Component-level Performance-based Seismic Assessment and Design Approach for Concrete Moment Frames

1.1. Development of Performance-Based Seismic Assessment and Design (PBSAD)

Since the 1990s, performance-based seismic engineering concepts and approaches have been developed by a series of documents including SEAOC version 2000 Report [1], ATC 40 Report [2], FEMA 273 Report [3] and its companion documents the FEMA 274 [4], FEMA 356 Report [5], FEMA 343 Report [6], ASCE/SEI 31-03 standard [7], ASCE/SEI 41-06 standard [8] and its Supplement 1 [9], and the latest Edition of ASCE/SEI 41 [10] published in 2013 and many other important reports. These documents 1) outlined the initial concept of performance levels related to vulnerability and varied levels of seismic hazard; 2) introduced the concept of performance in terms of discretely defined performance levels with names intended to connote the expected level of damage: Collapse, Collapse Prevention, Life Safety, Immediate Occupancy, and Operational Performance, performance objectives were developed by linking one of these performance levels to a specific level of earthquake hazard; and 3) introduced the concept of performance related to damage of both structural and non-structural components. Acceptance criteria of structural performance levels for each type of structural components are basic datas for engineering aplications of these documents. One of most important steps of performance-based assessment procedures of RC buildings relies on comparison of deformations obtained from nonlinear structural analyses (static or dynamic) with deformation performance limits, or acceptance criteria on the other words. These deformation limits significantly affect the assessment result so their accuracy plays a critical role. Performance-based seismic assessment method has been constantly updated, before the next-generation performance-based seismic assessment method is proposed, each development of this method was based on the new engineering practice with the tendency to release the acceptance criteria because the acceptance criteria was considered very conservative in engineering practice.

In 2001, under the ATC-58 Project, ATC began working on the next-generation performance-based seismic design criteria for new and existing buildings. In 2003, Moehle and Deierlein [11] first published paper about the performance-based seismic engineering framework which was developed by the Pacific Earthquake Engineering Research Center (PEER). The PEER framework expresses earthquake performance in terms of the probable values of key performance measures, such as casualties, repair costs, and occupancy loss derived from an application of the total probability theorem. In 2006, T.Y. Yang et al. [12] developed an application of this framework that utilized a modified Monte Carlo approach to implement the integration using inferred statistical distributions of building response obtained from limited suites of analyses. The ATC project team ultimately adopted and expanded this approach into the FEMA P-58 methodology. In the same year, FEMA 445 Report [13] was published and acted as the guidelines for the next-generation procedures. The primary objective of the next-generation procedures focuses on these aspects of 1) how to communicate with stakeholders effectively; 2) procedures for estimating the probable repair costs, casualties, and time of occupancy interruption; 3) assessment of economic loss associated with damaging earthquakes; 4) investigation of the conservatism and reliability of present second-generation acceptance criteria and modification of performance assessment based on global response parameters, so that the response of individual components does not unnecessarily control the prediction of overall structural performance. In 2012, FEMA P-58 [14] was published as the final product of ATC-58 project, which uses a probabilistic approach to characterize performance so that the reliability with which performance may be attained can be fully understood. Rather than using discrete performance states like that used in ASCE/SEI 41 methodology, the FEMA P-58 methodology characterizes performance in the form of loss distributions, from which the probability of incurring earthquake impacts, exceeding various levels can be directly obtained.

1.2. Problems and Criticism

In the development of performance-based seimic engineering, there exists a fundamental problem about the conservatism of the acceptance criteria for each structural performance level (generally known as the deformation limits of deformation-controlled components), which may lead to excessive cost of strengthening and reconstruction, sometimes even incorrect performance evaluation results . G. Siahos and S. Dritsos [15] compared ASCE 41-06 Supplement 1, FEMA 356 and the Eurocode 8 based on Greek Retrofitting Code via pushover analyses for the seismic assessment of RC buildings designed to old codes and results showed all procedures overestimated the experimentally observed limited damage. B. Acun and H. Sucuoglu [16,17] tested 12 full-scale column specimens designed for pure flexure failure and proved that the deformation-based performance limits proposed for substandard columns by ASCE/SEI 41-06 were found very conservative in view of the test results, which may lead to misleading results in the seismic risk assessment of existing substandard concrete structures. P. Ricci [18] also tested older-type reinforced concrete columns with plan bars and observed a significant conservatism in the plastic deformation capacity model of ASCE/SEI 41 provisions and proved that deformation limits could be relaxed while still meeting code safety requirements.

