Rapid heat-activated post-tensioning of damaged reinforced concrete girders with unbonded near-surface mounted (NSM) NiTiNb shape-memory alloy wires

Abstract

Concrete girders can suffer from serviceability issues due to excessive cracking and deflection. In response to this problem, a novel heat-induced post-tensioning technique utilizing unbonded near-surface mounted nickel–titanium–niobium (NiTiNb) shape-memory alloy (SMA) wires was proposed and evaluated. SMAs are a class of smart materials that can recover seemingly permanent plastic deformation when heated. The post-tensioning forces, thus, can be generated by restrained heat-induced shape recovery of SMA wires. Material characterization tests showed that 3.92-mm diameter NiTiNb wires with 2.5% prestrain can generate recovery stress of approximately 500 MPa when actuated via Ohmic heating in a restrained condition. The proposed post-tensioning system was experimentally evaluated in reinforced concrete girders measuring 2.3 m in length and 23 × 41 cm in cross-sectional dimensions. The girders were initially cracked to simulate typical girder damage. NiTiNb wires were then installed in the bottom cover of the girders and anchored at both ends. Subsequently, the wires were actuated via Ohmic heating, which triggered shape-recovery and generated post-tensioning stresses in the girder. The post-tensioning technique reduced the crack widths by up to 74% (370 μm) and recovered the residual midspan deflection by up to 49% (1.52 mm) in the cracked girders. Following post-tensioning, flexural loading up to failure showed that the cracked stiffness and ultimate moment capacity of the girders had increased by up to 31% and 45%, respectively, with a relatively small NiTiNb reinforcement ratio of up to 0.17%.

1 Introduction

Structural components, carrying flexural stresses, can suffer from serviceability issues due to excessive cracking and deflection. Traditional post-tensioning techniques used to repair such damage utilizing steel [1] and fiber-reinforced polymer (FRP) composite tendons [2] require heavy hydraulic jacking equipment and intricate anchorage which results in long construction times with implications to structure’s functionality. To overcome the shortcomings of the traditional post-tensioning techniques, a novel post-tensioning technique using unbonded near-surface mounted (NSM) nickel–titanium–niobium (NiTiNb) shape-memory alloy (SMA) wires is proposed and evaluated in this study.

SMAs are a class of alloys that can recover significant and seemingly plastic deformation by a phenomenon called shape-memory effect (SME) when an external stimulus (e.g., heat) is applied. SMAs have two material phases depending on their crystalline structure: (1) the high-temperature and high-stiffness phase—austenite (cubic crystalline structure), and (2) low-temperature and low-stiffness phase—martensite (tetragonal, orthorhombic, or monoclinic crystalline structure). The transformation from martensite to austenite starts when the SMA is heated through the austenite start temperature (A_s) and is completed at the austenite finish temperature (A_f). The martensite phase can further have two variations: (1) twinned martensite (in which crystals are oriented in varying directions), and (2) detwinned martensite (in which one crystal orientation is dominant). The transformation from twinned to detwinned martensite is accomplished by the application of external stress. The detwinning process is initiated at the detwinning start stress ($\sigma_{\text{s}}$), and completed at the detwinning finish stress ($\sigma_{\text{f}}$) (Fig. 1a). The detwinned configuration is retained upon subsequent unloading and results in some seemingly plastic deformation (prestrain) in the SMA. Heating the detwinned martensite above $A_{\text{f}}$ will result in the recovery of the plastic deformation (shape-recovery) through transformation to austenite (Fig. 1). Cooling the material below martensitic start temperature ($M_{\text{s}}$) and beyond martensitic finish temperature ($M_{\text{f}}$) transforms the SMA from austenite to martensite phase [3].

Fig. 1

Reused with permission from [3]

Thermomechanical behavior of SMA during: a shape-recovery; and b superelastic behavior.

The restrained shape-recovery of SMA leads to the generation of recovery stress which can be transferred as upward corrective forces to achieve a reduction in crack-widths and residual midspan deflections in damaged RC girders. For the post-tensioning to be successful, the A_s must be higher than the maximum service temperature so the SMA does not accidentally transform to austenite phase during transportation and installation. Conversely, the M_s should be lower than the minimum service temperature so that the reverse transformation from austenite to martensite does not occur (resulting in loss of prestress). The SMA can be tailored by altering the molar ratio of the alloying elements so that the difference between the M_s and A_s (also known as thermal hysteresis range) is sufficiently wide to encompass the temperatures temperature range typical for interior and exterior applications.

