DE202023101791U1 - A system for RC bridge pier damage assessment using a simplified damage index - Google Patents

Abstract

A system for RC bridge pier damage assessment using a simplified damage index, the system includes:
an RC pier modeled with a beam-with-hinges element model;
a computing device for:
performing pushover analysis on the pier models to determine yield and final displacements;
receiving ground motion data from various earthquakes and normalizing to different ground motion excitations;
analyzing a non-linear time history on the pillar models to obtain dynamic displacements and calculating an ultimate ductility, displacement ductility and hysteretic ductility to determine the damage index according to the Park-Ang damage model; And
Generation of a simplified damage index by performing a regression analysis on the damage model developed by Park-Ang to predict the non-linear response of the RC bridge pier structure.

Description

FIELD OF THE INVENTION

The present disclosure relates to a system for RC pier damage assessment using a simplified damage index. More specifically, the system provides yield strength and fracture displacement formulas for RC bridge piers based on analytical studies.

BACKGROUND OF THE INVENTION

Bridges are an important part of any highway system and are vulnerable to earthquakes, which can have severe impacts on emergency response, financial losses and the local economy. Metrics such as damage probability functions or fragility curves to determine the performance and vulnerability of highway bridges under seismic action are essential and of paramount relevance for the development of a Performance-Based Earthquake Engineering (PBEE) framework. Fragility curves are conditional statements of probability that indicate how likely a structure will suffer damage equal to or greater than a specified threshold for a specified measure of ground motion intensity (IM). The purpose of bridge seismic assessment studies is to calculate the risk associated with loss of serviceability, severe damage, or collapse. With the risk quantified, rational decisions can be made, such as: B. Retrofit, replace or accept the risk and leave the bridge as is.

Recent earthquake damage around the world underscores the importance of bridges as possibly the most vulnerable part of any road or rail system. For this reason, numerous approaches to assess bridge vulnerability have been developed in recent years, mainly related to the construction of fragility curves. The main problems with all the methods described in the literature are the probabilistic seismic demand model, the intensity measure used for the fragility analysis, the selection of the technical demand parameters (EDPs) and the corresponding limit state thresholds for the capacity estimation, and the analysis method for the demand.

For the design of reinforced concrete (RC) bridge piers to conform to performance-based seismic design, a high level of confidence in the prediction of intermediate damage conditions is required. With the development of robust software packages, the performance-based earthquake engineering (PBEE) methodology has been found to be an excellent alternative to the force-based design methodology because it explicitly demonstrates structural performance. The research community has clearly recognized its importance as this method can evaluate the seismic assessment of structures. A predefined damage index is required to assess the damage status of a structure. The damage status of the structure is calculated using the damage index. The definition of damages and their calculation is a complex problem. Although linear structural analysis can calculate some damage parameters, inelastic analysis is the more reasonable method. Static and dynamic evaluations of inelastic structures can be performed using various software tools. Although these systems are commonly used in research, they are often not used formally for damage prediction.

From the above discussion, it is clear that a system for RC pier damage assessment using a simplified damage index is needed.

SUMMARY OF THE INVENTION

It is an object of the invention to provide a system for RC pier damage assessment using a simplified damage index. Seismic vulnerability assessment of structures, particularly bridges, has been an area of interest for several decades. The survivability of a structure under strong seismic excitations is often measured using available damage indices. Using the Performance-based Earthquake Engineering (PBEE) methodology, a new simplified damage index is proposed based on a parametric study performed on RC bridge piers. The Hinged Beam model was adopted to model the pier. Rebar and Concrete 01 material models were selected to model steel and concrete, respectively. Different parameters, i.e. slenderness ratio, different longitudinal and transverse reinforcements and different concrete grades were taken into account to carry out the parametric study. A total of 7200 non-linear time history analyzes are performed. This system also proposes formulas for yield strength and ultimate load for RC bridge piers based on analytical studies. The damage index is compared to the damage indices for various damage states that are generally accepted in the literature. The comparison showed that the damage index matched well.

