Contribution of Steel Casing to Single Shaft Foundation Structural Resistance (2018)

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20 2.1. Introduction The research approach conducted in this project is presented in two general categories of analytical and experimental programs. Section 2.2 presents the study done by conducting several pushover and cyclic finite element analyses, in order to address the objectives defined in the ana- lytical program of the project. The results of the analytical program are presented in 12 sections, each focused on addressing a specific objective that was investigated. These results are presented in subsections 2.2.5 to 2.2.16 of Section 2.2. Based on the findings of the analytical program, two series of tests were conducted includ- ing cyclic tests of six large-scale flexural RCFST shafts cantilevering from a reinforced concrete foundation and seven cyclic shear tests on RCFST shafts. The details of the test specimens, their test setups, construction, and preparation are presented in Section 2.3. The flexural specimens were designed to investigate the composite action in RCFSTs with different diameters, steel tube thicknesses, shaft heights, axial loads, and steel casing-to-concrete core interface conditions. This latter issue was investigated by testing specimens with natu- ral steel-to-concrete bonds, and specimens with reduced interface friction created by applying either bentonite slurry or grease on the interior surface of the steel tube. Also, one specimen in the flexural testing program had an alternative transition zone detail at the connection between the reinforced concrete column and the RCFST shaft to investigate a shear-head concept devel- oped to transfer the column forces to the composite shaft. Finally, another specimen used a shear transfer mechanism at the top of the RCFST shaft to achieve the desired composite action in which insufficient interface friction is present between the steel and concrete. The shear tests were designed to investigate the shear behavior of the composite RCFST shafts when subjected to a double curvature shear condition (such as exists when the shaft spans across a liquefiable soil layer). The shear experimental program consisted of the largest diameter RCFST shafts tested under cyclic loading to date. 2.2. Analytical Program Information and results on the work conducted as part of the analytical program are orga- nized in subsections as follows: • Sections 2.2.1 to 2.2.3 present the analytical program matrix and the details of the finite element models that were used for the parametric studies and their validation using exper- imental results from previous research by Murcia-Delso (2013) and Brown (2013). • A study on the respective contributions of the casing and reinforced concrete core parts to the total flexural strength of RCFST shafts is presented in Section 2.2.5. The results are presented C h a p t e r 2 Research Approach

research approach 21 for different diameter-to-thickness ratios (D/t) and reinforcement ratios, and the importance of material properties of steel tube and reinforced concrete cores for different values of the D/t ratio is observed. • Section 2.2.6 presents results investigating the importance of the friction coefficient at the interface of the casing and reinforced concrete core. It is shown that this friction is important (and necessary in absence of other shear transfer mechanisms) to achieve composite action in RCFST and CFST shafts (CFST essentially being RCFST without internal reinforcement). Alternatively, in absence of friction, the use of shear transfer mechanisms at the top of the shaft can make it possible to achieve the same composite strength and behavior. The physics of this load transfer from the casing to the concrete core in a composite section is described in this section. • The non-composite behavior of RCFST and CFST that happens in absence of friction or shear transfer mechanism is described in Sections 2.2.7 and 2.2.8. • In Section 2.2.9, the effect of reinforcement on the composite behavior of RCFST is studied by comparing the flexural strength of composite and non-composite RCFST shafts with various D/t and reinforcement ratios. • Results of investigating the effect of shaft height on the composite action of RCFST shafts are presented in Section 2.2.10. The behavior of RCFST shafts is presented for shafts having different height-to-diameter ratios and different bond conditions at the reinforced concrete- to-steel tube interface. The minimum friction needed to develop composite action is studied for different shaft heights and the amount of force that needs to be transferred between the reinforced concrete and steel tube to develop a full composite section is calculated and com- pared for those shafts. • Section 2.2.11 presents results for analyses of shafts with different diameters (but same D/t ratios) to investigate the effect of shaft diameter on the composite action of RCFST shafts. The mechanics of force transfer between the reinforced concrete and steel tube is studied in this section. • The mechanism of force transfer from a reinforced concrete column to an RCFST (or CFST) shaft (together with the effect of that reinforced concrete column on the composite action of RCFST shafts) is studied in Section 2.2.12 by introducing a reinforced concrete column on top of the RCFST shaft in the existing finite element model. Also presented in this section is a simplified method for calculating how far the reinforced concrete column rebars should be extended into the shaft (complementing the standard minimum anchorage requirements) to ensure the integrity of the reinforced concrete column and shaft up to the point when the shaft reaches its plastic flexural strength. • Section 2.2.13 presents results of a study of the effect of axial loads on the composite behavior of RCFST and CFST shafts. The axial load-moment interaction curves for composite and non-composite RCFST and CFST shafts are presented in this section and the moment capac- ity of those shafts is compared for different axial load values. • Effect of the D/t ratio of the RCFST shaft’s steel tube on composite behavior is investigated in Section 2.2.14. Finite element results of RCFST shafts having different D/t ratios are compared to each other and the effect of D/t ratios on the relative contribution of the reinforced concrete core and steel tube parts to the total strength is studied. • Section 2.15 presents the results of cyclic analyses performed on shafts that have been inves- tigated when subjected to monotonic loading in previous sections. The observed differences between monotonic and cyclic behavior of RCFST shafts are described in this section. • In Section 2.16, the behavior of a shaft embedded in soil is compared to that of the corre- sponding cantilever RCFST shaft. This was done to ensure that the conclusions made in the analytical program (obtained by analyzing a cantilever RCFST shaft) remain valid for shafts surrounded by soil. • Conclusions from the studies done in analytical programs are presented in Section 2.3.

22 Contribution of Steel Casing to Single Shaft Foundation Structural resistance 2.2.1. Enlarged Pile Shaft Simulation In order to develop a finite element model that is able to simulate the nonlinear behavior of drilled shafts, the results of a large-scale drilled shaft cyclic pushover test from Murcia-Delso (2013) were used as a benchmark for verification. Finite element models were developed using Abaqus and LS-Dyna. Analyses results from both software packages were compared to the test results, and advantages of each software were pointed out. Figure 2.1 shows the details of the large-scale drilled shaft tested by Murcia-Delso (2013). The reinforced concrete column has a diameter of 4 ft and the diameter of the reinforced concrete shaft is 6 ft. A total of 18 No. 11 and 28 No. 14 rebars are used for column and shaft parts, respectively. Compressive strength of the concrete is f ′c = 5.0 ksi. The reinforcement is Grade 60 complying with ASTM A706 with yield, ultimate tensile strengths, and geometric properties that are presented in Table 2.1. An axial load of 800 kip is acting on the column. 8' 4' 4' 2' 15' 9' 4' 14' 6' 6' 6' 7'– 6' Figure 2.1. Details of the pile shaft tested by Murcia-Delso (2013). Bar No. , in. , ksi , ksi 11 1.41 65 91.5 14 1.69 70 97.4 Table 2.1. Properties of reinforcement rebars.

research approach 23 Only half of the specimen was modeled due to the symmetry of the column. The damage plasticity concrete constitutive model in Abaqus has been used for modeling concrete material. The stress–strain relationship of concrete has been calculated according to Mander et al. (1988), however a residual tensile resistance was assumed to overcome convergence problems. A dam- age which is proportional to the maximum strain of the concrete was assigned to the constitutive model. Three dimensional 8-node linear brick elements with reduced integration were used for modeling the concrete. Bilinear isotropic material was considered for steel rebars. In the Abaqus model, the slippage of the column rebars was modeled by considering bond– slip behavior. Perfect bond was considered for shaft rebars. Transverse reinforcement was also embedded in the concrete (perfect bond). Longitudinal reinforcing bars were modeled by wire elements with a beam section, and truss elements were used for transverse reinforcement. The concrete mesh has been separated at the interface of column and shaft to simulate the opening and closure of large flexural cracks, which can occur at that location. Certain contact conditions were introduced at the interface of column and shaft. A hard contact surface condition (rigid in normal direction) combined with a tangential coulomb friction model was assumed for the inter- face. The friction coefficient for the concrete-to-concrete crack surface was taken as µ = 1 accord- ing to Section 11.6.4.3 of ACI 318 (2011). Figure 2.2 shows the model developed in Abaqus. A comparison between the finite element analysis results obtained from the Abaqus model and the results from test and finite element analysis done by Murcia-Delso (2013) is shown in Figure 2.3. It is observed that the developed finite element model has acceptably reproduced the Murcia-Delso results. The damage plasticity concrete constitutive model in Abaqus is not able to model the pinch- ing behavior resulting from opening and closing of the cracks in the concrete. That was the Figure 2.2. Finite element analysis (FEA) model of the specimen tested by Murcia-Delso (2013) developed in Abaqus.

24 Contribution of Steel Casing to Single Shaft Foundation Structural resistance reason that an explicit crack was modeled by separating the mesh at the interface of the column and shaft where the cracks were most likely to happen. Work by Imani (2014) showed that the existing Winfrith model in LS-Dyna is able to properly model this phenomenon. Figure 2.4 shows the LS-Dyna finite element model of the same Murcia-Delso enlarged pile shaft previously analyzed with Abaqus. Half of the specimen was modeled, as done previously for the Abaqus model. Longitudinal rebars were modeled using beam elements with an elastic, perfectly plastic kinematic material. Stirrups were modeled using elastic material. The Winfrith concrete material model with constant stress solid elements was used for the concrete part. Table 2.2 presents the properties of the concrete material model. Perfect bond was considered for the rebars. Column, shaft, and foundation parts were meshed independently and tied together using surface-based tied contact. A comparison between the finite element analysis results obtained here and the results from the test done by Murcia-Delso (2013) is shown in Figure 2.5. It is shown that the developed finite element model in LS-Dyna can acceptably simulate the response of the enlarged shaft pile. 2.2.2. Finite Element Modeling of RCFST Shaft In order to develop a model that is capable of simulating the behavior of CFSTs with internal reinforcement, an RCFST recently tested by Brown (2013) has been modeled in this section. Figure 2.6 shows the setup of Brown’s test. Twelve large-scale reinforced concrete steel tubes with different reinforcing and D/t ratios were tested under reversed cyclic load using a four point bending test setup. Three specimens with the same diameter of 24 in. and different D/t ratios were chosen from the Brown (2013) tests for finite element modeling. Table 2.3 presents the properties of these specimens. Concrete and steel properties for each of those tests are presented in Table 2.4. For simplicity, a quarter of each specimen was modeled in LS-Dyna, and appropriate boundary conditions were defined on both symmetry planes. Figure 2.7 shows the scheme of the finite element model simplification. Cyclic displacement was applied at a distance of 36 in. from the symmetry plane (location of applied load in actual specimen). Figure 2.8 shows the applied boundary conditions. Details of the element type and material model used for modeling the concrete and reinforc- ing rebars are identical to those used for modeling the reinforced concrete column-enlarged shaft model in Section 2.2.1. For the steel tube, LS-Dyna’s default shell element with two (or more) integration points through the element thickness was used. Figure 2.3. Lateral load–lateral displacement comparison for an enlarged pile shaft modeled in Abaqus.

research approach 25 Figure 2.4. Finite element model of the specimen tested by Murcia- Delso (2013) developed in LS-Dyna. Material Model Tangent Modulus, ksi Poisson Ratio Compressive Strength, ksi Tensile Strength, ksi Winfrith Concrete (MAT 84) 4757 0.2 6.2 0.001 Table 2.2. Properties of the concrete material model. Figure 2.5. Lateral load–lateral displacement comparison for enlarged pile shaft modeled in LS-Dyna.

HYDRAULIC ACTUATOR STEEL “SHOE” Steel frame used for load application RCFST 6' 25' 2'–6' 9' 30' Figure 2.6. Setup of the test done by Brown (2013) on RCFSTs. Test No. Diameter, in. Tube Thickness, in. D/t Ratio Longitudinal Rebar Transverse Rebar (Spiral) Number Size Ratio ( Size Spacing, in. 9 24 0.125 192 8 #6 0.78% #3 3 11 24 0.1875 128 8 #6 0.78% #3 3 5 24 0.281 85 12 #7 1.60% #3 12 Table 2.3. Properties of Brown (2013) test specimens used for finite element model validation. Test No. Concrete , ksi Steel tube , ksi Reinforcing Rebar , ksi 9 5.80 50 60 11 5.40 44 65 5 5.22 79 68 Table 2.4. Properties of the concrete and steel material used in Brown (2013) tests.

research approach 27 (a) (b) (c) Figure 2.7. (a) Specimen tested by Brown (2013). (b) Half FE model of the test by Brown (2013). (c) Quarter FE model of the test by Brown (2013). Figure 2.8. Boundary conditions applied to the finite element model.

28 Contribution of Steel Casing to Single Shaft Foundation Structural resistance Longitudinal and transverse reinforcements were embedded in the concrete using the Constrained_ Lagrange_in_Solid command, which provides a coupling mechanism for rebars and concrete elements (i.e., perfect bond). The embedment of the reinforcement elements can also be done by merging them with the nodes of the solid elements of the concrete part. In this case, the concrete part has to be meshed accordingly in order to have solid elements with coincident nodes with the reinforcement’s beam elements. This technique is less computationally expensive as it avoids the use of additional constraints such as Constrained_Lagrange_in_Solid in the model. The contact at the interface of the tube and concrete core was defined using the Automatic Single Surface Contact algorithm. This contact type is a penalty-based contact, which allows the compression load to be transferred between slave nodes and master segments. The Automatic Single Surface Contact algorithm is a two-way treatment contact, which means that the master and slave nodes are checked for penetration through each other (analyses using one-way treatment contact algorithms were also conducted, but those contact elements only check the penetration of slave nodes through the master segments at the contact interface; results from those analyses were unsatisfactory and are not reported here). In the surface contact model used, a friction force develops at the interface when the adjacent parts press on each other and want to slide against each other. Sliding will occur when the shear force between the two surfaces reaches the sliding force resistance, which is equal to the compression force at the contact multiplied by a correspond- ing friction coefficient. A coefficient of friction of 0.5 between the concrete and steel tube was specified for this purpose. Incidentally, this value approximately corresponds to the coefficient of friction of 0.57, 0.47, and 0.47 that has been measured by Rabbat and Russell (1985), Baltay and Gjelsvik (1990), and Moon et al. (2012), respectively. This contact algorithm automatically con- siders the thickness of the shell element and this was taken into account when defining the finite element model geometry. Figure 2.9 shows a 3D view and mesh details of the finite element model. A comparison of the finite element analysis results for different D/t ratios is presented in Fig- ures 2.10, 2.11, and 2.12. As shown, the modified finite element model has been able to simulate the response of RCFST with acceptable accuracy. 3D View Mesh details Figure 2.9. Mesh details of the developed finite element model.

research approach 29 FEA Experimental Figure 2.10. Lateral load–midspan deflection comparison for RCFST test done by Brown (2013) with D/t = 192. FEA Experimental Figure 2.11. Lateral load–midspan deflection comparison for RCFST test done by Brown (2013) with D/t = 128. D/t = 85 Figure 2.12. Lateral load–midspan deflection comparison for RCFST test done by Brown (2013) with D/t = 85.