Another property of the SMA is superelasticity by which the SMA can undergo shape-recovery in its austenite state when a sufficiently large stress is applied. This behavior occurs by the transformation to detwinned martensite starting at detwinning start stress ($\sigma^{{M_{\text{s}} }}$) and completing at the detwinning finish stress ($\sigma^{{M_{\text{f}} }}$). Complete shape-recovery occurs when the stress is removed and the SMA transforms to austenite starting at a stress of austenite start stress ($\sigma^{{A_{\text{s}} }}$) and completing at a stress of austenite finish stress ($\sigma^{{A_{\text{f}} }}$) (Fig. 1b) [3].

Limited prior research evaluated the potential of SMAs as post-tensioned reinforcement in concrete structures. One of the earliest attempts to implement SMAs in repair applications was by Soroushian et al. [4] who applied externally installed iron-based SMA (Fe-SMA) rods to repair shear cracks in bridge girders by heat-induced post-tensioning. The shear crack widths were reduced by up to 40% following force transfer; however, the authors noted a 32% post-tensioning loss due to slip at the anchorage. Multiple studies also evaluated nickel–titanium (NiTi) SMAs as flexural reinforcement. The ability to successfully transfer prestress from heated NiTi wires in beams was shown through camber measurements on small beam specimens (45–50 cm long) [5, 6]. In these experiments, the resistance of NiTi wires was found to change with the stress in wires, demonstrating potential of SMAs to be used as a structural health monitoring sensor [6]. Ozbulut et al. [7] attempted activating post-tensioning by NiTiNb SMA with the heat of hydration of cementitious grouts. Although the proposed “self-post-tensioning” concept would eliminate the need for external actuation or jacking, the heat of hydration of the grouts was not sufficient to induce complete shape-recovery. The NiTiNb SMA wires failed to generate the maximum recovery stress due to incomplete transformation of martensite to austenite.

Czaderski et al. [8] demonstrated the feasibility of using a less expensive Fe-based SMA strips (in place of NiTi wires) in prestressing and strengthening of concrete structures. The Fe-SMA were deemed suitable for post-tensioning applications; however, the strips generated 36% less recovery stress than NiTi SMAs. Subsequently, prestressing of reinforced concrete (RC) beams using NSM Fe-SMA strips and ribbed bars were also studied [9,10,11]. Strengthening with Fe-SMA was proven to be effective and resulted in an increase of the flexural load-carrying capacity of up to 226% over the non-prestressed beams. Thermomechanical characterization of the Fe-SMA also revealed a relatively low relaxation of 10% over a period of 1000 h, rendering Fe-SMAs highly suitable for strengthening applications [12].

NiTi SMAs were previously used mainly as primary reinforcement to post-tension undamaged girders. No studies have evaluated unbonded NiTiNb SMAs as supplementary reinforcement in damaged or deteriorated RC beams under flexural loading. The current research addresses the gap in knowledge by providing an insight into the post-tensioning of damaged girders using unbonded NiTiNb SMA wires. The novelty of the post-tensioning technique discussed in this paper is that the procedure can be carried out using relatively simpler equipment like heat sources (Ohmic heating, open-flame torch, or infra-red heating) over traditional hydraulic jacking equipment with significantly reduced construction time. The use of simple equipment also makes this technique an attractive option for situations that involve space constraints and difficulty of access. The SMA wires are maintained unbonded and exposed to facilitate inspection and easy access for maintenance. Completely unbonded wires are also easily replaceable. Finally, the effect of added reinforcement on displacement ductility reduction is expected to be less for an unbonded system over bonded. The proposed post-tensioning process can be applied rapidly, and if deemed necessary, even during periodic inspections of structures (e.g., bridges). Moreover, NiTiNb is uniquely suited for unbonded post-tensioning applications given its negligible stress relaxation and high corrosion resistance [13, 14].

2 Materials and methodology

The objective of this study is to experimentally evaluate a rapid heat-induced post-tensioning repair technique on damaged RC girders using unbonded NSM NiTiNb SMA wires through thermo-mechanical characterization of the NiTiNb SMA wires and proof-of-concept experiments on structural-scale RC girders.

2.1 Overview of experimental program

A series of experiments were conducted to verify the feasibility of the proposed post-tensioning procedure. The experimental program consisted of:

• 1. Differential scanning calorimetry (DSC) experiments to characterize the NiTiNb transformation temperatures.

• 2. Restrained recovery tests on NiTiNb wires to measure the maximum recovery stress generated during post-tensioning.

• 3. Tensile tests on NiTiNb wires to evaluate the stress versus strain behavior of the reinforcement under a variety of conditions.

