Proposed AASHTO Seismic Specifications for ABC Column Connections (2020)

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152 4.1 Introduction The findings of the state-of-the-art literature review of four precast column connections conducted for this study are presented in Chapter 2. After the available test data and the per- formance of accelerated bridge construction (ABC) column connections were reviewed, the research team, in conjunction with the panel for NCHRP Project 12-105, selected three types of connections for development of guidelines: • Mechanical bar coupler connections, • Grouted duct connections, and • Pocket/socket connections. The common criteria among these three were the readiness of the technology and the ease of construction. Some of the knowledge gaps identified for these three types of connections were addressed through component testing, as described in Chapter 3. The present chapter focuses on addressing the remaining knowledge gaps through analytical work. Table 4-1 presents a summary of the analytical work undertaken in the present project to develop comprehensive design and construction guidelines for the selected column connec- tions. The analytical work performed in this study included nonlinear analyses of different components, statistical analyses of test data, synthesis of previous analytical and experimental studies, and verification of the proposed design methods by using the available test data. Details of these tasks are presented in this chapter. Design of bridges incorporating the three types of ABC column connections is described Appendices B and C. 4.2 Mechanical Bar Splices The knowledge gaps identified as a result of the literature review for bar couplers (Chapter 2) were categorized as gaps regarding the performance of individual mechanical bar couplers and gaps with respect to the seismic performance of columns incorporating mechanical splices. The gaps identified for mechanical bar splices were as follows: Gap 1. Because couplers are banned in plastic hinges of bridge columns in moderate and high seismic zones, the current acceptance criteria for couplers (Table 2-1) do not reflect seismic performance requirements; therefore, the criteria should be revised. Gap 2. A material model is needed for computer modeling of bar couplers. Gap 3. There is a lack of a unified testing protocol for bar couplers. Monotonic, cyclic, and dynamic loading protocols should be established. C H A P T E R 4 Analytical Programs

Type of Connection Objective Analytical Studies (NCHRP Project 12-105) Analysis Parameters Deliverable Mechanical bar splices 1. Develop unified acceptance criteria for mechanical bar splices that are independent of the manufacturer to facilitate evaluation and adoption of couplers for use in earthquake- resistant ABC column connections. 2. Develop constitutive models for couplers for use in moment curvature analysis of columns with couplers and pushover analysis of bridges incorporating these columns. 1. Draft acceptance criteria, the required tests, test procedures, and coupler constitutive model; make necessary refinements and finalize the criteria combined with experimental studies (Chapter 3). 2. Use existing constitutive models as a starting point and refine on the basis of the available test data. 1. The criteria consist of protocols for monotonic and cyclic loading. The parameters are the number of loading cycles and strain amplitudes. The data to be collected for each loading type and the acceptance criteria for the measured data are specified. 2. Parameters include the length of the coupler relative to the bar diameter, the rigidity of the coupler, and effective strain characteristics. 1. Testing methods and minimum acceptable measured parameters for qualifying the coupler for application in ABC seismic connections. 2. A general, simple analytical model to account for the geometric and stiffness characteristics of couplers. Mechanically spliced column connections 1. Quantify the effect of couplers on the seismic performance of columns with emphasis on the displacement ductility or drift capacity or both. 2. Develop a standard testing protocol for columns with couplers. Conduct an extensive parametric study in the form of moment curvature and pushover analyses by using verified modeling methods. 1. The coupler parameters studied are coupler length, coupler rigid length factor, coupler location, and effect of two couplers on each bar. 2. The parameters studied are axial load, aspect ratio, ductility, number of columns in bents, and bar debonding. 1. A design equation for estimating the ductility capacity of columns with couplers. 2. A modified plastic hinge length accounting for the couplers. 3. A testing protocol for columns with couplers. Grouted duct design equation Develop preliminary design equation(s) for grouted ducts that use conventional high-strength grouts by statistical analysis of existing data. Identify the key parameters in the existing test data on grouted ducts and incorporate them in representative equations. The parameters include grout compressive strength, anchorage length, concrete compressive strength, duct diameter, and other important parameters that have been identified in the tests. Design equations that include all critical parameters for bars anchored in ducts filled with conventional high-strength grouts. Grouted duct column connections Recommend minimum dimensions of integral cap beam cross sections, footings, and pile shafts to resist biaxial loading. Conduct detailed finite element analyses to determine the minimum size of column adjoining members. Models with typical dimensions of pile shafts, pile caps, and cap beams serve as benchmarks. Subsequently, the sizes of the column connecting members are increased in the weak direction with 0.1D increments until the full plastic moment of the column is developed without connection failure. Minimum dimensions of column adjoining members to accommodate grouted duct connections. Pocket/socket connections 1. Develop design equation(s) using the available test data. 2. Recommend minimum dimensions of integral cap beam cross sections, footings, and pile shafts to resist biaxial loading. Conduct detailed finite element analyses to determine the minimum size of column adjoining members. Models with typical dimensions of pile shafts, pile caps, and cap beams serve as benchmarks. Subsequently, the sizes of the column connecting members are increased in the weak direction with 0.1D increments until the full plastic moment of the column is developed without the connection failure. 1. Design equation for embedment length of column in the pocket/socket. 2. Minimum dimensions of column adjoining members to accommodate pocket/socket connections. Note: D = column diameter. Table 4-1. Analytical programs for three types of column connections in accelerated bridge construction.

154 Proposed AASHTO Seismic Specifications for ABC Column Connections Gap 4. Comprehensive test data are needed for couplers under monotonic, cyclic, and dynamic tensile loading using the unified loading protocol (Gap 3) and the new acceptance criteria (Gap 1) to determine suitability of a coupler for precast column connection and to establish the coupler material model properties for use in analysis and design (Gap 2). Gaps 1 through 3 for mechanical bar splices are addressed in this section. First, a set of new acceptance criteria is presented. Then, a material model is proposed for all types of tension- compression couplers. Finally, testing protocols are presented for monotonic, cyclic, and dynamic loading. Note that Gap 4 was addressed in the previous chapter. 4.2.1 Proposed Acceptance Criteria for Mechanical Bar Splices Current U.S. bridge design codes specify certain limitations for mechanical bar splices (see Table 2-1) mainly for use in noncritical sections or in bridge columns located in low seismic zones. The AASHTO LRFD Bridge Design Specifications, or AASHTO LRFD (AASHTO 2013), categorizes couplers as a “full-mechanical connection” when they resist a stress of at least 1.25 times the specified yield strength of the spliced bar. The AASHTO LRFD also specifies the total slip of a bar within the splice on the basis of the California Department of Transportation (Caltrans) Seismic Design Criteria (SDC) (Caltrans 2013). The AASHTO Guide Specifications for LRFD Seismic Bridge Design, or AASHTO SGS (AASHTO 2014), does not allow the use of “full-mechanical connections” in the plastic hinge of bridge columns located in Seismic Design Categories C and D. To consider the use of mechanical bar splices in column plastic hinges, new acceptance criteria that reflect column seismic loading are needed to determine the suitability of these splices. To facilitate certification of existing and new splices for seismic application, the acceptance criteria need to be universal, encompassing various couplers with a variety of characteristics. On the basis of the available information and the results of the tests performed on cou- plers (Chapter 3), the following minimum acceptance criteria for couplers in column plastic hinges are proposed: 1. The total length of a mechanical bar splice (Lsp) shall not exceed 15 times the diameter of the smaller of the two spliced bars in columns. 2. A spliced bar shall fracture outside the coupler region with a strength of at least 95% of the ultimate tensile strength of its reference bar, regardless of the loading type (e.g., mono- lithic, cyclic, or dynamic). The length of the coupler region (Lcr) is defined as Lcr = Lsp + 2αdb, where α is a variable limited to 2db (Figure 4-1) and db is the diameter of the larger spliced bar. Only ASTM A706 Grade 60 reinforcing steel bars shall be used for seismic applications. Couplers that meet both requirements are referred to in this report as “seismic mechanical bar splices” or “seismic couplers.” The limitation of the coupler length is to minimize the adverse effects of couplers on the rotational capacity of the structural member due to possible reduction in the length of the plastic hinge. Another reason for the length limit is that test data are available only for columns Figure 4-1. Coupler and bar regions.

Analytical Programs 155 with a coupler length of 15db or less. The literature review confirmed that bridge columns incorporating couplers that cannot develop the stress–strain capacity of the spliced bars fail prematurely (e.g., columns with short shear screw couplers). Therefore, only couplers in which the bar fractures outside the coupler region are acceptable. The AASHTO SGS presents the expected mechanical properties for ASTM A706 reinforcing steel bars. These requirements were adopted in the present study. Other types of steel bars shall not be used as longitudinal reinforcement in bridge columns in moderate and high seismic zones, owing to a lack of suf- ficient data. The 95% strength requirement guarantees that a seismic coupler is achieving large strains with sufficient strength. 4.2.2 Proposed Material Model for Mechanical Bar Splices As was discussed in Chapter 2, Tazarv and Saiidi (2016) proposed a material model for mechanically spliced bars, which was adopted in the present study. The model is repeated here for completeness. When a spliced bar is in tension (Figure 4-2), it can be assumed that a portion of the coupler (βLsp) is rigid and does not contribute to the elongation of the coupler region. Lsp is the coupler length, and β is the coupler rigid length ratio and is determined from tensile testing of a spliced bar. This ratio depends on the force transfer mechanism between the bar and coupler and is affected by deformation of the coupler region, including elongation of the bar within the cou- pler, elongation of the coupler, and any bar slippage (not to be confused with bar pullout). The reduction in the total elongation of the splice results in smaller overall strain in the coupler region compared to that measured in the bar alone (Figure 4-2). Therefore, the strain in the coupler region (esp) is estimated as (4-1) sp cr sp cr L L Ls ε ε = − β where es is the strain of an unspliced bar. The axial stiffness of the coupler region may vary, depending on the coupler stiffness and anchoring mechanism, such as the size and bearing strength of the threads in threaded couplers or the bond behavior between the sleeve and the grout in grouted sleeve couplers. Another example is the extent of penetration of screws into the spliced bars and the strength of screws in shear screw couplers. The coupler rigid length ratio ranges theoretically from 0.0 to 1.0. Figure 4-3 shows coupler region stress–strain relationships for coupler rigid length ratios of 0.25 and 0.75 for a No. 10 ASTM A706 Grade 60 bar. Figure 4-2. Generic stress–strain model for mechanical bar splices. (a) Coupler region (b) Coupler stress–strain model Source: Tazarv and Saiidi (2016). St re ss Strain Bar Region Coupler Region

156 Proposed AASHTO Seismic Specifications for ABC Column Connections Mechanical bar couplers that meet the proposed minimum requirements do not alter the strength of spliced bars, because the connection strength is controlled by the spliced bars. Couplers that do not exhibit fracture outside the coupler region are not acceptable. Examples include fracture of bars within the coupler due to stress concentration under the screws in some shear screw couplers, any bar pullout in grouted couplers, and thread failure in some taper- threaded couplers. In summary, mechanical bar couplers do not increase the strength beyond the strength of the spliced bars; thus, no adjustment in the overstrength factor beyond that required in the AASHTO SGS is necessary. Only ASTM A706 reinforcement is allowed to be incorporated in mechanically spliced bridge columns (Appendix C). Table 4-2 lists the mechanical properties of spliced bars on the basis of the proposed model specifically for ASTM A706 Grade 60 reinforcing bars. The model parameters are shown in Figure 4-4. Note that the coupler rigid length ratio should be determined through testing according to the standard testing methods proposed for couplers, as discussed next. 4.2.3 Proposed Method of Testing for Mechanical Bar Splices California Test 670 (California Department of Transportation 2004) and ASTM A1034 (ASTM 2015) set forth testing procedures for reinforcing steel bar mechanical splices. Since the ASTM standard provides neither a modeling method for couplers nor acceptance criteria, the present study adopted the California test method. However, further modifications were made Figure 4-3. Stress–strain relationships for mechanically spliced No. 10 bars. (a) Low rigidity (a = 0.25) (b) High rigidity (a = 0.75) 0 100 200 300 400 500 600 700 800 0 20 40 60 80 100 120 0 0.02 0.04 0.06 0.08 0.1 St re ss ( M P a) St re ss ( ks i) Strain (in./in.) Reinforcing Steel Coupler Region Including Coupler Effects 0 100 200 300 400 500 600 700 800 0 20 40 60 80 100 120 0 0.02 0.04 0.06 0.08 0.1 St re ss ( M P a) St re ss ( ks i) Strain (in./in.) Reinforcing Steel Coupler Region Including Coupler Effects eulaV raB gnitcennoC fo eziS noitatoN ytreporP Expected yield stress (ksi) No. 3 to No. 18 68 Expected tensile strength (ksi) No. 3 to No. 18 95 Expected yield strain No. 3 to No. 18 Modulus of elasticity (ksi) No. 3 to No. 18 Onset of strain hardeninga No. 3 to No. 18 Ultimate tensile strain No. 4 to No. 10 No. 11 to No. 18 Note: Lsp = coupler length; β = coupler rigid length ratio; Lcr = coupler region (Lsp + 2αdb); alpha shall not exceed 2. aMay need to reduce in analytical models for convergence issues but shall not be less than the yield strain. Table 4-2. Coupler mechanical properties connecting ASTM A706 Grade 60 reinforcement.

Analytical Programs 157 to accommodate the requirements for couplers presented in the previous sections. For example, the California test procedure only allows testing of couplers with a length of 10db or less. This limitation is removed in the proposed method. Preliminary testing procedures for mechanical bar couplers to be used in the plastic hinge region of bridge columns were developed prior to performing the coupler tests presented in Chapter 3. The test methods were further modified upon completion of the coupler tests. A summary of the major changes is presented below to support the final proposed testing methods presented in Appendix B. • A strength limit (the strength of a spliced specimen shall not be less than 95% of the ulti- mate tensile strength of its reference unspliced bar) was added to the general requirements for seismic couplers. This change was made to account for material variability and to pro- vide some tolerance in the acceptance criteria. The anecdotal feedback from the industry indicated that without this flexibility, splice manufacturers might resort to heat treatment of spliced bars, which potentially could have undesirable consequences. • A quantitative measure was added to identify a seismic coupler through testing (all of the four spliced bar specimens within each loading type should meet the proposed requirements to be considered acceptable as a seismic coupler). • The length of the coupler region was increased from (Lsp + 2.0db) to a maximum of (Lsp + 4.0db). This was done to accommodate different strain-measuring devices. • A range of 0.5 to 1.0 was recommended for the coupler rigid length ratio. • The target dynamic strain rate was reduced from 75,000 µe/s (7.5%/s) to 30,000 µe/s (3.0%/s). This strain rate is more reflective of the strain rates of column longitudinal bars during actual earthquakes. Table 4-3 presents the measured strain rates for longitudinal bars of scaled columns tested on shake tables. These strain rates were converted to the correspond- ing rates in full-scale models. The average strain rate for the full-scale equivalent models was 16,256 µe/s, and the standard deviation was 12,053 µe/s. On the basis of this data, the average strain rate plus 1 standard deviation was recommended for the dynamic tensile testing of unspliced and spliced reinforcing steel bars. 4.2.4 Validation of Proposed Material Model for Mechanical Bar Splices The accuracy of the proposed coupler material model was evaluated by using the test data from previous studies and those obtained in the present study. Three types of No. 10 (32 mm) Figure 4-4. Stress–strain model for mechanical bar splices connecting ASTM A706 bars. Note: expected tensile strength (ksi); modulus at the onset of strain.

158 Proposed AASHTO Seismic Specifications for ABC Column Connections mechanical bar splices—grouted, headed, and swaged—were tested according to the proposed test methods (Appendix B), on the basis of which the coupler rigid length ratios were established (Chapter 3, Section 3.2.5). Note that the coupler rigid length ratio could vary according to the size and type of couplers. Therefore, the ratio used in design has to be determined for the particular coupler type and bar size to be used in the bridge. Figure 4-5 shows the calculated and measured stress–strain relationships for grouted, headed, and swaged couplers splicing No. 10 (32 mm) bars. The data obtained from the litera- ture for No. 8 (25 mm) grouted and headed couplers are also included in the figure. It can be seen that, except for the initial stiffness in headed bar splices, the proposed stress–strain model captured key parameters for different coupler types and reproduced the coupler behavior with a reasonable accuracy in all cases. In displacement-based design, ultimate strains and ultimate displacements are the design targets. The proposed model captured the ultimate strains for different mechanical bar splices with good accuracy. The deviation in the pre-yield branches of the coupler behavior (e.g., headed bar splices) does not affect the seismic design of bridge columns because the cou- pler length is negligible with respect to typical column heights; thus, the coupler effect on the column’s overall stiffness is minimal. The previous experimental studies did not report any premature cracking at the coupler levels or any noticeable reduction in the initial stiffness of mechanically spliced bridge columns. 4.3 Mechanically Spliced Bridge Columns The objectives of the work presented in this section are to (1) quantify coupler effects on the seismic performance of mechanically spliced bridge columns and (2) recommend a standard testing protocol for columns with couplers. The main gap identified about the seismic performance of mechanically spliced column connections was the scarcity of the available test data from column model testing. The avail- able data, including those obtained in the present study (Chapter 3), were not sufficient to quantify the effect of couplers on the seismic behavior of bridge columns. To address variations in coupler type, anchoring mechanism, coupler length, and coupler location inside columns, a substantial number of test data beyond the available information are required. To address this Column Bar Strain Rate (ld/s) References Column Scale Scaled Column Full-Scale Column Laplace et al. (2001) 0.33 10,000 5,774 Nada et al. (2003) 0.40 21,810 13,794 Johnson et al. (2006) 0.25 59,702 29,851 Phan et al. (2005) 0.33 25,200 14,549 Brown and Saiidi (2009) 0.25 18,875 9,438 Zaghi and Saiidi (2010) 0.20 92,500 41,367 Mehraein and Saiidi (2016) 0.27 10,200 5,267 Benjumea et al. (2019) 0.35 16,912 10,005 Average 16,256 SD 12,053 Average + 1.0SD 28,309 Table 4-3. Measured bridge column longitudinal reinforcement strain rates in dynamic testing.

