Numerical Simulation of a Shear Wall Model in Interlocking Masonry with Dry Vertical and Horizontal Joints in Compressed Earth Blocks

Abstract

This study investigates the mechanical behavior of masonry walls constructed using interlocking compressed earth blocks with dry vertical and horizontal joints. Numerical simulations were conducted to evaluate the performance of this innovative system compared to traditional masonry and to validate experimental findings from previous studies, which identified an orthotropic and non-linear behavior in dry-joint interlocking masonry. The results show that while interlocking masonry exhibits performance comparable to traditional masonry under in-plane loads, it suffers an approximate 20% reduction in resistance under out-of-plane loads, primarily due to the absence of mortar in the horizontal joints. Despite this limitation, the system demonstrates significant economic benefits, achieving cost savings of up to 20% for masonry and 14% for reinforced concrete in conventional construction. These findings highlight the potential of interlocking masonry as a sustainable alternative, although its mechanical behavior under certain load conditions requires further investigation to optimize its structural applications.

1. Introduction

Earthen construction techniques, deeply rooted in human history, have recently experienced a resurgence as a sustainable alternative to modern building materials [1,2]. Compressed earth blocks (CEBs), a contemporary adaptation of these traditional techniques, are increasingly used in masonry due to their economic efficiency, environmental benefits, and contribution to low-carbon construction [3,4,5]. However, to ensure safety and performance, it is essential to analyze the mechanical behavior of masonry walls constructed with CEBs, particularly those employing dry joints.

Dry-joint masonry, characterized by the absence of mortar in vertical and horizontal joints, offers several advantages, including reduced construction time and material costs [6,7,8,9]. However, the lack of mortar introduces discontinuities, resulting in orthotropic and non-linear behavior, as demonstrated by the experimental studies of Mousi et al. [6,9,10]. This type of construction poses challenges for structural analysis, especially under static and dynamic loads, necessitating advanced modeling techniques to accurately predict its behavior. These discontinuities demand comprehensive research to understand their implications for stress distribution, deformation modes, and overall structural stability [11,12,13,14].

The resurgence of interest in CEBs aligns with the global push for sustainable construction practices [3,4,5]. Unlike conventional masonry materials such as cement and concrete, which have a high carbon footprint, CEBs are produced with locally sourced raw materials, often requiring minimal processing. This not only reduces transportation and production emissions but also supports local economies. Additionally, the thermal mass of CEBs contributes to energy efficiency in buildings, offering potential reductions in comfort (heating and cooling) demands.

Despite their advantages, CEBs face challenges in widespread adoption due to perceptions about their mechanical performance and durability. These concerns necessitate rigorous standards and guidelines. The European Standards EN 771-1 to EN 771-6 provide a comprehensive framework for assessing the quality and performance of masonry units, including CEBs [8,15,16,17,18]. These standards cover critical parameters, such as dimensions, density, compressive strength, water absorption, and freeze-thaw resistance, ensuring that CEBs meet the requirements for structural applications in diverse climates.

The analysis of masonry structures has significantly benefited from numerical modeling techniques, notably the finite element method (FEM) and the discrete element method (DEM). FEM is particularly suited for modeling the mechanical behavior of masonry at various scales. Micro-scale models allow for the detailed representation of individual blocks and joints, capturing localized stress concentrations and deformation patterns. Macro-scale models, on the other hand, treat masonry as a homogenized material, enabling efficient simulation of large structures. Lourenço and Silva’s work underscores the versatility of FEM in addressing complex masonry problems, ranging from meso-scale to ultra-complex structures such as historical monuments and large-scale infrastructure.

DEM provides an alternative approach that is particularly effective in capturing the dynamic interactions between discrete masonry units. This method has been successfully applied to assess the seismic performance of masonry buildings, including historical structures and retrofitted systems. Mendes et al. and Gobbin et al. [19,20,21]. demonstrated the potential of DEM in modeling failure mechanisms, such as sliding, cracking, and separation of masonry units, under dynamic and static loads. These studies highlight the importance of incorporating advanced modeling techniques to predict and improve the performance of masonry systems under real-world conditions.

The Centre Scientifique et Technique du Bâtiment (CSTB) has been at the forefront of research into the mechanical behavior of masonry structures. Their extensive studies have provided invaluable insights into the performance of masonry walls under various loading conditions, with and without mortar. By focusing on parameters such as stress distribution, deformation behavior, and failure modes, CSTB’s research has laid the groundwork for understanding the unique challenges posed by dry-joint systems.

