The influence of construction joint on the seismic behavior of reinforced concrete frame structure

Abstract

A new model that can simulate the behavior of construction joint subjected to seismic forces was proposed. Nonlinear time-history analysis was carried out for reinforced concrete regular frame structures designed in different seismic intensity regions as well as with different height-to-width ratios. Two kinds of numerical models are adopted to simulate the seismic behavior of each frame, one with construction joint using the new proposed model and the other without construction joint using the conventional model. Results show that the influence of construction joint on the seismic behavior of reinforced concrete frame is strongly related to structural nonlinearity. It may increase the top displacement and the inter-story drift, change the inter-story drift distributions, and exacerbated the local reaction of key members. The influence of construction joint cannot be ignored for structures with low emergency capacity against major earthquake. Seismic design suggestions are proposed from the aspect of calculation analysis method.

Keywords

construction joint model nonlinear time-history analysis reinforced concrete frame structure seismic behavior seismic design

Introduction

The objective of seismic design for reinforced concrete (RC) frame structures is to form the strong-column weak-beam (SCWB) yielding mode which could dissipate much seismic energy. However, the preferred SCWB mode has not been observed in most damaged RC frame structures in the Wenchuan earthquake (Zhao et al., 2009), while the weak-column strong-beam (WCSB) yielding mode developed in almost all the collapsed frame structures. Interestingly, frames designed according to the code provisions (GB50011, 2010, “Chinese Code” for short) also suffered such damage although theoretically possessing SCWB failure mode.

It is necessary to find out the cause of the contrast. One of the most likely reasons is that the calculation model does not match with the actual building. As is known to all, during construction of a cast-in-situ RC structure, continuous casting of concrete is not available. When the casting time interval exceeds the initial setting time of the concrete, construction joints are formed. Construction joints typically occur in the column ends of the frame structure, where large forces and key connected structural members exist. Most of the observed structural failures have been initiated by damage or failure in the beam–column joints as known from the literatures (Lu et al., 2012; Zhou and Zhang, 2014). And numerous research has been carried out to study the complex mechanism and the behavior of joints under seismic loadings (Hwang and Lee, 2000; Kim et al., 2007; Sharma et al., 2011; Unal and Burak, 2012). They all agree with the opinion that joints are often the greatest risk parts in a structural system. Some believe that the working stresses mainly concentrated within the joints due to the larger dimension than the members joined, while others believe that the weakest part lies in the link. But almost all the research objects are the monolithic structure, and the influence of construction joint is neglected.

The most typical mechanical property of concrete with joint is that its tensile strength and shear strength are much lower than the ones of integrally cast concrete (Clark and Gill, 1985; Jensen, 1975; Monks, 1974; Waters, 1954). Test results show that construction joints can reduce the cracking load of structural member. Obvious stress concentration is observed in the joint surface. The shear dislocation along the joint will increase the shear deformation and the longitudinal bar slip at the bottom of the column, resulting in concentrated failure area and reduced length of plastic hinge (Isao et al., 1998; Mattock, 1981). It is reasonable to assume that the structure will crack in the construction joints where tensile strength is lower when subjected to large earthquake action.

In this study, two numerical models, “monolithic frame” (formed by continuous casting of concrete) and “jointed frame” (formed by interval casting of concrete), are established for regular RC frame structures in different seismic fortification intensity regions (“intensity region” for short) as well as with various height-to-width ratios, for nonlinear time-history analysis (NTHA). The influence of construction joints on seismic behavior of RC frame was studied through comparison. Then, the simplified seismic design recommendations were proposed for RC frame structures with construction joints.

Mechanical properties and force transfer mechanism of construction joint

A construction joint is the surface between the new and the old concretes during discontinuous placement in the construction of a cast-in-situ RC structure. Therefore, the mechanical properties of the construction joint consist of two parts, that is, mechanical properties of jointed concrete and the influence of the steel bars crossing the joint surfaces.

Test results show that the tensile strength of the joint surface is 41%–86% of that of the monolithic concrete (Waters, 1954). The construction joints had little impact when subjected to bending load alone, and slip failure was likely to develop when subjected to shear load alone (Monks, 1974). Concrete around the construction joint transfers shear force by bond force and friction. For a smooth construction joint surface (i.e. the joint surface is left untreated), the bond between the joint surface concretes was 60% lower than that of integrally cast concrete (Clark and Gill, 1985; Jensen, 1975). It was also found that a damaged bond of the joint surface led to rapid degradation in shear force transfer under cyclic loading, with the shear strength transferred only 60% of that under monotonic loading (Mattock, 1981).