30 Contribution of Steel Casing to Single Shaft Foundation Structural resistance 2.2.3. Analytical Program Matrix The limited finite element analyses that were conducted allowed reviewing the state of exist- ing techniques to model the complex behavior of some load transfer mechanisms. Beyond these preliminary analyses, an extensive analytical program was conducted to better understand the mechanisms that must be developed to achieve the load transfer from the reinforced con- crete column to the shaft and develop the full composite action of the shaft at the point of maxi- mum moments. A number of analyses were also considered to investigate the effect of different geometric and material parameters. Table 2.5 outlines the analytical program performed for this purpose. In addition to the parametric analyses listed in Table 2.5, models of the test specimens were analyzed, and results were used to predict the behavior of the specimens that were tested in the Structural Engineering and Earthquake Simulation Laboratory (SEESL) lab. The performed parametric study presented in Table 2.5 was divided into 12 analysis groups. Each group focuses on the investigation of the effect of certain parameters on the shaft behavior. Results of Analysis Groups G-1, G-2, and G-11 are presented in Sections 2.2.6, 2.2.10, and 2.2.15. Analysis Groups G-3, G-4, G-8, and G-10 are related to analyses of the combined reinforced con- crete column-RCFST shaft, for which results are presented in Section 2.2.12. Results of Analysis Groups G-5, G-6, and G-12, related to the effect of axial loads on RCFST shafts, are presented in Section 2.2.13. Results of Analysis Group G-9, investigating the effect of change in the D/t ratio of steel tube, are presented in Section 2.2.14. Based on the observations reported in Section 2.2.15, it was determined that cyclic analyses were not necessary for Analysis Groups G-3, G-4, G-8, and G-10, and that the specific questions on behavior sought in those cases was adequately answered by the findings from the pushover analyses performed on those groups. The parameters used in Table 2.5 are defined as follows: • Ds = Diameter of the shaft (Figure 2.13), chosen to be slightly less than the minimum value of 30 in. in the AASHTO LRFD Bridge Design Specifications (2012) and the maximum limit of 144 in. recommended by FHWA (Brown et al. 2010). • e = Distance between the interior edge of the shaft and the column (Figure 2.13), determined based on the design of the column, taking into account the constraint in the experimental phase of this project that the column must remain elastic until the shaft reaches its moment capac- ity. Note that e = 0 represents the case when the column diameter is equal to the shaft inside diameter, i.e., the case when the maximum possible e is considered as an analysis parameter. • Dc = Diameter of the column (Figure 2.13), calculated using Ds and e per Equation 2.1. As mentioned earlier, the diameter of the column must be chosen such that the column will remain elastic during the analyses and experiments conducted as part of this project. 2 (2.1)= −D D ec s • Hc = Height of the column (Figure 2.13), chosen as five times the diameter of the column (Dc) for all the prototype models considered here. • Hs = Height of the shaft (Figure 2.13), which is the length of the shaft considered in the proto- type models. Height of shaft was chosen as 3, 5, and 7.5 times the diameter of the shaft (Ds) for the analyses. • hd = Length required to develop the full composite action in the shaft (Figure 2.13), which is expected to depend on the load transfer mechanism between steel tube and the shaft. • ld = Development length required for column longitudinal rebars extended into shaft (Figure 2.14a), which depends on the concrete material properties, diameter of rebars, and dimensions of the column and shaft. A conservative value was chosen based on requirements and recommendations of AASHTO LRFD Bridge Design Specifications (2012), AASHTO SGS (2011), Caltrans Seismic Design Criteria (2013), Murcia-Delso (2013), and WSDOT Bridge Design Manual (2012).

Analysis Group Loading Scenario , in. e Load Transfer Mechanism Shaft Reinforcement To Investigate G-1 Pushover, cyclic, no axial load 24 N/A 3,5,7.5 F(1),(2) 85 RCFST, CFST The effect of shaft height ( ) on the length required for full composite action ( ). G-2, G-11 Pushover, cyclic, no axial load 100 N/A 3,5,7.5 F 85 RCFST, CFST The effect of diameter change ( ) on and plastic hinging in steel encased reinforced concrete shafts. G-3 Pushover, no axial load 100 0.06 7.5 F 85 RC(6) column attached to RCFST/CFST The effect of different shaft ( ) and column ( ) diameters on full composite action. The effect of shaft reinforcement. G-4 Pushover, with axial load 100 0.06 7.5 F 85 RC column attached to RCFST/CFST The effect of large axial force. G-5, G-12 Pushover, cyclic, with axial load 100 N/A 7.5 F 85 RCFST, CFST The effect of large axial force and plastic hinging in steel encased reinforced concrete shaft. G-6 Pushover, cyclic, with axial load 24 N/A 7.5 F 85 RCFST, CFST The effect of diameter change ( ) considering the case with large axial force. G-7 Pushover, cyclic, no axial load 100 N/A 7.5 FB(3), RB(4), SS(5) 85 RCFST The effect of different load transfer mechanisms. G-8 Pushover, no axial load 100 0.06 7.5 FB, RB, SS 85 RC column attached to RCFST G-9 Pushover, cyclic, no axial load 100 N/A 7.5 F, FB (or RB or SS) 100 RCFST, CFST The effect of change in steel tube thickness. G-10 Pushover, no axial load 100 0.06 7.5 F, FB (or RB or SS) 100 RCFST, CFST (1) F: Only the friction between concrete and steel tube is considered as load transfer mechanism. (2) Case of low friction between concrete and steel tube also was used to simulate slurry on casing surface. (3) FB: Flat Bar. (4) RB: Round Bar. (5) SS: Shear Stud. (6) RC: Reinforced Concrete. Table 2.5. Performed analytical study (prototype models).

32 Contribution of Steel Casing to Single Shaft Foundation Structural resistance • t = Thickness of the steel tube (Figure 2.14a), which was calculated by considering different values for the Ds/t ratio. Ds/t = 85 and 100 were considered for all prototype models. • Sc = Distance from the center of the column rebars that extend into the shaft to the inner sur- face of the shaft casing (Figure 2.14a), which is calculated using e, the cover for the column reinforcement cage, and dimensions of the column rebars. • s = Offset distance between column and shaft rebars (Figure 2.14b), which is calculated using e, the cover for shaft and column reinforcement cages, and dimensions of the shaft and column rebars. To investigate different mechanisms for transferring forces from reinforced concrete column reinforcement to the shaft and steel tube, mechanical shear transfer mechanisms (shown in Fig- ure 2.15) were considered in this analytical study. It is recognized that shear studs are the least desirable option of those shown in Figure 2.15a. In addition, shear transfer via friction at the interface of the shaft and steel tube itself was also considered for the case without mechanical connectors. In this case, the coefficient of the friction between the shaft’s concrete and the steel tube was varied to reflect various conditions for the surface of the steel tube in contact with shaft concrete. Two cases of actual (ordinary steel tube surface) and low friction (slurry surface) were considered in the parametric study. The following information describes characteristics and/or purposes of the analysis cases presented in Table 2.5: • Group G-1 focuses on the effect of shaft height on the length required to develop full com- posite action, for which three different heights were analyzed. Shaft and column diameters are the same for this analysis group. For those cases, column reinforcing is extended into the shaft for a distance equal to the required development length of the rebars, and no reinforcement is considered in the shaft itself. • The Ds/t ratio is considered equal to 85 for all analysis groups, except for cases where the thick- ness of the casing is the purpose of the investigation (i.e., Groups G-9 and G-10). • Analyses in Group G-2 investigated the effect of change in shaft diameter (Ds) on the full composite action of the shaft. A larger shaft diameter of 100 in. with the same Hs/Ds ratios as Group G-1 was considered for this analysis group. • One of the analysis cases of the Group G-2 was repeated in Group G-3 (Hs/Ds = 7.5) but with a smaller column diameter with respect to the shaft diameter (e ≠ 0 in Figure 2.13). Figure 2.13. Column and shaft parameters. 2” Cover (Typical) 3” Cover (Typical) 3” Cover (Typical) (a) (b) Figure 2.14. Prototype model parameters.

research approach 33 • For the case when shaft and column diameters are different from each other, two analyses with and without shaft reinforcement were conducted to investigate the effect of shaft reinforcement on the confinement of the concrete and full composite action of the encased shaft. • To investigate the effect of a large axial force, analyses of Groups G-1 (only one case of Hs/Ds), G-2 (only one case of Hs/Ds), and G-3 were repeated with a large axial load. These are pre- sented as Groups G-6, G-5, and G-4 respectively in the table. • For all aforementioned analysis groups, the friction on the interface of shaft concrete and steel tube was considered as the load transferring mechanism. To investigate the performance of different load transfer mechanisms, shown in Figure 2.15a, two different types of prototype models, one with similar shaft and column diameters (e = 0) and one with different shaft and column diameters (e ≠ 0), were analyzed including the mechanical load transfer mecha- nisms (Group G-7 and G-8). • The effect of different Ds/t ratios was investigated in Groups G-9 and G-10. • A Ds/t ratio equal to 100 was considered on four analysis cases selected from Groups G-2, G-7, G-3 (or G-4), and G-8 to investigate the effect of a larger Ds/t ratio (see Groups G-9 and G-10). • To investigate the case for which the maximum moment and therefore the plastic hinge occurs in the CFST shaft also having a reinforcement cage inside the shaft, an RCFST shaft prototype model (without the column part) was considered, as shown in Figure 2.16. For this case, the height of the shaft is set to 7.5 times its diameter. Analyses were done for cyclic loading with and without large axial loads on the shaft. Different diameter-to-thickness ratios were con- sidered to investigate the effect of steel tube thickness. Details of the prototype RCFST shaft models are presented in Table 2.5 (Groups G-11 and G-12). • To investigate the effect of surrounding soil on the transferring of load from steel tube to the reinforced concrete core of the shaft, and the length required for the required level of compos- ite action, one selected case from Group G-1 or G-2 was analyzed considering three different kinds of soil stiffness. • To investigate the effect of low friction (slurry) at the interface of the steel tube and the rein- forced concrete core of the shaft, one selected case from Group G-1 or G-2 was analyzed with a reduced interface friction. The column part of the prototype models was designed to remain elastic for all the models considered in this parametric study, as the research objective is to determine the conditions (a) (b) Figure 2.15. Shear transfer mechanisms. (a) Typical shear transfer mechanisms. (b) Placement of shear transfer mechanisms on shaft casing. 3” Cover (Typical) Figure 2.16. Prototype encased shaft model parameters.

34 Contribution of Steel Casing to Single Shaft Foundation Structural resistance needed to develop the composite strength of the shaft. Figure 2.17 shows schematic moment diagrams corresponding to different shaft heights of prototype models. The same column sec- tion (i.e., longitudinal reinforcement ratio and diameter of rebars) was used for all the models in each analysis group indicated in Table 2.5, the section being designed according to the highest strength demand in each analysis group. Transverse reinforcement of the column was designed to provide shear strength and to be in compliance with confined concrete requirements. Maxi- mum column diameter margin with respect to the shaft diameter, emax, was chosen considering that the column should remain essentially elastic before the shaft reaches its moment capacity (as mentioned earlier). All prototype models were also analyzed under a cyclic displacement history of progressively increasing magnitude, with the understanding that information on elastic response up to maxi- mum strength (for non-cyclic applications) will be given by the results from the early phase of this loading protocol. Axial load was also considered as an analysis parameter, to investigate its effect on the contribution of steel tube to shaft strength. 2.2.4. Finite Element Models Used in This Study To understand the load transfer mechanism between the casing and the reinforced con- crete core inside, and in order to perform the parametric study discussed in Section 2.2.3, the validated finite element model was modified to specifically focus on the mechanisms that contribute to developing the flexural strength of the composite member, including the effect of friction contact between the steel tube and the concrete core and others. For that purpose, the boundaries of the RCFST model were changed to simulate a fixed bottom canti- lever beam. Pushover and cyclic analyses were then performed. For pushover analyses, monotonically increasing displacements up to a maximum drift ratio of 5.5% were applied at the top of the Figure 2.17. Prototype model moment diagram.

research approach 35 model. For cyclic analyses, loading was also applied in the same region using a displacement protocol that is described in Section 2.2.15. Figure 2.18 shows the details of the modified model. No constraints (i.e., shear transfer mechanisms) were used to prevent sliding between the steel tube and concrete core at the top of the column (Figure 2.18a) in that particular model. How- ever, for cases where physical shear connectors are present at the top of the shaft, an additional model including such a constraint (at the top of the CFST) was considered for comparison (Fig- ure 2.18b). The constraint was applied using tie contacts at the interface of the tube and the concrete core at the top of the RCFST. In all cases, displacement loading was applied only to the concrete part of the RCFST and not to the steel tube. This would be the case where a column is attached to a shaft and the lateral load is transferred from the column to the shaft and then from the concrete shaft to the steel tube to develop the total shaft strength. For the finite element analyses presented here, the properties of the concrete, reinforcing rebars, and steel tube were taken to be similar to those measured for Test No. 5 reported by Brown (2013), presented in Table 2.4, unless otherwise stated in the text for a specific analysis. Those values used in analyses are the actual material strength values measured by Brown (2013) for that particular test specimen. Properties of the finite element models used in parametric study are presented in Appendix F. 2.2.5. Contribution of Casing and Reinforced Concrete Core The bending strength of RCFST consists of two parts: the moment that is carried by the steel tube and the moment that is carried by the reinforced concrete core. The moment carried by each part can be calculated from their respective normal stress distribution at the cross- sections of interest in the corresponding part. As an indicator of composite behavior, when full (a) (b) Figure 2.18. Cantilever column details. (a) Without constraint at the top. (b) With constraint at the top.

36 Contribution of Steel Casing to Single Shaft Foundation Structural resistance composite strength is developed, the neutral axis of steel tube and the reinforced concrete core cross-sections will be the same. However, for a non-composite section under bending, the neu- tral axis of each part will be independent of each other. Figure 2.19a shows the moment response of the RCFST with D/t = 85 and r = 1.6% [Test No. 5 done by Brown (2013)] obtained from finite element analysis. Those results were also compared to the moment capacity of the corresponding fully composite section, calculated using the PSDM and verified using fiber-section analysis in Mazzoni et al. (2006). The details of the PSDM calculations are presented in Appendix E. Figure 2.19b shows the moment carried by each part. The confining effect of transverse reinforcing was neglected, and the confining effect of the steel tube was taken into account using the relationship proposed by Susantha et al. (2001), which Figure 2.19. Finite element analysis moment response of the RCFST with D/t = 85 and q = 1.6% [Test No. 5 done by Brown (2013)]. (a) Total response. (b) Response of each part. (a) (b)

research approach 37 is described in Appendix E. The results show that the maximum composite strength predicted by the PSDM is in good agreement with the experimental results. Using the PSDM equations validated as shown above, it is possible to calculate the respec- tive contribution of each part to the total strength for a fully composite section. The portion of the moment strength of RCFST that is carried by the casing or the reinforced concrete core depends on the D/t ratio, the reinforcing ratio (r), and the strength of the steel and concrete materials. Figure 2.20 shows the portion of the bending strength of the RCFST that is carried by the steel tube part of the RCFST for different D/t ratios and steel tube materials. It also pro- vides a comparison between different reinforcing ratios. As shown in Figure 2.20, for lower D/t ratios, the strength of RCFST mostly depends on the steel tube, but this contribution progressively decreases as D/t increases. In other words, when full composite action is developed, the structural properties of the steel tube govern the global response of the RCFST for lower D/t ratios, and as D/t increases, the contribution of the reinforced concrete core increases (for example, becoming the dominating part when D/t exceeds 120 for a reinforc- ing ratio of 1%, by interpolation). One consequence of this observation is that the progressive loss of strength that develops at large drifts due to local buckling of the steel tube in the inelastic (a) (b) Figure 2.20. Ratio of bending strength of the steel tube to the total bending strength of RCFST.

