Dynamic Shaking Table Test of a Constructive Sytem With Timber Frame Structure and Light Earth Enclosure

doi:10.21203/rs.3.rs-4475058/v1

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Dynamic Shaking Table Test of a Constructive Sytem With Timber Frame Structure and Light Earth Enclosure

https://doi.org/10.21203/rs.3.rs-4475058/v1

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There is a large deficit of housing and equipment in Latin America, which needs to be addressed with more construction alternatives offering seismic safety, in addition to economical, comfortable, and sustainable solutions. The proposal of a modular system of prefabricated elements of a timber frame structure and light earth enclosure panels is a feasible option for seismic-prone regions. This article describes a shaking table test performed on a proposed timber frame structure with a light earth enclosure and sheathing of diagonal wooden laths as part of a larger framework that seeks to propose a constructive solution. The test aims to assess the model’s seismic performance, determine its fragilities, and calculate the system’s dynamic properties. The seismic performance showed two stages of damage: an elastic stage during frequent and rare earthquakes, where the immediate occupancy and operational states of the structure were proven, and an over-resistance stage during a very rare earthquake, where life-safety performance with reparable damage was observed. The model’s dynamic properties showed an overall increase in dumping related to the reduction of lateral stiffness, with the ability to deform and dissipate energy. Even though the system performed well, the test has shown some limits of the structure that should be considered for the construction of a future dwelling prototype.

light-frame timber buildings

seismic performance

shaking table test

sustainable construction

The housing and equipment deficit in Latin America, particularly in Peru, is a persistent problem, with the qualitative housing deficit in the urban areas reaching around 40% (Daude et al., 2017). In response to this reality and the pressing need to address the gaps in this area, Objective 11 of the Sustainable Development Goals justifies the commitment to ensure access to adequate, safe, and affordable housing and basic services for all people by 2030 (Naciones Unidas, 2018). Expanding the range of construction alternatives offering safe, economical, comfortable, and sustainable solutions is necessary to achieve this objective. With their mechanical efficiency, high industrialization, and prefabrication, timber structures have been consolidated in recent decades as a viable option for seismic zones, making timber frame structures, or platform frames, a feasible solution (Piazza et al., 2015).

Within a larger research framework, which seeks to propose a constructive solution based on a wooden structure and light earth enclosures adapted to the Peruvian context (Meli et al., 2019), this article presents the considerations and results of a dynamic test on a shaking table. The proposal can be summarized as a modular system of prefabricated elements, consisting of (i) a modular wooden framework based on composite elements with pieces of reduced thickness, (ii) an enclosure of prefabricated blocks of light earth of reduced thickness, (iii) an exterior earthquake-resistant reinforcement sheathing composed of wooden laths, and (iv) a light earth coating (see Figure 1). It seeks to take advantage of the structural qualities of the wood; and the light density of the enclosure, which is variable between 600 and 1200 kg/m³, depending on the project site’s climatic requirements. Furthermore, the use of natural materials such as wood and straw to make the blocks, as well as wood for the structure, guarantees the biocompatibility and biodegradability of the system at the end of the building’s life cycle.

It is important to highlight that this construction proposal has been validated not only from a thermal perspective in terms of its ability to provide comfort (Wieser et al., 2020), but also from a structural standpoint to ensure seismic safety based on previous results of a cyclic lateral load test conducted on a wall using this proposal (Becerra et al., 2023). Moreover, the findings illustrated in this article have been used to improve the system for the construction of a full-scale module in 2020–2022, which is currently being thermally monitored.

The development of timber frame structures (TFSs) has emerged as a recurring and accessible option for construction in high-seismic-risk regions (Benedetti et al., 2022; Piazza et al., 2015). Although TFSs can suffer some damage during earthquakes, there is generally little loss of life (Kirkham et al., 2014). This is because the lightweight nature of the timber allows for greater flexibility and ductility of the structure, which enables it to absorb seismic forces without catastrophic failure. Additionally, the redundancy of the components in TFSs helps to distribute forces and ensure that the building remains stable in the event of an earthquake (CWC, 2023). Past earthquakes, such as those in Kocaeli in 1999 and Kashmir in 2005, have highlighted the resilience of traditional TFSs, such as the “hımış” and “dhajji-dewari” structures, which have remained standing amidst the earthquake ruins of modern buildings around them (Langenbach, 2007). Similar examples of TFSs have also been developed in Peru, utilizing the technique known as “quincha”. This ancient construction method, dating back approximately 5,000 years to the Caral civilization, involves the use of a frame structure constructed from timber and canes. These structures have demonstrated highly efficient seismic-resistant behavior, primarily due to their remarkable ability to dissipate the energy generated by earthquakes (Vargas et al., 2012).

