Quantitative evaluation method of structural safety status of ancient Chinese three-hole stone arch bridges—A case study of the Yongchang Bridge

Figures & data

Figure 1. Statistical results regarding types and holes of ancient stone arch bridges in Jiangsu Province.

Table 1. Statistics of the key information of ancient stone arch bridges in Jiangsu Province.

Name	Type	Holes	Length (m)	Name	*Type	Holes	Length (m)
City	Huaian			City	Wuxi
Banzha stone Bridge	Stone	1	12.8	Yinglong Bridge	Stone	1	23.5
Dadongdongfanghong Bridge	Brick	1	40	Diaozhudu Bridg	Stone	3	40.9
City	Lianyungang			Xuntang Bridge	Stone	1	17.2
Jiulong Bridge	Brick	9	98
Xichang street Dashi Bridge	Stone	3	35	Liangtang Bridge	Stone	1	21
Xiexiaolou Bridge	Stone	1	8.7	Dacheng Bridge	Stone	1	22
Qiantan Bridge	Stone	3	54	Zhang Bridge	Stone	1	13.42
City	Suqian			Qingming Bridge	Stone	1	43.2
Tonghui Bridge	Brick &Stone		12.5	Yangming Bridge	Stone	3	49.5
Tongyun Bridge	Brick		6	City	Xuzhou
Jiazhuang Bridge	Brick	1	21	Cao Bridge	Stone	1	21
City	Taizhou			Caihong Bridge	Stone	1	32
Sunjia Bridge	Stone		21.2	Dengyun Bridge	Stone	1	18.8
Taishan Bridge	Stone		-	Feihong Bridge	Stone	1	38
City	Yancheng			Gang Bridge	Stone	1	15
Dingwan Bridge	Brick	3	75	Guangji Bridge	Stone	3	48.25
City	Yangzhou			Longxing Bridge	Stone	1	10.5
Dadongmen Bridge	Brick &Stone	1	10.7	Maojia Bridge	Stone	1	27.2
Xiaohong Bridge	Brick &Stone	1		Nanyang Bridge	Stone	1	14.4
Ruyi Bridge	Brick &Stone	1	15	Qinglong Bridge	Stone	1	19
Yingen Bridge	Brick &Stone	1	12.5	Sanyuan Bridge	Stone	1	18.8
Yingxun Bridge	Brick	1	7.05	Taiping Bridge	Stone	1	12.75
Gongyuan Bridge	Brick &Stone	1	7.8	Wenheng Bridge	Stone	3	41
Ouxiang Bridge	Stone	1	29.1	Wanan Bridge	Stone	1	37.9
Sajin Bridge	Brick &Stone	1	21.2	Wanfu Bridge	Stone	1	23
Dahong Bridge	Stone	3		Zhongshi Bridge	Stone	1	18.4
Niansi Bridge	Brick	1	24	Zhouchen Bridge	Stone	1	15
City	Zhenjiang			Zhenlong Bridge	Stone	1	17.7
Zhanlong Bridge	Stone	1	16.8	Benshan Bridge	Stone	1	30.18
Lujiang Bridge	Stone	3	29	Zhuangchen Bridge	Stone	1	37
Haier Bridge	Stone	1	8	Xinfang Bridge	Stone	1	34.8
Taiping Bridge	Stone	3	39	Wanyuan Bridge	Stone	1	40
Guantang Bridge	Stone	1	12.25	Wudong Bridge	Stone	5	31
City	Nanjing			Guanlian Bridge	Stone	1	30
Nei Bridge	Brick	1	23.7	Shetou Bridge	Stone	3	31
Jinhu Bridge	Stone	7	75	City	Suzhou
Beimen Bridge	Stone	3	21.5	Caiyun Bridge	Stone	3	38
Wende Bridge	Stone	3		Fenghuang Bridge	Stone	1	38
Huaiqing Bridge	Stone	1	17	Guan Bridge	Stone	1	28.7
Han Bridge	Stone	1	12	Houtang Bridge	Stone	1	22.45
Maotang Bridge	Brick	5	74.6	Juqufengyu Bridge	Stone	3	32.2
Jiannanheshang Bridge	Stone	1	27	Lishu ancient Bridge	Stone	1	12.5
Yongyueyoufang Bridge	Stone	1	19.4	Puan Bridge	Stone	1	21.5
Dashi Bridge	Brick &Stone	1	30	Puji Bridge	Stone	3	38.69
Saihong Bridge	Stone	3	50	Shangjin Bridge	Stone	1	42.45
Jishan Bridge	Stone	3	20	Shouxing Bridge	Stone	1	18
Tongnan Bridge	Stone	1	15.3	Shijia Bridge	Stone	1	28.7
Putang Bridge	Stone	9	91.3	Xijin Bridge	Stone	1	22
Qiqiaoweng	Stone	7		Taian Bridge	Stone	1	16.75
Yongchang Bridge	Stone	3	27.8	Wulong Bridge	Stone	5	42
Xianhui Bridge	Stone	1	20	Xingchun Bridge	Stone	9	54
Shuyun Bridge	Stone	1	14.2	Xiajin Bridge	Stone	1	58
Qi Bridge	Stone	3	39	Yuecheng Bridge	Stone	1	33.2
Jiangxia Bridge	Stone	3	44	Yongan Bridge	Stone	1	13.7
Lujia Bridge	Stone	1	24	Miedu Bridge	Stone	1	81.3
Pei Bridge	Stone	3	32	Xianghua Bridge	Stone	1	8.5
Changle Bridge	Stone	3	36	Wumen Bridge	Stone	1	66.3
Xuanjin Bridge	Stone	3	41.6	Hongen Bridge	Stone	1	13.31
Jiulong Bridge	Stone	5	51	Guangfu Bridge	Stone	1	18.5