38 Contribution of Steel Casing to Single Shaft Foundation Structural resistance range (after attainment of the maximum plastic flexural strength) will result in more significant, noticeable loss of strength for shafts having lower D/t ratios. Likewise, the benefits of concrete confinement due to steel tubes or transverse reinforcement in the concrete core will not provide substantial increases in strength, except for in higher D/t ratios. 2.2.6. Effect of Friction Coefficient (Friction Force) The case with D/t = 85 was analyzed using pushover analysis for the RCFST tested by Brown (2013) but for models having different friction coefficients at the steel tube and concrete core interface. Figure 2.21 compares the pushover analysis results for the case with D/t = 85, r = 1.6% and various friction coefficients. As shown in the figure, the general response of RCFST depends on the friction condition at the interface of the steel tube and the concrete core. In fact, under bending deformation, without friction resistance, the steel tube and concrete core slide against each other. The presence of friction resistance at the interface of the casing and concrete core allows the development of a tangential force along the interface to resist sliding. Analyses revealed that the tangential force that is transferred between the casing and the concrete core produces a com- pressive axial force on the concrete part and a tensile axial force on the steel tube (that adds up to the flexural stresses). The amount of this internal axial force is proportional to the lateral drift. Full composite action can be expected if a load transfer mechanism exists at the interface, which is able to transfer this axial force between the casing and concrete at the interface. This mechanism can be provided by friction forces acting at the interface, or by mechanical load transferring devices. Identical flexural strength (and overall bending response) is achieved for the case with friction at the interface and the case without friction but having a discrete load transfer mechanism at the end of the shaft. This axial load that transfers between steel tube and the concrete core is referred to as the transferred internal axial load throughout the report. Figure 2.22a shows the axial strain profile for the RCFST with no friction at the casing-to- concrete core interface (obtained by setting the coefficient of friction to zero in the analysis). As observed in that figure, the neutral axes of the casing and concrete core are not the same, which means that the system does not act like a composite section. The neutral axis of the steel tube is at its center of gravity, as expected for a steel tube in pure bending. The neutral axis of the Figure 2.21. Flexural response (Moment– Displacement curve) for RCFST with D/t = 85 and q =1.6% for different friction coefficients.

research approach 39 reinforced concrete section is closer to the compression edge, as in a reinforced concrete column in pure bending. The axial strain profiles for the steel tube and concrete core for the RCFST case with no fric- tion are compared in Figure 2.22b. As shown in that figure, beyond the mismatch in neutral axis, the concrete core and steel tube strains also differ, as the sections slide with respect to each other. Results from finite element analyses indeed show such an axial sliding of the concrete core compared to the steel tube. Figure 2.23 shows the deformation of RCFST along its axial direction (Z direction) at 2% lateral drift ratio; as shown in this figure, the reinforced concrete core and steel tube slide with respect to each other. Figure 2.24 shows the curvature of the RCFST section at Z = 30 in.; as shown in the figure, the sliding happens because the concrete core and steel tube rotate around different axes (their neutral axis). Overall, comparing the strains at the center of gravity in that figure, the reinforced concrete section elongates with respect to the steel tube. Concrete Core Z Strain Profile (a) Steel Tube Z Strain Profile (b) Figure 2.22. Z strain profile for RCFST with no friction. (a) For each part. (b) Comparison at height of z = 20 in.

40 Contribution of Steel Casing to Single Shaft Foundation Structural resistance When the friction force (or mechanical load transferring device) is sufficient to develop com- posite action, the friction at the steel tube-to-concrete core interface generates forces along the shaft to prevent the relative sliding observed above for the no-friction case. This interface force, preventing relative axial sliding of the concrete core with respect to the steel cases, causes com- pression on the concrete core and a tensile force on the casing to achieve identical curvature and neutral axis position. Figure 2.25 shows the axial strain profile obtained for an RCFST for the case with effective friction. As shown in that figure, the casing and concrete core have practically the same neutral axes, which confirms composite action. Figure 2.26 compares the response when a friction coefficient (µ) of 0.5 is used in the analysis, without friction but when constraints are applied at the free end of the shaft using tie contacts to provide a load transferring mechanism. Results are provided for both a specimen tested by Brown (2013) and the cantilever model described. As shown in the figure, both cases exhibit the same behavior. This indicates that an effective way to achieve composite action in absence of friction is to provide a localized shear transfer mechanism at the end of the shaft, without the need for shear transfer mechanism along the entire length of the shaft. 2.2.7. Non-Composite Behavior of RCFST As described in the previous section, the friction at the casing and reinforced concrete inter- face develops a tangential force, which results in composite action of the RCFST. However, when there is no friction, the steel tube and reinforced concrete core behave like two independent structures. Figure 2.27 shows the finite element analysis results for the response of a cantilever XZ Elevation 3D View Z Y X Figure 2.23. Deformation of RCFST along its axial direction (Z direction) at 2% lateral drift ratio, magnified by 10 (deformations in other directions not shown—i.e., magnified by zero). Figure 2.24. Rotation of RCFST section at Z = 30 in. for 2% lateral drift ratio.

research approach 41 (a) (b) Figure 2.26. Comparison of the response of the case with friction (l = 0.5) and without friction with constraints at end of the shaft. (a) RCFST tested by Brown (2013). (b) Cantilever RCFST. Steel tube Z Strain Profile Concrete Core Z Strain Profile Figure 2.25. Z strain profile for RCFST with friction (l = 0.5). RCFST with no friction at the interface, together with the respective results from fiber-section analyses of the steel tube alone and the reinforced concrete section alone. As shown in the figure, the response of the RCFST that cannot develop friction at the casing- to-concrete interface is similar to that obtained by summing the independent steel tube and reinforced concrete responses. It should be noted that, in those fiber-section analyses, it was assumed that the steel tube can reach its plastic moment capacity before any local buckling occurs, and the confining effect of the steel tube on the reinforced concrete core (which finite element analysis shows develop to a small degree) has been considered by specifying the maxi- mum confined uniaxial compressive stress of the concrete based on the relationship proposed by Susantha et al. (2001) (described in Appendix E).

42 Contribution of Steel Casing to Single Shaft Foundation Structural resistance The reduction of flexural strength with increased displacement is due to the local buckling that develops in the steel tube shaft (as shown in Figure 2.27, the moment in the casing part reduces after 3.5 in. displacement due to development of local buckling). For the composite section, when there is enough friction at the interface to allow composite action to develop, the loss in strength of the steel tube is compensated by the reinforced concrete part of the section (as shown in Figure 2.36). However, if the friction is not enough to transfer the internal forces (as discussed in Section 2.2.6) between the steel tube and the reinforced concrete core (which happens with friction coefficients of less than 0.5 in this case), the reinforced concrete part does not compensate for this loss of strength of the steel tube, and the corresponding total strength drops. As a consequence of the loss of strength of the steel tube, the relative contribution of the concrete part to the total strength becomes more significant after development of local buckling in the steel tube. 2.2.8. Non-Composite Behavior of CFST A similar comparison was done for CFSTs. The CFST model was created by removing the reinforcing cage of the concrete core from the RCFST model. Figure 2.28 shows the resulting bending response of the CFST for the cases with friction (µ = 0.5) and without friction. Results show that the general response of CFST also depends on the friction condition at the interface of the steel tube and concrete core. Figures 2.29 and 2.30 show the axial strain pro- file for both CFST cases when their maximum strength is reached. As can be observed, the steel tube and concrete core share practically the same neutral axis for the CFST case with friction, but the CFST with no friction at the casing-to-concrete interface has different neutral axes for the steel tube and the concrete core. This confirms that the CFST with friction exhibits a composite flexural behavior. Figure 2.31 shows the moment carried by each part for the CFST with no friction. It is observed that there is no moment-resisting capacity in the concrete core with no reinforcing (neglecting the tensile strength of concrete), and the strength of the CFST with no friction is similar to that of the steel tube alone. The tensile strength of the concrete was set to zero in this analysis. An analysis was also conducted considering a concrete tensile strength equal to 10% of its uniaxial Figure 2.27. Bending response of cantilever RCFST with no friction.

research approach 43 Figure 2.28. Bending response of cantilever CFST for the case with (l = 0.5) and without friction. Steel Tube Z Strain Profile Concrete Core Z Strain Profile Figure 2.29. Z strain profile for CFST with friction (l = 0.5). compressive strength. In this case, the concrete part carried a small amount of moment, and the total strength was again the sum of the two individual parts, without composite action. In Figure 2.31, concrete starts to contribute slightly to the total flexural strength. Although of marginal significance on total strength, this behavior can be explained as follows. At large deformations and after local buckling of the steel tube near the base of the cantilever shaft, plane sections are not plane anymore. At that point, an increase in contact pressure between the casing and concrete core develops in the lower part of the shaft, resulting in a compressive stress at the cross-section of the concrete core that increases the amount of the moment carried by concrete core. Figure 2.32 shows this interface contact pressure in the lower part of the shaft for 1% and

44 Contribution of Steel Casing to Single Shaft Foundation Structural resistance Steel Tube Z Strain Profile Concrete Core Z Strain Profile Figure 2.30. Z strain profile for CFST with no friction. Figure 2.31. The moment carried by each part for the CFST with no friction.

research approach 45 5.5% drift ratios. This normal contact pressure causes an increase in the compression stress in concrete core, which is shown in Figure 2.33 for 5.5% drift ratio. It is this compression stress that produces the small moment contribution observed in Figure 2.31. 2.2.9. Effect of Reinforcement in Composite RCFST and CFST Figure 2.34 shows the response of RCFST with D/t = 85 and r = 1.6% (with friction coefficient of µ = 0.5) compared to a CFST with similar properties for the concrete core and steel tube. This figure shows that adding longitudinal reinforcement where r = 1.6% results in an 18% increase in the strength of the shaft. This may seem to be a marginal increase in strength for a significant amount of longitudinal reinforcement when composite action is developed (contrary to the case when no-composite action is developed, where rebars are necessary for the concrete core to contribute to the total shaft strength). To better understand how longitudinal reinforcement affects the composite action of the shaft as well as the steel tube performance, the flexural response of each part (contributing to (a) (b) Figure 2.32. Interface contact pressure region at lower part of the shaft. (a) 1.0% drift ratio. (b) 5.5% drift ratio. Figure 2.33. Principal stress at lower part of the shaft at 5.5% drift ratio.

46 Contribution of Steel Casing to Single Shaft Foundation Structural resistance the total strength shown in Figure 2.34) is presented in Figures 2.35 and 2.36. Figure 2.35 shows the moment that is carried by the steel tube for both RCFST and CFST considered in Figure 2.34. It is observed that the contribution of the steel tube to the total response does not change notice- ably in the presence of reinforcement. Detailed review of the results revealed that this is because the addition of reinforcement only marginally changed the location of the neutral axis. As can be concluded from Figure 2.36, the difference in flexural strength between an RCFST and a CFST is equal to the flexural strength provided by the reinforcing bars alone, without significantly affecting the response of other parts. Figure 2.37 shows the normalized moment capacity of composite RCFST with respect to non-composite sections for different D/t ratios and arbitrarily chosen reinforcement ratios ranging from 1% to 3.2%. Also shown in that figure are results for CFSTs (i.e., shafts with- out reinforcement, shown as 0%). Figure 2.37a shows the results for a steel tube with a yield strength of 79 ksi, and Figure 2.37b shows those results for a tube yield strength of 50 ksi. It is observed that the strength of the composite RCFST sections considered here are only 5–12% Figure 2.34. Response of RCFST where D/t = 85 and q = 1.6% compared to a CFST with similar properties. The friction coefficient is 0.5 in both cases. Figure 2.35. Contribution of steel tube in moment response of RCFST and CFST.

research approach 47 (a) Moment carried by concrete (b) Moment carried by reinforcement Figure 2.36. Contribution of concrete core and reinforcement in moment response of RCFST and CFST. greater than the non-composite one. The increase in benefit from composite action increases as the reinforcement ratio of the reinforced concrete core decreases, and benefit is the great- est for CFST. This suggests that, while achieving composite section is of great benefit in CFST shafts, it may not be cost effective to develop composite action in RCFST shafts if this requires any special detailing or mechanical shear transfer devices (which would be required if a clean inside surface of the steel tube cannot be guaranteed and, as a result, friction cannot be relied upon to develop composite action). 2.2.10. Effect of Shaft Height 2.2.10.1. Behavior of RCFST Shaft for Different Height-to-Diameter Ratios In order to investigate the effect of change in RCFST shaft’s height on the length that is required to develop full composite action at the bottom of the shaft, three RCFST shafts with different heights were analyzed (Analysis Group G-1). In these analyses, friction at the interface of the steel tube and the reinforced concrete core was the only mechanism implemented for transferring loads between the steel tube and concrete core. In addition to the analyses done in Group G-1, for comparison, an RCFST shaft with a larger diameter of 100 in. was also analyzed with three different H/D ratios.

48 Contribution of Steel Casing to Single Shaft Foundation Structural resistance (a) (b) Figure 2.37. Ratio of composite to non-composite flexural strength of RCFST as a function of reinforcement ratio. Figure 2.38 compares responses of composite RCFST shafts with different heights. As shown in the figure, all shafts, irrespective of height, reach the same plastic moment. That value is reached at different drifts because of the different shaft stiffness. In this figure, the friction coefficient for H/D = 7.5 is 0.5 and for H/D = 5.0 and 3.0 is 0.8. Figure 2.39 shows the response of RCFST shafts with different friction coefficients at their interface and a comparison of those cases with the case when the steel tube and the concrete core are tied to each other at the top of the shaft. As shown in the figure, the responses of the RCFST shaft with an H/D ratio of 7.5 are the same for a friction coefficient of µ = 0.5 and higher, which suggests that full composite action can be achieved when µ ≥ 0.5. However, for lower H/D ratios, a larger value of friction coefficient is needed to achieve the same full com- posite action. According to the analyses done on H/D = 5 and 3, a friction coefficient of µ ≥ 0.8 would be required to achieve the full composite action for those H/D ratios. However, although a slightly lower maximum flexural strength was obtained in those two cases for µ = 0.5, it is noteworthy that the plastic strength was still reached (MP being equal to 1.86 × 104 kip.in. and 1.40 × 106 kip.in. for the 24 in. and 100 in. cases, respectively, when calculated by the PSDM using the material properties described in Section 2.2.3).

research approach 49 As described in Section 2.2.6, in order to develop full composite action in an RCFST shaft, the slippage at the interface of the steel tube and concrete core must be prevented—by means of friction or load transfer mechanisms—such as to transfer the internal axial load that devel- ops between those parts. The behavior that leads to the development of this differential inter- nal axial load has been described in Section 2.2.6. These transferred internal axial forces in the concrete and steel are in self-equilibrium and develop in the absence of externally applied axial loads. Figure 2.40 shows the axial load distribution in the steel tube part of the RCFST shaft, obtained from finite element analysis, when it reaches the plastic moment capacity for both the case with friction and the case when ties are used in the upper 0.6D length of the RCFST, per the model described in Section 2.2.3 (this length of 0.6D was chosen arbitrarily here, based on considerations of model mesh size to allow transfer of the internal axial load over a certain length; it is not implied that actual load transfer mechanisms should be placed over that specific length, as the actual length needed for this purpose will be dictated by prop- erties and strength of shear connectors used). The label “PSDM” in that figure indicates the axial load value predicted by simple plastic analysis, obtained as described in Appendix E. For the case with friction, the axial load in the steel tube starts from zero at the top of the shaft and progressively increases along the length of the steel tube, whereas for the case with ties at top, it rapidly increases along the length of the tube over which ties are used and remains constant over the rest of the tube length. (b) D=100 in. (a) D=24 in. Figure 2.38. Flexural response of RCFST shafts with different H/D ratios at full composite action (l = 0.5 for H/D = 7.5; l = 0.8 for H/D = 5.0 and 3.0).