• 4. Post-tensioning tests on damaged (cracked) structural-scale RC girders to observe the reduction in crack widths and residual midspan deflections; and

• 5. Four-point flexural tests on unstrengthened control RC girder and post-tensioned RC girders to evaluate the increase in cracked stiffness, service and ultimate moment capacities of the girders.

2.2 Materials

A ternary NiTiNb SMA was selected for this research over a more common binary NiTi due to the wider thermal hysteresis of the NiTiNb alloy. The greater difference between M_s and A_s makes NiTiNb more suitable for a range of ambient temperatures experienced in outdoor applications. The NiTiNb wires, measuring 2.4 m in length and 3.92 mm in (prestrained) diameter, were prestrained to 2.5% by the manufacturer. The selected wire diameter was the largest that the manufacturer could supply, while the length was limited by manufacturer’s tensioning frame. The wires do not necessarily have to be prestrained by the manufacturer and thus, could be longer. In this study, the prestraining was conducted by the manufacturer to reduce variability. The authors acknowledge the possibility of using multi-strand cables of SMA to increase the cross-sectional area, but that is beyond the scope of the current research. The minimum A_s of the material in the prestrained state was 60 °C and the M_s of the material is well below − 150 °C, as per the manufacturer.

All RC girders were cast at the same time and from the same batch of ready-mix concrete, having cementitious material, sand, coarse aggregate and water in the ratio of 1:2.73:4.04:0.49. The cementitious material consisted of a 3:1 mixture of Type I/II Portland cement and Type C fly ash. The coarse aggregate was a 3.7:1 mixture of grade A gravel and pea gravel. Water reducing admixture and air-entraining admixture were used to improve workability and prevent segregation of the concrete mixture. The ratio of water-to-cementitious material (w/cm) was 0.49. The quantities of the mix were adjusted to account for the moisture content of the aggregates. The 28-day compressive strength of 10 × 20 cm concrete cylinders, conducted according to ASTM C39/C39M-18 [15], was 35 MPa.

The steel bars used in RC girder specimens consisted of: (1) #13 metric (#4 imperial) deformed bars as top and bottom longitudinal reinforcement; and (2) #10 metric (#3 imperial) deformed bars as stirrups. The steel had a yield strength of 475 MPa and ultimate tensile strength of 735 MPa, as reported by the mill.

2.3 Experimental procedures

2.3.1 Differential scanning calorimetry

DSC test specimens were prepared by cutting 100 mg pieces from the 2.5% prestrained wire and placing them 20 µl crucibles. The crucibles were coated with mineral oil to facilitate heat transfer to the specimen. DSC experiments were performed in a nitrogen atmosphere in a Netzch DSC 214 differential scanning calorimeter. The machine was programmed to initially cool the specimen to –60 °C and subsequently heat the specimen to 300 °C at a rate of 10 °C/min. After reaching 300 °C, the specimen was cooled to −60 °C. The temperature and heat flow data were recorded at a 300 Hz acquisition rate.

2.3.2 Restrained recovery tests

Three SMA wires of 28 cm length were prepared. The test specimens were fixed in the grips of a 100-kN MTS universal testing machine (UTM) with 5-cm grip length on each end of the wires with a grip pressure of 3.5 MPa (Fig. 2a). A constant current of 44 A was passed through the specimen until the recovery stress in the wire plateaued. Subsequently, the specimens were cooled down to room temperature (approximately 25 °C) to record any loss in the recovery stress. The specimens were instrumented with Type-K thermocouple probes attached with high-temperature resistant tape to record the temperature. The recovery force was recorded by the load cell of the MTS machine.

Fig. 2

Schematic diagrams of test setup for: a restrained recovery test; and b tensile test

2.3.3 Tensile tests

Twelve 28 cm long SMA wires were cut for tensile testing. Three specimens used for characterization of the tensile properties of austenite were heated in an unrestrained condition above A_f via Ohmic heating by passing a current of approximately 44 A until the temperature of the wire exceeded 150 °C. The heating-initiated shape recovery and consequent transformation from martensite to austenite. Additional three tensile tests were performed on wires that were first subjected to restrained recovery prior to conducting the tensile test to evaluate the effect of recovery stress on the tensile behavior. The remaining six “untransformed” specimens were used to evaluate the effect of additional prestrain (0.003 mm/mm and 0.006 mm/mm) over manufacturer-induced prestrain on the recovery stress and tensile behavior of the wires.

All tensile tests were performed in a 100-kN MTS UTM at a constant displacement rate of 10 mm/min (Fig. 2b). Top and bottom grip length of 5 cm each were maintained in all the specimens with a grip pressure of 3.5 MPa. An enhanced travel axial extensometer of gage length 5 cm was attached to the specimen during the test to collect the strain data.