Analytical Programs 159 Figure 4-5. Accuracy of proposed stress–strain model for mechanical bar splices. (a) No. 8 grouted coupler, a = 0.70 (b) No. 8 headed bar coupler, a = 0.85 (c) No. 10 grouted coupler, a = 0.55 (d) No. 10 headed bar coupler, a = 0.50 (e) No. 10 swaged coupler, a = 0.90 Note: εu = strain at peak stress. 0 100 200 300 400 500 600 700 800 0 20 40 60 80 100 120 0 0.02 0.04 0.06 0.08 0.1 St re ss ( M P a) St re ss ( ks i) Strain (in./in.) Measured in Coupler Region Calculated for Coupler Region Steel Bar Only Test data: Haber et al. (2015) Unspliced Bar: εu = 0.15 Spliced Bar: εu = 0.058 0 100 200 300 400 500 600 700 800 0 20 40 60 80 100 120 0 0.02 0.04 0.06 0.08 0.1 St re ss ( M P a) St re ss ( ks i) Strain (in./in.) Measured in Coupler Region Calculated for Coupler Region Steel Bar Only Test data: Haber et al. (2015) Unspliced Bar: εu = 0.132 Spliced Bar: εu = 0.076 0 100 200 300 400 500 600 700 800 0 20 40 60 80 100 120 0 0.02 0.04 0.06 0.08 0.1 St re ss ( M P a) St re ss ( ks i) Strain (in./in.) Measured in Coupler Region Calculated for Coupler Region Steel Bar Only Test data: NCHRP 12-105 Unspliced Bar: εu = 0.105 Spliced Bar: εu = 0.05 0 100 200 300 400 500 600 700 800 0 20 40 60 80 100 120 0 0.02 0.04 0.06 0.08 0.1 St re ss ( M P a) St re ss ( ks i) Strain (in./in.) Measured in Coupler Region Calculated for Coupler Region Steel Bar Only Test data: NCHRP 12-105 Unspliced Bar: εu = 0.0973 Spliced Bar: εu = 0.0697 0 100 200 300 400 500 600 700 800 0 20 40 60 80 100 120 0 0.02 0.04 0.06 0.08 0.1 St re ss ( M P a) St re ss ( ks i) Strain (in./in.) Measured in Coupler Region Calculated for Coupler Region Steel Bar Only Test data: NCHRP 12-105 Unspliced Bar: εu = 0.111 Spliced Bar: εu = 0.047

160 Proposed AASHTO Seismic Specifications for ABC Column Connections issue, an extensive analytical parametric study was performed to better understand the seismic behavior of spliced columns and to quantify coupler effects. Through the use of the results of the parametric studies, simple design equations were proposed. As part of the parametric studies, the effect of the debonding of mechanically spliced column longitudinal reinforcement on displacement capacities was also investigated. To address the second objective of the study discussed above, the research team reviewed the available seismic testing guidelines for columns. 4.3.1 Parametric Studies An extensive parametric study was carried out to investigate coupler effects on the seismic performance of bridge columns. Fifteen reference cast-in-place (CIP) reinforced concrete columns with no couplers were designed according to the AASHTO SGS (AASHTO 2014) to achieve displacement ductility capacities of 3, 5, and 7. Two axial load indexes of 5% and 10%, and three column aspect ratios of 4, 6, and 8 were included in the analyses. The axial load index is defined as the ratio of the column axial load to the product of the specified column concrete compressive strength and the column gross section area. The aspect ratio is the ratio of the column height to the column diameter. Table 4-4 presents basic properties assumed in the design and analysis, and Figure 4-6 shows pushover relationship for a few reference CIP columns. Note that the transverse reinforcement in some of the columns was intentionally low, to determine the coupler effect when the displacement ductility capacity was low (about 3). OpenSees (2013) was used in all pushover analyses of mechanically spliced columns and their corresponding CIP columns. 4.3.1.1 Mechanically Spliced Column Model Figure 4-7 shows the detail of the spliced column model incorporating single- and double- level couplers (two couplers per column longitudinal bar). It is assumed that shifting the coupler location by using a pedestal would alleviate the demand on the couplers from plastic hinge rota- tion. The height of the pedestal is reduced to near zero to simulate cases with no pedestal. For modeling purposes, a pedestal is needed to monitor the stress–strain behavior and to calculate the ultimate displacement. Pedestals add an extra step in construction that might outweigh the Table 4-4. Reference column design parameters for reinforced concrete. Parameter Value Column diameter (Dc) 4 ft Aspect ratio (AR) 4, 6, 8 Column length (L) 16 ft, 24 ft, 32 ft Concrete compressive strength (fc' ) 5.0 ksi Axial load index (ALI) 5% (452 kips); 10% (905 kips) Longitudinal reinforcement 22 No. 9 (ρl = 1.21%) Transverse reinforcement (sample values for AR = 6) ALI 5%, ductility 3: No. 3 hoops @ 10 in. (ρs = 0.1%) ALI 5%, ductility 5: No. 4 hoops @ 4 in. (ρs = 0.45%) ALI 5%, ductility 7: No. 5 hoops @ 3.5 in. (ρs = 0.81%) ALI 10%, ductility 3: No. 3 hoops @ 6 in. (ρs = 0.17%) ALI 10%, ductility 5: No. 4 hoops @ 3.5 in. (ρs = 0.52%) ALI 10%, ductility 7: No. 5 hoops @ 3 in. (ρs = 0.94%) Concrete cover 2 in. Reinforcing steel bar properties AASHTO SGS (AASHTO 2014) Note: ρl = longitudinal steel ratio; ρs = transverse steel bar volumetric ratio.

Analytical Programs 161 benefits of shifting the plastic hinge. However, they are included in the present study to provide an alternative for designers. For the single-level coupler model, three force-based elements, each with five integration points, were used to model the pedestal, coupler region, and the remaining portion of the column. This type of analytical element is called a distributed plasticity model. An alternative column element is a lumped plasticity model, which assumes a plastic length, usually equal to an empirical plastic hinge length, at the end of the element. The AASHTO SGS does not specify the type of column element in a pushover analysis; however, the use of a lumped plasticity element is more common in practice, since AASHTO specifies the analytical plastic hinge for conven- tional nonspliced columns. One may use a lumped plasticity element for mechanically spliced bridge columns. In this case, the AASHTO analytical plastic hinge length should be modified to account for the coupler effects. In the parametric study described in this section, only the dis- tributed plasticity model was used to directly allow the inclusion of the coupler length, location, Figure 4-6. Sample pushover curves for reference reinforced concrete columns. (a) AR = 4, ALI = 10%, ductility = 3 (b) AR = 4, ALI = 10%, ductility = 7 (c) AR = 6, ALI = 5%, ductility = 3 (d) AR = 6, ALI = 5%, ductility = 7 (e) AR = 8, ALI = 5%, ductility = 3 (f) AR = 8, ALI = 5%, ductility = 7 Note: AR = aspect ratio; ALI = axial load index; µ = displacement ductility capacity. 0 200 400 600 800 1000 1200 0 50 100 150 200 250 300 0 1 2 3 4 5 6 7 8 9 10 B as e S he ar ( kN ) B as e S he ar ( ki ps ) Drift (%) Actual Idealized l =2.92 RC-AR4-ALI10-D3 0 200 400 600 800 1000 1200 0 50 100 150 200 250 300 0 1 2 3 4 5 6 7 8 9 10 B as e S he ar ( kN ) B as e S he ar ( ki ps ) Drift (%) Actual Idealized l =6.93 RC-AR4-ALI10-D7 0 200 400 600 800 1000 1200 0 50 100 150 200 250 300 0 1 2 3 4 5 6 7 8 9 10 B as e S he ar ( kN ) B as e S he ar ( ki ps ) Drift (%) Actual Idealized l =3.17 RC-AR6-ALI5-D3 0 200 400 600 800 1000 1200 0 50 100 150 200 250 300 0 1 2 3 4 5 6 7 8 9 10 B as e S he ar ( kN ) B as e S he ar ( ki ps ) Drift (%) Actual Idealized l =7.33 RC-AR6-ALI5-D7 0 200 400 600 800 1000 1200 0 50 100 150 200 250 300 0 1 2 3 4 5 6 7 8 9 10 B as e S he ar ( kN ) B as e S he ar ( ki ps ) Drift (%) Actual Idealized l =3.03 RC-AR8-ALI5-D3 0 200 400 600 800 1000 1200 0 50 100 150 200 250 300 0 1 2 3 4 5 6 7 8 9 10 B as e S he ar ( kN ) B as e S he ar ( ki ps ) Drift (%) Actual Idealized l =7.12 RC-AR8-ALI5-D7

162 Proposed AASHTO Seismic Specifications for ABC Column Connections and behavior in the analysis. A modified analytical plastic hinge length is presented later in this chapter for completeness. The properties of the steel fibers in sections within the coupler region were based on the proposed coupler stress–strain relationship, while the original reinforcing steel fibers were used for other fiber sections. Pushover analysis was performed to investigate the coupler effect on the force-displacement behavior of spliced columns. The ultimate displacement of each column was determined when the • Core concrete failed (i.e., when the core concrete strain was 1.5 times the ultimate strain capacity of the calculated core concrete), • Reinforcing steel bars at the column–footing interface fractured [i.e., when the steel strain reached the ultimate strain capacity specified in the AASHTO SGS (AASHTO 2014)], or • The lateral load dropped by 15% relative to its peak. The displacement ductility capacity was calculated as the ratio of the ultimate displacement capacity to the effective yield displacement, as defined in the AASHTO SGS (AASHTO 2014). The P-D effect was included in the analyses. The effect of double-level couplers spaced vertically at Ssp on center was also studied. Headed bar and threaded couplers typically require two levels of couplers in precast con- struction because of tolerance requirements. The modeling method for these columns (Fig- ure 4-7b) was the same as that discussed for the spliced columns with single-level couplers, but two more elements were added in which one element was to model the column sections between the two levels of the couplers and the second was to include the second coupler region. 4.3.1.2 Validation of Proposed Mechanically Spliced Column Model Haber et al. (2014) tested five half-scale bridge columns under reversed slow cyclic load- ing to failure: four precast columns incorporating mechanical bar splices in the plastic hinge Figure 4-7. Analytical model details for mechanically spliced columns. (a) Columns with single-level couplers (b) Columns with double-level couplers Source: Tazarv and Saiidi (2016). Note: Lsp = coupler length; Hsp = pedestal height; Ssp = vertical distance of couplers. C ou pl er s L Column Section sp 22-#9 [22-Ø29mm] Elem. 1 Elem. 3 Footing Single-Level Couplers 4 ft [1.22 m] L Footing C ou pl er s Diam. 4 ft [1.22 m] Two-Level Couplers Cover: 2 in. [51 mm] Elem. 2 Elem. 4 Elem. 1 Elem. 2 L H sp L E le m . 3 E le m . 5 sp S sp H sp 4 ft [1.22 m] sp L

Analytical Programs 163 region and one CIP column as reference model. The grouted coupler column test speci- men with pedestal (GCPP) was selected for the validation of the proposed coupler modeling method. Haber et al. (2015) developed an analytical model for this column to simulate the measured response. The bond slip at the column–footing interface, bar slip at both ends of the couplers, coupler force-displacement relationship, and precast pedestal with grouted ducts were included in the model. To validate the coupler modeling method in bridge column analysis, the research team used the analytical model developed by Haber et al. (2015), but the elements representing the coupler bond-slip effects and the coupler force-displacement relationship were replaced by steel fibers, mimicking the proposed coupler stress–strain behavior discussed in Section 4.2. The bond slip of longitudinal bars at the footing level was also included in this model. Figure 4-8 shows the measured force-drift ratio envelope and the calculated pushover curve. It can be seen that the correlation between the calculated and the measured data is close. To further investigate the accuracy of the proposed modeling method, a pushover analy- sis similar to that discussed above was performed for the GC10 column [grouted sleeve with No. 10 (32 mm) bars] tested in the present study (Chapter 3, Section 3.3.2). Figure 4-9 shows the calculated and the measured force-drift relationships for GC10. It can be seen that Source: Tazarv and Saiidi (2016). 0 50 100 150 200 250 300 350 0 10 20 30 40 50 60 70 80 0 1 2 3 4 5 6 7 B as e S he ar ( kN ) B as e S he ar (k ip s) Drift (%) GCPP Measured GCPP Calculated Footing C ou pl er D uc ts Precast Pedestal Precast Column Figure 4-8. Force-drift for grouted coupler column test specimen with pedestal measured and calculated with proposed coupler model. 0 50 100 150 200 250 300 350 0 10 20 30 40 50 60 70 80 0 1 2 3 4 5 6 7 8 9 10 L at er al F or ce ( kN ) L at er al F or ce ( ki ps ) Drift (%) Calculated Based on AASHTO SGS Calculated w/ Measured Properties Measured Figure 4-9. Force-drift for GC10 measured and calculated with proposed coupler model.

164 Proposed AASHTO Seismic Specifications for ABC Column Connections the calculated drift capacity (6.87%) was lower than the measured drift capacity (7.95%) by 10% when the AASHTO expected mechanical properties for steel bars were used in the analysis. The strength was also underestimated, since the measured bar strength was higher than the AASHTO expected values. Both the calculated drift capacity (7.64%) and lateral load strength became closer to the measured data when the measured mechanical proper- ties were used. In both analyses, the initial stiffness was overestimated, mainly due to the exclusion of the bond-slip effects. The same trend exists in conventional pushover analyses of reinforced concrete (RC) columns that use distributed plasticity elements. Overall, the proposed pushover analysis incorporating the coupler size, location, and properties in the finite element (FE) model was found viable. 4.3.1.3 Parameters of Analytical Study on Mechanically Spliced Columns Effects of variation in important parameters related to couplers were studied for the columns described in the previous section. These parameters were the coupler length (Lsp), the pedestal height (Hsp), the coupler rigid length ratio (β), and the vertical distance of couplers (Ssp) in the case of columns with a pair of couplers on each bar. The focus of the study was on the displacement ductility capacity of columns. Three coupler lengths (Lsp = 5db, 10db, and 15db), four pedestal heights (Hsp = 5db, 10db, 20db, and 30db), three rigid length ratios (β = 0.25, 0.50, 0.75), and two vertical coupler spaces (Ssp = 2Lsp and 4Lsp) were included in the analysis, addressing all practical combinations of these parameters. Note that the coupler rigid length ratios were selected to establish the general trend of mechanically spliced bridge column behavior for a wide range of coupler properties and not a specific coupler. 4.3.1.4 Results of Parametric Studies More than 660 pushover analyses were carried out in the parametric study to investigate the effect of couplers on the displacement ductility capacity of bridge columns. The effect of couplers on the lateral strength of columns was not included in the parametric studies because the strength of spliced columns is the same as that of nonspliced columns, as long as bars fracture outside the coupler. Therefore, no modification of the overstrength factor is needed for the design of mechanically spliced columns if the couplers meet the minimum requirements of seismic couplers as proposed in the previous chapter. Figures 4-10 to 4-12 show samples of the results. The spliced column ductility (µsp) was normalized to its counterpart CIP column ductility (µCIP). Therefore, a normalized ductility ratio of 1 or greater indicates that the coupler had no adverse effect on the displacement ductility capacity. These figures clearly show that larger couplers, couplers closer to the column– footing interface, and more-rigid couplers could significantly reduce the spliced column dis- placement ductility capacity. That is, coupler length (Lsp), pedestal height (Hsp), and coupler rigid length ratio (β) are the most critical parameters that affect the displacement ductility capacity of mechanically spliced columns, but the effect of other parameters such as axial load index or the column aspect ratio is minimal. Shifting the couplers away from the column–footing interface by one-half the column diam- eter (0.5Dc) significantly improved the displacement ductility capacity of the spliced columns and made them comparable to their corresponding CIP columns. Another finding was that the coupler effect was more profound on columns with higher ductility. For example, the dis- placement ductility of a spliced column is expected to be 90% of the CIP column displacement ductility when the CIP column is designed for a displacement ductility capacity of 3. However, this ratio is 80% when the target CIP displacement ductility capacity is 7.

Figure 4-10. Effect of coupler length on ductility of columns with aspect ratio = 6 and axial load index = 5%. (a) Ductility = 3, a = 0.25 (b) Ductility = 3, a = 0.5 (c) Ductility = 3, a = 0.75 (d) Ductility = 5, a = 0.25 (e) Ductility = 5, a = 0.5 (f) Ductility = 5, a = 0.75 (g) Ductility = 7, a = 0.25 (h) Ductility = 7, a = 0.5 (i) Ductility = 7, a = 0.75 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l R C ) Hsp/db 5 10 15 Target lCIP = 3.0 Axial Load Index = 5% Coupler Rigid Length Factor (a) = 0.25 Lsp /db Average Deviation = 2% 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io (l sp / l C IP ) Hsp/db 5 10 15 Target lCIP = 3.0 Axial Load Index = 5% Coupler Rigid Length Factor (a) = 0.5 Lsp /db Average Deviation = 2% 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db 5 10 15 Target lCIP = 3.0 Axial Load Index = 5% Coupler Rigid Length Factor (a) = 0.75 Lsp /db Average Deviation = 2% 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io (l sp /l C IP ) Hsp/db 5 10 15 Target lCIP = 5.0 Axial Load Index = 5% Coupler Rigid Length Factor (a) = 0.25 Lsp /db Average Deviation = 3% 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db 5 10 15 Target lCIP = 5.0 Axial Load Index = 5% Coupler Rigid Length Factor (a) = 0.5 Lsp /db Average Deviation = 6% 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db 5 10 15 Target lCIP = 5.0 Axial Load Index = 5% Coupler Rigid Length Factor (a) = 0.75 Lsp /db Average Deviation = 8% 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db 5 10 15 Target lCIP = 7.0 Axial Load Index = 5% Coupler Rigid Length Factor (a) = 0.25 Lsp /db Average Deviation = 3% 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db 5 10 15 Target lCIP = 7.0 Axial Load Index = 5% Coupler Rigid Length Factor (a) = 0.5 Lsp /db Average Deviation = 5% 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db 5 10 15 Target lCIP = 7.0 Axial Load Index = 5% Coupler Rigid Length Factor (a) = 0.75 Lsp /db Average Deviation = 8%

Figure 4-11. Effect of coupler rigid length factor on ductility of columns with aspect ratio = 6 and axial load index = 5%. (a) Ductility = 3, Lsp = 5db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 3.0 Lsp = 5db (b) Ductility = 3, Lsp = 10db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 3.0 Lsp = 10db (c) Ductility = 3, Lsp = 15db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 3.0 Lsp = 15db (d) Ductility = 5, Lsp = 5db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 5.0 Lsp = 5db (e) Ductility = 5, Lsp = 10db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 5.0 Lsp = 10db (f) Ductility = 5, Lsp = 15db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 5.0 Lsp = 15db (g) Ductility = 7, Lsp = 5db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 7.0 Lsp = 5db (h) Ductility = 7, Lsp = 10db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 7.0 Lsp = 10db (i) Ductility = 7, Lsp = 15db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 7.0 Lsp = 15db

Figure 4-12. Effect of coupler spacing on ductility of columns with aspect ratio = 6 and axial load index = 5%. (a) Ductility = 3, Lsp = 5db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 3.0 Lsp = 5db Ssp = 2Lsp (b) Ductility = 3, Lsp = 10db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 3.0 Lsp = 10db Ssp = 2Lsp (c) Ductility = 3, Lsp = 15db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 3.0 Lsp = 15db Ssp = 2Lsp (d) Ductility = 5, Lsp = 5db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 5.0 Lsp = 5db Ssp = 2Lsp (e) Ductility = 5, Lsp = 10db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 5.0 Lsp = 10db Ssp = 2Lsp (f) Ductility = 5, Lsp = 15db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 5.0 Lsp = 15db Ssp = 2Lsp (g) Ductility = 7, Lsp = 5db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 7.0 Lsp = 5db Ssp = 2Lsp (h) Ductility = 7, Lsp = 10db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 7.0 Lsp = 10db Ssp = 2Lsp (i) Ductility = 7, Lsp = 15db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 25 30 35 Hsp/Dc D uc ti lit y R at io ( l s p/ l C IP ) Hsp/db β=0.25 β=0.5 β=0.75 Aspect Ratio = 6 Axial Load Index = 5% Ductility = 7.0 Lsp = 15db Ssp = 2Lsp

