The composition of the soil, according to the analysis of granulometry and index properties of the material, is characterized by its content of inorganic clays of medium plasticity, with fine-grained dark brown sands (CL SUCS classification) (17).

The manufacturing process of adobe bricks consisted of mixing soil, sand, straw, and water in a 1:1:0.1 volume ratio until a paste-like composition was obtained, leaving it to stand for a minimum of 24 hours, and then proceeding to the manual manufacture of adobe pieces whose dimensions are, 10 cm wide, 16 cm long and 3 cm high, which were dried outdoors for 30 days.

The mechanical tests for adobe were carried out based on Peruvian Standard N.E. 080 (18) regarding design and construction with earth, and Standard NMX-C-464-ONNCCE-2010 (19) regarding clay and concrete pieces, the tests performed were as follows:

Table 1 shows the number of specimens, loading rate and allowable stress obtained in each test to know the physical-mechanical properties of the masonry to be used in the models.

Additionally, the compressive strength test of concrete specimens was performed in accordance with Mexican standard NMX-C-083-ONNCCE 2014. (20); 3 cylinders identified with the letters CC, with an average resistance of f'c= 14.91 MPa, representing the concrete used in the confining elements and roof slab in models H-2 and H-3 at 1:3 scale, were subjected to compression tests.

For the seismic simulation, three dwellings models of 12.96 m² each were built, on a wooden and polystyrene base at a scale of 1:3, identified with the letters H, Table 2, Figure 2., with an interior area of 9.00 m², value that represents an area to develop a rest-activity in a dwelling, the construction specifications are mentioned in the development of each one of them.

For the three models, the foundation is 12 cm wide by 15 cm deep, based on a stone of 5 to 10 cm in diameter joined with cement-sand mortar 1:3. This type of foundation was chosen because it is the most commonly used for this type of construction in Mexico and Latin America (10).

Table 3 shows the actual weights of the models obtained with a scale, as well as the calculated weight of the 1:1 scale prototypes according to the volumetric weight of the materials (21), which serve as the basis for the analytical calculation of their displacements.

The walls are supported on stone foundations, the adobe pieces are glued with the same material they were made of, in a running bond pattern, and in overlapping form in the joints of two or more walls, Figure 3 and 4.

In the 1:3 scale model, the lintels on doors and windows are 2 cm high by 10 cm wide, protruding from the span on both sides by 10 cm. The roof is made of wooden beams 2 cm wide by 6 cm high, with 18 cm spacing from axles, on which a 0.3 cm wooden cover is placed, covered with sand. Figure 5.

The structural plan and elevation drawings of both specimens are shown with their respective dimensions, the only difference between the two specimens is the direction of the lightened concrete ceiling beams in one direction; it corresponds in the X direction for room H-2, Figure 6a, and in Y direction for specimen H-3, Figure 6b. Two types of dimensions are noted on the drawing, the dimensions in parentheses indicate the actual dimensioning of the model, the dimensions not in parentheses indicate the dimensioning of a 1:1 scale prototype.

The vertical reinforcement elements that serve as confinement to the walls are anchored to the foundation.

At the intersections of the walls, 10 cm x 10 cm K-1 ties columns have been placed, reinforced with 4 # 2 bars (∅6 mm) 10-gauge stirrups every 6 cm, Figure 7a. In door and window openings, the K-2 tie piers, are reinforced 5 cm x 10 cm with 2 # 2 bars, 10-gauge stirrups every 6 cm (21), Figure 7b.

D-1 lintels, Figure. 8a, are reinforced 5 cm x 10 cm with 2 # 2 bars, 10-gauge stirrups every 6 cm (21). 10 cm x 5 cm; D-2 roof slab perimeter tie beam, Figure 8b, reinforced with 2 # 2 bars in the lower bed, 2 10-gauge bars in the upper bed, 10-gauge stirrups every 6 cm;

The roof slab L-1, is made of 7 cm thick concrete lightened with 2.5 cm thick polystyrene plates (22), beams in one direction every 33 cm, with 4 cm x 7 cm section, reinforced with 2 x 10-gauge bars, 12-gauge stirrups every 6 cm, Figure 9, the compression layer is 2 cm reinforced with 21-gauge mesh, the concrete ratio is 1:2:2 (one cement to two sand and two gravel).

