Study on seismic performance of base-isolated and base-fixed Ancient timber buildings in hanging-wall/footwall Earthquakes

ABSTRACT This study aims to quantify effects of hanging-wall/footwall fault parameters on dynamic responses of base-isolated and base-fixed ancient timber buildings. Finite element models of a real timber building with and without isolation technology are first built and verified by comparison with existing studies. Fitting analysis of three typical models, Abrahamson-Silva-Kamai, Campbell-Bozorgnia and Chiou-Youngs models, as well as 622 recorded ground motions, is then conducted to determine the optimal model to generate earthquake waves. Finally, effects of hanging-wall/footwall fault parameters on seismic performance of the based-isolated and base-fixed buildings are investigated. The results show that the Abrahamson-Silva-Kamai model achieves the best fitting results with the lowest computational errors. Isolation technology can improve seismic performance for ancient timber buildings with different ages. Isolation effectiveness of the base-isolated models decreases with increasing building ages in different fault parameters. The isolation effectiveness remains unchanged with different fault dip angles in footwall earthquakes, whereas it decreases with the increase of fault dip angles in hanging-wall earthquakes at the same site distance. The structural isolation effectiveness in hanging-wall earthquakes is better than that in footwall earthquakes.


Introduction
Dynamic responses of near-fault ground motions have received much attention in recent years due to the obvious impulsive effects on structures (Sun et al. 2020;Bilgin and Hysenlliu 2020;Güllü and Karabekmez 2017;Todorov and Muntasir 2021). The significant hanging-wall/footwall effect may aggravate the damage of structures (Sapkota et al. 2013). The hanging-wall ground motion has large acceleration peaks and high input energy, which amplifies the ground motion during propagation (Abrahamson 1996). Many studies can be found focusing on the effects of near-fault ground motions on civil structures, such as buildings, tunnels and bridges (Aghamolaei et al. 2021;Xie and Sun 2021;Abd-Elhamed and Mahmoud 2019;Faherty et al. 2022;Bedon, Rinaldin, and Frgiacomo 2015;Bedon et al. 2019;Shehata, Mohamed, and Tarek 2014;Hadianfard and Sedaghat 2013). In ancient China, most architectures are timber buildings of towers, temples, palaces and other forms, accounting for more than 50% of the total ancient architectures (Hu, Han, and Yu 2011a). Timber, as a construction material, is worth studying for its mechanical properties in earthquakes (Humbert et al. 2014). Timber structures present many qualities, including good earthquake resistance due to the excellent strength-to-density ratio and the ductility of joints with metal fasteners, providing limited inertia forces and good energy dissipation, respectively (Oudjene and Khelifa 2009). But, as time goes by, it is inevitable that the ancient timber structure will be damaged to a certain extent under baptism of time and various natural and man-made disasters. As a result, the material and structural properties will deteriorate and the risk of damage under the earthquake will increase. For example, the Yunyan Temple with a timber structure is damaged with roof failure and overhanging wooden beams broken in Wenchuan earthquake (Jia, Liu, and Ye 2014), and the timber Changu Temple is collapsed in Yushu earthquake (Huang 2017).
Obviously, although existing studies highlight the importance of near-fault ground motion effects on the above-mentioned structural responses, investigations of the hanging-wall/ footwall effect on ancient timber structures are very limited, especially for those baseisolated ancient timbers. Many works should be done to enrich the research results of this field so as to provide effective control strategies for the safety of ancient wooden buildings under earthquakes. Therefore, it is meaningful to explore the specific seismic responses and control effectiveness of ancient timbers with and without base-isolated technology in hanging-wall/footwall earthquakes. An optimal model of generating hanging-wall/footwall earthquake waves is provided based on fitting analysis results of 622 recorded ground motions. The main aim of this study is to explore whether base-isolated technology can improve structural seismic performance in near fault earthquakes and to clear the corresponding parameter influence laws. Based on the research results, better seismic methods and isolation measures can be suggested to protect ancient timber buildings in future unpredictable hanging-wall/footwall earthquakes.