168 Proposed AASHTO Seismic Specifications for ABC Column Connections The effect of double-level couplers on the displacement ductility capacity is shown in Figure 4-12. It was found that the ductility of columns with two couplers on a reinforcing bar was approximately the same as the ductility of columns with single-level couplers when the couplers were vertically spaced at least 2Lsp on center (or 1.0Lsp face to face). 4.3.2 Proposed Equation for Reduction of Ductility Capacity The findings of the parametric study indicated that the most important parameters that control the displacement ductility capacity of mechanically spliced columns are the coupler length, the coupler rigid length ratio, and the coupler location within the plastic hinge. There- fore, only these parameters were included in the development of reduction factors for the ductility capacity of columns with couplers. It was found that when the pedestal height (Hsp) was normalized to the coupler length (Lsp), the ductility ratio (µsp/µCIP) against Hsp/Lsp followed a hyperbolic relationship for a given coupler rigid length factor (β), as shown in Figure 4-13. Figure 4-13d incorporates the results from more than 660 analyses. On the basis of this obser- vation, a hyperbolic equation accounting for the coupler effect based on the lower bound of the parametric study results was developed, as follows: 1 0.18 (4-2) sp CIP sp sp 0.1H L ( )µ µ = − β     β where µsp is the spliced column displacement ductility capacity and µCIP is the nonspliced CIP column displacement ductility capacity. For columns in which the couplers are installed imme- diately above the footings or below the cap beam, Hsp = 0.1 in. (2.5 mm) should be used. (a) Shown for ductility = 3 (b) Shown for ductility = 5 (c) Shown for ductility = 7 (d) Shown for all ductility values Note: Eq. = equation. 0.6 0.7 0.8 0.9 1 1.1 0 1 2 3 4 5 6 7 D uc til ity R at io ( µ s p/µ C IP ) Hsp/Lsp β=0.25 β=0.5 β=0.75 Ductility= 3.0 Solid lines are based on proposed Eq. = 0.75 = 0.5 = 0.25 0.6 0.7 0.8 0.9 1 1.1 0 1 2 3 4 5 6 7 D uc til ity R at io (μ sp /μ C IP ) Hsp/Lsp β=0.25 β=0.5 β=0.75 Ductility= 5.0 Solid lines are based on proposed Eq. 0.6 0.7 0.8 0.9 1 1.1 0 1 2 3 4 5 6 7 D uc til ity R at io ( μ s p/μ C IP ) Hsp/Lsp β=0.25 β=0.5 β=0.75 Ductility= 7.0 Solid lines are based on proposed Eq. 0.6 0.7 0.8 0.9 1 1.1 0 1 2 3 4 5 6 7 D uc til ity R at io (μ sp /μ C IP ) Hsp/Lsp β=0.25 β=0.5 β=0.75 Ductility= 3.0 to 7.0 Solid lines are based on proposed Eq.   Figure 4-13. Proposed design equation accounting for coupler effects versus analysis results.

Analytical Programs 169 The proposed equation is shown in solid curves in Figure 4-13 for different coupler rigid length ratios and is repeated in all the graphs. It can be seen that the combined effect of the three parameters (β, coupler length, and coupler location) can reduce the displacement ductility capacity of a mechanically spliced column from 10% to 40%. The latter value occurs when very long and rigid couplers are used at the interface of the column and the adjoining member. The former value occurs when small couplers are used a few inches away from the interface. The equation was based on the lower bound of normalized ductility ratios, and thus is conservative in estimating the ductility capacity of spliced columns. Furthermore, the pro- posed equation was independent of the displacement ductility itself, even though the para- metric study showed that the nonspliced columns with a lower target displacement ductility were less sensitive to the incorporation of couplers (e.g., Figure 4-13, a–c). The proposed design equation is relatively simple and offers several advantages, the most important of which is that designers can consider a mechanically spliced column as a conven- tional column, design it according to current codes (e.g., AASHTO SGS), calculate its displace- ment ductility capacity, and then estimate the displacement ductility capacity of the spliced column by using the proposed equation. Three mechanically spliced columns discussed in Chapter 2 and the GC10 column tested as part of this project (Chapter 3) were used to validate the proposed design equation (Table 4-5). The three columns from the literature were selected because they did not incor- porate nonroutine details such as debonded longitudinal reinforcement, grouted ducts, or Reference/Column Calculated Measured Haber et al. (2014)/GCNP: Column with grouted sleeve couplers immediately above the footing surface use thus Haber et al. (2014)/HCNP: Column with headed bar couplers 5 in. (127 mm) above the column– footing interface or 4 in. (102 mm) from the footing surface to the bottom of the coupler thus Pantelides et al. (2014)/GGSS-1: Column with grouted sleeve couplers immediately above the footing surface use thus NCHRP 12-105/GC10: Column with grouted sleeve couplers immediately above the footing surface use thus Table 4-5. Verification of design equation accounting for coupler effects.

170 Proposed AASHTO Seismic Specifications for ABC Column Connections fiber-reinforced polymer jackets in the plastic hinges and their coupler rigid length ratios were known. Grouted sleeve couplers were used immediately above the column–footing interface in two of the columns. The third column utilized headed bar couplers. The column longitudinal bars were No. 8. Number 10 grouted couplers were used in GC10 immedi- ately above the footing surface. Since no reference CIP column reinforced with No. 10 bars was tested in the present project, the response of GC10 was compared with that for the CIP column reinforced with No. 8 bars tested by Haber et al. (2014). Table 4-5 presents the calculated reduction in the displacement ductility capacity for the four spliced columns obtained by using Equation 4-2. The measured reduction in the displacement ductility capacity relative to the reference nonspliced column is included for comparison. It can be seen that the calculated reductions in the displacement ductility capacity for all spliced col- umns were close to those measured in the tests. Furthermore, the results show that mechanical bar splices can reduce the displacement ductility capacity of the spliced column by up to 40% when rigid and relatively long couplers are installed immediately above the column–footing interface. The findings of the analytical studies also agree with this observation. 4.3.3 Proposed Modified Plastic Hinge Length The displacement capacity of bridge columns can be estimated through either moment cur- vature or pushover analysis, according to the current AASHTO SGS (AASHTO 2014). Plastic hinge length (Lp) is required in either method, as specified by AASHTO: 0.08 0.15 0.3 (4-3)ye yeL L f d f dp b b= + ≥ where L = length of column (in.) from point of maximum moment to inflection point, fye = expected yield strength (ksi) of longitudinal column reinforcing steel bars, and db = nominal diameter (in.) of longitudinal column reinforcing steel bars. The results of the experimental and analytical investigations presented in the previous sections revealed that mechanical bar splices incorporated in the plastic hinge region of a duc- tile member change its displacement capacity. The bulk of test data on mechanically spliced columns is not sufficient to empirically establish an equation for the plastic hinge length. There- fore, an equation for the plastic hinge length of spliced columns (Lp sp) was developed on the basis of the conventional column plastic hinge length as well as the coupler mechanical properties: 1 (4-4)sp sp spL L H L L Lp p p p= − −   β ≤ where Lp is the plastic hinge length of the nonspliced conventional column, according to the AASHTO SGS (Equation 4-3). When the coupler is embedded in the adjoining member (the footing or cap beam), Hsp is defined as the distance from the connection interface to the coupler face close to the interface. All other parameters were defined in previous sections. The main assumption in Equation 4-4 is that the rigid portion of the coupler in the plastic hinge region does not contribute to the plastic lateral displacement of the column; thus, it can be excluded from the original plastic hinge length. The term (1 – Hsp/Lp) was used to include the coupler location effect, in which couplers installed at column ends will have a minimal plastic hinge length, and thus a minimal displacement capacity. Columns with couplers outside the plastic hinge length are essentially the same as those of nonspliced columns in terms of displacement capacity.

Analytical Programs 171 Table 4-6 presents the calculated and measured displacement ductility capacities for the four spliced columns discussed in Section 4.3.2. The calculated displacement ductility capac- ities were based on the proposed modified equation for plastic hinge length (Equation 4-2) through moment curvature analyses according to the AASHTO SGS (AASHTO 2014). It can be seen that the proposed equation for the plastic hinge length of mechanically spliced bridge columns resulted in displacement ductility capacities that were in good agreement with those measured in the tests. Overall, the modified plastic hinge length proposed here was found to be simple, generic, and reasonably accurate for the design of mechanically spliced bridge columns. Of the two proposed equations, Equation 4-2 and 4-4, the former may result in a more con- servative design, although the difference is not significant. For example, the calculated displace- ment ductility capacity of HCNP obtained by using Equation 4-2 was only 2% lower than that obtained by using Equation 4-4. 4.3.4 Effects of Bar Debonding on Performance of Mechanically Spliced Columns Three phenomena usually cause premature failure of a steel reinforcement in RC members: (1) stress concentration, (2) low cycle fatigue, and (3) strain concentration. Stress will be con- centrated on a portion of a bar where the cross section or mechanical properties are abruptly changed (e.g., because of a notch, welding) either intentionally or by construction errors. Low cycle fatigue, in which a bar fractures in tension after a few occurrences of buckling in com- pression, is usually seen in members with low confinement or a small concrete cover, or when the concrete cover fails. Strain concentration, which is a relatively less familiar term, occurs when deformation in a portion of a bar is restricted and the deformation is thus shifted to other parts of the bar. For example, when a deformed bar is embedded in concrete, strains are concentrated between the ribs (local strain concentration); thus, the total deformation of the bar is less than that of a free bar with the same length tested in the air. Debonding of reinforcement from concrete eliminates localized plasticity and increases the overall deforma- tion to the level of a free bar. Strain concentration can also occur near rigid and long couplers in the plastic hinge. In this case, all the deformation must take place over the unspliced portion of the reinforcement in the plastic hinge area, resulting in strain concentration (global strain concentration) and a reduction of ductility capacity. To spread plasticity over a longer portion of the column longitudinal bars, the bars may be debonded from concrete near the coupler. When a bar is debonded from concrete, the strain compatibility assumption between the bar and the surrounding concrete is violated, which makes analytical modeling of debonded bars very complex. Three analytical methods to simulate debonded bars in RC members were found in literature: 1. Model the debonded portion of reinforcement as an individual truss element with modified formulation (Kim 2008), 2. Use conventional truss elements to represent the debonded portion of reinforcement (Mantawy and Sanders 2016), and 3. Modify the stress–strain relationship of debonded reinforcing bars (Tazarv and Saiidi 2014). Method 3 was selected for further investigation because (1) Method 1 and Method 2 require additional nodes and elements to simulate the reinforcement location inside a section, (2) Method 1 is not available in most FE software packages, and (3) only Method 3 can be used in fiber-section analysis. A summary of bar debonding Method 3 and the results of the parametric study on the effect of bar debonding on the seismic performance of mechanically spliced columns follows.

Table 4-6. Verification of proposed plastic hinge length for mechanically spliced columns. derusaeMdetaluclaCnmuloC/ecnerefeR Haber et al. (2014)/GCNP: Column with grouted couplers immediately above the footing surface Nonspliced Column (CIP): Bar size: No. 8, column length = 108 in., Lp = 20.4 in. Moment curvature analysis: Idealized yield curvature ( ): 0.00023 rad/in. Ultimate curvature ( ): 0.0032 rad/in. Spliced Column: Note: Displacement ductility capacity for a reference column is not needed in this method. It is provided for comparison. μ (3.4% difference) μ (0.7% difference) Haber et al. (2014)/HCNP: Column with headed bar couplers 5 in. (127 mm) above the column–footing interface Nonspliced Column (CIP): Bar size: No. 8, column length =108 in., Lp = 20.4 in. Moment curvature analysis: Idealized yield curvature ( ): 0.00023 rad/in. Ultimate curvature ( ): 0.0032 rad/in. Spliced Column: μ (3.4% difference) μ (8% difference) Pantelides et al. (2014)/GGSS-1: Column with grouted couplers immediately above the footing surface Nonspliced Column (CIP): Bar size: No. 8, column length = 93 in., = 20.4 in. Moment curvature analysis: Idealized yield curvature ( ): 0.00028 rad/in. Ultimate curvature ( ): 0.0043 rad/in. μ Spliced Column: , , μ μ (5.4% difference) μ (1.5% difference) NCHRP 12-105/GC10: Column with grouted couplers immediately above the footing surface Nonspliced Column (CIP): Bar size: No. 10, Column Length =108 in., = 25.91 in. Moment curvature analysis: Idealized yield curvature ( ): 0.00025 rad/in. Ultimate curvature ( ): 0.00278 rad/in. μ Spliced Column: , , μ Note: Displacement ductility capacity for a reference column is not needed in this method. Also, note that no test was done on a reference CIP reinforced with No. 10 bars. However, using the CIP data in Haber et al. (2014): μ (0.7% difference) μ (1.9% difference)

Analytical Programs 173 4.3.4.1 Bar Debonding Model Experimental studies have shown that the bond strength of plain bars is less than 30% of that of deformed bars (Mo and Chan 1996; Verderame et al. 2009). A European design code (CEB- FIP Model Code 1990) recommends a plain bar bond strength of only 10% of the deformed bar bond strength (Comité Euro-International Du Beton 1993). Considering that cyclic loads tend to further reduce bond strength, the research team decided to ignore the bond strength of plain bars in the present study. The bond behavior of debonded deformed bars was assumed to be the same as the plain bar bond behavior with negligible bond strength. Thus, it can be assumed that the behavior of a debonded bar embedded in concrete is similar to the behavior of a bar that is not connected on its surface to concrete. Level B in Figure 4-14a illustrates this condition, at which the bar is debonded between Levels A and B. The modified strain of the debonded bar at Level B is calculated on the basis of cumulative displacements at this level, which consists of 1. The bar deformation at Level B, assuming full bond (original bar force-deformation relationship); 2. Displacement due to slippage of the bar at Level A relative to the concrete below; and 3. The bar elongation of the anchored portion of the bar at Level A. The modified strain of the debonded bar (es′) at Level B is (4-5)elong F k Ls s b ′ε = ε +    + ε 78.5 (4-6)emdk d L ub d= 9.5 800 psi, for #11 bars and smaller 6 for #14 and #18 bars (4-7)u f d f c b c = ′ ≤ ′     4 (4-8)embL F d u f d u L b s b= π = ≤ where es = strain (in./in.)of the original bar; F = bar force (lb); kb = bond force-slip stiffness (lb/in.), valid when bar pullout is prevented; (a) Steel bar embedded in concrete Source: Tazarv and Saiidi (2014). kb A B Concrete B ar C ra ck (F) B ar B on d Fo rc e Bar Slip B ar F or ce Deformation Lemb Se rie s S pr in gs Footing 0 100 200 300 400 500 600 0 20 40 60 80 100 0 0.02 0.04 0.06 0.08 0.1 0.12 St re ss ( M Pa ) St re ss ( ks i) Strain (in/in) Original Reinforcing Steel Modified Reinforcing Steel Including Debonding Effect (b) Modified stress–strain relationship Figure 4-14. Bond-slip and bar debonding effect on stress–strain relationship.

174 Proposed AASHTO Seismic Specifications for ABC Column Connections db = diameter (in.) of the bar; Lemd = embedment length (in.) of the bar in the connection; u = bond strength (psi) of the bar; f c′ = compressive strength (psi) of concrete; L = effective development length (in.) required to resist the applied load; and fs = bar stress (psi) due to F. It is proposed that the modulus of elasticity of the bar be modified to account for the softening effect of bond slip on the overall bar stiffness: (4-9)fs y y′ε = ′ε where fy is the yield strength (or the expected yield, depending on which AASHTO code is selected) of the bar and ey′’ is the modified yield strain. eelong can be found by using Wehbe’s method (Wehbe et al. 1997), as follows: 2 2 2 (4-10)elong 1 f f L L f f s s y y s s y ε = ε ≤ ε + ε >      4 (4-11)1L f f d u L s y b( )= − ≤ Strain-related parameters were modified according to the proposed method to account for bond-slip and bar debonding effects, while strength-related parameters such as yield and ulti- mate stresses remained the same as the original values (Figure 4-14b). This led to an increase in the yield and ultimate strains, which eventually resulted in greater displacement of the debonded bar and higher displacement capacity for the column. 4.3.4.2 Verification of Proposed Debonding Model Tazarv and Saiidi (2015b) tested a half-scale bridge column incorporating shape memory alloy reinforcement, engineered cementitious composite, and mechanical bar couplers in the plastic hinge region. The column, referred to as “HCS,” was reviewed previously in Section 2.2.4. Since the surface of shape memory alloy bars is smooth, it was assumed that they were fully debonded from the surrounding engineered cementitious composite and that, therefore, the equations presented for bar debonding were applicable. Figure 4-15 shows the measured and calculated Source: Tazarv and Saiidi (2015b). 0 50 100 150 200 250 300 350 0 10 20 30 40 50 60 70 80 0 2 4 6 8 10 12 La te ra l Fo rc e (k N ) La te ra l Fo rc e (k ip s) Drift (%) Measured Calculated w/ Bond-Slip & Bar Debonding Effects Calculated w/o Bond-Slip & Bar Debonding Effects Figure 4-15. Response of analytical models with bar debonding.

Analytical Programs 175 force-drift relationship of HCS. The calculated relationships include the response of analyti- cal models with (1) the original stress–strain properties for reinforcement and (2) modified stress–strain properties accounting for bond-slip and bar debonding effects based on the pro- posed model. It can be seen that the proposed model significantly improved the accuracy of the calculated response, with better match to the measured data. Furthermore, the figure clearly shows that debonding of column longitudinal reinforcement reduces the column stiffness and increases the yield displacements. 4.3.4.3 Parametric Studies on Debonding Effects A parametric study was carried out to investigate the effect of bar debonding on the displace- ment capacity of mechanically spliced bridge columns. The spliced column model was the same as that presented in Section 4.2.3. It was assumed that column longitudinal bars in the pedestal (with the height of Hsp in Figure 4-7) were debonded. Then the stress–strain relationship of steel fibers in the pedestal was modified according to the proposed method. The other column and coupler parameters (e.g., the coupler length, the pedestal height, the coupler rigid length factor, the column geometry, and axial load) and their intervals were the same as those presented in Section 4.3.1. 4.3.4.4 Results of Parametric Studies on Effect of Bar Debonding More than 100 pushover analyses were initially conducted to determine the trends (Fig- ure 4-16). It was found that the displacement ductility capacity is not a suitable measure for investigating the bar debonding effect, since debonding alters both the yield and ultimate displace- ments. For example, the ultimate displacement capacity of the column could increase by 10% as a result of debonding, but the calculated displacement ductility capacity might be lower because of the higher idealized yield displacement of the debonded column relative to the original col- umn. Therefore, the displacement capacity was selected as the main parameter for investigating (a) Coupler length variation (b) Coupler rigid length ratio variation (c) Column ductility variation Hsp/db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 0 5 10 15 20 25 30 35 Hsp/Dc D isp la ce m en t R at io (Δ sp -d eb /Δ sp ) 5 10 15 Target μCIP = 7.0 Axial Load Index= 5% Coupler Rigid Length Factor (β)= 0.25 Lsp /db 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 0 5 10 15 20 25 30 35 Hsp/Dc D isp la ce m en t R at io (Δ sp -d eb /Δ sp ) Hsp/db 0.25 0.5 0.75 Target μCIP = 7.0 Axial Load Index= 5% β 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 0 5 10 15 20 25 30 35 Hsp/Dc D isp la ce m en t R at io (Δ sp -d eb /Δ sp ) Hsp/db 3 5 7 Axial Load Index= 5% Coupler Rigid Length Factor (β)= 0.75 μ Figure 4-16. Bar debonding effect on displacement capacity of mechanically spliced columns.

