Zheng et al 2021b - Revision history

Rimni at 10:53, 16 March 2022

2022-03-16T10:53:46Z

Rimni: /* References */

2022-03-16T10:51:03Z

‎References

Rimni at 10:49, 16 March 2022

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Rimni: /* 1. Introduction */

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‎1. Introduction

Rimni at 10:45, 16 March 2022

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Rimni at 10:24, 16 March 2022

2022-03-16T10:24:00Z

Rimni: /* 5. Assessment of the robustness of the cable-stayed bridge */

2022-03-16T09:53:53Z

‎5. Assessment of the robustness of the cable-stayed bridge

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Rimni at 09:36, 16 March 2022

2022-03-16T09:36:09Z

Rimni at 09:30, 16 March 2022

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Rimni at 15:51, 15 March 2022

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 <div class="center" style="font-size: 75%;">'''Table 2'''. Maximum stress in the truss girder under the two alternative load path plans'''</div>
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	[1] Xu F.Y., Zhang M.J., Wang L., Zhang J.R. Recent highway bridge collapses in China: Review and discussion. Journal of Performance of Constructed Facilities, 30(5):04016030, 2016.		[1] Xu F.Y., Zhang M.J., Wang L., Zhang J.R. Recent highway bridge collapses in China: Review and discussion. Journal of Performance of Constructed Facilities, 30(5):04016030, 2016.

← Older revision		Revision as of 10:49, 16 March 2022
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−	For the degraded truss girder with two alternative path plans, most of the members were compressed; the maximum principle compression stress occurred in the bottom chord near the pylon, and the maximum principle tension stress occurred in the bottom chord in the middle span. Compared to AP1, AP2 was found to more effectively reduce the compression and tension stresses (~~''σ''~~<~~sub~~>cm</~~sub~~> and ~~''σ''~~<~~sub~~>tm</~~sub~~>) in the truss members, with a decrease in compression stress of about 2 MPa and a decrease in tension stress in the range of 1.4 to 8.7 MPa. This indicates that AP2 provided more effective paths for load absorption, especially in the scenario of the loss of the chords near the pylon, as exhibited in [[#tab-2\|Table 2]].	+	For the degraded truss girder with two alternative path plans, most of the members were compressed; the maximum principle compression stress occurred in the bottom chord near the pylon, and the maximum principle tension stress occurred in the bottom chord in the middle span. Compared to AP1, AP2 was found to more effectively reduce the compression and tension stresses (<math>\sigma_{cm}</math> and <math>\sigma_{tm}</math>) in the truss members, with a decrease in compression stress of about 2 MPa and a decrease in tension stress in the range of 1.4 to 8.7 MPa. This indicates that AP2 provided more effective paths for load absorption, especially in the scenario of the loss of the chords near the pylon, as exhibited in [[#tab-2\|Table 2]].

	===4.2 Alternative load paths for cables===		===4.2 Alternative load paths for cables===