Numerical modeling
Xi'an Bell Tower, a representative ancient timber building, is adopted as an object of investigation of this study. This two-storey tower of the Bell tower is built in 1384 and has a total height of 36 m and an area of 1377.4 m 2 , as shown in Figure 1(a). The tower has a square plane with the dimension of 35.5 m. The tower is considered as the largest and most complete ancient timber structure in China (Wang and Meng 2017). Three main components compose the Bell tower, namely, the foundation base, the tower body and the roof, in which the tower body is the wood frame structural system. Specific parameters of the cross-sections of the beams and columns are shown in Table 1. The corresponding section numbers of the beams and columns are shown in Figure 1(b). The tower body and the roof are primary concerns of this study, as the foundation base is a huge masonry structural platform with passageways through it, on which the tower body and the roof are supported. Obviously, integral stiffness and mass of the foundation base are far higher than those of the upper tower body and the roof, which therefore can be ignored in the computational model.
Commercial analysis software SAP2000 (version 16) (SAP2000 Version 16, 2013) is used to establish the finite element model of the tower body and the roof. The wooden beam and column are modeled by frame beam elements. Mortise-tenon joints are adopted to connect structural members of beams, columns and trusses, which are actually a kind of semi-rigid and semi-articulated joint. The simulation of semi-rigid node in SAP2000 can be realized by end release of line element. The end release includes 3 translational degrees of freedom (axial load, principal axis shear and sub-axis shear) and 3 rotational degrees of freedom (torque, principal axis bending moment and sub-axis bending moment). When the end part is released, the spring stiffness values of the starting point and the end point are defined to partially constrain the node, so as to achieve the effect of simulating semi-rigid node (Yokoyama et al. 2009). Material elastic modulus and the connection stiffness of mortise-tenon joints between the beam and the column can be calculated based on the literature (Wang and Meng 2017), as shown in Table 2. Therefore, the three-dimensional finite element model of the Bell tower can be established, as shown in Figure 1(c), in which the column bottom of the wooden frame is fixedly connected. Besides, it is worth mentioning that the density of wood material, 410 kg/m3, is assumed to be constant for all the investigated models since the wood density is found to be increased by only 2.05% for 600 years (Jia, Liu, and Ye 2014). The wall and roof loads are modeled as masses and uniformly loaded on the beam-column joints. The total mass of one beam-  column joint is 6850 kg, which is the same as the reference (Meng 2009). More details of introducing the establishment of the finite element model, such as element selection, constitutive model and parameter design, can be found in previous research studies of the author's team (Huang 2017). It is known that there are many ancient timber buildings in China and also around the world. A common knowledge on ancient timber buildings is that their mechanical properties are affected by time, indicating that considering the influence of aging on mechanical properties is necessary. To investigate the influence of construction time on structural responses of ancient timber buildings in near-fault ground motions, four computational models that are 100, 300, 500 and 640 years old, respectively, are considered, in which the age of 640 years represents the real building time of the Bell tower. The timber performance adjustment factor provided by Technical code for maintenance and strengthening of ancient timber buildings (GB/50165-1993) is used to consider the aging influence, namely, the adjustment factors of 95%, 85%, 75% and 68% for the corresponding ages of 100, 300, 500 and 640 years. According to the adjustment factors, material elastic modulus of the ancient timber buildings with different construction times and the connection stiffness of mortise-tenon joints between beam and column are calculated, as also shown in Table 2, in which the spring stiffness of the mortise-tenon joints can be calculated based the equations of Hu, Han, and Yu (2011b).

Model verification
The dynamic characteristics of the Bell tower are compared with the results of existing literature studies (Meng 2009;Han 2011;Wen 2015) of the Bell tower. The comparison results are shown in Table 3. Figure 2 shows the first three mode shapes. It can be seen that the first-order and second-order frequencies of the Bell tower are around 0.95 Hz, and the thirdorder frequencies are between 1.0 Hz and 1.2 Hz. The maximum error in comparison to the three literature studies is 2.16% for the first-order, 1.90% for the second-order and 15.56% for the third-order. However, the first two models are the main control models with great modal participation coefficients, namely, 86% for the first modal with X-direction transposition and 99% for the second modal with Y-direction transposition as shown in Table 3. It can Note: M640, M500, M300 and M100 represent models with ages of 640, 500, 300 and 100 years.  then be found that the finite element model of the Bell tower established in this study is reasonable and can be used for the following discussion.

