Seismic performance of the existing piloti-type masonry structure

Abstract

The piloti-type masonry structure (PTMS) consists of a concrete frame-shear wall structure in the bottom storey and a masonry structure in the upper storey, which has problems such as large differences in material properties and non-uniform distribution of lateral stiffness. In this paper, two model specimens of the PTMS were designed and fabricated. The effect of the opening on the seismic performance of the PTMS was investigated by the proposed static test and the numerical analysis based on OpenSees. The results revealed that regardless of the presence of openings, the PTMS with specification design requirements has excellent seismic performance. Both the brick masonry structure and the frame-shear wall structure showed satisfactory deformation performance and stable load-carrying capacity. The failure mode of PTMS was related to the storey stiffness ratios (SSRs), and as the SSRs increased the failure gradually shifted to the bottom frame-shear storey, and the openings weakened the overall energy dissipation capacity of the structure and exacerbated the damage of the masonry storey. Numerical analysis revealed that when the opening ratio was less than 30%, the impact on the structural load-carrying capacity was minimal, while when the opening ratio was greater than 50% and the opening aspect ratio was greater than 1, the load-carrying capacity decreased significantly. The irregular arrangement of openings reduced the load-carrying capacity on one side of the structure and led to inefficient material usage or overdesign on the opposite side.

Keywords

piloti-type masonry structure seismic performance quasi-static test numerical analysis storey stiffness ratio opening

Introduction

The PTMS consists of a frame-shear wall structure and a masonry structure. The bottom storey is frame-shear wall structure and the upper storeys are masonry structure. The larger space on the bottom storey of a house can be used for commercial activities and the upper storey is used for human habitation. These buildings have been widely used in street-front buildings in towns and cities in China, South Korea (Lee and Ko, 2002), Mexico (Grossi et al., 2020) and other countries because of its excellent economy and applicability. There is a significant difference in seismic performance between the bottom storey and the upper storey, due to the differing material properties of reinforced concrete and brick masonry, as well as the non-uniform distribution of lateral storey stiffness (Lee and Ko, 2007; Sohn et al., 2020). In the 2017 Pohang earthquake (Kim et al., 2023) in South Korea and the 2022 Luding earthquake in China (Pan et al., 2023), some of the PTMS buildings were severely damaged causing large casualties and economic losses. Most of the existing buildings in the form of PTMS are located in earthquake-prone areas with high risk of failure, so there is an urgent need to enhance the research on the seismic performance of existing PTMS.

A wealth of experimental studies and theoretical analyses have been carried out by scholars on the seismic performance of existing PTMS buildings. Zheng (Zheng et al., 2004) et al. investigated the seismic performance of PTMS by shaking table tests. The results show that the weak floors of the structure are the masonry transition storeys. The flexible bottom storey can mitigate the seismic response of the upper structure. Liang (Liang et al., 1999) analyzed the mechanical and deformation characteristics of the PTMS and the transition storey by the quasi-dynamic test. The results show that the PTMS with reasonable design can be controlled within the severe damage state under the action of rare earthquake. It is recommended to mitigate the seismic response of masonry walls by adding structural columns in the middle of the wall at the transition storey to improve its seismic capacity. Lee (Kim et al., 2023) conducted shaking table tests on the Piloti structure and the results showed that the piloti stories was dominated by shear and overturning deformations. In recent years, many scholars had applied high-performance materials and new structural configurations to PTMS, Zhang et al. (2023) applied weakly bonded ultra-high-strength reinforcing bars to PTMS, and the structure obtained good seismic performance and repairable performance. Zhang (Wang et al., 2024), Kim (ACI Structural Journal, 2021) Shin (Shin et al., 2014) used CFRP and buckling-restrained braces to strengthen PTMS, and the results showed that the strengthened structure exhibited good seismic resistivity.

Most existing research focus on PTMS without openings in the upper masonry. However, in practice, door and window openings are often required to meet functional needs such as ventilation and lighting (Kayırga and Altun, 2021; Singhal and Rai, 2018; SP-211: Large-Scale Structural Testing, 2003; Vargas et al., 2023). Relevant studies have shown (Shariq et al., 2008; Tripathy and Singhal, 2024; Hwang et al., 2022), masonry wall with openings reduce overall stiffness and effective load-bearing area, leading to stress concentrations near openings. Damage typically propagates diagonally from opening edges to corners, weakening the wall’s load-bearing and deformation capacity and reducing the structure’s energy dissipation ability. The study by Parisi (Parisi and Augenti, 2012) found that irregular opening locations of the wall can cause localized damage and brittle failure of the structure, which can lead to premature collapse of the wall. Liu (Liu and Crewe, 2020) showed that as the size of the openings increases the in-plane load-carrying capacity of masonry walls decreases, and that variations in the number and shape of the openings usually alter the failure mechanisms in masonry walls and may lead to the soft-storey type failure, which can significantly reduce the load-carrying capacity of the wall.