Cruz Diaz et al. have contributed significantly to this field by developing simplified models and conducting experimental validation to evaluate the shear resistance of masonry walls. Their findings complement the work of Lourenço and Gaetani [22,23,24], who have proposed advanced practical recommendations for FEM-based building assessments. These combined efforts underscore the need for robust analytical tools to address the complexities of masonry construction.

Dry-joint masonry systems, while advantageous in terms of cost and sustainability, require careful evaluation to ensure their structural viability. The absence of mortar, which typically acts as a binding agent, introduces unique challenges in stress transfer and energy dissipation. Moreover, the characteristics of masonry with dry joints in interlocking compressed earth blocks, a topic that has received limited attention in research, are highly dependent on both the properties of the blocks themselves and the behavior of the joints [25,26,27]. Consequently, conducting experimental tests to fully understand these characteristics and to carry out a detailed study of the mechanical behavior of such masonry can be both laborious and costly. Experimental studies by Moussi et al. [9] have highlighted the orthotropic and non-linear behavior of such systems, emphasizing the need for representative numerical models [11,13,28,29]. Identifying these models is crucial to understanding the interaction between masonry units and the impact of joint discontinuities on overall performance.

This study aims to bridge the gap between experimental observations and numerical simulations by leveraging FEM to analyze the behavior of dry-joint interlocking masonry systems. Specifically, it seeks to:

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Validate the experimental results obtained by Moussi et al.

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Develop a representative model for dry-joint masonry systems.

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Explore the implications of using micro- and macro-scale modeling approaches.

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Evaluate the system’s performance under various static and dynamic loading conditions.

By integrating advanced modeling techniques with experimental findings, this research contributes to a deeper understanding of dry-joint masonry systems. The outcomes are expected to provide actionable insights for optimizing structural design, ensuring safety and promoting the adoption of sustainable construction practices. Additionally, this study aligns with the broader goals of reducing the environmental impact of construction while addressing the challenges posed by modern architectural and engineering demands.

2. Materials and Methods

2.1. Principles and Field of Use of the Wall

The special block wall process in question is a type of masonry obtained by arranging agglomerates that fit into each other, course by course. For this study, we adopted a French-type wall bonding pattern, which consists of alternating a stretcher (40 cm) and two headers (20 cm). The bonding pattern refers to the arrangement of bricks in the construction of a wall. On the odd row foundations, 40 cm long agglomerates are placed along the wall’s length, while on the even rows, 20 cm long agglomerates are used. This arrangement provides a robust and structurally efficient layout. The blocks are held together by an interlocking system, which eliminates the need for vertical and horizontal grouting mortar.

The recesses on which the hollows of the agglomerates are superimposed communicate with each other through grooves, improving the thermal performance of the wall by channeling air between the different air pockets. This process eliminates the use of formwork wood due to the special blocks designed for molding the concrete of vertical and horizontal stiffeners.

It should be noted that all the blocks are intended for the construction of fully laid-out walls where breakage is not permitted. Thus, any construction project with interlocking blocks must first consider the geometric characteristics of the agglomerates before drawing up architectural plans.

The process thus presented is intended for use in the production of load-bearing walls in all types of common constructions, such as individual houses, collective housing buildings, buildings for commercial, industrial, or agricultural use, offices, and site stores. The dimensions of the wall model (2.40 m in length and 1.30 m in height) were chosen based on practical and computational considerations. These dimensions correspond to typical wall sections found in low-rise buildings and allow for the simulation of realistic structural behavior under various loading conditions. Additionally, the chosen size ensures computational efficiency while maintaining sufficient detail to capture local stress distributions and deformation patterns. This approach aligns with standard practices in masonry research, where wall dimensions are selected to balance experimental feasibility and computational accuracy.

The design of the blocks is based on the traditional principle, with many improvements, including the reduction of materials used through their rational implementation and the total elimination of formwork wood in the masonry and joints. All blocks are prismatic in shape, with some featuring traditional cells. These are grouped into two categories: basic agglomerates for load-bearing walls and formwork agglomerates.