In one embodiment, a system for RC pier damage assessment using a simplified damage index is disclosed. The system includes an RC pier modeled with an element model using beams and hinges. The system further includes a computing device for performing pushover analysis on the pier models to determine yield and final displacements; for receiving ground motion data from different earthquakes and normalizing to different ground motion excitations; to analyze a non-linear time history on the pier models to obtain dynamic displacements and to calculate a final ductility, displacement ductility and hysteretic ductility to determine the damage index according to the Park Ang damage model, thereby generating a mathematical model for yield and final displacements where the yield shift mathematical model is validated with the yield shift mathematical model. The computing device is configured to generate a simplified damage index by performing regression analysis on the damage model developed by Park-Ang to predict the non-linear response of the RC bridge pier structure, validating the damage index with the models.

An object of the present disclosure is to provide formulas for the elongation and final displacements for RC piers based on analytical studies.

Another object of the present disclosure is to assess the extent of seismic damage in RC piers.

In order to further clarify the advantages and features of the present disclosure, the invention will be described in more detail with reference to specific embodiments thereof illustrated in the accompanying drawings. It should be understood that these drawings represent only typical embodiments of the invention and are therefore not to be considered as limiting its scope. The invention will be described and illustrated with additional specificity and detail with the accompanying drawings.

character list

• 1 veranschaulicht ein Blockdiagramm eines Systems zur Schadensbewertung von RC-Brückenpfeilern unter Verwendung eines vereinfachten Schadensindex gemäß einer Ausführungsform der vorliegenden Offenbarung;
• 2 die verschiedenen Modelle gemäß einer Ausführungsform der vorliegenden Offenbarung darstellt;
• 3 eine Pushover-Kurve für 4,5-m-Brückenpfeilermodelle mit einem Abstand von 250 mm Querverstärkung gemäß einer Ausführungsform der vorliegenden Offenbarung veranschaulicht;
• 4 veranschaulicht, dass Tabelle 1 Details von Pfeilermodellen gemäß einer Ausführungsform der vorliegenden Offenbarung darstellt; Und
• 5 zeigt, dass Tabelle 2 Ausbeute- und Endverdrängungswerte gemäß einer Ausführungsform der vorliegenden Offenbarung zeigt.

These and other features, aspects and advantages of the present disclosure will be better understood when the following detailed description is read with reference to the accompanying drawings, in which like characters represent like parts throughout the drawings, wherein:

• 1 12 illustrates a block diagram of a system for RC pier damage assessment using a simplified damage index in accordance with an embodiment of the present disclosure;
• 2 illustrates the various models according to an embodiment of the present disclosure;
• 3 12 illustrates a pushover curve for 4.5 m pier models with a 250 mm cross reinforcement spacing according to an embodiment of the present disclosure;
• 4 Illustrates that Table 1 presents details of pillar models according to an embodiment of the present disclosure; And
• 5 Figure 12 shows that Table 2 shows yield and final displacement values according to an embodiment of the present disclosure.

Furthermore, those skilled in the art will recognize that elements in the drawings are shown for simplicity and are not necessarily drawn to scale. For example, the flowcharts illustrate the method in terms of the salient steps involved to help improve understanding of aspects of the present disclosure. Moreover, with respect to the construction of the device, one or more components of the device may have been represented in the drawings by conventional symbols, and the drawings may only show such specific details as are relevant to an understanding of the embodiments of the present disclosure around the drawings not to be obscured with details that would be readily apparent to one of ordinary skill in the art benefiting from the description contained herein.

DETAILED DESCRIPTION:

For the purposes of promoting an understanding of the principles of the invention, reference will now be made to the embodiment illustrated in the drawings and specific language will be used to describe the same. It should be understood, however, that no limitation on the scope of the invention is intended thereby, contemplating such changes and further modifications to the illustrated system, and such further applications of the principles of the invention illustrated therein, as would normally occur to one skilled in the art to which the invention relates.

Those skilled in the art will understand that the foregoing general description and the following detailed description are exemplary and explanatory of the invention and are not intended to be limiting.

Reference throughout this specification to "an aspect," "another aspect," or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present disclosure is. Thus, the phrases "in one embodiment," "in another embodiment," and similar phrases throughout this specification may, but need not, all refer to the same embodiment.

