The Case Study of the Characteristic Analysis and Reinforcement Measures of RC Diaojiaolou Structures Under Different Seismic Intensities

Abstract

China is strengthening the construction of the disaster resistance capacity of its mountain buildings, which increases the demand for RC Diaojiaolou reinforcement technology. In this paper, the performance of RC Diaojiaolou structures (unreinforced and carbon-fiber cloth-reinforced) in an earthquake is studied by a physical model test. The results show that carbon-fiber cloth can effectively improve the seismic capacity. The natural vibration period and acceleration- and displacement-increment coefficients of DF and CDF conformed to the exponential law. The damage process can be divided into three stages: DS, YS, and PS. After reinforcement, the development law of the average value of the acceleration-increment coefficient changed from the N type to the V type, and the development law of the average value of the displacement-increment coefficient changed from the concave type to the V type. The Diaojiaolou was the least affected by the acceleration at I. The displacement deformation of DF was the least affected by the seismic waves at DZ1. The displacement deformation of CDF was the least affected by the seismic waves at I. These findings provide a theoretical basis for the seismic design of mountain Diaojiaolous.

1. Introduction

China possesses diverse terrain, which can be categorized into five main types: plateaus, mountain ridges, plains, hills, and basins [1]. Additionally, China is highly susceptible to earthquakes. According to official data from the China Earthquake Networks Center, there were approximately 1280 earthquakes with magnitudes greater than 3 in China in 2024, including 7 earthquakes with magnitudes greater than 6 [2]. The north–south seismic belt (Sichuan–Yunnan–Gansu–Shaxi) accounts for about 48%, Xinjiang accounts for about 28%, and other regions account for about 24%. It can be seen that China’s seismic activity is mainly distributed in mountainous areas, and the number of seismic activities above magnitude 3 in recent years has shown a gradual increasing trend (see Figure 1). In earthquake-prone areas, building collapse is the most important factor causing casualties. In the 2008 Wenchuan earthquake, the number of victims reached 69,226, the number of injured reached 374,643, and the number of missing reached 17,923. Among the former, the number of deaths directly caused by the building collapse was about 53,000~55,000, accounting for more than 75% of the total number of deaths [3]. This has directly promoted the reform of the seismic design of Chinese buildings. Therefore, many scholars have carried out research on the impact of earthquakes on buildings.

When an earthquake occurs, energy is transmitted to the surface through seismic waves so that the building structure is subjected to complex dynamic loads, resulting in different degrees of damage or even the collapse of the building. Therefore, the characteristics of ground motion directly affect the structural response. For example, Heydarpour and Tehrani [4] studied the seismic responses of 21 horizontal-bending and vertical RC four-span bridges with different abutment types and found that compared with straight bridges, abutment characteristics and boundary conditions have a significant impact on the seismic response evaluation of curved bridges. Massumi and Gholami [5] estimated structural responses by using different combinations of principal component analysis and parameters. The results showed that frequency-related parameters can better predict damage criteria than time-related parameters. Pachla et al. [6] designed a five-story, irregularly shaped reinforced concrete (RC) building model to withstand earthquakes of different magnitudes. It was found that the earthquake that caused the building damage was characterized by high strength, a long duration, and high velocity. In the Lisbon earthquake in 1755, the correlation between building collapse and geological structure was first recorded [7]. Subsequently, many scholars have carried out a lot of research through the elastic rebound theory [8,9,10], the random vibration theory [11,12,13,14], and so on. The seismic response mechanisms of a wide range of building structures, such as reinforced concrete (RC) structures [15,16,17], steel structures [18,19,20], masonry structures [21,22,23], and timber structures [24,25,26], have been also studied in depth in recent years. Liu [27] carried out an experimental study on the use of steel braces on stilt buildings to reduce the irregularity of stiffness. It was found that the setting of steel braces can change the failure modes of stilt buildings and improve the ductility and deformation capacities of stilt buildings. Li [28] proposed the lateral stiffness ratio of stilt buildings as the floor stiffness ratio (SSR) and found that the SSR is an important factor affecting the seismic failure mode of stilt buildings. With the development of manufacturing technology, the introduction of the electro–hydraulic-servo shaking-table has greatly facilitated the development of physical model tests. For example, Kumar [29] studied the influence of tunnel excavation on the responses of buildings with different types of frames at the foundation through shaking-table tests. Zhou [30] studied the seismic performance of a four-tower (frame shear wall) building through shaking-table tests and numerical simulation. In recent years, with the rapid development of artificial intelligence technology, machine learning [31,32,33] and digital twin technology [34,35] have gradually begun to realize the intelligent prediction and monitoring of earthquakes. At present, many scholars are constantly optimizing artificial intelligence and machine learning algorithms [36,37,38,39], which can be applied to predict the responses of building structures and improve disaster resistance in architectural design. At the same time, data-driven insights and advanced modeling are used to improve the safety of earthquake-prone areas.

In summary, many scholars have studied the influence of ground-motion characteristics on various building structures. At the same time, the seismic response mechanisms and seismic design-method improvement of various building structures are also being studied. However, there are few studies on the influence of ground-motion characteristics on RC Diaojiaolou (traditional Chinese stilted dwellings) structures. RC Diaojiaolous are mainly distributed in ethnic-minority gathering places and tourist areas such as southeastern Guizhou, northern Guangxi, and northeastern Yunnan and are concentrated in the north–south seismic belt. Also, China’s Diaojiaolou, which has been passed down for thousands of years, is one of the oldest building types in China. The stilt design of the Diaojiaolou is not only the crystallization of the architectural wisdom of the mountain residents but also the inheritance and development of Chinese traditional culture. In the Luding earthquake, many Diaojiaolous and local residents were seriously injured. However, there are few special studies on China’s Diaojiaolous for earthquakes. Therefore, in order to continue to inherit the architectural culture of the Diaojiaolou and reduce the risk of earthquakes in the above areas, this paper explores the influence of ground-motion characteristics on RC Diaojiaolou structures (without carbon-fiber cloth reinforcement and with carbon-fiber cloth reinforcement) through physical model tests. The research results can provide some reference values for the seismic design of ethnic-minority buildings in the mountainous areas of China. This not only enhances the emergency response capacity of China’s ethnic-minority areas but also is an important manifestation of the firm implementation of the basic national policy of national unity.

2. Test Method

The physical model test research in this paper produced two RC-suspension frame models with a similarity ratio of 1:8 and the same parameters. Carbon-fiber cloth reinforcement measures were added to one of the models. The connection material between the carbon-fiber cloth and the Diaojiaolou was an epoxy resin adhesive. The basic structure of the epoxy resin was composed of an epoxy group and a resin group. During the curing process, the epoxy group reacted with the curing agent or hardener to form a three-dimensional network structure, which gave the epoxy resin excellent mechanical properties and chemical resistance. The RC Diaojiaolou model without the carbon-fiber cloth reinforcement measures was named DF. The RC Diaojiaolou model with the carbon-fiber cloth reinforcement measures was named CDF. Shaking-table tests were carried out on the two models to explore the influence of ground-motion characteristics on the two RC Diaojiaolous.