50 Contribution of Steel Casing to Single Shaft Foundation Structural resistance D=24 in., H/D=7.5 D=100 in., H/D=7.5 D=24 in., H/D=5.0 D=100 in., H/D=5.0 D=24 in., H/D=3.0 D=100 in., H/D=3.0 Figure 2.39. Flexural response (moment–displacement curve) of RCFST shafts with D = 24 in. and 100 in. diameters and D/t = 85 for different friction coefficients.

research approach 51 The distribution of frictional forces at the interface of the steel tube and the concrete core was calculated by taking the derivative of the axial load along the steel tube height. Figure 2.41a shows the distribution of the friction force ( fs) and interface force vectors along the height, as resultants of the normal and tangential contact forces, when the plastic moment is reached; Figure 2.41b shows the same at the onset of buckling. As shown in that figure, the maximum transfer of axial load at the interface, happens at a distance of 1.5D from the bottom of the shaft, and after this point it decreases almost linearly toward the top of the shaft. The friction force at the interface is also significant at a concentrated point at the top of the shaft due to the transfer of forces from the concrete core to the steel tube, due to the external force applied by the concrete core at the D=24 in., H/D=7.5 D=100 in., H/D=7.5 Figure 2.40. Internal axial load distribution along the steel tube of RCFST shaft. 1.880e+01 1.504e+01 1.128e+01 7.519e+00 3.760e+00 0.000e+00 2.256e+01 Fringe Levels (a) at the moment Mp reaches 1.880e+01 1.504e+01 1.128e+01 7.519e+00 3.760e+00 0.000e+00 2.256e+01 Fringe Levels (b) at onset of local buckling Figure 2.41. Distribution of the friction force (fs ) and interface force vectors along the steel tube part of RCFST shaft.

52 Contribution of Steel Casing to Single Shaft Foundation Structural resistance top of the shaft (recall that load comes to the shaft from the concrete column). As shown in this figure, the distribution pattern of frictional forces is similar for shafts of different diameters. Also as shown in part (b), at the onset of local buckling, the area at the base of the column where local buckling is going to develop (right side in figure) shows no contact forces, which means that there is no contact between the steel tube and concrete core at that point during the response. Figure 2.42 shows the axial load distribution in the steel tube for different H/D ratios. The axial load distributions in this figure are those that develop when the moment at the bottom of the shaft reaches its maximum moment capacity (fully plastic) and before local buckling devel- ops at the bottom of steel tube. Part (a) of this figure shows the axial load distribution for the case with µ = 0.5 friction. As shown, the transferred internal axial load is lower for H/D ratios of 5.0 and 3.0, but recall that, according to Figure 2.39, while these shafts developed a strength in excess of the theoretical MP, they did not exhibit composite action to the same extent, developing a lower maximum strength (an average of 95% of the maximum moment achieved by H/D = 7.5 was achieved in these cases). However, as shown in part (b) of this figure, for the case with ties at the top, the transferred axial load does not change significantly for different H/D ratios. It should be emphasized that, although shorter shafts were not able to reach the flexural capacity of the H/D = 7.5 shaft, they reached the plastic strength of the section calculated by PSDM. The value of the transferred internal axial load is also a function of lateral displacement of the shaft. It starts from a zero value at zero drift and keeps increasing with greater lateral displacement (a) D=100 in., µ=0.5 D=100 in., µ=0.0 & tied at top (b) D=24 in., µ=0.0 & tied at top D=24 in., µ=0.5 Figure 2.42. Axial load distribution in the steel tube part for different H/D ratios. (a) For µ = 0.5 friction coefficient at the interface. (b) For no friction at the interface but tied at top of the shaft.

research approach 53 of the shaft. This value would be calculated differently, depending on whether the behavior of the RCFST shaft is elastic, plastic, or beyond the point when local buckling develops at the point of maximum moment in the shaft. In the elastic range, the transferred internal axial load is a func- tion of the relative axial stiffness of the steel tube and reinforced concrete parts of the shaft. This is presented in Section 2.2.10.3. However, when a shaft reaches its plastic moment (MP) capacity, this axial load depends only on section properties. The physics of the transferred internal axial load at the plastic level is presented in Section 2.2.10.2. From a strength point of view, behavior at the plastic level is more significant and of greater interest here. In that perspective, the observations on behavior in the elastic range (presented in Section 2.2.10.3) are more of academic interest, as it focuses on the interim transferred internal axial load mechanism that develops for moment values lower than the shaft’s plastic strength, as moment increases from zero to the plastic level. That the transferred internal axial load after local buckling starts to develop at the bottom of the steel tube is of lesser interest, although it has been observed to increase due to the progressively greater strength that must be carried by the concrete during this buckling process (as described earlier). 2.2.10.2. Transferred Internal Axial Load in Plastic Range For a fully plastic composite section, the value of the axial load that develops into the steel tube, and that therefore needs to be transferred between the steel tube and concrete core to achieve self-equilibrium, can be estimated by calculating the resultant normal force on either the reinforced concrete core or the steel tube. In other words, in order to satisfy equilibrium in the composite section, the sum of normal forces on the entire section must be zero. This means that for a full composite section, the resultant force vector on the reinforced concrete part (which is a compressive force) must be equal to and in opposite direction of the resultant force vector on the steel tube part (which is a tensile force). This transferred internal axial load can be calcu- lated using the PSDM described in Appendix E by first finding the position of the neutral axis (obtained when the sum of normal stresses action on the entire cross-section is equal to zero) and then calculating the resultant normal force on the steel tube by summing the stresses act- ing on that part alone. Using the cross-section and stress distribution shown in Figure 2.43, the resulting axial force is: 4 (2.2)=P RtFps y where j is a central angle showing the location of the neutral axis, as shown in Figure 2.43, and R, t, and Fy, are the radius, thickness, and yield stress of the steel tube respectively. The subscript ps indicates that this axial force is calculated from the plastic section. In the equation above, the properties of the reinforced concrete part are implicitly considered because the neutral axis posi- tion depends on all parts of the section, including concrete and reinforcing bars. Although the (a) Reinforced concrete part (b) Steel tube part Figure 2.43. RCFST plastic section stress distribution.

54 Contribution of Steel Casing to Single Shaft Foundation Structural resistance same transferred internal axial force would be obtained by equilibrium on the reinforced con- crete part of the cross-section, using the steel tube part for this transferred internal axial load results in a governing equation that is more straight-forward, making it possible to compare results for shafts having different diameters and thicknesses. The theoretical axial forces obtained from this equation have been labeled “PSDM” in Figures 2.40 and 2.42. It consistently provided a conservative value compared to finite element results, which makes it suitable for design if shear transfer mechanisms are chosen to develop composite action. Variations of the j for 24 in. and 100 in. shafts with different D/t ratios, calculated by PSDM, are shown in Figure 2.44. The parameters in Equation 2.2 indicate that, in a fully plastic section, the axial load that needs to be transferred is related to the properties of the section alone and does not depend on the height of the shaft. Comparing that theoretical value with the results shown in Figure 2.42a, it is observed that the axial load transferred by friction for the case “µ = 0.5” was not enough to develop the full composite plastic moment in shafts having H/D = 5 and 3 because the trans- ferred internal axial loads observed in those cases is lower compared to the H/D = 7.5 case. In those cases, the friction at the interface was able to transfer an average of 53% of the internally transferring axial load for H/D = 7.5; however, it is noteworthy that this resulted in only a 5% reduction in moment strength on average. For the case where ties were used at top of the shaft (Figure 2.42b), the axial load was transferred through those ties and the full composite section of the shaft was achieved. As shown in that figure, the amount of this axial load does not change significantly for different H/D ratios. These observations are only valid for fully plastic sections. Ties at the top of the shaft in the numerical model have been used to represent the shear transfer mechanisms used there to transfer the internal axial load. Those shear transfer mecha- nisms can be designed on the basis of the strengths experimentally obtained from the series of large-scale push-through tests done by Gebman et al. (2006), or using the equations provided by API 2A-LRFD (1993) to transfer the force required by Equation 2.2. A typical view of the place- ment of shear transfer mechanisms is presented in Figure 2.45. 2.2.10.3. Transferred Internal Axial Load in Elastic Range Figure 2.46 shows the axial load distribution in the steel tube part of the section in the elastic range for different H/D ratios and for a friction coefficient of µ = 0.8. This friction coefficient was chosen here to ensure a comparison of full composite behavior for all H/D ratios. This figure shows the axial load distribution developed in the steel tube when the same moment is reached at the base of the shaft (which happens at different drift ratios) in the elastic range. As shown in Figure 2.46, the internal axial load that is transferred between the shaft parts in the full composite section is nearly the same for all H/D ratios. For the µ = 0.5 case, for which there is no full composite section for some H/D ratios, the trend is different and the same conclusion cannot be made. Figure 2.44. Variations of i for different D/t ratios.

research approach 55 In the elastic range, assume that in a full composite shaft the slippage between the steel tube and reinforced concrete parts is totally prevented by axial shortening in the reinforced concrete part (because according to the stress distribution on the fully composite section, this part is in compression) and axial elongation in the steel tube part (because it is in tension). In other words, the transferred internal axial load between a steel tube and the reinforced concrete part prevents the slippage by shortening the reinforced concrete part and elongating the steel tube part. The axial deformation of each part and, subsequently, the transferred internal axial load can be cal- culated by knowing the axial stiffness of each part: (2.3)∝ +     ×P E A E A E A E A s H es s s c g s s c g where, Pes is the transferred internal axial load in elastic range of shaft behavior. Es and As are the elastic modulus and area of the steel tube respectively, Ec and Ag are the elastic modulus and gross area of the reinforced concrete part of the shaft respectively, H is the height of the shaft, and s is the amount of slippage between the steel tube and the concrete core that would occur in a non- composite shaft, and that therefore needs to be prevented from occurring in order to achieve (a) (b) Figure 2.45. Shear transfer mechanisms. (a) Typical shear transfer mechanisms. (b) Placement of shear transfer mechanisms on shaft casing. D=100 in., µ=0.8 Figure 2.46. Axial load distribution in the steel tube part of the shaft, in elastic range (for same moment at base of shaft) for different H/D ratios and for a friction coefficient of l = 0.8.

56 Contribution of Steel Casing to Single Shaft Foundation Structural resistance composite action. The subscript es indicates that the axial force is calculated from elastic section properties. In Equation 2.3, it is assumed that the axial stiffness of both parts remains constant in the elastic range. Although it is recognized that the actual axial stiffness of reinforced concrete depends on its reinforcement ratio and the extent of cracking, for simplicity, it was assumed here to be proportional to the elastic modulus and gross area of the concrete. Two shafts with similar cross-sections but different heights are respectively represented by the subscripts 1 and 2 in the following equations: (2.4) 2 1 2 1 1 2 = × P P s s H H es es Figure 2.47 shows the relation between the incremental slippage (s) and section curvature (γ). According to this figure, the total amount of slippage (s) can be calculated using Equation 2.5. (2.5) 00 s ds D z dz HH ∫∫ ( )= = α γ where 0 < α < 0.5 is a constant that indicates the distance between neutral axes of the steel tube and the concrete core, and D and γ(z) are the diameter and curvature of the section at height of z along the shaft, respectively. Considering the elastic deformation of an elastic cantilever column, the amount of curvature along the height of the shaft can be calculated using Equa- tion 2.6 below: (2.6)( ) ( )γ = −z F H z EI where F is the lateral load applied at top of the elastic shaft, and H, E, and I are the height, elastic modulus, and moment of inertia of a section of the elastic shaft, respectively. Therefore: 2 (2.7) 0 2∫ ( )( )= α − = αs D F H zEI dz DFHEIH In this case, Equation 2.4 can be written as: (2.8) 2 1 2 2 2 1 1 2 1 2 ( ) ( )= × P P F H F H H H es es Figure 2.47. Schematic of slippage at the interface of steel tube and concrete for non-composite RCFST shaft.

research approach 57 Comparing two shafts with similar sections, different H/D ratios, and same moment at the base (i.e., F1H1 = F2H2), the equation above simplifies to: 1 (2.9) 2 1 2 2 2 1 1 2 1 2 2 2 1 1 2 1 1 2 ( ) ( )= × = ×   × =PP F H F H H H F H FH H H H H es es which shows that for similar elastic base moments, the transferred internal axial load is the same for different H/D ratios. This confirms what is observed in Figure 2.46. Equations 2.4 and 2.5 assume an ideal elastic cantilever column in order to develop a simple way to compare RCFST shafts with different H/D ratios, and therefore, some slight differences in results are expected when finite element results are compared. 2.2.10.4. Summary As shown in this subsection, in order to achieve the full composite action in an RCFST shaft when maximum strength is developed, the friction at the interface of the steel tube and concrete core, or the shear transfer mechanism, should be able to transfer the axial load that is calculated by Equation 2.2. For a friction coefficient of µ = 0.5, the shaft with H/D = 7.5 was able to achieve the flexural capacity of the composite section calculated by PSDM, while lower H/D ratios were not. As described in Section 2.2.2, this value approximately corresponds to the coefficient of friction that has been measured for the steel-concrete interface from experiments (Baltay and Gjelsvik 1990; Moon et al. 2012; Rabbat and Russell 1985). In cases where only partial transfer of that internal axial load would be achieved, the maximum strength of the section is typically only partially reduced, and the theoretical MP value can still be exceeded. For example, the dif- ference between the maximum moment achieved by using a friction coefficient of 0.5 (partially composite section) and a full composite section, on average, amounts to only 4% for H/D = 5.0 and 3.0. In comparison, all shafts with various H/D ratios were able to achieve the full composite section by using shear mechanisms at the top of the shaft. 2.2.11. Effect of Shaft Diameter The effect of change in shaft diameter on achieving composite action is investigated in this section. According to Equation 2.2, the transferred internal axial load is proportional to the diameter and thickness of steel tubes, but at the same time, in shafts of greater diameter there is a larger area on which friction forces can develop. More importantly, if shear transfer mechanisms are relied upon to achieve composite action, the design of those elements will directly depend on the magnitude of that transferred internal axial force. For this purpose, the results of two RCFST shafts having diameters of 24 in. and 100 in. with similar height-to-diameter (H/D = 7.5) and diameter-to-thickness (D/t = 85) ratios were com- pared to each other in order to see the effects of changing the shaft diameter from 24 in. to 100 in. on the behavior of RCFST shafts. It should be noted that to be able to compare these two shafts with each other, the internal reinforcement ratio, uniaxial unconfined compressive strength of concrete, and yield stress of steel bars and tube were kept same. Also, transverse reinforcement was designed to provide the same theoretical confinement for both diameters. To make the columns more proportionally similar to each other, it would have been required to increase the clear cover above the reinforcement, such as to keep it proportional to the shafts’ diameters. However, in practice, a constant thickness of cover is typically used irrespectively of different shaft diameters. Therefore, here, the clear cover was kept the same for both shafts. The response of the RCFST shaft with D = 100 in. and having different friction coefficients at the concrete-to-steel tube interface was previously shown in Figure 2.39, where results were compared with those for the case with D = 24 in. As shown in the figure, a friction coefficient of µ = 0.5 was