The following illustrations show the assembly of roof slab L-1, for specimen H-2 in the X-X direction, Figure 10a; and for specimen H-3 in the Y-Y direction, perpendicular to the door and window openings, Figure 10b.

Table 4 shows the ratio of the cross-sections of the structural elements and the areas of reinforcing steel between the 1:3 scale specimen and the full-scale 1:1 prototype.

The seismic simulation tests were carried out on a 1.20 m x 1.20 m shaking table, which can have three independent movements: two horizontal movements (X and Y) with a load capacity of 900 kg, and a vertical movement (Z) with a load capacity of 300 kg. Its source of movement is pneumatic with a maximum working pressure of 8 kg/cm2, frequency from 0.1 to 15 Hz, and a horizontal displacement of 7 cm, and 5 cm in the vertical axis.

Its operation is through LabVIEW software, with which you can control the frequency, duration of the test, axis movements, and obtaining data from motion sensors, Table 5, shows its functional characteristics.

The specimen (model) is placed on the dynamic simulation table and anchored to the base in such a way that it is adequately secured, after which the linear and angular displacement of the model is instrumented, after calibration of the sensors. The instrumentation is divided into two parts: the one corresponding to the X, Y, and Z axes of the vibrating table based on ultrasonic linear distance sensors with a speed of 7 readings per second and the one corresponding to the test model, with ultrasonic linear distance sensors and angular measurement bending sensors, both with a speed of 7 readings per second.

The frequency of movement of the table and the duration of its phase are programmed, the air pressure necessary for its operation is verified and the instrumentation is sending the signal correctly; the test is started and the data of displacement, accelerations, periods and damages in the testing process in the different phases are recorded.

For the dynamic test, frequencies from 0.6 Hz to 6 Hz are proposed, comprising periods of less than 0.3 seconds, close to the period of a one-story masonry dwelling house typology, with accelerations ranging from 10 to 600 gal; Table 6 shows the phases and accelerations for the 1:3 scale models.

In this stage, the parameters for the structural analysis of unconfined and confined walls are given, and the influence of the stiffness of the lightweight concrete slab (23) on the walls forming the test specimens, for the purpose of comparing their displacements and stiffness’s under seismic loading, considering the zone aspects, weight and properties of materials.

The deformation analysis is performed according to the linear homogeneous and isotropic elastic behavior (24), using the wide column model. The horizontal seismic force Pi applied at the center of mass of level i acting on the 1:1 scale prototype is obtained Equation [1]:

Where Wi is the weight of the level or story, Hi is the height of the force application mass Pi, and C is the seismic coefficient. The structure is classified according to its destination, soil type, and seismic behavior factor Q, (25). For the calculation of the displacement and lateral stiffness K at the centroidal point in solid unconfined cantilevered walls Figure 11, the following expressions, Equation [2 and 3], are used:

Where P is the lateral force at its centroid point, h is the height of the wall, E is the modulus of elasticity, A is the cross-sectional area of the wall and G is the shear modulus.

For the analysis of the adobe masonry walls confined with concrete elements, Figure 12, the wide column analogy model is used where the wall is replaced by a column in the geometric center (24).

The system of equations is solved by means of the direct stiffness method (26), the displacements d and the lateral stiffness of the wall K _∆ are obtained with equations Equation [4 and 5]:

Where P is the force acting on the node, and S^-1 is the inverse of the general matrix.

Table 7 shows the walls of the 1:1 scale prototypes to be analyzed by the wide column model, according to the axes shown in Figures 11 and 12.

Results are presented under horizontal dynamic loading applied to the three 1:3 scale models with 68 days of drying, which describes the response of the specimens in relation to the applied frequency and acceleration, the displacements of its base and the walls perpendicular to the movement are shown, according to the reading of the sensors placed specifically for this purpose.

A comparison is made of the dynamic behavior of the specimens with emphasis on the wall-to-wall junction and the wall-to-roof junction.

Due to the characteristics of the type of construction, its natural period and the capacity of the vibrating table, periods between 1.67 and 0.17 seconds were used. The results shown include the scale factor according to the similarity laws corresponding to the physical and mechanical properties of the specimen.