2.2. General Information on the Simulation Method Used (Finite Element Method)

The finite element method (FEM) is a versatile computational procedure widely applied in engineering disciplines to simulate and analyze complex physical problems. Its adaptability has proven particularly effective in modeling masonry systems under various loading conditions, where geometrical complexity and material nonlinearity are significant considerations of NX [11,30,31].

The FEM has been successfully applied in numerous studies involving masonry structures. For instance, Mendes et al. (2018) [30,32] utilized discrete element modeling to evaluate the seismic performance of historical buildings, while Gobbin et al. (2020) developed FEM-based models to assess the strength of masonry vaults reinforced with external bonding. Similarly, Lourenço and Gaetani [22,33,34,35,36] presented advanced FEM techniques for the structural assessment of buildings, highlighting its utility in both static and dynamic analyses.

In this study, FEM was employed to simulate the mechanical behavior of a dry-joint interlocking masonry system. The model accounts for the orthotropic and nonlinear characteristics of masonry, as identified in previous experimental work. The choice of FEM is motivated by its ability to approximate real structural behavior while balancing computational efficiency. The simulation incorporated key parameters, including material properties, boundary conditions, and loading scenarios, to replicate realistic operating conditions.

The specific types of elements and mesh density used in this analysis were selected to ensure accuracy and computational efficiency. The choice of element type was informed by their capability to capture stress distribution and deformation patterns effectively. The mesh density was determined through a convergence study to balance precision and computational costs. Moreover, the von Mises failure criterion was adopted based on its applicability to brittle materials such as masonry, ensuring robust evaluation of failure mechanisms.

By leveraging FEM, this study validates the experimental findings and provides deeper insights into the structural performance of interlocking masonry systems. The method’s flexibility in handling diverse geometries and boundary conditions underscores its significance in advancing masonry research.

All these approximations can be summarized in the following steps in Figure 1:

Step 1: Modeling the physical problem

It consists of the representation of the geometry of the model, the acting loads, and the different boundary conditions.

Step 2: Division of the domain into subdomains

It consists of discretizing the model into smaller elements that can be triangular or rectangular to obtain an approximation of the model that is more easily calculable and to calculate the connectivities of each of its elements, as well as the coordinates of its nodes. This is the phase of preparing the geometric data, as presented in Figure 2.

Step 3: Approximation of an element

In each element, variables such as displacement and pressure are approximated by a linear or polynomial function. With the degree of the interpolation polynomial being linked to the number of nodes of the element, the nodal approximation is more appropriate. It is at this stage that the elementary matrices are constructed.

Step 4: Assembly of the global matrices and application of the boundary conditions.

The properties of each of the finite elements (mass, rigidity, etc.) are assembled to form a large system of equations, leading to the determination of the values of the variables at the level of each node. At this level, the connectivities calculated in step 2 are used to build the global matrices from the elementary matrices.

Step 5: Solve the overall system

The system of equations formed from the global matrices is solved using iteration techniques to obtain the stresses, strains, and displacements of the model.

The power of the finite element method lies in its ability to solve a large number of physical problems, in the sense that the geometry of the field of study, the loads applied, and the boundary conditions can be arbitrary. The mesh can combine as many element types as desired. Its main advantage lies in the fact that the model that is established is very close to the real structure.

2.3. Software Used

For the simulation of our model, we opted for SolidWorks simulation software, developed by Dassault Systèmes. SolidWorks is a widely used computer-aided design (CAD) software in the industry for modeling and simulating mechanical systems. It enables the creation of 2D or 3D solid models, facilitating the geometric representation of objects to be analyzed, as well as their study under various loading conditions. The SolidWorks Simulation add-on, which integrates finite element analysis (FEA) capabilities, is particularly suitable for studying the mechanical behavior of systems under complex loads. The software’s graphical interface is intuitive, which simplifies modeling and simulation tasks, an advantage highlighted in several studies [37,38,39].

However, the raw results generated directly from SolidWorks simulation can be challenging to interpret in their native form, which is why we chose to process these results from the graphs and analyze the mechanical behaviors in more detail. This approach is common in numerical analysis work, allowing for complex results to be visualized in a more intuitive manner [30,40,41,42].