58 Contribution of Steel Casing to Single Shaft Foundation Structural resistance sufficient to develop composite action for both diameters (comparing shafts with H/D = 7.5). How- ever, as shown in Figure 2.40, the internal axial load that needed to be transferred between the concrete and steel tube to be able to develop full composite action was greater for the larger shaft diameter. Using knowledge that the amount of internal axial load that needs to be transferred can be calculated using Equation 2.2 for a fully plastic section, a simple relationship can be obtained to establish how the magnitude of this axial load increases as a function of diameter. Accord- ing to Figure 2.44, by comparing the amount of j for different diameters and D/t ratios, it can be assumed that the value of j remains same for both diameters considered here (which is approximately the case when the internal reinforcing ratio, material properties, and D/t ratio of the steel tube remain same). As a result, the transferred internal axial load (Pps) is proportional to the radius, R, and thickness, t, of the steel tube (in accordance with Equation 2.2). Therefore: (2.10) 2 1 2 1 2 1 = × P P R R t t ps ps where Pps1 and Pps2 are the transferred internal axial loads corresponding to two different shafts having steel tube diameters D1 and D2, respectively, and steel tube thicknesses, t1 and t2, respec- tively. Therefore, for a same D/t ratio: (2.11) 2 1 2 1 2 =  PP D D ps ps Equation 2.11 shows that the transferred axial load is proportional to the square of the ratio of diameters. Therefore, if the axial load in the steel tube of a shaft of diameter D = 24 in. is magnified by the ratio of (100/24)2 = 17.4, it should be equal to the axial load in the steel tube of a shaft with D = 100 in. Figure 2.48 shows the distribution of the axial load in the steel tube for shaft diameters of D = 24 in. and 100 in. In this figure, the axial load for the case of D = 24 in. was multiplied by (100/24)2 and compared to the axial load in the steel tube of the shaft with D = 100 in. The axial force in the 24 in. diameter shaft, magnified by the factor defined in Equation 3.7, does not give an exact match, but results are within an average of 19% of each other, which is a reasonable agreement given that the magnification factor used is 17.4. The remaining differences could be attributed to other phenomena not considered by Equation 2.2. As such, as shown above, it is reasonable to assume that the axial load that needs to be trans- ferred between the concrete and steel tube over the height of the shaft, in order to develop full H/D=7.5, µ=0.5 H/D=7.5, µ=0 & tied at top Figure 2.48. Distribution of the axial load in the steel tube for different shaft diameters of D = 24 in. and 100 in.

research approach 59 composite action in the shaft, changes with the diameter of the shaft and is proportional to the square of the shaft diameter (D2). If shear transfer mechanisms are used to develop this axial force, their number and strength of the shear transfer devices will need to be increased accord- ingly. However, as demonstrated in Section 2.2.10, if friction is relied upon to develop composite behavior, irrespectively of the diameter D, the same friction coefficient at the interface between concrete and the steel tube is sufficient to transfer this axial load for a given H/D. 2.2.12. Effect of Attached Column In this section, the behavior of an RCFST shaft with a column attached to the top of the shaft is investigated. The finite element model considered for this purpose used a reinforced concrete column attached to the top of the same RCFST shafts that were previously used in the analyses for Group G-2. This model was analyzed to study if the column had an effect on the development of the full composite section and, more specifically, to investigate how loads were transferred from the attached reinforced concrete column to the shaft. Recall that the objective is to investi- gate the nonlinear behavior of the RCFST shaft. In other words, the plastic hinge should develop in the shaft. Therefore, it was desirable that the reinforced concrete column framing into the shaft remain elastic throughout the system’s inelastic response, and the column was designed accordingly to satisfy this design objective. Diameter and reinforcement ratios of the considered reinforced concrete column (Dc) were 0.88 of the shaft diameter (Ds) and 2.76%, respectively; this reinforced concrete column was verified to remain elastic while plastic hinging developed in the shaft. In the column-to-shaft connection region, the reinforcement of the reinforced concrete col- umn was extended into the shaft for a length equal to the shaft diameter. Figure 2.49 shows the details of the finite element model of the combined reinforced concrete column and RCFST shaft model. The shaft was analyzed with and without internal reinforcement; these two cases are referred to as RCFST and CFST, respectively, throughout the report, and the contact interface condition was analyzed for the cases with various friction coefficients (µ = 0.0 to 1.0) and for the case without friction but with constraints at top of the shaft part. Figure 2.50 shows the response of the RCFST shaft for different coefficients of friction. Comparing this figure with Figure 2.39 shows that the presence of the reinforced concrete column framing into the shaft helped the shaft achieve the same ultimate flexural capacity with a slightly lower friction coefficient (µ = 0.4). This observation is rational in light of the mechanism of load transfer from column to the shaft that is described in Section 2.2.12.1. Finer mesh Figure 2.49. Details of the finite element model of RCFST shaft with column.

60 Contribution of Steel Casing to Single Shaft Foundation Structural resistance 2.2.12.1. Column-to-Shaft Transition Zone In the connection of a column to an enlarged reinforced concrete shaft, transfer of loads from column rebars to shaft rebars can be explained by the transfer mechanism that has been pro- posed by McLean and Smith (1997). This model is based on a truss analogy that describes the load transfer mechanism between individual rebars. However, in the case of a composite shaft, presence of the steel tube makes possible the devel- opment of alternative load transfer mechanisms. In that case, at the reinforced concrete column to RCFST shaft connection, a part of the column force can be directly transferred to the steel tube in addition or replacement of the behavior proposed above by McLean and Smith (1997). This is best illustrated by considering the extreme case of a reinforced concrete column trans- ferring loads to a CFST shaft (i.e., without shaft reinforcement). Finite element analyses revealed that, in such a case, load transfer from the column to the steel tube occurs by means of two normal contact regions between the concrete core and the steel tube, namely, one at the top of the shaft and the second one at the bottom of the column reinforcing cage, which is extended into the shaft. Figure 2.51 shows a schematic view of the load transfer mechanism between the reinforced concrete column and CFST shaft’s steel tube that is derived from the observed stress distribution resulting from finite element analysis, as shown in Figure 2.52. In Figure 2.51, F is the lateral load that is applied at the top of the column, and Hc and ld are the height of the reinforced concrete column and the length over which it is extended into the shaft part, respectively. As shown in Figure 2.52, the lateral load applied at the top of the column is transferred to the shaft by two contact areas, one at the top of the shaft and the other one at the bottom of the extended reinforced concrete column reinforcement. Figure 2.53 shows the free-body diagram for this load transfer mechanism in the absence of shaft reinforcing. This is equivalent to the development of a shear head in the top part of the shaft to resist and transfer the flexural moment developed at the base of the column. Using this free-body diagram, the lateral load that is transferred at the top of the shaft steel tube (Ft) can be calculated as: 1 (2.12)= + F F H l t c d Figure 2.50. Flexural response (moment– displacement curve) of RCFST shaft with column for different friction coefficients.

research approach 61 where Hc, ld, and F are the height of the column, the length of the column longitudinal rebars embedded into shaft, and the force that is applied at the top of the column, respectively. According to Equation 2.12, the value of Ft decreases as the extension length of column rebars (ld) increases. The maximum amount of load that can be transferred to the steel tube at the top of the shaft (Ft) depends on the bearing strength of the steel tube at the contact area. Excessive load at that location will result in yielding and tearing of the steel tube where the bearing load is being transferred from the reinforced concrete column to the shaft part. Therefore, the embedment length of column rebars (ld) should be chosen long enough to keep that force (Ft) within an allowable range. Figure 2.54 shows the shear force diagram along the steel tube (shaft part) for column-shaft models that were analyzed considering different values of this embedment length, namely: ld = 0.5Dc, Dc, and 2Dc. Results are compared to those obtained analytically using Equation 2.12. Column Part Shaft Part Contact areas F Figure 2.51. Schematic view of the reinforced concrete column-to- RCFST shaft’s casing load transfer. Figure 2.52. Stress distribution in reinforced concrete column to CFST shaft connection zone.

62 Contribution of Steel Casing to Single Shaft Foundation Structural resistance (a) (b) (c) Figure 2.53. Free-body diagram (FBD) of reinforced concrete column to RCFST shaft’s casing load transfer. (a) Reinforced concrete column–CFST shaft FBD. (b) Reinforced concrete column part FBD. (c) Steel tube part FBD. (a) (b) (c) H /D c (Shear Force)/F H /D c (Shear Force)/F(Shear Force)/F H /D c Figure 2.54. Shear force diagram along the steel tube (shaft part) of reinforced concrete column–CFST shaft for different values of ld . (a) 0.5 Dc (b) 1.0 Dc (c) 2.0 Dc .

research approach 63 This figure only shows the shear diagram for the upper parts of the shaft, as the objective is to investigate the load transfer mechanism from the column to the shaft. Finite element results in Figure 2.54 are for the case where there is no reinforcement in the shaft beyond the column-to-shaft transition zone, and all the column load is transferred to the steel tube per the mechanism described above. Results are normalized by a force, F. For the cases ld = Dc and ld = 2Dc, the column-to-shaft transfer mechanism allowed the application of sufficient forces to develop full plastic strength of the shaft, as F was taken as the maximum load applied at top of the shaft when the plastic moment capacity of the shaft was achieved. For the case ld = 0.5Dc, the steel tube yielded at the top of the shaft (due to excessive contact force at this loca- tion) before the shaft reached its plastic moment capacity; because of this, the column-to-shaft load transfer mechanism was unable to transfer the force needed to develop the plastic strength at the bottom of the shaft. For this reason, the finite element results for the case with ld = 0.5Dc, shown in Figure 2.54a, are normalized by the maximum load that could be transferred through the column-to-shaft region, which is smaller than other cases in the figure (i.e., the F value is lower for the case with ld = 0.5Dc). Comparing the analytical and finite element analyses results in Figure 2.54 shows that the assumed column-to-shaft load transfer mechanism and the derived analytical solution reasonably matched the finite element analysis results. Also, as shown in this figure, the analytical solution matches better for larger ld values. In addition, as shown in the figure, the shear diagram increases at the top of the shaft where the reinforced concrete column transfers a lateral load of Ft through contact between the steel tube and concrete core. This increase occurs at a length of about 0.25Dc from the top of the shaft for all values of ld. However, the shear force in the steel tube decreases and becomes smoother at the bottom of the transition zone, which shows that the Fb force is transferred over a larger area compared to that of Ft. This difference is because the analytical solution considered these loads as point loads acting on the steel tube. According to the column-to-shaft load transfer mechanism and Equation 2.12, for a maxi- mum allowable value of Ft, the column rebar extension length (i.e., the transition zone) that is required to develop a moment of Ms at the bottom of the steel tube can be calculated by solving Equation 2.12 in terms of ld: (2.13)( )= + − ×l M F H H M Hd s t c s s c It should be noted that, as shown in this section, the transfer of forces from the reinforced concrete column to the steel tube at the top of the shaft develops through direct normal con- tact at the interface of the concrete and steel tube and is therefore independent of friction at that interface. The above column-to-shaft load transfer mechanism model considered that there is no reinforcement in the shaft part (i.e., equivalent to a CFST shaft), except in the column-to- shaft transition zone. Therefore, all the flexural forces in the reinforced concrete column had to be transferred to the CFST composite shaft, in which the steel tube provides most of the flexural resistance. However, in an RCFST shaft, this mechanism is more complicated because part of the reinforced concrete column flexural force can be transferred to the rebars in the shaft by the non-contact lap splices mechanism. In that case, the load that is locally transferred to the steel tube in the transition zone is less, compared to a CFST shaft. However, in RCFST, calculating the percentage of the force that transfers into the reinforcement of the shaft through non-contact lap splices mechanism is not necessary, as lap splices are designed to transfer the full force.

64 Contribution of Steel Casing to Single Shaft Foundation Structural resistance 2.2.13. Effect of Axial Load In order to study the effect of axial force on the composite action of RCFST, the finite element models used for the analyses of Groups G-1 and G-2 were re-analyzed with an axial compressive force applied at the top of the shaft, as a uniform pressure applied only to the concrete core and not to the steel tube. The amount of the axial force was set to 0.1 f ′c Ag, where f ′c and Ag are the uniaxial compressive strength of concrete and the gross area of the concrete cross-section, respectively. Figure 2.55 shows the flexural response of axially loaded RCFST and CFST with different bond conditions at the casing-to-concrete interface (consid- ering the cases without friction, with friction (µ = 0.5), and without friction with ties at the end). Results show that all behaviors observed are sensibly similar to the cases without axial loads, except for that flexural strength is greater for the case with axial force, for the reason explained below. Figures 2.56 and 2.57 compare RCFST responses with and without axial load. Figure 2.56 shows this comparison for RCFST having friction at the casing-to-concrete core interface and Figure 2.57 shows it for the case without friction. As shown in these figures, the axial load does not significantly change the flexural strength of the RCFST. Additionally, taking into account (a) RCFST (b) CFST Figure 2.55. Response of axially loaded RCFST and CFST with different bond conditions. (a) Total (b) Each part Figure 2.56. Comparison of composite RCFST response with and without axial load.

research approach 65 that the axial load was applied to the concrete core, it is observed from part (b) of each figure (i.e., the right side of each figure) that axial load only has a small effect on the response of the steel tube for the RCFST having friction at the casing-to-concrete interface, while it had almost no effect on the response of the steel tube for the RCFST with no friction. Similar results were also observed for CFST. Figure 2.58 shows axial load-moment interaction curves for the RCFST section with D/t = 85 and r = 1.6%, the CFST with same properties, and for the different parts that constitute the RCFST cross-section but taken as if acting individually. The analysis was done using the PSDM and did not account for local or global buckling. To develop an interaction curve for the non-composite RCFST case, as shown in Section 2.2.7, it was assumed that no axial load can be transferred to the steel tube; therefore, the flex- ural strength of the steel tube remains the same and similar to a steel tube under no axial load in that case. Then, the interaction curve was developed by adding the value of the flex- ural strength of a steel tube considering no axial load to the reinforced concrete interaction curve. The same approach was used to calculate the non-composite CFST interaction curve by adding the flexural strength of steel tube under no axial load to the concrete interaction curve. These results are shown in Figure 2.59, together with the corresponding composite interaction curves. (a) Total (b) Each part Figure 2.57. Comparison of non-composite RCFST response with and without axial load. Figure 2.58. Axial load-moment interaction curve for RCFST, CFST, reinforced concrete and concrete section.