The shaking-table equipment was an electro–hydraulic-servo one-way seismic simulation shaking table produced by the ANCO Company in the United States. The size of the table was 3.0 (m) × 3.0 (m), the rated load was 10 (t), the maximum load was 20 (t), the peak acceleration was 1.5 (g), the test frequency was 0~50 (Hz) (Hertz), the maximum overturning moment was 300 (kN · m), and the maximum displacement was ±10 (cm). The material performances of C30 concrete and micro-concrete were tested by a 3000 (kN) microcomputer-controlled electro–hydraulic-servo pressure-testing machine. The performance test of a galvanized iron wire material was carried out by a 600 (kN) microcomputer-controlled electro–hydraulic-servo universal testing machine. The test equipment is shown in Figure 2.

2.1. Similarity Relation Calculation

We considered the size of the shaking table, the bearing range of the shaking table, and the similarity of the physical characteristics between the physical model and the prototype structure. According to the similarity theory [40], the geometric similarity constant of the physical model was determined to be 1/8, the stress-similarity constant of the micro-concrete material was 1/3, and the acceleration-similarity constant was 2.0. Then, the other parameters were determined by dimensional analysis. The specific similarity constants are shown in

Table 1. Structure-similarity constants of the physical model.

Physical Property	Physical Parameter	Similarity Constant	Dimension of Quantity	Relation	Value
Geometrical properties	Length	$S_l$	$[L]$	$S_l$	$1/8$
	Area	$S_A$	$[L^2]$	${(S_l)}^2$	$1/64$
	Linear displacement	$S_l$	$[L]$	$S_l$	$1/8$
	Angular displacement	$S_u$	$[1]$	$S_{\sigma }/S_E$	$1.0$
Material properties	Strain	$S_{\epsilon }$	$[1]$	$S_{\sigma }/S_E$	$1.0$
	Elastic modulus	$S_E$	$[M{L}^{-1}{T}^{-2}]$	$S_E=S_{\sigma }$	$1/3$
	Stress	$S_{\sigma }$	$[M{L}^{-1}{T}^{-2}]$	$S_{\sigma }$	$1/3$
	Mass density	$S_{\rho }$	$[M{L}^{-3}]$	$S_{\sigma }/(S_a\cdot S_l)$	$1.333$
	Mass	$S_m$	$[M]$	$S_{\sigma }\cdot {(S_l)}^2/S_a$	$2.604\times {10}^{-3}$
	Concentrated force	$S_F$	$[ML{T}^{-2}]$	$S_{\sigma }\cdot {(S_l)}^2$	$5.208\times {10}^{-3}$
Load properties	Line load	$S_q$	$[M{T}^{-2}]$	$S_{\sigma }\cdot S_l$	$4.167\times {10}^{-2}$
	Surface load	$S_p$	$[M{L}^{-1}{T}^{-2}]$	$S_{\sigma }$	$1/3$
Dynamic properties	Moment	$S_M$	$[M{L}^2{T}^{-2}]$	$S_{\sigma }\cdot {(S_l)}^3$	$6.510\times {10}^{-4}$
	Period	$S_T$	$[T]$	${(S_l)}^{0.5}\cdot {(S_a)}^{-0.5}$	$0.25$
	Frequency	$S_f$	$[T^{-1}]$	${(S_l)}^{0.5}\cdot {(S_a)}^{0.5}$	$4$
	Speed	$S_v$	$[L{T}^{-1}]$	${(S_l\cdot S_{\sigma })}^{0.5}$	$0.5$
	Acceleration	$S_a$	$[L{T}^{-2}]$	$S_a$	$2.0$
	Gravity	$S_g$	$[L{T}^{-2}]$	$S_g\cdot S_a$	$1.0$

.

2.2. Material Performance Test

2.2.1. C30 Concrete Material Performance Test

The main materials used in the physical model in this paper are as follows: steel bars, C30 concrete, micro-concrete, galvanized iron wire, etc. The main structure adopted galvanized iron wire and micro-concrete, and the base adopted HRB400 steel bars and C30 concrete.

In order to ensure the quality of the C30 concrete, a concrete cube sample with a size of 100 (mm) × 100 (mm) × 100 (mm) was made to test the cube’s compressive strength [41]. The C30 concrete specimens were numbered HL1, HL2, and HL3, respectively. The average compressive strength of the three specimens was 27.20 (MPa). The test results verify the stability and reliability of C30 self-mixing concrete, and the test results are shown in

Table 2. C30 concrete material performance test results.

Numbering	Size (mm)	Failure Load (kN)	Compressive Strength (MPa)	Average Compressive Strength (MPa)	Error (Absolute Value)
HL1	100 × 100 × 100	301.58	28.65	27.20	5.06%
HL2		264.90	25.17		8.07%
HL3		292.32	27.77		2.05%

.

2.2.2. Material Performance Test of Micro-Concrete

According to the similarity calculation above, for the physical model, a mix ratio of cement, yellow sand, and water of 1:7:2 [42] was selected to make micro-concrete. The material performance test of the micro-concrete was carried out. The performance tests of the micro-concrete materials mainly included a compressive strength test and an elastic modulus test. Two kinds of specimens were made in this experiment, which were cube specimens and cuboid specimens. The cube sample size was 100 (mm) × 100 (mm) × 100 (mm), which was used to test the compressive strength of the micro-concrete [41]. The cube samples were numbered WL1~WL9. The size of the cuboid specimen was 100 (mm) × 100 (mm) × 300 (mm), which was used for the elastic modulus test of the micro-concrete [41]. The cuboid specimens were numbered WC1~WC9. The test results are shown in

Table 3. Compressive strength test results of different micro-concretes.

Numbering	Size (mm)	Failure Load (kN)	Compressive Strength (MPa)	Average Compressive Strength (MPa)	Error (Absolute Value)
WL1	70.7 × 70.7 × 70.7	20.81	8.32	7.40	11.06%
WL2		18.23	7.29		1.51%
WL3		19.58	7.83		5.49%
WL4		18.44	7.38		0.27%
WL5		17.09	6.84		8.19%
WL6		15.98	6.39		15.81%
WL7		20.36	8.14		9.09%
WL8		17.44	6.98		6.02%
WL9		18.57	7.42		0.27%

and

Table 4. Elastic modulus test results of different micro-concretes.