Three dynamic tests were applied to the model in the direction horizontal to the X-axis, parallel to the plane of door and window spans with factored time duration (t/3), Table 8.

Figure 13 shows the physical condition of the specimen before testing, which shows no damage.

Description: Figure 14 shows the relationship of Acceleration with respect to Displacement and Period. First visible damage appears for an acceleration between 90 gals and 174 gals, with a displacement of 10 cm, which corresponds to a period between 0.30 s to 0.22 s, and moderate damage for an acceleration between 174 gals and 244 gals corresponding to a period between 0.22 s and 0.17 s.

Figure 15 shows the damages where there is stress concentration, mainly in the door and window openings, where cracks and fissures can be seen at an angle of approximately 45, which starts at the vertices of the span outwards from them, there is no damage to the rest of the structure. The structure remains stable but with moderate damage that may be repairable.

Description: Moderate to heavy damage is observed in an acceleration range between 10 gals and 40 gals, which corresponds to a period between 1.5 s to 0.56 s, fractures in the foundation for accelerations between 22 s and 36 gals, which corresponds to a period of less than 1.0 s.

Figure 16 shows how the cracks are more accentuated around the door and window openings, with an approximate angle of 45 through the wall, door and window frames are separated from the wall, foundation failures are observed with different cracks in its perimeter, no damage is visible at the corner junction between walls, nor on walls perpendicular to the openings. Regarding the roof, the separation of the longitudinal wooden beams from the adobe walls can be observed. The structure due to the damage severity, is considered unstable and uninhabitable.

Description: Heavy to extreme damage is observed in an acceleration range of 10 to 26 gal, which corresponds to a period between 1.6 to 0.63 s, for the period between 0.83 s and 0.71 s, fractures are accentuated in the entire structure until total collapse is reached.

Figure 17 shows the damage sequence, the total detachment between the span frames and the wall can be seen, cracks increase in size to the point of partial or complete separation of parts of walls, for the period between 0.83 and 0.71, fractures are accentuated throughout the foundation, shifting away from the wall axis., no damage is seen at the corner junction between walls, but total separation leading to collapse (out-of-plane failure) in the central axis of the specimen passing through the spans, the roof is completely separated from the walls when collapse occurs.

In the specimen tests, 3 readings were taken with previously calibrated ultrasonic sensors to know the linear displacement on the outer walls perpendicular to the movement of the base (X-axis), and four readings with 5 cm high variable resistance bending sensors attached to the same exterior walls at a height of 2.00 m with previous calibration, to know the angular deformation caused by the different frequencies.

The maximum displacement with the similarity factor applied was 0.61 cm at the stage of structural damage, phase 3 was not implemented to avoid damage to the sensors in the event of model collapse.

Three dynamic tests were performed in the horizontal direction along the X axis equal to specimen H-1, the stability of the structures of H-2 and H-3, a fourth phase was added, all of them parallel to the plane of door and window openings with factored time duration (t/3), Table 9.

Description: No visible damage was observed during the four dynamic test phases, the reinforcements in door and window openings, wall junction, walls, foundation and roof, preserved their structural integrity.

Figure 18 and 19, show the structural integrity of specimen H-2 and H-3, there is no visible damage to the entire structure.

The model with structural confinement based on concrete elements in walls and roof slab, elements showed an efficient performance under the same dynamic loads as the model without confinement., there was no damage around the door and window openings, foundation and concrete roof.

The direction of the concrete roof beams parallel to the spans (specimen H-2), and perpendicular to them (specimen H-3), provided the necessary stiffness for the stability of the structure.

Structural analysis of unconfined and confined walls is carried out, and the stiffness contribution of the bond between the lightweight concrete slab and the adobe walls confined with concrete elements; the results of the displacements and lateral stiffness’s of the adobe walls analyzed are given below. The data on the mechanical properties of the materials are taken from section 2.1. Equation 1 was used to obtain the horizontal seismic force, and Table 10 shows the data and coefficient used.

As they are unconfined walls and due to the type of wood sheathing roof proposed, their restriction at the junction with the wall is disregarded, and were therefore analyzed as cantilever walls. For the evaluation of confined walls, the wide column method was used through the direct stiffness matrix method.

Table 11 shows the results of the displacement and lateral stiffness analyses of the walls under different constraint conditions.