Finite element methods are valuable tools for characterizing and analyzing the mechanical behavior of various materials. Within a broad spectrum of finite element strategies, nonlinear analysis plays a pivotal role, particularly in implementing damage and plasticity models. These methodologies provide a deeper understanding of material failure under different loading conditions and cycles. Numerous elastoplastic damage models have been developed [25], [26], [27], [28], [29], [30]. and the implementation in finite element programs has been widely studied [31], [32], [33].

To carry out the failure analysis on the adobe unit and wallettes, the microplane plasticity–damage model reported in [24]. was employed. This model defines stress–strain relations on multiple oriented planes—known as microplanes—allowing the simulation of directional cracking, frictional slip, and compression splitting, which are characteristic of quasi-brittle materials like adobe [23], [24]. The model was selected over other plastic-damage formulations due to its ability to independently represent tensile and compressive responses and to handle complex nonlinear behavior under cyclic or combined loading conditions [34].

Additionally, the model includes a separation of damage mechanisms in tension and compression, allowing for more accurate stress redistribution during cracking. It also incorporates implicit gradient enrichment to mitigate numerical instability and mesh sensitivity. Implemented in the ANSYS 2022 R1 finite element software, this model has been validated in applications involving heterogeneous granular materials like concrete and is applied here to adobe.

To analyze the adobe units with the microplane plasticity–damage model, the parameters presented in Table 1 were defined, including Young’s modulus (E) and Poisson’s ratio (ν), which were directly calculated from laboratory results. Other parameters, such as compressive strength (f_c, f_b), tension strength (f_t), and non-local parameters (R_t, D, σ_cv, R_c, γ_t, γ_c, β_t, β_c), were derived through model calibration based on experimental data.

Table 1 Table 1 General parameters of the microplane model used for both adobe units and mortar Source: Authors own creation.

The experimental results were obtained from three laboratory tests conducted on real adobe blocks, collectively referred to as the Block Compression Test (BCT). Each test, labeled as BCT1, BCT2, and BCT3, produced load versus displacement curves. Since the tests involve compression, the material experiences a reduction in length along the loading axis, resulting in a negative displacement commonly referred to as shortening. Accordingly, Figure 1, along with subsequent figures for other tests, presents load versus shortening graphs. From these experimental results, an average curve (BCT) was derived to represent the overall behavior of the material under compression. This curve was then used to calibrate the model, resulting in the numerical curve labeled BCS (Block Compression Simulation), which accurately replicates the mechanical behavior observed during the laboratory tests.

Figure 1 Figure 1 Compression adobe block model Source: Authors own creation.

Following the calibration of the adobe block model, the adobe wallette model was developed. It consists of five rows of one-and-a-half blocks, joined by a soil-based paste; hereafter referred to as mortar. This mortar is a non-cementitious mixture of clay, sand, and natural fibers, applied to the contact surfaces of the blocks. The soil used in the paste is classified as A-6 clayey soil with a group index of 0 (AASHTO classification) and as CL, indicating low-compressibility clay, in the Unified Soil Classification System (USCS), with an initial absorption rate of 0.0024 g/cm²/min [21]. As an alternative to cement, this paste bonds the blocks and enhances structural resistance, as will be discussed further.

Using a similar methodology to the block model, meshing, contact conditions, and other critical aspects were carefully defined to ensure the accurate performance of the wallette model. Simulations of compression and diagonal tension tests were conducted, utilizing calibration derived from experimental data. As with the adobe block simulation, linear and nonlinear parameters, as shown in Table 1, were set to calibrate the tests. The compressive strength parameters (f_c, f_b) were established through numerical calibration of the experimental compression wallette tests, while the tension strength parameter (ft) was determined from the results of diagonal tension. Lastly, the non-local parameters, such as (R_t, D, σ_cv, R_c, γ_t, γ_c, β_t, β_c), can’t be regarded as singular to the material as they fluctuate depending on the type of test conducted on the materials. The overall procedure for defining and calibrating material properties is summarized in Figure 2.

Figure 2 Figure 2 Flowchart of the procedure for assigning material properties and calibrating the numerical model Source: Authors own creation.

Based on the load-displacement graphs obtained in the compression test of five unreinforced wallettes (UWCT), polynomial functions of the mechanical behavior of each one were defined to generate an average curve used for calibrating the numerical model. From these experimental tests, the behavior within the linear range was ascertained via numerical simulation, resulting in the derivation of elasticity and Poisson’s ratio. Afterwards, the microplane model was employed to define the wallette’s behavior within the nonlinear range. Following the calibration of the model pertaining to the non-reinforced wallette under compression, a similar procedure was applied with the experimental data of three tests on wallettes with vertically oriented Guadua strips reinforcement. The mean curve was defined, and the model shown in Figure 3 was developed.

