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In this paper a structural damage detection algorithm using static test data is presented. Damage is considered as a reduction in the structural stiffness (Axial and/or Flexural) parameters. Change in the static displacement of a structure is characterized as a set of non-linear undetermined simultaneous equations that relates the changes in static response of the structure to the location and severity of damage. An optimality criterion is introduced to solve these equations by minimizing the difference between the load vector of damaged and undamaged structures. The overall formulation leads to a non-linear optimization problem with non-linear equality and linear inequality constraints. A method based on stored strain energy in elements is presented to select the loading location. Measurement locations are selected based on Fisher Information Matrix. Numerical and experimental results of a 2D frame represent good ability of this method in detecting damages in a given structure with presence of noise in measurements.

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By identifying the damage index of a structure, in addition to a correct understanding from real behavior of the structure, the required criterion for strengthening would be given. Researchers have given many relations for determination of damage index but such relations have been based upon laboratory methods which challenge their usage in a broad term. In this paper two new methods are given for calculation of damage index. Surveying the first crack limit and total structure failure is based upon the formation of plastic joints in the first column and basic floor columns. To give a qualitative simple and functional damage index, the functional method was given in the form of a qualitative method with statistical analysis and collection of different views. Using this method is very simple and meantime offers suitable accuracy. With a numerical study on three models it was made clear that the difference of new method with amended method of Papadopolos in approximate 3%. This shows that given qualitative method is suitable to be used in a broad terms.

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This paper presents an experimental study on seismic repair of damaged square reinforced concrete columns with poor lap splices, 90-degree hooks and widely spaced transverse bars in plastic hinge regions according to ACI detailing (pre.1971) and (318-02) using GFRP wraps. Three specimens were tested in “as built” condition and retested after they were repaired by glass fiberreinforced plastic sheets. They were tested under numerous reversed lateral cyclic loading with a constant axial load ratio. FRP composite wraps were used for repairing of concrete columns in critically stressed areas near the column footings. Physical and mechanical properties of composite wraps are described. Seismic performance and ductility of the repaired columns in terms of the hysteretic response are evaluated and compared with those of the original columns. The results indicated that GFRP wraps can be an effective repair measure for poorly confined R/C columns due to short splice length and widely spaced ties with 90-degree anchorage hooks. Both flexural strength and ductility of repaired columns were improved by increasing the existing confinement in critical regions of them.

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 Neither damage mechanics model nor elastoplastic constitutive law can solely describe the behavior of concrete satisfactorily. In fact, they both fail to represent proper unloading slopes during cyclic loading. To overcome the disadvantages of pure plastic models and pure damage approaches, the combined effects need to be considered. In this regard, various classes of plastic-damage models have been recently proposed. Here, the theoretical basics of the plastic-damage model originally proposed by Lubliner et al. and later on modified by Lee and Fenves is initially presented and its numerical aspects in three-dimensional space are subsequently emphasized. It should be mentioned that a part of the implementation in 3-D space needs to be reformulated due to employing a hyperbolic potential function to treat the singularity of the original linear form of plastic flow proposed by Lee and Fenves. The consistent algorithmic tangent stiffness, which is utilized to accelerate the convergence rate in solving the nonlinear global equations, is also derived. The validation and evaluation of the model to capture the desired behavior under monotonic and cyclic loadings are shown with several simple one-element tests. These basic simulations confirm the robustness, accuracy, and efficiency of the algorithm at the local and global levels. At the end, a four-point bending test is examined to demonstrate the capabilities of the model in real 3-D applications.

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In recent years, different damage indexes have been introduced in engineering literature. The most prominent one among other

counterparts is the 1985 Park and Ang's damage index (DIPA), which demonstrates well calibration against experimental

results. Hence, it has traditionally had broad application in the field of structural engineering. Commonly, in DIPA relevant

parameters are assessed based on plastic-hinge approach, which is not well suited to consider the coupled response between

stress resultants (axial force and flexural moment) especially in grossly nonlinear domain. The reason is that named approach

is utilized constant shape plastic moment-curvature curve, which is not capable of varying the shape throughout loading history.