66 Contribution of Steel Casing to Single Shaft Foundation Structural resistance As shown in Figure 2.59, for non-composite CFST and RCFST sections, with increase in the compressive axial load acting on the concrete core (expressed in the vertical axis as normalized to the maximum axial load capacity of the concrete section, Pc), the difference between response of the non-composite and composite sections decreases, and at P/Pc = 0.5, the flexural strength of the non-composite and composite sections are similar. Figure 2.60 shows how position of the neutral axis (in ordinate) varies in various components as a function of axial load (abscissa). More specifi- cally, this figure compares the neutral axes of a fully composite RCFST section; a similar fully com- posite CFST section (i.e., without internal reinforcement); a reinforced concrete section similar to the reinforced concrete core of the RCFST; a concrete section similar to the concrete core of the CFST; and a steel tube similar to the steel tube of the RCFST, for various axial load cases. As shown in this figure, for all sections considered, with an increase in the compressive axial load acting on the section, the neutral axis of the section moves toward the center of the cross-section. As shown, for P/Pc = 0.5, the neutral axes of the reinforced and unreinforced concrete sections, steel tube, RCFST, and CFST are all at the center of the section. In other words, the neutral axes for composite and non-composite sections reach the center of the cross-section at that axial load value. As the reinforcing bars are placed symmetrically they have no effect on the position of the neutral axis of the RCFST (compared to the CFST) at that normalized axial load of 0.5. Figure 2.61 shows the normalized interaction curves for RCFST and CFST. In this figure, the vertical axis shows the axial load normalized to the maximum axial load capacity of the P/Pc Figure 2.59. Axial load-moment interaction curve for composite and non-composite RCFST and CFST. P/Pc N .A . P os iti on , i n. Figure 2.60. Neutral axis position of RCFST and CFST for axial load variations.

research approach 67 concrete section, and the horizontal axis shows the ratio of the strength of the composite sec- tion to the strength of the corresponding non-composite section. As shown, with an increase in axial load for P/Pc < 0.5, the composite to non-composite strength ratio becomes smaller for both cases. The flexural strength of the non-composite section becomes equal to that of the composite section when the axial load reaches 0.5 Pc. In other words, the composite section loses its strength advantage over the non-composite section as the axial load increases. Figures 2.62 and 2.63 compare flexural response of the reinforced concrete column RCFST shaft that was described in Section 2.2.10 for the case with and without axial load. Figure 2.62 shows this comparison for shaft with friction at the casing-to-concrete core interface and Figure 2.63 shows it for the case without friction. The full composite section was achieved for the case with friction. As shown in these figures, similar to the case of the RCFST shaft with no reinforced concrete column attached (see Figures 2.56 and 2.57), the axial load only has a small effect on the response of reinforced concrete column–RCFST shafts. 2.2.14. Effect of Steel Tube Thickness (Effect of D/t) The effect of steel tube thickness was studied by analyzing the 100 in. diameter shaft (H/D = 7.5) with a larger D/t = 100 and comparing results to the case with D/t = 85. The RCFST shaft with P/Pc Figure 2.61. Normalized interaction curves for RCFST and CFST. Total Each part Figure 2.62. Comparison of composite reinforced concrete column–RCFST shaft response with and without axial load.

68 Contribution of Steel Casing to Single Shaft Foundation Structural resistance D/t = 100 was analyzed for different friction coefficients under monotonically increasing load to find out what friction coefficient is enough to achieve the full composite action. These results are presented in Figure 2.64. As shown in the figure, the improvement in the strength of the RCFST section by increasing the friction coefficient is more significant for the D/t = 100 case, compared to the case with D/t = 85, which was shown in Figure 2.39. However, in both cases the friction coefficient of µ = 0.5 is sufficient to develop full composite action. According to Equation 2.2, using a thinner tube for the casing of a shaft of a given diameter would require less axial load to be transferred between the steel tube and the reinforced concrete core to achieve full composite action, which explains why a smaller friction coefficient is needed to develop full composite action as D/t increases. Using Equation 2.2, the relationship between the axial load obtained by Equation 2.1 for D/t = 85 and D/t = 100 is: 1.06 0.85 0.9 (2.14) 100 85 85 100 85 100 = × = × = P P t t Total Each part Figure 2.63. Comparison of non-composite reinforced concrete column–RCFST shaft response with and without axial load. Figure 2.64. Flexural response of RCFST shaft with D = 100 in. and D/t = 100 for different friction coefficients.

research approach 69 where the value of j can be obtained from Figure 2.44 for each D/t ratio. According to Equa- tion 2.14, the axial load that needs to be transferred to achieve a composite section is 10% less for the case where D/t = 100 than for the case with D/t = 85. This is in good agreement with results obtained from finite element analyses. From such finite element analyses results, Figure 2.65 shows the axial load in the steel tube for the case D/t = 100 compared to the cor- responding values for the case D/t = 85 multiplied by the value calculated above. As shown, the resulting curve matches reasonably well with the curve for case D/t = 100. Figure 2.66 compares the flexural behavior of RCFST shafts with D/t = 85 and D/t = 100. As shown, the flexural capacity of the shaft with D/t = 85 is greater than the one with D/t = 100, which is principally because of the thicker steel tube used in that case. As shown in part b of this figure, the moment that is carried by the reinforced concrete part of the composite section does not change significantly for both cases, which confirms that the increase in total response is pri- marily because of the increase in flexural capacity of the steel tube. In order to compare the rela- tive contribution of each part of the RCFST shaft to its total flexural response, each RCFST shaft’s response was normalized by its plastic moment capacity calculated using the PSDM. Figures 2.67 and 2.68 show the comparison of these normalized curves for total response and contribution of each part respectively. As shown in Figure 2.67, the total normalized response remains the same for both cases, which shows that the pushover behavior of a composite RCFST shaft is H/D=7.5, µ=0.5 H/D=7.5, µ=0 & Tied at top Figure 2.65. Comparison of axial load in the steel tube for D/t = 100 and D/t = 85. (a) Total response (b) Moment carried by each part Figure 2.66. Comparison of flexural response for RCFST shafts with D/t = 85 and D/t = 100.

70 Contribution of Steel Casing to Single Shaft Foundation Structural resistance not affected by changes in D/t ratio (over the ranges of D/t considered), although as shown in Figure 2.68, the relative contribution of each part changes. For example, the contribution of the steel tube to the total composite plastic moment drops by an average of 8% for the case with D/t = 100 compared to the case with D/t = 85. The respective contribution of each part was obtained by calculating the resulting moment produced by the stresses acting on each part with respect to the center of the gravity of the section. These relative proportions would change if the moment was calculated with respect to a different reference axis (although there is no compelling reason to select another such axis), but the comparison would still remain qualitatively valid. The same comparison also was done for the case when there is a reinforced concrete column attached to the top of the RCFST shaft. Figure 2.69 shows the flexural response of the column- shaft for different friction coefficients. As shown in the figure, the friction coefficient of µ = 0.4 was enough to develop composite action in this case for both the column-shaft with D/t = 85, and the one with D/t = 100. Normalized responses of D/t = 85 and D/t = 100 cases were also compared with each other to show the differences in their behavior. Figure 2.70 shows the total normalized response for both cases and Figure 2.71 shows the contribution of each part of the RCFST shaft to the total composite flexural strength. As shown in these figures, the total behavior is similar for both cases, but the relative contribution due to steel tube drops for the case with D/t = 100. (a) Steel tube contribution M tu be /M p (b) Reinforced concrete contribution M R C /M p Figure 2.68. Normalized flexural contribution of each part of RCFST shafts with D/t = 85 and D/t = 100. M /M p Figure 2.67. Normalized flexural responses of RCFST shafts with D/t = 85 and D/t = 100.

research approach 71 Figure 2.69. Flexural response of the reinforced concrete column–RCFST shaft with D = 100 in. and D/t = 100 for different friction coefficients. M /M p Figure 2.70. Normalized flexural responses of reinforced concrete column–RCFST shafts with D/t = 85 and D/t = 100. (a) Steel tube contribution (b) Reinforced concrete contribution M tu be /M p M R C /M p Figure 2.71. Normalized flexural contribution of each part of reinforced concrete column–RCFST shafts with D/t = 85 and D/t = 100.

72 Contribution of Steel Casing to Single Shaft Foundation Structural resistance 2.2.15. Cyclic Response of RCFST Shaft Cyclic finite element analyses were performed on the RCFST shaft models, and results are presented in this section. The cyclic loading history that was applied to the models is shown in Figure 2.72. In this figure, Dy is the displacement at the first yield point, calculated using push- over analysis in OpenSees (Mazzoni et al. 2006), using a fiber model to calculate the section forces. The response of RCFST shafts with different diameters for the case with friction (µ = 0.5) and without friction (µ = 0.0) at the interface were analyzed, and results are compared with those obtained for their monotonic response. Results are presented in Figure 2.73. Also, in order to investigate the cyclic response of an RCFST shaft with a larger D/t ratio, RCFST shafts with D/t = 100 were analyzed and results are presented in Figure 2.75. Figure 2.73 shows a comparison of an RCFST shaft’s cyclic and monotonic responses for shafts having diameters of 24 in. and 100 in. As shown in this figure, while the hysteretic curves for cyclic response exhibit some pinching due to stiffness degradation between the peaks of response, their moment–displacement curve obtained from monotonic loading is nearly equiva- lent to an envelope of the peak strength reached during the cyclic response. In other words, there is no significant difference in strength at the peak displacement of each cycle of the shaft compared to the monotonic response. This is true both for the composite and non-composite shafts, with the significant strength degradation of the non-composite shaft captured by both the cyclic and non-cyclic analyses being in good agreement. It was shown in Section 2.2.7, when investigating non-cyclic behavior, that the strength of a non-composite section is not significantly less than that of a full composite section and that the (a) Analysis Time (b) Displacement B as e Sh ea r Figure 2.72. (a) Loading history. (b) First and equivalent yield points.

research approach 73 non-composite response of an RCFST shaft can be obtained by summing the individual behav- iors of the steel tube and internal reinforced concrete. These observations are significant, so this behavior was therefore investigated for the case of cyclic loading. Figure 2.74 compares the composite and non-composite behavior of RCFST shaft to cyclic loading for two different shaft diameters. It shows that the maximum strength reached in each case is different in the same proportions as shown earlier in Figure 2.37, but also that this (a) (b) D=100 in., D/t=85, µ=0.5D=24 in., D/t=85, µ=0.5 D=100 in., D/t=85, µ=0.0D=24 in., D/t=85, µ=0.0 Figure 2.73. Comparison between cyclic and monotonic flexural behavior of RCFST shaft with D/t = 85. (a) Composite (l = 0.5). (b) Non-composite (l = 0.0). D=100 in., D/t=85, µ=7.5D=24 in., D/t=85, µ=7.5 Figure 2.74. Comparison between composite (l = 0.5) and non-composite (l = 0.0) cyclic flexural response of RCFST shaft with D/t = 85.

74 Contribution of Steel Casing to Single Shaft Foundation Structural resistance difference increases with drift (and can become quite significant) due to the strength degrada- tion that occurs for the non-composite shaft. The same observation can be done for the case with larger D/t ratio. Figures 2.75 and 2.76 show the response of RCFST shaft with D/t ratio of 100. As shown in this case, there is also no significant difference between the cyclic and monotonic responses. To be able to compare the fullness of the hysteretic loops for shafts having different diameters or diameter-to-thickness ratios, flexural strength was divided by the sections’ respective theoretical plastic moment, and displacement was divided by the yield displacement. The resulting normalized cyclic behavior of shafts with 24 in. and 100 in. diameter is shown in Figure 2.77. As shown in this figure, although the shaft with smaller diameter has more strain hardening comparing to the one with larger diameter, the difference is not significant. The same comparison, done for same diameter and D/t ratios of 85 and 100, is presented in Figure 2.78. As shown in this figure, there is no signifi- cant difference in cyclic behavior of RCFST shafts with different D/t ratios; however, admittedly, D/t ratios of 85 and 100 are relatively close to each other. (b) D=100 in., D/t=100, µ=0.0 (a) D=100 in., D/t=100, µ=0.5 Figure 2.75. Comparison between cyclic and monotonic flexural behavior of an RCFST shaft with D = 100 in. and D/t = 100. (a) Composite (l = 0.5). (b) Non-composite (l = 0.0). D=100 in., D/t=100 Figure 2.76. Comparison between composite (l = 0.5) and non-composite (l = 0.0) cyclic flexural response of an RCFST shaft with D/t = 100.

research approach 75 The relative contribution of the steel tube and the reinforced concrete parts of the composite cross-section to the total flexural behavior of the RCFST shaft is shown in Figure 2.79. As men- tioned in Section 2.2.8, the loss in the strength of the steel tube is due to the local buckling that develops at the bottom of the shaft. As shown in the figure, the reinforced concrete contribution to the total strength increases after the steel tube locally buckles. In order to ensure that the compressive stresses in the concrete part did not excessively exceed the uniaxial compressive strength of the concrete (due to assumptions in confinement models that do not necessarily reflect experimental observations), these stresses were checked at the bottom of the shaft for two different values of the drift ratios, namely at the drift corresponding to the onset of local buckling and at a drift of 5.5% (which corresponds to an arbitrary point after significant local buckling developed, according to finite element analysis results). Figure 2.80 shows the con- tours of vertical stresses in concrete at the bottom of the shaft for those two drift ratios, obtained under monotonic loading. As shown in the figure, development of local buckling in the steel tube causes a local increase in the magnitude of the stresses in the concrete. However, this increase is not excessive compared to the unconfined uniaxial compressive strength of the concrete (f ′c ), reaching values of up to 9.3 ksi for the expected compressive strength of 5.2 ksi considered in the model. Figure 2.81 quantifies the percentage of vertical stress levels in the compressive part of Figure 2.77. Normalized cyclic behavior comparison between D = 24 in. and D = 100 in. RCFST shafts. Figure 2.78. Normalized cyclic behavior comparison between D/t = 85 and D/t = 100 RCFST shafts.

76 Contribution of Steel Casing to Single Shaft Foundation Structural resistance Figure 2.79. Contribution of steel tube and reinforced concrete parts to cyclic flexural strength of the RCFST shaft. Buckling onset (3.1% drift ratio) Maximum Drift (5.5% drift ratio) 0.5D D -8.000e+00 -6.400e+00 -4.800e+00 -3.200e+00 -1.600e+00 -4.441e+16 Z Y X Contours of Z-stress Fringe Levels, ksi -8.000e+00 -6.400e+00 -4.800e+00 -3.200e+00 -1.600e+00 -4.441e+16 Displacement Scale Factor=2.0 Z Y X Contours of Z-stress Fringe Levels, ksi Figure 2.80. Contours of vertical stresses in the concrete part at the bottom of the shaft. Figure 2.81. Vertical stress levels in the compressive part of the section for concrete part.

research approach 77 the cross-section that exceeds specific thresholds. As shown in the figure, at a drift ratio of 5.5%, only 15% of the stresses on the compression side of the cross-section exceed 1.4f ′c and none of the elements in the cross-section have a compressive stress greater than 1.8f ′c . The pinching effect that is shown in the cyclic behavior of the shaft is due to the closure of cracks in the concrete part. This can be seen in Figure 2.82, which shows the contribution of the longitudinal reinforcement and the concrete part to the flexural response of the reinforced con- crete part of the RCFST shaft. As shown in this figure, in each cycle, as the displacement reduces from the peak value (i.e., in reversing cycle), the contribution to the total flexural strength that is provided by the concrete alone drops to zero. This is because cracks developed in the concrete when it was pushed toward a peak of displacement, and zero flexural strength is produced in the reversing cycle until that crack is closed. Therefore, the flexural strength provided by the concrete remains zero as the displacement is progressively reversed until the point where those cracks in the concrete section that developed during previous displacement excursion are closed. After crack closure, compressive stresses can develop anew in the concrete, which can then contribute to the total flexural strength of the shaft. A significant portion of the pinching in the hysteretic response of the RCFST shaft is attributed to this behavior of the concrete. In every cycle, the strength contributed by the reinforcing bars remains relatively constant as they yield and drops a little as the neutral axis shifts, but the contribution due to concrete increases due to the loss of flexural strength in the steel tube after it develops local buckling. The monotonic and cyclic behavior contributed by each part of the RCFST shaft is compared in Figure 2.83. Only a quadrant of the hysteretic curve is shown to better highlight the differ- ences. As shown in that figure, the monotonic results generally matched well but overestimated the strength of steel tube at large deformations while it generally slightly underestimated the con- tribution to total strength of the reinforced concrete part. This is consistent with what was shown in Figure 2.73, where the total response of the RCFST shaft remained approximately the same for both monotonic and cyclic loadings. The difference between the monotonic and cyclic behavior is related to the severity of local buckling, with the buckled shape growing in amplitude in subsequent cycles due the same steel being plastically elongated during the part of the cycle acting in the other direction. As a result, for same drift ratio, the size of the local buckling in the steel tube is larger for the cyclic loading case compared to the monotonic one. This results in more strength degradation in the steel tube, which is compensated by the reinforced concrete part. The local buckling of the steel tube at the bottom of the shaft is shown in Figure 2.84 for monotonic and cyclic loadings. As shown, the amplitude of buckling that develops at the peak of the fourth cycle is more than for the monotonic loading case, while for second cycle, it is less. Figure 2.82. Contribution of concrete and rebars to the cyclic flexural strength of the reinforced concrete part of the RCFST shaft.