@@ Line 30: / Line 30: @@
 Cable-stayed bridges with a steel truss girder have been widely constructed to carry both vehicle and train loads over rivers and valleys, and are characterized by a super large span and sufficient stiffness due to the steel truss girder. However, due to their weak robustness, serious bridge collapses have occurred, leading to devastating damages in traffic systems and severe injuries. For example, due to the damage of its individual chords and joints by fatigue, the I-35W Highway Bridge over the Mississippi River in Minneapolis, Minnesota, USA, suddenly collapsed, causing the deaths of 13 people, and injuries to 145 others. Similarly, due to the sudden rapture of a single rod leading to the fracture of a series of rods, the Silver Bridge over the Ohio River between Ohio and West Virginia, USA, resulted in the collapse of the entire bridge and the deaths of 46 people. An overview of similar catastrophes has found that highway bridge collapses are caused by human error (2000–2014), including the inadvisable management of the engineering owner, design deficiencies, poor construction practice, dereliction of supervision, vehicle overloading, vessel collision, and a lack of maintenance and inspection <span id='cite-_Ref93700818'></span>[[#_Ref93700818|[1]]]. There are three categories of existing approaches for structural robustness assessment, namely deterministic methods, probability and reliability methods, and risk-based approaches.
-Deterministic methods are used to assess the robustness of structures under different loads via the system strain energy, load-carrying capacity, and structural stiffness. Based on reliability theory, the System Factor Table has been developed for simple and continuous bridges with multi-girders, and the step-by-step calculation procedure is recommended to assess the robustness of bridges with complex systems <span id='cite-_Ref93700844'></span>[[#_Ref93700844|[2]]]. By investigating the collapse behavior of suspension and cable-stayed bridges in cable loss scenarios, Scheller revealed that a dynamic amplification factor of 2.0 is required to meet the safety requirements for cables and pylons; moreover, it was found that a cable-stayed bridge cannot bear simultaneous sudden failure in more than two of its cables <span id='cite-_Ref93700859'></span>[[#_Ref93700859|[3]]]<span id='cite-_Ref93700863'></span>[[#_Ref93700863|[4]]]. To identify various possible collapse modes, Jiang established a topological hierarchy model of the collapsed bridge at Florida International University (FIU), Miami, Florida, USA, using the Improved Structural Vulnerability Theory (ISVT) clustering process. The findings revealed that the maximum vulnerability index of the bridge increased dramatically due to the failure of one of its components <span id='cite-_Ref93700870'></span>[[#_Ref93700870|[5]]]. By investigating the collapse accident of the Heyuan Dongjiang Bridge, Heyuan, Guangdong Province, China, Sun found that the deck-type arch bridge was sensitive to the foundation displacement, and an overlarge foundation displacement may have caused the collapse of the bridge <span id='cite-_Ref93700878'></span>[[#_Ref93700878|[6]]]. To explore the effect of collapse control on a continuous girder bridge, Li considered three collapse control systems, namely the Collapse High Damping Rubber (CHDR), Collapse Fluid Viscous Damper (CFVD), and Collapse Lock-Up Clutch (CLUC) systems, to analyze the respective collapse modes and collapse control strategies <span id='cite-_Ref93700884'></span>[[#_Ref93700884|[7]]]. Khoei numerically simulated the progressive collapse of the Hongqi Bridge, Zhuzhou, Hunan Province, China, and found that the impacting force of the deck-to-pier collision was several times greater than the shear capacity of the piers; these findings were verified by field observations. Based on the results, it was suggested that collapse propagation or deck-to-pier collision be prevented using other alternatives <span id='cite-_Ref93700889'></span>[[#_Ref93700889|[8]]]. Seyedkhoei investigated the collapse behavior of regular, semiregular, and irregular bridges under earthquake conditions, and the results indicated that progressive collapse occurs far more easily in regular bridges than in semiregular and irregular bridges due to the effects of the ground slope and different pier heights <span id='cite-_Ref93700895'></span>[[#_Ref93700895|[9]]]. Lin proposed a digital twin-based collapse fragility assessment method for long-span cable-stayed bridges under the condition of strong earthquakes, and accordingly provided valuable information for the lifetime maintenance and management of this type of bridge in engineering practice <span id='cite-_Ref93700901'></span>[[#_Ref93700901|[10]]]. Wang investigated the collapse process and failure mechanism of long-span cable-stayed bridges under strong seismic excitations, and the findings indicated that the piers and main pylons are critical components that contribute to the collapse of cable-stayed bridge structures <span id='cite-_Ref93700908'></span>[[#_Ref93700908|[11]]]. Cao presented a computational forensic investigation of the collapse of the Skagit River Bridge, Mount Vernon, Washington, USA, and found that the bridge could not provide alternative load paths to transfer the dead and live loads after losing one of the upper chords <span id='cite-_Ref93700912'></span>[[#_Ref93700912|[12]]].
+Deterministic methods are used to assess the robustness of structures under different loads via the system strain energy, load-carrying capacity, and structural stiffness. Based on reliability theory, the System Factor Table has been developed for simple and continuous bridges with multi-girders, and the step-by-step calculation procedure is recommended to assess the robustness of bridges with complex systems <span id='cite-_Ref93700844'></span>[[#_Ref93700844|[2]]]. By investigating the collapse behavior of suspension and cable-stayed bridges in cable loss scenarios, Scheller revealed that a dynamic amplification factor of 2.0 is required to meet the safety requirements for cables and pylons; moreover, it was found that a cable-stayed bridge cannot bear simultaneous sudden failure in more than two of its cables <span id='cite-_Ref93700859'></span><span id='cite-_Ref93700863'></span>[[#_Ref93700859|[3,4]]]. To identify various possible collapse modes, Jiang established a topological hierarchy model of the collapsed bridge at Florida International University (FIU), Miami, Florida, USA, using the Improved Structural Vulnerability Theory (ISVT) clustering process. The findings revealed that the maximum vulnerability index of the bridge increased dramatically due to the failure of one of its components <span id='cite-_Ref93700870'></span>[[#_Ref93700870|[5]]]. By investigating the collapse accident of the Heyuan Dongjiang Bridge, Heyuan, Guangdong Province, China, Sun