176 Proposed AASHTO Seismic Specifications for ABC Column Connections the bar debonding effect. The displacement capacity of debonded spliced columns (Dsp−deb) was divided by the corresponding spliced column displacement capacity (Dsp), as shown in Figure 4-16. A displacement ratio of 1 or higher indicates that the debonding of the spliced column longitudinal reinforcement was effective in terms of improving the displacement capacity. The preliminary analyses showed that the improvement in the displacement capacities of mechanically spliced columns due to debonding was independent of the coupler length (Figure 4-16a) and the coupler rigid length ratio (Figure 4-16b). The most important parameters affecting the performance of mechanically spliced columns with debonded bars were the displace- ment ductility capacity of the reference column (Figure 4-16c) and the location of the couplers (or the pedestal height, which was also equal to the debonded length in these analyses). Furthermore, it was found that columns (conventional or spliced) in which the mode of failure was bar fracture (e.g., highly confined sections) would benefit most from longitudinal bar debonding, while debonding in columns with other modes of failure (core concrete fail- ure or significant reduction in lateral strength) would not improve the displacement capacity unless the length of the debonded zone exceeded 20db. This is because debonding is spe- cific to reinforcement and will not change the strain capacity of concrete. Figure 4-16c shows that lightly confined columns (those with smaller target displacement ductility) are adversely affected by debonding when the debonded length is small, while highly confined columns exhibit an average 8% increase in displacement capacities due to debonding. On the basis of the aforementioned findings, 24 additional pushover analyses were performed on columns with a target displacement ductility capacity of 7 and different geometries and axial loads (Figure 4-17). The longitudinal bar fractured in all the 24 columns. It was found that highly confined mechanically spliced columns with a debonded reinforcement length of 15db or more in the pedestal exhibited an average increase of 10% or more in displacement capacity. 4.3.4.5 Requirements for Bar Debonding in Mechanically Spliced Columns The displacement capacity of a mechanically spliced column may be increased by 10% if all of the following requirements are met: • The mode of failure of a spliced column is bar fracture. • The column longitudinal bars are properly debonded with a length of at least 15db. The debonded length may be partially in the column plastic hinge with the rest in the adjoining member, with the latter limited to 5db. • Debonding is done by covering the bars with materials such as tape. Waxing of deformed bars does not provide sufficient debonding. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.95 1.00 1.05 1.10 1.15 1.20 1.25 0 5 10 15 20 25 30 35 Hsp/Dc D isp la ce m en t R at io (Δ sp -d eb /Δ sp ) Hsp/db Target μCIP = 7.0 Figure 4-17. Bar debonding effect on displacement capacity of highly confined spliced columns.

Analytical Programs 177 4.3.5 Summary of Modeling Methods for Mechanically Spliced Columns A mechanically spliced column can be analyzed by three different modeling methods, as summarized in Table 4-7. The design of conventional (CIP) columns is included for com- pleteness. If Method 1 is selected, the modeling method for columns with couplers is the same as that for conventional nonspliced CIP columns. In this case, the displacement capacity of the CIP column is first calculated according to the current AASHTO SGS; then the calculated ductility is modified on the basis of the coupler location and properties by using the proposed equation. When Method 2 is selected, the modeling method for a mechanically spliced column is the same as that for CIP, but a modified plastic hinge length should be used. Either moment cur- vature or pushover analysis can be used in Method 2. In Method 3, the coupler stress–strain model is incorporated in the analysis, and the only acceptable method is a pushover analysis with distributed plasticity fiber-section elements, as moment curvature analysis is not sensitive to the location of couplers in the column. The verification of these methods using all available test data was presented in the previous sections. 4.3.6 Multicolumn Bents with Mechanically Spliced Columns With the same column geometry and details, the lateral displacement capacity of a single- column bent is generally lower than that of multicolumn bents because of the higher redundancy of multicolumn bents. It is expected that mechanically spliced multicolumn bents exhibit better seismic performance than their single-column counterparts; thus, the modeling methods proposed in the previous section for single-column bents may be conservatively used for the design of multi- column bents that incorporate couplers. Currently, there are no test data in the literature to validate the proposed modeling methods for the design of mechanically spliced multicolumn bents. Table 4-7. Modeling methods for mechanically spliced columns. Design Method Analysis Type Column Element in Pushover Analysis Analysis Requirements CIP columns Moment curvature or pushover Usually conducted with a lumped plasticity model, which requires an analytical plastic hinge length; however, a distributed plasticity model can also be utilized Current AASHTO Guide Specifications for LRFD Seismic Bridge Design Method 1. Spliced columns using proposed equation for displacement ductility Use CIP analysis results Use CIP analysis results μ μ Method 2. Spliced columns using proposed equation for plastic hinge length Moment curvature or pushover Lumped plasticity model only Similar to CIP but with Method 3. Spliced columns using proposed stress–strain model for couplers Pushover only Distributed plasticity model only Coupler stress–strain model (Table 4-2) Note: μ = mechanically spliced bent displacement ductility capacity, μ = corresponding nonspliced CIP bent displacement ductility capacity, β = coupler rigid length ratio, = distance (in.) from column end to nearest face of coupler embedded either inside column or inside column adjoining member, = coupler length (in.), = length (in.) of modified plastic hinge for mechanically spliced bridge columns, and Lp = analytical length (in.) of conventional column plastic hinge according to current AASHTO SGS.

178 Proposed AASHTO Seismic Specifications for ABC Column Connections 4.3.7 Testing Method for Mechanically Spliced Columns ACI 374.2R-13 presents guidelines for testing of RC members for seismic applications (ACI Committee 374 2013). FHWA prepared an internal report on the seismic testing of bridge columns (Handbook for Seismic Performance Testing of Bridge Piers, 2003) but this report is not currently available in the FHWA database. Either the ACI or the FHWA report can be used for the testing of bridge columns with mechanical bar splices. However, the loading should be cyclic under quasi- static or dynamic testing on a shake table. Results of a mechanically spliced column test should be compared with those of a reference nonspliced CIP column with the same geometry, reinforce- ment ratios, axial load, and material properties tested under the same loading protocol. The testing method for the grouted coupler column in the present study (see Chapter 3) was based on the ACI 374.2R-13 (2013) guidelines. The recommendations presented in this document were found to be sufficient for the testing of mechanically spliced bridge columns. 4.3.8 Summary of Study on Mechanically Spliced Bridge Columns The knowledge gaps regarding the performance of mechanically spliced bridge columns are identified in previous chapters. A material model for bar couplers is proposed in Chap- ter 3. This model was verified by using the available coupler test data, and the verified material model was then used in an extensive parametric study to quantify the effect of mechanical bar couplers on the displacement ductility capacity of bridge columns. It was found that stiff and long couplers installed at the interface of the column and the adjoining member may reduce the column displacement ductility capacity by as much as 40%. Three analytical methods for the design of mechanically spliced columns were proposed on the basis of the findings of the parametric study and were verified against experimental data. Further parametric study showed that debonding of longitudinal bars in the vicinity of couplers may improve the displacement capacity of columns with couplers. The information provided in this section should be treated as the background for the final proposed specifications. Refer to Appendices B and C for the design of actual bridge columns incorporating mechanical bar splices. 4.4 Grouted Duct Design Equation Four types of precast column connections suitable for ABC were introduced in previous chapters, and the related state-of-the-art literature review was presented. The main knowl- edge gaps identified in the literature for grouted duct connections were (1) the lack of a comprehensive design equation for the embedment length of straight deformed bars in ducts and (2) the minimum size of column adjoining members in the weak direction. Both analytical and experimental programs were planned to address these gaps. For the first gap, which is discussed here, the analytical program includes a thorough review of the previous pullout test data as well as development of an embedment length design equation. The experi- mental work done on grouted duct connections is presented in Chapter 3. With regard to the second gap, detailed FE analysis was performed, which is discussed in Section 4.5. 4.4.1 Bond Behavior of Grouted Duct Connections Figure 4-18a shows a typical test model for tensile testing of grouted ducts, and Figure 4-18, b–g shows all possible modes of failure for the type of connection under tensile loading. The bar fractures outside the connection if the embedment length is sufficient (Figure 4-18b). In contrast,

Analytical Programs 179 the bar pulls out when the embedment length is insufficient (Figure 4-18c). The pullout may be associated with failure of a part of the grout if the grout is not sufficiently strong (Figure 4-18d). A different failure mode occurs if the bond at the grout–duct interface or the duct–concrete inter- face is weak, which leads to the duct pulling out (Figure 4-18e). When the concrete around the duct is not sufficiently strong or thick to resist the ultimate bar forces, it fails in a conical shape (Fig- ure 4-18f). Another mode of failure could be expected when the bar or the duct pulls out because of splitting failure of the grout or the concrete, respectively (Figure 4-18g). This is an unlikely mode of failure for grouted duct connections, because confinement provided by the duct and the relatively large concrete cover on the duct would prevent this failure mode. The modes of failure shown for grouted duct connections indicate that two bond surfaces and bond average strengths should be considered: (1) bar bond strength, which is defined as the ratio of the peak tensile force to the surface area of the bar and (2) duct bond strength, which is defined as the ratio of the peak tensile force to the surface area of the duct. The strength of the grout and the concrete surrounding the duct needs to be included in design equations. This is usually done by normalizing the bond strength. The normalized bar bond strength (tb,n) was defined as the ratio of the bar bond strength to the square root of the compressive strength of the grout f g )( ′ (Equation 4-12). Similarly, the normalized duct bond strength (td,n) was defined as the ratio of the duct bond strength to the square root of the compressive strength of the concrete f c )( ′ (Equation 4-13). (4-12), ag F d L f b n b g τ = π ′ (4-13), ag F d L f d n d c τ = π ′ where F = peak tensile load (kips) applied to the connection, db = diameter (in.) of the bar, dd = diameter (in.) of the duct, Lag = embedment length (in.) of the bar (assumed the same for the bar and the duct), f g′ = compressive strength (ksi) of the grout, and f c′ = compressive strength (ksi) of the concrete. (a) Pullout specimen (b) Bar fracture (c) Bar pullout, grout–bar bond failure (d) Bar pullout, grout mass failure (e) Duct pullout, concrete–duct– grout bond failure (f) Duct pullout, concrete conical failure (g) Duct–bar splitting failure Source: Tazarv and Saiidi (2014). Figure 4-18. Modes of failure in grouted duct connections.

180 Proposed AASHTO Seismic Specifications for ABC Column Connections Note that the unit of the normalized bond strength defined here is the square root of the stress unit and is different from the bond strength unit, which has the unit of stress. Normalized bond strength is an intermediate parameter used in deriving the design equations and does not appear in the final equations. Figure 4-19 illustrates the strength parameters of the grouted duct bond. It is clear that, to be complete, a new design equation for the embedment length of bars in grouted duct connections must include both the duct bond strength and the bar bond strength. 4.4.2 Previous Test Data As discussed in the previous section, a comprehensive design equation should include the effect of both bar and duct bond strengths. Table 2-12 presents a summary of findings from experimental studies on grouted duct pullout tests as well as design equations proposed in those studies. It can be seen that these equations were developed primarily on the basis of the bar bond strength and excluded the duct bond strength and the modes of failure shown in Figure 4-18, e and f; thus, they may not be reliable. The previous studies were reviewed as part of the current project to collect the necessary data and to develop a new design equation. A total of 119 pullout test specimens on conventional grout-filled duct connections were found in the literature. Eight parameters were extracted from each study to calculate the bar and duct bond strengths: • Bar diameter, • Duct diameter, • Embedment length of the bar, • Number of bars bundled (if any), • Number of ducts per specimen, • Compressive strength of the concrete, • Compressive strength of the grout, and • Peak tensile force. The mode of failure in the test models (e.g., bar pullout or bar fracture) was also taken into account to establish whether the tests provide sufficient information about the bond strengths. To deter- mine the trends in the effect of different parameters, only specimens with common or similar test parameters were selected for further analysis. Therefore, specimens incorporating straight uncoated deformed reinforcing steel bars and corrugated steel ducts were selected. Specimens with headed or epoxy-coated bars, steel pipes (which have thicker walls than typical post- tensioning ducts used in grouted duct connections), and plastic ducts were excluded. The data for 61 of the 119 test specimens could not be used in the present study because the information for these tests was incomplete. In the remaining 58 tests, only 31 specimens exhibited either bar or duct pullout from the connection and provided bond strength data that could be used in the present study (Table 4-8). The remaining test reports provided data only the lower bound bond strength because of either bar fracture or early termination of the tests as a result of the limited capacity of the test setup. Note that the bar pullout or duct pullout could consist of different failure modes, as shown in Figure 4-18. For example, “duct pullout” refers to the modes of failure shown in Figure 4-18, e and f. In an actual grouted duct pullout test, a combination of bar and duct modes of failure may occur. Furthermore, identification of a specific mode of failure for a bar or duct is not needed for the development of embedment length design equations, since the bond strength is lower bound only if the bar fractures. Therefore, Table 4-8 does not refer to a specific mode of failure. Confinement by the axial load in a self-reacting test setup may alter the bond strength. The test specimens in Table 4-8 were not confined by the axial load. Figure 4-19. Grouted duct connection.

Table 4-8. Preliminary pullout test database for grouted duct connections. Test Data Bar Dia. Duct Dia. Emb. Length Emb. Length Ratio No. of Bundled Bars No. of Ducts Concrete Strength Grout Strength Force Failure Mode Normalized Bar Bond Strength Normalized Duct Bond Strength Notation db dd L ag L ag /db nb nd f'c f'g F na tb,n td,n Reference SP. ID/Unit in. in. in. na na na ksi ksi kip na ksi0.5 ksi0.5 1 Matsumoto et al. (2001) VD01 1.41 4 12 8.51 1 1 5.40 4.20 76.00 Bar/Duct Pullout 0.70 0.22 2 Matsumoto et al. (2001) VD04 1.41 4 18 12.77 1 1 5.60 3.10 94.00 Bar/Duct Pullout 0.67 0.18 3 Brenes et al. (2006) 1 1.41 4 11.28 8.00 1 1 5.40 5.00 90.48 Bar/Duct Pullout 0.81 0.27 4 Brenes et al. (2006) 3 1.41 4 16.92 12.00 1 1 5.40 6.40 135.72 Bar/Duct Pullout 0.72 0.27 5 Brenes et al. (2006) 10 1.41 4 16.92 12.00 1 1 4.50 5.60 124.80 Bar/Duct Pullout 0.70 0.28 6 Brenes et al. (2006) 13 1.41 4 22.56 16.00 2 2 4.70 5.20 271.44 Bar/Duct Pullout 0.60 0.22 7 Brenes et al. (2006) 15 1.41 4 22.56 16.00 2 2 4.70 5.40 268.32 Bar/Duct Pullout 0.58 0.22 8 Brenes et al. (2006) 17 1.41 4 16.92 12.00 2 2 5.20 4.80 184.08 Bar/Duct Pullout 0.56 0.19 9 Brenes et al. (2006) 19 1.41 4 11.28 8.00 1 1 5.50 5.10 76.44 Bar/Duct Pullout 0.68 0.23 10 Brenes et al. (2006) 21 1.41 4 16.92 12.00 1 1 5.50 5.40 115.44 Bar/Duct Pullout 0.66 0.23 11 Brenes et al. (2006) 23 1.41 4 16.92 12.00 2 2 6.10 6.00 212.16 Bar/Duct Pullout 0.58 0.20 12 Brenes et al. (2006) 31 1.41 4 22.56 16.00 3 3 6.10 5.80 341.64 Bar/Duct Pullout 0.47 0.16 13 Ou (2007) F5M-4db-1 0.625 3.2 2.5 4.00 1 1 4.05 8.10 12.59 Bar/Duct Pullout 0.90 0.25 14 Ou (2007) F5M-4db-2 0.625 3.2 2.5 4.00 1 1 4.05 8.10 15.28 Bar/Duct Pullout 1.09 0.30 15 Ou (2007) F8M-4db-1 1 3.2 4 4.00 1 1 4.05 8.10 29.23 Bar/Duct Pullout 0.82 0.36 16 Ou (2007) F8M-4db-2 1 3.2 4 4.00 1 1 4.05 8.10 38.71 Bar/Duct Pullout 1.08 0.48 17 Ou (2007) F5C-4db 0.625 3.2 2.5 4.00 1 1 4.05 8.10 13.95 Bar/Duct Pullout 1.00 0.28 18 Ou (2007) F8C-4db 1 3.2 4 4.00 1 1 4.05 8.10 45.82 Bar/Duct Pullout 1.28 0.57 19 Steuck et al. (2009) 08N08 1 4 8 8.00 1 1 8.07 7.79 60.30 Bar/duct Pullout 0.86 0.21 20 Galvis et al. (2015) 3B-45-1 1.74 4 17.72 10.20 3 1 8.40 5.24 83.18 Bar/Duct Pullout 0.38 0.13 21 Galvis et al. (2015) 3B-30 1.74 4 11.81 6.80 3 1 7.69 3.90 148.37 Bar/Duct Pullout 1.17 0.36 22 Galvis et al. (2015) 3B-24 1.74 4 9.45 5.44 3 1 7.56 3.67 93.07 Bar/Duct Pullout 0.94 0.29 23 Galvis et al. (2015) 3B-19 1.74 4 7.48 4.31 3 1 7.95 4.56 67.89 Bar/Duct Pullout 0.78 0.26 24 Galvis et al. (2015) 3B-15 1.74 4 5.91 3.40 3 1 7.56 5.09 50.13 Bar/Duct Pullout 0.69 0.25 25 Galvis et al. (2015) 2B-30 1.42 4 11.81 8.33 2 1 7.69 5.31 117.80 Bar/Duct Pullout 0.97 0.29 26 Galvis et al. (2015) 2B-25 1.42 4 9.84 6.94 2 1 8.04 5.40 125.44 Bar/Duct Pullout 1.23 0.36 27 Galvis et al. (2015) 2B-20 1.42 4 7.87 5.55 2 1 8.50 5.35 77.78 Bar/Duct Pullout 0.96 0.27 28 Galvis et al. (2015) 2B-15-1 1.42 4 5.91 4.16 2 1 7.08 5.17 54.18 Bar/Duct Pullout 0.91 0.27 29 Galvis et al. (2015) 2B-15-2 1.42 4 5.91 4.16 2 1 8.38 5.17 33.27 Bar/Duct Pullout 0.56 0.15 30 Galvis et al. (2015) 1B-25 1 4 9.84 9.84 1 1 8.59 5.25 73.29 Bar/Duct Pullout 1.03 0.20 31 Galvis et al. (2015) 1B-15 1 4 5.91 5.91 1 1 7.83 4.86 35.30 Bar/Duct Pullout 0.86 0.17 Average= 0.81 0.26 Standard Deviation= 0.23 0.09 Note: na = not applicable.