Numbering	Size (mm)	Elastic Modulus (MPa)	Average Elastic Modulus (GPa)	Error (Absolute Value)
WC1	100 × 100 × 300	9475.3	8.31	12.30%
WC2		7045.9		17.94%
WC3		8535.6		2.64%
WC4		7756.7		7.13%
WC5		8232.2		0.95%
WC6		9843.1		15.58%
WC7		8417.6		1.28%
WC8		7332.7		13.33%
WC9		8174.0		1.66%

. The average compressive strength of the micro-concrete was 7.40 (MPa), and the average elastic modulus was 8.31 (GPa).

2.2.3. Performance Test of Galvanized Iron Wire Material

The constitutive relationship and elastic modulus of galvanized iron wire are similar to those of steel bars. In the physical model, the integrity of the structure was maintained, and the performance of steel bars in real buildings was simulated. Moreover, the galvanized iron wire had good toughness and plasticity, which is convenient for the production and construction of the wire cages of beam and column members. The types of galvanized iron wire used in this test were 14^#, 16^#, and 18^#, respectively. The detailed parameters are shown in

Table 5. Performance test results of galvanized iron wire materials.

Type	Section Diameter (mm)	Cross-Sectional Area (mm2)	Tensile Strength (MPa)			Elastic Modulus (MPa)
			Test Value	Average Value	Error (Absolute Value)	Test Value	Average Value	Error (Absolute Value)
14#	2.11	3.49	248	251	1.21%	331	362	9.37%
			264		4.92%	383		5.48%
			230		9.13%	364		0.55%
			266		5.64%	371		2.43%
			248		1.21%	362		0.00%
16#	1.60	2.01	246	236	4.07%	358	334	0.91%
			223		5.83%	314		12.79%
			247		4.45%	336		8.24%
			220		7.27%	324		9.97%
			242		2.48%	338		7.73%
18#	1.20	1.14	214	215	0.47%	323	316	4.53%
			231		6.93%	341		17.49%
			219		1.83%	301		13.19%
			204		5.39%	305		14.82%
			207		3.86%	310		12.71%

.

In order to test the tensile strength and elastic modulus of the galvanized iron wire, the iron wire samples were pre-stretched to ensure that they were upright. Different types of galvanized iron wire were cut into samples with lengths of 10 (cm), and 5 samples were prepared for each type: a total of 15 samples. All samples were not bent before the test and remained upright. The test results are shown in Table 5.

2.2.4. Carbon-Fiber Cloth Material Performance

In the physical model test, the unidirectional carbon-fiber cloth of the national standard of 200-gram grade I (10-cm wide) was used for the reinforcement of the Diaojiaolou. The physical parameters of the material are shown in

Table 6. Physical parameter table of unidirectional carbon-fiber cloth [43].

Unidirectional Carbon-Fiber Cloth	Physical Parameter
Tensile strength standard value (MPa)	≥3400
Tensile elastic modulus (MPa)	≥2.4 × 105
Elongation (%)	≥1.7
Bending strength (MPa)	≥700
Interlaminar shear strength (MPa)	≥45
The positive tensile bond strength between the fiber composite and concrete under the condition of upward bonding (MPa)	≥2.5
Mass per unit area (gram/m2)	200
Calculation of the thickness (mm/layer)	0.111

.

2.3. Structure Design of the Diaojiaolou

2.3.1. Prototype Structure Design of the Physical Model

According to the ‘Code for design of concrete structures’ [44], the ‘Technical specification for concrete structures of tall building’ [45], the ‘Code for seismic design of buildings’ [46], and other regulatory requirements and the actual construction of the Diaojiaolou, the prototype structure was designed. The prototype design parameters of the Diaojiaolou structure are shown in

Table 7. Prototype structure parameters.

Project	Parameter
Size	14.4 (m) × 9.6 (m)
Number of layers	Diaojiaolou layer 1 (layer), standard layer 2 (layer)
Layer height	Diaojiaolou layer: 4 (m); standard layer: 3 (m)
X-direction span number	3
Y-direction span number	2
Span length	4.8 (m)
Column section size	500 (mm) × 500 (mm)
Beam section size	300 (mm) × 500 (mm)
Thickness of floor	120 (mm)
Concrete material	C30 concrete, volumetric weight of 27 (kN/m3)
Steel bars	HRB400 longitudinal bar, HRB400 stirrup, HPB300 slab reinforcement, volumetric weight of 27 (kN/m3)

, below.

The seismic fortification intensity of the project was 7 (degrees). The design earthquake group was the second group. The design basic seismic acceleration was 0.15 (g). The site class was Class II. The seismic grade of the Diaojiaolou was Grade II. The characteristic period was 0.4 (s). The period reduction coefficient was 0.8, and the damping ratio was 0.05. The structure of the Diaojiaolou is shown in Figure 3.

2.3.2. Physical Model Design

Based on the model prototype and similarity theory, the physical model of the shaking-table test was made at a ratio of 1:8. The physical model design parameters are shown in

Table 8. Structural parameters of physical model.

Project	Parameter
Size	1.8 (m) × 1.2 (m)
Number of layers	Diaojiaolou layer 1 (layer), standard layer 2 (layer)
Layer height	Diaojiaolou layer: 0.5 (m); standard layer: 0.375 (m)
X-direction span number	3
Y-direction span number	2
Span length	0.6 (m)
Column section size	62.5 (mm) × 62.5 (mm)
Beam section size	37.5 (mm) × 62.5 (mm)
Thickness of floor	15 (mm)
Concrete material	Micro-concrete, volumetric weight of 24 (kN/m3)
Steel bar	14#, 16#, 18#

. The base of the physical model adopted C30 concrete, and the base had four steps, numbered DZ1, DZ2, DZ3, and DZ4, respectively, as shown in Figure 4. The specific size information of the physical model is shown in Figure 4. Because the base of the physical model needed to be installed on the vibration table, a water drill was used to drill the hole after the concrete of the base was finalized, and the bolt hole of the base was aligned with the screw hole of the vibration table. The size of the shaking table was 3000 (mm) × 3000 (mm), there were 225 screw holes with diameters of 20 (mm), and the spacing of the screw holes was 200 (mm). The arrangement of the shaking table and the physical model is shown in Figure 4.

2.3.3. Physical Model Counterweight Calculation

In the experiment with the physical model, in order to ensure that the dynamic characteristics of the physical model were consistent with the model prototype, the physical model needed to be counterweighted. Based on the actual mass and similarity principle of the model prototype, concrete counterweights with specific sizes and weights were added to each layer of the physical model and fixed with expanded foam glue to increase the mass rather than the stiffness. The parameters of the concrete counterweight block used are as follows: trapezoidal concrete counterweight block, mass of 10 (kg), bottom size of 200 (mm) × 200 (mm), top size of 150 (mm) × 150 (mm), and height of 150 (mm). The concrete cube counterweight block had a mass of 1 (kg) and a size of 75 (mm) × 75 (mm) × 75 (mm). The counterweight information for each layer of the physical model structure is shown in

Table 9. Physical model counterweight information.