As a result, the joint surface between new and old concretes is inferior to the integrally cast concrete in tensile and shear strength. Meanwhile, a construction joint is composed of the joint surface and steel bars crossing the joint surface. Therefore, the mechanical properties of the construction joint are combined by the two components, as shown in Figure 1. The cooperation and interaction between the joint surface and steel bars vary with the change of reinforcement-concrete mix proportion, geometric conditions, and loading systems, and it is difficult to obtain a detailed understanding of their mechanical properties through experiments. Therefore, in this study, the jointed concrete and the steel bars are considered separately as two materials. This allows for the adoption of abundant test data related to mechanical properties of the jointed concrete and steel bars. And separated analysis of concrete from steel bars coincides with the modeling approach used by most of the finite element analysis software, which helps the establishment of a construction joint model and its application in NTHA.

Figure 1.

Schematic diagram of construction joint.

Mechanical properties of construction joint are defined by the load. Along the normal direction, the construction joint subjected to compressive force and tensile force, while along the tangential direction, it subjected to shear force. The jointed concrete and the steel bars crossing the surface support these forces, as shown in Figure 1. It can be expressed using the simple equation

N = N_{S} + N_{C}

(1)

V = V_{S} + V_{C}

(2)

where N and V are the normal force and tangential force, respectively, of the construction joint; $N_{C}$ and $V_{C}$ are those of the jointed concrete; and $N_{S}$ and $V_{S}$ are those of the steel bars.

As is known to all, for a RC structure or structural member, the compressive force is mainly borne by the concrete, while the tensile force is mainly borne by the steel bars. These two parts work together through the bond force. Therefore, steel bars have a greater impact on normal tensile behavior, while jointed concrete is believed to contribute more to its normal compressive behavior.

The tensile behavior of steel bar is closely related to the bond. With respect to the bond slip mechanism between steel bars and concrete, scholars have made a great deal of experimental and numerical studies (Aslani and Nejadi, 2012; Goksu et al., 2014; Hassan et al., 2012; Weathersby, 2003). The results suggest that before cracking of the concrete, the bond strength of deformed bars consists of three parts: chemical adhesion between the cement gel in concrete and the surface of steel bars, friction of the interface between steel bars and concrete, and mechanical interlocking due to roughness of steel bar surface. The test methods to measure bond slip include pullout test and beam test.

By analyzing the test methods of measuring bond slip, it is known that the above test results can be used as a reference to evaluate the bond behavior between the jointed concrete and the steel bars before cracked. However, because of low tensile strength, the joint surface would crack under a relatively low tensile load. If so, most of the tensile force here is transferred to steel bars. When calculating the bond slip strength, the joint surface can be considered as a crack.

The test results show that the presence of steel bars effectively increases the shear strength of the jointed concrete. The greater the steel ratio $ρ_{s}$ is, the more the shear strength increases; compared with unreinforced test specimens, when ρ_s = 0.34%, the average shear strength improves by 81.1% (Hu et al., 2009).

Modeling of construction joint

Based on research of the finite element model, joint element models include discrete plane model, discrete entity model, and section model. The discrete plane model is commonly used in two-dimensional (2D) plane structures, with four-node isoparametric elements of small thickness; the discrete entity model is commonly used in three-dimensional (3D) structures, with eight-node isoparametric elements of small thickness as well; the section model can be used in 2D or 3D structures, depending on the selected degree of freedom. The section can be endowed with different material properties along different degrees of freedom.

Considering the formation and mechanical properties of construction joint, section model is adopted to simulate it. Depending on the material property given to it, the section model allows the simulation of various mechanical properties of construction joint in different degrees of freedom. In addition, relevant research of fiber section can be used in the model to obtain high-accuracy calculation results by selecting an appropriate uniaxial constitutive relation of materials.

