Energy dissipation of rammed earth-timber joints under cyclic loading
Introduction
Despite the lack of advanced theories, modern construction materials, and design methods, ancient buildings that have survived hundreds of years in seismic zones are significantly important resources (e.g. Ref. [1]), which can help to understand the mechanisms behind their seismic resistance and provide guidance for modern seismic design practice.
Fujian Tulou buildings are historic Hakka rural dwellings in the Fujian Province of southeastern China, and many are still in service after hundred years of frequent earthquakes, flooding, and typhoons [2,3]. A typical Tulou building has large, enclosed rammed earth walls that function as both external cladding and structural members to support several floors of timber frames (see Fig. 1). Hakka Fujian Tulou has demonstrated excellent earthquake resistance, and withstood seismic impacts from seven earthquakes exceeding M5 since the eleventh century, including one M7 earthquake in 1918 [4], without showing unrepairable structural damages. Their seismic performance can be attributed to different factors, in terms of high-quality design following the ancient Chinese standards (e.g., the “Treatise on Architectural Methods or State Building Standards” [5]) and brilliant construction techniques (e.g., timber and bamboo reinforcement, mortise and tenon joint, and rammed earth-timber joint).
The structural stability of rammed earth walls in Hakka Tulou buildings is significantly enhanced by the large and heavy-hipped timber roof, which has the form of a closed ring [6]. As shown in Fig. 1, the bottom chords of the roof truss extend from the rammed earth wall, enabling the entire roof to slip as a diaphragm ring without compromising the structural stability. Similar roof design schemes have also been applied in highly seismic regions with completely different cultural backgrounds (e.g., Turkey) [1]. Under normal service loads, the frictional and bonding forces at the joint between the roof beam and the rammed earth wall are sufficient to prevent slippage. During earthquake scenarios, the interface between the timber and the rammed earth shows the debonding phenomenon, to work as a slip-friction damper [7] that dissipates the kinetic energy in the building. The similar energy dissipation mechanism is always applied to the joints between the timber elements by mortise and tenon, and the timber frames are infilled with earth or masonry bricks [8,9], thus fully separating the infill mass from the timber frames without causing a global collapse.
In historic rammed earth buildings, the slipping joints of the timber beams penetrating the walls were generally used as temporary formwork [10]. In addition to the thrust impact from the timber beams, the rammed earth wall directly beneath the beam can also be damaged by shear. The research on modeling the rammed earth using the Mohr-Coulomb criterion indicated that the shear strength of rammed earth was significantly related to the soil cohesion, if its friction angle was not too small [11]. When the slip interfaces were subjected to seismic actions, the reactions between the two materials were complicated, because loss of adhesion at the interface was an irreversible process, even though a new adhesion surface could be formed after a sufficient duration (the vertical load could compress the two materials together) [12].
During earthquakes, the cyclic pushing-pulling motion of timber beams inside the rammed earth walls is an important structural failure mode for a typical Fujian Tulou. Timber frames collapse if the pull-out deformation of their beams exceeds the beam embedment length. When the cyclic deformation remains below a critical limit and structural instability does not occur, significant energy dissipation at the joint can be achieved through the debonding process and the frictional damper behavior. Concurrently, the timber beam transfers the cyclic shear forces to the rammed earth. The shear behavior of rammed earth has been numerically modeled based on the Mohr-Coulomb failure criterion [13].
Although many studies have focused on the response of rammed earth as a building material in rammed earth structures, the energy dissipation mechanisms of the joints between the timber frames and the rammed earth walls are not fully explained by the current theoretical models. This study was conducted to understand the energy damping mechanism of rammed earth-timber joints under cyclic loading. A linear frictional and nonlinear geotechnical hysteretic model and a multi-linear model were proposed to simulate the joint behavior, which was calibrated against the cyclic pulling-pushing experiments on rammed earth-timber joint specimens. The energy dissipation mechanisms for rammed earth-timber joints in Tulou buildings were comprehensively discussed.
In practice, a Fujian Tulou can experience cyclic lateral forces throughout its service life, because of repeated wind actions and potential earthquake excitations. The cyclic force applied to the structure can be transferred from the rammed earth wall to the timber beam through rammed earth-timber joints. At each joint, the timber beam and the surrounding rammed earth can slide against each other along the interface. Energy dissipation then occurs in the rammed earth, the timber beam, and the associated interface. The action occurring at the interface is much more complicated than that in the timber or the rammed earth as a separate structural member. This is because the rammed earth material is highly anisotropic [14]. When the stress or the strain in the rammed earth remained below a particular level, its behavior could be approximated as linear-elastic. Furthermore, the secant modulus of rammed earth was highly relevant to moisture content of the soil. However, with the increase of stress or strain, the rammed earth tended to behave as a discontinuous material that could be characterized by a friction angle [15]. This implies that the slippage response of rammed earth-timber joint shows two distinctive behaviors, depending on the interface integrity: friction between two elastic solids or friction between an elastic timber and a soil-type material.