Model	Layer	Counterweight (kg)	Number of Counterweight Blocks (1 (kg))	Number of Counterweight Blocks (10 (kg))
DF	I	326	6	32
	II	327	7	32
	III	151	1	15
CDF	I	326	6	32
	II	327	7	32
	III	151	1	15

.

2.4. Physical Model-Making Process and Monitoring Point Layout

The specific making process of the physical model is shown in Figure 5.

The number of wrapped carbon-fiber cloths was one layer, and the wrapping direction was counterclockwise. The coverage area of a single column was 25,000 (mm²), and the total coverage area of three columns was 75,000 (mm²). The reinforcement position of the carbon-fiber cloth in the physical model is shown in Figure 6.

In the vibration test, a total of 16 YX-1210 IEPE acceleration sensors, eight KS15 cable displacement sensors, and one INV3065N2 dynamic data-acquisition system were used. The INV3065N2 dynamic data-acquisition system has a strong data-acquisition capability and can better ensure the reliability of data. Since the seismic wave only considered the X-direction, the sensors were arranged along the X-direction. Additionally, INV3065N2 has only 16 data interfaces, so each group of vibration tests used four KS15 cable displacement sensors and eight YX-1210 IEPE acceleration sensors. The displacement sensor was arranged on the outermost middle column of the physical model in the X-direction, which could greatly reduce the influence of the model on the displacement data of the cable. At the same time, in order to monitor the acceleration data of the frame structure and the base more comprehensively, the acceleration sensor was arranged diagonally. The acceleration sensors of DF were numbered AT-B-1, AT-B-2, AT-1-1, AT-1-2, AT-2-1, AT-2-2, AT-3-1, and AT-3-2. The displacement sensors of DF were numbered DT-B-1, DT-1-1, D-2-1, and DT-3-1. The acceleration sensor numbers of the CDF were RAT-B-1, RAT-B-2, RAT-1-1, RAT-1-2, RAT-2-1, RAT-2-2, RAT-3-1, and RAT-3-2. The displacement sensors of CDF were numbered RDT-B-1, RDT-1-1, RDT-2-1, and RDT-3-1. The distribution of the sensors is shown in Figure 7.

2.5. Loading Method of Seismic Wave

According to the dynamic characteristics of the prototype structure of the physical model, the site conditions, and other factors, five-seismic-wave information was selected as the test seismic waves. The five seismic waves were ACC (artificial seismic wave), El Centro, Kobe, Taft, and Wenchuan. The peak accelerations of the seismic waves of the prototype structure are shown in

Table 10. Seismic peak accelerations of prototype structure (cm/s²).

Seismic Intensity	7-Degree	8-Degree	9-Degree
Frequent earthquakes	35	70	140
Design-basis earthquake	100	200	400
Maximum considered earthquake	220	400	620

.

In order to adapt to the proportions of the physical model and the test requirements, the time similarity constant, $S_T=0.25$, and the acceleration-similarity constant, $S_a=2.0$, were used to adjust the relevant parameters of the five seismic waves to ensure the rationality and effectiveness of the test. The adjusted values of the durations of the seismic waves are shown in

Table 11. Adjustment of seismic wave duration.

Seismic Wave	Absolute Value of PGA (cm/s2)	Time Interval (s)	Duration (s)	Adjusted Duration (s)
ACC	100.00	0.01000	30	7.5
El Centro	210.00	0.02000	30	7.5
Kobe	216.37	0.01000	20	5.0
Taft	176.80	0.01000	54	13.5
Wenchuan	1046.59	0.00125	70	17.5

. The peak acceleration adjustment coefficients of the seismic waves are shown in

Table 12. Adjustment of seismic wave peak acceleration.

Seismic Intensity	Absolute Value of PGA (cm/s2)	Adjustment Coefficient
		ACC	El Centro	Kobe	Taft	Wenchuan
7-degree frequent earthquakes (PGA = 0.07 (g))	70	0.7000	0.3333	0.3235	0.3959	0.0669
7-degree design-basis earthquake (PGA = 0.20 (g))	200	-	0.9524	-	-	-
7-degree maximum considered earthquake (PGA = 0.45 (g))	440	-	2.0952	-	-	-
8-degree maximum considered earthquake (PGA = 0.82 (g))	800	-	3.8095	-	-	-
9-degree maximum considered earthquake (PGA = 1.26 (g))	1240	-	5.9048	-	-	-

.

The adjusted ACC seismic wave, Kobe seismic wave, Taft seismic wave, Wenchuan seismic wave, and El Centro seismic wave are shown in Figure 8 and Figure 9.

The acceleration peaks of the five seismic waves were adjusted to 0.1 (g), and then the response spectrum analysis with a damping of 5% was performed, respectively. The response spectra of the five seismic waves were compared with the design response spectrum of the ‘Code for seismic design of buildings’ [46], as shown in Figure 10. It can be seen from Figure 10 that the errors between Kobe, Taft, and Wenchuan and the standard response spectrum are large, so only these three waves were used for the analysis of the 7-degree frequent earthquake conditions. The response spectrum errors of ACC and El Centro were smaller than that of the standard, but the shaking-table test mainly explores the influence of seismic waves on structures in nature, so the El Centro wave was selected for the subsequent tests.

At the beginning of the test, the dynamic characteristics, such as the natural frequency of the model, were evaluated by inputting random white-noise waves with a frequency range of 0.1~50 (Hz). A white-noise sweep lasting 120 s was inserted between seismic waves of different intensities to further monitor the dynamic characteristics of the two physical models after experiencing different seismic waves.

After the completion of the test of the 9-degree maximum considered earthquake condition, a new seismic condition was introduced to carry out the failure test, and the peak acceleration was increased until the model was destroyed. The test steps of the physical model are shown in

Table 13. Test condition information.

Condition		Seismic Wave	Peak Acceleration (g)	Direction
1	W1	White noise
2	F7KX	ACC	0.07	X
3	F7EX	El Centro
4	F7TX	Kobe
5	F7AX	Taft
6	F7WX	Wenchuan
7	W2	White noise
8	B7EX	El Centro	0.20	X
9	W3	White noise
10	R7EX	El Centro	0.45	X
11	W4	White noise
12	R8EX	El Centro	0.82	X
13	W5	White noise
14	R9EX	El Centro	1.26	X
15	W6	White noise
Supplementary working conditions	160%R9EX	El Centro	2.02	X
	W7	White noise
	240%R9EX	El Centro	3.02	X
	W8	White noise

. W1~W8 represent the white-noise sweep test. F7, B7, R7, R8, and R9 represent the 7-degree frequent earthquake, 7-degree design-basis earthquake, 7-degree maximum considered earthquake, 8-degree maximum considered earthquake, and 9-degree maximum considered earthquake, respectively. AX, EX, KX, TX, and WX represent the ACC wave X-direction input, El Centro wave X-direction input, Kobe wave X-direction input, Taft wave X-direction input, and Wenchuan wave X-direction input, respectively.