Optimization of fitting models
The NGA (Next-Generation Attenuation) program, published by the Pacific Earthquake Engineering Research Center (PEER) in conjunction with the U.S. Geological Survey (USGS) and the Southern California Earthquake Center (SECE), represents the frontier research on the ground motion attenuation relationship. Based on the NGA program, three typical models of fitting hang-wall-footwall ground motions, Abrahamson-Silva-Kamai (ASK) model (Abrahamson et al., 2014), Campbell-Bozorgnia (CB) model (Campbell and Bozorgnia 2014) and Chiou-Youngs (CY) model (Chiou et al. 2010), are used to describe the ground motion attenuation relationship. Comparison among the three fitting models is conducted to determine the optimal fitting model of hanging wall/footwall ground motions. Considering the attenuation relationship between the acceleration response spectrum and the seismic magnitude and fault distance, the ASK model is proposed in the literature (Abrahamson et al., 2014) with a magnitude range of [3.0, 8.5] and a fault distance of [0 km, 300 km] and expressed as (1) where f 1 , f 4 , f 5 , f 6 , f 7 , f 8 , f 10 and f 11 are the basic form, hanging-wall/footwall model, site response model, depth-to-top of the rupture model, reverse fault model, normal fault model, soil depth model and aftershock scaling model, respectively. M is the moment magnitude, R RUP is the rupture distance and R x is the horizontal distance from the top edge of rupture. W is the downdip rupture width, and Z TOR is the depth-to-top of rupture. R JB is the Joyner-Boore distance. CR JB is the aftershocks distance. sa 1180 is the Median peak spectral acceleration for V S30 = 1180 m/s, and V S30 is the shearwave velocity over the top 30 m. F RV , F NM , F AS and F HW are reverse faulting earthquakes, normal faulting earthquakes, aftershocks and hanging wall sites, respectively.
Considering the synthesized parameter influence of site reaction and source depth models, basin effects, hanging-wall/footwall factors, fault dip models, etc., the CB model (Campbell and Bozorgnia 2014) is proposed with a magnitude range of [3.0, 8.5] and a fault distance of [0, 300 km] and expressed as ( 2) where Y is the acceleration peak or acceleration response spectrum value, f mag is the magnitude term, f dis is the distance term, f fit is the style of the faulting term, f hng is the hanging wall term, f site is the shallow site response term, f sed is the vasin response term, f hyp is the hypocentral depth term, f dip is the fault dip term and f atn is the anelastic attenuation term.
Considering the same synthesized influence with the CB model, the CY model (Chiou et al. 2010) is proposed with a magnitude range of [3.0, 8.5] and a fault distance of [0, 300 km] and expressed as where dependent variable y ij is the ground motion amplitude for earthquake i at station j, variable y refij is the population median for the reference condition V S30 = 1130 m/s, random variables η i (between-event residual or event term) and ε j (within-event residual) represent the two modeling errors that contribute to the variability of predicted motion. φ 1 , φ 2 , φ 3 , φ 4 , φ 5 and φ 6 are correction factors. Based on Equations (1) -(3), 622 natural ground motions from NGA database, including 327 hangingwall earthquakes and 295 footwall earthquakes, are fitted using the above ASK, CB and CY models, respectively. Random fitting error y i and its mean value (MV) u and standard deviation (SD) σ, defined in Equations (4) -(6), respectively, are adopted to determine the optimal model of fitting hanging-wall/footwall ground motions, σ ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi where y E and y R are the estimated value and real value. N is the earthquake number. Figure 3 shows the distribution of the random error of the 622 hanging wall/footwall ground motions calculated by ASK, CB and CY models, respectively. Table 4 shows the mean value and standard deviation of the random errors. It can be found that the random errors are all within the range of −2.5-2.5, and most of them are within the range of −1-1, indicating that the three models can fit the hanging-wall/footwall ground motions with certain accuracy. However, if further examination on the mean value and standard deviation of the random errors is performed, it can be found that the fitting result of the ASK model is superior to that of the CB and CY models because the results of the ASK model have the minimum mean and standard  deviation among the three models. For example, as shown in Table 4, the mean values of the 327 hangingwall ground motions are 0.105 for T = 0.3s and 0.047 for T = 3s, which is less than half of that of CB and CY models, indicating that the fitting error calculated by the ASK model shows the best, followed by the CB model, and the CY model is the worst. Similar results can also be found for the mean values of the 295 footwall ground motions. Therefore, the ASK model is determined to be the optimal model for generating the hanging-wall/footwall ground motions of this study.