2.3.4 Post-tensioning and flexural tests on reinforced concrete girders

The proof-of-concept experiments were conducted on structural-scale lightly reinforced concrete girders designed according to ACI 318-14 [16]. The girders measuring 2.3 m in length and 23 × 41 cm in cross-sectional dimensions were reinforced with 3–#13 (#4 imperial) steel bars as tensile reinforcement (reinforcement ratio of 0.52%) and #10 (#3 imperial) bars as stirrups placed at 10 cm on-center (Fig. 3). A clear cover of 6.3 cm was maintained at the bottom of the girders to facilitate NSM installation of the NiTiNb wires. The dimensions of girders were selected to maximize the effective depth of steel for a girder length of 2.3 m. The length of the girders was limited by the maximum length of NiTiNb wires supplied by the manufacturer. The girders to be post-tensioned were first cracked by loading in a four-point flexural test setup to simulate typical damaged girder. Grooves measuring 1 cm in width and 4 cm in depth were introduced in the bottom cover of the cracked girders to accommodate the NiTiNb wires (Fig. 4a). Two 2.4 m long NiTiNb wires were placed in each of the grooves and kept unbonded throughout. The wires were embedded in poly-vinyl chloride (PVC) tubing with an inner diameter of 4.7 mm to ensure debonded condition near the support regions (Fig. 4b) and the grooves were subsequently grouted in the support regions to provide an adequate bearing surface for the girders (Fig. 4c). The wires were anchored at girder ends with strand chucks (Fig. 4d). The strand chucks were selected due to them being part of standard practice in pretensioning and post-tensioning construction, a relatively low cost, and widespread availability.

Fig. 3

Details of the RC girder specimen: a elevation view; and b cross-section

Fig. 4

RC girder specimen showing: a grooves in the cover region; b PVC tubes to ensure debonding at supports; c grouted support with steel bearing plates and NiTiNb wires; and d strand chuck anchorage

The number of NiTiNb wires used for post-tensioning was a test variable. RC girders subject to post-tensioning were named 8-SMA, 10-SMA, and 12-SMA according to the number of wires used to post-tension the girders corresponding to the NiTiNb reinforcement ratios of 0.11%, 0.14% and 0.17%, respectively. The maximum number of NiTiNb wires used for post-tensioning was determined by ensuring that analytically computed maximum tensile stress generated during post-tensioning at the top concrete fiber (assuming cracked section) does not exceed the tensile strength of concrete.

Three RC girders, to be post-tensioned, were cracked by loading in stages in a four-point flexural setup to develop cracks and residual midspan deflection, thus simulating typical girder damage. The maximum moment during cracking the girders was higher than the maximum service moment. The rationale behind choosing the loading moment was to introduce significant cracks and residual midspan deflection so that the effects of post-tensioning would be clearly visible. One layer of SMA wires was placed in the girders during cracking in an unanchored and unbonded condition to prevent them from being strained during preloading. The sides of the RC girders were denoted as follows: the side of the girder facing negative z-direction in Fig. 5a is denoted as side 1 and the side facing positive z-direction denoted as side 2. Subsequently, NiTiNb wires were anchored against a steel  plates for bearing support (Fig. 4c), and heated by passing current using a 3000 W switching direct current (DC) power source until the temperature increased above 150 °C and the wires underwent complete shape-recovery. Each groove contained two NiTiNb wires which were numbered in an ascending order starting from side 1 and proceeding in a clockwise direction (Fig. 5b). The sequence of heating was as follows: (1) wires numbered 1, 2, 3 and 4 were heated together; (2) the remaining wires were heated individually by insulating them from the steel bearing plate with a heat-resistant insulating tape. The power source used to heat the wires was not large enough to heat more than four wires simultaneously. The above-mentioned heating sequence was followed to maintain symmetrical application of post-tensioning force. The two largest cracks on each girder, within the constant moment region, were instrumented with linear voltage displacement transducers (LVDT) to monitor the change in crack widths (Crack1, Crack 2) during post-tensioning. The NiTiNb wires were instrumented with K-type thermocouples to measure the change in temperature of wires. The thermocouples were denoted as T1, T2, T3, etc., where the numeric part indicates the wire number they were attached to. The change in residual midspan deflection (MD1 and MD2) was tracked with two LVDTs. The strain in the top fiber of concrete (SG1 and SG2) on both sides of the girder were measured using strain gages. Positions of LVDTs and strain gages along with the wire numbering are shown in Fig. 5.