Authors survey this conservatism from another point of view. Considering the basic performance level concept and the application procedures proposed by ASCE/SEI 41, it can be pointed that the target building performance level controls the acceptable structural performance level and further controls acceptance criteria of all structural components, in other words, performance levels of a building and its components are associated with each other, thus not independent from each other. However, it is unreasonable to judge that a building or structure fails to meet the target performance level if only one component fails to meet the acceptance criterion. On the other hand, releasing the acceptance criteria of components could not address the problem effectively and may lead to unsafe assessment results in some cases. J. Moehle and G.G. Deierlein [19] also criticized that it is one of shortcomings that the overall system performance is assumed to be equal to the worst performance calculated for any component in the building. FEMA 445 [13] also realized this problem and stated that one of the main goals of the next-generation performance-based seismic engineering is to investigate the conservatism and reliability of present acceptance criteria, and to modify current structural procedures to assess structural performance based more on global response parameters, so that the response of individual components does not unnecessarily control the prediction of overall structural performance. FEMA P-58 report is just the product of this target. Although FEMA P-58 method has been available for seismic assessment and design, however most designers are far unfamiliar to the concept of PBEE framework and the probability-based assessment method, then it is meaningfull for a simplified performance-based seismic assessment method that can be easily understood and applied, which is the main research object of this paper.

1.3. Framework of this Paper

From authors’ point of view, authors [20-26] have put forward a new concept of component performance levels (hereinafter referred to as CPLs, while CPL refers as its singular form) and redefined them based on the damage degree of component itself and developed basic deformation limits for RC members of moment frames for these CPLs of new concept, which are similar to the acceptance criteria of RC members in ASCE/SEI 41. If component performance was divided into several discrete CPLs and graded according to corresponding strutural performance level in ASCE/SEI 41, acceptance criteria in ASCE/SEI 41 can be considered as deformation limits for CPLs. The major difference between these two limits is whether the component performance level is dependent/independent on the corresponding structural performance level. Obviously, CPL’s defination of author’s research findings is independent, while that of ASCE/SEI 41 is dependent.

To evaluate the seismic performance of structure based on these component performance levels defined and achieved by authors, an alternative method has also been proposed in this paper by establishing a new relationship between one given target structural performance level and the statistical distribution of structural component performance levels. The non-structural component performance level shall also be considered in terms of establishing another relationship between one selected target structural performance level and the statistical distribution of non-structural component performance levels, which can refer to research results by Yang and Ou [27]. Finally, evaluation of one typical concrete moment frame with masonry infills has been illustrated as a case study.

2.1. Structural Performance Levels (Hereinafter Reffered to as SPLs, while SPL Refers as its Singular form) and Ranges in China and Their Limitations

In China, Code for seismic design of buildings (GB50011-2010)[28], and the Technical specification for concrete structures of tall building (JGJ3-2010)[29] and its local Edition of Guangdong province [30] has introduce the performance-based seismic design idea and put forward concept of structural performance levels related to vulnerability and varied levels of seismic hazard, similar to the ASCE standards but with more detailed discrete performance levels, including Integrity Level (S-1) , Minor Damage Level (S-2), Limited Moderate Damage Level (S-3), Moderate Damage Level (S-4), Limited Serious Damage Level (S-5), Serious Damage Level (S-6) and Unacceptable Level (S-7). Compared descriptions of damage for each performance levels defined by Chinese Codes to those by ASCE Standards, S-1 is similar to Operational Performance Level, S-2 similar to Immediate Occupancy Level, S-4 similar to Life Safety Level, S-6 similar to Collapse Prevention Level and S-7 similar to Collapse Level. Although there are still some differences between each pair of similar performance levels, it can help understand definitions of structural performance levels in Chinese Codes for researchers outside Mainland China as well as structural performance levels referred to Chinese codes in context.