Figure 3 Figure 3 Reinforced adobe wallette model for compression testing Source: Authors own creation.

In the elastic range, the modulus of elasticity and Poisson’s ratio were determined for adobe blocks, mortar, and Guadua strips. After calibrating the model of the compression wallette reinforced with vertical Guadua strips, variations were made in the orientation of these strips, changing their inclination concerning the horizontal plane to establish the influence of the inclination of the strip on the mechanical behavior of the wallette; the different inclinations are shown in Figure 4.

Figure 4 Figure 4 Models4of reinforced wallettes with different inclinations of Guadua strips for compression testing Source: Authors own creation.

The diagonal tension test serves to determine the masonry shear strength and stiffness, subjecting these specimens to a compressive load along their diagonals as shown in Figure 5. This load generates tension stresses perpendicular to the direction of the load. The type of failure that occurs in the specimen varies according to the composition of the materials.

Figure 5 Figure 5 Reinforced adobe wallette model for diagonal tension testing Source: Authors own creation.

Experimentally, the results of three tests of wallettes without reinforcement were compiled. From these, load and displacement (shortening) curves were extracted. These were approximated through polynomial functions and averaged to obtain a reference curve (UWDTT, Unreinforced wallette diagonal tension test), as can be shown in Figure 6.

Figure 6 Figure 6 Unreinforced wallette diagonal tension Source: Authors own creation.

As with the compression wallette, the analysis was initially conducted within the linear elastic range. To define the elastic behavior of the wall model, the modulus of elasticity (E) and Poisson’s ratio (ν) were first determined individually for both the adobe units and the mortar. These values were obtained from the initial (linear) portion of the stress–strain curves derived from compression tests performed on each component separately. Once calibrated, the values were assigned to their corresponding domains in the finite element wallette model to ensure an accurate representation of each material’s contribution to the global response.

Subsequently, the microplane model was applied to define the behavior of the wallette in the nonlinear range. After having calibrated the model of the unreinforced wallette, simulations were carried out with non-linear calibrated parameters for different grades of Guadua strip inclination. Models with the inclinations presented in Figure 7 were used.

Figure 7 Figure 7 Models of reinforced wallettes with different inclinations of Guadua strips under diagonal tension Source: Authors own creation.

The contact between the mortar and the adobe units was modeled as bonded, meaning the surfaces behave as permanently fused with no penetration, separation, or sliding. In contrast, the contact between the steel plates and the wallette was defined as rough, which prevents penetration and sliding by locking the surfaces together upon contact, while still allowing separation.

To analyze the mechanical behavior of the wallette, simulations were conducted using four different mesh sizes. Although all materials were assumed to behave linearly in the initial portion of the response, the coarser meshes produced noticeable variations in stiffness. This is attributed to their reduced ability to capture localized deformations at contact zones, which affects the accuracy of the elastic response. As shown in Figure 8, the selected 15 mm mesh offered a consistent and reliable representation.

Figure 8 Figure 8 Sensitivity analysis of compression wallette without reinforcement Source: Authors own creation.

Based on these results, a 15 mm mesh size was selected for subsequent simulations. Although a 10 mm mesh was also tested, it yielded only minor differences in the global response compared to the 15 mm mesh, while significantly increasing the computational cost. Therefore, the 15 mm mesh was considered an optimal compromise between accuracy and efficiency. In this configuration, the material properties were defined with a modulus of elasticity of 20 MPa for the adobe units and 8.3 MPa for the mortar in the linear elastic range. For the plastic range, the material response was calibrated using the microplane model, with parameters detailed in Table 2.

Table 2 Table 2 Microplane model parameters in the compression model of the unreinforced wallette Source: Authors own creation.

By comparing the load-displacement graphs obtained from the numerical model (UWCS, Unreinforced wallette compression simulation) with the averaged experimental data (UWCT, Unreinforced wallette compression test), illustrated in Figure 9, the maximum simulated and experimental stresses were determined.

Figure 9 Figure 9 Adobe wallette model under compression Source: Authors own creation.

In Figure 10, the stresses in the corners of the wallette exhibit minimum values of 0.6 MPa. When compared with the experimental results, it is evident that failure typically begins in these locations. This observation is corroborated by the laboratory test results shown in Figure 11, where the failure patterns align with the stress concentrations identified in the simulations.

Figure 10 Figure 10 Minimum principal stress of the wallette and the mortar under the compression test Source: Authors own creation.