Fig. 5

Flexural test setup on RC girder: a elevation view; and b end view

Following post-tensioning, each of the girders was loaded in stages in a four-point bending test setup until the concrete crushing in compression (Fig. 5). The support deflections (SD1 and SD2), were measured during the four-point bending test. The load was applied using an actuator driven by a hydraulic pump and distributed over two point loads with an American Institute of Steel Construction (AISC) W8 × 25 spreader beam. The control girder without NiTiNb reinforcement was first loaded in stages up to failure to serve as a baseline for comparing the yield moment and ultimate moment capacity of the post-tensioned girders. The load and midspan deflection were recorded throughout the test.

3 Results and discussion

3.1 Differential scanning calorimetry

DSC results (Fig. 6) indicated that transformation from martensite to austenite is initiated at A_s= 56 °C and finished at A_f = 99 °C as indicated by sharp changes in the slope of DSC curves during heating cycle. During the cooling cycle, no significant changes in the slope of the DSC curves were observed indicating that M_s of the NiTiNb wire is below −30 °C. Hence, the DSC tests confirm the suitability of the NiTiNb alloy for a wide range of service temperatures and climates.

Fig. 6

DSC heat flow versus temperature of NiTiNb

3.2 Restrained recovery tests

Figure 7 shows representative data from the retrained recovery tests. Recovery stress was generated in the restrained NiTiNb wire as the temperature was increased by passing a constant current of 44 A through the specimen. The maximum recovery stress, of approximately 500 MPa is generated as the temperature reaches 150 °C and remains constant beyond that temperature. Once each wire reached at least 180 °C, the power source was turned off and wires were allowed to cool down to ambient temperature (23−25 °C) to determine the residual recovery stress. At room temperature, each wire retained approximately 92% of the maximum recovery stress, or 460 MPa.

Fig. 7

Variation of recovery stress with temperature

3.3 Tensile tests

The typical stress versus strain curve (Fig. 8) of the austenite NiTiNb wire exhibit a nearly linear response characterized by an initial modulus of elasticity of approximately 69 GPa before the material undergoes transformation to detwinned martensite. The transformation started at approximately 580 MPa and was completed at approximately 620 MPa. As expected, the detwinned martensite demonstrates lower modulus of elasticity than austenite. The test ended with the rupture of the wire at approximately 1030 MPa. The average strain at rupture was found to be approximately 35%. The results from all three specimens displayed excellent repeatability.

Fig. 8

Stress versus strain curve of NiTiNb wire

The SMA wire showed significant changes in the mechanical properties when subjected to restrained recovery before the tensile test (Fig. 8). The initial elastic modulus of the NiTiNb wires was approximately 56 GPa before the detwinning stress is reached. The SMA wire experienced an approximately 23% increase in the detwinning stress (up to approximately 700 MPa) shape-recovery in a restrained condition over unrestrained austenite. The ultimate tensile strength is of these wires was approximately the same as that of austenite (1005 MPa), but the ultimate strain in the SMA wire subject to restrained recovery is lower because the wire had some residual stress (about 460 MPa) and zero strain at the beginning of the tensile test.

The recovery stress increased linearly by up to 13% with the application of 0.006 mm/mm prestrain before restrained shape-recovery (Fig. 9) which is in agreement with the previous research [17]. The stress versus strain response after the recovery of samples subjected to additional prestrain shows that the material stiffness and detwinning stress continue to increase over that of unprestrained samples to up to 731 MPa (Fig. 8). Additional prestrain in the wires resulted in the reduction of ultimate tensile strength and ultimate strain when compared to the unprestrained specimens.

Fig. 9

Variation of recovery stress with prestrain

3.4 Post-tensioning of reinforced concrete girders

The girders, to be post-tensioned, were loaded in stages until significant cracks and residual midspan deflection developed to simulate typical girder damage. Summary of the preloading moment (M_pre) is provided in Table 1.

Table 1 Summary of post-tensioning test results

Following cracking, the girders were post-tensioned by heating the NiTiNb wires above 150 °C. Example data collected during post-tensioning for the 12-SMA girder are shown in (Fig. 10). The results from the 12-SMA girder are representative of the results of all the post-tensioning tests. Summary of results of the post-tensioning tests of all the girders is shown in Table 1. It should be noted that the temperature in wire number 12 (T12) was not recorded due to the malfunction of the data acquisition system. The temperature T2, T3, T4 and T11 did not reach 150 °C which implies that the maximum recovery stress may not have been reached in these wires.