Current researches on PTMS are focused on the evaluation of its seismic performance under dynamic loading, the reasonable value of SSRs, and the seismic performance after structural reinforcement, etc. However, there is a lack of theoretical analysis and quasi-static experimental studies on PTMS with openings at the masonry storey. Therefore, it is of great practical significance to carry out research on the seismic performance of PTMS with openings in the masonry story. In this paper, based on the existing code (JGJ 248-2012, 2012), a two-bay 1/3 scaled down model structure was designed, one without opening and one with double openings (500 mm × 500 mm). A combination of experimental and numerical simulation studies were adopted to investigate the effects of opening in the masonry storey on seismic performance, which provide a reference for the design and seismic evaluation of the existing PTMS buildings.

Experimental program

Specimens design

Two PTMS specimens were designed and fabricated in this test, named FS-1 and FS-2. Each specimen has two storeys, the first storey is a frame-shear wall structure, and the second storey is a masonry structure. The scaling of the specimens is 1/3. The study variable for the experiment is the presence of openings in the masonry walls of the second story. The specimens are designed with reference to the codes GB/T50011-2010 (GB/T 50011-2010, 2024), GB50010-2010 (GB/T 50010-2010, 2024) and GB50003-2011 (GB 50003-2011, 2011) and other specifications. With reference to the existing building design, the openings were opened in the second floor of FS-2 and used to change the SSR of the two specimens. The design values of the lateral SSRs are 1.95 and 1.09 for FS-1 and FS-2, respectively. To simulate the reinforcing effect of the slab on the stiffness of the first floor frame beams, the frame beams were designed as T-section. The design thickness of the masonry walls on the second floor is 120 mm, the wall is constructed of ordinary sintered clay bricks. Horizontal reinforcement mesh is set along the height direction of the wall, with both ends extending into the structural columns to enhance the integrity of the masonry wall. Table 1 shows the reinforcement design parameters of the specimens. Figure 1 shows the reinforcement and geometry dimensions details of the specimens.

Table 1.

Detailed reinforcement design parameters of specimens.

Type	Frame beam	Frame column	Shear wall	Structural column	Floor slabs
Sectional size	130 mm × 200 mm	150 mm × 150 mm	600 mm × 80 mm	80 mm × 120 mm	630 mm × 50 mm
Longitudinal bars	4Φ14	4Φ12	Φ6@85	4Φ8	Φ4@100
Hoop and tie bars	Φ6@100/50	Φ6@50	Φ6@85	Φ4@100/50	Φ4@100

Figure 1.

Reinforcement and dimensions details. (a) Elevation of FS-1 (b) Elevation of FS-2 (c) Section of specimens.

Material properties

Concrete

The bottom frame-shear wall structure and the structural columns of the specimen were made of ordinary concrete. The cement used is ordinary silicate cement with a P.O.42.5 R. The coarse aggregate consists of crushed stone with a particle size ranging from 5 to 20 mm, while the fine aggregate is river sand with a moisture content of 6.5%. Table 1 shows the concrete mix proportion. According to relevant code (GB/T 50081-2019, 2019), three standard concrete cubes and three concrete prisms were reserved during the casting process of specimens to get the mechanical properties of concrete. The measured mechanical properties of the concrete are shown in Table 2.

Table 2.

Mixture ratio of concrete.

Type	Mix proportion (kg/m³)							f_cu (MPa)	E_c (GPa)
Type	Water	Cement	Mineral powder	Fly ash	River sand	Coarse aggregate	Plasticizer	f_cu (MPa)	E_c (GPa)
C30	220	360	45	45	639	1187	3.75	38.6	30.5

Masonry bricks and mortar

The masonry wall on the second floor was built with sintered clay bricks. The compressive strength of a single brick was measured at 18.6 MPa. According to GB/T2542-2012 (GB/T 2542-2012, 2013), The dimension of the standard brick masonry column is 240 mm × 370 mm×720 mm, the compressive strength of the brick masonry column was measured to be 6.0 MPa. Figure 2 shows the process of testing the mechanical properties of concrete and brick columns.

Figure 2.

Mechanical property test of concrete and brick masonry columns. (a) Concrete prisms (b) Standard brick masonry columns.

Steel bar

The specimens’ rebars were Hot-rolled ribbed bar (HRB) and cold-rolled bar (CRB). The rebar mesh was made of galvanized iron wire. Table 3 shows the measured mechanical properties of the steel bars.

Table 3.

Mechanical properties of steel bars.

Category	Diameter (mm)	Yield strength (MPa)	Ultimate strength (MPa)	Elongation (%)	Elastic modulus (GPa)
HRB	14	430	602	26.1	195
HRB	12	445	595	23.9	200
HRB	8	495	699	19.8	203
CRB	6	563	616	5.3	198
Galvanized wire	4	296	379	23.5	196

Test setup and measurements

The test utilized the low cycle loading method. Figure 3 shows the loading device employed during the test. The vertical load of the specimen was applied through two jacks on the steel beam, each with an application load of 185 kN. The axial compression ratios for frame columns and shear walls are 0.12 and 0.09, respectively. The horizontal load was applied through a horizontal actuator fixed to the reaction wall.

Figure 3.

Test setup. (a) Photography of test setup (b) Schematic of the loading device.