182 Proposed AASHTO Seismic Specifications for ABC Column Connections A statistical analysis was carried out to determine the design bond strength, which was defined as the average bond strength less 1 standard deviation. This statistical method was previously used in studies by Brenes et al. (2006) and Tazarv and Saiidi (2016) for grouted duct connec- tions. The average normalized bar bond strength for the 31 specimen was 0.81 ksi0.5 with a standard deviation of 0.23 ksi0.5 resulting in a design bar bond strength of 0.59 ksi0.5. Similarly, the average normalized duct bond strength was 0.26 ksi0.5 with a standard deviation of 0.09 ksi0.5 resulting in a design duct bond strength of 0.17 ksi0.5. Equations 4-12 and 4-13 were rearranged for the embedment length as follows: 4 (4-14)ab , , , l F d f A f d f d f fb b n g s s b b n g b s b n g = π τ ′ = π τ ′ = τ ′ 4 (4-15)ad , , 2 , l F d f A f d f d f d fd d n c s s d d n c b s d d n c = π τ ′ = π τ ′ = τ ′ The design equation was then finalized by using the design bond strengths for bars and ducts. 4.4.3 Preliminary Proposed Design Equation for Grouted Ducts The proposed embedment length of straight deformed bars anchored in conventional grout- filled duct connections on the basis of the statistical analysis of the available test data is: max and (4-16) 2.35 1.5 ag ab ad ab b1 ad b1 2 l l l l d f f l d f d f s g s d c ( )≥ = ′ = ′ where lag = anchored length (in.) for straight deformed bars in grout-filled duct connections; lab = anchored length (in.) of longitudinal reinforcing bars into ducts installed in cap or footing, on the basis of the bar bond strength; lad = anchored length (in.) of longitudinal reinforcing bars into ducts installed in cap or footing, on the basis of the duct bond strength; dbl = nominal diameter (in.) of longitudinal column bar or equivalent diameter when bars are bundled; dd = actual, rather than nominal, inner diameter (in.) of duct; fs = bar stress (ksi) (the greater of 1.5fye and fue); fye = expected yield stress (ksi) of the longitudinal column bar; fue = expected tensile strength (ksi) of the longitudinal column bar; f c′ = nominal compressive strength (ksi) of concrete; and f g′ = nominal compressive strength (ksi) of grout. 4.4.4 Updated Pullout Test Database for Grouted Duct Connections Twelve monotonic pullout tests were performed in the present study (see Chapter 3) to inves- tigate the aforementioned knowledge gaps for grouted duct connections. Of 12 specimens, three (G1-4, G2-5, and G2-6) failed as a result of bar or duct pullout. The data for these specimens were added to the pullout test database (Table 4-9). Specimen G1-1, in which the bar fractured, was also included in the database. This specimen had the shortest embedment length; therefore, the bond

Table 4-9. Updated pullout test database for grouted duct connections. Test Data Bar Dia. Duct Dia. Emb. Length Emb. Length Ratio No. of Bundled Bars No. of Ducts Concrete Strength Grout Strength Force Failure Mode Normalized Bar Bond Strength Normalized Duct Bond Strength Notation d b d d L ag L ag /d b nb nd f'c f'g F na t b,n td,n Reference SP. ID/Unit in. in. in. na na na ksi ksi kip na ksi0.5 ksi0.5 1 Matsumoto et al. (2001) VD01 1.41 4 12 8.51 1 1 5.40 4.20 76.00 Bar/Duct Pullout 0.70 0.22 2 Matsumoto et al. (2001) VD04 1.41 4 18 12.77 1 1 5.60 3.10 94.00 Bar/Duct Pullout 0.67 0.18 3 Brenes et al. (2006) 1 1.41 4 11.28 8.00 1 1 5.40 5.00 90.48 Bar/Duct Pullout 0.81 0.27 4 Brenes et al. (2006) 3 1.41 4 16.92 12.00 1 1 5.40 6.40 135.72 Bar/Duct Pullout 0.72 0.27 5 Brenes et al. (2006) 10 1.41 4 16.92 12.00 1 1 4.50 5.60 124.80 Bar/Duct Pullout 0.70 0.28 6 Brenes et al. (2006) 13 1.41 4 22.56 16.00 2 2 4.70 5.20 271.44 Bar/Duct Pullout 0.60 0.22 7 Brenes et al. (2006) 15 1.41 4 22.56 16.00 2 2 4.70 5.40 268.32 Bar/Duct Pullout 0.58 0.22 8 Brenes et al. (2006) 17 1.41 4 16.92 12.00 2 2 5.20 4.80 184.08 Bar/Duct Pullout 0.56 0.19 9 Brenes et al. (2006) 19 1.41 4 11.28 8.00 1 1 5.50 5.10 76.44 Bar/Duct Pullout 0.68 0.23 10 Brenes et al. (2006) 21 1.41 4 16.92 12.00 1 1 5.50 5.40 115.44 Bar/Duct Pullout 0.66 0.23 11 Brenes et al. (2006) 23 1.41 4 16.92 12.00 2 2 6.10 6.00 212.16 Bar/Duct Pullout 0.58 0.20 12 Brenes et al. (2006) 31 1.41 4 22.56 16.00 3 3 6.10 5.80 341.64 Bar/Duct Pullout 0.47 0.16 13 Ou (2007) F5M-4db-1 0.625 3.2 2.5 4.00 1 1 4.05 8.10 12.59 Bar/Duct Pullout 0.90 0.25 14 Ou (2007) F5M-4db-2 0.625 3.2 2.5 4.00 1 1 4.05 8.10 15.28 Bar/Duct Pullout 1.09 0.30 15 Ou (2007) F8M-4db-1 1 3.2 4 4.00 1 1 4.05 8.10 29.23 Bar/Duct Pullout 0.82 0.36 16 Ou (2007) F8M-4db-2 1 3.2 4 4.00 1 1 4.05 8.10 38.71 Bar/Duct Pullout 1.08 0.48 17 Ou (2007) F5C-4db 0.625 3.2 2.5 4.00 1 1 4.05 8.10 13.95 Bar/Duct Pullout 1.00 0.28 18 Ou (2007) F8C-4db 1 3.2 4 4.00 1 1 4.05 8.10 45.82 Bar/Duct Pullout 1.28 0.57 19 Steuck et al. (2009) 08N08 1 4 8 8.00 1 1 8.07 7.79 60.30 Bar/duct Pullout 0.86 0.21 20 Galvis et al. (2015) 3B-45-1 1.74 4 17.72 10.20 3 1 8.40 5.24 83.18 Bar/Duct Pullout 0.38 0.13 21 Galvis et al. (2015) 3B-30 1.74 4 11.81 6.80 3 1 7.69 3.90 148.37 Bar/Duct Pullout 1.17 0.36 22 Galvis et al. (2015) 3B-24 1.74 4 9.45 5.44 3 1 7.56 3.67 93.07 Bar/Duct Pullout 0.94 0.29 23 Galvis et al. (2015) 3B-19 1.74 4 7.48 4.31 3 1 7.95 4.56 67.89 Bar/Duct Pullout 0.78 0.26 24 Galvis et al. (2015) 3B-15 1.74 4 5.91 3.40 3 1 7.56 5.09 50.13 Bar/Duct Pullout 0.69 0.25 25 Galvis et al. (2015) 2B-30 1.42 4 11.81 8.33 2 1 7.69 5.31 117.80 Bar/Duct Pullout 0.97 0.29 26 Galvis et al. (2015) 2B-25 1.42 4 9.84 6.94 2 1 8.04 5.40 125.44 Bar/Duct Pullout 1.23 0.36 27 Galvis et al. (2015) 2B-20 1.42 4 7.87 5.55 2 1 8.50 5.35 77.78 Bar/Duct Pullout 0.96 0.27 28 Galvis et al. (2015) 2B-15-1 1.42 4 5.91 4.16 2 1 7.08 5.17 54.18 Bar/Duct Pullout 0.91 0.27 29 Galvis et al. (2015) 2B-15-2 1.42 4 5.91 4.16 2 1 8.38 5.17 33.27 Bar/Duct Pullout 0.56 0.15 30 Galvis et al. (2015) 1B-25 1 4 9.84 9.84 1 1 8.59 5.25 73.29 Bar/Duct Pullout 1.03 0.20 31 Galvis et al. (2015) 1B-15 1 4 5.91 5.91 1 1 7.83 4.86 35.30 Bar/Duct Pullout 0.86 0.17 32 NCHRP 12-105 G1-1 1.27 4 15.50 12.20 1 1 6.56 9.05 134.90 Bar Fracture 0.72 0.27 33 NCHRP 12-105 G1-4 1.27 4 15.50 12.20 1 1 6.56 12.01 124.00 Duct Pullout 0.58 0.25 34 NCHRP 12-105 G2-5 1.8 5.26 24.00 13.33 2 1 6.56 12.01 198.60 Duct Pullout 0.42 0.20 35 NCHRP 12-105 G2-6 1.8 5.26 24.00 13.33 2 1 6.56 12.01 242.50 Duct Pullout 0.52 0.24 Average= 0.78 0.26 Standard Deviation= 0.23 0.09 Note: na = not applicable.

184 Proposed AASHTO Seismic Specifications for ABC Column Connections strength obtained from this specimen would constitute a lower bound value, which is conservative. The bars in the other nine test specimens were fully developed and fractured outside the duct; thus, the data for these specimens were excluded from the database that was used in the derivation of the design equation. Including those would artificially increase the embedment length. Similar to what was done in the previous section, a statistical analysis was carried out to determine the design bond strength, which was defined as the average bond strength less 1 standard deviation. The average normalized bar bond strength for the 35 specimens (Table 4-9) was 0.78 ksi0.5, with a standard deviation of 0.23 ksi0.5, resulting in a normalized design bar bond strength of 0.55 ksi0.5. Similarly, the average normalized duct bond strength was 0.26 ksi0.5, with a standard deviation of 0.09 ksi0.5, resulting in a normalized design duct bond strength of 0.17 ksi0.5. The preliminary embedment length design equation (Equation 4-16) was subsequently updated, as presented in the next section. The updated embedment length associated with the bar bond strength was increased by 7%, while there was no change in the embedment length associated with the duct bond strength. Note that the grouted duct specimens tested in this project (see Chapter 3) were designed on the basis of the preliminary design equation (Equation 4-16). Both the preliminary and the updated design equations are conservative and sufficient for the design of grouted duct connec- tions, as the failure in the six test specimens (Groups G3 and G4) that satisfied Equation 4-16 was outside the embedment length. Of the four new test data used in the database (G1-1, G1-4, G2-5, and G2-6), two incorporated 4-in. ducts and two incorporated 5.26-in. ducts. The effect of the duct diameter could not be estab- lished, since the pullout test data for the other eight specimens, including the reference specimens, presented lower bound strengths. Nonetheless, the duct diameter affects the duct–concrete inter- face area, and therefore is included in both the preliminary and revised equations for embedment length. The effect of the duct thickness could not be established either, since the bars fractured outside the embedment length in G1-3 and G3-9, in which the duct thickness was varied. When the results from G1-4 and G1-1 are compared, it can be concluded that the bar eccentricity can reduce the duct bond strength by 20% and the bar bond strength by 7%. As mentioned above, the proposed equation provides sufficient conservatism to accommodate this reduction in the bond strength. Note that bundling bars in grouted duct connections is feasible, but the embedment length needs to be increased by replacing the bundled bars with a bar with an equivalent cross-sectional area. 4.4.5 Updated Design Equation and Guidelines for Grouted Duct Connections The updated embedment length of straight deformed bars anchored in conventional grout- filled duct connections based on the statistical analysis of the updated database is max and (4-17) 2.2 1.5 ag ab ad ab b1 ad b1 2 l l l l d f f l d f d f s g s d c ( )≥ = ′ = ′ where lag = anchored length (in.) for straight deformed bars in grout-filled duct connections; lab = anchored length (in.) of longitudinal reinforcing bars into ducts installed in cap or footing on basis of bar bond strength;

Analytical Programs 185 lad = anchored length (in.) of longitudinal reinforcing bars into ducts installed in cap or footing on basis of duct bond strength; dbl = nominal diameter (in.) of longitudinal column bar or equivalent diameter when bars are bundled; dd = actual, rather than nominal, inner diameter (in.) of duct; fs = bar stress (ksi) (the greater of 1.5fye and fue); fye = expected yield stress (ksi) of longitudinal column bar; fue = expected tensile strength (ksi) of longitudinal column bar; f c′ = nominal compressive strength (ksi) of concrete; and f g′ = nominal compressive strength (ksi) of grout. Compared to Equation 4-16, the first limit in Equation 4-17 requires a slightly longer embed- ment for bars in grouted duct connections. However, for typical grouted ducts and concrete and grout properties, it is the duct embedment length (the second limit) that controls the design. The expression for the duct embedment length remained unchanged when the addi- tional data were included in the analysis. The following requirements should be met: • Only corrugated galvanized strip metal ducts conforming to ASTM A653 shall be used. Ducts made with other materials, such as plastics, are not allowed, either because of a lack of data, or in the case of plastics, the low bond strength of plastic surfaces. • Duct wall thickness shall not be less than 0.018 in. (0.46 mm). Duct wall thickness affects confinement, and thus the bond strength. Data for thinner ducts are lacking. • Bundling of bars is allowed in grouted duct connections. However, the number of bars grouped together in a single duct shall not exceed three. A diameter corresponding to the equivalent area of bundled bars shall be used in the equations. • Transverse reinforcement shall be provided around the ducts in the member adjoining the column. The transverse reinforcement ratio shall be no less than the column transverse reinforcement ratio in the adjacent plastic hinge region. • Duct diameter (dd) should not be less than 2.75 times the diameter of the largest column longitudinal bar that is being anchored (2.75db). The duct diameter should be sufficiently larger than the anchored bar diameter to facilitate construction and to ensure sufficient capac- ity for the duct against pullout. For bundled bars, the minimum duct diameter should be based on the equivalent bar diameter, to result in the same total cross-sectional area of the bundled bars. The duct/bar diameter minimum limit of 2.75 may be reduced for bundled bars by 10% to avoid large ducts that might be impractical. • The clear distance between adjacent ducts shall not be less than the greater of (a) 2 in. and (b) 1.3 times the largest aggregate size used in concrete. • The embedment length based on the bar bond strength (lab) shall be amplified for different bar coating conditions, according to current AASHTO LRFD requirements. The use of any factors resulting in lower embedment length is not allowed. • The longitudinal column reinforcement shall be extended to the far face of adjacent footings and cap beams while maintaining the necessary clear cover. This could mean that the actual embedment length exceeds that from Equation 4-17. 4.4.5.1 Comparison of Proposed Equations with Test Data and AASHTO Equation Figure 4-20 shows the experimental data points used to derive the proposed equation super- imposed on plots of the proposed equations for bar and grout embedment lengths. Also shown are the required embedment length base on the AASHTO LRFD (2013). The experimental data are for various duct and bar diameters and concrete and grout compressive strengths.

186 Proposed AASHTO Seismic Specifications for ABC Column Connections However, the plots for the proposed equations and AASHTO are for dd = 4 in., db = 1.41 in. (No. 11), fs = 110 ksi, f c′ = 4 ksi, and f g′ = 7 ksi. It can be seen that the proposed equations for both the bar and the grouted duct embedment lengths are conservative relative to the test data, with the AASHTO equation being even more conservative. Points 1 and 2 fell below the proposed equation for bar anchorage because the grout strength in both cases was at least 25% lower than the assumed 7 ksi. Even for these two points, the duct bond strength controls. 4.4.5.2 Comparison of Proposed Equation with Equations from Previous Studies Table 2-12 presents a summary of design equations developed in previous studies for the embedment length of bars in grouted duct connections. It was discussed that the previously developed equations excluded one or more critical bond parameters, such as the duct diameter or the compressive strength of both grout and concrete. The proposed design equation (Equa- tion 4-17) includes all of the critical bond parameters. Furthermore, it was found that the duct bond surface is typically the weak link in this type of connection. For example, Figure 4-21 shows the stress developed in an anchored bar in a grouted duct connection versus the normalized embedment length using the proposed equation and assuming dd = 4 in., db = 1.41 in. (No. 11), fs = 110 ksi, f c′ = 4 ksi, and f g′ = 7 ksi. It can be seen that the embedment length based on the duct bond strength is significantly larger than that based on the bar bond strength. Figure 4-20. Comparison of experimental data, proposed equation, and AASHTO. Note: Ld = development length (also called the embedment length). 0 100 200 300 400 500 600 700 800 0 20 40 60 80 100 120 0 5 10 15 20 25 30 35 40 45 50 Ba r St re ss , f s (M Pa ) Ba r St re ss , f s (k si) Ld / db Ld-duct Ld-bar Figure 4-21. Comparison of bar and duct required embedment lengths.

Analytical Programs 187 Figure 4-22 shows the design embedment length for a No. 10 Grade 60 ASTM A706 bar in a grouted duct connection based on different studies for two cases: Case A, a 3.2-in. duct, and Case B, a 4-in. duct. The proposed design equation shows that a 25% increase in the duct diameter from Case A to Case B shortens the embedment length by 25% (a drop from 30.48db to 24.38db). Previously developed design equations for grouted ducts do not account for the duct diameter. Another advantage of the proposed equation is that both concrete and grout strength are included in the design, while other studies used only one of these parameters in design equations. As was seen in the grouted duct specimens tested in the present study (see Chapter 3), there might be a significant difference between the footing–cap beam concrete strength and grout strength. It is worth mentioning that the proposed guidelines prohibit Case A, since the duct diameter is less than 2.75 times the bar diameter. However, on the basis of the previously developed equations, this case is permissible because the duct diameter does not enter into the equations. For Case B, the required bar embedment length matches those from previous studies. The graphs also show that the embedment length of a bar in grouted duct connections can be significantly shorter than that in conventional connections determined on the basis of the AASHTO LRFD (AASHTO 2013). However, bars and ducts should be extended to near the far face of the connecting members to allow for formation of a strut and tie mechanism. 4.4.6 Summary of Study on Grouted Duct Design Equation The knowledge gaps regarding the performance of grouted duct connections were identified in previous chapters. The most important gap was the lack of a comprehensive design equation, since previously developed equations excluded one or more of the bond strength parameters. In the present study, all of the previous studies of grouted duct bonds were reviewed to generate a database. The database was filtered to eliminate specimens with unknown parameters or with lower bound bond strengths. Out of 119 test data, 31 specimens were found suitable for the present study. Four additional data points were collected from the pullout test of grouted duct connections carried out in the present study. A statistical analysis was carried out to calculate the design bond strengths. Then, a design equation as well as guidelines were proposed. The com- parison of the proposed equation with the previous bond studies showed that the duct diameter is an important parameter in the design of grouted duct connections. The information provided in this section should be treated as the background for the final proposed specifications. Refer to Appendix C of the present document for the design of actual bridge columns incorporating grouted duct connections. (a) Duct diameter = 3.12 in (b) Duct diameter = 4.0 in. 0 10 20 30 40 50 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 L d / d b Proposed Design Eq. Matsumoto et al. (2001) Brenes et al. (2006) Galvis et al. (2015) AASHTO LRFD (2013) f'g = 1.0 f'c Concrete Compressive Strength, c (ksi) 0 10 20 30 40 50 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 L d / d b Proposed Design Eq. Matsumoto et al. (2001) Brenes et al. (2006) Galvis et al. (2015) AASHTO LRFD (2013) f'g = 1.0 f'c Concrete Compressive Strength, c (ksi) Figure 4-22. Comparison of design equations for grouted duct connections.

