Mechanical Model for Unbonded Seven-Wire Tendon with Single Broken Wire

This paper presents the derivation and experimental validation of a mechanical model for unbonded seven-wire prestressing tendons with a single broken outer wire. The model has practical significance because corrosion of these tendons typically causes a single outer wire to fail first. The tendency for the tendon to deflect toward the broken wire causes strains in the unbroken wires to be unequal at any cross section. As a result, the strains in the two wires adjacent to the broken wire increase significantly due to the wire break. Equations are presented for: (1) the strains along the lengths of the broken and unbroken wires; (2) the affected length, where the broken wire can be detected because its strain is less than the strains in the unbroken wires; and (3) the prestress force remaining after the break occurs. Experimental data obtained from tests of seven-wire tendons performed on an 18.3?m (60?ft) long strongback beam validate the model.     

CFRP Tendons for the Repair of Posttensioned, Unbonded Concrete Buildings

The deterioration attributable to corrosion of concrete structures reinforced with unbonded, posttensioned tendons is a costly problem. Recent research has shown composite materials such as fiber-reinforced polymers (FRP) to be suitable alternatives to steel because they provide similar strength without susceptibility to electrochemical corrosion. Carbon-FRP (CFRP) in particular has great promise for prestressed applications because it shows resistance to corrosion in environments that might be encountered in concrete and experiences less relaxation than steel. This paper outlines the testing and implementation of a posttensioned system that uses CFRP tendons to replace corroded, unbonded posttensioned steel tendons. This system was then implemented in a parking garage in downtown Toronto. To the writers’ knowledge, this is the first example of an unbonded, posttensioned tendon replacement using FRP tendons. The system used split-wedge anchors designed specifically for CFRP tendons. The dead end was anchored by directly bonding the tendon to the concrete slab. The CFRP tendon was successfully inserted in the opening created by the removal of the corroded tendon and stressed. Although the system was shown to be feasible, the current anchorage configuration results in load losses of up to 60% during the transfer. Changing the orientation of the anchor was found to reduce the load loss to an acceptable range of 1–9%.     

Cyclic Response of Unbonded Posttensioned Precast Columns with Ductile Fiber-Reinforced Concrete

A precast segmental concrete bridge pier system is being investigated for use in seismic regions. The proposed system uses unbonded posttensioning (UBPT) to join the precast segments and has the option of using a ductile fiber-reinforced cement-based composite (DRFCC) in the precast segments at potential plastic hinging regions. The UBPT is expected to cause minimal residual displacements and a low amount of hysteretic energy dissipation. The DFRCC material is expected to add hysteretic energy dissipation and damage tolerance to the system. Small-scale experiments on cantilever columns using the proposed system were conducted. The two main variables were the material used in the plastic hinging region segment and the depth at which that segment was embedded in the column foundation. It was found that using DFRCC allowed the system to dissipate more hysteretic energy than traditional concrete up to drift levels of 3–6%. Furthermore, DFRCC maintained its integrity better than reinforced concrete under high cyclic tensile-compressive loads. The embedment depth of the bottom segment affected the extent of microcracking and hysteretic energy dissipation in the DFRCC. This research suggests that the proposed system may be promising for damage-tolerant structures in seismic regions.     

Computer-Based Mathematical Model for Performance Prediction of Corroded Beams Repaired with Fiber Reinforced Polymers

A new mathematical model for predicting the inelastic flexural response of corroded reinforced concrete (RC) beams repaired with fiber reinforced polymer (FRP) laminates is presented. The model accounts for the effect of the change in the bond strength at the steel-to-concrete interface due to corrosion and/or FRP wrapping on the beam load–deflection response. The effects of FRP strengthening and the reduction in the steel reinforcement area due to corrosion on the beam strength are predicted by the model. A computer program was coded to carry out the modeling procedure and the model’s predictions were compared with the results of an experimental study undertaken to investigate the model’s reliability. A comparison of the predicted and the experimental results showed that the model accurately predicted the load–deflection relationships for corroded RC beams repaired with FRP laminates.     

Modified Skew Bending Model for Segmental Bridge with Unbonded Tendons

Segmental bridges with unbonded prestressed tendons have some advantages over conventional concrete bridges, such as weather-independent construction and the corrosion protection of the prestressing tendons. This paper analyzes the behavior of a prestressed segmental bridge with unbonded tendons under combined loading of torsion, bending, and shear. According to experimental research, a modified skew bending model was developed to calculate the load-carrying capacity of segmental bridges subjected to combined bending, shear, and torsion. A finite element method (FEM) was used to investigate the deflection behavior of such a structure and to check the theoretical model. The theoretical and FEM research results compared favorably with test results. Finally, suggestions for the design and construction of segmental bridges with external prestressing were made.     

Full-Scale Application of a Dynamic Model for High-Rate Anaerobic Wastewater Treatment Systems

High-rate anaerobic treatment systems are becoming increasingly popular to treat industrial wastewater containing large amounts of organic matter in the form of carbohydrates or proteins. Mathematical models of these systems can serve as tools for equipment sizing, process design, control and optimization, plant operation, and operator training. Several models for these plants have been proposed which have been validated and tested on laboratory-scale systems. Information on full-scale application of these models is not readily available. In this paper, a model only previously validated on laboratory scale was applied at full scale. The model was used to predict the behavior of two full-scale plants of different designs treating brewery wastewater under dynamic conditions. Influent and effluent liquid streams and gas flows were sampled over a 4 and 10 day period for the two plants, respectively. Limited characterization to just total carbon in feed over only four days was sufficient to predict the gas production rate or total volatile organic acid concentration in the effluent of the methanogenic reactor. Elaborate measurements over 10 days of feed characteristics including organic acid concentrations were important in obtaining good full-scale predictions of all variables that were modeled. Apart from the operating variables, the key parameter that required re-estimation for the full-scale system was the solids retention time in the methanogenic stage.     