The specimen loading process was controlled by displacement, with increments of 0.125% per stage up to 0.5% drift angle. After reaching 0.5% drift angle, the increments were reduced to 0.25% per stage. Each stage was repeated twice until reaching 1% drift angle, after which it was repeated once per stage. The loading program of the specimen is illustrated in Figure 4. In each loading cycle, a thrust force was applied to the structure followed by a tension force. The thrust was specified as positive loading and the tension as negative loading. The test was ended when the horizontal load on the specimen decreased to 85% of the peak load.

Figure 4.

Loading program.

To measure the deformation of the specimens, a total of 18 linear variable differential transducers (LVDTs) were arranged on the specimen as shown in Figure 5. To monitor the development of reinforcement strain in key positions, reinforcement strain gauges were placed at the locations of the reinforcements of the frame beams, frame columns, frame-shear walls, and the structural columns. Figure 6 shows the arrangement of the reinforcement strain gauges.

Figure 5.

The arrangement of LVDTs.

Figure 6.

The arrangement of strain gauges.

Test results and analysis

Test phenomenon

In order to facilitate the description of the damage phenomenon in each part of the specimen, the parts have been labelled as in Figure 7.

Figure 7.

Schematic diagram of component number.

Figures 8 and 9 show the overall failure pattern and the damage development of two specimens, respectively. The crack development process in both specimens, FS-1 and FS-2, was similar during the initial phase of loading. However, in the later phase of loading, the damage to the masonry storey in FS-2 was more severe due to the presence of the openings. Both two specimens were in an elastic state before cracking, without obvious damage. When the cracking load was reached, diagonal and horizontal cracks appeared in the middle of the shear wall and at the end columns of the shear wall, respectively. When the horizontal drift angle at the top of the structure was less than 0.75%, crack generation and development concentrate in the bottom storey. At the time, the diagonal cracks of the shear wall were fully developed, several long stepped cracks appeared in the masonry wall for two specimens. However, due to the stress concentration at the corners of the opening, the cracks in the masonry wall extended diagonally from the four corners of the opening in FS-2. When the horizontal drift angle exceeded 0.75%, the rate of crack development in the upper masonry storey accelerated and several uniformly spaced horizontal cracks appeared in the structural columns. In FS-1, the existing cracks continued to extend and widen. In FS-2, a diagonal crack extended from the lower-left beam-column joint in region W1 to the upper-left corner of the opening, and the integrity of the window wall segment was further weakened. When the horizontal drift angle reached 1.25%, diagonal cracks were clearly visible on the surface of the bricks of the upper masonry wall, and the brick crushing phenomenon was obvious at this time. When the top horizontal drift angle reached 1.75%, under the influence of large overturning moment of the masonry wall in the second storey, the structural columns of FS-1 and the lower node area were seriously damaged, with spalling concrete and exposed reinforcement. For FS-2, the presence of openings reduced the overall stiffness of the masonry wall, weakening its ability to resist lateral forces, leading to more severe damage compared to FS-1. FS-2 structural column (GZ1) showed obvious shear damage, the vertical crack on the left side of wall section (W1) extended to the openings wall, and there was also a large area of crushed bricks falling off at the upper right of the wall section (W1). For the PTMSs with SSRs of 1 to 2 designed for this test, the damage accumulation of the masonry structure was faster than that of the frame-shear wall structure, resulting in severe damage to the masonry structure and causing the final failure of the structure.

Figure 8.

Failure mode of specimens. (a) FS-1 (b) FS-2 (c) FS-1 (d) FS-2 (e) FS-1 (f) FS-2.

Figure 9.

Damage development process of shear wall. (a) FS-1 (b) FS-2.

There was a difference in damage development in the shear walls of the two specimens, as shown in Figure 9. When the horizontal drift angle was less than 0.75%, there were significantly more cracks in the FS-1 shear wall than in FS-2, and spread over almost the entire shear wall. In contrast, the cracks in the upper masonry wall of FS-2 appeared earlier than those of FS-1, and were more numerous, wider, and developed more drastically. When the horizontal drift angle exceeded 0.75%, the FS-2 shear wall exhibited more new cracks than the FS-1. Once the horizontal drift angle reached 1%, the number of cracks on the shear wall and the end columns on both sides tended to be constant, but the width of the cracks increased significantly. Currently, the width of the horizontal cracks at the end column (Z2) of the FS-1 and FS-2 had reached 1.3 mm and 1.0 mm, respectively. The maximum crack width was the horizontal crack at the bottom of the end column, indicating that the bottom shear wall has flexural-shear failure characteristics. Compared to the shear wall, the frame columns on both sides sustained less damage and exhibited smaller maximum crack widths. This reflects that, regardless of masonry storey openings, the shear walls will carry greater horizontal shear effects of earthquakes as the first line of defense against earthquakes, which helps to concentrate the damage in the more ductile bottom storey.