A series of material tests was conducted on the timber beam and the rammed earth to understand the behavior of each separate material as illustrated in Fig. 2. Three cubical rammed earth specimens with dimensions of 150 mm × 150 mm × 150 mm were tested under compression. Three dog bone shaped timber beam coupons were tested under compression and tension, respectively. The measured force-displacement curves of timber and rammed earth specimens are shown in Fig. 3. The strength values for different element are summarized in Table 1, Table 2, Table 3. One can see that the compressive strength of timber beam was much higher than its tensile strength, being about 3 times. It is interesting that the tensile strength of timber beam was approximately more than 23 times the compressive strength of rammed earth. Hence, when a rammed earth-timber joint experiences pull-out forces, the timber beam can hardly be ruptured prior to the failure of the soil. Hence, the rammed earth can easily experience nonlinear responses, being equivalent to a discontinuous material rather than a solid element, featuring with a friction angle. Essentially, the rammed earth is anticipated to fail firstly in a rammed earth-timber joint. However, the response of rammed earth is not linear once the peak strength is exceeded. In addition, the timber beam also does not behave linearly under compression. All these nonlinearities in the materials add complexity in the response of rammed earth-timber joint.
When two solid elastic materials contact each other under compression, the bonding strength at the interface typically consists of two components: friction due to the surface roughness under compression and cohesion (or adhesion) resulting from the material contact.
Cohesion is related to the surface roughness, the cohesive properties of the material, and the duration of contact. Frictional energy dissipation between two elastic materials that have flat, rough surfaces has been investigated [16], and the rate of energy dissipation could impact both the surface roughness and the loading condition. The slip-friction between rammed earth and bamboo bolt was tested upon fracture, and the dissipated energy during the entire slip-friction process were estimated individually, including the elastic, softening, friction, and decoupling mechanisms [17]. It is well recognized that the relative sliding between two solids can only begin once the bonding strength is overcame, and the majority of the cohesion at the interface can be lost due to debonding under the action of initial loading. Therefore, the remaining bonding strength comprises only the friction component. Conventionally, a simple linear-elastic material model can be employed to describe the behavior of rammed earth-timber joint under cyclic loading as illustrated in Fig. 4.
In this simple model, both the timber beam and the rammed earth are assumed to behave linear-elastically, such that the joint behavior can be expressed by Eqs. (1), (2), (3), (4):where is the cyclic loading; is the relative displacement between timber beam and rammed earth; and are the stiffness of the timber beam and the rammed earth, respectively; is the maximum frictional force; is the friction coefficient; is the relevant vertical compression force, resulting from the effect of friction; is the maximum displacement, at which the reverse unloading is applied.
In this simple linear-elastic hysteretic model for rammed earth-timber joint, both the cohesion and the friction components can be considered. The stiffness at the rammed earth-timber interface that represents the maximum static frictional resistance (to overcome the contribution of cohesion), is essentially composed of two parts, namely and . The two stiffnesses of timber beam and rammed earth are in parallel. This suggests that the behavior of rammed earth-timber joint before the occurrence of sliding is distinctly different from the response of timber beam or rammed earth alone. Instead, a rammed earth-timber joint is considered as a composite element, as a function of surface roughness, cohesive properties of the material, and duration of contact. Once the value is reached, the behavior of rammed earth-timber joint is simplified as a dynamic friction problem, where the frictional resistance is purely related to the friction coefficient at the interface. When the system experiences unloading and reloading, the resistance at the joint is dependent on the stiffness of the timber beam, and the contribution from the rammed earth becomes negligible since dynamic friction is mobilized. However, this simple model has many limitations: e.g., (1) the nonlinearities of both timber and rammed earth cannot be considered (see Fig. 3); (2) the failure propagation in the rammed earth is not taken into account; (3) the contribution of damping is neglected; (4) the residual stress in the rammed soil is ignored, etc.
It should be emphasized that the plastic behavior of rammed earth can serve as another important source for energy dissipation. Even for wooden frames under cyclic loading, energy dissipates at the joints due to friction. In a Tulou structure, when the timber beams are subjected to dynamic loading, the occurrence of energy dissipation depends substantially upon the properties of the rammed earth wall [[18], [19], [20], [21]]. Compared with other rammed earth buildings [22], Chinese Hakka Fujian Tulou were constructed with fine aggregate mixed materials, where the content of fine grained materials, such as soil and silt, was generally greater than 40% [23]. An alternative is to simulate the rammed earth as a soil-type material, since the plasticity nature of soil can dissipate the energy from cyclic loading extensively. Hence, a rammed earth-timber joint behaves in the same way as a wooden pile inside clayey soils. The rammed earth can undergo nonlinear deformations independent of the interface debonding mechanism. Furthermore, the frictional energy generated during the sliding process changes the temperature of both the timber beam and the rammed earth, leading to different responses especially for soils (temperature dependent properties of soils).
A nonlinear hysteretic model for rammed earth-timber joint is illustrated in Fig. 5.