The need to carry out a dynamic test on a shaking table was evident to characterize the seismic performance of the proposed TFS module, following the guidelines of FEMA (2007). In Peru, these tests have been carried out at the Laboratory of Anti-Seismic Structures (LEDI-PUCP), which is equipped with a one-directional 4 × 4 m dynamic shaking table, capable of a maximum acceleration of 1.6 g and a maximum amplitude of 150 mm. Similar proposals have been tested on said shaking table, such as the one carried out by Bariola et al. (1990) of a conventional one-story TFS made of “quincha”, measuring 4.0 × 4.0 m and 2.4 m in height. The test was conducted using the seismic signal “mayo70”. The specimen failed at a 5% drift when the sheathing started falling off the structure and damping of 8% was estimated. One of the most recent tests, conducted by Ordoñez and Lugo (2016), involved a full-scale three-story 4.0 × 3.0 m and 8.60 m tall TFS prototype. The prototype was constructed with a conventional wood frame consisting of 42 × 90 mm @40 cm studs and sheathed with 9.5 mm OSB panels. It was also subjected to the seismic signal “mayo70”, and the test results demonstrated good seismic performance, as the module remained within the elastic range during all three phases of movement. The prototype exhibited a consistent damping period (Td) of 0.085 s; however, high stresses were observed on the module’s anchorage to the foundation.

Another notable experiment conducted at the Laboratory of Civil Engineering of Lisbon involved a shaking table test of four different types of timber housing systems (Piazza et al., 2015). This test’s primary objective was to evaluate these systems’ seismic performance using a three-dimensional (3D) shaking table. The systems tested included a log house, a platform frame, and a cross-glued laminated timber structure. The test’s results revealed that all the timber housing systems exhibited excellent seismic performance, with no notable damage observed except for minor cracks in the corners of the cladding.

Throughout this research, the proposed system was subjected to various tests to validate it from a constructive and structural point of view. The proposal consists of wood-framed shear walls designed to resist seismic and wind loads. The proposal underwent its first test through a cyclic lateral load in accordance with the ASTM 2126-11 standards. A wall specimen measuring 2.7 × 2.3 m and 0.14 m thick was subjected to reversed cyclic loading, resulting in drifts of up to 3% until failure (Becerra et al., 2023). As for lateral resistance, the National Design Specification (NDS) for Wood Construction (AWC, 2024) establishes that the wall’s lateral strength is mostly provided by the sheathing. Therefore, an auxiliary structure of diagonal wood laths at 45° (4 × 1 cm each 15 cm) is proposed on both sides of the wall, oriented in opposite directions, fixed with 2 in nails, to serve as the wall’s structural sheathing. The sheathing is finally finished with a 2.5 cm thick layer of light earth cladding, made with a mixture of sifted earth and grass straw like the composition of the block.

The test revealed that the predominant failure mode was the cracking of the earth cladding, followed by the ultimate failure of the wall’s anchorage to the ground. The system’s nominal shear capacities were determined based on the preliminary test, including a maximum shear strength of 6.23 kN and a lateral elastic stiffness of 3.401 kN/mm (see Fig. 3).

Based on the results, the system was modified with an emphasis on improving the mechanical properties of the connections between the sheathing panels and the wall’s anchorage to the base. The following improvements were made (see Fig. 4):

The anchoring of the walls was done with steel expansive bolts with a diameter of 16 mm @ 90 cm.
The density of the cladding was reduced to approximately 1,000 kg/m³, incorporating a higher amount of fiber in it.
The walls’ reinforcement was increased by reducing the space between the slats from 30 cm to 15 cm. This reduction increased the number of connections to the frame, resulting in a stronger and more secure fixation.

To evaluate the proposed structure’s seismic response, a shaking table test was conducted at LEDI-PUCP in Lima, Peru. This dynamic experimentation involved subjecting a regular specimen to a one-direction shaking table movements, which followed the seismic signal of a tragic earthquake that occurred in the highlands of northern Peru in 1970. The shaking table test followed a protocol methodology that aimed to assess the light earth specimen’s seismic performance. The test followed the recommendations of the Federal Emergency Management Agency (FEMA) and the Applied Technology Council’s “Interim Testing Protocol for Determining the Seismic Performance Characteristics of Structural and Nonstructural Components” (FEMA, 2007). The test’s objective was to determine the model’s fragilities and interpret the design’s weaknesses to improve the structure’s seismic performance. The dynamic test involved several stages: (1) the design and fabrication of the test specimen; (2) the definition of the seismic signal; (3) the performance limit states and phases; (4) the instrumentation of the specimen; (5) the system identification test; and finally, (6) the test execution and data analysis. Each of the stages is detailed below.