Hysteresis curves

The hysteresis curves of the specimens at the loading point is shown in Figure 10. In this paper Δ denotes the horizontal displacement and θ denotes the inter-story drift angle. It can be seen that the shape of the hysteresis curves of the two specimens is similar. The specimens was in the elastic state when the loading drift angle was less than 0.375%, the shape of the hysteresis loop at all levels was narrow and slender. Before the loading drift angle reached 0.75%, the structural damage and residual deformation gradually increased due to the full development of diagonal cracks in the first shear wall. At this time, the energy dissipation of the specimen increases and some slippage occurred in the masonry wall. After the drift angle exceeded 0.75%, the hysteresis loop exhibited the “Shuttle” shape with obvious pinching effect and the loading stiffness was obviously reduced. Due to the presence of the openings in FS-2, the effective bearing area and integrity of the masonry storey was reduced, resulting in less energy dissipation in the overall structure, and therefore the shape of hysteresis curve of FS-1 was fuller compared to that of FS-2.

Figure 10.

Hysteretic curves of the loading point.

The first storey hysteresis curves of the specimens are shown in Figure 11. The first storey hysteresis curves of the two specimens are similar in shape. During the initial loading stage, the specimen was in the elastic stage. With the increase of horizontal drift, more diagonal cracks were formed on the shear wall, and the plastic damage on the bottom storey of the specimen increased. At this time, the hysteresis loop area gradually increased, the energy dissipation capacity of the specimen increased, the loading stiffness decreased. The pinch characteristics of the hysteresis curve became more obvious. During the late loading stage, the hysteresis loop shape exhibited a more visible pinching phenomenon due to the accumulation of damage and slippage of the masonry wall. However, due to the larger SSRs of FS-1, its damage is mainly concentrated in the lower node area of the structural column, resulting in the horizontal shear force not being effectively transferred to the bottom storey during loading, and the bottom storey deformation of FS-1 is relatively smaller.

Figure 11.

Hysteretic curves of the first floor.

Skeleton curves and characteristic points

The Figure 12 gives the skeleton curves of two specimens. Table 4 shows the measured average load capacity and displacement of each characteristic point of the specimen. The yield point is obtained by the energy equivalence method (Park, 1989), and the ultimate point is taken as the load and displacement corresponding to the time when the load is reduced to 85% of the peak load.

Figure 12.

Skeleton curves of specimens.

Table 4.

Experimental results of characteristic points for specimens.

Specimens number	Floor	Yield point			Peak point			Ultimate point
Specimens number	Floor	Δy	θ %	F _y	Δ _m	θ %	F _m	Δ _u	θ %	F _u
FS-1	1	6.67	0.51	352.91	14.64	1.13	424.37	-	-	377.30
	2	3.38	0.27		10.81	0.86		-	-
	Whole	10.05	0.39		25.45	1.00		42.59	1.67
FS-2	1	7.65	0.59	354.29	16.81	1.29	430.94	19.00	1.46	380.21
	2	4.83	0.39		12.12	0.97		25.20	2.02
	Whole	12.48	0.49		28.93	1.13		44.20	1.73

Note: The load unit in the table is (kN), and the displacement unit is (mm).

The skeleton curves of FS-1 and FS-2 show similar progressions, passing through the elastic stage, the elastic-plastic stage and the failure stage, with the load value of per stage is relatively close. Due to larger SSR and faster development damage of FS-1, the yield point of the shear wall was lower than that of FS-2, the elastic-plastic stage occurred earlier than that of FS-2. At the peak point, the horizontal drift angle of FS-1 and FS-2 reached 1.13% and 1.29%, respectively, which was within the 1% limit specified (GB/T 50011-2010, 2024). This indicated that the bottom storey had excellent lateral deformation capacity, and there was no obvious damage in the frame-shear wall structure at this time. Meanwhile, for the masonry storey, the inter-storey displacement angles of the masonry storey for the two specimens reached 1.13% and 1.29% at the peak point, which satisfy the limit value of inter-storey displacement angle of 1/150 for the collapse damage criteria of masonry structure suggested by Su Qi-wang et al. (Su et al., 2013). It can be seen that regardless of openings or not, the PTMS designed according to the code (JGJ 248-2012, 2012)showed good deformation performance.

Strength and stiffness degradation

The rate of strength degradation λ can indicate the pattern of carrying capacity degradation of the specimen and reflect the degree of damage accumulation in the structure. Figure 13 shows the relationship between the rate of strength degradation and the loading drift angle. Prior to the specimen reaching its peak load-carrying capacity, the rate of strength degradation remains above 0.9, indicating less damage accumulation and better load-carrying capacity. As the main lateral force-resisting element, the accumulation and development of damage to the shear wall directly affected the structural load-carrying capacity of the structure. Compared to FS-2 with openings, the accumulation and development of damage to the bottom shear wall of FS-1 was more rapid due to more seismic shear force distributed to the bottom frame-shear storey, which resulted in a smaller strength degradation rate of FS-1 than that of FS-2. This indicates that the greater the SSR of the structure, the faster its load capacity decreases.

Figure 13.

Strength degradation curves.