Parameter Optimization and Sensitivity Analysis for Disturbed State Constitutive Model

Constitutive models for geologic materials and interfaces involve a number of parameters that need to be determined from appropriate laboratory tests. Because the test behavior is influenced by a number of factors such as material variability in test specimens, initial density, mean pressure, and stress paths, the parameters determined from such tests need to be averaged or optimized. The averaging procedure is often used. However, in view of the importance of the parameters in analysis and design, it is desirable and necessary to use advanced procedures such as optimization methods so as to find their improved and realistic values. This paper presents an optimization procedure for the determination of parameters in the unified disturbed state concept constitutive models. A series of multiaxial laboratory tests on a sand under different initial mean pressures, density, and stress paths are used to evaluate the optimized parameters. The stress-strain and volume change behavior is then back-predicted using the parameters from the conventional averaging procedure and the proposed optimization procedure. The results show that the optimized parameters provide improved predictions of the test data. The optimized parameters are used in a finite element procedure to predict cyclic behavior in a boundary value problem involving a shake table test. The proposed procedure can provide a useful methodology for the optimization of parameters for a wide range of available (plasticity, creep, damage, etc.) constitutive models. It can lead to improved analysis and design of geotechnical problems, particularly while using computer (finite element) procedures.     

Constitutive Model for Concrete with Embedded Sets of Reinforcement

In this paper a constitutive relation is developed for concrete reinforced with two orthogonal sets of steel bars. The formulation incorporates a homogeneous deformation mode, prior to cracking, as well as a localized mode associated with formation of macrocracks. In the latter case, the representative volume comprises the reinforced fractured zone and the “intact” material. The stiffness of the reinforcing network is evaluated by considering the individual steel bars to be rigidly embedded in the adjacent intact material. An extensive numerical analysis is conducted examining the performance of the proposed framework in pure shear and axial tension for different reinforcement intensities and orientations. The results are compared with the available experimental data.     

Analytical Model for Concrete Confined with Fiber Reinforced Polymer Composite

An analytical model to predict the behavior of concrete confined with fiber reinforced plastic (FRP) composites subjected to axial compressive loads was developed. First, a constitutive model for plain concrete was formulated from past experimental results obtained from triaxial compression tests of concrete, in which concrete specimens were maintained under constant confining stresses. This was an orthotropic constitutive model based on the concept of equivalent uniaxial strain. Subsequently, in the analytical model for FRP confined concrete, the proposed constitutive model for concrete materials was incorporated. The FRP was assumed to be a linear elastic material. Force equilibrium and strain compatibility between the concrete and the FRP as well were satisfied. When the proposed model was applied to FRP confined concrete, the model overestimated the axial stress. To rectify this, a subsequent maximum strength criterion was introduced to control the maximum strength in the postpeak region when confining stress was continuously increased. The proposed analytical model with the addition of the subsequent maximum strength criterion is in good agreement with the experimental results.     

Simplified Finite-Element Model for Tissue Regeneration with Angiogenesis

A simplified finite-element model for tissue regeneration is proposed. The model takes into account the sequential steps of angiogenesis (neo-vascularization) and wound closure (the actual healing of a wound). An innovation in the present study is the combination of both partially overlapping processes, yielding novel insights into the process of wound healing, such as geometry related influences, and could be used to investigate the influence of local injection of hormones that stimulate partial processes occurring during wound healing. These insights can be used to improve wound healing treatments. The models consist of nonlinearly coupled diffusion-reaction equations, in which transport of oxygen, growth factors, and epidermal cells and mitosis are taken into account.     

Microplane Model M5 with Kinematic and Static Constraints for Concrete Fracture and Anelasticity. II: Computation

Following the formulation of the constitutive model in the preceding Part I in this issue, the present Part II addresses the problems of computational algorithm and convergence of iterations. Typical numerical responses are demonstrated and the parameters of the model are calibrated by test data from the literature.     

Microplane Model M5 with Kinematic and Static Constraints for Concrete Fracture and Anelasticity. I: Theory

Presented is a new microplane model for concrete, labeled M5, which improves the representation of tensile cohesive fracture by eliminating spurious excessive lateral strains and stress locking for far postpeak tensile strains. To achieve improvement, a kinematically constrained microplane system simulating hardening nonlinear behavior (nearly identical to previous Model M4 stripped of tensile softening) is coupled in series with a statically constrained microplane system simulating solely the cohesive tensile fracture. This coupling is made possible by developing a new iterative algorithm and by proving the conditions of its convergence. The special aspect of this algorithm (contrasting with the classical return mapping algorithm for hardening plasticity) is that the cohesive softening stiffness matrix (which is not positive definite) is used as the predictor and the hardening stiffness matrix as the corrector. The softening cohesive stiffness for fracturing is related to the fracture energy of concrete and the effective crack spacing. The postpeak softening slopes on the microplanes can be adjusted according to the element size in the sense of the crack band model. Finally, an incremental thermodynamic potential for the coupling of statically and kinematically constrained microplane systems is formulated. The data fitting and experimental calibration for tensile strain softening are relegated to a subsequent paper in this issue, while all the nonlinear triaxial response in compression remains the same as for Model M4.