Local Stress Behavior of Post-Tensioned Prestressed Anchorage Zones in Continuous Rigid Frame Arch Railway Bridge

Abstract

The concrete stress behavior and cause of cracking at the anchorage zones of top and bottom slabs of a post-tensioned prestressed concrete box beam were studied. Based on the complex stress distribution under local anchor problem for the Yichang Yangtze River Bridge, which is the longest continuous rigid frame arch railway bridge in the world, model tests were conducted. Two full-scale specimens of top and bottom slabs were fabricated and gradually loaded based on principle of equivalent stress. The goal was to analyze the longitudinal and transverse stress distributions of cross sections of specimens at various loading cases during the experiment. From the experimental results, it can be concluded that the mechanical behavior of the concrete and steel bars were in good agreement when prestressed tendons were loaded. Tensile stress of concrete in prestressed anchorage zone gradually increased and surpassed the ultimate tensile strength of concrete with the increasing load. Consequently, local longitudinal cracking was formed at the anchorage block. Some recommendations to avoid the concrete at the anchorage zone continuing to crack are summarized in this paper.

1. Introduction

Post-tensioning techniques have been widely applied to design bridge piers and decks, building slabs, and long-span girders [1]. However, high prestress and concrete creep can generate several issues for designing prestress of concrete bridges. One important issue is cracking in prestressed concrete member, for example, in the construction of continuous rigid frame bridge, the bottom slab of box girder in the main span cracked due to excessive local stress [2,3]. Similarly, a prestressed concrete beam with 40 m span of highway bridge also cracked during the construction [4]. In addition, the vertical and lateral thermal movement of prestressed concrete bridge girders may also cause concrete cracking [5]. Cracking provides a path for penetration of moisture and salts, thus presents a potential corrosion and frost damage threat. Moreover, concrete at the anchorage zone of the prestressed concrete member is easier to crack. Based on the above analysis, we can see that several prestressed concrete bridges and buildings have experienced severe cracking along the tendon path when prestress force has been transferred in the anchorage zone [6]. Consequently, one of the most critical characteristics of post-tensioned prestressed members is stress distribution and cracking in anchorage zone.