78 Contribution of Steel Casing to Single Shaft Foundation Structural resistance (a) Steel tube part (b) Reinforced concrete part (c) Concrete core part (d) Reinforcing rebar part Figure 2.83. Cyclic and monotonic response comparison for contribution of each part of RCFST shaft to flexural strength. Second cycle Fourth cycle Figure 2.84. Local buckling profile at bottom of RCFST shaft with different displacements (D = 24 in., l = 0.5).

research approach 79 The cyclic behavior of an RCFST shaft with an axial load was also compared to its monotonic behavior. Figure 2.85 shows the response of this RCFST shaft with axial load under cyclic and monotonic loading. As shown in the figure, again there is no significant difference between the cyclic and monotonic responses. Figure 2.86 compares the response of the RCFST shaft with and without axial load; in both cases, it is seen that the axial load has slightly increased the flexural capacity of the section, by a magnitude consistent with what has been explained for the mono- tonic response of RCFST shaft in Section 2.2.13. According to the results in this section, since there is no significant difference between mono- tonic and cyclic response of RCFST shafts, all the observations made earlier when comparing the monotonic responses of composite and non-composite sections remain valid for the cyclic response of shafts. 2.2.16. Effect of Surrounding Soil The effect of surrounding soil was studied by analyzing a 100 in. diameter RCFST shaft embedded in sand having the properties shown in Table 2.6. These properties correspond to Mason sand, as measured by Thomas and Chitty (2011), and was selected only for the purpose of comparing results obtained for an RCFST shaft with surrounding soil and one without soil. The finite element model of the RCFST shaft used in the analyses presented above was modi- fied to consider the soil by introducing solid elements around the shaft. The LS-Dyna material model used for modeling the soil was MAT_005, recommended by Thomas and Chitty (2011). In addition, in the analyses considering soil, the steel tube mesh of the previously used RCFST (a) (b) D=24 in., D/t=85, µ=0.5, with axial load D=100 in., D/t=85, µ=0.5, with axial load D=24 in., D/t=85, µ=0.0, with axial load D=100 in., D/t=85, µ=0.0, with axial load Figure 2.85. Comparison between cyclic and monotonic flexural behavior of RCFST shaft with D/t = 85 and axial load. (a) Composite (l = 0.5) section. (b) Non-composite (l = 0.0) section.

80 Contribution of Steel Casing to Single Shaft Foundation Structural resistance (a) (b) D=24 in., D/t=85, µ=0.5 D=100 in., D/t=85, µ=0.5 D=24 in., D/t=85, µ=0.0 D=100 in., D/t=85, µ=0.0 Figure 2.86. Comparison between axial and no axial load cyclic flexural behavior of RCFST shaft with D/t = 85. (a) Composite (l = 0.5) section. (b) Non-composite (l = 0.0) section. Density, Shear Modulus, ksi Bulk Modulus, ksi Poisson’s Ratio 100 3.56 5.36 0.23 Table 2.6. Properties of the sand used for analysis. model was refined in the region where the maximum moment occurred, since this happened above the base of the shaft. Figure 2.87 shows the details of the analyzed finite element model. Figure 2.88 shows the diagram of the moment carried by the steel tube for the case with sur- rounding soil and the case without soil, at a maximum drift of 5.5%. It also shows the plastic regions along the steel tube. As shown in this figure, the location of maximum moment changes due to the presence of the soil, shifting toward the top of the soil (because of the reaction forces applied to the shaft by the soil when it is being pushed). Also, as shown in the figure, the moment diagram is smoother as compared to the case with no soil, which results in a larger plastic region in the shaft for the case with surrounding soil. Moment–curvature diagrams at the maximum moment location along the shaft are presented in Figure 2.89 for these two cases. Also, the moment–curvature diagram obtained from section analysis using OpenSees is shown in this figure. Analyses were conducted up to curvatures of at least 0.00515 and 0.0008 in.–1 for the models with and without soil, respectively. As shown in that figure, the surrounding soil does not affect the moment–curvature behavior of the shaft section. It is also observed that both shafts developed the same flexural strength.

research approach 81 (a) Embedded in soil (b) Without soil (c) Comparison Yielded St ee l t ub e Yielded St ee l t ub e Figure 2.88. Diagram of the moment carried by the steel tube for (a) the case with surrounding soil, (b) the case without soil, and (c) their comparison. (a) Scheme (b) Finite element model Soil level RCFST Shaft Figure 2.87. Finite element model of the RCFST shaft surrounded by soil.

82 Contribution of Steel Casing to Single Shaft Foundation Structural resistance Comparing the curvature at the critical section as a function of the drift ratio for the shaft, in Figure 2.90, shows that for a same drift ratio, the curvature in the critical section of the shaft in the absence of soil is larger than for the shaft that is embedded in the soil. For the shaft embedded in the soil, no local buckling developed in the steel tube throughout the analysis, up to 6.5% drift (corresponding to curvature of 0.00515 in.–1). This can be attributed to the lower curvature that develops in the shaft surrounded by soil for a given drift. Curva- ture along the shaft obtained at the points corresponding to the yield moment, the plastic moment (calculated by the PSDM), the onset of buckling, and a maximum drift ratio of 5.5%, are shown in Figure 2.91 for these two shafts. The same results are also compared to each other in Figure 2.92. As shown, beyond the elastic moment, the magnitude of curvatures are lower in the shaft surrounded by soil. The above results, comparing behavior of the shaft embedded in soil with that of the shaft without soil, indicate that the same composite flexural strength can be developed, but that local buckling of the steel tube will occur sooner for the case without soil. Accordingly, the surround- ing soil does not appear to have a significant effect on the behavior of the composite shaft other than changing the shape of the moment diagram, the location of maximum moment along the shaft, and the drift at which this moment is reached. Local Buckling in No Soil W/Soil No Soil Section Analysis Figure 2.89. Moment–curvature curves of shafts with and without surrounding soil. Figure 2.90. Curvature–drift ratio curves of shafts with and without surrounding soil.

research approach 83 (a) Embedded in soil St ee l t ub e Yielded Yield Plastic 5.5% Drift St ee l t ub e Yielded Yield Plastic 5.5% Drift Buckled (b)Without soil Figure 2.91. Curvature diagram for (a) the case with surrounding soil and (b) the case with no soil. (a) at yield moment (b) at plastic moment (c) at maximum drift Figure 2.92. Comparison of curvature diagrams. (a) Yield moment. (b) Plastic moment. (c) Drift of 5.5%.

84 Contribution of Steel Casing to Single Shaft Foundation Structural resistance 2.3. Testing Program 2.3.1. Test Specimens The testing program is presented in Tables 2.7 and 2.8 for flexural and shear tests, respectively. Some of the parameters that define the specimens to be tested are described in Table 2.7, where Ds and Hs are outer diameter and height of the shaft, respectively; t is the thickness of the shaft casing; and Dc and Hc are diameter and height of the column, respectively. All specimens Specimen , in. Loading Scenario Test Objective Cyclic Axial S1 20 80 2.5 8 Yes No Flexure, no axial load (RCFST composite action) S2R 20 80 2.5 8 Yes Yes Flexural strength under axial load Column-to-shaft Transition zone S3 20 80 2.5 8 Yes No Repeat Specimen S1 with slurry on the tube interior surface S4 20 80 2.5 8 Yes No Repeat Specimen S1 with grease on the tube interior surface S5 30 96 2.5 8 Yes No Effect of larger D Effect of larger D/t Spiral welded steel tube S6R 20 80 2.5 8 Yes No Repeat Specimen S3 or S4 with shear transfer mechanism at the top Table 2.7. Flexural test specimens (properties and test objectives). Shear Specimen Outside Diameter ( ), Wall Thickness ( ), Height (H), , , Reinforcing SH3 12.75 0.25 10.0 51 0.39 Hollow Hollow Hollow SH4 12.75 0.25 10.0 51 0.39 55 4.0 N/A SH5 12.75 0.25 10.0 51 0.39 55 4.0 Long. 6#4 ( 1%) No Trans. SH6 12.75 0.25 10.0 51 0.39 55 4.0 Long. 6#6 ( 2.2%) No Trans. SH7 12.75 0.25 10.0 51 0.39 55 4.0 Long. 6#4 Spiral #3@4” SH1R 12.75 0.25 10.0 51 0.39 55 4.0 Long. 6#4 Spiral #3@3” SH2 16.0 0.25 13.0 64 0.41 55 3.0 N/A Note: All specimens are made with Electric Resistance Welded (ERW) pipes. Table 2.8. Shear test specimens’ properties.

research approach 85 were fabricated using pipes having vertical welded-seams (i.e., Straight-Seam Electric Resistance Welding [ERW] Pipe), except for Specimen S5, which had a spiral welded pipe. The purpose of each specimen is briefly described as follows. Some additional specific infor- mation on final dimensions of each specimen is provided in Section 2.3.2. • Specimen S1 investigates the flexural limit state of RCFST shafts. A generous transition zone was provided in the column-to-shaft connection to ensure effective transfer of all forces and development of the composite strength of the shaft. (This was the case for all specimens, except Specimen S2R.) • Specimen S2R investigates the mechanics of the load transfer between a reinforced con- crete column and a CFST shaft. According to observations presented in Section 2.2.12.1, full transfer of loads from the reinforced concrete column to the CFST shaft can be done by a mechanism that is equivalent to a shear-head mechanism, in the absence of shaft reinforcement, as long as the column reinforcement extends an adequate length into the shaft. Testing a specimen to verify the existence of this load transfer mechanism observed from the finite element analyses will be most useful in providing design recommendations for the transition zone from the reinforced concrete column to the shaft. Additionally, an external axial load was applied at the top of Specimen S2R to investigate the flexural behav- ior of the reinforced concrete column–RCFST shaft under axial load. For this purpose, the bottom part of the shaft had a reinforced column cage to represent an RCFST shaft. The external axial load of 81 kips (that is equal to 0.1 f ′c Ag of the reinforced concrete column) was applied by placing a DYWIDAG bar along the longitudinal axis of the specimen, in a sleeve provided in the center of the specimen’s cross-section, and post-tensioning it to achieve the desired axial load. • Specimen S3 is a repeat of Specimen S1 for which the inside surface of the steel tube was covered with slurry before casting the concrete as a way to simulate the effect of soil coatings in reduc- ing the bond between the concrete and steel tube. According to observations in Sections 2.2.6 and 2.2.10, the presence of a reduced friction coefficient at the concrete-to-steel tube interface (intended to make the shaft non-composite) will result in a small reduction in the maximum flexural strength comparing to the composite shaft. However, based on the finite element analy- ses in the analytical program, a more substantial loss of strength was expected to develop at an increasing drift ratio. • Specimen S4 is a repeat of Specimen S3 but with a grease coating on the inside surface of the steel tube instead of slurry. The grease coating provides less friction at the interface of concrete core and the steel tube compared to the slurry case. This was intended to provide a specimen that is ideally behaving non-composite, for comparison purposes. • Specimen S5 investigates whether results would differ if a spiral welded casing is used. This specimen also has a 30 in. diameter. Additionally, a D/t of 96 was used for this specimen in order to provide information on the behavior of RCFST shafts with a larger D/t. • Specimen S6R investigates the effect of using shear transfer mechanisms to develop full compos- ite action in an RCFST shaft in a case where no adequate friction can develop at the concrete- to-steel tube interface (which would result in a non-composite shaft in the absence of the shear transfer mechanisms). According to findings obtained in the analytical program, in the case where adequate friction cannot develop at the concrete-to-steel tube interface, composite action can be achieved by providing shear transfer mechanisms (e.g., shear studs, welded strips, etc.) over a certain length at the top of the RCFST shaft, with a quantity and strength sufficient to resist the transferred internal axial load described in Section 2.2.10.2. This can be investigated by testing a specimen (Specimen S6R) similar to the Specimen S3 or S4 (one with an interior surface of steel tube coated in slurry or grease), but with shear transfer mechanisms provided at the top of the shaft. A thick layer of grease coating was used on the interior of the steel tube of Specimen S6R.

86 Contribution of Steel Casing to Single Shaft Foundation Structural resistance Designed flexural test specimens and their relationship with others specimens (for comparison of experimental results to establish how various factors affect behavior) can be summarized as shown in Figure 2.93. Detailed design of the specimens is presented in Appendix G. The flexural testing setup is presented in Section 2.3.4. In addition to the testing matrix provided in Table 2.7, a series of shear tests on the CFST and RCFST shafts was done in order to investigate the shear resistance properties of those shafts. The shear testing program is presented in Table 2.8. In this table, D, t, and H are nominal outer diameter, wall thickness, and height of the shear specimen, respectively, and α is the shear span (i.e., H/2 in double curvature shear). rs is the ratio of the longitudinal reinforcement area to the cross-sectional area of the specimen. Shear tests were done using a pantograph shear testing device, which was used to test shear link connections by Berman and Bruneau (2006). Figure 2.94 Figure 2.93. Relationship of the flexural test specimens to each other. 440 kips Actuator Specimen 48” Figure 2.94. Shear test setup used by Berman and Bruneau (2006).

research approach 87 shows the test setup used by Berman and Bruneau (2006). All of the shear specimens were tested under double curvature setup and up to their ultimate strength and failure. Specimen SH3 is a hollow HSS tube, which was tested in order to provide the shear strength of the steel tube itself. Specimen SH4 is a CFST that uses the same steel tube as Specimen SH3 but is filled with 4 ksi normal weight concrete. In order to investigate the effect of longitudinal reinforcement on the shear behavior of the RCFST shafts, Specimen SH5 with rs = 1% and Speci- men SH6 with rs = 2.2% were tested and results were compared to Specimen SH4. The objective of testing Specimens SH7 and SH1R were to investigate the effect of transverse reinforcement on the shear behavior of RCFST shafts. Specimens SH7 and SH1R are similar to Specimen SH5 but with two different ratios of transverse reinforcing ratios. Specimen SH2 has similar testing objectives as SH3 but has a larger tube dimension and different D/t and H/D ratios. This speci- men was tested in order to investigate the failure behavior of CFST shafts with different D, D/t, and H/D and to verify the finite element models. The shear testing program setup is presented in Section 2.3.4. The shear test specimens and their relationship with other specimens can be summarized as shown in Figure 2.95. 2.3.2. Flexural Specimen Design Procedure Figure 2.96 shows a schematic configuration of the flexural test specimen to be designed, with a schematic of the moment diagram along its height. Design of the flexural test specimens was done assuming that the reinforced concrete column that frames into the shaft remains essentially elastic until the shaft reaches its plastic moment capacity. While this may not be the case in practice, it is required to proceed this way here to experimentally assess the ultimate strength of the shaft, such as to be able to validate design equations and assumptions. There- fore, the geometry and properties of the specimens were chosen to satisfy this requirement. The design procedure for the test specimen followed—in a simplified way—the flowchart shown in Figure 2.97. Figure 2.95. Relationship of the shear test specimens to each other.