Fig. 10

Variation of strain on top of concrete, residual midspan deflection and crack width with temperature of 12-SMA girder

The crack widths continuously decrease during the post-tensioning process (Fig. 10). The restrained shape-recovery of the NiTiNb wires generated a compressive recovery force that was transferred to the concrete via end anchorage resulting in the crack closure. The maximum reduction in crack width ($\Delta w_{\text{cr}}$) was found to be up to 74% in the girder with the highest NiTiNb reinforcement ratio (12-SMA). The final crack width (0.18 mm) conforms to the acceptable crack width limit for structures in dry air or protected by membranes (0.41 mm) and in humid and moist air or surrounded by soil (0.30 mm) as suggested by ACI 224R-01 [18].

The reduction of residual midspan deflection (MD1 and MD2 for side 1 and 2, respectively) is due to the negative moment induced by the post-tensioning forces transferred via end anchorage. The maximum reduction in the residual midspan deflection ($\Delta \delta$) was 49% for 10-SMA. The reason for a greater reduction of residual deflection in 10-SMA over 12-SMA is the lower cracked stiffness and greater residual midspan deflection after cracking in 10-SMA due to the higher loading moment during cracking the 10-SMA.

The compressive stress generated at the bottom of the girders due to post-tensioning led to the development of tensile stresses on top of the girders causing tensile strain ($\varepsilon$) on the top concrete fiber of up to 180 × 10⁻⁶ mm/mm in the 10-SMA girder. During the heating of some of the wires, the tensile strain in the top of concrete was found to reduce on one side of the girder while increasing on the other side. This behavior can be explained by lateral bending during successive shape recovery of NiTiNb wires. Furthermore, imperfections in geometry during casting the girders may have led to a slight asymmetry in the RC girders which would have further amplified these effects.

3.5 Flexural test of post-tensioned reinforced concrete girders

Following post-tensioning, the girders were loaded in stages in a four-point bending setup until each specimen failed in flexure by concrete crushing. The loading stages for cracking were: (1) up to the cracking moment observed in control girder; (2) beyond cracking and below yield moment; and (3) beyond yield and below ultimate moment. The loading stages following post-tensioning were: (1) beyond cracking and below yield moment; (2) above yield moment; (3) above yield and below ultimate moment; and (4) to the ultimate moment capacity. The offset between the unloading deflection and the deflection at the beginning of loading following post-tensioning is due to the camber as a result of the post-tensioning forces. The yield moment (M_y), ultimate moment capacity (M_n) and cracked stiffness of the post-tensioned girders were compared to those of the control girder (Fig. 11). M_y was chosen as the ordinate value corresponding to a significant decrease of the stiffness. The cracked stiffness of the post-tensioned girders was calculated as the secant stiffness of region between the first crack and just before the yield point. All girders failed in flexure by concrete crushing in compression with the exception of 12-SMA girder that experienced failure by crushing at the support (Fig. 12).

Fig. 11

Midspan moment versus midspan deflection of: a control; b 8-SMA; c 10-SMA; and d 12-SMA girder

Fig. 12

12-SMA girder with grooves in the side cover showing: a cracking; and b spalling at support regions

10-SMA girder exhibited a higher yield moment than control and 12-SMA girders during the “cracking” stage (blue line in Fig. 11) which is likely due to the partially bonded condition of a single layer of unanchored SMA wires despite making the best effort to keep SMA unbonded during preloading. The authors suggest trying out alternative tubing materials, with larger diameter and lower friction coefficient, to carry out the debonding of SMA wires.

Moment versus deflection curves clearly indicate up to 52% increase in M_y of the post-tensioned girder over the Control girder. M_n increased by up to 45% due to the additional moment contribution of the NiTiNb wires. The cracked stiffness of the post-tensioned girders was compared to the cracked stiffness of the girder before post-tensioning and was found to increase by up to 31% with the addition of NiTiNb reinforcement. The maximum increase in strength was observed in the 10-SMA girder despite the 12-SMA girder having a higher NiTiNb ratio. This can be attributed to a premature failure of the 12-SMA by concrete crushing at the support; the failure originated from the ungrouted side NSM grooves (Fig. 12). The cracked stiffness of the control girder (16 kN-m/mm) was less than the cracked stiffness of the 8-SMA (17.5 kN-m/mm), 10-SMA (18.5 kN-m/mm) and 12-SMA (18 kN-m/mm) girders. The recovery of deflection after each stage of loading beyond the yield of the 12-SMA girder (about 60%) was greater than in the control girder (53%). This behavior can be accredited to post-tensioning force in NiTiNb and the superelastic property of the austenite NiTiNb SMA by which the post-tensioned girders can recover large deformations. The residual deflection after failure ($\Delta_{\text{r}}$) in the control girder (20 mm) was greater than that observed in 8-SMA (17 mm), 10-SMA (13 mm) and 12-SMA (15 mm). Beyond yield, the control girder develops large residual deflections after unloading due to the inelastic strains in the tensile steel. The ultimate deflections at failure of the post-tensioned girders did not change significantly in comparison with the control girder (Fig. 11).

