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STRUCTURAL INTEGRITY ASSESSMENT OF THE CAST STEEL UPPER ANCHORAGE ELEMENTS USED IN A CABLE STAYED BRIDGE
J. Terán-Guillén1, S. Cicero2*, T. García2, J.A. Alvarez2, M. Martínez-Madrid1, J.T. Pérez-Quiroz1. 1
Instituto Mexicano del Transporte
Km. 12 Carretera Querétaro-Galindo, Sanfandila Querétaro, CP 076700. México 2
Universidad de Cantabria.
Dpto. Ciencia e Ingeniería del Terreno y de los Materiales, Universidad de Cantabria, Av Los Castros 44, ETS. Ingenieros de Caminos, 39005, Santander, Cantabria, *corresponding author: e-mail:
[email protected], tlf: +34 942200917
ABSTRACT This paper presents the structural integrity assessment of the cast steel upper anchorage elements of a cable-stayed bridge, which presents numerous fabrication defects. One of the elements failed in 2000. The assessment is performed by using Failure Assessment Diagrams (FADs), includes the effect of residual stresses and considers three different types of defects: postulated surface semi-elliptical cracks (with three different aspect ratios), an existing elliptical embedded crack, and an existing surface semiellipticalcrack. These last two represent two actual defects found in the material. Moreover, two loading hypotheses are also considered: one caused by a 30 year prediction of the ordinary traffic conditions, with a 6% annual increment, and another one caused by the loads produced by the total weight of four heavy trucks crossing the cable-stayed bridge. Material tensile properties were obtained using the ASTM E-8 standard, whereas fracture properties were obtained using the ASTM 1820 standard for both cracked and notched conditions. The results reveal that the anchorage elements work
under safe conditions only if the first hypothesis is considered and no residual stresses are taken into account. In case of the second hypothesis, the conditions are unsafe even for null residual stresses. KEYWORDS: Cable-stayed bridge, anchorage, cast steel, notch, failure assessment diagrams. 1.
INTRODUCTION
The use of cast steels in bridge construction is a common practice which on many occasions entails material heterogeneities derived from the fabrication process, given that if this process is not performed properly, defects such as pores, inclusions, cavities or microstructural deficiencies will appear in the material. This may jeopardise the structural integrity of the cast steel structural component and, eventually, the structural integrity of the whole bridge. In this context, some analyses performed in the Rio Papaloapan bridge, which is a cable-stayed bridge located in the Gulf of Mexico (see Figure 1), have been a matter of scientific and engineering interest, given that one of its 112 upper anchorage elements, connecting the stays to the pillars, failed in 2000. The bridge has two pillars, a main span of 203 m, and 112 cables distributed in 8 semi-harps (14 cables each) (see Figure 2). In [1] it was concluded that the above mentioned failure was caused by the material’s low fracture toughness, derived from an excessively large grain size. Since then, several reports have been completed in order to determine the structural integrity conditions of the bridge. These studies have analysed the presence of defects in the material by using ultrasonic techniques [2], have simulated by finite elements the acting loads in the bridge [3], have applied new techniques for damage detection [4], and have applied probabilistic approaches for the structural integrity assessment of the bridge [5]. The analyses gathered in [2] reported the presence of numerous randomly distributed volumetric defects (pores) in the cast steel of the anchorage elements, which obliged those components presenting the largest defects to be replaced (20 out of 112). However, the cast steel of the remaining anchorage elements still presents significant fabrication defects that generate stress concentrations which may cause structural failures. These defects are non-sharp, so that their structural integrity assessment
should consider that they may not behave as cracks (i.e., the material load-bearing capacity in notched conditions may be significantly higher than in cracked conditions, e.g., [6-10]). Moreover, when performing structural integrity assessments, Failure Assessment Diagrams (FADs) constitute one of the main engineering tools, as they allow fracture-plastic collapse analyses to be performed through the definition of two non-dimensional parameters (Kr and Lr) and the Failure Assessment Line (FAL) [11-16]. The FAD methodology also allows welded components to be analysed and residual stresses to be included in the assessment. Given that the anchorage elements analysed here present defects that may cause fracture-plastic collapse processes, and given that the defects may appear in the vicinity of a welded area (as explained below), the FAD methodology will be used in this paper for the structural integrity assessment of the anchorage elements. Thus, it will be determined whether or not these components work under safe conditions when subjected to different loading hypotheses. With all this, Section 2 presents an overview of the FAD methodology, Section 3 gathers a description of materials and methods, Section 4 develops the results of the experimental programme and the structural integrity assessments, together with the corresponding discussion, and Section 5 summarises the conclusions. 2.
