Clay Blocks Research Articles

Assessing the Impact of Vertical Greenery Systems on the Thermal Performance of Walls in Mediterranean Climates

This study investigates the impact of vertical greenery systems (VGSs) applied to several typical wall configurations on indoor thermal conditions in a building module situated in the Mediterranean climate of Catania, Italy. By means of dynamic simulations in TRNSYS vers.18, the research compares the thermal behavior of walls made of either hollow clay blocks (Poroton) or lava stone blocks against a lightweight wall setup already in place at the University of Catania. The primary focus is on evaluating the VGSs’ capability of reducing peak inner surface temperatures and moderating heat flux fluctuations entering the building. The findings indicate that adding an outer vertical greenery layer to heavyweight walls can decrease the peak inner surface temperature by up to 1.0 °C compared to the same bare wall. However, the greenery’s positive impact is less pronounced than in the case of the lightweight wall. This research underscores the potential of green facades in enhancing the indoor thermal environment in buildings in regions with climates like the Mediterranean one, providing valuable insights for sustainable building design and urban planning.

Scenes of Men in the Seal Impressions of Tell Abu Sha'af from the Iraqi Museum

The research presents and describes the scenes of men on the seal impressions of Tell Abu Sha'af from the Iraqi Museum, which came from the excavations of the Iraqi mission at the Tell Abu Sha'af site in 1978, which lasted for five months, and revealed 800 clay blocks (Bulla) of different shapes, sizes and colors, and the number of impressions found in a building known as the fortified palace. Some of the impressions are damaged, some are broken, and others are clear, bearing different scenes, based on which they were divided into several groups. The results of the excavations were published in the Sumer magazine in a special issue on the excavations of the Hamrin Dam Basin, and the impressions remained preserved in the stores of the Iraqi Museum, and since then they have not received a study that would reveal their nature and importance. Among the 800 clay blocks discovered at the site of Tell Abu Sha'af, (81) pieces of seal impressions (unpublished) were selected and studied in detail. They were dated by comparison to the period of the Sassanid occupation in Mesopotamia. In this study, we relied on the practical, descriptive and analytical method. Accordingly, these impressions were divided into four main groups (the group of scenes of men, the group of decorations and inscriptions, the group of animal scenes, and the group of mythical creatures). Our research is limited to the first group, which includes scenes of men only, and we chose only twelve models from it. In this study, we relied on the practical, descriptive and analytical method as well as comparison.

Experimental and Numerical Characterization of the In-Plane Shear Behavior of a Load-Bearing Hollow Clay Brick Masonry System with High Thermal Performance

Modern masonry systems are generally built with hollow clay bricks with high thermal insulating properties, fulfilling the latest sustainability and environmental criteria for constructions. Despite the growing use of sustainable masonries in seismic-prone countries, there is a notable lack of experimental and numerical data on their structural behavior under lateral in-plane loads. The present study investigates the in-plane shear behavior of load-bearing masonry walls with thin bed joints and thermal insulating hollow clay blocks. Shear-compression tests were performed on three specimens to obtain information about their shear strength, displacement capacity and failure modes. The experimental characterization was supplemented by three shear tests on triplets, along with flexural and compression tests on the mortar for the thin joints. Furthermore, two Finite Element (FE) models were built to simulate the shear-compression tests, considering different constitutive laws and brick-to-brick contact types. The numerical simulations were able to describe both the shear failure modes and the shear strength values. The results showed that the experimental shear strength was 53% higher than the one obtained through Eurocode 6. The maximum shear load was found to be up to 75% greater compared to similar masonry specimens from the literature. These findings contribute to a better understanding of the potential structural applications of sustainable hollow clay block masonry in earthquake-prone areas.