Numerous studies on the anchorage zones have been performed using the theory of elasticity, experiments, and finite element analyses. Manisekar and Gou et al. [7,8] studied stress at ultimate in unbonded post tensioning tendons in simply supported concrete. Hassan et al. [9] reported a simple function that can be used to assess post-tensioning cable forces in semi-cable stayed bridge under the action of the dead load. Experimental and analytical studies were conducted by Kwon et al. [10] to develop an efficient anchorage device and to design an equation of the bearing strength in the posttensioning anchorage zone. Ellobody et al. [11] evaluated mechanical behavior of unbonded post-tensioned one-way concrete slabs. They found that the ultimate loads obtained using current codes are conservative for these concrete slabs. Yong et al. [12] carried out a specimen test and 3-D finite-element analysis to study transverse shear force effects on the stress and strain distributions of post-tensioned, rectangular, concrete anchorage blocks. They found that the transverse shear forces on the beams cause a significant reduction in the values of the transverse tensile strains, but have relatively little effect on the lateral tensile strains. Yun et al. [1] estimated the ultimate strength of post-tensioned beams using AASHTO LRFD (American Association of State Highways and Transportation Officials Load and Resistance Factor Design) approximate stress analysis/design method, the critical section concept, and bearing strength equation. Marceau et al. [13] presented a numerical study of a mono-strand anchorage device, and two different representations of the jaw/tendon device, either as two distinct components or as a single equivalent, were examined. A comprehensive experimental and analytical study was conducted by oh et al. [5] to explore characteristics of the local stress distribution and to study the failure mechanism on the anchorage zones of precast prestressed concrete structures. Combined with the measured stress of box girder concrete near the anchor plate, a spatial finite element model was established by Zheng et al. [14] to study the stress distribution in anchorage zone; moreover, the theoretical calculation and measured data were analyzed and compared. Zhou et al. [15] proposed two possible models for longitudinal anti-cracking analysis at the anchor end of post-tensioned concrete voided slab girders. The practical analysis method for longitudinal anti-cracking is established by differential element analysis. Tensile tests for the new strands were carried out with seven different types of mono-strand anchorages by Kim et al. [16] to investigate the tensile behavior of a newly developed uncoated strand according to various types of mono anchorages and appropriate anchorages for both strands were proposed. Considering the deformations due to anchorage slip, Fallah et al. [17] studied the influence of bond slip on the seismic behavior of RC structure using nonlinear dynamic and static pushover analysis. Chen et al. [18] studied the stress distribution and stress transfer mechanism of the cable-to-girder anchorage structure of tensile anchor plate type under the designed load. The results of the test and analysis indicated that the cable-to-girder anchorage structure could meet the requirements of the designed bearing capacity. For existing problems in Near Surface Mounted (NSM) technique, a promising approach for flexural strengthening of RC members, U-wrap end anchorage with carbon fiber reinforced polymer (CFRP) fabrics, was proposed by Hosen et al. [19] to eliminate the concrete cover separation failure. An experimental investigation was presented by Ghasemi et al. [20] to show the flexural behavior of continuous two-span unbonded post-tensioned high strength concrete (HSC) beams, strengthened by end-anchored CFRP laminates of different configurations in the hogging region. Okumus et al. [21] investigated reasons for crack growth in the anchorage zones after detension. In this study, differential cooling, creep, and shrinkage of bulb-tee cross sections are studied as potential reasons of crack growth. Kim and Gou et al. [22,23,24,25,26,27,28,29,30] conducted experiments and comparisons between experimental results and design-equation predictions to determine the effects of steel–fiber and rebar reinforcements on the ultimate bearing strength of the local anchorage zone. The test and the comparisons between the design-equation predictions and the test results showed that the ultimate bearing strength and the section efficiency were highly affected by the reinforcement details and the concrete strength. Through theoretical analysis, numerical simulation and experimental validation, high order longitudinal guided waves (HOLGW) were studied by Pan et al. [31] for damage detection in the anchorage zone of stayed cable.

Although much research has been conducted on anchorage zone, especially the new anchorage devices, ultimate capacity, simulation analysis, etc., there are limited studies on stress transfer and distribution of the anchorage zone of post-tensioned prestressed concrete members, in particular, with full scale specimens being applied in tests. Based on the Yichang Yangtze River Bridge, which is the longest continuous rigid frame arch railway bridge in the world, and the first application of this type of bridge in railway transportation, model tests were conducted. It has spans of 130, 275, 275, and 130 m. It is on the China Yi-Wan Railway Line with a design speed of 175 km/h. The bridge is composed of a prestressed concrete rigid frame with box girders, reinforced concrete piers, and two concrete filled steel tube arches at the two internal spans, as depicted in Figure 1a. Section A-A of the main girder, as illustrated in Figure 1b, was considered due to its thinner top and bottom slabs resulting in remarkable local bearing pressure effect.

For a long-span prestressed concrete continuous rigid frame arch bridge, optimizing arrangement of prestressing tendons in the box beam is a key issue. It is very prone to cracks, affecting the durability and even the normal service due to the relative restricted distance between the prestressed ducts and anchorage device, and the small cross-section of the box beam [3]. In addition, compared with other sections, stress concentration is more serious in the mid-span because of comparatively thinner top and bottom slabs.

The primary objectives of this study were to enrich the experimental data and investigate the detailed local stress distributions of the post-tensioned prestressed anchorage zones in continuous rigid frame arch railway bridge. Two full-scale specimens of the top and bottom slabs were fabricated and gradually loaded based on principle of equivalent stress. The goal was to analyze the longitudinal and transverse stress distributions of the cross-sections of specimens at various loading cases during the experiment. Meanwhile, causes of cracking of the concrete at the anchorage zones were analyzed.