3.1 Design and fabrication of the test specimen

The light earth specimen that has been tested was built at LEDI. It was a 2.87 m × 2.87 m room 2.5 m in height, with a door (axis 4) and a window (axis 1), built with the submitted proposal of a TFS and a light earth envelope, reinforced with diagonal wooden laths and earth plastering at the covering (see Fig. 5). The specimen was built over a reinforced concrete foundation ring, which allowed the specimen to be moved and fastened to the shaking table.

The wooden structure is connected to the foundation ring through a sole plate, fixed with steel expanding bolts with a diameter of 16 mm @ 90 cm. The walls are constructed using composite studs consisting of two to four 4 × 4 cm pieces every 80 cm, braced by a 2 × 8 cm horizontal crossbar at 45 cm intervals. The wall enclosure is made of two layers of prefabricated light earth panels measuring 45 × 45 × 4 cm, with a density ranging from 600 to 800 kg/m³, which are screwed to the wooden structure with 3-inch screws. As structural reinforcement, a sheathing made of wooden slats of 4 × 0.8 cm were used, placed diagonally at 45° every 15 cm, fixed with 1-inch (2.5 cm) nails. A flat roof was built consisting of four 5 × 12 cm beams, a 2 cm thick wooden deck, and finally, two layers of light earth blocks of low density (600 kg/m³). The wall was covered with a 2 cm layer of light earth of the same composition as the blocks. Finally, the outer surface of the specimen was painted white to better show any damage during the test (see Fig. 6).

3.2. Definition of the seismic signal

To generate the seismic excitation, a recorded signal from the earthquake that occurred on May 31, 1970, in the department of Ancash, Peru, was used (see Fig. 7). The input signal was used to program the shaking table’s displacement and frequency. It came from the longitudinal component (N8°W, Mw 7.9) of the acceleration measured in Lima. The original record was obtained from an analog accelerograph processed by the United States Geological Survey (Orta et al., 2009). This input signal is a standard choice in the laboratory for testing different construction proposals and making comparisons, as it caused significant damage and casualties (Salazar, 2022). It is appreciated that the input signal’s predominant frequency goes from around 2.5 to 3.5 Hz.

3.3. Performance limit states and phases

The objectives for the building’s seismic performance were based on the structure’s limit states for different global damage levels, proposed by Ghobarah (2004). Three performance limit states were defined, related to the association of the roof’s maximum drift at each damage level. The three performance damage levels, conducted by the variation of the displacement length of the seismic signal, were: (i) immediate occupancy (IO), as an elastic stage; (ii) life-safe (LS), as a nonlinear stage; and (iii) near collapse (NC), as a ductility stage. Table 1 describes the damage state limit objectives in relation to the maximum table displacement for each phase and the commonly used performance criteria proposed by the ASCE in FEMA 356 (2000). The first of the maximum table shaking displacements is established at 30 mm, which corresponds to a light or frequent earthquake; in the second phase, the displacement is set to 70 mm, similar to an intermediate/severe earthquake; and in the third phase, the displacement is set to 120 mm, which is considered a catastrophic/very rare earthquake. Before each phase of the test, and after the last phase as well, a free vibration pulse is supplied to the model to determine the value of a set of intrinsic parameters of the model that condition its dynamic behavior, particularly the seismic behavior.

Table 1

Damage states limit objectives.
Structural performance levels of wood stud wall structure		Drift FEMA 356	Table displacement	Hard soil acceleration
			Do (mm)	Ao (g)
Light or frequent earthquake	Immediate occupancy. Elastic performance of the structure.	1% temporary	30	0.25 g
		0.25% permanent
Rare earthquake	Life-safe. Important inelastic incursion with losses of resistance and stiffness. The structure can be repaired.	2% temporary	70	0.40 g
		1% permanent
Catastrophic/very rare earthquake	Near collapse. Severe inelastic incursions, absolute loss of resistance, and stiffness. The structure cannot be repaired.	3% temporary or	120	0.50 g
		permanent

3.4. Instrumentation of the model

The next stage involved instrumenting the specimen by installing 10 motion sensors and four accelerometers to measure the seismic excitation and analyze the system’s dynamic behavior (see Fig. 8). Linear displacement transducers (LVDTs) were strategically positioned to measure absolute lateral displacements (D1, D2, D5, and D6), as well as capture anchorage fixation and torsional effects through relative displacements (D3, D4, D7, D8, D9, and D10). The accelerometers were placed to measure absolute transverse acceleration (A1 and A3) and the acceleration of the module itself (A2 and A4).