The terms "comprising," "comprising," or other variations thereof are intended to cover non-exclusive inclusion such that a process or method that includes a list of steps includes not only those steps but may include other steps not expressly listed or any inherent in such process or procedure. Similarly, without further limitation, one or more devices or subsystems or elements or structures or components preceded by "comprises...a" does not exclude the existence of other devices or other subsystems or other elements or other structures or other components or additional devices or additional subsystems or additional elements or additional structures or additional components.

Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The system, methods, and examples provided herein are illustrative only and are not intended to be limiting.

Embodiments of the present disclosure are described below in detail with reference to the accompanying drawings.

With reference to 1 Illustrated is a block diagram of a system for RC pier damage assessment using a simplified damage index in accordance with an embodiment of the present disclosure. The system 100 includes an RC pier 102 modeled using a beam-and-hinged element model.

In one embodiment, a computing device 104 is used to perform pushover analysis on the pier models to determine yield and final displacements.

In one embodiment, computing device 104 is used to receive ground motion data from various earthquakes and normalize to different ground motion excitations.

In one embodiment, the computing device 104 is used to analyze a non-linear time history on the pier models to obtain dynamic displacements and calculate a final ductility, displacement ductility, and hysteretic ductility to determine the damage index according to the Park Ang damage model.

In one embodiment, the computing device 104 is used to generate a simplified damage index by performing regression analysis on the damage model developed by Park-Ang to predict the non-linear response of the RC pier 102 structure.

In another embodiment, a set of parameters selected from aspect ratio, plastic hinge length, modulus ratio, reinforcement ratio, and transverse reinforcement spacing are used to develop a mathematical model for the displacement yield, with the parameters selected from concrete, percentage of longitudinal steel, transverse reinforcement spacing being kept constant , to determine the variation of aspect ratio with flow displacement and the variation of flow displacement with plastic hinge length, keeping the remaining parameters constant, to determine the variation of flow displacement of modular ratio and the variation of flow displacement with longitudinal reinforcement ratio, and where at least two transverse reinforcement distances are only taken into account to compare another model that was created with 200 mm transverse reinforcement distances.

In another embodiment, the parameters selected from aspect ratio, plastic hinge length and longitudinal reinforcement ratio are considered to generate a mathematical model for the final displacement, keeping the parameters selected from concrete, longitudinal steel, transverse reinforcement spacing constant to determine the variation of Breaking load with the aspect ratio, being selected from concrete and longitudinal steel Parameters are kept constant to determine the variation of failure load with plastic hinge length and where the parameters are selected from aspect ratio, concrete grade, transverse reinforcement spacing parameters are kept constant to determine the variation of failure displacement with longitudinal reinforcement ratio.

In another embodiment, earthquake ground motion intensity is often described using peak ground acceleration (PGA) and peak ground velocity (PGV) indices, with the nonlinear time history analyzes for the selected input ground motions preferably selected from Kobe. Northridge, Chi-Chi normalized to various levels of arousal, preferably 0.5g - 2.5g.

In another embodiment, fifty ground motions in each direction, selected from longitudinal and transverse, are considered to perform non-linear analyses, with pier damage then being quantified by a damage index (DI) calculated using the Park - Ang 1985 damage model is obtained .

In another embodiment, the piers are modeled for nonlinear analysis by integrating element and material level nonlinear properties, and bridge damage due to ground motion is obtained by running a series of nonlinear static (pushover) and dynamic analyzes with the above parameters .

In another embodiment, the damage ranks in each damage state are calibrated using the threshold limits, where bridge column damage states are well defined in the damage index.

In another embodiment, the damage index reduces the difficulty and time of researchers and engineers in performing nonlinear analyzes on bridge piers, particularly when performing fragility analyses.

In another embodiment, a set of 100 ground motions from the PEER NGA database is available on the Open Sees-MS Bridge website, scaled and 300 longitudinal and transverse ground motions are generated to account for the higher intensity ground motions to reach.

Problem Description

Most hysteresis models used to estimate hysteresis energy govern the rules for determining loading and unloading paths only by calculating maximum strain points in both directions, which can overestimate the results. In this system, a simplified damage index for the RC pier 102 seismic assessment is presented. A total of 72 pillars with different aspect ratios, different concrete qualities, longitudinal steel proportions and transverse reinforcement distances were modeled and analyzed. A model for assessing structural damage in RC piers 102 under various seismic ground movements is proposed. The damage is expressed as a power function of the dynamic and final ductility ratio. To propose a damage index, available nonlinear static and time history data are analyzed to evaluate the statistics of the corresponding parameters.

methodology

To achieve this goal, a parametric study was conducted.