3. Analysis of Model Test Results

This part analyzes the above test results. The damage development for DF during the test is shown in Figure 11, and the damage development for CDF during the test is shown in Figure 12. When the PGA was 0.07 (g), the vibration amplitudes of DF and CDF were not obvious, and no cracks were found. Therefore, Figure 11 and Figure 12 are the test results of the El Centro seismic wave.

It can be seen from Figure 11 and Figure 12 that when the PGA is 0.20 (g), there are no cracks in DF and CDF, and only the putty of some nodes has slight peeling. When the PGA is 0.45 (g), small cracks begin to appear in both DF and CDF. When the PGA is 0.82 (g), the cracks of DF and CDF expand rapidly, and the joints of the beams and columns begin to loosen. When the PGA is 1.26 (g), both DF and CDF have large cracks. When the PGA is 2.02 (g), DF has collapsed, and the plastic deformation of CDF continues to intensify, but CDF still has not collapsed. When the PGA is 3.02 (g), CDF has collapsed. This shows that after carbon-fiber reinforcement, the Diaojiaolou can withstand greater earthquake action and significantly enhance the seismic capacity of the structure. The PGA when CDF collapsed increased by 49.5% compared with the PGA when DF collapsed. At the same time, the collapse of DF was mainly due to the failure of the connection between the column base and the base and the failure of the beam–column joints, and the failure points of the beam–column joints were mainly concentrated on the first and second layers. The reason for the collapse of CDF is similar to that of DF, but the failure points of the beam–column joints of CDF were mainly concentrated in the first layer. It can be seen that the failure modes of DF and CDF are mainly node failure, which is the same as the typical failure mode of RC structures under earthquakes. Additionally, after the collapse of CDF, there is no obvious shedding and cracking of the carbon-fiber cloth. This also shows that it is reasonable to use epoxy resin adhesive as adhesive.

3.1. Dynamic Characteristic Analysis

The variations in DF and CDF’s natural frequencies were obtained by a white-noise random-wave sweep-model structure, as shown in

Table 14. Natural vibration period and natural vibration period growth rate.

Condition	DF				CDF
	Natural Frequency	Natural Vibration Period	Growth Rate	Relative Growth Rate	Natural Frequency	Natural Vibration Period	Growth Rate	Relative Growth Rate
W1	8.34375	0.120	0	0	12.7187	0.078	0	0
W2	8.25	0.121	0.83%	0.83%	12.2917	0.081	3.85%	3.85%
W3	7.5625	0.132	10.00%	9.09%	10.8125	0.092	17.95%	13.58%
W4	4.625	0.216	80.00%	63.64%	6.125	0.165	111.54%	78.35%
W5	3.90625	0.256	113.33%	18.52%	5.6875	0.176	125.64%	6.67%
W6	2.09375	0.478	298.33%	86.72%	3.8125	0.262	235.90%	48.86%
W7	-	-	-	-	2.25	0.44	464.10%	67.94%
W8	-	-	-	-	-	-	-	-

.

It can be seen from Table 14 that the natural vibration period of DF is 0.12 (s) at W1. After being reinforced by carbon-fiber cloth, the natural vibration period of CDF is shortened to 0.078 (s). This shows that carbon-fiber cloth reinforcement measures can effectively improve the stiffness of structures, resulting in the reduction in the natural vibration period. This improved the bending and shear resistance of CDF. At W2, the natural vibration periods of DF and CDF increase by 0.83% and 3.85%, respectively, and the natural vibration periods of both begin to increase slightly. No cracks were found during the crack and damage inspection. At W3, the natural vibration periods of DF and CDF increase by 10.00% and 17.95%, respectively. During the crack and damage inspection, it was found that no obvious cracks were found on the components of DF and CDF, but the putty at some beam–column joints was slightly peeled off. At this time, under the earthquake action, slight damage began to appear inside the structure, and the structural rigidity began to decrease. At W4, the natural vibration periods of DF and CDF increase by 80.00% and 111.54%, respectively. During the crack and damage inspection, it was found that many horizontal cracks appeared at the beam–column joints of the structure. This shows that the internal damage of DF and CDF began to increase significantly and the structural stiffness decreased significantly. At W5, the natural vibration periods of DF and CDF increase by 113.33% and 125.64%, respectively. The sloshing amplitudes of the DF and CDF model structures are very large. During the crack and damage inspection, the existing cracks continued to develop, new cracks began to appear on the top and foot of the column in the third layer, and the foot of the column began to be damaged. At W6, the natural vibration periods of DF and CDF increase by 298.33% and 235.90%, respectively. At this time, both the DF and CDF structures showed obvious plastic deformation. DF collapsed when the PGA = 2.02 (g). At W7, the natural vibration period of CDF increases by 464.10%. CDF collapsed when the PGA = 3.02 (g).

Through Figure 13, it can be seen that the natural vibration period of CDF is lower than that of DF and that CDF can withstand a greater PGA during the whole test process. This confirms the inference that carbon-fiber cloth can effectively improve the stiffness of these structures. At the same time, based on the stiffness-enhancement effect, it was found that after the Diaojiaolous were reinforced by the carbon-fiber cloth, the local stiffnesses of the Diaojiaolous increased sharply, which changed the shape of the structural vibration mode and shortened the natural vibration period. Additionally, with an increase in the PGA, the difference between the natural vibration periods of DF and CDF gradually increased. At 0~0.45 (g), the natural vibration periods of DF and CDF show a concave trend. At 0.45~0.82 (g), the natural vibration period curves of DF and CDF are relatively flat, showing a horizontal development trend. After 0.82 (g), the natural vibration period curves of DF and CDF begin to increase rapidly, showing a linear development trend. Therefore, according to the development trend of the natural vibration period of the structure, the damage process of the structure is divided into three stages. When the PGA is between 0 (g) and 0.45 (g), the structure is in the damage-development stage (DS). When the PGA is between 0.45 (g) and 0.82 (g), the structure is in the yield stage (YS). When the PGA is greater than 0.82 (g), the structure is in the plastic-hardening stage (PS). Through the fitting results, it can be seen that the development law of the natural vibration periods of DF and CDF conforms to the development law of the exponential function (see expression (1)). The fitting function of DF is $N=0.0526+0.02051\exp \left(\left(P+0.81994\right)/0.68779\right)$, and its coefficient of determination ($R^2$) is 0.98262. The fitting function of CDF is $N=-0.17778+0.00984\exp \left(\left(P+7.5196\right)/2.30586\right)$, and its coefficient of determination ($R^2$) is 0.98772. According to the coefficient of determination, DF and CDF have achieved good fitting results:

$$N=\delta +A\exp \left(\left(P+P1\right)/T1\right)$$

(1)

In the above expression, $\delta$, $A$, $P1$ and $T1$ are all fitting coefficients.