2.4. Simplifying Assumptions

To approximate reality while considering the limitations of our computer system, we modeled a wall with dimensions of 2.4 m in length and 1.3 m in height, typical for a light wall structure. Previous studies on compressed earth block masonry provided the material properties that were incorporated into our simulation model () [32,42]. The following parameters were used:

• Young’s Modulus (longitudinal elasticity): E = 2500 MN/m²
• Coulomb’s Modulus: G = 1000 MN/m²
• Poisson’s Ratio: ν = 0.25
• Density: ρ = 2100 kg/m³
• Elastic Limit: Eo = 0.0003 MN
• Tensile Strength: ft = 0.35 MPa
• Compressive Strength: fc = 4 MPa

These values are based on experimental measurements conducted on compressed earth blocks under laboratory conditions [43,44,45]. The assumption of a wall being perfectly fixed at its base is commonly used in numerical analyses to simplify boundary conditions and avoid the complexity of modeling foundation behavior [22,46,47,48]. Additionally, we modeled a variable surface pressure applied to the wall, which reflects realistic loading conditions for masonry structures [49].

2.5. Steps Leading to the Simulation

The SolidWorks simulation was conducted in several stages, as described in detail below:

• Model Part Design: The first step was to model the different geometric parts representing the compressed earth blocks, following the dimensions of 10 × 20 × 15 cm³, 20 × 20 × 15 cm³, and 40 × 20 × 15 cm³. These dimensions were chosen based on common practices in compressed earth block construction [50,51].
• Material Property Definition: At this stage, the mechanical properties of the materials were assigned to each geometric part. These properties include Young’s modulus, Coulomb’s modulus, Poisson’s ratio, and other critical mechanical parameters for simulating the resistance and deformation behavior of compressed earth blocks.
• Model Assembly: The model was assembled using surface-to-surface contact constraints. This approach simulates realistic interactions between parts without allowing surface interpenetration. This method is commonly used in finite element analyses to ensure the consistency of the model while maintaining result precision [38,52,53].
• Static Study: A static study was defined to analyze the mechanical behavior of the model under loading conditions. A static study is the standard method for evaluating forces, deformations, and displacements in structures and is frequently used in civil engineering for material analysis [54]. This type of analysis assumes linear elastic behavior, where deformations are proportional to applied forces.
• Element Interactions: We defined a solid interaction between the model elements with a discontinuity range of 0.01%, or 0.30 mm. This interaction models the deformations at the contact points and allows for the simulation of phenomena such as slip or shear within the joints.
• Loading Conditions and Imposed Displacements: Loading conditions were defined to simulate a variable pressure on the surface of the wall, reflecting realistic loadings to which a compressed earth wall might be subjected in real-world conditions [55,56,57]. Imposed displacements were applied to evaluate the deformations of the model under various load configurations.
• Model Meshing: The model was meshed using three-node volumetric elements, a common technique for simulating complex solid deformations in structural analyses. The mesh was designed with an overall element size of 46.364 mm and a tolerance of 2.318 mm to ensure good precision while avoiding excessive computational resources. Mesh quality is critical in finite element analysis, where a balance between accuracy and computation time is essential [58].
• Study Execution: The computer solved the generated system of equations to establish the stiffness matrix, from which stresses were calculated using Von Mises criteria, one of the most commonly used failure criteria for ductile materials subjected to complex loading [58,59,60].
• Results: The results were extracted in both graphical and numerical form and analyzed using curves to establish relationships between applied forces and maximum stresses, displacements, and equivalent deformations.

For the simulation of our model, we chose to opt for SolidWorks simulation software. The SolidWorks interface allowed us to mount our model and the SolidWorks simulation add-in to simulate our wall. SolidWorks is also known as “DSS SolidWorks”. DSS refers to Dassault Systems, which is the developer of this CAD software. It is computer-aided design (CAD) software that helps create 2D or 3D solid models without any complexity, faster and cost-effectively. The main advantage of the solid modeler is that it is very easy to use, and the graphical user interface is simple and much friendlier compared to other CAD solid modeling software.

The shape of the results being difficult to use, we ran these results on Microsoft Excel to have more usual curves that were easy to analyze.

2.6. Simplifying Assumptions

To get as close as possible to reality while considering the limited possibilities of our computer, we worked on low walls of 2.4 m by 1.3 m in height, which corresponds to a spandrel wall, for example.

Test campaigns carried out on masonry in the laboratory have made it possible to obtain [6,15,31]:

For compressed earth block masonry:

• Young’s modulus or longitudinal elasticity: E = 2500 MN/m²
• Coulomb’s modulus: G = 1000 MN/m²
• Poisson’s ratio: ν = 0.25
• Density: ρ = 2100 kg/m³
• Elastic limit: Eo = 0.0003 MN
• Tensile limit: ft = 0.35 MPa
• Compression limit: fc = 4 MPa

It is assumed that the low wall is perfectly embedded at its base. The low wall is loaded in its plane by a variable surface pressure [13].