Defining and characterizing the phenomenon of river-bottom tearing scour (RBTS): A case study of the Middle Yellow River

River-bottom tearing scour (RBTS) in natural rivers refers to the incipient motion and transport processes of clay blocks formed by fine cohesive sediment after deposition and consolidation in riverbeds. The RBTS phenomenon can lead to significant channel erosion and changes in river planview morphology, and has, thus, attracted the attention of hydrologists and engineers. In the study, a new determination measure (K) for the occurrence of a RBTS event is derived based on the theoretical expression for the critical incipient velocity of the clay block, K=α2(CL+2λ22), which is a combination of the coefficients of the velocity (i.e., α is a local velocity coefficient), lift force (i.e., CL is the lift coefficient), and clay block size (i.e., λ2 is the ratio of block thickness to length). Furthermore, to explain river behavior during a RBTS event, the Fugu, Xiaobeiganliu, and Weihe river reaches in the Middle Yellow River (MYR) were selected as study areas. Analysis of hydrological data from 1950 to 2023 in the examined reaches implies that a single discharge or sediment threshold cannot predict the occurrence of RBTS. The cross-sectional erosion and deposition volume (CEDV) and the migration intensity of the channel thalweg (MI) also were calculated at the section and reach scales for the examined reaches during the RBTS events. It was observed that RBTS typically causes significant channel erosion originating from the most upstream portion of the study reach with CEDV values ranging from 61 to 6034 m2, while MI values during the RBTS events were close to the multi-year average for the study reach. Finally, a flume experiment simulating RBTS was done to discuss and verify the threshold value of K. Field survey and experimental results indicated that RBTS occurs if K > 0.5, thus, providing theoretical support for the prediction and prevention of RBTS.

Empirical seismic fragility of masonry buildings in historical centres accounting for structural interventions

Fragility models are widely employed to forecast seismic damage in built environments. However, the actual conditions of buildings, depending on their construction systems and transformations, are crucial for model reliability, especially in historical centres.In this paper, an empirical fragility model for residential masonry buildings from data collected within 19 historical centres struck by the 2016 Central Italy earthquake is proposed. The dataset includes both traditional unreinforced and hybrid buildings, where reinforced concrete elements were applied in the 1980s according to seismic reinforcement prescriptions for existing structures.This study acknowledges the impact of such structural modifications on the seismic performance of buildings, which can alter their vulnerability classification either improving or worsening it. The intensity measure for the fragility functions is the peak ground acceleration obtained from actual records through interpolation for each centre. Damage data and vulnerability assessment of 2134 traditional and hybrid structural units are conducted in the framework of the European Macroseismic Scale (EMS-98). The fragility functions are plotted for both structural types and EMS-98 vulnerability classes, also considering the contribution of structural interventions, and then compared to literature empirical models. Hybrid buildings achieve a behaviour similar to traditional buildings when floors are strengthened but walls are not. However, when both masonry walls and floors are strengthened, their performance significantly improved, approaching that of modern clay block buildings with rigid floors. Compared to literature models, the proposed one showed good compatibility for the most vulnerable buildings, whereas less vulnerable ones appeared even stronger thanks to interventions.

Efficiency of FRPU strengthening of a damaged masonry infill wall under in-plane cyclic shear loading and elevated temperatures

This paper presents results of in-plane shear tests carried out at the ZAG laboratory in Ljubljana (Slovenia) on a RC frame with masonry infill made of clay blocks (KEBE OrthoBlock). The frame was loaded with constant vertical loads at the top of the columns and then by gradually increasing horizontal cyclic loads at the top beam level. Acquired forces and measured displacements allowed capturing hysteretic behavior for determination of dissipation energy. In addition, two Digital Image Correlation (DIC) systems, Aramis and the CivEng Vision, were used to visualize the behavior of the tested specimens, with an emphasis on computing locally required information about the behavior of highly deformable interfaces. Three types of specimens were tested in-plane: the reference specimen in form of plain RC frame, the reference specimen with constructed masonry infill without any strengthening and the specimen, previously damaged and then strengthened on both sides using glass mesh bonded to the infill and the RC frame using flexible adhesive made of polyurethane matrix (Glass Fiber Reinforced PolyUrethane - GFRPU system). The strengthening process, allowed the specimen to withstand additional cyclic loads, reaching a maximum drift of 3.6 % without serious damage disqualifying the structure from further exploitation. The GFRPU strengthening system was found to be highly effective in preventing infill collapse of damaged masonry infill wall during in-plane loading. Additionally, the results of extended thermal analysis of PU are presented as polymers are, in general, a material, poorly resistant to heat. However, the analyzed PU manifested stable properties up to 200 degrees Celsius, which makes this material promising in civil engineering applications at elevated temperatures.