The RC pier 102 is modeled using a pinned beam element model. The material combination reinforcement steel - concrete 01 is used for modeling steel or concrete.

Pushover analyzes are performed on the pillar models to determine yield and final displacements.

Ground motion data from different earthquakes are selected and normalized to different ground motion excitations.

Nonlinear time history analyzes are performed on the pillar models to obtain dynamic displacements.

Damage model Park - Ang calculates the elongation at break, the displacement ductility and the hysteretic ductility.

Mathematical models for fluidity and final displacements are proposed and validated.

The yield shift mathematical model is validated with the yield shift mathematical model proposed by Priestley.

A new simplified damage index is proposed by performing a regression analysis on the damage model proposed by Park - Ang.

The damage index is validated with the literature models.

2 illustrates the different models according to an embodiment of the present disclosure. As can be concluded from the results of the "Beam with hinges" model, material models for steel and concrete are adopted for the element modeling Reinforcement steel - concrete 01 in this study. By adopting this combination of elements and materials for a 5.5m RC Pier 102, fragility curves were developed.

Parametric study

A parametric study was performed by varying structural and material properties to study the nonlinear responses. Pillars of different heights (4.5 m, 5.5 m, 6.5 m, 7.5 m) were taken into account by keeping the diameter of the pillar constant at 2.5. The aspect ratio varies from 1.8 to 3.0. Three different percentages of longitudinal reinforcement, ie 0.84%, 1.14% and 1.44%, and three grades of concrete, M35, M40 and M45, were taken. Two different transverse reinforcement distances (diameter 12 mm), namely 150 mm and 250 mm, were taken into account. Damage indices are calculated for each ground movement. Details of the models are in Table 1 and shown.

Results of nonlinear static analyses

Recently, a lot of attention has been paid to the nonlinear static methods for seismic vulnerability assessment and assessment of structures, especially bridges. Normally, a nonlinear static analysis is used to systematize the inelastic response of the structure, with a focus on the inelastic displacements rather than the forces. Potential damage losses and eventual failure are directly related to the post-yield behavior of components, i.e. inelastic displacement capacity. In this system, a total of 72 non-linear static analyzes are performed for all 72 models. The yield and final shift values obtained are shown in Table 2.

Mathematical model for yield displacement

To develop a mathematical model for yield shift, the following parameters are considered. a) degree of slenderness b) plastic tape length c) modulus ratio d) degree of reinforcement e) spacing of the transverse reinforcement.

Variation of the flow displacement with the slenderness ratio: When the slenderness ratio is varied with the flow displacement, the parameters of concrete quality, proportion of longitudinal steel and transverse reinforcement spacing are kept constant. For the aspect ratios 1.8, 2.2, 2.6 and 3, the flow displacements of concrete of grade M35, 1.14% longitudinal steel with 150 mm spacing of transverse reinforcement are plotted. A linear adjustment results. From this it is concluded that the flow displacement is linearly proportional to the aspect ratio.

L = Höhe des Pfeilers
f_y = Streckgrenze von Stahl
d_b = Durchmesser des LängsstabesVariation of the flow displacement with plastic hinge length: When varying the flow displacement with plastic hinge length, the parameters concrete quality, longitudinal steel, transverse reinforcement spacing are kept constant. The plastic hinge length is calculated according to the Priestley formula shown in Equation 1. Yield displacements of M35 concrete grade 1.14% longitudinal steel with 150 mm spacing of transverse reinforcement are taken into account for aspect ratios 1.8, 2.2, 2.6 and 3. The variation is shown in and a linear fit is found. $$\text{plastic hinge}\ddot{\text{a}}\text{ng}\left({\text{L}}_{\text{p}}\right)=0.08\text{L}+0.022{\text{f}}_{\text{y}}{\text{i.e}}_{\text{b}}$$

L = height of the pillar
f _y = yield strength of steel
d _b = diameter of the longitudinal bar

Yield displacement variation with modular ratio

The variation of the yield shift of the modular ratio, other parameters are kept constant. Module ratios for concrete types M35, M40, M45 for slenderness ratio 2.2, longitudinal steel 1.14% with transverse reinforcement distance 150 mm considered. The modulus of elasticity of the concrete is calculated according to IS 456:2000. i.e. 5000√(f _ck ). The yield displacement ratio varies inversely with the modular ratio.