3.5. System identification test

The system identification test, also known as free vibration pulses, involves applying a low-intensity acceleration-controlled sinusoidal input, consisting of four pulses with a small amplitude of 1.5 mm. This preliminary test is useful for verifying the proper functioning of the equipment and determining the dynamic characteristics of the test specimen. To evaluate the shear walls’ free vibration performance in the direction of movement, data recorded by the accelerometers (A1 and A3) located on the roof is utilized. To assess the performance of walls stressed by bending due to seismic forces perpendicular to the plane, accelerometers (A2 and A4) positioned in the central part of the wall are used (see Fig. 8). These characteristics include (i) the natural period (Tn) in seconds, (ii) the damped natural period (Td) in seconds, (iii) the natural frequency (ωn) in rad/sec, (iv) the damped frequency (ωd) in rad/sec, and (v) the damping percentage (ξ). The recorded parameters vary throughout the test but maintain relationships among them, which are expressed in the equations presented by Chopra (2001) and shown below. These equations involve the module’s stiffness (k) and mass (M).

\({T}_{d}=\frac{{T}_{n}}{\sqrt{1-{\xi }^{2}}}\) (1);

\({\omega }_{n}=\frac{{\omega }_{d}}{\sqrt{1-{\xi }^{2}}}\) (2);

\({\omega }_{d}=\frac{2\pi }{{T}_{d}}\) (3);

\({T}_{n}=\frac{2\pi }{{\omega }_{n}}\) (4);

\({\omega }_{n}=\sqrt{\frac{k}{M }}\) (5)

3.6. Test execution and data analysis

The test execution involved initiating a preliminary free vibration pulse, followed by moving the table according to the signal of each phase, and concluding with another free vibration pulse after each phase. By electronically recording the data from these free vibration pulses, it becomes possible to determine dynamic properties such as the damping coefficient (ξ) and basal shear stress (V). The damping coefficient (ξ) is calculated by evaluating the logarithmic decrease of the structure’s displacement response over a specific period of time (Td), as expressed in Eq. (6); (δ) represents the logarithmic decrease of the module’s acceleration. The basal shear force, obtained from the shear walls (as shown in Eq. 7), is calculated as the difference between the force applied to the table simulator (F) and the product of the table acceleration (Ao) and the combined mass of the table and foundation ring of the module (Mt + Mf). Finally, the shear walls’ lateral stiffness (k) can be determined with the relation between the basal shear force and the displacement of the wall (see Eq. 8).

\(\epsilon =\frac{\delta }{2m\pi }=\frac{1}{2m\pi }ln\frac{{A}_{i}}{{A}_{i+m}}\) (6);

\(V=F-Ao(Mm+Mc)\) (7);

\(V=k\times \varDelta\) (8)

4.1. Measured data and seismic-resistant performance

The load cell installed on the table allowed the measurement of the module’s actual weight, including both the module itself and the concrete collar beam on which it was built. The measured weight was found to be 5781.0 kgf (56.693 kN). This measured weight was then compared to the theoretical weight. Table 2 indicates that the difference between the two weights is less than 5%, which confirms the accuracy of the theoretical densities used in the calculations.

Table 2

Specimen real and theoretical weight.
Total Weight	Beam weight	Real weight	Theoretical weight	Difference
Wt	Wb	W_R	W_T	(W_T - W_R) / W_R
5781.0 kgf	2332.8 kgf	3448.2 kgf	3559.5 kgf	3%

Throughout the entire test, detailed data were recorded to evaluate the seismic performance and describe the extent of damage to the module in each phase (refer to the video). In relation to Ghobarah’s (2004) criteria, in Phase 1, which simulated a frequent earthquake, immediate occupancy (IO) was confirmed, as no significant cracks were observed. The maximum measured drift was 0.16% at an acceleration of 0.264 g. In Phase 2, representing a rare earthquake scenario, operational limit state (O) was confirmed, as no significant damage occurred, except for slight out-of-plane movements of the walls perpendicular to the direction of motion, but a gradual loss of resistance and stiffness. The maximum measured drift was 0.50% at an acceleration of 0.809 g. Finally, in Phase 3, simulating a very rare earthquake, the shear walls exhibited the first cracks in the earth cladding, following the position of the timber structure and diagonal laths. Additionally, noticeable movement was observed in the bending walls, but no cracks in the cladding were observed. The autopsy revealed noticeable movement of the light earth infill and wall heel anchorage (see Fig. 9). The life safety (LS) structural performance level of the structure was defined for this stage, considering its transition into the inelastic phase characterized by losses in resistance and stiffness. However, it was confirmed that the timber structure could restore its original shape after the movement. The maximum measured drift reached 4.57% at an acceleration of 1.436 g.