Optimising of thermal insulation thickness based on wall orientations and solar radiation using heating-degree hour method

Buildings consume more than a third of the world's energy demand, and painstaking adjusting the insulation thickness of external walls is an effective way to save energy. Thermal insulation plays an important role by reducing the heat transfer rate to save energy, and it is important to determine the thickness of the appropriate insulation material in the walls. In this research, considering only the heating factor, four different building materials (Pumice, Hollow concrete block - HCB, Hollow red clay block - HRCB and Reinforced concrete - RC) and eight different insulation materials (Extruded polystyrene - XPS, Expanded polystyrene - EPS, Expanded polyurethane - PUR, Wood fiber - WF, Hemp fiber - HF, Linen fiber - LF, Fiber glass - FG and Sheep wool - SW) are investigated on the exterior of a building in Sivas province of Türkiye. To reach more accurate results, life cycle cost analysis is taken as a basis, and the optimal insulation thicknesses, payback periods and energy savings of 32 different wall + insulation combinations with solar radiation (SR) are estimated using heating degree-hours. The heating requirement of a building covers more than three quarters of the year in Sivas, depending on different facing walls. These rates are calculated as 85 % (without SR), 80 % (North), 78 % (West), 77 % (East) and 75 % (South). Results also showed that the total minimum heating cost, the total maximum energy saving cost and the shorthest payback period are obtained HRCB + FG + South with 14.19 €/m2, RC + FG + solar radiation free with 72.76 €/m2 and RC + LF + solar radiation free with 1.60 year.

A parametric study in reinforced concrete frames with different infill wall materials

Understanding the behavior of structures during earthquakes is crucial for ensuring safety. Despite their significant impact on buildings, infill walls are often overlooked in seismic assessments, contributing to the complexity of a structure. Because of their intricate nature and modeling difficulties, infill walls are frequently excluded from seismic models. However, given the prevalence of reinforced concrete buildings with various infill wall materials in earthquake-prone areas, it is essential to incorporate infill walls for a more realistic evaluation of seismic behavior. This study scrutinizes a building that sustained damage in the Izmir earthquake in Turkey. The building was represented in four distinct models using the SAP2000 V24 finite element program: without infill walls, with porotherm clay blocks, burnt clay brick, and autoclaved aerated concrete blocks. Real parameters of the building were utilized in the modeling process. Upon comparing the results of the time history analysis, it was observed that the presence of infill walls had a positive impact on various building properties, including period, ground floor shear force, column bearing capacity, and inter-story drift ratio. Additionally, infill walls increased base shear forces on the ground floors and the overall base shear force. Notably, similar outcomes were obtained with porotherm clay blocks and burnt clay brick as infill wall types, while autoclaved aerated concrete blocks exhibited lower stiffness than other infill wall models.

Test of three-storey confined masonry structure built from clay blocks and PU glue

The paper presents an experimental test of a nearly full-scale three-storey model of a confined masonry structure. The walls were constructed using newly developed clay masonry blocks, with large holes filled with thermal insulation and polyurethane glue instead of mortar. In the construction,relatively thick 38 cm walls and large tie-columns with 25 cm × 25 cm plan dimensions. The test model was built as confined masonry according to Eurocode 8. The innovative materials and construction were developed for thermal efficiency and the test was intended to verify the structural response. The model, test setup, and test procedures are described, and the results of the tests are analysed. The building responded primarily in shear, and ultimately failed in the ground floor in a storey mechanism, but there was also substantial damage on the floor above. Due to the non-standard dimensions of the tie-columns and because masonry was thicker than the tie-columns, the in-plane loaded walls developed an interesting response mechanism in which protruding masonry sheared off. Although this did not significantly impact the overall response, it led to the earlier onset of the significant damage limit state of the structure. The model responded well with wide hysteretic loops and distributed damage, which indicated large energy dissipation capacity, and the response envelopes showed gradual strength deterioration after peak load. The response of the model was quantitatively estimated using the N2 method. Calculations showed that the tested model could withstand a design seismic load corresponding to a 0.21 g peak ground acceleration with significant damage and almost 0.52 g before collapsing. The overstrength was estimated at 1.71.