Another drawback of plastic-hinge method is the difficulty of representing precisely partial yielding of the cross-section. To

remedy the situation, the fiber discretization technique is used in this paper. Based on the fiber discretization strategy, not only

have the stiffness and strength degradation been characterized more accurately, but also the distribution of plasticity along the

plastic zone has been considered. Besides, the multi-directional effect of axial force and flexural moment is considered to assess

DI parameters. Additionally, this strategy directly incorporates the effect of transverse confinement into cross sectional

constitutive behaviour.

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An energy based damage index based on a new nonlinear Finite element (FE) approach applicable to RC structures subjected to cyclic, earthquake or monotonic loading is proposed. The proposed method is based on the evaluation of nonlinear local degradation of materials and taking into account of the pseudo-plastic hinge produced in the critical sections of the structure. A computer program is developed, considering local behavior of confined and unconfined concretes and steel elements and also global behavior and damage of reinforced concrete structures under cyclic loading. The segments located between the pseudoplastic hinges at critical sections and the inflection points are selected as base-models through simulation by the proposed FE method. The proposed damage index is based on an energy analysis method considering the primary half-cycles energy absorbed by the structure during loading. The total primary half-cycles absorbed energy to failure is used as normalizing factor. By using the proposed nonlinear analytical approach, the structure's force-displacement data are determined. The damage index is then calculated and is compared with the allowable value. This damage index is an efficient means for deciding whether to repair or demolish structures after an earthquake. It is also useful in the design of new structures as a design parameter for an acceptable limit of damage defined by building codes.  The proposed approach and damage index are validated by results of tests carried out on reinforced concrete columns subjected to cyclic biaxial bending with axial force.

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An important concern in rock mechanics is non-homogeneity as joints or fault. This noticeable feature of failures in rock is

appearance of slip surfaces or shear bands, the characteristics of that are associated with deformation being concentrated in a

narrow zones and the surrounding material remaining intact. Adopting the joints as fractures, fractures are well known for their

effects on the mechanical and transport properties of rock. A damaged pro-elasticity multi-plane based model has been developed

and presented to predict rock behavior. In this multi-plane model, the stress–strain behavior of a material is obtained by

integrating the mechanical response of an infinite number of predefined oriented planes passing through a material point.

Essential features such as the pro-elasticity hypothesis and multi-plane model are discussed. The methodology to be discussed

here is modeling of slip on the local and global levels due to the deformation procedure of the existing/probable joints of rock and

this method has a potential of using different parameters on different sampling planes to predict inherent anisotropy of rocks.

Upon the presented methodology, more attention has been given to slip initiation and propagation through these joints. In

particular, softening in non-linear behavior of joints in going from the peak to residual strengths imparts a behavior often

associated with progressive failure. The predictions of the derived stress–strain model are compared to experimental results for

marble, sandstone, Quartz mica schist and anisotropic schist. The comparisons demonstrate the capability of this model to

reproduce accurately the mechanical behavior of rocks.

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Corrosion of reinforcing steel and other embedded metals is the main cause of severe deterioration in reinforced concrete structures which subsequently imposes adverse effects on ultimate and serviceability limit state performance of the whole structure. In this paper, a new corrosion detection method for reinforced concrete beams, based on wavelet analysis is presented. To evaluate the capability and efficiency of the method, a simply supported RC beam was modeled in 3-D taking into account the behaviors of concrete, steel and bond degradation. Deflection profile and mode shapes were extracted numerically and analyzed by wavelet transform. From the findings of the modeling, it can be concluded that this wavelet-based method is capable of detecting corrosion at its earliest stage. It is also concluded that both discrete and continuous wavelet transforms can be used and mother wavelet type has no significant effect on the results.

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Concrete bridge deck damage detection by measurement and monitoring variables related to vibration signatures is one of the main tasks of any Bridge Health Monitoring System (BHMS). Generally damage puts some detectable/discoverable signs in the parameters of bridge vibration behavior. However, differences between frequency and mode shape before and after damage are not remarkable as vibration signatures. Therefore most of the introduced methods of damage detection cannot be used practically. Among many methods it seems that models based on artificial intelligence which apply soft computing methods are more attractive for specific structures. In this paper an Adaptive Neuro-Fuzzy Inference System (ANFIS) is used to detect the damage location in a concrete bridge deck modeled by finite element method. Some damage scenarios are simulated in different locations of the deck and accelerations as representatives of response at some specific points are calculated. Excitement is done by applying an impact load at the center of the deck. In the proposed ANFIS damage detection model accelerations are inputs and location of the damage is output. Trained model by simulated data can show the location of the damage very well with a few training data and scenarios which are not used in training stage. This system is capable to be included in real-time damage detection systems as well.