88 Contribution of Steel Casing to Single Shaft Foundation Structural resistance Therefore, the design of each specimen started by considering the RCFST shaft section and a shaft height, which were chosen according to test objectives and limitations. The specific diameter and D/t ratio of the steel tube was chosen taking into account availability accord- ing to pipe manufacturer catalogues, to be relatively close to the desired target values. ASTM A252 Grade 2 steel, having a nominal yield strength of 35 ksi, was selected for the steel tube. This material is typically approved (e.g., per the 2014 WSDOT Bridge Design Manual) for use as steel casing. The expected yield strength of this steel grade is not provided by ASTM and manufacturers; in order to have enough safety margin to develop the expected flexural plastic strength of the shafts, when designing the specimens, a value of 1.6 fy was considered to be the expected yield strength for ASTM A252 Grade 2 steel. The longitudinal reinforcing ratio (rs) in the shaft was chosen as 1% because lower reinforcement ratios make it easier to design the reinforced concrete column framing into the shaft. A few testing laboratory limitations governed some of the specimen design parameters. First, it was determined best to limit the maximum height of the horizontally acting actuators to 24 ft above the strong floor; this consequently limited the maximum height of the specimen (i.e., the sum of the height of the foundation, of the height of the shaft [Hs], and of the column framing Figure 2.96. Flexural test specimen scheme. Figure 2.97. Flexural specimen design procedure flowchart.

research approach 89 into it [Hc]). Second, the maximum 40 tons capacity of the overhead crane in the testing area limited the total weight of the specimen and its foundation. The maximum operating height of the crane of 28 ft was also considered in the design of the flexural specimens. As shown in Figure 2.96, the reinforced concrete column should be designed to have a yield moment capacity that is more than the moment demand at the top of the shaft when the moment at bottom of shaft reaches the plastic moment capacity of the RCFST shaft (Mps). In other words: 1.0 (2.15)α = > M FH c yc c where Myc and F are the nominal yield moment capacity of the column and maximum lateral force that is acting at the top of the specimen, respectively. Note that Myc is used here instead of Mpc to ensure that the column does not develop any inelastic behavior that could decrease flexural or shear strength. According to the AASHTO SGS (2011), the nominal yield moment is reached when either the concrete strain reaches a magnitude of 0.003 or the reinforcing steel strain reaches a reduced ultimate tensile strain. However, for the same reasons mentioned above, in calculating the nominal yield moment of the column, the yield strain of the reinforcing steel was considered here instead of the reduced ultimate tensile strain. Likewise, the nominal values for material properties were used (rather than expected values). However, the plastic moment capacity of the RCFST shaft (Mps) is calculated using the PSDM considering the expected material properties. In the design of this specimen, as well as of all other flexural specimens of this testing program, the confined compressive strength of the concrete and expected yield strength of steel were con- sidered in calculating the expected plastic moment capacity of the RCFST shaft. The confining effect of the transverse reinforcement in the reinforced concrete column was calculated accord- ing to Mander et al. (1988), while the confining effect of the steel tube in the shaft was calculated according to Susantha et al. (2001), using the approach described in Appendix E. In order to consider possible variations in the delivered concrete’s compressive strength, the amount of f ′c that was used in calculations to determine the adequacy of the testing equipment to develop the full composite plastic flexural strength of the specimen was increased by 50% for all designed specimens. However, sensitivity analyses showed that changes in the value of f ′c do not have a significant effect on the strength of RCFST shafts. (Recall that, in Section 2.2.5, the contribution of concrete to the total flexural strength was shown to be relatively small.) The clear cover for the reinforced concrete core was taken to be 1 in. Design aspects and some details specific to each of the specimens are presented in Appendix G. Table 2.9 presents the summary of the final details for each flexural specimen design. The last column of this table shows the design safety factor for each specimen. 2.3.3. Loading Protocol To address non-seismic as well as seismic behavior, all specimens tested for flexural resistance were subjected to cycles of lateral loads, starting with small lateral loads to represent non-seismic design performance and increasing the lateral loads until the point where specimen strength was reached. Cyclic loading continued with progressively larger displacements to investigate seismic performance. Figure 2.98 shows the cyclic loading history. In this figure, the first four cycles were elastic loading, increasing in amplitude up to first yield strength of the specimen (i.e., force-controlled cycles). After reaching first yield in the specimen at the end of cycle 4, testing continued (in displacement-controlled cycles), by subjecting the specimen to displacement amplitudes equal

90 Contribution of Steel Casing to Single Shaft Foundation Structural resistance Sp ec im en RCFST Shaft Part Reinforced Concrete Column Part Outside Diameter ( ), in. Wall Thickness (t), in. , ksi Long. Reinforcing % Trans. Reinforcing , in. , in. , ksi Long. Reinforcing % Trans. Reinforcing 1 20 0.25 80 8 4 12 #5 A706Gr60 1.25 #4 @4” A706Gr60 16 40 2.5 4 20 #7 A706Gr60 6.0 #4 @4” A706Gr60 1.42 2R 20 0.25 80 8 4 12 #5 A706Gr60 1.25 #4 @4” A706Gr60 16 40 2.5 4 20 #7 A706Gr60 6.0 #4 @4” A706Gr60 1.43 3 20 0.25 80 8 4 12 #5 A706Gr60 1.25 #4 @4” A706Gr60 16 40 2.5 4 20 #7 A706Gr60 6.0 #4 @4” A706Gr60 1.79 4 20 0.25 80 8 4 12 #5 A706Gr60 1.25 #4 @4” A706Gr60 16 40 2.5 4 20 #7 A706Gr60 6.0 #4 @4” A706Gr60 1.79 5 30 0.312 96 8 4 24 #5 A706Gr60 1.05 #5 @5” A706Gr60 24 60 2.5 4 32 #8 A706Gr60 5.6 #5 @4” A706Gr60 1.64 6R 20 0.25 80 8 4 12 #5 A706Gr60 1.25 #4 @4” A706Gr60 16 40 2.5 4 20 #7 A706Gr60 6.0 #4 @4” A706Gr60 1.42 Note: For steel tube of all the specimens, 35 ksi A252 Grade 2 steel was assumed. , , Table 2.9. Design summary of the flexural specimens. Figure 2.98. Cyclic loading history for testing program. No rotation at top Cap at the top Figure 2.99. Loading and boundary conditions for shear tests.

research approach 91 to multiples of the equivalent yield displacement (Dy), with two cycles applied at each displace- ment amplitude (at 2Dy, 3Dy, 4Dy, etc.), until the specimen fails. Similar loading protocol was also used for the shear tests. For the shear tests, using the pan- tograph shown in Figure 2.94, specimens are subjected to a pure translation at their top. Cyclic lateral loading was applied at the top of the specimen, as shown in Figure 2.99. 2.3.4. Test Setup Details The designed test specimens were tested at the UB SEESL. Flexural specimens that are pre- sented in Table 2.7 were prepared to test using the test setup shown in Figure 2.100. The flexural test specimen consists of a circular RCFST shaft part, from which a circular reinforced concrete column part with a smaller dimension extends at its top. The RCFST shaft part is connected to a reinforced concrete foundation, which is post-tensioned to the strong floor using DYWIDAG Figure 2.100. Schematic view of the flexural specimens test setup.

92 Contribution of Steel Casing to Single Shaft Foundation Structural resistance bars. The connection of the RCFST shaft part to the reinforced concrete foundation consists of an embedded part of the shaft in the foundation and a circular base plate that is connected to the bottom of the shaft. Details of the connection part are shown in Figure 2.101. Designs of the flexural test specimens are presented in Appendix G. Cyclic load is applied at the top of the reinforced concrete column part by an actuator that is connected to the strong wall at its other end. The connection of the actuator to the specimen is by means of a column head part that is shown in Figure 2.102. The column head was designed to be able to transfer the force from the actuator to the reinforced concrete column part of the specimen. The effect of large deformations (at 10% drift) that could produce additional shear and moment locally at the top of the column was considered in the design of the column head. Figure 2.103 shows plan views of the location of the flexural test specimen in the SEESL, as well Strong floor Foundation Specimen DYWIDAG bars Internal reinforcement Stiffeners Base plate Embedded part of the RCFST shaft Figure 2.101. Details of the RCFST shaft-to-reinforced concrete foundation connection. Column head Loading plates Actuator attachment bars RC column 220kips actuator Figure 2.102. Schematic view of the connection of the actuator to the flexural specimen.

research approach 93 as location of the actuator that is attached between the column head and the strong wall. The axial load on the Specimen 2R was applied by a DYWIDAG bar installed through a sleeve at the center of the cross-section and post-tensioned to the desired value of axial load. One end of this DYWIDAG bar was fixed at the top of the reinforced concrete column part of the specimen, and the other end was fixed under the strong floor. The construction of the flexural specimens and their test setup preparation process are presented in Section 2.3.5. Shear specimens that are presented in Table 2.8 were prepared to be tested using the pan- tograph device shown in Figure 2.104 (without a specimen inserted). This pantograph device was designed and constructed by Berman and Bruneau (2006). As shown in the figure, in this loading device, an actuator applied a force to a loading beam, such that the action line of the force passes through the mid height of a shear specimen connected to the pantograph by the top and bottom mounting plates. Cyclic load can be applied by a 440 kips capacity actua- tor up to displacements of ±20 in. (although shear specimens can only typically resist much smaller displacements before failure). The pantograph diagonals on the left side prevent the rotation of the top loading beam during the test providing a double curvature shear test- ing ability, with pure shear at mid height of the specimen. Figure 2.105 shows the displaced positions of the pantograph diagonals and connections when a displacement is applied by the actuator. (a) (b) Figure 2.103. (a) Specimen testing location in SEESL. (b) Specimen position in front of strong wall.

94 Contribution of Steel Casing to Single Shaft Foundation Structural resistance Foundation Beam (FB) W24×146 Mounting Plates (MP) Figure 2.104. Schematic view of the pantograph setup. Pantograph Positions Zero positionLB moving path Figure 2.105. Pantograph diagonals displacements under pull from actuator. As indicated in Table 2.8, the various shear specimens were circular RCFST (with different diameters and internal reinforcing configurations), CFST, and a hollow steel tube for compari- son. The minimum available distance between the mounting plates of the pantograph device was 44 in. To ensure a shear dominated failure in the specimens, for the chosen cross-sections and material properties, the specimen length would have to be on the order of 10 in. Therefore, to create such a free shear span length and fit the minimum 44 in. specimen length required for installation into the pantograph, the strength of the specimens outside of that free span was increased by using auxiliary reinforcing steel plates. A modular test setup was designed for testing the 12.75 in. outside diameter (OD) shear specimens (labeled as 12OD shear specimens for simplicity). Based on findings from preliminary finite element analyses and because of cost constraints, it was decided to design stiffener modules

research approach 95 that could be bolted together with the shear specimen on the pantograph testing apparatus and then be re-used for all 12OD shear specimens. Figure 2.106 shows a schematic view of the 12OD shear specimen and the re-usable stiffener modules. The modules have been sized such as to provide the desired shear span for the specimens. For illustration purposes, Figure 2.107 shows a typical deformed shape and stresses from a finite element model of the shear specimen subjected to a horizontal top displacement similar to what it will be subjected to when mounted into the Shear span 12OD Shear specimen Specimenmounting modules Shear specimen 10 Figure 2.106. Schematic view of the designed modular shear test setup for 12OD shear specimens. Figure 2.107. Deformed finite element model of the shear specimen mounted on the modular shear test setup.

96 Contribution of Steel Casing to Single Shaft Foundation Structural resistance testing apparatus, showing how the designed stiffener modules limit shear yielding to the free length. The exception was the 16 in. OD shear specimen (Specimen SH2), which was built with welded stiffeners at both ends of the shear span. Figure 2.108 shows a schematic view of this specimen. Figure 2.109 shows schematic views of a shear specimen mounted on the pantograph device. The construction of the shear specimens and their test setup preparation processes are presented in Section 2.3.5. 2.3.5. Construction and Preparation of the Specimens The majority of the construction process of the test specimens was performed in the SEESL lab. The construction process, test setup preparation, instrumentation, and test of the material properties of all the flexural and shear test specimens are presented in Appendix H. The CAD drawings and instrumentation plans of the specimens are available in Appendix M. In testing of the flexural specimens, Specimen S1 was constructed and tested first as the “reference” flexural specimen against which behavior of other specimens was to be compared. Figures 2.110 and 2.111 show the ready-to-test views of a typical 20 in. diameter specimen and of the 30 in. diameter Specimen S5, respectively. The average measured material properties of the steel tube and shaft concrete for each flexural specimen are presented in Table 2.10. Average yield and ultimate stress for rebars were 75.2 ksi and 96.6 ksi, respectively. Figure 2.112 shows a 12OD shear specimen’s ready-to-test state, as a representative example of shear test setup. The average measured material properties of the steel tube and shaft concrete for each shear specimen are presented in Table 2.11. Stiffeners 16OD Shear specimen Shear span Side View Figure 2.108. Schematic view of the designed stiffeners for Specimen SH2 (16 in. diameter).

research approach 97 (a) (b) 12OD shear specimen mounted on pantograph using A490 bolts Figure 2.109. Schematic views of the shear specimens mounted on the pantograph device. (a) 12 in. diameter specimen. (b) 16 in. diameter specimen.

98 Contribution of Steel Casing to Single Shaft Foundation Structural resistance Figure 2.110. Global view of the flexural specimen’s test setup (20 in. diameter specimen is shown). Figure 2.111. Global view of Specimen S5 (30 in. diameter) ready for test.

research approach 99 Figure 2.112. The assembled 12OD shear specimen and its ready-to-test state in the pantograph. Specimen Steel Tube Concrete , ksi , in./in. , ksi , ksi , ksi S1 46.0 1500 55.1 30100 5.0 S2R 51.9 1700 63.1 30900 5.7 S3 46.1 1600 57.0 29400 5.8 S4 47.4 1400 62.1 33400 6.0 S6R 55.0 1900 66.8 29600 5.6 S5 41.5 1400 68.0 30300 8.3 Table 2.10. Average material properties obtained from uniaxial tests for flexural specimens. Shear Specimen Steel tube Concrete , ksi , in./in. , ksi , ksi , ksi 12OD specimens 58.0 1900 71.5 30100 4.5 16OD specimen (SH2) 50.6 1700 68.3 29000 2.9 Table 2.11. Average material properties obtained from uniaxial tests for shear specimens.