Architectural technology and labour organisation at the late Neolithic Liangzhu City, Yangtze Delta region, China

Building the UNESCO World Cultural Heritage site of Liangzhu City and its hinterlands was an enormous undertaking that required an unprecedented level of architectural innovations, clever logistic planning, and sophisticated labour organisation. We draw on environmental, archaeological and experimental data on the preparation and construction of grass-wrapped clay blocks at the Liangzhu City and investigate the importance of technological innovations to understand architectural energetics and labour organisation behind the unprecedented urbanisation at Liangzhu and beyond in prehistoric Yangtze Delta region. We estimate that each clay block took only around 5 min to prepare by 2–4 workers. Considering digging and other tasks, a small group of 3–4 workers would have been the most efficient arrangement in the preparation of grass-wrapped clay blocks. We reproduced different types of clay blocks, classified their sizes, and identified the standard sized (45x15 × 15cm) clay blocks that match with archaeological finds. Our results also show that standard-sized clay blocks had a more optimal grass-earth ratio which increased the drainage efficiency of the built clay-blocked structures and their resistance to weathering in wet conditions. The different architectural technologies applied by the Liangzhu builders constituted the Liangzhu builders’ earth-building toolkit. To maximize the efficiency, labour was divided and organised according to different construction tasks. The clay-blocked structures and stone beddings were mostly built by smaller groups, who were responsible for the preparation, transportation and construction tasks. Mobilization and division of labour during these construction activities might not follow the classical top-down process. Instead, the need to apply different architectural technologies, each restrained by availability of resources, convenience of transportation, and/or intrinsic engineering properties, at construction sites in a predominantly aquatic environment, prompted a creative form of labour organisation. Our study therefore provides fresh insights into understanding labour organisation, social structure and power relations at the Liangzhu Civilisation.

Between Islands – an Intergenerational Contact and Creative Practice Program

ABSTRACT Addressing ageism is a serious social issue in need of targeted, empirically based solutions. Facilitating intergenerational contact is one promising means of reducing ageism. Between Islands was a creative practice and intergenerational contact intervention designed to promote connection while challenging stereotypes about aging and older adults. Before the intervention began, young and older adults received two 2.5 pound blocks of clay, paints, and paintbrushes. During the four-week online intervention, participants learned about the history of hand-weights and circuit training, engaged in creative practice (designed, sculpted, and decorated hand-weights), and got to know one another through group based discussion as well as smaller group prompts and zoom breakout rooms. Among young adults, paired t-tests demonstrate a significant decrease in benevolent ageism and intergenerational tension. In addition, open-ended responses illustrate how the intervention challenged stereotypes about older adults, supported the recognition of similarities between young and older adults, and facilitated connection between participants. Results from Between Islands, an intervention rooted in theory, offer promise for reducing ageism and intergenerational tensions using unique and creative programming.

Calibrating failure surfaces for vertically perforated clay block masonry using a validated numerical unit cell model

Finite element software is nowadays an essential part of a structural engineer’s modeling process. The simulations range from trivial linear elastic models to highly non-linear ones, accounting for contact, plasticity, viscoelasticity, or fracture. Though fired clay blocks are an excellent and widely used building material, little effort has been made to extend available failure surfaces for simulating vertically perforated clay block masonry in modern FE Software. Therefore, developing reliable and efficient ways to predict the effective strength of vertically perforated clay block masonry subjected to different loading states is critical. In this study, we aim to qualitatively analyze the failure surface of vertically perforated clay block masonry under in-plane loading, using numerical simulations. Using a previously validated unit cell FE model, we derived the peak stresses from 471 simulations. Subsequently, we compared these results with two failure surfaces from the literature and identified qualitative differences. Taking these differences into account, we propose a concept for numerically calibrating the parameters of the Rankine–Hill failure surface proposed by Lourenço (1997).

Design standards for residential N-ZEBs in mild Mediterranean climate

In this paper the authors intend to investigate into the possibility of obtaining the Net Zero Energy Building (N- ZEB) standard for a residential building type widespread in Mediterranean climate. To this aim, the study considers a terraced-house apartment building with an external envelope made of clay blocks and concrete structure, which is a very common solution in Italy. At first, the building is thought to be designed according to the current national regulations concerning the insulation level of the envelope; for such configuration, the current energy needs for heating, air conditioning, lighting and hot water production are calculated through dynamic simulations tools. Then, the study discusses the interventions, both on the envelope and on the energy systems, needed to transform this conventional building into an N-ZEB, avoiding excessive modifications to its design. Due to the diffusion of this typology, the case considered in the paper is very representative, and the conclusions might be extended to a significant portion of the building real estate. The final aim is to define a construction standard that might become a reference for the design of future residential N-ZEBs in Mediterranean countries.