2. Nature of the Anchorage Zone Stress

In the post-tensioned prestressed structure, prestress is transferred by the anchor device and anchor base plate to concrete. According to Principle of Saint Venant [32], the local bearing pressure zone is defined as shown in Figure 2a,b. Load transfer and stress distribution is very complex in this area.

The concrete under anchor base plate is in a triaxial compression stress state due to influence of local bearing pressure effect. For concentrically loaded compression members, the longitudinal stress can exhibit pressure and tension stresses in the anchorage zone, as shown in Figure 2c. The longitudinal compressive stress reaches a plateau in the middle of the stress distribution and gradually decreases away from the center in transverse direction of the cross section at or near the anchorage zone. The stress level gradually decreases, resulting in uniform compressive stress distribution. Consequently, the effect of local bearing pressure progressively weakens, as illustrated in Figure 2d. Tensile stress only appears at the anchorage zone. However, the stress level gradually decreases as the vertical distance from the anchorage zone progressively increases until disappearance.

Moreover, some factors influence the transfer of longitudinal stress such as the cross section of the member, ratio of height to thickness of the member, eccentricity, etc. Thus, it is necessary to study the stress transfer and distribution in the locally stressed areas.

3. Experimental Program

3.1. Specimens

In this research, full-scale top and bottom slabs of Section A-A, as shown Figure 1b, were fabricated due to small height and thinner top and bottom slabs at this section. Figure 3 illustrates specimens of the top and bottom slabs.

To fully simulate the stress distribution in the anchorage zone, reduce the influence of box girder web and reduce the unreasonable local model size on the test, before the test, the overall box girder model and the top and bottom model were established respectively, as shown in the Figure 4.

To determine the reasonable widths of the specimens, a commercial FE package, ANSYS, was used to analyze the stress distribution of the anchorage zones of the top and bottom slabs. Before the test, as shown in Figure 4, compared with the integral box girder model, the stress of the top slab model agreed well with the box girder when the transverse dimension was 1.4 m. The same is true for the bottom slab when the width was 1.6 m, as shown in

Table 1. Comparison of local and overall maximum stress (Unit: MPa).

Stress		Box Girder	Top Slab	Box Girder	Bottom Slab
X direction	Tensile stress	4.52	5.25	2.94	3.32
	Compressive stress	27.9	35.00	8.66	10.00
Y direction	Tensile stress	6.91	4.00	3.06	3.42
	Compressive stress	7.75	12.20	11.9	11.40
Z direction	Tensile stress	1.54	2.20	2.92	3.35
	Compressive stress	38.6	37.5	42.9	39.4

.

Therefore, the top slab was of 1.4 m × 0.4 m cross-section and 6 m in length. The bottom slab had dimensions of 7 m × 1.6 m with variable thickness from 0.35 m to 0.356 m. Figure 5 and Figure 6 show the detailed locations of sections and dimensions for the top and bottom slab specimens, respectively.

3.2. Material Properties

The materials and prestressing tendons used to fabricate the specimens were the same as those used in the real bridge. The top and bottom slabs were cast using concrete with a 28-day compressive strength of 55.3 MPa. Tensile strength was 2.35 MPa. Young’s modulus was 32.5 GPa.

Low-relaxation and high-strength prestressing strand (Ø 15.24 mm) with a tensile strength of 1860 MPa was used. Ø 14 (mm) and Ø 16 (mm) deformed steel bars with a tensile strength of 455 MPa and yield strength of 335 MPa were used for the main steel bars [32]. The stirrups and local reinforcing bars in the slabs were Ø 10 and Ø 16 deformed steel bars; the specific layout is shown in Figure 7. The anchorage devices of the top and bottom slabs were YM15-31 and YM15-19, respectively, as shown in Figure 8. The dimensions of the base plates of the top and bottom slabs were 190 mm × 190 mm and 320 mm × 320 mm, respectively.