Variation of the flow displacement with the longitudinal reinforcement ratio: The variation of the flow displacement with the longitudinal reinforcement ratio, keeping the remaining parameters constant, namely slenderness ratio, steel content, concrete grade. Reinforcement ratios 2.2 Slenderness of Pillar with concrete quality M35 and 150 mm transverse reinforcement, the relationship is logarithmic.

δ_y = Ertragsverschiebung
λ_s _ = Schlankheitsverhältnis
Lp = Kunststoffscharnierlänge
Es = Elastizitätsmodul von Stahl
Ec = Elastizitätsmodul von Beton
l _ = LängsbewehrungsgradVariation of flow displacement with transverse reinforcement spacing: Since only two transverse reinforcement spacings are considered, another model with 200 mm transverse reinforcement spacing is created for this special comparison. Slenderness ratio 2.2, concrete grade M35 with 1.14% longitudinal steel three different transverse reinforcement spacings, ie 150 mm, 200 mm and 250 mm are considered. It turns out that the transverse reinforcement has no influence on the flow displacement. Therefore, the influence of the transverse reinforcement is neglected in the mathematical model. Aspect ratio, plastic hinge length, modular ratio and longitudinal percentage of steel are considered and a multivariable nonlinear regression analysis is performed using SPSS software to propose a mathematical model for the yield displacement calculation. $$\mathrm{\delta }\text{y}={}_{\mathrm{9,348}}*\mathrm{\lambda }\text{s}+0.021*\text{LP}+\mathrm{89,378}/\left(\text{It/Ec}\right)+\mathrm{7,047}\ast \text{In}\mathrm{\rho }\text{l}$$

δ _y = yield shift
λ _s _ = aspect ratio
Lp = plastic hinge length
Es = modulus of elasticity of steel
Ec = modulus of elasticity of concrete
l _ = degree of longitudinal reinforcement

The mathematical model is validated with the results of the non-linear static analysis. The mathematical model agrees well with the results of the nonlinear static analysis with an R ² value of 0.97.

Validation of the proposed mathematical model for yield displacement with the model proposed by Priestley.

ε_y= Streckgrenze von Stahl
H = Höhe des Pfeilers
Lsp = Dehnungseindringlänge, die 0.022 f_yd_bl beträgt
f_y = Streckgrenze von Stahl N/mm ²
d_bl = Durchmesser des Längsstabes
D = Durchmesser des PiersA mathematical model proposed by Priestley for calculating flow displacement is given in Equation 3. Therein the dependent parameters are the yield strain of the steel, the height, the diameter of the pillar and the strain penetration length (Lsp). $$\text{income shift}=\frac{2.25{\mathrm{e}}_y{\left(H+L_{sp}\right)}^2}{3D}$$

ε _y = yield point of steel
H = height of the pillar
Lsp = strain penetration length, which is 0.022 f _y d _bl
f _y = yield strength of steel N/mm ²
d _bl = diameter of the longitudinal bar
D = diameter of the pier

The mathematical model shown in Equation 2 is validated against the mathematical model proposed by Priestley. The mathematical model for yield displacement agrees well with the mathematical model proposed by Priestley with an R ² value of 0.91.

Mathematical model for the ultimate shift

To develop a mathematical model for the final displacement, the following parameters are considered. a) Slenderness b) Plastic hinge length c) Longitudinal reinforcement ratio

Change of fracture displacement with slenderness ratio: The change of fracture displacement with slenderness ratio, remaining parameters, viz. concrete grade, longitudinal steel, spacing of transverse reinforcement are kept constant. For the slenderness ratios 1.8, 2.2, 2.6 and 3, the shifts in breaking load of concrete quality M35, 1.14% longitudinal steel with 150 mm spacing between transverse reinforcement are taken into account.