Deflection at yield ($\Delta_{\text{y}}$) in post-tensioned girders increased with the $M_{\text{pre}}$. This was expected as the state of residual concrete strain (prior to post-tensioning) in compression varied with the applied $M_{\text{pre}}$. However, deflections at ultimate ($\Delta_{ \hbox{max} }$) between control and post-tensioned girders were not significantly different which indicates that addition of small amount of NiTiNb unbonded reinforcement does not significantly affect the displacement capacity of the girders. Girder 12-SMA had a slightly greater $\Delta_{ \hbox{max} }$ than the other three girders which is likely due to the rigid body movement of the test specimen induced by premature failure at the support.

The cracking patterns (as shown in Fig. 13) in the post-tensioned girders were different from the control girder which was clearly displayed in the 12-SMA girder. All girders had well-distributed crack patterns typical for lightly reinforced concrete flexural members. It was noted that the largest crack width upon unloading in the control girder was 5 mm, whereas the largest crack width in the post-tensioned girders was 3.05 mm. The cracks in post-tensioned girders are narrower because of the compressive forces acting on the girders as a result of post-tensioning prior to loading the girders. Another reason for the narrower crack widths in the post-tensioned girders might be the superelastic recovery of the NiTiNb wires. On the other hand, the absence of post-tensioning force prior to loading and significant plastic strain in the steel reinforcement led to formation of wider cracks in the control girder.

Fig. 13

Crack patterns of the RC girders after failure. Numbers indicate applied load in kN

3.6 Effective prestress

The effective prestress in NiTiNb wires during post-tensioning was back-calculated from the experimental data by assuming that the sum of camber caused by the post-tensioning forces and the deflection caused by the self-weight is equal to the reduction in residual midspan deflection recorded from the experimental data:

$$\frac{{P_{\text{sma}} eL^{2} }}{{8E_{\text{c}} I_{\text{eff}} }} - \frac{{5wL^{4} }}{{384E_{\text{c}} I_{\text{eff}} }} = \Delta \delta$$

(1)

where $P_{\text{sma}}$ is the effective prestressing force in the NiTiNb wires after immediate losses, $e$ is the actual measured eccentricity of the NiTiNb wires with respect to the neutral axis, E_c is the modulus of elasticity of concrete, $I_{\text{eff}}$ is the effective moment of inertia of all the girders calculated by considering the reduced girder stiffness obtained from the experimental data, $w$ is the self-weight of the girders assumed to be uniformly distributed, $L$ is the length of the girder, and $\Delta \delta$ is the reduction in the residual midspan deflection after the NiTiNb wires had cooled down and the deflections in the girder had stabilized. The computed $P_{\text{sma}}$ represents effective prestress as it accounts for immediate losses in the post-tensioning stress due to the elastic shortening of concrete, the initial sag of the NiTiNb wires, and slip at the anchorage.

The above approach revealed that the effective prestress in the NiTiNb wires is 340 MPa, 600 MPa and 460 MPa for the 8-SMA, 10-SMA and 12 SMA girders, respectively. Restrained recovery tests on NiTiNb wires have previously indicated that maximum recovery stress of 460 MPa can be generated due to heat-induced restrained recovery. While computed effective prestress in 8-SMA and 12-SMA girders is within a realistic range (< 500 MPa), the effective prestress of the 10-SMA girder appeared to be greater than the maximum recovery stress. This is, of course, not possible—the erroneous estimate of post-tensioning stress might be due to the measurement errors during experiments combined with the underlying assumptions and approximations in Eq. (1). The difference in the post-tensioning stress between the 8-SMA and 10-SMA girders can be attributed to the manual installation of the wires in the girder resulting in different losses due to: (1) variation in sag of the wires; and (2) fluctuating slip at the anchorage due to insufficient bearing when the wires start transforming. Even though herein conducted back-of-the-envelope calculations are rough estimates of the effective prestress they, nonetheless, suggest that the generated post-tensioning force is quite significant. Numerical analysis of the system is necessary to estimate the of the post-tensioning stresses more accurately.