For the three phases of movement, Table 3 presents the maximum set of electronically recorded data used to determine the key parameters necessary to analyze the module’s dynamic response. The LVDTs D1, D2, D5, and D6 measured the lateral displacement, showing low displacements between 4 and 12 mm until Phase 2, followed by a sudden increase to 115 mm when the first cracks in the cladding appeared. Additionally, the vertical displacement (D7 to D10) showed a gradual increase until Phase 3, reaching almost 12 mm. The instruments measured the maximum absolute and relative displacement, as well as the acceleration of the table and roof. By comparing the maximum acceleration at the top of the structure with the acceleration at the base for each phase, the dynamic amplification factor (DAF) was calculated.

Table 3

Absolute and relative data of lateral displacement, and acceleration of the table and roof.
Measured data		PHASE 1	PHASE 2	PHASE 3
Vertical displacements (D7, D8, D9, D10)	DV (mm)	0.73	1.794	11.809
Absolute lateral displacement (D1, D2, D5, D6)	DL (mm)	31.598	75.211	146.2
Relative lateral displacement (D1, D5, D6)	DR (mm)	4.031	12.692	115.194
Lateral drift	Δ	0.16%	0.50%	4.57%
Structural performance level (limit state)	LS	IO	O	LS
Table acceleration (A0)	Ao (g)	0.264	0.809	1.436
Roof acceleration (A1, A3)	AR (g)	0.596	2.671	5.577
Dynamic amplification factor	DAF	2.26	3.30	3.88

4.2. Model dynamic properties

The test’s initial step included the system identification test, which aimed to determine the model’s dynamic properties. These free-vibration pulses were processed to identify the pulse with the best characteristics for extracting the desired parameters. Figure 10 represents the variation of the damping recorded by each accelerometer during the stages of the free vibration pulses. Throughout the test, there is an observable increase in shear wall damping (ξ). Sensors A1 and A3, located on the module’s roof, recorded very similar values, and their damping coefficients exhibited a stepped consistent increase throughout the test, with their curves practically matching for each phase from 5–17%. The damping curves of the bending walls, corresponding to Sensors A2 and A4, also showed a more gradual increasing trend, although they exhibited a slight decrease to 12% at the last free vibration pulse.

The module’s lateral stiffness (k) was determined using the relationship between the mass and the natural frequency (Eq. 5). The estimated stiffness values recorded for each movement sensor are presented in Table 4. Figure 11 illustrates the overall decrease in stiffness observed across all sensors during the test. In general, the graph demonstrates a linear decrease in stiffness until Phase 2. However, in Phase 3, which simulated a very rare earthquake scenario, a more significant decrease in stiffness is observed due to the formation of cracks and an increase in the period by up to 30%. It is worth noting that an increase in damping corresponds to a reduction in stiffness.

Table 4 presents the average values of the damping coefficient and natural period for the shear and bending stress of the module’s walls. In both types of movement, the natural and damping periods exhibit a gradual increase from 0.14 s to 0.18 s until Phase 2, followed by a significant increase to 0.26 s in Phase 3. For the structural analysis purpose, a damping period of 10%, a natural period of 0.191 s, and a natural frequency of 23 Hz can be summarized. It is worth noting that the module’s natural frequency is significantly different from the predominant frequency of the seismic signal (as shown in Fig. 7), indicating that the module remains far from the resonance condition. Regarding the system’s stiffness, all the sensors recorded comparable values with a consistent decrease over time. This decrease in stiffness was observed in each phase of the test. However, in Phase 3, a notable decrease in stiffness was observed specifically in the sensor located in one of the bending walls. This significant decrease indicates that the system experienced an incursion into the inelastic range during this phase.

Table 4

Dynamic properties of shear and bending stress walls.
Absolute dynamic properties			FV 0	FV 1	FV 2	FV 3
Shear stress walls (A1 and A3)	Damping coefficient	ξ (%)	5.052	8.327	10.017	16.980
	Natural period	Tn (s)	0.143	0.164	0.186	0.271
	Natural frequency	ωn (rad/s)	43.959	38.362	33.798	23.189
	Lateral shear stiffness	k (kN/mm)	6.664	5.073	3.938	1.854
Bending stress walls (A2 and A4)	Damping coefficient	ξ (%)	10.257	10.829	12.600	12.593
	Natural period	Tn (s)	0.141	0.154	0.175	0.231
	Natural frequency	ωn (rad/s)	44.519	40.760	35.896	27.571
	Bending stiffness	k (kN/mm)	6.833	5.727	4.442	2.645