3.2. Analysis of Acceleration Characteristics

In order to better reflect the variation in acceleration with structure height, this paper introduces the acceleration-increment coefficient ($\zeta$) to carry out the research. The calculation method of the acceleration-increment coefficient is shown in expression (2):

$$\zeta =L/DL$$

(2)

In this expression, $\zeta$ is the acceleration-increment coefficient; L is the maximum acceleration of each floor; and DL is the maximum acceleration of DZ1.

Under the influences of different seismic waves, the acceleration-increment coefficients of DF and CDF are shown in

Table 15. The X-direction maximum accelerations (m/s²) and acceleration-increment coefficients of DF were obtained (PGA = 0.07 (g)).

Layer	ACC		Kobe		Taft		Wenchuan		El Centro
	L	$\mathit{\zeta }$	L	$\mathit{\zeta }$	L	$\mathit{\zeta }$	L	$\mathit{\zeta }$	L	$\mathit{\zeta }$
DZ1	0.9579	1	0.5202	1	0.4386	1	3.1556	1	0.3550	1
DZ4	0.9845	1.0278	0.5322	1.0230	0.4425	1.0088	3.1893	1.0107	0.3589	1.0109
I	1.2664	1.3220	0.6165	1.1850	0.4097	0.9340	3.223	1.0213	0.4435	1.2494
II	0.9725	1.0152	0.8219	1.5798	0.3189	0.7272	2.093	0.6632	0.7621	2.1471
III	1.4083	1.4703	1.0638	2.0448	0.4782	1.0903	3.6563	1.1587	0.8529	2.4028

and

Table 16. The X-direction maximum accelerations (m/s²) and acceleration-increment coefficients of CDF were obtained (PGA = 0.07 (g)).

Layer	ACC		Kobe		Taft		Wenchuan		El Centro
	L	$\mathit{\zeta }$	L	$\mathit{\zeta }$	L	$\mathit{\zeta }$	L	$\mathit{\zeta }$	L	$\mathit{\zeta }$
DZ1	0.9445	1	0.7417	1	0.7535	1	0.5104	1	0.6382	1
DZ4	0.9449	1.0005	0.7513	1.0129	0.7554	1.0025	0.5208	1.0204	0.6465	1.0130
I	0.9901	1.0483	0.8023	1.0816	0.7479	0.9915	0.5404	1.0587	0.6613	1.0362
II	1.3325	1.4109	0.8671	1.1691	1.0235	1.3584	0.6572	1.2875	0.5360	0.8399
III	1.7997	1.9055	1.1879	1.6016	1.6194	2.1493	1.0151	1.9888	0.7935	1.2434

, respectively. The height of AT-B-1 (RAT-B-1) on DZ1 is set to 0 (m).

The variations in the acceleration-increment coefficients of DF and CDF with the height of the Diaojiaolou are shown in Figure 12.

Through Figure 14, it can be seen that the acceleration-increment coefficient of DF shows high discreteness after the height is greater than 0.3 (m). However, the overall trend of the acceleration-increment coefficient is increasing with the increase in height. At this time, the function expression of the acceleration-increment coefficient with the height is $\zeta =0.96647+0.00101\exp \left(\left(H+1.62163\right)/0.44299\right)$ by fitting. However, in DF, $R^2$ only reaches 0.3021. After being reinforced by the carbon-fiber cloth, the acceleration-increment coefficient of CDF begins to present discrete characteristics after the height is greater than 0.5 (m). After fitting, the function expression of the acceleration-increment coefficient of CDF with the height is $\zeta =0.98113+0.00331\exp \left(\left(H+0.39931\right)/0.30081\right)$ and $R^2$ increases to 0.74896. This shows that after strengthening with carbon-fiber cloth, under the influence of different seismic waves, the development law of the acceleration-increment coefficient of the Diaojiaolou gradually tends to be consistent and gradually conforms to the development law of exponential function (see expression (3)).

$$\zeta ={\delta }^{\prime }+A^{\prime }\exp \left(\left(H+P2\right)/T2\right)$$

(3)

In this expression, ${\delta }^{\prime }$, $A^{\prime }$, $P2$ and $T2$ are all fitting coefficients.

Under the influence of the El Centro seismic wave, the acceleration-increment coefficients of DF and CDF are shown in

Table 17. The X-direction acceleration-increment coefficients of DF (El Centro).

Layer	DZ1	Error (Absolute Value)	DZ4	Error (Absolute Value)	I	Error (Absolute Value)	II	Error (Absolute Value)	III	Error (Absolute Value)
0.07 (g)	1.0000	0.00%	1.0109	9.71%	1.2494	25.02%	2.1471	45.93%	2.4028	42.23%
0.20 (g)	1.0000	0.00%	1.0325	7.42%	1.2210	23.28%	1.6133	28.04%	1.8791	26.12%
0.45 (g)	1.0000	0.00%	1.0101	9.80%	1.2683	26.14%	1.3991	17.02%	1.7662	21.40%
0.82 (g)	1.0000	0.00%	0.8457	31.15%	1.0558	11.27%	0.9473	22.56%	1.0240	35.57%
1.26 (g)	1.0000	0.00%	2.5270	56.11%	0.5953	57.37%	0.7046	64.77%	0.9645	43.93%
2.02 (g)	1.0000	0.00%	0.2284	385.60%	0.2309	305.72%	0.1544	651.94%	0.2924	374.76%
Average value	1.0000	-	1.1091	-	0.9368	-	1.1610	-	1.3882	-

and

Table 18. The X-direction acceleration-increment coefficients of CDF (El Centro).

Layer	DZ1	Error (Absolute Value)	DZ4	Error (Absolute Value)	I	Error (Absolute Value)	II	Error (Absolute Value)	III	Error (Absolute Value)
0.07 (g)	1.0000	0.00%	1.0130	2.34%	1.0362	23.90%	0.8399	6.04%	1.2434	8.72%
0.20 (g)	1.0000	0.00%	1.0459	5.41%	1.2191	35.32%	1.7764	49.86%	2.4275	53.24%
0.45 (g)	1.0000	0.00%	0.7833	26.30%	1.0028	21.37%	1.4063	36.67%	1.6382	30.72%
0.82 (g)	1.0000	0.00%	0.8240	20.06%	1.0565	25.37%	0.9233	3.54%	1.1425	0.66%
1.26 (g)	1.0000	0.00%	2.0241	51.12%	0.8399	6.12%	1.0248	13.10%	1.1296	0.48%
2.02 (g)	1.0000	0.00%	0.2577	283.90%	0.0983	702.14%	0.0815	992.76%	0.1161	877.61%
3.02 (g)	1.0000	0.00%	0.9773	1.23%	0.2666	195.76%	0.1819	389.61%	0.2475	358.59%
Average value	1.0000	-	0.9893	-	0.7885	-	0.8906	-	1.1350	-

, respectively.