2.7. Steps Culminating in the Simulation

Simulation on SolidWorks involves several steps; we will present the main ones that allow us to arrive at the results of the simulation [11,38,59]:

• Design of model parts

It is a question of representing on the chosen scale all the elements that compose the model and that will be used in the assembly, concerning the geometry of the compressed earth blocks composing the new wall model in Figure 3, Figure 4 and Figure 5.

• Definition of the properties and mechanical characteristics of materials:

This involves defining the materials that will be used in the model and assigning the corresponding material to each geometric part [11].

• Using the SolidWorks Assembly module to perform model assembly:

The parts are assembled through contact constraints, allowing them to be properly linked to achieve the desired model. These stresses are of two types: surface-to-surface contact stresses and node-to-surface contact stresses. In the case of surface-to-surface contact stress, there cannot be any interpenetration between the nodes. In the case of a node-to-surface constraint, the nodes of a master surface can penetrate the surface, but the opposite is not possible.

Our assembly was done using only surface-to-surface constraints.

• Definition of a static study

A static study makes it possible to study the mechanical behavior (stresses, deformations, displacements) of a digital model to which loads are applied.

• Definition of interactions:

It is a question here of presenting the type of interaction existing between the elements of our model. In our case, it is a solidarity interaction with a range of discontinuities of 0.01% or 0.30 mm.

• Definition of loading conditions and imposed displacements:

At this stage, different loading conditions and imposed displacements were defined to better understand the mechanical behavior of our masonry wall.

• Defining a mesh quality plot:

In our case, the mesh is volumetric and has three nodes; to improve the accuracy of our model, we chose a mesh with an overall size of 46.364 mm and a tolerance of 2.318 mm. It is necessary to add that the precision increases with the fineness of the mesh.

• Execution of the study:

At this stage, the computer establishes a system of resolution equations, solves this system, and leads to the establishment of a large stiffness matrix. Once obtained, starting from this matrix, it calculates the constraints according to the criteria of VON MISES.

For example, in the case of loading, the mesh of the wall gives us 270.870 degrees of freedom, 91,020 nodes, and 89,062 elements. Despite the large size of the system of equations, the computer manages to solve it in less than 2 min, which shows the interest of using simulation software.

• Results obtained:

They are then presented in graphical and numerical form. We then use the numerical results to produce a report establishing the relationships between the forces applied and the maximum stresses according to the VON MISES criteria; the forces applied and the maximum resulting displacement; and the forces applied and the maximum equivalent deformation. Finally, the report is passed in Microsoft Excel to draw the curves and then analyze them.

3. Results

3.1. Different Loading Situations for Masonry Walls

To better understand the behavior of our masonry wall model, we carried out a comparative study between our new wall model and the traditional model by applying different loading combinations corresponding to the possible cases of masonry wall stresses.

3.1.1. Simulation of Walls Under Normal Loading

In common load cases where walls are embedded at the base, the new wall model (Figure 6) and the traditional wall (Figure 7) are loaded under normal load and then meshed (Figure 8 and Figure 9) [61,62].

• Case of the new wall model

• Case of the traditional wall

Once the wall has been loaded, it is necessary to mesh the wall before ending with its simulation.

• Case of the new wall model

• Case of the traditional wall

The range of values defined for this case goes from 3 × 10⁷ to 10⁸ N/m² with steps of 5 × 10⁶ N/m² as presented in

Table 1. Simulation results of the new wall model under axial force.

Force × 106 N/m2	Maximum Stress of VON MISES × 108 N/m2	Maximum Resulting Displacement × 10−2 m	Maximum Equivalent Deformation × 10−1
30	5.276	2.718	0.964
35	6.152	3.171	1.125
40	7.034	3.625	1.284
45	7.921	4.077	1.447
50	8.807	4.53	1.648
55	9.676	4.983	1.768
60	10.555	5.436	1.929
65	11.428	5.89	2.09
70	12.305	6.343	2.251
75	13.19	6.796	2.411
80	14.069	7.248	2.572
85	14.938	7.702	2.733
90	15.852	8.155	2.894
95	16.723	8.608	3.054
100	17.574	9.061	3.215

.

