Comparative Study of Three-Dimensional Stress and Crack Imaging in Concrete by Application of Inverse Algorithms to Coda Wave Measurements.

The intrinsic heterogeneity property of concrete causes strong multiple scatterings during wave propagation, forming coda wave that follows very complex trajectories. As a superposition of multiply scattered waves, coda wave shows great sensitivity to subtle changes, but meanwhile lose spatial resolution. To make use of its sensitivity and turn the limitation into advantage, this paper presents an experimental study of three-dimensionally imaging local changes in concrete by application of inverse algorithms to coda wave measurements. Load tests are performed on a large reinforced concrete beam that contains multiple pre-existing millimeter-scale cracks in order to match real life situation. The joint effects of cracks and stresses on coda waves have been monitored using a network of fixed transducers placed at the surface. The global waveform decorrelations and velocity variations are firstly quantified through coda wave interferometry technique. Subsequently, two inverse algorithms are independently applied to map the densities of changes at each localized position. Using this methodology, the stress changes and subtle cracks in the concrete beam are detected and imaged for both temporal and spatial domains.

Crack Detection of FRP-Reinforced Concrete Beam Using Embedded Piezoceramic Smart Aggregates.

In this paper, the authors present a stress wave-based active sensing method to detect the crack in FRP-reinforced concrete beams. The embedded smart aggregates (SAs), which utilize Lead Zirconate Titanate (PZT) as transducers, are employed in this research to generate and sense the stress wave. Three specimens are involved in the experimental program and each is made of concrete, longitudinal distributed reinforcement, steel stirrups, main bar (FRP bar or steel bar), and four SAs. A pair of SAs installed on the lower part of the main bar and the other pair of SAs mounted on the upper part of main bar are utilized to monitor the crack occurrence and development in the three test specimens. The signals received by the SA sensors are analyzed in both time domain and frequency domain. The wavelet packet energy is used to extract damage features. The applied load-vertical displacement curves of mid-span in the specimen are obtained. Experimental results show the test specimens experience crushing failure when the concrete compression exceeds its compressive strength. Increasing the contact area between FRP bar and concrete can effectively improve the cracking load of the FRP-reinforced concrete beam and reduce the cracking speed and depth of FRP-reinforced concrete beam; on the other hand, increasing the elastic modulus of the main bar can slow down the crack development of concrete on the upper side of the main bar and decrease the displacement of reinforced concrete beam during the loading test process. The research results show that the developed piezoceramic-based active sensing method, though low-cost, can monitor the crack-induced damage and estimate the process of damage degree in real-time, and has potentials to provide an early warning of crack occurrence and development for FRP-reinforced concrete beams.

Numerical Sensing of Plastic Hinge Regions in Concrete Beams with Hybrid (FRP and Steel) Bars.

Fibre-reinforced polymer (FRP)-reinforced concrete members exhibit low ductility due to the linear-elastic behaviour of FRP materials. Concrete members reinforced by hybrid FRP⁻steel bars can improve strength and ductility simultaneously. In this study, the plastic hinge problem of hybrid FRP⁻steel reinforced concrete beams was numerically assessed through finite element analysis (FEA). Firstly, a finite element model was proposed to validate the numerical method by comparing the simulation results with the test results. Then, three plastic hinge regions-the rebar yielding zone, concrete crushing zone, and curvature localisation zone-of the hybrid reinforced concrete beams were analysed in detail. Finally, the effects of the main parameters, including the beam aspect ratio, concrete grade, steel yield strength, steel reinforcement ratio, steel hardening modulus, and FRP elastic modulus on the lengths of the three plastic zones, were systematically evaluated through parametric studies. It is determined that the hybrid reinforcement ratio exerts a significant effect on the plastic hinge lengths. The larger the hybrid reinforcement ratio, the larger is the extent of the rebar yielding zone and curvature localisation zone. It is also determined that the beam aspect ratio, concrete compressive strength, and steel hardening ratio exert significant positive effects on the length of the rebar yielding zone.

Experimental Study on Residual Bending Strength of Corroded Reinforced Concrete Beam Based on Micromagnetic Sensor.