It can be seen from Table 17 and Table 18 that DF collapsed after the PGA reached 2.02 (g). After the PGA reached 3.02 (g), CDF collapsed. This shows that carbon-fiber cloth effectively increases the anti-collapse performance of Diaojiaolou structures. It can be seen from Figure 15 that the average value of the acceleration-increment coefficient of CDF is generally smaller than the average value of the acceleration-increment coefficient of DF. This shows that reinforcement with carbon-fiber cloth can effectively reduce the transmission effect of acceleration in a Diaojiaolou. Additionally, in DF, the average value of the acceleration-increment coefficient shows an N-shaped development law with the height. In the CDF, the average value of the acceleration-increment coefficient shows a V-shaped development law with the height. When the height is 0.3 (m), the average value of the acceleration-increment coefficient of CDF decreases. This shows that the carbon-fiber cloth effectively changes the development law of the average value of the acceleration-increment coefficient, making it change from N-shaped to V-shaped. The average value of the acceleration-increment coefficients of DF and CDF reaches the minimum at a height of 0.5 (m). This shows that the Diaojiaolou structure is least affected by acceleration at I.

3.3. Analysis of Displacement Characteristics

In this test, the pull-line displacement meters were arranged in the X-directions of DZ1, I, II, and III of DF and CDF, respectively. Through these displacement sensors, the displacement values of the structure during the test could be directly measured and output. The height of DT-B-1 (RDT-B-1) on DZ1 was set to 0 (m). When the PGA was 0.07, the displacement value and displacement-increment coefficients (${\zeta }^{\prime }$) of DF and CDF affected by different seismic waves were as shown in

Table 19. The maximum displacement values (mm) and displacement-increment coefficients of DF were obtained (PGA = 0.07 (g)).

Layer	ACC		Kobe		Taft		Wenchuan		El Centro
	${\mathit{L}}^{\prime }$	${\mathit{\zeta }}^{\prime }$	${\mathit{L}}^{\prime }$	${\mathit{\zeta }}^{\prime }$	${\mathit{L}}^{\prime }$	${\mathit{\zeta }}^{\prime }$	${\mathit{L}}^{\prime }$	${\mathit{\zeta }}^{\prime }$	${\mathit{L}}^{\prime }$	${\mathit{\zeta }}^{\prime }$
DZ1	1.1749	1.0000	0.8022	1.0000	0.1629	1.0000	1.4084	1.0000	0.7031	1.0000
I	1.1971	1.0189	0.9809	1.2228	0.1852	1.1369	1.5102	1.0723	0.8567	1.2185
II	1.4214	1.2098	1.2553	1.5648	0.2523	1.5488	2.1007	1.4916	1.1887	1.6907
III	1.4889	1.2673	1.3448	1.6764	0.2864	1.7581	2.2306	1.5838	1.2674	1.8026

and

Table 20. The maximum displacement values (mm) and displacement-increment coefficients of CDF were obtained (PGA = 0.07 (g)).

Layer	ACC		Kobe		Taft		Wenchuan		El Centro
	${\mathit{L}}^{\prime }$	${\mathit{\zeta }}^{\prime }$	${\mathit{L}}^{\prime }$	${\mathit{\zeta }}^{\prime }$	${\mathit{L}}^{\prime }$	${\mathit{\zeta }}^{\prime }$	${\mathit{L}}^{\prime }$	${\mathit{\zeta }}^{\prime }$	${\mathit{L}}^{\prime }$	${\mathit{\zeta }}^{\prime }$
DZ1	1.2855	1.0000	1.0512	1.0000	0.3281	1.0000	0.7306	1.0000	0.9165	1.0000
I	1.3724	1.0676	1.0985	1.0450	0.3513	1.0707	0.7564	1.0353	0.9535	1.0404
II	1.4279	1.1108	1.1443	1.0886	0.3732	1.1375	0.7680	1.0512	0.9824	1.0719
III	1.4967	1.1643	1.1792	1.1218	0.3924	1.1960	0.7860	1.0758	1.0050	1.0966

, respectively. The calculation method of the displacement-increment coefficient is shown in expression (4).

$${\zeta }^{\prime }={L^{\prime }/DL}^{\prime }$$

(4)

In this expression, ${\zeta }^{\prime }$ is the displacement-increment coefficient; $L^{\prime }$ is the maximum displacement of each floor; and $D{L}^{\prime }$ is the maximum displacement of DZ1.

The variations in the displacement-increment coefficients of DF and CDF with the heights of the Diaojiaolous is shown in Figure 14.

It can be seen from Figure 16 that the displacement-increment coefficient of DF has high discreteness as a whole, but the displacement-increment coefficient shows an increasing trend with the increase in height. At this time, the function expression of the displacement-increment coefficient with the height is ${\zeta }^{\prime }=-0.42779+0.17449\exp \left(\left(H+6.70712\right)/3.21531\right)$ by fitting. $R^2$ is 0.74607. After being reinforced by the carbon-fiber cloth, the development trend of the displacement-increment coefficient of CDF shows a low discreteness. After fitting, the function expression of the displacement-increment coefficient of CDF with the height is ${\zeta }^{\prime }=-7.30092+3.72704\exp \left(\left(H+63.85585\right)/79.74574\right)$ and $R^2$ increases to 0.75586. This shows that after strengthening with the carbon-fiber cloth, the development law of the displacement-increment coefficient is more consistent under the influences of different seismic waves. The development trend of the displacement-increment coefficients of DF and CDF with the heights conforms to the development law of exponential function (see expression (5)).

$${\zeta }^{\prime }={\delta }^{″}+A^{″}\exp \left(\left(H+P3\right)/T3\right)$$

(5)

In this expression, ${\delta }^{″}$, $A^{″}$, $P3$ and $T3$ are all fitting coefficients.

Under the influence of the El Centro seismic wave, the displacement-increment coefficients of DF and CDF were as shown in

Table 21. The displacement-increment coefficients of DF (El Centro).

Layer	DZ1	Error (Absolute Value)	I	Error (Absolute Value)	II	Error (Absolute Value)	III	Error (Absolute Value)
0.07 (g)	1.0000	0.00%	1.2185	16.42%	1.6907	30.32%	1.8026	26.27%
0.20 (g)	1.0000	0.00%	1.0398	2.06%	1.2177	3.26%	1.2777	4.02%
0.45 (g)	1.0000	0.00%	1.1592	12.15%	1.4346	17.89%	1.5414	13.77%
0.82 (g)	1.0000	0.00%	1.2014	15.23%	1.2837	8.23%	1.5077	11.85%
1.26 (g)	1.0000	0.00%	1.0961	7.09%	1.2493	5.71%	1.3543	1.86%
2.02 (g)	1.0000	0.00%	0.5953	71.07%	0.7046	67.19%	0.9645	37.80%
Average value	1.0000	-	1.0184	-	1.1780	-	1.3291	-

and

Table 22. The displacement-increment coefficients of CDF (El Centro).