K₀ is defined as the positive and negative mean secant stiffness of the first cycle at the first stage of cyclic loading. The stiffness degradation rate is defined as the ratio of the positive and negative average secant stiffness K to K₀ for the first cycle at each stage of cyclic loading. Figure 14 shows the stiffness degradation rate of the specimen versus the loaded drift angle. The stiffness degradation curves of the two specimens are very similar. Prior to loading the drift angle to 0.75%, the specimens exhibit a faster rate of stiffness degradation due to the gradual development of specimen damage. After loading the drift angle to 0.75%, the rate of stiffness degradation gradually stabilizes with the full development of cracks in the shear wall. In addition, the rate of stiffness degradation of the specimens is affected by the SSR. When loading is initiated until the drift angle reaches 0.25%, the degree of stiffness degradation of the two specimens is roughly comparable. After the loading drift angle exceeded 0.25%, the rate of stiffness degradation in FS-1 was faster than that in FS-2. This was due to faster crack development and more concrete cracking in the bottom shear wall of FS-1.

Figure 14.

Stiffness degradation curves.

Equivalent viscous damping coefficient

The coefficient of equivalent viscous damping he reflects the fullness of the hysteresis curve, which is an important index for evaluating the energy dissipation capacity of the specimen. The calculation method of he can refer to the specification JGJ/T 101–2015 (JGJ/T 101-2015, 2015). Figure 15 shows the equivalent viscous damping curves of two specimens. Before the drift angle was increased to 0.5%, with the gradual cracking of the specimen, the equivalent viscous damping coefficient value of the specimen gradually decreased, and at this time, the seismic input energy is mainly dissipated through the cracking of the structure. As the loading drift angle increased, the reinforcement gradually yielded and the damage to the masonry wall gradually developed and accumulated, the equivalent viscous damping coefficient value of the specimen gradually increased, and the energy dissipation capacity gradually increased. Due to the opening weakening the integrity and effective bearing area of the masonry storey of FS-2, resulting in a decrease in the SSRs of the structure, a decrease in the seismic shear force allocated to the bottom frame shear storey, and a lower degree of damage to the shear wall as the main energy-consuming element than that of FS-1, the equivalent viscous damping coefficient value of FS-2 is smaller than that of FS-1, indicating a weaker overall energy dissipation capacity.

Figure 15.

Equivalent viscous damping coefficient curves.

Structural inter-storey displacement

The ratio of the displacement between the first and second floors of the specimen is denoted by R to indicate the variation of the structural stiffness ratio. The relationship between the value of R and the loading drift angle is shown in Figure 16. The drift angle of the opening specimen and the first storey are shown in Figure 17(a) and Figure 17(b), respectively. At the beginning of loading, the structure’s displacement is mainly concentrated in the frame-shear wall structure at the bottom storey under the designed SSR. The lateral stiffness of FS-1 between floors is greater than that of FS-2, resulting in a more obvious deformation concentration phenomenon in the first floor; With an increase in horizontal displacement, the R-value decreases. This is due to faster damage accumulation and stiffness degradation of the masonry wall and with decreasing of SSRs, the structural damage transfer to the upper masonry storey. As a result, the percentage of inter-storey displacements in the upper masonry storey increases. When the horizontal drift angle was loaded to 1.5%, the bottom frame-shear wall inter-story displacement of FS-1 was smaller than that of upper masonry story, which is due to the main damage of FS-1 is concentrated in the joint area of the bottom part of the structural columns, the horizontal shear force being unable to transfer efficiently to the bottom storey.

Figure 16.

Ratio of the first inter-storey drift angle to the second inter-storey drift angle.

Figure 17.

Proportion of inter-storey displacement. (a) The drift of the w opening specimen (b) The drift of the first storey.

For PTMS, as the stiffness deterioration rate of masonry is faster than that of framed shear wall structures, the SSR will gradually decrease, leading to a gradual transfer of the main structural damage to the masonry structure under sustained seismic action, which is detrimental to the seismic performance of the overall structure. Therefore, it is necessary to install additional structural measures and restrict the size of openings in the upper masonry storey to reduce the deterioration rate of the masonry storey stiffness, and at the same time, appropriately increase the design SSR of the structure to ensure that the frame-shear wall structure bears the main structural damage.

Deformation analysis

Based on the measurement of the displacement gauges arranged on the structure, the deformation composition of the specimen can be calculated using the geometrical relationship of deformation (Ali Blash et al., 2024). During the test, it was observed that the specimen did not exhibit any significant foundation rotation or steel slip phenomenon. The deformation of the specimen is mainly composed of shear deformation and bending deformation. The overall deformation composition of the first storey in Figure 18. The deformation composition of the shear wall is shown in Figure 19. The study observed the overall shear-type deformation pattern of the opening specimen. The ratio of shear deformation to bending deformation is 9 and this ratio becomes more stable with increasing horizontal displacement. The analysis of shear wall deformation reveals that the proportion of bending deformation is slightly greater than that of shear deformation, indicating that the shear wall exhibits significant bending-shear failure characteristics. Due to the non-opening of FS-1, its masonry wall has greater stiffness and SSR compared to FS-2, and the FS-1 shear wall carried a greater seismic shear force, the wall generated significantly more bending moments, and it had a greater proportion of bending deformation.