The maximum basal shear stress was calculated for each phase to analyze its relationship with the lateral displacements (using Eq. 7). Figure 12 illustrates the hysteretic behavior of the wall in axis 4, using the displacement (D6), which has been identified as the most flexible, in each phase. During Phases 1 and 2, there is a noticeable increase in the structural response due to the intensity of the seismic signal. Phase 3 also exhibits some increment, albeit with more disorder. Table 5 presents the data of the relative displacements of the sensors located on the roof (D1, D5, and D6) and the basal shears (V), organized by phases. Throughout all the phases, the values of D5 and D6 exhibit a slight difference, which becomes more pronounced in Phase 3. This difference in displacement indicates a variation in stiffness, which can be attributed to the influence of the spans of the door and window.

Table 5

Basal shears and relative displacements.
	Phase 1	Phase 2	Phase 3
DR1 (mm)	4,031	12,692	60,136
DR5 (mm)	2,270	6,195	62,738
DR6 (mm)	3,287	9,299	115,194
V max (kN)	20.462	47.736	96.938

Figure 13 presents the envelope curve of shear stress and deformation for each phase, using data from the three sensors positioned on the roof (D1, D5, and D6). In the first phase, the sensors’ relative displacements were relatively small, with the highest displacement slightly exceeding 4 mm. During the second phase, the relative displacements nearly tripled compared to the first phase, while shear forces increased by 2 to 3 times. However, an overall relationship between force and displacement can still be observed. In the third phase of the test, where the shear force doubled once again, a significant increase in relative displacements was observed. This increase, combined with the reduction in stiffness mentioned earlier, suggests that the light earth material experienced a notable decrease in its ability to resist shear forces. Indeed, the TFS demonstrated its ability to absorb and redistribute shear forces during the shaking table test. This behavior resulted in the model’s overall integrity and indicated an over-resistance stage. By effectively dissipating and transferring the applied forces, the TFS prevented the module from reaching failure even under severe seismic conditions.

4.3. Model allowable capacities

Regarding the model’s shear performance, Sensors D5 and D6 were positioned on the walls in the direction of movement. The wall at Sensor D5 contained a window, while the one at D6 had a door. Due to the model’s geometric symmetry, it can be hypothesized that each shear wall should resist half of the shear force acting in the wall’s plane. By considering half of the shear force induced on the model for each phase of the test, along with the displacements recorded by the corresponding sensors, Table 6 and Fig. 15 can be created (see Eq. 8). These present the shear stiffnesses of Sensors D5 and D6. As can be seen in the graphic, the shear stiffness also tends to decrease in each phase, the reduction being more marked in the last phase. The graph also shows that the wall containing the door has lower values, as expected. It is interesting to mention that, in the cyclic lateral load test previously carried out, a lateral stiffness in the elastic range of the wall of 3.853 kN/mm was determined. This value is quite close to the average of the values obtained for the shear walls in the first phase, in which the effect of block separation was not yet significant (see Fig. 14).

Table 6

Shear stiffness by phase.
Phases	50% V max (kN)	DR5 (mm)	DR6 (mm)	k5 (kN/mm)	k6 (kN/mm)
Phase 1	10.231	2.270	3.287	4.507	3.113
Phase 2	23.868	6.195	9.299	3.853	2.567
Phase 3	48.469	62.738	115.194	0.773	0.421

Finally, the seismic coefficient is determined as the ratio between the basal shear force and the weight of the structure. Knowing that the light earth model’s weight is 34.21 kN, and considering the shear forces that acted in each phase of the test, Fig. 15 is presented below. We can observe that the seismic coefficient’s increase in each phase of the test is directly related to the shear forces applied. In the third phase, the acting force was 2,867 times the weight of the structure, reaching a maximum relative displacement of 115.194 mm. However, the structure was able to resist the catastrophic earthquake.

4.4. Discussion

The shaking table test performed on the proposed TFS demonstrated good seismic performance, providing valuable insights into the system’s dynamic properties. The module’s real weight enabled the calculation of an average weight per square meter of 0.4 ton/m2, less than half of the nominal 1 ton/m2 predictable for structures of reinforced concrete. Table 7 compares the proposed TFS’s seismic performance with the analytical performance levels of conventional TFSs and the drift limits prescribed by commonly used performance criteria. The analysis reveals that the TFS exhibited a higher initial stiffness compared to conventional TFSs. However, it also exhibited increased brittleness, particularly in the immediate occupancy (IO) and operational (O) performance states, during the elastic range until Phase 2, where no damage was observed. In Phase 3, there were visible cracks on the cladding and noticeable movement of the bending and shear walls, indicating some level of structural damage and the life safety (LS) limit state. The TFS exhibited elastic behavior during both frequent and rare earthquakes, indicating its ability to withstand moderate seismic activity without experiencing significant damage. Additionally, during a severe earthquake, the TFS exhibited a subsequent inelastic stage, where it displayed over-resistance and substantial displacements without reaching failure.