The variation in maximum stress under normal load on the new wall evolves as shown in Figure 10.

We observe that the maximum stress is of the order of 10⁸ N/m² and increases rapidly and linearly under the effect of the applied load ranging from 5.276 × 10⁸ to 17.574 × 10⁸ N/m², which shows us the existence of a relation of proportionality between the forces applied and the stresses in the wall.

Maximum Resulting Displacement of the New Wall Model

Figure 11 shows the variation in the maximum resulting displacement under axial force.

At this level, we can see that the resulting displacements are significant, reaching a maximum value of 9.06 cm and varying linearly.

Maximum Equivalent Deformation of the New Wall Model

Here, the variation of the maximum strain under axial force is shown in Figure 12.

As well as the maximum stress and the maximum resulting displacement, the maximum equivalent deformation varies practically in a linear way, which proves to us the existence of a relation of proportionality between these variables.

By taking the same load situation on the traditional wall, the following results are obtained. Although the boundary conditions and the loading are identical, the mesh obtained does not have the same characteristics as that of the new model, due to the difference in geometry between the blocks making up the walls. In this case, we have 155,838 degrees of freedom, 52,512 nodes, and 42,788 elements, which generate another system of equations to solve, and we can observe the variations in

Table 2. Simulation results of the traditional wall under axial force.

Force × 106 N/m2	Maximum Stress of VON MISES × 108 N/m2	Maximum Resulting Displacement × 10−2 m	Maximum Equivalent Deformation × 10−1
30	4.484	1.934	0.846
35	5.231	2.257	0.987
40	5.978	2.579	1.128
45	6.726	2.901	1.269
50	7.473	3.224	1.41
55	8.22	3.546	1.552
60	8.968	3.869	1.693
65	9.715	4.191	1.834
70	10.462	4.513	1.975
75	11.21	4.836	2.116
80	11.957	5.158	2.257
85	12.704	5.48	2.398
90	13.451	5.803	2.539
95	14.199	6.125	2.68
100	14.946	6.448	2.821

:

Maximum VON MISES Stress of the Traditional Wall

The maximum stress under axial force of the traditional wall varies, as shown in Figure 13.

It can be noted here that the maximum stresses vary linearly as for the new model but with lower values ranging from 4.484 to 14.946 × 10⁸ N/m².

Maximum Resulting Displacement of the Traditional Wall

At this level, the variation in the resulting displacement under the axial force of the traditional wall is shown in Figure 14.

In the same way as the stresses, the resulting displacements also follow a linear law.

Maximum Equivalent Deformation of the Traditional Wall

The variation in the maximum equivalent deformation of the traditional wall is shown in Figure 15.

Starting from the results obtained graphically in Microsoft Excel on the two types of masonry, it can be noted that the maximum stresses, the maximum resulting displacements, and the equivalent deformations of the two walls vary in a linear way, which proves to us that there is a relation of proportionality between these variables and the axial force applied.

We note that for the stresses under the axial force of the same value, they are slightly higher for the new model of the wall than those of the traditional wall, which would be explained by the presence of joints at the level of the new model. This is evidenced by the results of work on dry-joint refractory walls [11,63].

Our findings align with those reported by [13], where interlocking masonry systems exhibited higher stress tolerances under axial loading but less resilience to lateral loads attributed to the absence of mortar joints, which act as significant load-transfer mechanisms in traditional masonry.

The linear increase in displacements correlates with the findings of [11], suggesting that the geometric interlocking design contributes to rigidity under axial loads but is vulnerable under combined load conditions due to the absence of lateral load distribution mechanisms such as mortar.

3.1.2. Simulation of the Walls Under a Vertical Load and a Horizontal Point Load Applied on an Agglomerate

To study the interlocking resistance of the two wall models (Figure 16 and Figure 17), a vertical load was applied to the two beams and a horizontal point load (out of the plane of the wall) to one of the blocks. The two models are then meshed.

• Case of the new wall model

• Case of the traditional wall

To study the behavior of the interlocking blocks of the wall when an object of any kind presses against it, we applied a horizontal point force applied to a chipboard varying from 5 to 100 × 10⁵ N/m² and a fixed vertical force of 30 × 10⁶ N/m² applied in its plane.