found that the deck-type arch bridge was sensitive to the foundation displacement, and an overlarge foundation displacement may have caused the collapse of the bridge <span id='cite-_Ref93700878'></span>[[#_Ref93700878|[6]]]. To explore the effect of collapse control on a continuous girder bridge, Li considered three collapse control systems, namely the Collapse High Damping Rubber (CHDR), Collapse Fluid Viscous Damper (CFVD), and Collapse Lock-Up Clutch (CLUC) systems, to analyze the respective collapse modes and collapse control strategies <span id='cite-_Ref93700884'></span>[[#_Ref93700884|[7]]]. Khoei numerically simulated the progressive collapse of the Hongqi Bridge, Zhuzhou, Hunan Province, China, and found that the impacting force of the deck-to-pier collision was several times greater than the shear capacity of the piers; these findings were verified by field observations. Based on the results, it was suggested that collapse propagation or deck-to-pier collision be prevented using other alternatives <span id='cite-_Ref93700889'></span>[[#_Ref93700889|[8]]]. Seyedkhoei investigated the collapse behavior of regular, semiregular, and irregular bridges under earthquake conditions, and the results indicated that progressive collapse occurs far more easily in regular bridges than in semiregular and irregular bridges due to the effects of the ground slope and different pier heights <span id='cite-_Ref93700895'></span>[[#_Ref93700895|[9]]]. Lin proposed a digital twin-based collapse fragility assessment method for long-span cable-stayed bridges under the condition of strong earthquakes, and accordingly provided valuable information for the lifetime maintenance and management of this type of bridge in engineering practice <span id='cite-_Ref93700901'></span>[[#_Ref93700901|[10]]]. Wang investigated the collapse process and failure mechanism of long-span cable-stayed bridges under strong seismic excitations, and the findings indicated that the piers and main pylons are critical components that contribute to the collapse of cable-stayed bridge structures <span id='cite-_Ref93700908'></span>[[#_Ref93700908|[11]]]. Cao presented a computational forensic investigation of the collapse of the Skagit River Bridge, Mount Vernon, Washington, USA, and found that the bridge could not provide alternative load paths to transfer the dead and live loads after losing one of the upper chords <span id='cite-_Ref93700912'></span>[[#_Ref93700912|[12]]].
-Based on reliability and probability theory, reliability methods have been developed to assess the redundancy and robustness of bridges subjected to various loads while ensuring the reliability index. To determine the safety of bridge systems, a system reliability framework was constructed to assess the redundancy and robustness of multi-girder bridges under vehicle loads and some abnormal loads, and it was found that the system safety depends on the number of girders, the girder spacing, and the presence of diaphragms <span id='cite-_Ref93700844'></span>[[#_Ref93700844|[2]]]. The indexes of redundancy and robustness have also been expanded to many infrastructure networks to assess system safety, and have revealed that the target index can provide a good balance between safety and cost in infrastructure networks <span id='cite-_Ref93700939'></span>[[#_Ref93700939|[13]]]<span id='cite-_Ref93700942'></span>[[#_Ref93700942|[14]]]. It should be noted that the consequences of bridge collapses can take several forms in the range of structural damage and human injuries to functional downtime and environmental impacts, resulting in huge economic losses and social disasters <span id='cite-_Ref93700948'></span>[[#_Ref93700948|[15]]]. The multi-dimensional and variable aspects of the “cost of failure” have been discussed, and various types of consequences arising from structural failure have been examined <span id='cite-_Ref93700952'></span>[[#_Ref93700952|[16]]]. Based on a statistical analysis of past metallic bridge failures, it has been demonstrated that the decreasing trend of collapses can be attributed to limited knowledge, while there is an increasing trend in failures resulting from accidents and natural hazards <span id='cite-_Ref93700958'></span>[[#_Ref93700958|[17]]]. Moreover, a categorization procedure via which consequences arising from potential bridge failures can be estimated has been developed.
+Based on reliability and probability theory, reliability methods have been developed to assess the redundancy and robustness of bridges subjected to various loads while ensuring the reliability index. To determine the safety of bridge systems, a system reliability framework was constructed to assess the redundancy and robustness of multi-girder bridges under vehicle loads and some abnormal loads, and it was found that the system safety depends on the number of girders, the girder spacing, and the presence of diaphragms <span id='cite-_Ref93700844'></span>[[#_Ref93700844|[2]]]. The indexes of redundancy and robustness have also been expanded to many infrastructure networks to assess system safety, and have revealed that the target index can provide a good balance between safety and cost in infrastructure networks <span id='cite-_Ref93700939'></span><span id='cite-_Ref93700942'></span>[[#_Ref93700939|[13,14]]]. It should be noted that the consequences of bridge collapses can take several forms in the range of structural damage and human injuries to functional downtime and environmental impacts, resulting in huge economic losses and social disasters <span id='cite-_Ref93700948'></span>[[#_Ref93700948|[15]]]. The multi-dimensional and variable aspects of the “cost of failure” have been discussed, and various types of consequences arising from structural failure have been examined <span id='cite-_Ref93700952'></span>[[#_Ref93700952|[16]]]. Based on a statistical analysis of past metallic bridge failures, it has been demonstrated that the decreasing trend of collapses can be attributed to limited knowledge, while there is an increasing trend in failures resulting from accidents and natural hazards <span id='cite-_Ref93700958'></span>[[#_Ref93700958|[17]]]. Moreover, a categorization procedure via which consequences arising from potential bridge failures can be estimated has been developed.
 Many significant methodologies have been developed for the assessment of structural robustness, and promising results have been obtained; however, more research must be conducted to propose more methodologies applicable to long-span bridges, such as arch bridges and cable-stayed bridges. In this study, an approach adopting the radar chart is proposed to assess the robustness of the cable force of a double-pylon cable-stayed bridge with a steel truss girder. Via this approach, plans are developed to optimize the robustness of this bridge, and reflect the response of loads to transfer along alternative paths.