Ground motion fitting and parameter influence
Four main fault parameters of hanging-wall/footwall ground motions, earthquake magnitude, fault dip angle, soil shear-wave velocity and site distance are focused in this study although there are many other parameters, such as site classification, rupture direction and focal mechanism. To investigate the effect of near fault parameters on structural seismic performance systematically, each of the main parameters are set to be regular and serialized values. In other words, eight site distances (−40 km, −30 km, −20 km, −10 km, 10 km, 20 km, 30 km and 40 km), three earthquake magnitudes (M6, M7 and M8), five soil shear-wave velocities (200 mm/s, 400 mm/s, 600 mm/s, 800 mm/s and 1000 mm/s) and five fault dip angles (10°, 30°, 50°, 70° and 90°) are adapted. All hanging-wall/footwall ground motions considering the above four parameters are fitted using the ASK model. Table 5 summarizes the ground motions. As shown in Table 5, a total of 104 hanging-wall /footwall ground motions are fitted. The seismic duration of all the ground motions is designed to be the same, which is 40s with an interval of 0.02s. Figure 4 shows comparison of acceleration time histories and the corresponding response spectra between fitting and real results for a typical ground motion. It can be found that the fitting results on hanging-wall/footwall ground motion with the ASK model show good agreement with corresponding real earthquake records. It is worth mentioning that a soil shear wave velocity of 200-1000 m/s corresponds to the soft soil condition. However, the influence of the SSI effect is not considered. This research focuses on the comparison of isolation effects under the influence of Table 5. Design of the analysis scheme considering the four main parameters.

Isolation realization
One of the main objectives of this study is to compare the dynamic performance of base-isolated and basefixed ancient timber buildings subjected to near-fault ground motion with different fault parameters. Seismic isolators are generally classified into three types: linear natural rubber bearing (LNRB) (Tubaldi et al. 2017), lead rubber bearing (LRB) (Calugaru and Panagiotou 2014) and sliding bearing (Wang, Chung, and Liao 2015). Considering the different characteristics of LNRB and LRB, both of them are adopted in this study according to optimization analysis. The design process of LNRB and LRB has a basically similar program, and details can be found in the literature (Providakis 2008;Ryan and Earl 2010;Tzu and Po 2011). Definite, design and calculation of LRB are described here in brief. The elastic stiffness, equivalent stiffness and post-yield stiffness of LRB can be defined with the following equations: where k e ,k equ and k P are the elastic stiffness, equivalent stiffness and post-yield stiffness of LRB, respectively, F y is the yield strength, D y is the yield displacement, G is the shear modulus of rubber, A r is the cross-sectional area of the rubber layer, t r is the total thickness of the rubber, f L is a constant factor and taken usually to be 1.5 (Providakis 2008) and F m is the force occurring at a specified isolator displacement Δ.
The area E D of the hysteretic curve of LRB and equivalent damping ratio ξ equ are defined as where Q is the characteristic strength (force intercept at zero displacement). Based on the above equations, design parameters of base isolation of the tower can be determined and are shown in Table 6. The specimen layouts of LRB and LNRB are shown in Figure 5 in detail. The LRB and LNRB are installed between the bottom of the wooden frame column and the foundation. The section steel connecting plate shall be embedded on the column bottom and foundation base. The LRB and LNRB are connected with the embedded connecting plate by bolts.