This paper presents a nondestructive test method to evaluate the residual bending strength of corroded reinforced concrete beam by analyzing the self-magnetic flux leakage (SMFL) signals. The automatic scanning device was equipped with a micromagnetic sensor and sensor-based experimental details were introduced. Next, the theoretical formula of the normal component HS(z) of the SMFL signal that originated from the corroded region was derived based on the magnetic dipole model and the experimental results were discussed. The results indicate that the experimental data of HS(z) are consistent with the theoretical calculations, both location and extent of the steel bars corrosion can be qualitatively determined by using HS(z). The gradient K of HS(z) is approximately linearly related to the loss rate, S, of the bending strength, which can be used to evaluate the residual bending strength of the corroded reinforced concrete beam. This work lays the foundation for evaluating the residual bending strength of corroded reinforced concrete beams using the SMFL signal; the micromagnetic sensor is further applied to the civil engineering.

Modeling Heat and Moisture Transport in Steam-Cured Mortar: Application to Aashto Type Vi Beams.

During steam curing of concrete, temperature and moisture gradients are developed, which are difficult to measure experimentally and can adversely affect the durability of concrete. In this research, a model of cement hydration coupled to moisture and heat transport was used to simulate the process of steam curing of mortars with water-to-cement (w/c) ratios by mass of 0.30 and 0.45, considering natural convection boundary conditions in mortar and concrete specimens of AASHTO Type VI beams. The primary variables of the model were moisture content, temperature, and degree of hydration. Moisture content profiles of mortar specimens (40 mm in diameter and 50 mm in height) were measured by magnetic resonance imaging. The degree of hydration was obtained by mass-based measurements of loss on ignition to 1000 °C. The results indicate that the model correctly simulates the moisture distribution and degree of hydration in mortar specimens. Application of the model to the steam curing of an AASHTO Type VI beam indicates temperature differences (between the surface and the center) higher than 20 °C during the cooling stage, and internal temperatures higher than 70 °C that may compromise the durability of the concrete.

Tapered Polymer Fiber Sensors for Reinforced Concrete Beam Vibration Detection.

In this study, tapered polymer fiber sensors (TPFSs) have been employed to detect the vibration of a reinforced concrete beam (RC beam). The sensing principle was based on transmission modes theory. The natural frequency of an RC beam was theoretically analyzed. Experiments were carried out with sensors mounted on the surface or embedded in the RC beam. Vibration detection results agreed well with Kistler accelerometers. The experimental results found that both the accelerometer and TPFS detected the natural frequency function of a vibrated RC beam well. The mode shapes of the RC beam were also found by using the TPFSs. The proposed vibration detection method provides a cost-comparable solution for a structural health monitoring (SHM) system in civil engineering.

A review on experimental observation on structural performance of bamboo reinforced concrete beam.

Bamboo has many usages. Incorporating bamboo enhances the reinforced concrete beam's (RCB) performance, properties and behaviour as internal reinforcement. A summary of how bamboo influences the RCB properties shall be studied. This review paper discusses the use of bamboo to reinforce RCB and briefly describes the topic. Previous experimental observation results showed that RCB constructed with bamboo significantly improved the flexural, stress-strain, load-deflection, failure mode, crack pattern, tensile, compression, and shear modulus of RCB. Since this bamboo has superior strength, force, mounting and anchoring properties, it can be used as an alternate interior reinforcement, replacing normal steel reinforcing bars in RCB. The structural behaviour and performance of RCB can be enhanced by utilising bamboo in civil and structural engineering, especially in building construction projects.

Influence of ceramic waste powder on shear performance of environmentally friendly reinforced concrete beams.