Philips and Hashash [24] proposed some practical formulas to represent the cyclic loading-unloading-reloading behavior of soil. The pull-out force and displacement for the timber beam under cyclic loading can be represented similarly in Eqs. (5), (6).where is the pull-out force, K0 is the initial stiffness during the initial pull-out process, u is the pull-out displacement, and u0 is the reference displacement determined by fitting the test data. And are the dimensionless parameters based on the excise of curve fitting against the measured data. is the maximum displacement, is the reverse displacement, is the reverse push-in force, and the hysteresis damping reduction factor can be obtained from Eq. (7).where , and are the non-dimensional parameters selected to obtain the best fit with the target curve. As seen in Fig. 5, Eqs. (5), (6) can describe the target loading-unloading-reloading curve of rammed earth-timber joint under cyclic loading conditions. The area enclosed with the loop is then defined as the hysteresis damping. One needs to assume a hysteresis damping to derive the loop for comparing against the experimentally measured one, and the trail-and-error procedure can be conducted to interpret the correct value of hysteresis damping. is the stiffness at the maximum displacement, which can be obtained using Eq. (8).
Substituting Eq. (8) into Eq. (7), it gives
One can see that this nonlinear hysteretic model neglects the contribution of cohesion (or adhesion) at the rammed earth-timber interface. The rammed earth-timber joint is characterized into a pile-soil interaction problem, where failure in the pile is never considered and the soil plasticity governs the response completely. However, the surface roughness results in different friction coefficient at the interface only. The sliding mechanism at the rammed earth-timber interface cannot be captured well. It is also hard to capture the softening behavior of rammed earth.
Section snippets
Timber beam
Timber frames in Chinese Hakka Fujian Tulou were generally made from locally grown trees, called “Chinese Fir” (Cunninghamia sp.). Therefore, all timber beams used in this experimental program were made of Chinese Fir; and their material properties were measured as summarized in Table 4.
All timber beams were manufactured to follow the prototype-scale dimensions of Hakka Tulou. Two types of timber beams were made: Φ100 mm × 1000 mm and Φ100 mm × 1150 mm. The properties of timber beams, including
Failure modes
As illustrated in Fig. 9, the surrounding rammed earth experienced substantial cracks, but there was no obvious evidence of plastic deformation. Cracking and fracturing in rammed earth indicated that the interface between the timber beam and the rammed earth can sufficiently transfer forces, until significant cracks occurred in the rammed earth. Two failure modes of rammed earth-timber joint under cyclic loading were observed, including debonding at the interface and cracking in the rammed
Conclusions
Chinese Hakka Fujian Tulou has demonstrated excellent earthquake resistance in the past, which is partially resulted from the allowable slippage at the joints between the timber frame and the rammed earth wall. The kinetic energy transferred into the joints can be dissipated through the debonding process between the two materials. Under the action of cyclic loading, the energy was dissipated by thermal emission due to friction, cohesion along the interface, and plastic deformation of rammed
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work is financially supported by the Natural Science Foundation of China (51878302 and 52078225).
References (26)
- et al.
Degradation of rammed earth under wind-driven rain: the case of Fujian Tulou, China
Construct Build Mater
(2020) - et al.
Energy dissipation of a friction damper
J Sound Vib
(2004) - et al.
In-plane behaviour of rammed earth under cyclic loading: experimental testing and finite element modeling
Eng Struct
(2016) - et al.
Assessing the anisotropy of rammed earth
Construct Build Mater
(2009) - et al.
Effect of moisture content on the mechanical characteristics of rammed earth
Construct Build Mater
(2014) - et al.
Frictional energy dissipation in contact of nominally flat rough surfaces under harmonically varying loads
J Mech Phys Solid
(2011) - et al.
A hysteresis model for timber joints with dowel-type fasteners
Eng Struct
(2018) - et al.
Damping formulation for nonlinear 1D site response analysis
Soil Dynam Earthq Eng
(2009) - et al.
Unsaturated behavior of rammed earth: experimentation towards numerical modelling
Construct Build Mater
(2019) The local seismic culture. Ancient buildings and earthquakes
Fujian Tulou
Structural responses and finite element modeling of Hakka Tulou rammed earth structures
Cited by (4)
Pull-out test and numerical simulation of beam-to-wall connection: Masonry in earthen mortar and hardwood timber
2023, Engineering StructuresCitation Excerpt :The characterisation of such beam-to-wall connections helps to understand the seismic behaviour of masonry structures [10–12]. Cyclic loading tests evaluated the coefficient of friction between timber and brick masonry [13–15] and between timber and rammed earth [16]. Out-of-plane lateral loading tests were performed on strengthened beam-to-wall connections.
Insights into natural and carbonation curing of ancient Chinese rammed earth mixed with brown sugar
2022, Construction and Building MaterialsCitation Excerpt :The beneficial effect of gaseous CO2 was also found to enable the formation of magnesium carbonate from magnesia following the similar carbonation reaction mechanism [15–17]. Earthen buildings often perform well upon complex loading, such as wind load [18] and earthquake excitation [19]. However, rammed earth materials can degrade with time, showing slaking, mellowing, cracking, spalling, and even collapsing.
Effects of curing and processing on strength of raw earth stabilized with lime and sodium silicate
2022, Materials and Structures/Materiaux et ConstructionsInvestigation on Effect of Temperature Alternation on Mechanical Properties of Embedded Reinforcements in Rammed Earth
2022, International Journal of Electrochemical Science