3.7 Stress in SMA at ultimate

The stress at concrete crushing in SMA wires was calculated by considering the equilibrium of the section at ultimate condition under the compressive forces of concrete and the tensile force of the steel and the NiTiNb reinforcement according to:

$$0.85f^{\prime}_{\text{c}} ab = A_{\text{s}} f_{\text{sC}} + A_{\text{ps}} f_{\text{ps}}$$

(2)

where $f^{\prime}_{\text{c}}$ is the compressive strength of concrete, $b$ is the width of the section; $A_{\text{s}}$ is the area of tensile reinforcement; $f_{\text{sC}}$ = 650 MPa is the stress in tensile steel reinforcement at ultimate, assumed not to change between different girders, estimated by conducting classical moment–curvature analysis for control girder; $A_{\text{ps}}$ is the area of NiTiNb reinforcement; and $d_{\text{ps}}$ is the effective depth of the NiTiNb reinforcement.

Since Eq. (2) has two unknowns [i.e. the depth of compressive stress block (a) and the stress in NiTiNb ($f_{\text{ps}}$)], the moment contribution of the NiTiNb wires was also equated to the difference in the moment ($\Delta M$) at ultimate between the control ($M_{\text{C}}$) girder and the corresponding post-tensioned ($M_{\text{pt}}$) girders:

$$A_{\text{ps}} f_{\text{ps}} \left( {d_{\text{ps}} - \frac{a}{2}} \right) = \Delta M$$

(3)

where $\Delta M = M_{\text{pt}} - M_{\text{C}}$ is an approximate contribution of NiTiNb wires to the total moment capacity of post-tensioned girders, $M_{\text{pt}}$. Variables $a$ and $f_{\text{ps}}$ can be computed by simultaneously solving Eqs. (2) and (3).

The stresses in the NiTiNb wires at ultimate were found to be 900 MPa, 830 MPa, and 660 MPa for 8-SMA, 10-SMA and 12-SMA girders, respectively. The descending magnitude of stress in the NiTiNb at the ultimate stage of the experiment is expected as the reinforcement ratio increases. Strain gages could not be placed on the NiTiNb wires because of the difficulties associated with accessing the wires within the grooves after post-tensioning, so the computed stresses could not be verified experimentally. It is suggested that, in future work, specialized high-temperature strain gages be attached to NiTiNb wires prior to the heating cycles to facilitate collection of strain data. While the computed stresses are, at best, rough estimates of the true stresses in the NiTiNb wires, the computed values indicate effective utilization of NiTiNb reinforcement in the repaired girders.

4 Summary and conclusions

Reinforced concrete girders can face serviceability issues due to excessive cracking and deflections. Traditional external post-tensioning techniques for damaged reinforced concrete girders utilize external steel or carbon fiber reinforced polymer (CFRP) composite tendons which involve long construction times, use of heavy hydraulic equipment, and problems with anchorage. A novel repair technique utilizing heat-activated near-surface mounted (NSM) unbonded NiTiNb shape-memory alloy (SMA) wires was evaluated in this work as a means of alleviating the aforementioned problems with traditional post-tensioning techniques. The proposed method relies on the intrinsic ability of the NiTiNb to recover seemingly permanent deformation upon activation via heating. The herein presented study experimentally evaluated the proposed post-tensioning technique.

Materials characterization of NiTiNb wires was conducted to obtain the SMA’s tensile properties, recovery stress potential, and the viable service temperature range. The obtained material properties were used to design structural-scale RC girder specimens which were first precracked to simulate girder damage and, subsequently, post-tensioned and tested to ultimate failure in a four-point bending test setup. The following conclusions can be drawn from the presented work:

• DSC results indicated that austenite start temperature (A_s) is 56 °C, while martensite start temperature (M_s) is below − 30 °C.

• The initial elastic modulus of the NiTiNb wires after restrained recovery is approximately 56 GPa, the detwinning stress is approximately 700 MPa and the ultimate strength is approximately 1005 MPa as observed from the tensile test results. The tensile properties varied significantly due to initial prestrain.

• The restrained recovery test of 2.5%-prestrained NiTiNb wires generated a maximum recovery stress of 500 MPa at 150 °C. Following cooling down to ambient temperature, the wires retained approximately 460 MPa or 92% of the maximum recovery stress.

• Post-tensioning of cracked RC girders was successful as indicated by a reduction in crack widths and residual midspan deflection of up to 74% (370 μm) and 49% (1.52 mm), respectively, and tensile strain of up to 180 × 10⁻⁶ mm/mm in the top concrete fiber within the range of NiTiNb ratio considered in this study (0.11–0.17%).

• A NiTiNb reinforcement ratio of 0.14% resulted in an increase in the ultimate moment capacity and cracked stiffness of the damaged RC girders by 45% and 31% when compared to control RC girder, respectively. Deflection at ultimate was not affected by the small amount of NiTiNb reinforcement used in this study.