This investigation considered the usability of ceramic waste powder (CWP) in altered quantities in reinforced concrete beams (RCBs). In this way, it was aimed to reduce the environmental impacts of concrete by using CWP as a raw material in RCBs. 12 small-scale shear RCBs with the dimensions of 100 × 150 × 1000 mm were tested in this study. The variations of stirrups spacing and CWP ratio were examined in these specimens. The percentages of CWP by weight utilized in RCBs were 10%, 20%, and 30%, and stirrups spacings were adopted as 270 mm, 200 mm, and 160 mm. At the end of the study, it was determined that more than 10% CWP additive negatively affected the RCBs' compressive strength. The load-carrying capacity reduced between 30.3% and 59.4% when CWP increased from 0% to 30% as compared to RCB with stirrups spacing of 270 mm without CWP. However, compared to RCB with stirrups spacings of 200 mm and 160 mm without CWP, there were decreases in the load-carrying capacity as 21.4%-54.3% and 18.6%-54.6%, respectively. While the CWP ratio increased, the specimens with 160 mm, 200 mm, and 270 mm stirrups spacings obtained a lower maximum load value. However, with the increase of the CWP ratio in the specimens with 160 mm stirrups spacing, RCBs reached the maximum load-carrying capacity at an earlier displacement value. When stirrups spacing was selected as 270 mm, it was observed that the maximum load-carrying capacity of RCBs reached at a similar displacement value as the CWP ratio increased. Besides, it was resulted that the bending stiffness of RCBs reduced as the quantity of CWP enhanced. The bending stiffness decreased by 29.1% to 66.4% in the specimens with 270 mm stirrups spacing, 36.3% to 20.2% with 200 mm stirrups spacing, and 10.3% to 36.9% with 160 mm stirrups spacing. As an implication of the experiments, the use of CWP up to 10% in RCBs was realized as an economical and environmental approach and is suggested. There is some evidence to report that making use of CWP may be considered to be ecologically benign. This is due to the fact that reusing CWP may significantly reduce CO2 emissions, save energy, and reduce total power consumption. Furthermore, the experimental results were compared to the analytical calculations.

Experimental Study of the Flexural Performance of GFRP-Reinforced Seawater Sea Sand Concrete Beams with Built-In GFRP Tubes.

The use of seawater sea sand concrete (SSSC) and fiber-reinforced polymer (FRP) has broad application prospect in island and coastal areas. However, the elastic modulus of FRP reinforcement is obviously lower than that of ordinary steel reinforcement, and the properties of SSSC are different from that of ordinary concrete, which results in a limit in the bearing capacity and stiffness of structures. In order to improve the flexural performance of FRP-reinforced SSSC beams, a novel SSSC beam with built-in glass FRP (GFRP) tubes was proposed in this study. Referring to many large-scale beam experiments, one specimen was used for one situation to illustrate the study considering costs and feasibility. Firstly, flexural performance tests of SSSC beams with GFRP tubes were conducted. Then, the effects of the GFRP tubes' height, the strength grades of concrete inside and outside the GFRP tubes, and the GFRP reinforcement ratio on the flexural behaviors of the beams were investigated. In addition, the concept of capacity reserve was proposed to assess the ductility of the beams, and the interaction between the concrete outside the GFRP tube, the GFRP tube and concrete inside the tube was discussed. Finally, the formulas for the normal section bearing capacity of beams with built-in GFRP tubes were derived and verified. Compared to the beam without GFRP tubes, under the same conditions, the ultimate bearing capacities of the SSSC beam with 80 mm, 100, and 200 mm height GFRP tubes were increased by 17.67 kN, 24.52 kN, and 144.42 kN, respectively.

Experimental and Numerical Investigation of the Flexural Behavior of Reinforced-Concrete Beams Utilizing Waste Andesite Dust.

During the process of cutting andesite stones, the waste mud is kept in powder form once fully dried. It is difficult to store the waste that is produced as a consequence of the extensive utilization area and consumption of andesite. Thus, eliminating waste storage challenges and incorporating these wastes into the economy are crucial. For this reason, this study examined the effects of waste andesite dust (WAD) on the flexural behavior of reinforced-concrete beams (RCBs) using experimental testing and 3D finite-element modeling (FEM) via ANSYS. Thus, different rates of WAD up to 40% were used to investigate the influence of the WAD rate on the fracture and bending behavior of RCBs. While the RCB with 10% WAD had a slightly lower load-bearing and ductility capacities, ductility capacities significantly drop after 10% WAD. At 40% WAD, both the load-bearing capacity and ductility significantly reduced. Based on the experimental findings, using 10% WAD as a replacement for cement is a reasonable choice to obtain eco-friendly concrete. Moreover, the outcomes of 3D FEM were also compared with those of experiments conducted using ANSYS v19 software. The displacement values between the test and FEM findings are quite similar.

Study on Prestressed Concrete Beams Strengthened with External Unbonded CFRP Tendons.