Table 7

Maximum drift values in accordance with the triggered performance level.
Phases	Drift’s demands for code FEMA 356	Roof rift limit (1)	Drift performance of a numerical analysis of a TFD (2)	Shaking table test drift result	Seismic performance levels of the module during the test
1	1% temporary	0.2%	0.83%	0.16%	P1. Light or frequent earthquake	Immediate occupancy
1	0.25% permanent	0.2%	0.83%	0.16%	P1. Light or frequent earthquake	Immediate occupancy
2	2% temporary	1.5%	1.45%	0.50%	P2. Rare earthquake	Operational
2	1% permanent	1.5%	1.45%	0.50%	P2. Rare earthquake	Operational
3	3% temporary or	2.5%	2.27%	4.57%	P3. Very rare earthquake	Life safety
3	permanent	2.5%	2.27%	4.57%	P3. Very rare earthquake	Life safety

Ghoborah (2001) and SEAOC (1995) Vision 2000 drift limit states

Benedetti et al. (2022) analytical performance drift limits

The module’s shear walls exhibited a gradual increase in damping throughout the three phases, reaching a maximum value of 17%. This increase in damping can be attributed to the independent movement of the light earth panels, as confirmed during the autopsy of the structure. These panels’ movement allowed for the dissipation of energy, resulting in higher damping and a subsequent reduction in stiffness. In contrast, the bending walls initially demonstrated a significant damping effect, which gradually increased until Phase 3. However, beyond Phase 3, the damping decreased to 12%. This observation indicates a different behavior compared to the shear walls, with a decrease in damping over time.

The results indicate that in the module’s elastic range, which includes Phases 1 and 2, the stiffness values of both the shear walls and the bending walls were similar, averaging between 3.9 and 4.2 kN/mm. However, in the subsequent inelastic stage (Phase 3), a more significant decrease in stiffness is observed. The shear walls exhibit a stiffness of 1.9 kN/mm, while the bending walls show a stiffness of 2.6 kN/mm. These findings highlight the module’s structural response under seismic loading and illustrate the transition from elastic to inelastic behavior. The decrease in stiffness reflects the system’s ability to deform and absorb energy, which is important to mitigate the impact of seismic forces.

To assess the TFS’s lateral stiffness, a comparison was made with the standard lateral stiffness of a wood stud wall without cladding, as outlined in Table 8.6.8 of NTE E.010. According to this standard, a 2.80 m long wall should have a minimum lateral stiffness of 0.48 kN/m. It was found that the lowest stiffness value in the dynamic test, wall in axis 4, was much higher than this standard requirement. This comparison suggests that the light earth blocks, particularly in the last phase of the test, did not contribute significantly to the model’s stiffness. Instead, it was the timber structure itself that exhibited the most resistance during the destructive earthquake, approaching the limit of its structural capacity.

When comparing the proposed TFS with the Peruvian code of seismic design NTP 030 (Seismic-Resistant Design), it is important to consider different scenarios and conditions. In more severe conditions, such as a timber essential building with irregularities, built in a high seismic zone and on soft soil, the seismic coefficient specified in the code would be around 0.71. This value is slightly higher than the seismic coefficient used in the first phase of the test, during which the module did not suffer any damage. In usual design conditions for timber buildings, the seismic coefficient typically ranges between 0.18 and 0.25. This implies that the TFD, as tested in the dynamic test, demonstrated good seismic performance even under more severe conditions compared to the usual design scenarios. It suggests that the TFD has the potential to withstand seismic forces and can be a viable option for seismic-resistant design.

4.5. Recommendations

The preceding paragraphs show that the results observed in the test correspond to seismic conditions of unlikely severity. However, the test has shown some of the system’s limits, which must be considered, knowing that earthquakes cause accumulative damage. In general terms, it is necessary to reduce the lateral displacement of the walls, which caused the final reduction of the system’s overall stiffness.

It was proven that the triggered failure occurred due to the reduction in the stiffness of the shear walls with openings; it is recommended to increase the openings’ stiffness by adding a timber column on both edges of the opening. Sensors D3 and D4, located on the door, showed a high incrementation of displacement in Phase 3, related to the highly noticeable movement of the columns located on the doors (4.57% drift).