Isolation verification
Reasonability of seismic isolation of the Bell tower is evaluated by referring design code (GB/50001-2010;GB/50009-2012). Several factors, including vertical bearing capacity, wind-resistance performance and fundamental frequency, are adopted to verify the rationality of the above seismic isolation. As we know, the first two factors are very common verification ways of isolation design, which are ignored in this study for simplification purposes. The third factor, the fundamental frequency, is focused here. The dynamic characteristics of different models are summarized in Table 7. The fundamental period obtained by simulation is in the range of 2.78 s -2.84 s Hz for the base-isolated Bell tower, which is in the most common range of 1 s-4 s for isolation buildings. Ratios between base-isolated and base fixed structures are in the range of 2-4 as shown in Table 7, which is also in the common range of 2-5. Besides, if the baseisolated Bell tower is simplified as a single degree of freedom, its fundamental period can be calculated to be 1.08s based on theory formulation of T ¼ 2π ffi ffi ffi ffi ffi ffi ffi ffi ffi M=K p , where T is the period, M is the structural mass and K is the horizontal equivalent stiffness of the isolation layer. Obviously, the maximum period error between simulation and the simplified calculation is only 2.8%. It can be verified that the design parameters of the base-isolated Bell tower are rational.   Figure 6 shows the curves of base shear of the basefixed and base-isolated models with various earthquake magnitudes. The base shear increases with the increase of magnitude. As shown in Figure 6 Hanging-wall earthquakes have a significant influence on structural responses compared to footwall earthquakes at the same absolute site distance, especially for strong earthquakes. The base shears of the basefixed M100 at site distances of 10 km and 20 km in M8 are 343 kN and 300 kN, which are 1.6 and 1.9 times than that of the site distances of −10 km and −20 km, respectively. Similar tendency can also be found in Figures 6(b), 6(c) and 6(d) for the models of M300, M500 and M640. After the isolation layer is added to the four models, structural response is reduced effectively (as shown in Figures 7 and Table 8), indicating that the base isolation technology can improve seismic performance to a great extent. Relative peak displacement (RPD) between the structural top and bottom points of the superstructure is reduced for base-isolated models,  meaning that concentrated deformation appears at the isolation layer. As shown in Table 8, RPDs at the site distance of 10 km are reduced by 60% for M300 and 53% for M640 in M7. However, the isolatioin layer displacements (ILD) reach 86 mm for M300 and 77 mm for M640 in M7. The isolation effectiveness (IE) increases with the decrease of the absolute site distance. To further explore the IE, the relationship between the horizontal damping coefficient and the site distance for different models in various earthquake magnitudes is shown in Figure 8, in which the horizontal damping coefficient is defined by the base shear ratio between isolated and non-isolated structures. It can be found that the horizontal damping coefficient increases with the increase of earthquake magnitude, meaning that IE decreases with the increase of magnitude, especially in the site distance range of [−20 km, 20 km]. As shown in Figure 8(a), the horizontal damping coefficients of the base-isolated M100 are 0.45, 0.46 and 0.49, respectively, at a site distance of −20 km in M6, M7 and M8. The reason is that the larger the magnitude, the greater the energy input and thus the stronger the structural dynamic responses. In the same condition of isolation layer, the stronger the structual responses, the lower the IE. It can also be found that IE in hanging-wall earthquakes appears to be better than that in footwall earthquakes in the same earthquake magnitude. Taking Figure 8(c) as an example, the horizontal damping coefficients of the base-isolated M500 in M7 are 0.45 and 0.47 for the site distances of 10 km and 20 km, respectively, and 0.57 and 0.56 for −10 km and −20 km. The reason is  that the predominant period of hanging-wall earthquake is less than that of the footwall earthquake and is farther away from the basic period of the base-isolated models, which achieves the better IE. In additon, it can be found that IE decreases with the increase of building ages in the same magnitude. The older the building, the smaller the structural overall stiffness, and thus the greater the structural response. Consequently, IE of the base-isolated model with longer age will decrease in the condition of the same isolation parameters. For example, as shown in Table 8, IE of structural top peak acceleration (TPA) at the site distance of −10 km is 55% for M300, 43% for M640 in M7 and similarly, 50% for M300 and 36% for M640 in M8. IE of RPD at the site distance of −10 km is also the same, which are 50% for M300, 42% for M640 in M7 and similarly, 43% for M300 and 36% for M640 in M8. Figure 9 shows curves of base shear of the base-fixed and base-isolated models with the shear wave velocity. It can be seen that the bear shear decreases with the increase of shear wave velocity. The higher the absolute site distance, the lower the base shear in the same shear wave velocity. As shown in Figure 9(a), the base shears are 143.2 kN, 72.3 kN, 52.2 kN, 43.8 kN and 37.7 kN for V200, V400, V600, V800 and V1000, respectively, at the site distance of −10 km for the base-fixed M100, which is also for the base-isolated M100, namely, 65 kN, 29.5 kN, 21.7 kN, 18.8 kN and 18.6 kN for V200, V400, V600, V800 and V1000, respectively. Obviously, the base shear of the base-isolated model is reduced by comparing with that of the base-fixed model with different shear wave velocities and site distances. Further verification can be found for typical time history comparisons between the base-isolated and basefixed models, as shown in Figure 10, meaning that good IE is ensured by adding the isolation layer to the four models with different ages.