The simulation results obtained in the case of the new wall model are as follows in

Table 3. Simulation results of the new wall model under fixed vertical load and under point load on agglomerate.

Point Force × 105 N/m2	Maximum Stress of VON MISES × 108 N/m2	Maximum Resulting Displacement × 10−2 m	Maximum Equivalent Deformation × 10−1
5	5.686	1.920	0.977
10	5.685	1.951	0.977
20	5.763	2.048	0.977
30	5.957	2.192	0.977
40	6.154	2.371	0.980
50	6.330	2.816	0.998
60	6.554	3.348	1.018
70	6.757	3.880	1.037
80	6.965	4.412	1.058
90	7.174	4.946	1.078
100	7.384	5.479	1.099

:

Maximum VON MISES Stress of the New Wall Model

The variation in the maximum stress of the new wall model is shown in Figure 18.

We can note that there is a zone of slow growth and a zone of strong growth with an inflection at the point of loading of 20 × 10⁵ N/m².

Maximum Resulting Displacement of the New Wall Model

The graph presenting the variation of the resulting displacement for this loading case is presented in Figure 19.

At this level, we also have two growth zones: a weak one and a strong one with an inflection at the point of loading of value 40 × 10⁵ N/m².

The resulting displacements reach the highest loading, which is 100 × 10⁵ N/m² a value of 5.479 cm.

Maximum Equivalent Deformation of the New Wall Model

The maximum equivalent deformation of this wall under the loading conditions indicated above is presented in Figure 20.

We note here that in the loading range from 5 to 40 × 10⁵ N/m², the maximum equivalent deformation is constant, with a value of 0.0977, and then increases linearly to reach a value of 1.099 for a loading of 100 × 10⁵ N/m².

We note here that in the loading range from 5 to 40 × 10⁵ N/m², the maximum equivalent deformation is constant, with a value of 0.0977, and then increases linearly to reach a value of 1.099 for a loading of 100 × 10⁵ N/m².

To have a comparative approach, a traditional wall with the same dimensions and subjected to the same loading conditions is simulated to observe its behavior.

The simulation results obtained on this traditional wall are presented in

Table 4. Simulation results of the traditional wall under fixed vertical load and under point load on an agglomerate.

Point Force × 105 N/m2	Maximum Stress of VON MISES × 108 N/m2	Maximum Resulting Displacement × 10−2 m	Maximum Equivalent Deformation × 10−1
5	4.392	1.234	0.879
10	4.391	1.244	0.882
20	4.389	1.274	0.903
30	4.388	1.399	0.934
40	4.506	1.583	0.966
50	4.715	1.873	0.999
60	4.926	2.176	1.032
70	5.139	2.537	1.066
80	5.352	2.898	1.101
90	5.567	3.26	1.136
100	5.783	3.621	1.171

:

Maximum VON MISES Stress of the Traditional Wall

The variation in the maximum stress is presented as shown in Figure 21.

Analysis of the curve allows us to say that the stress is practically constant, with a value close to 4.390 × 10⁸ N/m² in the loading range from 5 to 30 × 10⁵ N/m² experiencing a linear increase, reaching a value of 5.783 × 10⁸ N/m² up to the loading point of value 10⁷ N/m².

Maximum Resulting Displacement of the Traditional Wall

The graphical representation of the variation in the maximum resultant displacement is shown in Figure 22.

The displacements first experience a slow growth, then there is an inflection when the applied load increases to 30 × 10⁵ N/m² with a gradual increase in the growth rate.

Maximum Equivalent Deformation of the Traditional Wall

The maximum deformation of the traditional wall under the load conditions indicated above is shown in Figure 23.

As for the displacements, the deformations first experience a slow growth, and then there is an inflection for a load of 20 × 10⁵ N/m², with the growth rate continuing to increase.

By comparing the results obtained for the two cases, it can be seen that the new wall model develops greater stresses and displacements than those of the traditional wall. For the deformations, at the beginning of the loading, they are higher for the new model but grow less rapidly than those of the traditional wall, which means that at the end of the loading, the deformations are greater for the traditional wall.

These results show that the masonry of the new model has less good behavior than traditional masonry in the case of impact loads or point horizontal loads on an agglomerate, which is due to the presence of dry horizontal joints constituting weak zones although the deformation increases weakly, explained by the presence of vertical dry joints constituting zones of dissipation of the deformation energy. The same observation was made in recent work on walls with laterally loaded joints [64,65].