Chinese Codes suggest a force-based design method which adopts load combination equation with different combination coefficients to represent the acceptable damage degree of each performance level, and recommends the limited elasto-plastic interstory drift ratio as macro-measurement for additional performance level indicator. From authors’ previous research, the elasto-plastic interstory drift ratio of a structure can reflect whether the deformation capacity is able to meet the functional requirement, but it cannot reflect damage distribution of components. The force-based design method lacks for knowledge about damage levels of components and for information of either displacement ductility or rotation ductility of components. Because the extent of damage is proportional to plastic deformation, it is the deformation demand rather than the force demand of components and/or elements and/or structures that should be taken as the basic indicator to the performance levels. Therefore, although Chinese Codes have adopted concepts of performance-based seismic engineering, they have not adopted an appropriate approach for performance-based seismic assessment.

Based on the analysis above, this paper will take the concepts of structural performance levels and ranges defined by Chinese Codes, and complement new concepts of component performance levels and ranges and their deformation performance limits, then put forward new acceptance criteria for structural perfomance assessment procedures.

2.2. Structural Component Performance Levels (CPLs) and Ranges

All components actions shall be classified as either deformation controlled or force controlled based on their ductility. If the ductility is less than 2, the action shall be classified as a force-controlled action, otherwise it shall be classified as a deformation-controlled action. In general, for common framing systems, shear, axial force and torsion shall be considered as force-controlled actions, while moment may be either deformation-controlled or force-controlled action. Similarly, components shall also be classified as either deformation controlled or force controlled. If the failure of a component is controlled by a force-controlled action, the component shall be classified as a force-controlled component; otherwise if the failure is controlled by a deformation-controlled action, it shall be classified as a deformation-controlled component.

As mentioned above, CPLs of deformation-controlled componets have been divided into a range of seven discrete levels, including Integrity Level (C-1), Minor Damage Level (C-2), Limited Moderate Damage Level (C-3), Moderate Damage Level (C-4), Limited Serious Damage Level (C-5), Serious Damage Level (C-6) and Failure Level (C-7). Their definitions and descriptions are listed in detail as follows, which are modified from previous researches those can be found in references [23-25].

Integrity Level (C-1), is defined as a post-damage state in which no apparent or visible damage occurs. Component remains its pre-damage strength and stiffness. In a broad sense, component is still in elastic state. However, minor cracks on concrete cover may be permitted but tensile longitudinal reinforcement should not yield. The maximum compression strain of concrete could not exceed 0.002, and the maximum tensile strain of steel could not exceed f_y/E_s, where f_y and E_s are the yield strength and the Young's modulus of steel respectively. The limited deformation is referred as the yield deformation Δ_y (in displacement) or θ_y (in rotation).

Minor Damage Level (C-2), is defined as a post-damage state in which some visible but slight damage occurs, component yields, the stiffness decreases while the strength has not reached the strength capacity. The edge of concrete cover has been crushed but the maximum width of residual cracks is less than 1mm. The maximum compression strain of concrete could not exceed 0.004, and the maximum tensile strain of steel could not exceed 0.015.

Limited Moderate Damage Level (C-3), is defined as a continuous range of post-damage state between the Moderate Damage Level (C-4) and the Minor Damage Level (C-2). The concrete cover has not fallen off, concrete core remains integrity and the maximum width of residual cracks shall be less than 2mm. The maximum compression strain of concrete could not exceed 0.0065, and the maximum tensile strain of steel could not exceed 0.030.

Moderate Damage Level (C-4), is defined as a post-damage state in which the strength has reached its capacity and maybe exhibited less than 5% decrease compared to the peak strength. Buckling or fracture of longitudinal reinforcing bars does not occur, and the concrete does not crush. The maximum compression strain of concrete could not exceed the ultimate compressive strain, marked as ε_cu in context, and the maximum tensile strain of steel could not exceed 0.050 and 0.6ε_su, where ε_su is the ultimate tensile strain of steel.

Limited Serious Damage Level (C-5), is also defined as a continuous range of post-damage state between the Moderate Damage Level (C-4) and the Serious Damage Level (C-6). The strength may have less than 10% drop from the peak strength. The maximum tensile strain of steel could not exceed 0.080 and 0.9ε_su.

Serious Damage Level (C-6), is defined as a post-damage state in which component is near failure. Buckling or fracture of longitudinal reinforcement may occur and the concrete core may crush with hoops failure. The maximum tensile strain of steel could not exceed 0.100 and ε_su. The ultimate deformation (Δ_uin displacement, or θ_uin rotation) shall be reached when component has a serious strength 20% drop from the peak strength.