Soil shear wave velocity
To clearly show the influence of shear wave velocity on the IE, the relationships of the horizontal damping coefficient versus site distance and typical structural responses in different parameters are shown in Figure 11 and Table 9. It can be seen that the structural horizontal damping coefficient and ILD have a certain degree of decrease with the increase of shear wave velocity, and the greater the shear wave velocity, the better the IE at the same site distance, especially for the larger absolute site distances, such as −30 km, −40 km, 30 km and 40 km. For example, as shown in Figure 11(b), the horizontal damping coefficients of the base-isolated M300 are 0.64, 0.59, 0.55, 0.48 and 0.43 for V200, V400, V600, V800 and V1000 at site distance of −30 km, respectively, and 0.61, 0.54, 0.50, 0.45 and 0.42 at a site distance of 30 km, respectively. The reason is that the greater the shear wave velocity, the harder the site soil and therefore the better the IE. Besides, it can be found that, in the site distance range of [−20 km, 20 km], the IE appears to be similar for shear wave velocity from V400 to It can also be found that IE in hanging-wall earthquakes seems to be similar to that in footwall earthquakes with the same absolute site distance and the same shear wave velocity although the latter has a slight advantage. Taking Table 9 as an example, the IEs of TPA of M300 are 37% and 38% for the site distance of −40 km and 40 km in V200, respectively, and 50% and 47% in V800, respectively. In additon, it can be found that IE decreases with the increase of building ages at the same shear wave velocity, which shows similar tendency to that in the same magnitude. For example, as shown in Table 9, IEs of structural top peak acceleration (TPA) at the  site distance of −40 km are 37% for M300 and 31% for M640 in V200 and similarly, 38% for M300 and 35% for M640 in V400. The RPD with isolation technology is much lower than that of ILD. For example, the RPD and ILD of M640 at the site distance of −10 km are 33.6 mm and 108.6 mm in V200, respectively, and 16.4 mm and 51.5 mm in V400 and 9.2 mm and 36.9 mm in V800. In other words, the RPD is lower than that of 1/3 ILD. Figure 12 shows the relationships between the base shear of the base-fixed and the base-isolated models with the fault dip angle. For one thing, it can be found that the bear shear of the base-fixed models remains unchanged with the fault dip angles from A10 to A90 in footwall earthquakes, whereas decreases with the increase of fault dip angles in hanging-wall earthquakes with the same site distance, especially for smaller site distances, such as 10 km and 20 km. For another, with the decrease of the absolute site distance, the base shears of the base-fixed models increase for both the hanging-wall and footwall earthquakes with the same fault dip angle, indicating significant growth for the former and slight growth for the latter. Similarly, relationships between the base shear and the site distance of the base-isolated models at different fault dip angles are the same as that of the base-fixed models. Further investigation on the horizontal damping coefficient is shown in Figure 13. It can be found that IE of the base-isolated models also remains unchanged with the fault dip angle changing from A10 to A90 in footwall earthquakes, whereas it decreases with the increase of fault dip angles in hanging-wall earthquakes with the same site distance. For example, as shown in Figure 13(c), the horizontal damping coefficients of M500 at a site distance of 30 km are 0.42, 0.45, 0.47, 0.5 and 0.52 for A10, A30, A50, A70 and A90, respectively, and remain constant at 0.51 at the site distance of 30 km for all the five fault dip angles. Besides, it can be found that the horizontal damping coefficients decrease with the decrease of absolute site distances in both the hanging-wall and footwall earthquakes with the same fault dip angle, and the horizontal damping coefficients in hanging-wall earthquakes are smaller than those in footwall earthquakes, indicating that models with a smaller site distance achieve better IE, especially in hanging-wall earthquakes. Furthermore, it can be found that IE decreases with the increase of building ages at the same fault dip angles, which also shows similar tendency with that of parameters of the magnitude and the shear wave velocity.