Structural behaviour of unbonded post-tensioned masonry walls with threaded rods in clay block

Structural behaviour of unbonded post-tensioned masonry walls with threaded rods in clay block

Sustainable Analysis of Building Materials for Social Housing: A Comparative Study of Embodied Energy of Concrete and Glued-Laminated Timber (GLT) Structures

This study aims to conduct a sustainable comparative analysis of embodied energy between different materials to produce social buildings in Brazil. The study compares structures and enclosure made of glued laminated timber (GLT) and reinforced concrete with enclosure made of ceramic block masonry to produce the same 48m² single-family housing unit following the COHAB MG standard. The accounting of materials used for building production was made through a BIM platform, and subsequently, total embodied energy was calculated, weighted according to the amount of each material used. Results indicates that buildings constructed with GLT in Brazil can achieve up to a 40% reduction in total embodied energy when compared to the traditional construction model of reinforced concrete and red clay blocks.

BETWEEN ISLANDS—A CREATIVE PRACTICE AND INTERGENERATIONAL CONTACT INTERVENTION

Abstract Addressing ageism is a serious social issue in need of targeted, empirically based solutions (WHO, 2021). Facilitating intergenerational contact is one promising means of reducing ageism (Lytle et al., 2020). Between Islands were a creative practice and intergenerational contact intervention designed to promote creativity and intergenerational connection between younger and older adults while challenging stereotypes about aging. Over a four-week intervention, younger and older adults meet virtually (on zoom) for an hour each Wednesday to learn, create, and discuss with one another. Before the intervention began, participants received two 2.5 lb blocks of air-drying clay, paints, and paintbrushes. During the four-week intervention, participants engaged in creative practice (designed, sculpted, and decorated two hand-weights out of the provided clay). In addition, participants learned about the history of hand-weights and circuit training and got to know one another through group-based discussion as well as smaller group prompts and breakout rooms. Prior to the start of the intervention, baseline attitudes and stereotyping toward older adults were assessed among the younger adult participants. Attitudes and stereotypes were again measured after the intervention concluded. Younger adults reported a significant decrease in benevolent ageism and intergenerational tension after the Between Islands intervention. In addition, themes that emerged from the open-ended responses illustrated that the intervention challenged younger adults’ stereotypes about older adults, encouraged recognition of similarities between younger and older adults, and facilitated the connection between participants.

Interaction of various parameters on the properties of semi-dry gypsum-based blocks produced by compression forming method

The utilization of hemihydrate gypsum to produce blocks can be a more sustainable alternative to conventional cement concrete blocks. This study explores the fabrication of semi-dry gypsum-based blocks using the compression forming method to address the drawbacks associated with traditional blocks (clay block and cement concrete block) manufacturing processes, including high energy consumption and lengthy production time. However, the low mechanical strength, low water resistance, and high water absorption of gypsum-based blocks limit their application in construction. Therefore, in this study, semi-dry gypsum-based blocks were prepared using the compression forming method by investigating the interactions between the ground granulated blast-furnace slag (GGBS) content (0%, 20%, 45%), water-to-binder (w/b) ratio (0.20, 0.25, 0.30), and compaction pressure (CP) (10 MPa and 20 MPa). The compressive strength, water resistance, mineralogical composition, and microstructure of the produced gypsum-based blocks were investigated and compared with gypsum-based blocks without GGBS. It was found that adding GGBS can lead to formation of AFt and C-S-H gel when the water content reaches the required level for the reaction. These hydration products are beneficial to improve the compressive strength and water resistance. In addition, the porosity of the specimens was examined using water immersion and the mercury intrusion porosimetry (MIP) method. It was observed that when the w/b ratio is 0.25 or 0.30, a lower CP (10 MPa) should be applied. This is because higher CP (20 MPa) caused paste overflow during the forming process, resulting in undesirable pores having an adverse impact on the compressive strength. The optimal performance was obtained with GGBS content, w/b ratio, and CP at 20%, 0.25, and 10 MPa, respectively. In summary, the compression forming method could produce semi-dry gypsum-based blocks with adequate compressive strength (35.3 MPa) and water resistance (softening coefficient of 0.68).