Figure 11 Figure 11 Failure of the masonry wallette under the compression test Source: Forero, 2022. [21]

With the model calibration, the mechanical behavior of the wallette reinforced with Guadua strips was established. Bonded contact type was established both between the Guadua strips themselves and between these strips and the wallette’s mortar, reflecting the bond developed during the construction process. Similarly, as there was no direct interaction between the adobe units and the Guadua, a frictionless contact type was determined.

n the analysis of the linear elastic range, the modulus of elasticity was determined to be 12.5 MPa for the adobe units, 4.5 MPa for the mortar, and 900 MPa for the Guadua strips. These values were derived from stress-strain curves obtained from compression tests for the adobe and mortar, and tensile tests for the Guadua strips. Poisson’s ratio for all materials was consistently set at 0.15, a typical value for such materials, as variations in this parameter have a negligible effect on the simulation results.

After confirming the similarity between the developed model (RWCS, Reinforced wallette compression simulation) and the average behavior of the tested wallettes (RWCT, Reinforced wallette compression test) as illustrated in Figure 12, the model validation was conducted.

Figure 12 Figure 12 Elastic behavior under the compression test of the wallette reinforced vertically with Guadua strips Source: Authors own creation.

Subsequently, various inclinations of Guadua strips were proposed for reinforcement. Leveraging the symmetry of the wallette structure, the reinforcement angle was analyzed in 15° increments, ranging from 0° (horizontal configuration) to 90° (vertical configuration), as shown in Figure 4. The analysis revealed that the most effective reinforcement for the wallettes under compression load was achieved at an angle of 90°, as depicted in Figure 13.

Figure 13 Figure 13 Behavior under the compression test of wallettes reinforced with different inclinations of Guadua strips Source: Authors own creation.

In both Figure 12 and Figure 13, an increase in stiffness is observed during the loading process, as indicated by the rising slope of the curves. This behavior may be attributed to the progressive consolidation and densification of the mortar layers between the adobe blocks, which enhances interfacial contact and improves load transfer as the test progresses.

Following a similar approach to the compression analysis, both linear and non-linear analyses were performed, calibrating the numerical models with experimental test data. To ensure consistency, a 15 mm mesh size was maintained, and the wallette materials were defined within the elastic range: 12 MPa and 7 MPa for Young’s modulus of the adobe units and mortar, respectively. For the non-linear range, the following parameters were applied as shown in Table 3.

Table 3 Table 3 Calibrated parameters in the microplane model for the wallette without diagonal tension reinforcement Source: Authors own creation.

After calibrating the models, the maximum principal stress in the non-linear range was analyzed, with the results presented in Figure 14. The failure pattern observed in the numerical model closely resembles the experimental results, as shown in Figure 15. The failure in the model occurs at the center of the wallette, particularly at the joints between the adobe blocks and the surrounding areas. This behavior highlights a low resistance in the contact zones between the adobe units, emphasizing their vulnerability under diagonal tension.

Figure 14 Figure 14 Maximum principal stress in the model of unreinforced wallettes under the diagonal tension test Source: Authors own creation.

Figure 15 Figure 15 Failure of masonry wallette under the diagonal tension test Source: Forero, 2022. [21]

Following the calibration of the unreinforced model, an analysis was conducted on a wallette reinforced with Guadua strips. The same parameters were maintained for the wallette, with the Guadua strips modeled using a Young’s modulus of 900 MPa. The Guadua strips were assumed to behave as orthotropic and elastic materials without non-linear parameters. These assumptions enabled the computational model to simulate the behavior without requiring further calibration, producing representative results, as illustrated in Figure 16.

Figure 16 Figure 16 Behavior of the wallette model reinforced with Guadua strips inclined at 45° under diagonal tension Source: Authors own creation.

The numerical simulation of reinforced wallettes produced a representative load-shortening curve (RWDTS, Reinforced Wallette Diagonal Tension Simulation) comparable to the experimental results (RWDTT, Reinforced Wallette Diagonal Tension Test). Figure 17 demonstrates more than a twofold increase in the wallette’s capacity under diagonal tension due to Guadua strip reinforcement.

Figure 17 Figure 17 Behavior of wallette models with and without reinforcement under diagonal tension test in the non-linear range Source: Authors own creation.

Using the computational model, a comparison was made for various Guadua strip inclinations to evaluate and recommend the optimal reinforcement angle for adobe wallettes. The load-shortening curves for different Guadua strip inclinations (RWDTS, Reinforced Wallette Diagonal Tension Simulation) were analyzed, with the inclinations evaluated every 30°, as illustrated in Figure 7. These simulations considered the load application direction, and the results are presented in Figure 18. It was observed that the behavior of the reinforced wallettes was generally consistent across all inclinations. However, the wallette reinforced with Guadua strips at an inclination of 150° exhibited lower maximum resistance and stiffness compared to other configurations. Although this orientation does not align with the principal tensile stress direction in diagonal tension, it was included to highlight the reduced effectiveness of unfavorable reinforcement angles.

Figure 18 Figure 18 Behavior of wallette models with reinforcement in different inclination configurations under the diagonal tension test Source: Authors own creation.