This study builds a refined finite element (FE) model to research the flexural behavior of a reinforced beam with prestressed CFRP tendons. The precision of the FE model is validated through a comparison with the experimental outcomes. The numerical findings align well with the experimental outcomes, encompassing the failure mode, load-deflection curve, load-strain curves of concrete, steel reinforcements and CFRP tendons. The variances between predicted values and experimental results are within 10%. Leveraging the verified FE model, an extensive parametric study has been carried out to examine the effects of various parameters, including the CFRP tendon prestress, the CFRP tendon diameter, the deviator layout, the anchorage height and the prestressing strand prestress. Leveraging the findings from the parametric study, some refined design recommendations are proposed for practical reinforcement applications: Increasing the CFRP tendon prestress in practical reinforcement designs is recommended; CFRP tendons with larger diameters are recommended for use in practical reinforcement designs; Employing a linear CFRP tendon profile for reinforcement is not considered optimal in practical applications; The prestress loss in the prestressing strands of PC beams should be considered in practice.

Comparison of Fracture Behavior in Single-Edge Notched Beams Reinforced with Steel Bars or CFRP Bars.

To explore and compare the failure modes, deformation behaviors, and load-bearing capacities of single-edge notched (SEN) beams strengthened with carbon fiber-reinforced polymer (CFRP) and steel bars, static and dynamic three-point bending tests on both types of concrete beams have been carried out in this study. During the static tests, the electro-hydraulic servo machine served as a loading device to apply pressure to CFRP beams and reinforced concrete (RC) beams. During the impact experiments, different impact velocities were imparted by adjusting the drop hammer's height. Thus, information regarding crack propagation, energy absorption, and deformation was obtained. The results from the static tests showed that the RC beams predominantly experienced shear failure. In contrast, the CFRP beams primarily exhibited bending-shear failure, attributed to the relatively weaker bond strength between the bars and the concrete. Impact tests were conducted at three different velocities in this study. As the impact velocity increased, both types of concrete beams transitioned from bending failure to bending-shear failure. At the lowest velocity, the difference in energy absorption between beams reinforced with different materials was insignificant during the bending process. However, at the highest velocity, CFRP beams absorbed less energy than RC beams. The study of structures' impact failure modes and their mechanical characteristics offers valuable references for the anti-collision design and protection of structures.

Investigational and Numerical Examination on Bending Response of Reinforced Rubberized Concrete Beams Including Plastic Waste.

In this investigational study, the fracture and bending performance of reinforced concrete beams (R-C-Bs) with varying proportions of plastic waste (PW), considered as fine aggregate (FA), were assessed via experimental and numerical examination. To achieve this aim, altered concrete series were designed, with the aggregate sizes changed within the range of 0 to 25 mm. To enhance the concrete, PW was selected to be used in combination with aggregate material measuring 0 to 5 mm in particle size, as an alternative FA, with proportions of 0%, 5%, 15%, 30%, and 45%. Experiments were performed to examine the performance of the R-C-Bs. It was found that a 30% PW proportion offered the optimum results in terms of displacement capability. Furthermore, ANSYS v.19 software was chosen to form 3D finite element models (F-E-Ms) of R-C-Bs to be compared with the experimental data. The experimental and 3D F-E-M investigations offered remarkably close-fitting bending and rupture performances. Then, a structure was modeled using SAP2000, and the strength of the R-C-Bs was then used in an RC structural model. The results show that the forces on the construction caused reductions while also increasing the PW proportion. Moreover, it was realized that the F-E-M simulations and experiments produced tiny cracks with highly matched formations.

Fracture Analysis of Short-Scale Corroded/Healthy Reinforced Concrete Beams under Bending Using Acoustic Emission.

In this work, the acoustic emission (AE) technique is used to evaluate the fracture process of corroded and healthy reinforced concrete (RC) beams subjected to a monotonic bending test. In fact, many researchers have conducted laboratory experiments considering different conditions to perform rebar corrosion monitoring in RC structures using the AE method. However, previous studies have not investigated the evolution of the bending performance of RC beams at different corrosion degrees, considering the interaction of single rebar with concrete. In this study, healthy and electrically corroded RC beams are evaluated, considering different corrosion levels. The analysis of the moving average of the AE maximum amplitudes was consistent to distinguish four stages of mechanical behavior that the healthy, and corroded specimens with low and medium corrosion levels of 0.9% and 3.2% experienced up to failure. Three damage stages were identified in the case of a high corrosion level of 9.3%. Then, the AE maximum amplitudes were suitable to establish an efficient clustering, which enabled the classification of the fractures into minor, medium, and major classes. Furthermore, the digital analysis method proposed in this study was suitable to visually reveal the influence of the preexisting corrosion-induced damages on the bending failure process of the RC beams.