Layer	DZ1	Error (Absolute Value)	I	Error (Absolute Value)	II	Error (Absolute Value)	III	Error (Absolute Value)
0.07 (g)	1.0000	0.00%	1.0404	14.85%	1.0719	6.54%	1.0966	8.44%
0.20 (g)	1.0000	0.00%	1.0412	14.92%	1.0729	6.63%	1.0964	8.45%
0.45 (g)	1.0000	0.00%	1.1872	25.38%	1.4217	29.54%	1.5023	20.85%
0.82 (g)	1.0000	0.00%	1.2047	26.46%	1.4417	30.51%	1.5526	23.41%
1.26 (g)	1.0000	0.00%	1.2000	26.18%	1.3397	25.22%	1.7053	30.27%
2.02 (g)	1.0000	0.00%	0.3442	157.38%	0.4292	133.41%	0.7231	64.44%
3.02 (g)	1.0000	0.00%	0.3379	162.18%	0.3055	227.92%	0.5551	114.21%
Average value	1.0000	-	0.8859	-	1.0018	-	1.1891	-

, respectively.

It can be seen from Table 21 and Table 22 that DF collapsed after the PGA reached 2.02 (g). After the PGA reached 3.02 (g), CDF collapsed. This also shows that the carbon-fiber cloth effectively increased the anti-collapse performance of the Diaojiaolou structure. It can be seen from Figure 17 that the average value of the displacement-increment coefficient of CDF is smaller than the average value of the displacement-increment coefficient of DF. This shows that after reinforcement with carbon-fiber cloth, the displacement change value in a Diaojiaolou can be effectively reduced. Additionally, in DF, the average value of the displacement-increment coefficient shows a concave shape with the development of the height. In CDF, the average value of the displacement-increment coefficient shows a V-shaped pattern with the development of the height. When the height is less than 0.5 (m), the average value of the displacement-increment coefficient of CDF decreases. This shows that the carbon-fiber cloth effectively changed the development law of the average value of the displacement-increment coefficient and made it change from concave to V-shaped. The average value of the displacement-increment coefficient of DF has its minimum value when the height is 0 (m). The average value of the displacement-increment coefficient of the CDF reaches its minimum at a height of 0.5 (m). This shows that when a Diaojiaolou structure is not reinforced by carbon-fiber cloth, DZ1 is the least affected by seismic waves. After the Diaojiaolou structure was reinforced by carbon-fiber cloth, I was the least affected by the seismic waves.

4. Conclusions

In this paper, the response characteristics of RC Diaojiaolou structures under different seismic intensities and the reinforcement of carbon-fiber cloth were studied using similar physical models. The specific research results are as follows:

(1) Based on the analysis results of the dynamic characteristics, it was found that carbon-fiber cloth can effectively improve the stiffness of these structures. According to the development trend of the natural vibration period of the structures, the damage process of the structures is divided into three stages. The PGA between 0 (g) and 0.45 (g) was divided into the damage-development stage (DS). The PGA between 0.45 (g) and 0.82 (g) was divided into the yield stage (YS). The range of PGA greater than 0.82 (g) was divided into the plastic-hardening stage (PS). It was concluded that the development law of the natural vibration period of DF and CDF conformed to the exponential function development law. The function expression of DF is $N=0.0526+0.02051\exp \left(\left(P+0.81994\right)/0.68779\right)$. The function expression of CDF is $N=-0.17778+0.00984\exp \left(\left(P+7.5196\right)/2.30586\right)$.

(2) Based on the analysis results of the acceleration characteristics, it was found that under the influence of different seismic waves, the development law of the acceleration-increment coefficients of Diaojiaolous tends to be consistent and gradually conforms to the development law of the exponential functions after reinforcement with carbon-fiber cloth. The function expression of the acceleration-increment coefficient of DF with the height is $\zeta =0.96647+0.00101\exp \left(\left(H+1.62163\right)/0.44299\right)$. The function expression of the acceleration-increment coefficient of CDF with the height is $\zeta =0.98113+0.00331\exp \left(\left(H+0.39931\right)/0.30081\right)$. After the reinforcement with the carbon-fiber cloth, the transmission effect of the acceleration in the Diaojiaolous could be effectively reduced. Additionally, it effectively changes the development law of the average value of the acceleration-increment coefficient, making it change from N-shaped to V-shaped. At the same time, it was also found that the Diaojiaolou structures were least affected by acceleration at I.

(3) Based on the analysis results of the displacement characteristics, it was found that the development law of the displacement-increment coefficients in DF and CDF conforms to the development law of the exponential functions. The development trend of the displacement-increment coefficient of CDF showed lower discreteness. The function expression of the displacement-increment coefficient of DF with the height is ${\zeta }^{\prime }=-0.42779+0.17449\exp \left(\left(H+6.70712\right)/3.21531\right)$. The function expression of the displacement-increment coefficient of CDF with the height is ${\zeta }^{\prime }=-7.30092+3.72704\exp \left(\left(H+63.85585\right)/79.74574\right)$. It was also found that carbon-fiber cloth can effectively change the development law of the average value of the displacement-increment coefficient so that it changes from concave to V-shaped. At the same time, it was also found that the displacement deformation of DF was least affected by the seismic waves at DZ1. The displacement deformation of CDF was least affected by the seismic waves at I.

(4) In this paper, the structural layer most affected by the seismic waves could be found according to the variation in the acceleration-increment coefficient and the displacement-increment coefficient with the height. Then, during the seismic design of the Diaojiaolou, the structural layer that was most affected by the seismic waves was strengthened to enhance the seismic performance of the structure. Moreover, carbon-fiber cloth and epoxy resin adhesive are not only low-cost but also simple to operate, which makes carbon-fiber reinforcement measures widely used in rural mountainous areas. However, the reinforcement method adopted in this paper is relatively simple, and only one-way seismic input was considered. This has some shortcomings with the response modes of full-scale structures under multi-directional earthquakes. In a follow-up study, more accurate function expressions of the acceleration-increment coefficient and displacement-increment coefficient need to be studied. The mathematical model proposed in this paper was compared with other results. At the same time, the influence of ground-motion characteristics on other types of buildings of the ethnic minorities in the mountainous areas will also continue to be explored. The response characteristics of a variety of reinforcement methods and full-scale structures under multi-directional earthquakes will be considered in order to improve the seismic design requirements of the buildings in the above areas and enhance their emergency response capacities.