188 Proposed AASHTO Seismic Specifications for ABC Column Connections 4.5 Grouted Duct Column Connections Four precast column connections were introduced and reviewed in previous chapters, and knowledge gaps for each type of connection were identified. The state-of-the-art literature review indicated that the main gap for grouted connections is the minimum embedment length of bars in ducts and the minimum size and detailing of the column adjoining members. The former gap was addressed in the previous section, and the latter is addressed here. The effect of cap beam and pile shaft sizes on the seismic performance of precast columns connected by grouted duct connections is investigated in this section through analytical studies. The study focused solely on the effect of the size of the column adjoining members on resisting seismic demands in both transverse and longitudinal directions of the bridge. The FE modeling of grouted duct connections is described next, followed by presentation of the results of parametric studies on the size of pile shafts and cap beams. 4.5.1 Grouted Duct Connection Finite Element Modeling 4.5.1.1 Introduction Analytical studies were conducted to determine the required minimum size of pile shafts and cap beams connected to columns incorporating grouted ducts. Abaqus/Explicit (Dassault Systèmes 2014b) was used to create detailed FE models to simulate the performance of this type of connection under lateral loads. The modeling method for grouted duct connections was based on the model that is developed and validated for pocket connections in Section 4.6 of the present report. 4.5.1.2 Description of Finite Element Modeling Method for Grouted Duct Connections Figure 4-23 shows the FE model for a grouted duct connection between column and pile shaft. The column plastic hinge and joint were modeled by using continuum elements with the con- crete damaged plasticity (CDP) material model (Dassault Systèmes 2014a). The reinforcing bars were defined with wire elements and constrained to the concrete elements by embedment region constraints, which restrain the translational degree of freedom of reinforcement to those of concrete elements. These constraints, along with the tension stiffening of the concrete material, Grouted duct Continuum elements with CDP Surface-to-surface tie constraint Figure 4-23. Finite element model for grouted duct connection between column and pile shaft.

Analytical Programs 189 simulate load transfer across the cracks as well as strain penetration in the reinforcement. The CDP material model was used to model grout in the ducts separately. Surface-to-surface tie con- straints were assigned between the grout and duct elements. Membrane shell elements with the average duct diameter were used to define the steel ducts. The steel ducts and the hoops around the ducts were constrained to the pile shaft elements by using embedment region constraints. Embedment region constraints were also used to constrain the column longitudinal reinforce- ment to the grout elements. [Please refer to the software manual (Dassault Systèmes 2014a) for terminologies regarding the modeling method.] 4.5.2 Typical Oversized Pile Shaft Grouted Duct Connections The minimum size of oversized (enlarged) pile shafts (or “pile shaft” in this report), or pile-caps with grouted duct connections should be determined to avoid connection fail- ure and to ensure that plastic hinges form in columns. In CIP construction, the pile shafts are usually enlarged to prevent damage in piles by shifting the plastic hinge to the column. The AASHTO SGS (AASHTO 2014) does not specify the minimum size of the enlarged pile shafts. However, the AASHTO SGS requires that an oversized pile shaft moment capacity shall be at least 1.25 times the column plastic moment. The Caltrans Seismic Design Criteria (SDC) (Caltrans 2013) requires that the diameter of an enlarged shaft shall be at least 24 in. larger than the column diameter and that an overstrength factor of 1.25 be applied to the column plas- tic moment to be used in flexural design of enlarged shafts (Type II shafts). Adding confining reinforcement was proposed for grouted duct connections in previous studies by extending the column hoops or spirals around the ducts in the shaft (Tazarv and Saiidi 2014). Consequently, the pile shafts must be larger than the column to satisfy the reinforcement clearance requirements while accommodating the ducts, hoops, and shaft reinforcement. A parametric study was per- formed to determine the minimum diameter of pile shafts with grouted ducts to ensure plastic hinging of the column rather than the pile shaft. A summary of the analyses and results follows. 4.5.2.1 Column-to-Oversized Pile Shaft Grouted Duct Connection Model The dimensions of an actual bridge incorporating a CIP column were used as the baseline in analytical studies (Figure 4-24a). A single-column CIP bent with a diameter of 75 in. was connected to a pile shaft with a diameter of 102 in. The superstructure consisted of three precast, post-tensioned bulb-tee girders bearing on the bent cap. Therefore, it was assumed that no moment was transferred from the superstructure to the column. On the basis of the geometry of the baseline bridge, a precast bent with a pile shaft grouted duct connec- tion was developed according to the guidelines proposed in Section 4.4.5. This precast bent with a column diameter of 75 in. and shaft diameter of 106 in. is referred to hereafter as the “Shaft-GD-t16” model. The shaft diameter was increased from 102 in. to 106 in. to investigate the behavior of an oversized shaft with a diameter larger than the minimum diameter recom- mended by Caltrans. The embedment length of bars in pile shaft ducts was assumed to be 72 in., whereas the required embedment length was only 34 in. according to Equation 4-17. This was done intentionally to eliminate pullout failure and to ensure maximum demand on the pile shaft. To investigate the effect of the pile shaft diameter on the connection performance, the research team executed pushover analyses on bent models with three diameters for the pile shaft while keeping the column diameter constant. Table 4-10 presents the key model param- eters. The increments of the shaft diameters were to practically accommodate the grouted duct connection components. For example, in the prototype bent as well as Shaft-GD-t16 and Shaft-GD-t12, the shaft concrete cover was 6 in. In Shaft-GD-t9, the clear cover was reduced to 3 in. to further investigate the effect of the shaft diameter on the seismic perfor- mance of the connection.

190 Proposed AASHTO Seismic Specifications for ABC Column Connections (a) Cast-in-place detail (c) Sections (b) Elevation view BOTTOM Figure 4-24. Typical pile shaft details with grouted duct connections. Table 4-10. Properties of analytical pile shaft grouted duct connections. Model Dcolumn [in. (mm)] Dshaft [in. (mm)] Dshaft/Dcolumn tshaft [in. (mm)] Clear Cover in Shaft [in. (mm)] Shaft-GD-t16 75 (1,875) 106 (2,650) 1.41 15.5 (388) 6 (152) Shaft-GD-t12 75 (1,875) 99 (2,475) 1.32 12.0 (300) 6 (152) Shaft-GD-t9 75 (1,875) 93 (2,325) 1.24 9.0 (225) 3 (76)

Analytical Programs 191 The length to the maximum moment in the pile shaft (or the point of fixity) should be suf- ficiently short to ensure maximum demand on the joint while causing minimal distortion to the stress at the lower part of the pile. The maximum moment occurs at a depth of one to two times the pile shaft diameter (Dshaft), according to Priestley et al. (1996). Recent column–pile shaft experimental studies used a pile shaft length of 1.0 to 1.4Dshaft to simulate pile depth to the point of fixity (Tran 2012; Mehraein and Saiidi 2016). The pile shaft in the present analytical study was assumed to be fixed at 11 ft below the column–shaft interface (Figure 4-25) resulting in the Figure 4-25. Finite element models for pile shaft grouted duct connections. (a) Shaft-GD-t16 (b) Shaft-GD-t12 (c) Shaft-GD-t9

192 Proposed AASHTO Seismic Specifications for ABC Column Connections range of the maximum moment occurring at 1.25 to 1.4 times the shaft diameter (Dshaft). Note that the actual location of the pile shaft maximum bending moment may be different, depend- ing on soil properties. The effect of soil on the lateral displacement of the pile was excluded. The calculated results were inspected at the lower part of the pile to ensure that the boundary conditions were reasonable. The expected compressive strength for both concrete and grout was assumed to be 5.2 ksi, corresponding to a specified compressive strength of 4 ksi. The steel casing was conservatively neglected in FE model. An axial load of 1,414 kips was applied at the top of the column, which corresponds to a column axial load index of 8%. The axial load index is defined as the ratio of the column axial load to the product of the column cross-sectional area and the specified compressive strength of the concrete. The following parameters were evaluated to assess the performance of the connections: force-displacement relationship, column reinforcement bar strains, plastic hinging of the column, and cracking of the pile shaft. Lateral displacement was applied at the top of the column. 4.5.2.2 Results of Parametric Study of Oversized Pile Shaft Grouted Duct Connections Figure 4-26 shows moment–drift relationships for different pile shaft diameters. The increase in the shaft wall thickness from 9 in. to 16 in. had a minor effect on the pushover relationships. The drift ratio capacity of the bents was in the range of 12.2% to 13.2%. The size of pile shafts had a negligible effect on the moment–drift response because the moment and drift capacities were controlled by the properties of the column section, which remained the same in all cases. Figure 4-27 shows the strain in the reinforcement at a drift ratio of approximately 10%. While a 10% drift ratio might be unrealistically high under seismic loading, it helps assess the perfor- mance of the models under extreme conditions. In all three models, the maximum tensile and compressive strains occurred within the columns and not the shafts. The column longitudinal bars buckled in Shaft-GD-t16. The failure mode of Shaft-GD-t12 and Shaft-GD-t9 was rup- ture in tension of the column longitudinal bars. Figure 4-28 presents the cracking patterns in the models at a drift ratio of approximately 10%. In all the bents, large cracks due to plastic hinging formed in the columns and around the top region of ducts that were in tension. Furthermore, two vertical cracks formed on the shaft of the Shaft-GD-t12 and Shaft-GD- t9 models, although there was no damage on Shaft-GD-t16 (Figure 4-29). The cracking in Figure 4-26. Moment–drift relationships for different shaft diameters with grouted duct connection.

Analytical Programs 193 (a) Shaft-GD-t16 (b) Shaft-GD-t12 (c) Shaft-GD-t9 Figure 4-27. Reinforcement strains at 10% drift ratio for different shaft diameters. Shaft-GD-t9 was more extensive than that in Shaft-GD-t12. The lack of damage in Shaft-GD-t16 suggests that the difference between the shaft and column diameter would need to be at least 32 in. However, because the cracking in Shaft-GD-t12 was relatively minor, it can be concluded that a difference of 24 in. might be acceptable. Figure 4-30 shows the moment curvature relationships for the shafts with different diam- eters as well as the column. The section analyses of shafts were performed conservatively; the column reinforcement was ignored. The shaft flexural capacities were 2.21 and 2.49 times the column capacity in Shaft-GD-t16 and Shaft-GD-t9, respectively; these capacities are significantly larger than the overstrength factor of 1.25 required by the Caltrans SDC. Even though the flexural capacity of the shaft substantially exceeded the column capacity, the shafts with diameters smaller than that of Shaft-GD-t16 were not sufficient to prevent damage in the connection.

194 Proposed AASHTO Seismic Specifications for ABC Column Connections (a) Shaft-GD-t16 (b) Shaft-GD-t12 Crack opening at interface Strain penetration in grout and ducts (c) Shaft-GD-t9 Cracks in shaft Figure 4-28. Cracking pattern in the joint at 10% drift ratio for different shaft diameters. 4.5.2.3 Results of Cast-in-Place Analysis The results of the parametric studies discussed in the previous section indicated that a 24-in. difference between the column and shaft diameters might be acceptable. The current Caltrans design method allows for a 24-in. difference for CIP construction. To compare the damage between CIP and precast grouted duct connections, a model similar to Shaft-GD-t12 but with a CIP connection between the column and the shaft was analyzed. This model is referred to as “Shaft-CIP-t12.” Figure 4-31 shows the moment–drift ratio relationship of the two models. It was found that the drift ratio capacity of Shaft-CIP-t12 was 5% higher than that for Shaft-GD-t12. In both cases, compressive failure of the core concrete of the column controlled the ultimate

Analytical Programs 195 Crack in shaft Crack in shaft and interface (a) Shaft-GD-t16 (c) Shaft-GD-t9 (b) Shaft-GD-t12 Figure 4-29. Surface cracking pattern at 10% drift ratio for different shaft diameters. Figure 4-30. Moment curvature relationships for different shafts and column sections

196 Proposed AASHTO Seismic Specifications for ABC Column Connections Figure 4-31. Moment–drift relationships for shafts with cast-in-place and grouted duct connections. displacement. The small difference between the two ultimate displacements is attributed to the larger stiffness of Shaft-GD-t12 because of the presence of the ducts. The difference in the reinforcement strain under a 10% drift ratio was also only 5% (Figure 4-32), for the same reason. The cracking pattern on the surface of the shafts is shown in Figure 4-33 for the two models. At a drift ratio of approximately 10%, the crack width on Shaft-GD-t12 was 0.12 in., while the crack width on Shaft-CIP-t12 was 0.24 in., twice that in the grouted duct connection. Fur- thermore, the length of the crack in Shaft-CIP-t12 was also higher than that in Shaft-GD-t12 (approximately 16 in. versus 12 in.). Comparison of cracks in the column for the two cases shows that the cracking in Shaft-GD-t12 was more extensive. It is believed that the increase in the stiffness of the shaft due to the ducts in Shaft-GD-t12 placed a higher deformation demand on the column and thus led to more cracking. Therefore, it can be concluded that an oversized pile shaft incorporating grouted ducts performs better than that an equivalent CIP shaft. Because of this and the wide use of CIP shafts in practice, the current code mini- mum size for an oversized pile shaft may be adopted for pile shafts incorporating grouted duct connections. 4.5.2.4 Summary of Analysis of Pile Shaft Grouted Duct Connection The AASHTO SGS (AASHTO 2014) does not specify a minimum size for CIP-enlarged pile shafts. The Caltrans SDC (Caltrans 2013) requires oversized CIP shafts to be at least 24 in. larger than the column diameter with an overstrength factor of 1.25 for the shaft moment capacity as compared with the column moment capacity. The findings of the parametric study indicated that the requirement of 24-in. for the shaft minimum diameter for CIP leads to larger cracks at the top of CIP shafts as compared with oversized pile shafts that use grouted duct connections. Therefore, it is recommended that the 24-in. difference between the column and shaft diameters of CIP column–shaft connections be adopted for column–shaft connections with grouted ducts. 4.5.3 Cap Beam Grouted Duct Connections As with pile shaft connections, cap beam connections must be sufficiently strong to ensure plastic hinging in columns while keeping the connections linear elastic [AASHTO SGS (AASHTO

Analytical Programs 197 (a) Shaft-CIP-t12 (b) Shaft-GD-t12 Figure 4-32. Comparison of reinforcement strain at 10% drift ratio in shafts with cast-in-place and grouted duct connections.

198 Proposed AASHTO Seismic Specifications for ABC Column Connections Crack in shaft Crack in shaft (a) Shaft-CIP-t12 (b) Shaft-GD-t12 Figure 4-33. Comparison of cracking pattern at 10% drift ratio in shafts with cast-in-place and grouted duct connections.

Analytical Programs 199 2014); Caltrans SDC (Caltrans 2013)]. Cap beam grouted duct connections are mostly used between columns and drop caps in which the bent cap is not integral with the superstructure (Tazarv and Saiidi 2015a). Seismic forces in the longitudinal direction of the bridge do not produce significant moments at the column–cap beam connections in these cases. In contrast, a moment must be transferred between the column and the cap beam in integral connections with a target performance of plastic hinging in the column. A parametric study was performed as part of NCHRP 12-105 to determine the minimum size of cap beams incorporating grouted duct connections subjected to seismic loads in the longitudinal direction of the bridge to avoid damage in connections. 4.5.3.1 Cap Beam Grouted Duct Connection Model Figure 4-34 shows a typical CIP single-column bridge bent with integral box girders. The cap beam width was 24 in. larger than the column diameter and conformed to the current AASHTO SGS (AASHTO 2014). This bent was modified (Figure 4-35) to incorporate a grouted duct con- nection between the precast bent cap and the precast column on the basis of the proposed design guidelines presented in Section 4.4. Because the ducts in the joint were distributed in a circular pattern, passing the bottom lon- gitudinal bars of the cap beam through the joint would be difficult in the field. Therefore, the longitudinal reinforcement of the beam bottom was clustered on the sides of the cap beam, but the top bars were distributed across the cap beam width. The column was precast with longi- tudinal reinforcement extending into the cap beam steel ducts, which were subsequently filled with a high-strength grout. The embedment length was assumed to be 72 in., while the required length was 34 in., per Equation 4-17. This was done to ensure high demand on the cap beam and to remove embedment length failure from the analysis. Hoops were assumed along the ducts, with the size and spacing equal to those of the column hoops. This model is referred to as “CB-GD-t12.” The FE model of the bridge was created in Abaqus by utilizing the method described in Section 4.6. Continuum elements were used to model the cap beam and the column plastic hinge. Embedment was used to constrain the steel reinforcement and steel ducts to the con- tinuum elements. The box girders were modeled by using elastic beam elements with the gross cross-sectional properties of the concrete box. The connection between the girders and the cap beam was modeled as a fixed joint. The other end of the girders was modeled as roller to simulate the abutments of the bridge. The column modeling assumed pinned support at midheight to represent the inflection point. Figure 4-36 shows the FE mesh and the loads. The compressive strength for both concrete and grout was assumed to be 6.5 ksi, which correspond to 5 ksi specified strength. The dead load, shown with downward arrows in the figure, was 6.60 kips per foot (kpf) and was distrib- uted along the girders, leading to an axial load of 1,065 kips in the column and resulting in an axial load index of 8%. Pushover analyses were performed in the longitudinal direction of the bridge (perpendicular to the cap beam) by applying displacement increments to the bottom of the column in the model. Failure was defined as the displacement at which the strain in the reinforcing bars reached the fracture strain. As was discussed, in CIP construction, both the Caltrans SDC and the AASHTO SGS require the minimum width of the cap beam to be 24 in. larger than the column diameter. Additionally, the joint is required to remain linear elastic while the full plastic hinge forms in the column. The width of the cap beam in CB-GD-t12 was 84 in., which was 12 in. larger than the column at each side. CB-GD-t8 was created with a cap beam width of 76 in., which exceeded the column width by only 8 in. on each side. This width would be the minimum practical width to accommodate the ducts, hoops, and cover concrete.

200 Proposed AASHTO Seismic Specifications for ABC Column Connections (a) Bridge elevation (b) Bent elevation Note: Reinf = reinforcement. Figure 4-34. Cast-in-place bridge bent.