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The main cause of structural damage in buildings subjected to seismic actions is lateral drift. In almost all reinforced concrete (RC) structures, whether designed with walls or frames, it is likely to be the code drift limits that control the design drift. The design drift limits and their contribution to damage may be represented indirectly through the material strain limits. The aim of this study is to investigate the seismic design indicators of RC columns using finite element analyses (FEA). The results of FEA have been compared with the results of experimental studies selected from literature. It is observed that the lateral load-deflection curves of analyzed columns are in agreement with the experimental results. Based on these lateral load-deflection curves, the drift limits and the material strain limits, given by the codes as performance indicator, are compared. It is observed that the material strain limits are non-conservative as performance indicator of RC columns, compared to the drift limits.

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It is well known that damaged structural members may alter the behaviour of the structures considerably. Careful observation of these changes has often been viewed as a means to identify and assess the location and severity of damages in structures. Among the responses of a structure, natural frequencies and natural modes are both relatively easy to obtain and independent from external excitation, and therefore, can be used as a measure of the structural behaviour before and after an extreme event which might have led to damage in the structure. This paper applies Charged System Search algorithm to the problem of damage detection using vibration data. The objective is to identify the location and extent of multi-damage in a structure. Both natural frequencies and mode shapes are used to form the required objective function. To moderate the effect of noise on measured data, a penalty approach is applied. Varity of numerical examples including beams, frames and trusses are examined. The results show that the present methodology can reliably identify damage scenarios using noisy measurements and incomplete data.

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An analytical nonlinear stress-strain model and a microscopic damage index for confined and unconfined concretes together with a macroscopic damage index for reinforced concrete (RC) structures under cyclic loading are proposed. In order to eliminate the problem of scale effect, an adjustable finite element computer program was generated to simulate RC structures subjected to cyclic loading. By comparing the simulated and experimental results of tests on the full-scale structural members and concrete cylindrical samples, the proposed stress-strain model for confined and unconfined concretes under cyclic loading was accordingly modified and then validated. The proposed model has a strong mathematical structure and can readily be adapted to achieve a higher degree of precision by modifying the relevant coefficients based on more precise tests. To apply the proposed damage indices at the microscopic and macroscopic levels, respectively, stress-strain data of finite elements (confined and unconfined concrete elements) and moment-curvature data of critical section are employed. The proposed microscopic damage index can easily be calculated by using the proposed simple analytic nonlinear stress-strain model for confined and unconfined concretes. The proposed macroscopic damage index is based on the evaluation of nonlinear local degradation of materials and taking into account the pseudo-plastic hinge produced in the critical section of the structural element. One of the advantages of the macroscopic damage index is that the moment-curvature data of the critical section is sufficient in itself and there is no need to obtain the force-displacement data of the structural member.

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Self-centering pier (SCP) has been viewed as a remarkable accomplishment which is able to sustain major lateral loading with reduced structure damage in seismic engineering. Stiffness deterioration observed in experiment is vital for the seismic performance of self-centering concrete pier. In this contribution, the associated stiffness deterioration with respect to the structural damage is modeled in a modified analytical model for SCP comprehensively. In the proposed modified theoretical model, the lateral force-displacement relation associated with the stiffness reducing is analyzed. Three damage factors are introduced in the stiffness deterioration analysis to illustrate the damage evolution caused by gradually increasing lateral displacement. The proposed modified quasic-static model with damage evolution or stiffness deterioration has been validated against an experiment we conducted, where a good agreement is clearly evident. Subsequently, a parametric investigation focusing on aspect ratio, initial pre-tension, and ratio of ED (Energy Dissipator) was conducted to evaluate the hysteretic behavior of SCP under quasi-statically cyclic loading.