Failure Level (C-7), is defined as a post-damage state that the component has failed. For deformation-controlled components, a residual strength that equals to 20% of the yield strength could be considered for numerical analysis.

For force-controlled components, there are only two component performance ranges:the Integrity Level (C-1) and the Failure Level (C-7). In the Failure Level (C-7) of the force-controlled components, the residual strength should be set as zero for numerical analysis, and the peak strength should be taken as the threshold indicator from the Integrity Level (C-1).

In previous research, the elasto-plastic rotation angle is selected as the deformation indicator. The elasto-plastic rotation angle is the rotation over the plastic hinging region at the end of the member. if member is under inelastic response, the elasto-plastic rotation consists the elastic rotation angle and the plastic rotation angle; if member is not yield, the elastio-plastic rotation angle only consists the part of elastic rotation angle. In any case, the elasto-plastic rotation angle is the total rotation of the end lateral section of the plastic hinging region. Deformation-controlled CPLs those meet latest updated required constructional details of Chinese Codes published from 2010, have been developed and listed in Table 1 for RC columns and Table 2 for RC beams, whose earlier editions could be found in references [23-25]. It shall be noted for values and special symbols appears in these tables that 1) values in each table refer to the elasto-plastic rotation angle; 2) values between those listed in each table should be determined by linear interpolation; 3) n_t is the axial compression ratio, which equals to the design axial force P divided by the gross sectional area A_g and concrete compressive strength f_c, where f_c is in MPa units, n_t=P/(A_gf_c); 4). m is the flexure shear ratio, which equals to the flexure strength of member M_u, caculated based on the actual reinforcement and concrete strength, divided by the shear strength V₀ and the nominal shear span ratio λ and the effective height of section h₀ , m= M_u/(λh₀V₀),; 5). v is normal shear stress ratio, which equals to the design shear force V divided by the gross sectional area A_g and the tensile strength of concrete f_t , where f_t is in MPa units, v= V/( A_gf_t).

2.3. Structure Seismic Performance Criteria

2.4. Component-level Performance-based Seismic Assessment Procedures

There are three key challenges for performance-based seismic assessment procedures:1) reliable elasto-plastic analysis result, 2) appropriate performance indicators, and 3) reasonable acceptance criteria for each SPL. For component-level performance-based seismic assessment procedures, deformation and force are selected as indicators for deformation-controlled components and force-controlled components respectively. Acceptance criteria of SPLs mentioned above are selected. Procedures should be conducted as the follow chart shown in Fig. (1), considering structural components and non-structural components (if modeled) in a reliable elasto-plastic analysis process.

1. For a given structure of a new building or an existing building, the first step is to obtain the structural layout, dimensions and materials. For a new building, there should be design documents; and for an existing building, more as-built information about the structure is necessary and must be investigated in detail, with source design documents as reference. As a result of this step, geometry parameter, cross-section reinforcement and necessary material strength of each member will be determined.
2. Classify structural components into critical components and general components. It will mainly depend on the expertise and experience of engineers.
3. Build the elasto-plastic analysis model for the structure. For an existing building, analysis should reflect the actual material strength, effective member stiffness, effective vertical/horizontal resistance systems, and accurate joint connections. For a new building, analysis model should reflect design details.
4. Select ground motion records those meet the site condition and the seismic hazard level of a given probability. Generally, no less than 3 records are needed for a comprehensive performance-based seismic assessment, performance evaluation should be conducted based on each selected record. Thus each performance assessment result is a certain analysis based on a given ground motion record, which just reflects one probable performance capacity of the structure.
5. For one selected ground motion record from step 4), the elasto-plastic dynamic analysis should be conducted to obtain three types of results. Result 1 includes the stress state of all members along elasto-plastic dynamic analysis history, Result 2 includes the deformation state for structural components, and Result 3 includes the drift state of stories at macro scale and/or deformation state of non-structural components if non-structural components are modeled. It’s noted that drift state of stories shall be used to estimate NPLs if non-structural components are not modeled.
6. Judge the action type of each member such as moment, shear, axial force, based on the geometry parameter, the cross-section reinforcement and the necessary material strength from step 1) and the stress state from step 5). If the member is deformation-controlled, then query deformation limits for each CPL of the member, whereas the normal strength or force limits shall be calculated or checked for force-controlled members. Performance indicator limits for non-structural components shall also be determined from research results of Yang and Ou [27].
7. Based on results of deformation limits, force limits and/or non-structural component performance indicator limits from step 6), and results of deformation state and stress state outputted from step 5), the CPL and/or NPL of component shall be determined.
8. Formulate statistic distribution of CPLs and/or NPLs separately, then evaluate performance level of the structure for the given ground motion record by acceptance criteria recommended in Table 4, Table 5 and Table 6.
9. For another ground motion records of a seismic hazard level of same or different probability, repeat 2) to 8).