Experimental Investigation of the Effect of Steel Fibers on the Flexural Behavior of Corroded Prestressed Reinforced Concrete Beams.

Rebar corrosion and its consequences are one of the most common damages to reinforced concrete (RC) structures. In structures with greater sensitivity, such as prestressed reinforced concrete (PRC) structures, where steel elements, including prestressed tendons, play a more significant role in supporting the structure, the importance of this issue increases. Methods for repairing and reinforcing such structures have been developed, including incorporating fibers into the concrete mixture to improve its mechanical properties, particularly its bending resistance. This paper presents the results of an experiment that studied the influence of steel fibers on the flexural behavior of PRC beams subjected to accelerated corrosion. Twelve beams with a rectangular cross-section of 150 mm × 300 mm and a length of 2000 mm were fabricated. The steel fibers used in the experiment were corrugated and hooked-end types, with volume fractions of 0.5% and 1.0% in the concrete. Nine beams were subjected to accelerated corrosion testing, with three of them being without fibers and the remaining six being reinforced with steel fibers at volume fractions of 0.5% and 1.0%. Each group of three beams was exposed to three different levels of corrosion, namely 5%, 10%, and 15%. The specimens were tested after exposure to corrosion through a four-point bending load. The accelerated corrosion was induced using an electric current on the prestressing tendons. The results indicated that different levels of corrosion reduced the final bearing capacity and other behavioral characteristics of the specimen, including the amount of energy absorption, effective hardness, and midspan displacement. Adding fibers to the concrete mixture positively affects the compensation of these reduced capacities. Moreover, the amount of this compensation was directly correlated with the volume fraction of used fibers.

Influence of Bonding Area on Dynamic Failure Behavior of Notched Reinforced Concrete Beams.

To study the effect of the bonding area on the dynamic failure process of a reinforced concrete beam with the same reinforcement ratio, the experimental and numerical researches on the impact response of notched reinforced concrete beams in the low-velocity regime (≤2.5 m/s) are presented. The tests are carried out with a drop hammer impact testing machine and then the structural responses under different impact velocities are analyzed. Additionally, the dynamic three-point bending simulation for specimens with different bonding areas, but the same reinforcement ratio is conducted. In this numerical model, the parameters of a cohesive model verified from a steel bar pullout test are applied to the bonding layer to simulate the bond-slip behavior of steel bars. Then, the energy dissipation for each component (e.g., concrete, a steel bar, and the bonding layer) are compared and discussed. The dynamic experimental results suggest that the energy absorbed during the impact process increases with the growth of the impact velocity, while the effect of the impact velocity on the reaction force can be ignored. The numerical results indicate that the failure pattern changes from a bending failure to shear failure with the increase in the bonding area and impact velocity. With the growth of the bonding area, the steel bars reach the plastic stage easily and the internal energy dissipation of the bonding layer decreases, which protects the bonding effect between the steel bar and concrete effectively.

Performance Prediction of Hybrid Bamboo-Reinforced Concrete Beams Using Gene Expression Programming for Sustainable Construction.

The building and construction industry's demand for steel reinforcement bars has increased with the rapid growth and development in the world. However, steel production contributes to harmful waste and emissions that cause environmental pollution and climate change-related problems. In light of sustainable construction practices, bamboo, a readily accessible and eco-friendly building material, is suggested as a viable replacement for steel rebars. Its cost-effectiveness, environmental sustainability, and considerable tensile strength make it a promising option. In this research, hybrid beams underwent analysis through the use of thoroughly validated finite element models (FEMs), wherein the replacement of steel rebars with bamboo was explored as an alternative reinforcement material. The standard-size beams were subjected to three-point loading using FEMs to study parameters such as the load-deflection response, energy absorption, maximum capacity, and failure patterns. Then, gene expression programming was integrated to aid in developing a more straightforward equation for predicting the flexural strength of bamboo-reinforced concrete beams. The results of this study support the conclusion that the replacement of a portion of flexural steel with bamboo in reinforced concrete beams does not have a detrimental impact on the overall load-bearing capacity and energy absorption of the structure. Furthermore, it may offer a cost-effective and feasible alternative.