Figure 18.

The overall deformation composition of the first storey. (a) FS-1 (b) FS-2.

Figure 19.

Ratios of different displacement components in the shear wall. (a) FS-1 (b) FS-2.

Rebar strain

Figure 20 shows the strain evolution of the reinforcement at key parts of the specimen. The strain development patterns of the vertically distributed bars in the shear wall of both specimens are similar. As the loading displacement increased, the strain value of the vertical distributed reinforcement in the shear wall also increased. For horizontal loading drift angle less than 1% the strain values in the vertically distributed reinforcement of the shear wall in FS-1 were relatively larger than those in FS-2, and entered the yielding state earlier. This confirmed the faster development of damage in the shear wall of FS-1. Due to the opening in FS-2 weakened the integrity and stiffness of the masonry storey, the accumulated damage to the structural second floor masonry wall was more serious, the longitudinal reinforcement strain of the structural columns gradually increased and reached an earlier yield state than FS-1. This indicated that the presence of openings reduced the SSRs of the PTMS while weakening the energy dissipation performance of the structure.

Figure 20.

Steel strain of specimens. (a) Strain of vertical distributed reinforcement of shear wall (b) Strain of longitudinal reinforcement of structural column.

Finite element analysis

In practical engineering, the size, location and shape of openings in masonry structures affect the seismic performance of the structure, therefore, 21 finite element models were established in this paper to investigate the effects of parameters such as opening ratios, locations of horizontal arrangement of openings, aspect ratios and structural columns on the seismic performance of the PTMS. Table 5 shows the specific study parameters.

Table 5.

Basic parameters of numerically analyzed specimens.

Specimens	Opening width (mm)	Opening height (mm)	Opening horizontal position	Aspect ratio	Opening ratio	Opening structural columns
FS-2-CC-1-0	0	0	CC	1.00	0.00	-
FS-2-CC-1-6.25	100	100	CC	1.00	6.25	-
FS-2-CC-1-12.5	200	200	CC	1.00	12.50	-
FS-2-CC-1-18.75	300	300	CC	1.00	18.75	-
FS-2-CC-1-25	400	400	CC	1.00	25.00	-
FS-2-CC-1-31.25	500	500	CC	1.00	31.25	-
FS-2-CC-1-37.5	600	600	CC	1.00	37.50	-
FS-2-CC-1-43.75	700	700	CC	1.00	43.75	-
FS-2-CC-1-50	800	800	CC	1.00	50.00	-
FS-2-CC-1-56.25	900	900	CC	1.00	56.25	-
FSC-2-CC-1-31.25	500	500	CC	1.00	31.25	Install
FSC-2-CC-1-37.5	600	600	CC	1.00	37.50	Install
FSC-2-CC-1-43.75	700	700	CC	1.00	43.75	Install
FS-2-LL-1-31.25	500	500	LL	1.00	31.25	-
FS-2-LC-1-31.25	500	500	LC	1.00	31.25	-
FS-2-RC-1-31.25	500	500	RC	1.00	31.25	-
FS-2-LR-1-31.25	500	500	LR	1.00	31.25	-
FS-2-CC-0.5-31.25	500	250	CC	0.50	31.25	-
FS-2-CC-0.75-31.25	500	375	CC	0.75	31.25	-
FS-2-CC-1.25-31.25	500	625	CC	1.25	31.25	-
FS-2-CC-1.5-31.25	500	750	CC	1.50	31.25	-

Note: “L”, “C”, and “R” indicated that the opening was located on the left side, center, and right side of the wall, respectively; the opening ratio was defined as the ratio of the horizontal cross-sectional area of the opening to the horizontal gross sectional area of the wall segment; “-” indicates that structural columns were not installed at the opening.

In this paper, based on the OpenSees (McKenna, 2011) finite element calculation platform, the finite element analysis models of the specimen were established by using the STKO (Scientific Toolkit for OpenSees) processing software. STKO is an OpenSees preprocessing software developed by the Italian software company ASDEA, which has a friendly GUI (Graphical User Interface) interaction function and can realize the masonry structure, frame structure and shear wall structures, etc. (Petracca et al., 2021; Camata et al., 2022) for the rapid establishment of models and the visualization of the analysis results.

Model establishment

Material modelling

Based on the recommendations of previous studies (Han et al., 2008; Meng et al., 2013; Xu et al., 2018), this paper used Concrete02(Yassin, 1994) to model the core concrete of frame beams, frame columns and structural columns. Concrete01, based on the uniaxial compressive stress-strain relationship of concrete proposed by Kent-Scott Park (Kent and Park, 1971), was selected for the cover concrete. For the steel reinforcement material, Steel02 (Braga et al., 2006) uniaxial material was used. The shear wall elements used the multidimensional steel material nDMaterial PlateRebar and the multidimensional concrete material nDMaterial PlateFromPlaneStress (Lu et al., 2015). The simulation of masonry walls used the material DamageTC3D (Petracca and Camata, 2019), developed by ASDEA, Italy, based on a tensile continuum media damage model. The constitutive relationship curve is shown in Figure 21. The DamageTC3D material has been used by some scholars (Giordano et al., 2021) to simulate masonry structures with satisfactory results.