Assessing the Effects of Refuse-Derived Fuel (RDF) Incorporation on the Extrusion and Drying Behavior of Brick Mixtures

This study explores the potential benefits of incorporating Recycled Demolition Waste (RDF) as an additive in ceramic mass for the brick industry, with a focus on applications such as thermoblocks. The research underscores the significance of sustainable waste management practices and environmental conservation by diverting waste from landfills. RDF, exhibiting combustion properties above 550 °C, emerges as a valuable candidate for enhancing clay-based materials, particularly in the brick production process where firing temperatures exceed 850 °C. Conducted in two phases, the research initially concentrated on RDF preparation, RDF integration with clay materials, and its influence on extrusion and drying phases. Employing innovative techniques involving brick and tile industry machinery coupled with sand incorporation yielded promising results. The grounding of RDF particles to less than 1 mm not only facilitated the mixing process but also ensured stable grinding temperatures within the hammer mill, reducing operational costs. During extrusion, challenges associated with unprocessed RDF material were addressed by utilizing ground RDF, leading to a more efficient and cost-effective process with enhanced plasticity and reduced water requirements. Practical implications for brick plant operations were identified, promoting resource and energy savings. Drying behavior analysis revealed the positive impact of RDF integration, showcasing reduced sensitivity, decreased drying linear shrinkage, and improved density properties. RDF’s role as an inert additive resulted in a 5% reduction in density, enhancing porosity and thermal insulation properties, particularly in thermoblock applications. In the brick industry, where durability, thermal performance, and cost-efficiency are paramount, this study emphasizes the potential benefits of incorporating RDF into clay-based materials. While further research is needed to address the firing procedure of RDF as a brick mass additive, the initial findings underscore the promise of this approach for sustainable and environmentally responsible brick production. This study contributes to the literature by shedding light on the advantages and challenges of integrating RDF into clay-based products, supporting sustainability and waste reduction in construction and manufacturing. The findings provide valuable insights into the performance and feasibility of these mixtures, offering crucial information for industries striving to adopt eco-conscious production methods. This article not only outlines the applied methodology and experimental setup but also presents results related to the behavior of RDF-inclusive clay block mixtures in the production environment. Anticipated to exert considerable influence on future practices and policies, this research contributes to the growing body of knowledge concerning eco-friendly and sustainable manufacturing processes.

Building for a sustainable future: investigating the thermal performance of innovative and local wall materials in an Egyptian housing unit

ABSTRACT Nowadays, the majority of nations are facing the challenge of global warming which has caused less thermal comfort in indoor environments with further energy consumption. To mitigate these negative impacts, selecting appropriate building materials with environmental design principles is crucial to meet user’s needs. This study aims to investigate the impact of implementing innovative and locally sourced building materials in the wall construction of a residential building in Egypt; to improve energy consumption and users’ thermal comfort. The thermal performance of six alternative walls was analyzed and compared using computer simulation software. Alternative wall systems included innovative materials, such as Marmox boards and aerogel panels, as well as local materials such as double wall, Singer clay blocks, and Mudbrick with strawbale. The simulation results demonstrated that the Mudbrick strawbale exhibited the best thermal performance among all alternatives. It reduced energy consumption by 45% and decreased discomfort hours to an average of 18 hours per year. The innovative materials, Marmox board, and Aerogel panel, also showed promising results that were comparable to those of Mudbrick strawbale. This confirms that local materials can offer superior thermal performance when used in appropriate wall techniques. The overall study results revealed that implementing alternative wall strategies using environmentally sustainable building materials in residential settings can lead to energy savings ranging from 29% to 45%, as well as a reduction in annual discomfort hours by over 50%. This study highlights the effectiveness of using alternative wall strategies as a solution for addressing environmental adaptation gaps in residential settings.

A numerical unit cell model for predicting the failure stress state of vertically perforated clay block masonry under arbitrary in-plane loads

As vertically perforated clay block masonry advances into more demanding building categories, knowledge of the effective masonry strength under different loading states becomes crucial. However, experimentally identifying macroscopic failure surfaces for such masonry requires a massive effort. In this study, we propose a FEM-based simulation concept to predict failure stress states of masonry under arbitrary in-plane loading. The proposed concept is validated using seven experiments from the literature. Subsequently, subjecting the validated model to various load cases allows for deriving a failure surface comparable to the Rankine–Hill surface. Thus, by applying the presented concept, we can effectively generate macroscopic failure surfaces for any perforated clay block design.