Variation of fracture displacement with plastic hinge length: The variation of fracture displacement with plastic hinge length, remaining parameters, namely concrete grade and longitudinal steel, are kept constant. The plastic hinge length is calculated according to the Priestley formula shown in Equation 1. The shifts in breaking load of the concrete type M35 1.14 % longitudinal steel with 150 mm spacing of the transverse reinforcement are taken into account for the aspect ratios 1.8, 2.2, 2.6 and 3.

Varying the breaking load with the degree of longitudinal reinforcement: When varying the breaking load with the degree of longitudinal reinforcement, the parameters (slenderness ratio, concrete quality, transverse reinforcement spacing) are kept constant. Longitudinal reinforcement values are taken into account for a slenderness ratio of 2.2 of the pillar with concrete quality M35 and 150 mm transverse reinforcement.

Wo,
δ _u = Ultimative Verschiebung
λs _ = Schlankheitsverhältnis
l _ = Längsbewehrungsgrad
Lp = KunststoffscharnierlängeAspect ratio, plastic hinge length and longitudinal percentage of steel are considered and a multivariate nonlinear regression analysis is performed using SPSS software to propose a mathematical model for the final displacement calculation. A mathematical model for calculating the final shift is shown in FIG $${\mathrm{\delta }}_{\text{and}}=174.56*{\mathrm{\lambda }}_{\text{s}}+\mathrm{22,651}\text{ln}{\mathrm{\rho }}_1-0.093*{\text{L}}_{\text{p}}$$

Where,
δ _u = Ultimate displacement
λs _ = aspect ratio
l _ = degree of longitudinal reinforcement
Lp = plastic hinge length

Validation of the proposed mathematical model for the final displacement with the results of the parametric study

Using the mathematical model, the final displacements for all 72 models are calculated and validated from nonlinear static analyses. The math agrees well with the pushover results with an R ² value of 0.99.

Nonlinear Time History Analysis

It is crucial to choose input motion properties that correlate with structural damage, but this is not an easy task. The intensity of earthquake ground motion is often described using the indices Peak Ground Acceleration (PGA) and Peak Ground Velocity (PGV). In this system, nonlinear time history analyzes are performed for the selected input ground motions i.e. Kobe, Northridge, Chi-Chi, normalized to different excitation levels (0.5g - 2.5g). Fifty ground motions in each direction (longitudinal and transverse) are considered in this system to perform non-linear analyses. The damage to the pier is then quantified by a damage index (DI) obtained using the Park - Ang 1985 damage model. For a nonlinear analysis, the pillars are modeled by integrating nonlinear properties at the element and material level. Using the above parameters, bridge damage due to ground motion is obtained by performing a series of non-linear static (pushover) and dynamic analyses.

A total of 72 non-linear static and 7200 time history analyzes are performed in this system. Using the damage data, damage ranks are classified into a damage classification adopted from HAZUS 2013. The damage index formula given is shown in Equation 5. These values have been considered on the ordinate and the ratios of dynamic and final ductility are plotted on the abscissa. A new simplified damage index shown in Equation 6 is obtained. The new simplified damage index is based on two engineering requirement parameters (EDPs), i.e. final ductility and displacement ductility.

3 12 illustrates a pushover curve for 4.5 m bridge pier models with a 250 mm cross reinforcement spacing according to an embodiment of the present disclosure.

4 FIG. 1 shows that Table 1 shows details of pillar models according to an embodiment of the present disclosure.

5 Figure 12 shows that Table 2 presents yield and final displacement values according to an embodiment of the present disclosure.

The results supported the damage index's ability to predict the severity of pier damage caused by varying intensities of ground movement. In addition, the damage index is compared to the already used Park Ang damage index. The comparison revealed that the proposed damage index is simpler than other damage models to classify pillar damage ranks for different damage states. The simplified expressions obtained in this parametric study are expected to be very useful to estimate the yield strength and final displacements for bridge abutments without performing the nonlinear static pushover analyzes that fall into the same category and properties.