*Note: All the bridges are masonry structure. The brick type means that the bridge is made of bricks and mortars, and the stone type means that the bridge is made of stones and mortars.

Figure 2. Schematic diagram of the structural components of ancient three-hole stone arch bridge.

Figure 3. Structural safety evaluation system of ancient three-hole stone arch bridge (V₁, V₂, … V₁₁ are the judgment matrices, which are introduced in Section 2.2).

Table 2. Indicator rating and scoring for an ancient three-hole stone arch bridge.

	Safety Grade
Rating	a	b	c	d
Scoring	100	67	33	0
Bearing capacity item	Structural resistance/Load effect ≥1.0	Structural resistance/Load effect ≥0.95	Structural resistance/Load effect ≥0.85	Structural resistance/Load effect <0.85
Displacement item	Displacement ≤Calculated length of component/450	Displacement≤ Calculated length of component/250	Displacement≤ Calculated length of component/200	Displacement> Calculated length of component/200
Crack item	No cracks	Crack width ≤3 mm	Crack width ≤5 mm	Crack width >10 mm
Configuration item	Connections and construction methods are good	Connections and construction methods are normal, there are some local surface defects	Connections and construction methods are inappropriate, there are some defects	Connections and construction methods are wrong, there are some serious defects
Structural system and arrangement item	No obvious defects, structure is intact	Some non-load-bearing components are missing	Some load-bearing components are missing	Some load-bearing components are severely missing
Connections between components item	Reliable connections, no disconnections, translocations and looseness	There are slight disconnections, translocations and looseness	There are some disconnections, translocations and looseness between load-bearing members	There are severe disconnections, translocations and looseness between load-bearing members
Deformation in the direction parallel to the bridge item	No obvious deformation	Ratio of deformation of the top of the arch to the height of the arch≤4/1000	Ratio of deformation of the top of the arch to the height of the arch≤10/1000	Ratio of deformation of the top of the arch to the height of the arch>10/1000
Deformation in the direction perpendicular to the bridge item	No obvious deformation	Ratio of deformation of the top of the arch to the height of the arch≤4/1000	Ratio of deformation of the top of the arch to the height of the arch≤10/1000	Ratio of deformation of the top of the arch to the height of the arch>10/1000

Table 3. Scoring method of structural safety status of three-hole stone arch bridges.

Evaluation score	75 ~ 100	50 ~ 75	25 ~ 50	0 ~ 25
Structural safety grade	I	II	III	IV
Structural safety Status	Generally safe	Marginally safe	Marginally dangerous	Seriously dangerous

Table 4. Scaling of judgment matrix and interpretations.

Quantity	Interpretation
1	Two factors are of equal importance compared to each other
3	One of the two factors is of little more importance compared to the other
5	One of the two factors is obviously more important compared to the other
7	One of the two factors is strongly more important compared to the other
9	One of the two factors is extremely more important compared to the other
2, 4, 6, 8	The value between two adjacent judgment values, meaning the transition between important judgements

Table 5. The average random consistency index values for the hierarchical analysis method.