3.3. Instrumentation and Testing

In the test, the specimens casted in lab were placed on the base in a simply supported way through the plate rubber bearings, and heading anchor was applied in the dead end. Prestressing force was transferred to concrete by Jack and anchor plate. In addition, to avoid the influence of the weight of the specimen, dead load strains were felt by the concrete prior to strand stressing.

Both the strain of concrete and embedded mild steel reinforcement were measured. Electrical resistive strain gauges were densely deployed on the surface of specimens and the steel bars inside to measure the strain distributions of the girder-arch-pier connections. Figure 9 illustrates the arrangement of the strain gauges in Sections A-A and I-I of the top slab specimen. Figure 10 illustrates the arrangement of the strain gauges in Sections B-B and D-D of the bottom slab specimen. The strain gauges deployed on steel bars were installed before concrete casting. A thin layer of two-part epoxy was applied on the surface of strain gauges for moisture isolation, and then covered by a piece of 3 mm thin foam to isolate the epoxy from the concrete. The strain gauges attached on concrete surface were installed before applying any loading with hydraulic jacks. There were 166 measurement points for concrete and 196 measurement points for steel bars in the top slab specimen.

3.4. Loading Cases and Protocols

ANSYS was used to analyze the carrying capacity of the box girder of this bridge. The equivalent loads which would cause the stress in the critical area to be the ultimate capacity of the tendons or that of the concrete were modeled. The loads on Section A-A of the top and bottom slabs were 6054 kN and 3711 kN, respectively. The specimens were deformed at various loading cases during this experiment. Eight load cases were applied.

Table 2. Loading forces of the specimens (Unit: kN).

Loading Case	10%	20%	40%	60%	70%	80%	90%	100%
Top slab specimen	605	1211	2422	3633	4238	4843	5449	6054
Bottom slab specimen	371	742	1484	2226	2597	2969	3340	3711

illustrates the detailed loading procedures for these two specimens.

4. Results and Discussion

4.1. Stress of the Anchorage Zone at the Top Slab

4.1.1. Stress Distribution of Steel Bars

The steel stresses of Sections A-A through I-I were measured. The steel bars at Sections A-A and I-I were under the tension condition. For the eight loading cases, the linear relationship between the stress and load of Section A-A can be observed in Figure 11.

The stress level of the steel bars at the upper layer was higher than that at the lower layer at Sections A-A and I-I due to the eccentricity of prestressing tendons (approximately 0.1 m). The tensile and compressive stresses at Section A-A were higher than those of Section I-I, which indicates the stress level of tension section is higher than that of anchorage section. The effect of local bearing pressure is more remarkable at tension section.

Test Points 3, 4, 10, and 11 at Section A-A and Test Points 161, 162, 168, and 169 at Section I-I were arranged at the mid-width of these two sections (see Figure 9). This causes their compressive stress levels to be higher than those of other test points under these eight loading cases. This result is a good agreement with principle of Saint Venant, as illustrated in Figure 2d.

The steel stresses at Sections A-A, B-B, and C-C were 295.26, 204.54, and 169.89 MPa, respectively, when the load was equal to the prestressing force of 100%. It can be concluded that the compressive stress level and effect of local bearing pressure at each section were gradually decreased when the distance from the anchorage zone increased along the longitudinal direction of the slabs. Although no stress exceeded the yield strength of reinforcement and the steel bars were in good mechanical performance and elastic condition, the anchorage zone was seriously compressed.

4.1.2. Stress Distribution of Concrete

Cracking was observed at the top surfaces of anchorage block at Sections A-A and I-I during the loading process. With the increase of load, the cracking gradually extended along the longitudinal direction. Cracking was also observed at the surface of concrete at Sections B-B and H-H when the load was equal to the prestressing force of 100%. The transfer path of the local stress inside anchorage block in the anchorage zone increased due to the development of cracks. The concrete was under compression condition at Sections C-C through G-G during the loading process. The stress level at the top surface of the concrete of section was higher than that at the bottom surface of concrete due to the eccentricity of the prestressing tendons.

