlocking structures have three-dimensionality embedded in their design (two-dimensional topological interlocking structures do not exist). In addition, the interlocking structures have a particular appeal and a remarkable visual appearance. Miodragovic Vella and Markovic (contribution 3) discuss the pedagogical aspect of topological interlocking structures in light of the increased educational relevance of computational architecture. They propose to use scaled-down topological interlocking structures as a primary architectural pedagogical tool. Two objectives are aimed at being achieved in the course of the education activity: (1) challenging traditional reductionist design thinking and the linear top-down architectural design process; (2) introducing geometrical processes that enhance students’ spatial understanding and proficiency in transforming between 2D representations and 3D forms. The second objective engages the constituent geometric relationships of topological interlocking assemblies. Most of the developed topological interlocking assemblies are defined by an identical configuration of their elements, the mutual arrangement of the elements and a boundary constraint that holds the whole assembly together. For the education process the mechanical properties of topological interlocking assemblies are not important, such that even paper-based topological interlocking blocks can be used. The paper discusses the case studies of topological interlocking assemblies of tetrahedra and Abeille’s flat vault, which are intersecting cones including the Truchet vault, octahedra, and osteomorphic blocks. The paper creates a new set of educational tools which develops three-dimensional ways of thinking.

3. Mechanics of TI Structures

Mechanical, structural, and acoustic aspects are studied in the remaining three papers.

Mousavian and Casapulla (contribution 4) consider the mechanical behavior of interlocking joints and multi-lock interfaces representing the block connection without a binder. The examples include TI structures, ancient (mortarless) structures, and the blocky rock mass where the effect of gouge can be neglected. Two types of numerical analysis are used for the determination of the torsion-shear capacity of corrugated interlocking interfaces in the structures: (1) A model SiDMACIB developed by the authors. This model implements static equilibrium. (2) The discrete element code 3DEC, assuming the blocks to be rigid. The SiDMACIB model returns higher torsion-shear capacity of the interfaces and contact points distribution considered as opposite to the 3DEC model. Using the SiDMACIB model, the number of locks involved in the torsion-shear capacity are considered and a heuristic formula is proposed. The paper develops designing tools which are important for practical engineers.

Hossain et al. (contribution 5) consider seismic-proof semi-interlocking masonry as a high energy absorption alternative to conventional infilled panels. A special analytical method was developed to determine the behavior of the semi-interlocking panels. A typical three-story, three-bay structure was considered and tested. Comparison of the analytical model and the results of experimental testing show good agreement. The analysis also suggests that the semi-interlocking panels exhibit larger displacement compared to the conventional structure and better energy dissipation, demonstrating enhanced performance during seismic events. These results are not surprising as the absence of mortar between the bricks leads to the reduction in effective stiffness of the interfaces, while the ability of bricks to have relative motion leads to enhanced energy absorption (see contribution 6). The proposed analytical model is important in practical engineering design.

Bending of topological interlocking structures under indentation is observed to produce localization of bending deformation. In order to investigate the effects of localization, Dyskin and Pasternak (contribution 6) introduce a simple interlocking beam model and show the formation of point deflection whereby the bending localizes at the point of loading. The model also explains the phenomenon of negative stiffness observed in the experiments on indentation. It was hypothesized that the elevated energy dissipation exhibited by the topological interlocking structures is associated with the transfer of oscillation energy to kinetic energy of air as the air is squeezed out in the process of relative block rotations during structure deformation.

The methods and models presented in this Special Issue, “Mortarless and Interlocking Structures: Towards Environmentally Friendly Construction”, will contribute to the development of the theory and applications of topological interlocking and methods of designing new planar and non-planar topological interlocking assemblies. This will lead to new attractive architectural solutions and the development of novel environmentally friendly solutions, achieving reduced CO₂ footprint and demolition waste, as well as engineering structures with elevated longevity and energy dissipation. The advancement of topological interlocking will also lead to the creation of new education opportunities focused on the three-dimensional aspects of architecture and design.