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Observations and investigations have proved that using traditional fire curves such as stand-ard fire curves and natural fire curves should be limited to small/medium compartments. In addition, when using the traditional fire curves, a uniform temperature is assumed throughout the compartment. However, for large open compartments, assuming uniform temperature is not compatible with real fires. To overcome this limitation, a non-uniform fire method named as travelling fire is employed as an alternative. A study is performed here on a seismic-damaged large plan 3-story reinforced concrete structure designed to meet the life safety level of performance when exposed to a travelling fire. To draw a comparison, the structural fire analysis is also performed using the traditional methods. The results show a notable difference – while the fire resistance based on the travelling fire is around 91 minutes, it is around 140 minutes when based on a uniform temperature. This shows that the structure studied is more susceptible to failure when subjected to the non-uniform fire than the uniform fire.

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One kind of the irregularities in structures, with considerable effect on seismic performance, is setback in elevation that causes large damage especially in the vicinity of the irregularity. The main objective of this research is to propose and develop drift based index to estimate damage to Reinforced Concrete Moment Resisting Frames (RCMRFs) with setback. For this purpose, first, inelastic dynamic time-history analysis is performed on several frames with different types of setbacks subjected to various earthquake records and damage to them is computed by the Park-Ang damage index. Then two relations between the damage and drift are derived by applying irregularity indices to account for setback effects. It is shown that the proposed damage indices are capable to estimate the damage index of setback frames.

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This paper describes both global and local versions of an energetic analytical model to quantify the damage caused to reinforced concrete (RC) structures under monotonic, cyclic or fatigue loading. The proposed model closely represents the damage to structures and yields a damage index (DI) for the RC members. The model is cumulative and is based on the energy absorbed. The energy under the monotonic envelope curve at the failure of the member is taken as a reference capacity. The data required to apply the model in any given situation or member can be obtained either by numerical simulation or from experimental tests. An analytical computer program was developed to simulate numerically the response of RC members taking into account the nonlinear behavior of the materials and structures involved. The proposed model was verified by comparison with practical tests undertaken by other researchers on over 20 RC columns. The comparison demonstrates that the model provides a realistic estimation of the damage of the RC structural members. The comparison between values of the proposed DI calculated based on experimental test data and numerical simulation results for a cyclic loading case shows that to calculate DI, it is not necessary to perform expensive experimental tests and that using a nonlinear structural analytical simulation is sufficient. The results are also compared to a damage model proposed by Meyer (1988).

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To reveal the deformation mechanism during tunneling in deep soft ground, triaxial unloading confining pressure tests and triaxial unloading creep tests were carried out on sandy mudstone specimens to study the dilatancy and fracturing behavior of soft rock. In the triaxial unloading confining pressure tests, the stress path and different unloading rates were considered to reflect the unloading characteristics of the excavation methods. The unloading rate effects and the rock damage evolution law are studied. The following conclusions are obtained from the results. Firstly, when the unloading rate is smooth, the peak strengths and deviatoric stress–strain curves under the unloading condition are close to those under the conventional loading condition. Secondly, the post-peak brittle characteristics are more apparent with the increasing unloading rates. Thirdly, the soft rock undergoes five deformation and failure regimes of elasticity, pre-peak unloading damage–dilatancy, post-peak brittle drop, linear strain softening and residual perfect plasticity under quasi-static smooth unloading of mechanized excavation which is mainly focused on in this study. Fourthly, the damage evolution law at the pre-peak damage–dilatancy stage follows an exponential function. Fifthly, during the post-peak stages, multistage microfractures are initiated, propagated and finally coalesced forming a shear-fragmentation band with a certain thickness, accompanied by significant volumetric dilatancy. In the triaxial unloading creep tests, multistep unloading of the confining pressure was applied, while the axial pressure was kept constant. The results show that when the deviatoric stress is larger and the experienced creep time is longer, the unloading effect and creep characteristics become more apparent accompanied with obvious lateral dilatancy, eventually leading to significant creep–dilatancy. The progressive failure with time is caused by the damage accumulating with time-dependent crack expansion, which can be called as ‘time-dependent damage and fracturing’. The reasons for the above evolution process are presented, then the deformation mechanism of soft rock is revealed. The soft rock deformation mainly consists of two parts. One part is the pre-peak damage–dilatancy and post-peak fracture–bulking produced at the excavation unloading instant. The other part is creep–dilatancy caused by time-dependent damage and fracturing in a period of time after excavation. The above-mentioned results of damage, dilatancy and fractures evolution process are in good agreement with the in situ monitoring results and previous studies about the surrounding rock convergence, fracturing and EDZ (excavation damaged zone) development.