It can be concluded that the compressive stress level and effect of local bearing pressure at Sections C-C and G-G gradually decreased when the distance from tension and anchorage sections progressively increased along the longitudinal direction of the slabs. The compressive stress gradually extended to the entire section, which caused the stress distribution to gradually become uniform. The stress level at Section E-E was the lowest. The value of stress gradient near the anchorage section was higher when compared with that near the tension section. In the same length scale, the stress dispersion was more remarkable. It can be concluded that the effect of local bearing pressure was more obvious at the tension section.

4.2. Stress of the Anchorage Zone at the Bottom Slab

4.2.1. Stress Distribution of Steel Bars

The steel stresses at Sections A-A through E-E were measured. For the eight loading cases, the top layer and bottom layer steel bars at Sections B-B were under the tension and compression conditions, respectively, due to the eccentricity of the prestressing tendons. All steel bars at Section D-D were under compression condition. The steel stress level at Section B-B was lower than that at Section D-D when the sections were under the same loading case. The linear relationship between the stress and load at Sections B-B and D-D can be observed in Figure 12. Moreover, compared with the yield stress of the steel bars, the maximum is much less than the yield stress. Thus, the steel bars showed good mechanical performance and elastic condition under each loading case.

Because Test Points 203, 205, 204, and 206 at Section B-B were arranged at the mid-width of this section, their compressive stress levels are higher than those of other test points at the same loading case, as shown in Figure 12. This result agrees with principle of Saint Venant, as shown in Figure 2d. It can be seen in Figure 12 that the stress distribution at Section D-D is more uniform than that at Section B-B at these eight loading cases.

The maximum stresses of the bottom layer steel at Sections D-D and E-E was 73.08 and 58.59 MPa, respectively when the load was equal to the prestressing force of 100%. It can be concluded that the compressive stress level and effect of local bearing pressure at each section were gradually decreased when the distance from the anchorage zone increased along the longitudinal direction of the slabs. No stress exceeded the yield strength of reinforcement. The steel bars showed good mechanical performance.

4.2.2. Stress Distribution of Concrete

Concrete stresses at Sections A-A through E-E were measured. Cracking was observed at the top surfaces of anchorage blocks at Sections B-B and C-C during the loading process. No cracking was formed at other sections. The linear relationship between the stress and load were observed. Therefore, the concrete was in good mechanical performance and elastic condition under each loading case.

When the prestressing tendons were tensioned, the top surface of concrete at Section A-A was under tension due to the tie-back actions of ahead anchors [33]. With the increase of prestressing force, the tensile stress was gradually increased. The maximum tensile stress of 1.02 MPa was measured at the top surface of Section A-A when the prestressing load was equal to the prestressing force of 100%. No cracking was formed due to no tensile stress exceeding its limit (2.35 MPa).

Higher tensile stress was formed at the top and lateral surfaces of tooth plate (Test Point 65) at Section B-B. The other test points at this section were under compression at various loading cases. Section C-C was under compression at these loading cases. The stress level at this section was relatively high due to the vertical eccentricity of prestressed ducts. The concrete at the top surface of anchorage block of Section C-C was under higher stress condition than other locations. It can be concluded that the stress concentration near the anchorage zone was very obvious.

The linear relationship between the stress and load were observed at Sections D-D and E-E during various loading cases. Therefore, the concrete showed good mechanical performance and elastic condition under each loading case. The reason for linearity is that the stress increasingly extended to the entire section, because the effect of local bearing pressure progressively decreased when the distance from anchorage section gradually increased. The relationship between concrete stress and load at Section D-D in the bottom slab is illustrated in Figure 13.

The tensile stress that was formed at the area near ahead anchor was relatively small when the triangular anchorage block was applied to the bottom slab of the box beam. No crack was observed at the concrete at this area. However, the tensile stress level that was formed at the top surface of the anchorage block was higher during the tensioning progress, which might make concrete crack. When the distance from anchorage section gradually increased, the tensile stress gradually decreased due to the effect of local bearing pressure.