Fatigue Reliability Assessment of RC Beams in Heavy-Haul Railways Based on Point Estimate Method.

Heavy-haul railways have a high passing frequency of trains with a large axle weight, causing rapid accumulation of fatigue damage in reinforced concrete (RC) bridge structures, which significantly affects the safety of the bridges. To study the fatigue reliability of RC beams in heavy-haul railways, the fatigue performance function for RC beams in heavy-haul railways was established, and the fatigue reliability assessment method for bridge structures in heavy-haul railways based on the point estimate method (PEM) was developed. An 8 meter-span plate beam in an existing heavy-haul railway illustrates the method. The train axle weight and dynamic coefficient were considered random variables, and the first four moments of equivalent stress ranges were obtained. The traffic quantity of the heavy-haul railways was investigated, and the fatigue reliability was evaluated using the proposed method. In addition, the effects of annual freight volume and train axle weight on fatigue reliability were discussed. Results indicate that PEM can effectively and accurately evaluate the fatigue reliability of RC beams in heavy-haul railways. In the first 20 years of operation, the fatigue failure probability was less than the limit value specified in the standard. The increase in annual traffic volume and train axle weight will cause a significant increase in fatigue failure probability. The research results of this paper are expected to provide an important basis for the design and maintenance of reinforced concrete bridges for heavy-haul railways in the future.

Research on an Optimized Evaluation Method of the Bearing Capacity of Reinforced Concrete Beam Based on the Bayesian Theory.

An optimized evaluation method of the bearing capacity of reinforced concrete beam based on the Bayesian theory was proposed in this paper. This evaluation method optimized the traditional Markov Chain-Monte Carlo (MCMC) sampling method, and proposed an improved Metropolis-Hastings (MH) sampling method and a transitive MCMC (TMCMC) sampling method based on the MCMC theory. These two derived sampling methods solved the problem that the traditional MCMC algorithm makes it difficult to achieve convergence when the number of modified parameters is large. Therefore, on the basis of obtaining the measured sample information and the prior information of uncertain parameters, this paper first used multiple "model components" to form a model sample, then carried out a sensitivity analysis based on the relevant response indicators and selected the key parameters that had a great impact on the bearing capacity, carried out static load tests, and extracted and analyzed the experimental data. Then, based on a large amount of analysis data, the improved MH sampling method and TMCMC sampling method were used to establish a posterior probability distribution database. Finally, multiple posterior probability distributions were used to identify and predict the bearing capacity. The results showed that the method was feasible and effective for the evaluation of the bearing capacity of reinforced concrete beam.

Simplified shear equation of deep concrete beam considering orientation effect of opening and mechanical properties of fibre-concrete interface.

In the present era of technology, the design of structural deep concrete beams is highly modernized through the use of computer-aided tools. However, theories for such design are the paramount aspects to be understood particularly when the beam has openings. To improve the mechanical properties of the deep beam with openings, recycled tyre steel fibres are required. To estimate the bond strength of the fibre-concrete interface, the concrete shrinkage strains for fibre lengths 30, 50 and 60 mm with a content of 0.5% were considered. To mitigate the conservativeness of some available shear models and improve the design of deep beams, the simplified shear equation model was developed. The model was established using a simplified compressive stress block, forces in steel reinforcement and shear stress at the fibre-concrete interface. The combined effect of opening height and length was also considered in the model. The results show that incorporating fibres in concrete increase the shear performance of deep concrete beams with openings due to high strains in the shear zone indicating high loads being transferred. For instance, beam BS2 had a strain of 0.0153 in the lower load path compared to 5.6 × 10-5 for beam BC2 There was a good correlation between measured and proposed shear capacities with t-test values of 0.46, 0.996 and 0.003 for beams without fibres, and with fibres and mesh respectively. Results also showed the model shear equation performed better compared to other equations with mean absolute error (MAE) and coefficient of variation (COV) of 9.3 and 18.9%, respectively for the control beams with openings. The model also showed a mean absolute error (MAE) and coefficient of variation (COV) of 11.6 and 7.4%, respectively for the beams with fibres. The COV and MAE for the proposed model were small than those in the database, therefore, the proposed model can provide the precise design of deep concrete beams with openings and fibres.