Analytical Programs 201 (a) Elevation (b) Section A-A (c) Section B-B (d) Plan (e) Column section Figure 4-35. Cap beam grouted duct connection. 4.5.3.2 Results of Parametric Study of Cap Beam Grouted Duct Connections Figure 4-37 compares the moment–drift relationship of the models with different cap beam widths. It can be seen that the width of the cap beam had essentially no effect on the strength and displacement capacity of the bent. The calculated strains (Figure 4-38) show that, in both models, failure was due to the rupture of the column longitudinal bars. Furthermore, the crack- ing patterns in the plastic hinge region and the strain in the grouted ducts indicate that the cap beam remained essentially linear elastic in both models (Figure 4-39). Figure 4-40 shows the calculated maximum principal strain in the ducts, which was 0.048 and 0.036 in./in. in CB-GD-t12 and CB-GD-t8, respectively. Despite the yielding in the ducts, the maximum strains were well below the ultimate strain, which was 0.1 in./in. Overall, the results indicate that the size of the cap beam did not affect the strength and stiffness of the joint because of the adequate

202 Proposed AASHTO Seismic Specifications for ABC Column Connections (a) Full-bridge model and loading (b) Model of cap beam grouted duct connection Note: Only the cap beam reinforcement is shown. The girder, deck, soffit, and skin reinforcement as well as the stirrups are omitted. Roller Bottom longitudinal bars are clusteredTop longitudinal bars are continued Elastic beam element Steel ducts, grouts, and hoops around them 6.60 kpf distributed dead load Displacement loading Figure 4-36. Finite element model for cap beam grouted ducts connections. Figure 4-37. Moment–drift relationship for different cap beam widths.

Analytical Programs 203 (b) CB-GD-t8(a) CB-GD-t12 Figure 4-38. Reinforcement strains at failure for cap beam grouted duct connections. (a) CB-GD-t12 (b) CB-GD-t8 Figure 4-39. Cracking pattern at failure for cap beam grouted duct connections.

204 Proposed AASHTO Seismic Specifications for ABC Column Connections (b) CB-t8 Max: 36.51E-03 (a) CB-GD-t12 Max: 48.63E-03 Figure 4-40. Maximum principal strains (in./in.) in steel ducts in cap beam grouted duct connections confinement provided by the joint hoops, cap beam transverse reinforcement, and girders. Therefore, the minimum cap beam size specified by current codes for CIP column–cap beam connections is sufficient for precast column–cap beam grouted duct connections. 4.5.3.3 Summary of Analysis of Cap-Beam Grouted Duct Connections The AASHTO SGS (AASHTO 2014) and Caltrans SDC (Caltrans 2013) require that the minimum width of the CIP integral bent cap should exceed the column diameter by at least 24 in. The parametric study showed that cap beam grouted duct connections perform ade- quately in the longitudinal direction of a bridge if the minimum width requirement for CIP integral cap beams is met. 4.5.4 Summary of Study on Grouted Duct Column Connections The effects of the size of an adjoining member connected to a precast column via grouted ducts were investigated through FE analysis. The analysis showed that the current AASHTO SGS requirements for a CIP integral cap beam are adequate to keep the capacity of the connection protected. The same requirements are needed for connection of a column to an enlarged pile shaft. Therefore, the minimum diameter of an enlarged pile shaft or the minimum width of an integral cap beam that uses grout duct connections should exceed the column diameter by at least 24 in. to ensure capacity-protected behavior.

Analytical Programs 205 The information provided in this section should be treated as the background for the final proposed specifications. Refer to Appendix C for the design of actual bridge columns incorpo- rating grouted duct connections. 4.6 Pocket Connections Four precast column connections were introduced and reviewed in the previous chapters, and knowledge gaps for each type of connection were identified. The state-of-the-art literature review indicated that the main gaps for pocket connections are the minimum size and amount of reinforcement and the detailing of column adjoining members. The effect of cap beam and pile shaft sizes on the seismic performance of precast column pocket connections was investigated through analytical studies. To be consistent with current design codes for CIP construction, the investigation focused solely on the effect of the size of adjoining members. This section describes the FE modeling methods for pocket connections and their validation and then presents the results of parametric studies on the size of pile shafts and cap beams. 4.6.1 Pocket Connection Finite Element Modeling 4.6.1.1 Introduction Abaqus/Explicit (Dassault Systèmes 2014b) was used to create FE models to simulate the performance of ABC column pocket connections. The modeling methods were validated by comparing the calculated results with the experimental data reported by Tran (2012, 2015). The sensitivity of the FE models to different boundary conditions, analysis accuracy, and mesh density was determined. On the basis of correlation between the results of the test and those of the analysis, a reliable modeling method for simulating the response of pocket connections was determined. The verified FE model was then used to determine the effect of the change in the dimensions of the column adjoining members on the performance of pocket connections. 4.6.1.2 Pocket Connection Test Model The seismic performance of precast columns connected to pile shafts was investigated by Tran (2012, 2015) through cyclic lateral loading (Figure 4-41). The research team selected this experimental study to develop and verify methods for pocket connection modeling. Two pre- cast test specimens, DS1 and DS2 (Table 4-11), were selected to validate the FE models. Both specimens had the same geometry and detailing, but the number of spirals in each shaft was different. The cross-sectional area of spirals in DS2 was one-half that of the spirals in DS1. The shaft spirals in DS-1 were designed according to the specifications in Sections 7.4.4 and 7.8.2 of the Washington State DOT Bridge Design Manual (2002), which determines the required shaft spiral on the basis of the noncontact lap splice method developed by McLean and Smith (1997). It should be noted that the concrete properties are slightly different in these models. Figure 4-42 shows the measured moment–drift relationships under cyclic lateral loads. The moment was measured at the column–shaft interface, and the drift ratio is the lateral displacement of the column at the actuator level divided by the vertical distance from the actuator centerline to the top of the shaft. 4.6.1.3 Description of Finite Element Model Two FE models were developed to simulate the response of pocket connections tested by Tran (2012, 2015), as shown in Figure 4-43. In the first model—full plastic hinge (fullPH)— the plastic hinge was created with continuum elements, while in the second model—spring

206 Proposed AASHTO Seismic Specifications for ABC Column Connections Source: Tran (2015). Figure 4-41. Column shaft specimen. Specimen Parameter DS-1 DS-2 Column diameter (in.) 20 20 Clear column height (in.) 60 60 Span–depth ratio 3 3 Column longitudinal reinforcement 10 No. 5 (1.0 %) 10 No. 5 (1.0 %) Shaft diameter (in.) 30 30 Shaft height (in.) 30 30 Transition length (in.) 28 28 Shaft longitudinal reinforcement ratio 0.9% (30 bundles of double No. 3) 0.9% (30 bundles of double No. 3) Shaft transverse reinforcement ratio 0.17% (two Gauge 9 at 3.0-in. pitch) 0.09% (one Gauge 9 at 3.0-in. pitch) Table 4-11. Details of test specimens.

Analytical Programs 207 Figure 4-42. Measured moment–drift relationship for pile shaft pocket connections. Source: Tran (2015). M om en t [ ki p- in .] M om en t [ ki p- in .] a). Specimen DS-1 moment-drift response b). Specimen DS-2 moment-drift response (a) Full plastic hinge (fullPH) (b) Spring plastic hinge (springPH) X Z P la st ic H in ge S pr in g Figure 4-43. Sketch of finite element models for pocket connections.

208 Proposed AASHTO Seismic Specifications for ABC Column Connections plastic hinge (springPH)—the plastic hinge was modeled with a zero-length spring and an elastic beam element elsewhere. Since the elastic deformation of the column in springPH was included by using the beam element and bond-slip effects were included by using continuum elements in the connection, the properties of the plastic hinge spring were determined to rep- resent only the plastic deformation of the column due to the reinforcement yielding. Both FE models were created in Abaqus/Explicit on the basis of modeling techniques devel- oped at the University of Nevada, Reno, for seismic and quasi-static loadings (Mehrsoroush and Saiidi 2014; Mehraein and Saiidi 2016). In fullPH, the connections as well as the lower 20 in. of the column were modeled with continuum elements to obtain detailed yielding and crack- ing patterns in the transition zone. Column longitudinal and transverse reinforcing bars were modeled by using beam and truss elements, respectively. The rest of the column was modeled with elastic beam elements. Gross cross-sectional properties were assigned to the upper 10.2 in. of the column, while the remainder of the column was modeled with cracked section properties. In springPH, only the shaft around the pocket connection was modeled with continuum ele- ments. The properties of the plastic hinge spring were calculated on the basis of a moment curva- ture analysis of the column section under axial load and the weight of the column. The moment curvature relationship was idealized by a bilinear curve by preserving energy in both curves (Figure 4-44). At the ultimate point, the plastic rotation was calculated by using the empirical formulations proposed by Paulay and Priestly (1992). The bond-slip rotation was excluded from the plastic rotations because the interaction between the reinforcement and concrete in the joint accounts for the bond-slip effect directly. The bond-slip effect was calculated by the method of Wehbe et al. (1997). The CDP model was utilized to simulate concrete behavior in the continuum elements. The parameters of the CDP model were calculated on the basis of the relationships suggested by Roesler et al. (2007) and Bažant and Jirásek (2002). The reinforcing steel bars were modeled by using elastic–plastic behavior. The interaction of the reinforcement with the continuum elements was simulated with the embedded element technique, in which the translational degrees of freedom of the reinforcement are constrained to those of the host elements. Those constraints, along with the tension stiffening of the concrete material, simulate load transfer across the cracks. The experimental results indicated that the pocket was sufficiently strong to prevent movement between the column and shaft. Therefore, surface-to-surface tie constraint Figure 4-44. Moment curvature relationship for column section tested by Tran (2012).

Analytical Programs 209 was used to model the interaction between the outer surface of the precast column and the pocket in the shaft. Since both specimens and loadings were symmetric about the xz plane (Figure 4-43) only one- half of the bent was modeled, so as to reduce the number of elements. Accordingly, the beam elements for the elastic part of the column were modeled with one-half of their full properties. Three degrees of freedom of each node on the plane of symmetry were constrained in translation in the y-direction, rotation about the x-axis, and rotation about the z-axis. The base of the shaft was assumed to be fixed. 4.6.1.4 Sensitivity Analysis Effect of Plastic Hinge Modeling Methods. Two techniques for the modeling of the plastic hinges (Figure 4-43) were discussed in the previous section. The calculated moment–drift relationships were compared with those of the test data to determine the best model in terms of accuracy and speed (Figure 4-45). The peak moments calculated by either method were approximately 11% lower than that measured in DS1. For DS2, the maximum errors between Figure 4-45. Comparison between results of full plastic hinge and spring plastic hinge. (a) Test Model DS1 (b) Test Model DS2

210 Proposed AASHTO Seismic Specifications for ABC Column Connections the measured and calculated peak moments were 8% and 10% in springPH and fullPH, respectively. While the overall calculated moment–drift relationships were close to those of the test data, the cracking patterns obtained in the fullPH model were closer to the observed pattern (Figures 4-46 to 4-48). For example, two large cracks were observed on the pile in DS2, as shown in Figure 4-47c. Of the two models, fullPH showed a better match with the observed damage in terms of the cracking pattern and the width of the crack (Figures 4-47 and 4-48). Therefore, it was decided to use continuum elements in the column plastic hinges in pocket connections. Effect of Calculation Precision. Pushover analyses were performed for DS1 and DS2 with single and double precision. Double-precision executables use 64-bit word lengths, whereas single-precision executables use 32-bit word lengths. Single precision tends to be inadequate in analyses that require more than 300,000 increments. DS1-fullPH was analyzed in 249,789 increments. Mehrsoroush and Saiidi (2014) showed that the accuracy of FE analy- ses improves significantly when the precision of the Abaqus/Explicit solver changes from single to double. However, Figure 4-49 shows that the increase in the numerical precision did not influ- ence the accuracy of the calculated moment–drift relationships in both test models. Therefore, the single precision model was selected for further analysis. Effect of Mesh Density. Two meshing techniques were considered for DS2 to investigate the effect of mesh density on the accuracy of the analysis. The shaft in DS2-fullPH was dis- cretized, first with 16 elements in the radial and tangential directions (Figure 4-50a) and then with 24 elements in the radial and tangential directions (Figure 4-50b). It was found that the effect of mesh density on both the moment–drift relationship and the cracking pattern was insignificant, as shown in Figures 4-51 and 4-52. Therefore, to expedite analysis, pile shafts in the parametric study section of the report were discretized with 16 elements in the radial and tangential directions. 4.6.1.5 Analytical Results The main objective of this part of the study was to the determine minimum dimensions of footings, pile shafts, and cap beams that would accommodate pocket connections under biaxial loading. According to the AASHTO SGS (AASHTO 2014), column connections are designed to form plastic hinges in columns rather than joints, since joints are capacity protected. As discussed, the overall response calculated with the selected numerical model was close to that of the experiments. However, more discussion is needed regarding hinging of the connection. The plastic hinge formation and the strain states in the models were investigated in detail to determine the location of the plastic hinges. Figure 4-53 compares the crack progression in DS1 and DS2 obtained from analytical studies. It can be seen that the first crack formed at the column–shaft interface in both models (Figure 4-53a). With the increase in the lateral deformation, cracking in DS1 extended mostly into the column, whereas cracking in DS2 extended to both the pile shaft and the column (Figure 4-53b). The difference in the cracking patterns was more apparent at 8% drift ratio (Figure 4-53c). There were also vertical cracks in the shafts (Figure 4-54). The cracks in DS1 were shorter and narrower than those in DS2, which indicated that hinging extended to the shaft in DS2. It can be concluded from the analyses that the shaft in DS2 was not adequate, even though the plastic hinge capacity of column was achieved. The same behavior was observed in the experiments. The calculated reinforcement strains in the analytical models also indicated that the shaft in DS2 failed. Figure 4-55 shows the axial component of true strains (LE11) in the reinforcing bars. It can be seen that the strain levels in the column reinforcement of DS1 and DS2 were

Analytical Programs 211 (a) DS1 - fullPH (b) DS1 - springPH (c) Observed cracking pattern (Tran 2012) Figure 4-46. Comparison of calculated and observed cracking patterns in DS1.

212 Proposed AASHTO Seismic Specifications for ABC Column Connections (a) DS2 - fullPH (b) DS2 - springPH (c) Observed cracking pattern (Tran 2012) Figure 4-47. Comparison of calculated and observed cracking patterns in DS2.

Analytical Programs 213 Figure 4-48. Comparison of calculated cracking patterns on the symmetry plane in DS2. (a) fullPH (b) springPH Figure 4-49. Comparison between single and double precision finite element analyses. (a) DS1 (b) DS2

214 Proposed AASHTO Seismic Specifications for ABC Column Connections (a) DS2-fullPH (b) DS2-fullPH (refined shaft mesh) Figure 4-50. Effect of mesh density on pocket connection analysis. Figure 4-51. Effect of mesh density on moment–drift relationship for DS2.

Analytical Programs 215 Figure 4-52. Effect of shaft mesh density on cracking pattern for DS2 (b) DS2-fullPH (refined shaft mesh)(a) DS2-fullPH approximately the same, while the strains in the shaft spirals of the two models were different (Figure 4-56). Four spirals of the shaft in DS2 reached the ultimate strain (10%) at 8% drift ratio, while the shaft spiral strains in DS1 were lower than the ultimate strain. Since the first spi- ral in the analytical model fractured at 3.8% drift ratio (or 2.3 in. displacement), there was both strength and stiffness degradation at this displacement in the calculated pushover relationship of DS2, as shown in Figure 4-45. The displacement at which the first spiral fractured in the DS2 test model was not reported. However, degradation of both strength and stiffness can be seen at approximately 3.5% drift ratio in the measured data for DS2 (Figure 4-45). Furthermore, the center of rotation shifted to within the shaft in DS2 (Figure 4-57b), whereas it was at the column–shaft interface in DS1 (Figure 4-57a). 4.6.1.6 Summary of Pocket Connection Modeling Methods Two FE models were developed to investigate the performance of pocket connections under lateral loads. The sensitivity analyses showed that the joint and plastic hinge regions need to be modeled with continuum elements to successfully simulate the plastic defor- mations. The calculation precision and the mesh density were optimized. It was found that the tie constraint between the column and the shaft was valid. On the basis of the find- ings of the sensitivity analyses, a reliable FE model was developed and was verified with test data. In-depth investigation of the analytical results with the selected model showed that reinforcement strains, hinging, the cracking pattern, and the moment–drift relationship should be studied simultaneously to investigate the suitability of pocket connections under lateral loading.

Figure 4-53. Horizontal cracks in DS1 (left) and DS2 (right) analytical models. First Crack Crack inside pile shaft Crack widening (a) First cracking at 0.9% drift ratio (b) Damage at 4.8% drift ratio (c) Damage at 8.0% drift ratio

(a) DS1 FE model (b) DS2 FE model Figure 4-54. Vertical cracks in analytical pile shaft pocket connections at 8% drift ratio. (a) DS1 finite element model (b) DS2 finite element model Shaft Surface Figure 4-55. Column reinforcement axial strains (LE11) at 8% drift.

218 Proposed AASHTO Seismic Specifications for ABC Column Connections (a) DS1 finite element model (b) DS2 finite element model (c) Failed spirals in DS2 (close-up view) Spiral Fracture 344.21E–03 Figure 4-56. Pile shaft reinforcement axial true strain (LE11).

Analytical Programs 219 (a) DS1 finite element model (b) DS2 finite element model Center of rotation Figure 4-57. Displacement contours for pile shaft pocket connections. 4.6.2 Typical Oversized Pile Shaft Pocket Connections Tran (2012) investigated the effect of transverse reinforcement on the seismic performance of precast columns connected to oversized pile shafts (or “pile shaft” in this report). However, the minimum size of cap beams, pile shafts, or pile caps should be determined to avoid damage of this type of connection. For pocket connections, pile shafts must be enlarged to accommo- date the pocket. The AASHTO SGS (2014) does not specify the minimum size of the enlarged pile shafts. The Caltrans SDC (Caltrans 2013) requires that the diameter of an enlarged shaft shall be at least 24 in. larger than the column diameter to avoid connection damage. A para- metric study was performed to determine the minimum diameter of pile shafts with pocket connections to ensure plastic hinges form in the column rather than the pile shaft. A summary of analyses and results follows. 4.6.2.1 Baseline Bridge and Pile Shaft Pocket Connection Modeling An actual bridge incorporating a CIP pile shaft connection was used as the baseline bridge in parametric studies. This bridge was part of a widening project of an existing bridge in California (Figure 4-58). The bent was built with a single 75-in.-diameter column sup- ported on a 102-in.-diameter pile shaft. The superstructure consisted of three precast post- tensioned bulb-tee girders bearing on the bent. Therefore, it was assumed that no moment was transferred from the superstructure to the column. A precast bent with a pile shaft pocket connection was developed on the basis of the geometry of the baseline bridge. The precast bent is referred to as the “reference model” hereafter. To investigate the minimum size of pile shafts with pocket connections, pushover analyses that used the verified FE model that was presented in the previous sections were executed on

Figure 4-58. Typical pile shaft details. Note: The steel casing was conservatively neglected in the finite element model. (b) Elevation view(a) Cast-in-place detail (c) Column section (d) Pile shaft section #7 HOOPS @ 6”

Analytical Programs 221 models with four shaft diameters while keeping the column diameter constant. Table 4-12 pre- sents the key parameters. The minimum thickness of the shaft around the precast column was approximately 10 in. for Shaft-t10, which was the minimum thickness to accommodate the shaft reinforcement with sufficient cover. The pile shaft was assumed to be fixed at 11 ft below the column–shaft interface (Figure 4-59), and the effect of soil on the lateral displacement of the pile was excluded. Note that the actual location of the pile shaft maximum bending moment may be different. An axial load of 1,414 kips, which corresponds to a column axial load index of 8%, was applied at the top of the column. The axial load index is defined as the ratio of the column axial load to the product of the column cross-sectional area and the compressive strength of the concrete. The lateral displacement was applied at the top of the column to obtain force-displacement relationships. Model Dcolumn [in. (mm)] Dshaft [in. (mm)] Dshaft/Dcolumn tshaft [in. (mm)] Shaft-t10 75 (1,875) 94 (2,388) 1.25 9.5 (238) Shaft-t14 (reference) 75 (1,875) 102 (2,590) 1.36 13.5 (343) Shaft-t16 75 (1,875) 106 (2,692) 1.41 15.5 (394) Shaft-t20 75 (1,875) 114 (2,896) 1.52 19.5 (495) Table 4-12. Properties of pile shaft pocket connections. (a) Shaft-t10 (b) Shaft-t14 (c) Shaft-t16 (d) Shaft-t16 Figure 4-59. Finite element models for pile shaft pocket connections.