The damage index offers a relatively simple approach and can be implemented in the seismic vulnerability assessment to assess the extent of seismic damage in RC piers. This is also in reasonable agreement with damage indices suggested in the literature. Damage ranks are calibrated for various damage states based on the newly proposed damage index for a range of 300 ground moves. This is in good agreement with the damage rank calibration based on HAZUS 2013. The mathematical system for calculating the flow displacement of RC bridge piers. The math agrees well with the mathematical model proposed by Priestley. The mathematical model to calculate the final displacement of RC bridge piers. The model agrees well with the results of the nonlinear static analysis.

The drawings and the above description provide exemplary embodiments. Those skilled in the art will recognize that one or more of the elements described may well be combined into a single functional element. Alternatively, certain elements can be broken down into multiple functional elements. Elements from one embodiment may carry to another embodiment be added. For example, orders of processes described herein may be changed and are not limited to the manner described herein. Furthermore, the actions of any flowchart need not be implemented in the order shown; also, not all actions have to be performed. Actions that are not dependent on other actions can also be performed in parallel with the other actions. The scope of the embodiments is in no way limited by these specific examples. Numerous variations, whether or not expressly stated in the description, such as differences in structure, dimensions and use of materials, are possible. The scope of the embodiments is at least as broad as indicated by the following claims.

Advantages, other benefits, and solutions to problems have been described above with respect to specific embodiments. However, the benefits, benefits, problem solutions, and components that may cause benefits, benefits, or solutions to occur or become more pronounced are not to be construed as critical, required, or essential features or components of any or all claims.

Reference List

100

A system for RC bridge pier damage assessment using a simplified damage index

102

RC bridge pier

104

computer device

Claims (7)

A system for RC bridge pier damage assessment using a simplified damage index, the system includes: an RC pier modeled with a beam-with-hinges element model; a computing device for: performing pushover analysis on the pier models to determine yield and final displacements; receiving ground motion data from various earthquakes and normalizing to different ground motion excitations; analyzing a non-linear time history on the pillar models to obtain dynamic displacements and calculating an ultimate ductility, displacement ductility and hysteretic ductility to determine the damage index according to the Park-Ang damage model; And Generation of a simplified damage index by performing a regression analysis on the damage model developed by Park-Ang to predict the non-linear response of the RC bridge pier structure. system after claim 1 wherein a set of parameters selected from aspect ratio, plastic hinge length, modulus ratio, reinforcement ratio and cross reinforcement spacing to develop a mathematical model for the flow displacement; the parameters selected from concrete, longitudinal steel fraction, transverse reinforcement spacing being held constant to determine the change in slenderness ratio with yield displacement and the change in yield displacement with plastic hinge length; the remaining parameters being held constant to determine the variation of flow displacement with modular ratio and the variation of flow displacement with longitudinal reinforcement ratio; And considering at least two transverse rebar spacing only for comparison of another model made with 200 mm transverse rebar spacing. system after claim 1 , wherein the parameters selected from aspect ratio, plastic hinge length and longitudinal reinforcement ratio are taken into account to generate a mathematical model for the final displacement; the parameters selected from concrete, longitudinal bar, transverse bar spacing being held constant to determine the change in final displacement with aspect ratio; the parameters selected from concrete and longitudinal steel being held constant to determine the final displacement variation with plastic hinge length; And where the parameters selected from aspect ratio, concrete grade, transverse rebar spacing parameters are kept constant to determine the final displacement variation with longitudinal rebar ratio. system after claim 1 , where the intensity of earthquake ground motion is often described using the indices Peak Ground Acceleration (PGA) and Peak Ground Velocity (PGV), with the non-linear time history analyzes being performed for the selected input ground motions, preferably selected from Kobe, Northridge, Chi-Chi, the are normalized to various levels of arousal, preferably 0.5 g - 2.5 g. system after claim 4 , considering fifty ground motions in each direction selected from longitudinal and transverse to perform non-linear analyses, the damage to the pier then being quantified by a damage index (DI) obtained using Park - Ang 1985 damage model. system after claim 4 , where for a nonlinear analysis, the piers are modeled by integrating element and material level nonlinear properties, and the bridge damage due to ground movements is obtained by performing a series of nonlinear static (pushover) and dynamic analyzes with the above parameters. system after claim 1 , where the damage ranks in each damage state are calibrated using the threshold limits, where bridge pier damage states are well defined in the damage index.

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