@@ Line 765: / Line 765: @@
 # Alternative cable plans AC1 and AC2 were designed to effectively decrease the cable forces, and the maximum reductions were respectively 30.1% and 34.3%. The forces in the long cables in AC2 were larger than those in AC1 with a maximum value of 9.4%. Similarly, with a maximum reduction of 28.2% in the main span, both plans were found to decrease the vertical displacement of the truss girder under gravity, and the reduction of AC1 was slightly larger than that of AC2.
 # For the truss without sufficient load transfer paths, the loss of chords was found to decrease the values of ''I<sub>TTSRF</sub>'' and ''I<sub>TCSRF</sub>''; in the scenario of the loss of chords A29-A30, these values were sharply decreased from 0.78 and 0.74 to 0.55 and 0.50, respectively. Consequently, the value of ''I<sub>Rob</sub>'' decreased from 0.75 to 0.66. By adding more transfer paths for absorbed loads, the two alternative load path plans increased the values of ''I<sub>TTSRF</sub>'' and ''I<sub>TCSRF</sub>'' of the truss girder to 0.67 and 0.71, respectively, leading to the increase in the value of ''I<sub>Rob</sub>'' to 0.74.
 #Due to the existing load paths of cables, the cable loss scenarios were found to reduce the values of ''I<sub>TTSRF</sub>'' and'' I<sub>TCSRF</sub>'', but not as effectively as the chord loss scenarios. In the scenario of the loss of cable M13, the values of ''I<sub>TTSRF</sub>'' and'' I<sub>TCSRF</sub>'' decreased from 0.78 and 0.74 to 0.75 and 0.73, respectively, and the value of ''I<sub>TCSRF</sub>'' decreased from 0.91 to 0.9. The two alternative cable plans increased the value of ''I<sub>TCSRF</sub>'' to 0.76 and 0.77, respectively, and the value of ''I<sub>TCSRF</sub>'' was increased to 0.92; these values were larger than the corresponding values of the intact cable-stayed bridge.