Figure 21.

The constitutive relationships of the DamageTC3D.

Section selection and unit modelling

Frame columns, frame beams, and structural columns are designed with fiber sections in this model. The fiber sections of frame-shear walls and masonry walls are the Layeredshell section. The masonry wall is divided into three layers along the thickness direction, and each layer is endowed with brick masonry material properties. A non-linear beam-column element (DispBeamColumn Element) based on the displacement method is used to simulate frame columns, frame beams and structural columns. Shear walls and masonry walls are modelled using a shell element (Shell MITC4) and the mesh is divided into a planar four-node rectangular for shear walls and masonry walls.

Model validation

Figure 22 shows the simulated hysteresis curves with the test hysteresis curves. The simulated predicted peak loads and peak displacements are compared with the test results in Table 5. Figure 23 show the residual deformation cloud and damage factor cloud of the sections of FS-1 and FS-2, where the larger the damage factor is the more serious the damage is at that place on the surface, which can be used to reflect the development trend of the cracks to some extent. In the case of brittle materials such as masonry and concrete, the structural residual deformation, especially its shear residual deformation concentration area, tend to correspond to the direction of crack development, and this method of damage demonstration was also widely used in the finite element simulation of structural (Zhang et al., 2023).

Figure 22.

Hysteretic curves comparison. (a) FS-1 (b) FS-2.

Figure 23.

Specimen residual deformation and damage factor cloud diagrams. (a) FS-1 (b) FS-2.

Table 6 shows that the numerical simulation results and the test results of the overall compliance is better, the load displacement response of each stage is relatively consistent. Due to the finite element model adopted the ideal homogeneous constitutions, without considering the local weakening of the materials and the slip or rotation of the foundation during the test, the initial stiffness and the peak load of finite element model is slightly larger than that of test. However, the peak load error of the simulation and test for the two specimens does not exceed 15%, and the peak displacement error does not exceed 9%. Therefore, the numerical analysis using OpenSees can effectively simulate the experimental process and provide reliable numerical support for parameter expansion analysis.

Table 6.

Comparison between test results and predicted results.

Specimen number	Test values		Simulated values		F_p/Fm	Δp/Δm
Specimen number	Load value F_m (kN)	Displacement value Δ_m (mm)	Load value F_p(kN)	Displacement value Δp (mm)	F_p/Fm	Δp/Δm
FS-1	424.37	25.45	487.84	25.71	1.15	1.01
FS-2	430.94	28.93	441.72	25.85	1.06	0.89

Note: The load displacement is taken as the average of the positive and negative directions.

Analysis of opening ratios

Figure 24 demonstrates the residual deformation and damage factor cloud of the structure under different opening ratios, and Figure 25 demonstrates the skeleton curves of the structure under different opening ratios. It can be found that as the masonry opening ratios increased, the damage of the upper masonry structure increased due to the gradual decrease in the effective bearing area and lateral stiffness of the masonry wall, which resulted in the weakening of the diagonal compression strut mechanism’s ability to distribute and bear the loads (Moreno-Herrera et al., 2020).

Figure 24.

Residual deformation and damage factor graph with different opening ratios. (a) FS-2- CC-1-0 (b) FS-2- CC-1-6.25 (c) FS-2- CC-1-12.5 (d) FS-2-CC-1-18.75 (e) FS-2- CC-1-25 (f) FS-2- CC-1-31.25 (g) FS-2- CC-1-37.5 (h) FS-2- CC-1-43.75 (i) FS-2- CC-1-50 (j) FS-2- CC-1-56.25.

Figure 25.

Skeleton curves diagram with different opening ratios.

Figure 26 shows the peak loads, peak displacements and ultimate displacements of the structure for different opening ratios. From Figure 26, it can be seen that the peak loads and peak displacements of the structure show an overall decreasing trend with the opening ratio increasing. When the opening ratio of the structure exceeded 30%, the peak displacements of specimens FS-2-CC-1-37.5, FS-2-CC-1-43.75, FS-2-CC-1-50, and FS-2-CC-1-56.25 decreased by 36.27%, 42.35%, 35.53%, and 34.86%, which were significantly lower than the drift angle 1% in the specification GB/T 50011-2010 (GB/T 50011-2010, 2024) (25.50 mm in the test). In particular, when the structural opening ratio was greater than 50%, the peak loads of FS-2-CC-1-50 and FS-2-CC-1-56.25 were reduced by 32.43% and 40.47%, respectively, and the ultimate displacement of FS-2-CC-1-50 and FS-2-CC-1-56.25 were reduced by 23.85% and 9.70%, respectively. This indicates that the deformation performance of the structure in the elastic-plastic stage has been significantly deteriorated when the opening ratio is greater than 30%, and the load carrying and ultimate deformation capacity of the structure is significantly decreased when the opening ratio is greater than 50%. Therefore, openings with an opening ratio greater than 50% should be avoided in the masonry storey of the piloti-type masonry structure. In addition, by comparing the line charts of peak load and peak displacement for the structural columns, it can be observed that the arrangement of structural columns in the openings could effectively improve the load-carrying and deformation capacity of the structure.