In the case of the flexion walls, the maximum drift of Sensor D1, at the center of the roof collar beam of 2.39% was slightly higher than the 2% temporary life safety drift recommended by the codes. To reduce the displacement of the flexion walls, assuming the worst-case scenario, where the collar beam takes the total maximum shear force of 48.469 kN, with a free length of 252 cm, it would need a moment of inertia of 3,044 cm4. It can be noted at this point that the collar beam used in the model was insufficient in terms of both its dimensions and its location in relation to the shear force’s line of action.

Finally, despite the improvement of the general anchorage of the wall to the base, the vertical displacement of the edges was more than is acceptable, which on the autopsy of the wall proved the stress of the connections. The vertical displacements can still be improved by incorporating edge anchorage that controls the vertical displacement of the module’s edge columns, which will reduce the general lateral drift.

The shaking table test showcased the proposed TFS’s satisfactory seismic performance, validating its suitability for regions prone to earthquakes. The structure exhibited remarkable resilience during three phases of frequent, rare, and severe earthquakes, sustaining minimal damage and nearing its maximum resistance capacity, primarily attributed to its flexible timber framework. The test provided an opportunity to compare the mechanical properties with those observed in the previous static test, proving that the modifications to the original wall design improved the system’s structural characteristics.

The system’s seismic performance showed two stages of damage during the three tested seismic phases: (i) an elastic stage, during Phases 1 and 2, where no significant damage was evidenced, securing the immediate occupancy (IO) or operational state (O) of the structure; (ii) a second stage of over-resistance in Phase 3, where the system entered its inelastic stage, experiencing reparable damage while still maintaining life safety performance (LS). These results suggest that the designed TFS provides a level of resilience and structural integrity that can withstand severe seismic events. The TFS showed an ability to undergo inelastic deformation while maintaining its overall integrity, withstanding large displacements without failing, demonstrating its capacity to absorb and dissipate seismic energy. In the inelastic, over-resistance stage, the light earth panels didn’t make a significant contribution to the system’s overall resistance. The space between every block due to the accumulative damage of the previous phases vibrated independently, reducing the model’s stiffness, which reflects the system’s ability to deform and absorb energy, which is important for mitigating the impact of seismic forces.

In addition to the model’s favorable seismic performance, certain recommendations were considered to address the limitations observed. These recommendations primarily aim to reduce the excessive displacement of the walls and include:

Increasing the dimensions of the collar beam; this step is crucial in minimizing deformations caused by earthquakes and promoting the structural integrity of the entire building.
Incorporating additional columns at the edges of the openings: By doing so, the aim is to mitigate the significant displacement experienced by the shear walls with openings, improving their overall performance.
Designing the structure under the assumption that the TFS is the sole load-bearing structure for the overall load.

It has been demonstrated that the life safety of the TFS remains intact even after experiencing an exceptionally rare earthquake. This positive outcome can be attributed to the adoption of a system that prioritizes high-quality mass reduction, effectively reducing the seismic demand without the need for excessive sheathing reinforcement. These findings underline the suitability of the proposed TFS for regions prone to seismic activity, as it combines elastic performance and resilience, ultimately ensuring the safety and survival of its occupants.

This work was supported by the National Council for Science, Technology and Technological Innovation (CONCYTEC), by the contract number Nº. 110-2017-FONDECYT.

The authors have no relevant financial or non-financial interests to disclose.

All authors contributed to the study conception and design. The construction of the specimen and the execution of the test was performed by Urbano Tejada, Silvia Onnis and Giuseppina Meli. Material preparation, data collection and analysis were performed by German Becerra and Urbano Tejada. The first draft of the manuscript was written by Martin Wieser and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Acknowledgments

The authors would like to thank the National Training Service for the Construction Industry (SENCICO), the National Council for Science, Technology and Technological Innovation (CONCYTEC), and the Pontifical Catholic University of Peru (PUCP), for the funding that made possible the development of this research.

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Dynamic Shaking Table Test of a Constructive Sytem With Timber Frame Structure and Light Earth Enclosure

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Version 1

Abstract

Figures

1. Introduction

2. Background

3. Methodology

3.1 Design and fabrication of the test specimen

3.2. Definition of the seismic signal

3.3. Performance limit states and phases

3.4. Instrumentation of the model

3.5. System identification test

3.6. Test execution and data analysis

4. Results and discussion

4.1. Measured data and seismic-resistant performance

4.2. Model dynamic properties

4.3. Model allowable capacities

4.4. Discussion

4.5. Recommendations

5. Conclusions

Declarations

Acknowledgments

References

Status:

Version 1