@@ Line 601: / Line 601: @@
 Compared with chord losses, due to the surplus alternative load paths in adjacent cables, cable losses only affect the values of <math>I_{TTSRF}</math>, <math>I_{TCSRF}</math>, and <math>I_{CSRF}</math>. In addition, other indexes, including <math>I_{PCSRF}</math>, <math>I_{DRF}</math>, and <math>I_{Rob}</math>, are not changed by the failures of cables, whereas the two alternative cable plans increased the values of these indexes to be larger than those of an intact bridge.
 By decreasing the longitudinal force in the truss girder, the loss of cable S9 decreased the values of <math>I_{TTSRF}</math> and <math>I_{TCSRF}</math> from 0.78 and 0.74 to 0.77 and 0.73, respectively, and the value of <math>I_{CSRF}</math> was slightly reduced from 0.91 to 0.90, as illustrated in [[#img-16|Figure 16]]. Regarding the truss girder and cables, AC1 increased the values of the three indexes to 0.79, 0.77, and 0.92, respectively, which were all larger than the corresponding values of the intact bridge. Similarly, AC2 increased the three values of the three indexes to 0.80, 0.77, and 0.93, respectively, which were all larger than the corresponding values of the intact bridge. Consequently, the two plans effectively increased the value of <math>I_{Rob}</math> from 0.75 to 0.77, which was also larger than the corresponding value of the intact bridge.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='img-16'></div>
- [[Image:Zheng_et_al_2021b_4438_test-image29-c.png|474px]] </div>
+{| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 Similarly, the loss of cable M8 decreased the value of <math>I_{TCSRF}</math> from 0.74 to 0.73, and the value of <math>I_{CSRF}</math> decreased from 0.91 to 0.89, as illustrated in [[#img-17|Figure 17]]. Regarding the truss girder and cables, AC1 increased the values of the three indexes to 0.81, 0.77, and 0.92, respectively, which were all larger than the corresponding values of the intact bridge. Moreover, AC3 increased the values of the three indexes to 0.80, 0.78, and 0.92, respectively, which were all larger than the corresponding values of the intact bridge.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='img-17'></div>
- [[Image:Zheng_et_al_2021b_4810_test-image30-c.png|474px]] </div>
+{| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
-By decreasing the longitudinal force in the truss girder, the loss of the long cable M13 decreased the values of ''I<sub>TTSRF</sub>'', ''I<sub>TCSRF</sub>'', and ''I<sub>CSRF</sub>'' from 0.78, 0.74, and 0.91 to 0.75, 0.73, and 0.90, respectively, and the value of ''I<sub>Rob</sub>'' was decreased from 0.75 to 0.74, as illustrated in Fig. 18. Regarding the truss girder and cables, AC1 increased the values of the three indexes to 0.78, 0.76, and 0.92, respectively, two of which were larger than the corresponding values of the intact bridge. Similarly, AC2 increased the values of the three indexes to 0.74, 0.77, and 0.92, respectively, two of which were larger than the corresponding values of the intact bridge. The values of these indexes and the radar charts regarding the cable loss scenarios are reported in Table 5.
+By decreasing the longitudinal force in the truss girder, the loss of the long cable M13 decreased the values of <math>I_{TTSRF}</math>, <math>I_{TCSRF}</math>, and <math>I_{CSRF}</math> from 0.78, 0.74, and 0.91 to 0.75, 0.73, and 0.90, respectively, and the value of <math>I_{Rob}</math> was decreased from 0.75 to 0.74, as illustrated in [[#img-18|Figure 18]]. Regarding the truss girder and cables, AC1 increased the values of the three indexes to 0.78, 0.76, and 0.92, respectively, two of which were larger than the corresponding values of the intact bridge. Similarly, AC2 increased the values of the three indexes to 0.74, 0.77, and 0.92, respectively, two of which were larger than the corresponding values of the intact bridge. The values of these indexes and the radar charts regarding the cable loss scenarios are reported in [[#tab-5|Table 5]].
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
@@ Line 669: / Line 678: @@
 |  style="text-align: center;"|0.87
 |-
-|  style="border-bottom: 1pt solid black;text-align: center;"|''I<sub>Rob</sub>''
+|  style="border-bottom: 1pt solid black;text-align: center;"|<math>I_{Rob}</math>
 |  style="border-bottom: 1pt solid black;text-align: center;"|0.75
 |  style="border-bottom: 1pt solid black;text-align: center;"|0.75
@@ Line 706: / Line 715: @@
 |  style="text-align: center;"|0.87
 |-
-|  style="border-bottom: 2pt solid black;text-align: center;"|''I<sub>Rob</sub>''
+|  style="border-bottom: 2pt solid black;text-align: center;"|<math>I_{Rob}</math>
 |  style="border-bottom: 2pt solid black;text-align: center;"|0.75
 |  style="border-bottom: 2pt solid black;text-align: center;"|0.75
@@ Line 743: / Line 752: @@
 |  style="text-align: center;"|0.87
 |-
-|  style="border-bottom: 2pt solid black;text-align: center;"|''I<sub>Rob</sub>''
+|  style="border-bottom: 2pt solid black;text-align: center;"|<math>I_{Rob}</math>
 |  style="border-bottom: 2pt solid black;text-align: center;"|0.75
 |  style="border-bottom: 2pt solid black;text-align: center;"|0.74

@@ Line 359: / Line 359: @@
 |  style="text-align: center;font-size: 75%;"|(b) Vertical displacement of the truss girder
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" style="padding:10px;"| '''Figure 10'''. Cable forces and vertical displacement of the truss girder in the scenario of the loss of cable M8
+| colspan="2" style="padding:10px;"| '''Figure 11'''. Cable forces and vertical displacement of the truss girder in the scenario of the loss of cable M8
 |}
@@ Line 392: / Line 392: @@
 |  style="text-align: center;"|17.5%
 |}
 ==5. Assessment of the robustness of the cable-stayed bridge==