222 Proposed AASHTO Seismic Specifications for ABC Column Connections 4.6.2.2 Results of Pile Shaft Parametric Study Figure 4-60 shows the moment–drift relationships for different pile shaft diameters. The increase in the thickness of the concrete from 10 in. to 20 in. had only a minor effect on the pushover curves. The drift ratio capacities of the bents were in the range of 11.3% to 11.9%. Figure 4-61 shows the strain in the longitudinal reinforcement. The maximum tensile and compressive strains occurred in the columns in all four models. The strains in the shaft reinforcement were lower. The failure mode of Shaft-t14, Shaft-t16, and Shaft-t20 was bar buckling at the compression face of the column. In Shaft-t10, the column longitudinal bars fractured in tension. Figure 4-62 presents the cracking patterns in the models. Large cracks resulting from plastic hinging formed in the columns in all the bents except for Shaft-t10. In Shaft-t10, a large crack also formed within the shaft, which indicated that the diameter of this shaft was not sufficient. Furthermore, two large vertical cracks formed on the shaft in Shaft-t10, with the maximum crack width measuring 0.34 in. (Figure 4-63). The crack widths in Shaft-t14, Shaft-t16, and Shaft-t20 were 0.1, 0.06, and 0.01 in., respectively. On the basis of the excessive damage to Shaft-t10, it can be concluded that the thickness of the concrete in this shaft was inadequate, although the pushover curves were not affected by this damage. In summary, the parametric study showed that the minimum size of pile shafts specified by the current Caltrans SDC is sufficient to accommodate pocket connections. 4.6.2.3 Summary of Pile Shaft Pocket Connection Analysis The AASHTO SGS (AASHTO 2014) does not specify a minimum size for CIP enlarged pile shafts. The Caltrans SDC (Caltrans 2013) requires CIP oversized shafts to be at least 24 in. larger than the column diameter with a moment capacity of 1.25 times the column moment capacity. The findings of the parametric study indicated that the Caltrans minimum requirements for the CIP pile shafts are also adequate for precast pocket connections. 4.6.3 Cap Beam Pocket Connections Similar to pile shaft pocket connections, cap beam pocket connections must be sufficient to form plastic hinges in columns while the connections remain linear elastic (AASHTO SGS 2014; Caltrans SDC 2013). Tazarv and Saiidi (2015a) developed design and construction guidelines for five types of cap beam pocket connections for dropped cap bents in which the bent cap is not integral with the superstructure. Seismic forces in the longitudinal direction of the bridge do not produce significant moments at column–cap beam connections in these Figure 4-60. Moment–drift relationships for different shaft diameters with pocket connections.

Analytical Programs 223 Figure 4-61. Reinforcement strains at failure for different shaft diameters with pocket connections. (d) Shaft-t20 (a) Shaft-t10 (b) Shaft-t14 (reference precast bent) (c) Shaft-t16

224 Proposed AASHTO Seismic Specifications for ABC Column Connections Figure 4-62. Cracking pattern at failure for different shaft diameters with pocket connections. (d) Shaft-t20 (a) Shaft-t10 (b) Shaft-t14 (reference precast bent) (c) Shaft-t16 Crack within joint Cracks outside joint Crack in shaft

Analytical Programs 225 Figure 4-63. Large vertical cracks in Shaft-t10 with pocket connections at failure. Crack in shaft cases. In contrast, a moment has to be transferred between the column and the cap beam in integral cap beams, with a target performance of plastic hinging in the column. Since the width of the cap beam is a key factor in ensuring column plastic hinging under longitudinal seismic loads, a parametric study was performed to determine the effect of the size of the cap beam on damage to the pocket connection. 4.6.3.1 Cap Beam Pocket Connection Models Figure 4-64 shows a typical CIP single-column bridge bent with integral box girders. This bent was modified to incorporate a pocket connection between a precast bent cap and a par- tially precast column based on the Alt-2 pocket connection developed by Tazarv and Saiidi (2015a), as shown in Figure 4-65. The pocket was formed by a corrugated steel pipe. The bottom reinforcing bars in the cap beam were bundled at the sides of the pipe, but the top bars were continuous in the cap beam. The column was precast below the joint, while the longitudinal and transverse reinforcement of the upper part of the column extended into the pocket. The pocket was filled with self-consolidating concrete subsequent to assembling the members. Corrugated pipes designed according to the guidelines proposed by Tazarv and Saiidi (2015a) can provide confinement pressure equal to that of the column confinement. As corrugated pipe with such a thickness was not available, the maximum available thickness of 0.168 in. was used (80% of the required thickness), according to ASTM A760 (ASTM 2015). Additional hoops were assumed in the lower half of the pipe, with size and spacing equal to those of the column hoops. Consequently, the hoops increased the confining pressure by 80%, which resulted in sufficient combined confinement provided by the pipe and the hoops. This reference model is referred to as “CB-t12.” The FE model of the bridge was created in Abaqus according to the method described in Section 4.6.1. Continuum elements were used to model the cap beam and the upper part of the column. The steel reinforcement and corrugated pipe were constrained to the continuum

226 Proposed AASHTO Seismic Specifications for ABC Column Connections Figure 4-64. Cast-in-place bridge bent. (a) Bridge elevation (b) Bent elevation (c) Column section

Analytical Programs 227 Figure 4-65. Cap beam pocket connection using Alt-2 detailing. (a) Elevation (b) Section A-A (c) Section B-B

228 Proposed AASHTO Seismic Specifications for ABC Column Connections elements with embedment constraint, in which the translational degrees of freedom of the reinforcement are constrained to those of the concrete elements. The box girders were modeled by using elastic beam elements with the gross cross-sectional properties of the concrete box. Coupling constraint was used to tie the ends of the girders at the cap beam to the cap beam surfaces, which were identical to the cross section of the girders. The other ends of the girders were modeled as rollers to simulate the abutments of the bridge. The modeling of the column assumed pinned support at the midheight of the column. Figure 4-66 shows the FE mesh and the loads. The dead load was 6.60 kpf distributed along the girders, which led to an axial force of 1,065 kips in the column and resulted in an axial load index of 8%. Pushover analyses were performed in the longitudinal direction of the bridge (per- pendicular to the cap beam) by applying displacement increments to the bottom of the column in the model. Failure was defined as the displacement at which the strain in the reinforcing bars reached the ultimate strain. As stated in previous sections, for CIP construction, the Caltrans SDC (Caltrans 2013) and AASHTO SGS (AASHTO 2014) require that the minimum width of the cap beam be 24 in. larger than the column diameter. Additionally, they require the joint to remain linear elastic while the full plastic hinge forms in the column. The width of the cap beam in the reference model, CB-t12, was 84 in., which is 24 in. larger than the column at each side. CB-t8 was created with a cap beam width of 76 in. (10% smaller than the minimum required), which is the minimum practical width to accommodate the corrugated pipe, hooks around the pipe, and the cover concrete. 4.6.3.2 Results of Cap Beam Parametric Study Figure 4-67 compares the moment–drift relationships of the models with different cap beam widths. It can be seen that the cap beam width had essentially no effect on the curves. The calculated strains (Figure 4-68) show that failure was due to the buckling of the column longitudinal bars in both models. Furthermore, the cracking patterns in the plastic hinge (a) Full-bridge model and loading (b) Cap beam pocket connection model Figure 4-66. Finite element model for cap beam pocket connections.

Analytical Programs 229 Figure 4-67. Moment–drift relationship for different cap beam width. (a) CB-t12 (b) CB-t8 Figure 4-68. Reinforcement strains at failure for cap beam pocket connections. region and the strain in the corrugated pipe indicate that the cap beam remained undamaged in both models (Figures 4-69 and 4-70). Overall, the results indicate that the size of the cap did not affect the strength and stiffness of the joint because of the ample confinement provided by the corrugated pipe, additional hoops, cap beam transverse reinforcement, and girders. Therefore, the minimum cap beam size specified by current codes is sufficient for precast pocket connections. 4.6.3.3 Summary of Cap Beam Pocket Connection Analysis The AASHTO SGS (AASHTO 2014) and Caltrans SDC (Caltrans 2013) require the minimum width of the CIP integral bent cap to be at least 24 in. larger than the column diameter. The para- metric study showed that cap beam pocket connections performed adequately in the longitudinal direction of a bridge if the minimum width requirement for CIP integral cap beams is met.

230 Proposed AASHTO Seismic Specifications for ABC Column Connections Figure 4-69. Cracking pattern at failure cap beam pocket connections. (a) CB-t12 (b) CB-t8

Analytical Programs 231 (a) CB-t12 (b) CB-t8 Figure 4-70. Maximum principal strains in corrugated pipe in cap beam pocket connections.

232 Proposed AASHTO Seismic Specifications for ABC Column Connections 4.6.4 Design and Detailing Guidelines for Pocket Connections The AASHTO SGS, Sections 8.9 to 8.13 (2014), provides a comprehensive design and detailing method for CIP capacity-protected members such as cap beams and joints. Restrepo et al. (2011) proposed design and construction guidelines for precast cap beams with pockets in NCHRP Report 681. Design and detailing guidelines for bent caps (seat type and integral type), footings, and pile shaft with pocket connections were developed on the basis of current code requirements, details and experimental findings reported in recent studies (Chapter 2), and the analytical findings presented in this chapter. Appendix C presents the proposed guidelines. 4.6.5 Summary of Study on Pocket or Socket Column Connections A reliable FE modeling method was developed for column pocket connections. This FE model was used in parametric studies to quantify the minimum size of cap beams and pile shafts under lateral loading. The analytical results indicated that the requirements for seismic design of the CIP joints can be extended to pocket connections with some modifications. On the basis of the available literature and the results of the analytical studies, design and construction guidelines were proposed for the design of pocket connections in cap beams, footings, and pile shafts. The information provided in this section should be treated as the background for the final proposed specifications. Refer to Appendix C of the present document for the design of actual bridge columns incorporating pocket or socket connections. 4.7 References AASHTO. (2013). AASHTO LRFD Bridge Design Specifications. American Association of State Highway and Transportation Officials, Washington, D.C. AASHTO. (2014). AASHTO Guide Specifications for LRFD Seismic Bridge Design. American Association of State Highway and Transportation Officials, Washington, D.C. ACI Committee 374. (2013). Guide for Testing Reinforced Concrete Structural Elements under Slowly Applied Simulated Seismic Loads. ACI 374.2R-13. American Concrete Institute, Farmington Hills, Mich. ASTM. (2015). ASTM A760: Standard Specification for Corrugated Steel Pipe, Metallic-Coated for Sewers and Drains. ASTM International, West Conshohocken, Pa. ASTM. (2015). ASTM A1034: Standard Test Methods for Testing Mechanical Splices for Steel Reinforcing Bars. ASTM International, West Conshohocken, Pa. ASTM. (2016). ASTM A706/A706M-16: Standard Specification for Low-Alloy Steel Deformed and Plain Bars for Concrete Reinforcement. ASTM International, West Conshohocken, Pa. Bažant, Z. P., and Jirásek, M. (2002). Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress. Journal of Engineering Mechanics, Vol. 128, No. 11, pp. 1119–1149. Benjumea, J., Saiidi, M., and Itani, A. (2019). Experimental and Analytical Seismic Studies of a Two-Span Bridge System with Precast Concrete Elements and ABC Connections. CCEER-19-02. Center for Civil Engineering Earthquake Research, Department of Civil and Environmental Engineering, University of Nevada, Reno. Brenes, F. J., Wood, S. L., and Kreger, M. E. (2006). Anchorage Requirements for Grouted Vertical-Duct Connectors in Precast Bent Cap Systems. FHWA/TX-06/0-4176-1. Center for Transportation Research, University of Texas at Austin. Brown, A., and Saiidi, M. S. (2009). Investigation of Near-Fault Ground Motion Effects on Substandard Bridge Columns and Bents. CCEER-09-1. Center for Civil Engineering Earthquake Research, Department of Civil and Environmental Engineering, University of Nevada, Reno. California Department of Transportation. (2004). Method of Tests for Mechanical and Welded Reinforcing Steel Splices. California Test 670. Division of Engineering Services, Sacramento. California Department of Transportation. (2013). Seismic Design Criteria Version 1.7. Sacramento. Comité Euro-International Du Beton. (1993). CEB-FIP Model Code 1990: Design Code. Thomas Telford, London. Dassault Systèmes. (2014a). Abaqus 6.14-1. Abaqus/CAE User’s Guide. Simulia Corp., Providence, R.I.

Analytical Programs 233 Dassault Systèmes. (2014b). Abaqus/Explicit, v. 6.14-1. Simulia Corp., Providence, R.I. Galvis, F., Correal, J. F., Betancour, N., and Yamin, L. (2015). Characterization of the Seismic Behavior of a Column-Foundation Connection for Accelerated Bridge Construction. VII Congreso Nacional de Ingeni- ería Sísmica, Bogotá, Colombia. Haber, Z. B., Saiidi, M. S., and Sanders, D. H. (2013). Precast Column-Footing Connections for Accelerated Bridge Construction in Seismic Zones. UNR/CCEER-13-08. Center for Civil Engineering Earthquake Research, Department of Civil and Environmental Engineering, University of Nevada, Reno. Haber, Z. B., Saiidi, M. S., and Sanders, D. H. (2014). Seismic Performance of Precast Columns with Mechanically Spliced Column-Footing Connections. ACI Structural Journal, Vol. 111, No. 3, pp. 639–650. Haber, Z. B., Saiidi, M. S., and Sanders, D. H. (2015). Behavior and Simplified Modeling of Mechanical Reinforcing Bar Splices. 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Assessment of an Earthquake Resilient Bridge with Pretensioned, Rock- ing Columns. CCEER-16-03. Center for Civil Engineering Earthquake Research, Department of Civil and Environmental Engineering, University of Nevada, Reno. Matsumoto, E. E., Waggoner, M. C., Sumen, G., and Kreger, M. E. (2001). Development of a Precast Bent Cap System. FHWA/TX-0-1748-2. Center for Transportation Research, University of Texas at Austin. McLean, D. I., and Smith, C. L. (1997). Noncontact Lab Splices in Bridge Column-Shaft Connections. WA-RD 417.1. Washington State Department of Transportation, Olympia. Mehraein, M., and Saiidi, M. S. (2016). Seismic Performance of Bridge Column-Pile-Shaft Pin Connections for Application in Accelerated Bridge Construction. CCEER-16-01. Center for Civil Engineering Earthquake Research, Department of Civil and Environmental Engineering, University of Nevada, Reno. Mehrsoroush, A., and Saiidi, M. S. (2014). 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Seismic Evaluation of Grouted Splice Sleeve Connections for Precast RC Bridge Piers in ABC. UT-14.09. Utah Department of Transportation, Salt Lake City. Paulay, T., and Priestley, M. (1992). Seismic Design of Reinforced Concrete and Masonry Buildings. John Wiley & Sons, Inc. Phan, V., Saiidi, M. S., and Anderson, J. (2005). Near Fault (Near Field) Ground Motions Effects on Reinforced Concrete Bridge Columns. CCEER-05-7. Center for Civil Engineering Earthquake Research, Department of Civil and Environmental Engineering, University of Nevada, Reno. Priestley, M. J. N., Seible, F., and Calvi G. M. (1996). Seismic Design and Retrofit of Bridges, John Wiley & Sons. Restrepo, J. I., Tobolski, M. J., and Matsumoto, E. E. (2011). NCHRP Report 681: Development of a Precast Bent Cap System for Seismic Regions. Transportation Research Board of the National Academies, Washington, D.C. Roesler, J., Paulino, G. H., Park, K., and Gaedicke, C. (2007). Concrete Fracture Prediction Using Bilinear Soften- ing. Cement and Concrete Composites, Vol. 29, No. 4, pp. 300–312. Steuck, K. P., Eberhard, M. O., and Stanton, J. F. (2009). Anchorage of Large-Diameter Reinforcing Bars in Ducts. ACI Structural Journal, Vol. 106, No. 4, pp. 506–513. Tazarv, M., and Saiidi, M. S. (2014). Next Generation of Bridge Columns for Accelerated Bridge Construction in High Seismic Zones. CCEER-14-06. Center for Civil Engineering Earthquake Research, Department of Civil and Environmental Engineering, University of Nevada, Reno.

234 Proposed AASHTO Seismic Specifications for ABC Column Connections Tazarv, M. and Saiidi, M. S. (2015a). Design and Construction of Precast Bent Caps with Pocket Connections for High Seismic Regions. CCEER-15-06. Center for Civil Engineering Earthquake Research, Department of Civil and Environmental Engineering, University of Nevada, Reno. Tazarv, M., and Saiidi, M. S. (2015b). Low-Damage Precast Columns for Accelerated Bridge Construction in High Seismic Zones. Journal of Bridge Engineering, Vol. 21, No. 3. 10. Tazarv, M., and Saiidi, M. S. (2016). Seismic Design of Bridge Columns Incorporating Mechanical Bar Splices in Plastic Hinge Regions. Engineering Structures, Vol. 124, pp. 507–520. Tran, H. V. (2012). Drilled Shaft Socket Connections for Precast Columns in Seismic Regions. M.S. thesis. Depart- ment of Civil and Environmental Engineering, University of Washington, Seattle. Tran, H. V. (2015). Drilled Shaft Socket Connections for Precast Column in Seismic Regions. Ph.D. dissertation. Department of Civil and Environmental Engineering, University of Washington, Seattle. Verderame, G. M., Carlo, G. D., Ricci, P., and Fabbrocino, G. (2009). Cyclic Bond Behaviour of Plain Bars. Part II: Analytical Investigation. Construction and Building Materials, Vol. 23, pp. 3512–3522. Washington State Department of Transportation. (2002). Bridge Design Manual. Olympia. Wehbe, N., Saiidi, M., and Sanders, D. (1997). Effect of Confinement and Flares on the Seismic Performance of Reinforced Concrete Bridge Columns. CCEER-97-2. Civil Engineering Department, Department of Civil Engineering, University of Nevada, Reno. Zaghi, A. E., and Saiidi, M. (2010). Seismic Design of Pipe-Pin Connections in Concrete Bridges. CCEER-10-01. Center for Civil Engineering Earthquake Research, Department of Civil and Environmental Engineering, University of Nevada, Reno.