Matrix orders (n)	1	2	3	4	5	6	7	8	9
Average random consistency index value RI	0.00	0.00	0.52	0.89	1.11	1.25	1.35	1.40	1.45

Table 6. The detailed judgment matrices for three-hole arch bridges.

judgment matrix	Interpretation	Formula
V1	the overall level of structural safety evaluation	$V_1=\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$
V2	structural level	$V_2=\left[\begin{array}{cc}1& 2\\ 1/2& 1\end{array}\right]$
V3	middle-hole arch level	$V_3=V_4=\cdots =V_9=\left[\begin{array}{cccc}1& 5& 7& 3\\ 1/5& 1& 3& 1/3\\ 1/7& 1/3& 1& 1/5\\ 1/3& 3& 5& 1\end{array}\right]$
V4	side-hole arch level
V5	diamond wall between middle hole and side hole level
V6	side-hole diamond wall level
V7	middle-hole spandrel wall level
V8	side-hole spandrel wall level
V9	balustrade column and railing panel level
V10	bridge structural integrity level	$V_{10}=\left[\begin{array}{c}1\begin{array}{cc}\hspace{0.17em}& 3\end{array}\\ \begin{array}{cc}1/3& 1\end{array}\end{array}\right]$
V11	bridge overall deformation level	$V_{11}=\left[\begin{array}{c}1\begin{array}{cc}\hspace{0.17em}& 3\end{array}\\ \begin{array}{cc}1/3& 1\end{array}\end{array}\right]$

Figure 4. Flow chart of calculation program of component importance

Figure 5. Distribution of importance coefficients per unit volume of the overall model.

Figure 6. Distribution of importance coefficients per unit volume of the mid-hole arch.

Figure 7. Distribution of importance coefficients per unit volume of the diamond walls between middle-hole and side-holes.

Figure 8. Distribution of importance coefficients per unit volume of the side-hole arch.

Figure 9. Distribution of importance coefficients per unit volume of the middle-hole spandrel walls.

Figure 10. Distribution of importance coefficients per unit volume of the side-hole spandrel walls.

Figure 11. Distribution of importance coefficients per unit volume of the side-hole diamond walls.

Figure 12. Distribution of importance coefficients per unit volume of the balustrade column and railing panel.

Table 7. The normalized weight coefficients of the structural components.

Structural component	Weight coefficient
middle-hole arch	0.30
diamond wall between middle hole and side hole	0.19
side-hole arch	0.17
middle-hole spandrel wall	0.14
side-hole spandrel wall	0.13
side-hole diamond wall	0.06
balustrade column and railing panel	0.01

Figure 13. Lateral view of the Yongchang Bridge.

Figure 14. Current situation of the diamond walls. (a) The side-hole diamond wall is generally in good condition. (b) Missing and loose stones of the diamond walls between the middle and side holes.

Figure 15. Current situation of the arches. (a) Missing stones and cracks of side-hole arch. (b) Cracking and deformation of the middle-hole arch.

Figure 16. Current situation of the spandrel walls. (a) Bulging and deformation of the spandrel wall of the side-hole. (b) Bulging and deformation of the spandrel wall of the middle-hole.

Figure 17. Current situation of the balustrade columns and railing panels. (a) Current situation at the upstream side of the balustrade column and railing panel. (b) Current situation at the downstream side of the balustrade column and railing panel.

Table 8. Scoring of displacement, crack and configuration items of Yongchang Bridge.

Component	Evaluation item	Current situation	Rating	Scoring
Middle-hole arch	Displacement	Arch span/250 ≤ Displacement ≤ Arch span/200	c	33
	Crack	3 mm ≤ width ≤ 5 mm	c	33
	Configuration	it was generally in good condition	b	67
Side-hole arch	Displacement	Displacement ≤ Arch span/250	b	67
	Crack	3 mm ≤ width ≤ 5 mm	c	33
	Configuration	one of the arch stones was missing	d	0
Diamond wall between middle hole and side hole	Displacement	Ratio of displacement difference between two sides to wall length ≤ 1/250	b	67
	Crack	Width ≤ 3 mm	b	67
	Configuration	Some blocks were missing, and some others were loose	c	33
Side-hole diamond wall	Displacement	Ratio of displacement difference between two sides to wall length ≤ 1/250	b	67
	Crack	Width ≤ 3 mm	b	67
	Configuration	it was generally in good condition	b	67
Middle-hole spandrel wall	Displacement	Ratio of bulge displacement to wall length > 1/200	d	0
	Crack	3 mm ≤ Crack width ≤ 5 mm	c	33
	Configuration	Inclined, with additional buttress walls	d	0
Side-hole spandrel wall	Displacement	Ratio of bulge displacement to wall length > 1/200	d	0
	Crack	Width ≤ 3 mm	b	67
	Configuration	Slanting, with additional buttress walls	d	0
Balustrade column and railing panel	Displacement	Displacement ≤ Railing span/250	b	67
	Crack	Crack width ≤ 3 mm	b	67
	Configuration	Completely replaced	d	0

Figure 18. Meshing of the overall FE model.