Seismic risk analysis for this method is not adopted in these procedures. It shall be taken account for more detailed evaluation procedures. However, this paper mainly deals with the evaluation method for one given seismic intensity of a certain and asuming equal probability.

3.1. Seismic Evaluation of Moment frame with Infill Masonry Walls Modeled as Dead Loads, MF1

The elasto-plastic analysis of MF1 has been conducted and statistic distributions of CPLs of general components and critical components are presented in Table 8 and Table 9 respectively. The last column of each table shows the assessment result for each seismic record just considering the listed statistics. Because infill masonry walls are considered as dead loads in the analysis model, so non-structural components’ influence on the structural performance level will not be considerd. Table 10 shows the comprehensive evaluation of MF1.

Table 8 shows that, the damage distribution of general components meets SPL of S-4 under five ground motion records, and meets SPL of S-3 and S-5 under the other two ground motion records respectively. Table 9 shows that there are four ground motion records under which the damage distribution of critical components meets SPL of S-3, one ground motion record that meets SPL of S-1 without any critical components damaged, one ground motion record that meets SPL of S-2 with only few critical components damaged, and the last ground motion record that meets much lower SPL of S-4. For entire structure, the lower SPL due to critical and general components should be selected as the structure’s SPL, as listed in the last column of (Table 10). Because most records meet SPL of S-4, and only one meets much more serious damage level S-5, it can be concluded that the structure of MF1 shall achieve a performance level not lower than SPL of S-4 with a probability of no less than 85%. If different damages of beams (referring to general components) and columns (referring to critical components) are both considered, beams seem to be much more seriously damaged than columns, so that the design target of “strong column and week beam” is achieved.

3.2. Seismic Evaluation of Moment Frame with Infill Masonry Walls Modeled as Diagonal Struts, MF2

The elasto-plastic analysis of MF2 has been conducted and statistic distributions of CPLs of general components and critical components are presented in Table 11 and Table 12 respectively, along with the statistic distribution of NPLs of non-structural components simulated as diagonal struts presented in (Table 13). Because infill masonry walls are considered as diagonal struts modeled, performance levels of non-structural components are assessed by the response of diagonal struts. Table 14 shows the comprehensive evaluation of this structure.

Table 11 shows that, there are four ground motion records under which the damage distribution of general components meets SPL of S-2 with no more than 30% of general components slightly damaged, all other records cause no damage to general components. Table 12 shows that, there is no damage to critical components under anyone of these seven ground motion records. On the contrary, Table 13 shows that non-structural components are damaged severely under all selected ground motion records. The damage distribution of non-structural components meets SPL of S-5 under three ground motion records and meets SPL of S-6 under other four records. Table 14 shows the comprehensive evaluation for entire structure, the lowest SPL shall be selected as the structure’s SPL, as listed in the last column of this table. Based on the judgment principle of SPL, S-6 shall be selected as the SPL of MF2 with no more than 15% probability of exceeding. In this case, structural components are damaged very slightly, while non-structural components are damaged seriously, it shall be predicted that this structure may cause a serious economic losses if it is luxuriously decorated.

Compared to the assessment result of MF1, it seems to be concluded that well infilled moment frames may lead to much more serious damage on the infill masonry walls instead of structural members. Although structural components are slightly damaged, economic loss due to the damage of non-structural components may be unacceptable. This is one of the major difference between performance-based seismic assessment procedures and traditional design approaches.

It is noteworthy that in the analysis model of MF2, all punches of doors and windows in the infill masonry walls are not considered, so stiffness and strength contributed by diagonal struts may be over-estimated, and the conservative definition of non-structural component performance levels by Yang and Ou [27] may also affected the outcome.