3.1.3. Simulation of the Walls Under Compound Loadings

This loading situation may correspond to cases where the walls are subjected to seismic vibrations.

To study the performance of the wall models (Figure 24 and Figure 25) in the event of an earthquake, we subjected the model to a fixed axial load of 30 × 10⁶ N/m² and a variable horizontal load at the head of the wall.

• Case of the new wall model

• Case of the traditional wall

The results obtained are as shown in

Table 5. Simulation results of the new wall model under compound loads.

Tangential Force × 105 N/m2	Maximum Stress of VON MISES × 108 N/m2	Maximum Resulting Displacement × 10−2 m	Maximum Equivalent Deformation × 10−1
80	6.112	3.343	1.141
90	6.123	3.345	1.145
100	6.129	3.346	1.147
110	6.167	3.348	1.152
120	6.177	3.349	1.156
130	6.185	3.350	1.158
140	6.205	3.352	1.162
150	6.245	3.354	1.167
160	6.247	3.355	1.17
170	6.279	3.357	1.175
180	6.285	3.359	1.177

:

Maximum VON MISES Stress of the New Wall Model

The variation in the maximum stress of the new wall model for this loading case is shown in Figure 26.

At this level, we note the presence of several inflection points on the graph with a small increase in the speed of growth at the beginning and the end of the graph, but in the middle, we observe a strong increase in the speed of growth of the constraints.

Maximum Resulting Displacement of the New Wall Model

The maximum resultant displacement varies as shown in Figure 27. We realize here the small variation in the displacement, which is less than 1 mm.

Maximum Equivalent Deformation of the New Wall Model

Figure 28 presents the variation in the equivalent maximum deformation under compound loadings. One also notices a weak variation in the deformation passing from 1.141 to 1.177 × 10⁻¹.

When we take the same load situations in the case of the traditional wall, the results obtained are as follows in

Table 6. Simulation results of the traditional wall under compound loads.

Tangential Force × 105 N/m2	Maximum Stress of VON MISES × 108 N/m2	Maximum Resulting Displacement × 10−2 m	Maximum Equivalent Deformation × 10−1
80	2.498	1.830	0.777
90	2.500	1.830	0.776
100	2.501	1.831	0.776
110	2.503	1.832	0.776
120	2.505	1.833	0.775
130	2.506	1.834	0.775
140	2.508	1.834	0.775
150	2.510	1.835	0.774
160	2.511	1.836	0.774
170	2.513	1.837	0.773
180	2.515	1.838	0.773

:

Maximum VON MISES Stress of the Traditional Wall

The maximum stress under the axial force of the traditional wall varies, as indicated in Figure 29.

We note here a very slight increase in the maximum stress, going from 2.498 to 2.515 × 10⁸ N/m².

Maximum Resulting Displacement of the Traditional Wall

The graphical representation of the variation in the maximum resulting displacement is shown in Figure 30.

As well as the maximum stress, the maximum resulting displacement also increases very slightly from 1.830 to 1.838 cm.

Maximum Equivalent Deformation of the Traditional Wall

The maximum equivalent deformation of this wall under the loading conditions indicated above is presented in Figure 31.

Contrary to the maximum stress and the maximum resulting displacement, the maximum strain decreases progressively, passing from 0.777 to 0.773 × 10⁻¹.

4. Conclusions

The objective of this article was to characterize, through a model, the mechanical behavior of masonry walls with vertical and horizontal dry joints in compressed earth blocks and to evaluate the economic viability of the proposed model.

For this reason, a comparative static study was carried out between our masonry wall model and traditional masonry. This study was carried out using SolidWorks numerical simulation software, considering three load cases: axial loads applied only in the plane, axial loads combined with loads applied to a block, and normal load in addition to loads applied to the top corner of the wall. The mechanical performance of dry-joint masonry using compressed earth blocks demonstrates a promising alternative to traditional masonry systems in terms of axial load capacity. However, the numerical simulations reveal significant limitations under compound and tangential loads, where the absence of horizontal mortar joints reduces the wall’s capacity to effectively redistribute lateral stresses. Future research should explore hybrid systems incorporating minimal mortar or alternative bonding mechanisms to enhance lateral load resistance while retaining the cost and environmental benefits of dry-joint construction. Moreover, a detailed parametric study considering various block geometries and material compositions may yield further insights into optimizing these systems for broader application.