Figure 19. Meshing of masonry part of FE model.

Table 9. Parameters of the main materials.

Materials	Compressive strength	Tensile strength	Elastic modulus	Density
*Masonry	1.75 MPa	0.07 MPa	1524 MPa	2200 kg/m^3
Filling soil	/	/	40 MPa	1800 kg/m^3

*The combination of stones and lime mortars.

Table 10. Mechanical analysis results under different load conditions.

Condition	Maximum principal tensile stress	Maximum principal compressive stress
Condition 1	0.15 MPa	0.69 MPa
Condition 2	0.18 MPa	0.76 MPa
Condition 3	0.16 MPa	0.74 MPa
Condition 4	0.16 MPa	0.74 MPa

Figure 20. 1st principal stress nephogram of the Yongchang Bridge under condition 2 (Unit: N/m²).

Figure 21. 3rd principal stress nephogram of the Yongchang Bridge under condition 2 (Unit: N/m²).

Table 11. Scoring of bearing capacity item of Yongchang Bridge.

Component	Evaluation item	Current situation	Rating	Scoring
Middle-hole arch	Bearing capacity	Structural resistance/Load effect = 0.70	d	0
Side-hole arches	Bearing capacity	Structural resistance/Load effect = 0.39	d	0
Diamond walls between middle hole and side holes	Bearing capacity	Structural resistance/Load effect = 1.06	a	100
Side-hole diamond walls	Bearing capacity	Structural resistance/Load effect = 1.39	a	100
Middle-hole spandrel walls	Bearing capacity	Structural resistance/Load effect = 0.91	c	33
Side-hole spandrel walls	Bearing capacity	Structural resistance/Load effect = 1.03	a	100
Balustrade columns and railing panels	Bearing capacity	Structural resistance/Load effect = 0.54	d	0

Table 12. Scoring of the evaluation items at structural level.

Evaluation item	Current situation	Rating	Scoring
Structural system and arrangement	some stones missing at the side-hole arch and the diamond walls between the middle and side holes	c	33
Connections between components	Some lime mortar between the arch stones and between the side wall stones are missing	c	33
Deformation in the direction parallel to the bridge	Ratio of displacement of the top of the arch to the height of the arch≤4/1000	b	67
Deformation in the direction perpendicular to the bridge	Ratio of displacement of the top of the arch to the height of the arch≤4/1000	b	67

Table 13. Quantitative evaluation of the structural safety status of the Yongchang Bridge.

Structural safety status score	Topic level	Weights	Sub-topic level	Weights	Indicator level	Weights	Comprehensive weights	Scoring
40.11	Component level	0.5	Middle-hole arch	0.30	Bearing capacity item	0.5650	0.0848	0
					Displacement item	0.1175	0.0176	33
					Crack item	0.0553	0.0083	33
					Configuration item	0.2622	0.0393	67
			Side-hole arch	0.17	Bearing capacity item	0.5650	0.0480	0
					Displacement item	0.1175	0.0100	67
					Crack item	0.0553	0.0047	33
					Configuration item	0.2622	0.0223	0
			Diamond wall between middle hole and side hole	0.19	Bearing capacity item	0.5650	0.0537	100
					Displacement item	0.1175	0.0112	67
					Crack item	0.0553	0.0053	67
					Configuration item	0.2622	0.0249	33
			Side-hole diamond wall	0.06	Bearing capacity item	0.5650	0.0170	100
					Displacement item	0.1175	0.0035	67
					Crack item	0.0553	0.0017	67
					Configuration item	0.2622	0.0079	67
			Middle-hole spandrel wall	0.14	Bearing capacity item	0.5650	0.0396	33
					Displacement item	0.1175	0.0082	0
					Crack item	0.0553	0.0039	33
					Configuration item	0.2622	0.0184	0
			Side-hole spandrel wall	0.13	Bearing capacity item	0.5650	0.0367	100
					Displacement item	0.1175	0.0076	0
					Crack item	0.0553	0.0036	67
					Configuration item	0.2622	0.0170	0
			Balustrade column and railing panel	0.01	Bearing capacity item	0.5650	0.0028	0
					Displacement item	0.1175	0.0006	67
					Crack item	0.0553	0.0003	67
					Configuration item	0.2622	0.0013	0
	Structural level	0.5	Bridge structural integrity	0.67	Structural system and arrangement	0.75	0.2513	33
					Connections between components	0.25	0.0838	33
			Bridge overall deformation	0.33	Deformation in the direction parallel with span	0.75	0.1238	67
					Deformation in the direction perpendicular to span	0.25	0.0413	67