Figure 26.

Peak load, peak displacement and ultimate displacement with different opening ratios.

Analysis of the opening location

Figure 27 illustrates the damage patterns, Figure 28 displays the skeleton curves, and Figure 29 compares the peak load, peak displacement, and ultimate displacement with different opening locations. It can be seen that the opening location significantly affected the peak load-carrying capacity and damage progression. When openings were concentrated on one side, as in FS-L-1-31.25, the structure exhibited uneven lateral stiffness, with a 17.06% discrepancy between the positive and negative peak loads. Figure 29 shows that as the width of the wall segments between adjacent windows increased, the integrity of masonry storey was enhanced, improving the masonry story’s ability to resist lateral loads. Therefore, designs with excessively narrow adjacent window walls and openings concentrated on one side should be avoided in practice.

Figure 27.

Residual deformation and damage factor graph with different opening locations. (a) FS-2-RC-1-31.25 (b) FS-2-LC-1-31.25 (c) FS-2-CC-1-31.25 (d) FS-2-LC-1-31.25 (e) FS-2-LR-1-31.25.

Figure 28.

Skeleton curves diagram with different opening locations.

Figure 29.

Peak load, peak displacement and ultimate displacement with different opening locations.

Analysis of the opening aspect ratios

Figures 30 and 31 show the damage and skeleton curves of different aspect ratios of the openings, respectively. And Figure 32 shows the peak loads, peak displacement and ultimate displacements of different aspect ratios of the openings. With the increase of the aspect ratio of the openings, the peak and ultimate load-carrying capacity of the structure was gradually reduced, and the damages of the first-floor beams and the walls on both sides of the openings were continuously aggravated. In the opening aspect ratio was larger than 1, and the height of the opening was greater than 50% of the storey height, the damage was mainly concentrated in the window infill wall section, which was due to the shorter internal stress transfer path of the wall section, and the damage along the path could be accumulated and developed more rapidly.

Figure 30.

Residual deformation and damage factor graph with different opening aspect ratios. (a) FS-2-CC-0.5-31.25 (b) FS-2-CC-0.75-31.25 (c) FS-2-CC-1.0-31.25 (d) FS-2-CC-1.25-31.25 (e) FS-2-CC-1.5-31.25.

Figure 31.

Skeleton curves diagram with different opening aspect ratios.

Figure 32.

Peak load, peak displacement and ultimate displacement with different opening aspect ratios.

Conclusion

In this paper, quasi-static tests were conducted on two PTMS models, one with openings in the upper masonry storey and one without. The tests aim to analyze the effect of the opening on the damage pattern, hysteresis performance, load-carrying and deformation capacity, strength and stiffness degradation pattern, energy dissipation capacity, and deformation coordination mechanism of the PTMS. The finite element models based on OpenSees were established based on the experimental results, and the effects of parameters such as opening ratios, opening locations and aspect ratios on the seismic performance of the structure were further analyzed. Based on the results of experiments and numerical simulation analyses, the main conclusions are as follows:

(1) Regardless of the presence of openings, the code-compliant design of PTMS has excellent seismic performance. When the peak load of the structure is reached, the bottom inter-storey drift angles of the specimens are 1.13% and 1.29%, respectively, and the inter-story displacement angles of the upper masonry storey are 0.86% and 0.97%, respectively. The lateral deformation capacity of the structure is satisfactory. The strength degradation rates are all above 0.9, and the structure has relatively stable load-carrying capacity.

(2) The damage modes of PTMS are related to the SSR. With the increase of the SSR, the damage of the structure gradually shifts to the bottom frame-shear wall structure. The openings weaken the overall energy dissipation capacity of the structure and aggravated the damage of the masonry storey, and with the accumulation of the damage of the upper masonry, the structure is eventually failure.

(3) The OpenSees finite element model can accurately simulate and predict the hysteretic performance of the PTMS. When the rate of open opening is less than 30%, the impact on the structural load-carrying capacity is small. When the ratio of opening is greater than 50% and the aspect ratio of the opening was greater than 1, the horizontal load-carrying capacity of the structure decreases significantly, and it is recommended that structural measures such as structural columns be set up on both sides of the opening to enhance the load-carrying capacity and ductility of the masonry storey.

(4) The irregular arrangement of openings leads to the low load-carrying capacity of one side in the structure under cyclic loading caused by earthquakes, compromises the overall stability, and wastes the design of the opposite side of the structure.

Footnotes

ORCID iDs

Jianwei Zhang

Haiyang Liang

Di Zhao

Author contributions

Jianwei Zhang: Conceptualization, Methodology, Project administration, Writing-review & editing, Funding acquisition. Haiyang Liang: Formal analysis, Writing-original draft, Writing-review & editing, Visualization. Di Zhao: Investigation, Data curation, Writing-review & editing. Haoyu Wang : Investigation, Writing-review & editing. Yuping Sun: Writing-review & editing.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research is supported by the National Key Research and Development Plan of China (Grant No.2019YFC1509302).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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