FAILURE ASSESSMENT DIAGRAMS: AN OVERVIEW
For a given structural component containing a crack (e.g., beam, plate, pipe, etc), Failure Assessment Diagrams (FADs) present a simultaneous assessment of both fracture and plastic collapse processes using two normalised parameters, Kr and Lr, whose expressions are equations (1) and (2), respectively, in those situations with primary loading only (e.g., [11-16]):
Kr
Lr
KI K mat P PL
(1)
(2)
P being the applied load, PL being the plastic collapse load, KI being the stress intensity factor, and Kmat being the material fracture resistance measured by the stress intensity factor (e.g., KIC, KJC, KJIc, etc). Lr may also be expressed following equation (3), which is totally equivalent to equation (2) [14]:
Lr
V ref VY
(3)
σref being the reference stress [13,14] and σY being the material yield strength (yield stress or proof strength). Lr evaluates the structural component situation against plastic collapse, and Kr evaluates the component against fracture, the assessed component being represented by a point of coordinates (Kr, Lr). Once the component assessment point is defined through these coordinates, it is necessary to define the component limiting conditions (i.e., those leading to final failure). To this end, the Failure Assessment Line (FAL) is defined, so that if the assessment point is located between the FAL and the coordinate axes, the component is considered to be under safe conditions, whereas if the assessment point is located above the FAL, the component is considered to be under unsafe conditions. The critical situation (failure condition) is that in which the assessment point lies exactly on the FAL. Figure 3 shows an example with the three different possible situations when performing fracture initiation analyses. In any case, the FAL follows expressions which are functions of Lr: Kr
f Lr
(4)
From an engineering point of view, and beyond the origins of the FAD based on the strip yield model, the f(Lr) functions are actually plasticity corrections to the linear-elastic fracture assessment (KI=Kmat), whose exact analytical solution is:
f Lr
Je J
(5)
J being the applied J-integral and Je being its corresponding elastic component [13-15]:
Je
K Ie E´
(6)
E´ is E (the Young modulus) in plane stress conditions and E/(1-ν2) in plane strain conditions (υ is the Poisson ratio). By combining equations (1), (4), (5), and (6), it is straightforward to demonstrate that the FAD methodology is actually providing an elasto-plastic analysis:
J
(7)
J mat
Jmat being the material fracture toughness in elastic-plastic conditions, which extend from purely linear-elastic conditions to situations with noticeable plasticity phenomena. In this sense, the analysis is limited by the cut-off, which corresponds to the load level causing the plastic collapse of the analysed component. This cut-off is defined by the maximum value of Lr (see Lrmax in Figure 3), which depends on the material flow stress (usually the average value of the yield stress and the ultimate tensile strength). In practice, structural integrity assessment procedures (e.g., [13-16]) provide approximate solutions to equation (5), which are defined through the tensile properties of the material. These approximate solutions are generally provided hierarchically, defining different levels of accuracy depending on the available information about the material stress-strain curve.. For instance, [13] defines an Option 0 (Basic) that only requires the yield or proof strength to define the FAL approximation, whereas Option 1 (Standard) requires both the yield or proof strength and the ultimate tensile strength, and Option 3 is defined through the full stress-strain curve (Option 2 in [13] is dedicated to mismatch analysis). As an example, Option 3 (which coincides with Level 2B in [14]) is defined by the following equations:
Kr
§ ¨ ¨ EH r L2rV Y ¨V § EH ¨ r 2¨¨ r ¨ © Vr ©
Kr
0
· ¸ ¸ · ¸¸ ¸¸ ¸ ¹¹
0.5
when Lr≤ Lrmax
(8)
when Lr> Lrmax
(9)
where εr is the material´s true strain obtained from the uniaxial stress-strain curve at a true stress σr of Lr·σY, where σY is the yield or proof strength of the material. Lrmax is defined by:
Lr max
§ V 0.5¨¨1 u © VY
· ¸¸ ¹
(10)
where σu is the ultimate tensile strength. As can be seen above, this definition of the FAL does not depend on the component being analysed (it depends only on the material properties). All the above explained methodology corresponds to a fracture initiation analysis. However, there are many practical applications in which there is considerable stable crack growth before the final failure. In such cases, it is also possible to perform a ductile tearing analysis. The position of the assessment point provides information about the predominant fracture mechanism. Following FITNET FFS [13], failures represented by assessment points above the Kr/Lr = 1.1 line (or in the area defined by Kr/Lr > 1.1) are fracture dominated, whereas failures represented by points located below the Kr/Lr = 0.4 line (Kr/Lr < 0.4) are plastic collapse dominated. In intermediate situations (0.4 < Kr/Lr