Based on the analysis above, we can see that both the concrete and reinforcement of the specimens under anchorage was mainly subjected to compression, and the stress was larger. Meanwhile, there was local tensile stress near the anchorage zone, especially on the anchorage block. However, no tensile stress exceeded the limit. When the tensile load gradually increased, excessive local deformation and increasing tensile stress may lead to concrete cracking in anchorage zone. Therefore, excessive deformation caused by concentrated compressive stress under anchorage had a negative effect on concrete in anchorage zone. Moreover, cracking of concrete may be caused, and even the normal service of the component might be affected.

4.3. Cause of Cracking at Anchorage Zone

Cracking of concrete was observed at the anchorage zone of the top and bottom slabs. The first cracking was formed at the concrete of the top surface of Section A-A at tension section when the top slab was loaded until prestressing force of 70% of the equivalent force. With the increase of the load, the cracking width gradually increased. When the load was equal to the equivalent force, crack was observed at the top surface of Section B-B. Finally, the cracking was formed at the top surface of the tooth plate of the top slab between Section A-A and Section C-C. The total length of cracking was 78 cm. The average width was 0.35 mm, as shown in Figure 14a. A crack was observed at the top surface of Section I-I when the load was increased to the prestressing force of 90%. The top surface of Section H-H started to crack when the load was equal to the prestressing force of 100%. The crack had a length of 62 cm and an average width of 0.1 mm. The cracking was also formed at the top surface of the anchorage block.

The two-longitudinal cracks were observed at the top surface of the triangular anchorage block when the bottom slab was loaded until the prestressing force of 80%. They were located at the top surface of Sections B-B and C-C and further extended when the load was equal to the prestressing force of 100%. The crack at Section B-B had a length of 59 cm and an average width of 0.2 mm. The crack at Section C-C extended to the end of the anchorage block. The final crack was 62 cm long and 0.1 mm wide, as illustrated in Figure 14b.

Through the analysis above, we can see that the concrete in the anchorage zone bear a great compressive stress under the large prestressed force. Accordingly, the transverse deformation of compressive concrete (extrusion and expansion) produced. However, influenced by the restraining effect of surrounding concrete, which is similar to the effect of stirrup, free deformation of the compressive concrete cannot be fully produced. Then, transverse tensile stress was formed in the surrounding concrete. With the increase of the load, the deformation and stress gradually increased. When the surrounding tensile stress exceeded the tensile ultimate strength, the local longitudinal crack was formed. Thus, the formation of crack is due to the fact that the deformation of compressed concrete in the anchorage zone is not fully restrained.

5. Conclusions

Based on the above investigations, conclusions can be drawn as follows:

• In the test of the top slab, cracking was formed at Sections A-A and I-I, and the tooth plate. The cracking was observed at the triangular anchorage block and Section C-C when testing the bottom slab. The other sections of the top and bottom slabs showed good mechanical performance and elastic condition during the eight loading cases. Higher local concrete stress level of the anchorage zone was only formed at a small area. The specimens were not destroyed under the equivalent force based on the design of the real bridge, which results in safety and reliability of the two slabs.
• For the eight loading cases, the linear relationship between the stress and load are observed at concrete and steel bars, respectively. It can be concluded that there was a good bond between the concrete and steel bars, which exhibits the entire structure is in a good condition. Consequently, the specimens were safe and reliable.
• The tensile stress of the concrete surrounding the post-tensioned prestressing anchorage zones surpassed the tensile strength of concrete when the deformation of the concrete could not be restrained.
• To avoid the concrete at the anchorage zone continuing to crack, some crack-control recommendations are summarized as follows: Firstly, the connection between tensile anchorage block and the bottom slab should arrange more reinforcing bars with hooks to improve the tensile capacity of this part. Secondly, the stirrups should be designed with closed-loop to increase the restraint of the stirrups. Therefore, they can effectively restrain the central concrete of the anchorage zone.