Construction joint has special mechanical properties, which means that loads are mainly borne by the jointed concrete and the longitudinal steel bars crossing the surface. The concrete only transfers the compressive stress and shear stress but almost no tensile stress in the normal direction, while longitudinal steel bars transfer all the three. Moreover, the axial force has a great impact on the mechanical properties of construction joints, which must be clearly manifested in the model. Therefore, the construction joint model herein is based on the fiber section model. However, a simple fiber model fails to account for the shear effect. The shear property can be described using the section-based shear hysteretic model obtained from the test that indicates the average shear effect at the vicinity of the joint (Yu, 2011). This helps not only to avoid the analysis of the complicated shear transfer mechanism of different components at the vicinity of the joint and thus significantly reduce workloads, but also to create a comprehensive description of the hysteretic curves of the construction joint. The drawback, however, is that it does not take into account the coupling of shear force with axial force and bending moment.

Thus, it is seen that both normal behavior and tangential behavior are taken into account in the model established, as shown in Figure 2. Since the construction joint is of zero length in the axial direction, the distance between node i and node j is set to 0. The normal mechanical property is depicted by “interface-TC spring” and the tangential mechanical property by “interface-shear spring.” Properties of the “interface-TC spring” are obtained by defining the fiber section model. For those of the concrete fiber and reinforcement fiber, material constitutive models that fit in with the mechanical characteristics of the jointed concrete and the steel bars (as described earlier) are selected, respectively. Fibers are divided separately for core concrete and cover concrete. For core concrete, the material parameters are determined by calculating the reinforcement coefficient K with consideration of the effect of stirrups. Properties of the “interface-shear spring” can be simulated by the section-based shear constitutive model obtained from the tests that indicate the average shear effect at the vicinity of the joint.

Figure 2.

Schematic diagram of construction joint model: (a) forces at construction joint, (b) fiber section model, (c) shear force on joint surface, and (d) construction joint model.

Set the force vector of the construction joint to ${p} = {\begin{matrix} N & M_{y} & M_{z} & V_{y} & V_{z} \end{matrix}}^{T}$ and deformation vector to ${d} = {\begin{matrix} ε & φ_{y} & φ_{z} & γ_{y} & γ_{z} \end{matrix}}^{T}$ without regard for the effect of torque, and the following equation is derived

{p} = [k_{s}] {d}

(3)

where $[k_{s}]$ is the stiffness matrix of the construction joint cross section.

From the basic description of the construction joint model above, it is noted that the axial force and bending moment of the joint surface are coupled with each other, while the shear force does not couple with them. It can therefore be concluded that the stiffness matrix $[k_{s}]$ is of the following form

\begin{matrix} [k_{s}] = [\begin{matrix} k_{11} & k_{12} & k_{13} & 0 & 0 \\ k_{21} & k_{22} & k_{23} & 0 & 0 \\ k_{31} & k_{32} & k_{33} & 0 & 0 \\ 0 & 0 & 0 & k_{44} & 0 \\ 0 & 0 & 0 & 0 & k_{55} \end{matrix}] \\ = [\begin{matrix} G & 0 \\ 0 & S \end{matrix}] \end{matrix}

(4)

The complete stiffness matrix of the joint surface can be obtained by finding the submatrices G and S. Submatrix G can be obtained with the traditional fiber model integration method; submatrix S, a decoupled shear stiffness matrix, can be calculated from slope of the section-based shear hysteric curve.

Assume that the X-axis of the coordinate system is along the length of the member and the origin of the local YZ-coordinate system is at the centroid of the cross section, as shown in Figure 2. The deformation vector of the fiber section is set to ${d^{*}} = {\begin{matrix} ε_{0} & φ_{y} & φ_{z} \end{matrix}}^{T}$ , where $ε_{0}$ , $φ_{y}$ , and $φ_{z}$ correspond to axial strain and curvatures around y- and z-axes, respectively. According to the plane section assumption, strain of the fiber at coordinate $(y, z)$ can be determined as follows

ε (y, z) = ε_{0} - z \cdot φ_{y} + y \cdot φ_{z} = [H] {d^{*}}

(5)

where $[H] = [\begin{matrix} 1 & - z & y \end{matrix}]$ . Based on the uniaxial stress–strain constitutive curve of the fiber material, the stress corresponding to strain $ε (y, z)$ can be defined by the following equation

σ (y, z) = E (y, z) ε (y, z)

(6)

where $E (y, z)$ is determined by the constitutive relation of the fiber material. The section forces can be determined by integration along the whole cross section

N = \int_{A} σ_{i} d A_{i} = \int_{A} E_{i} ε_{i} d A_{i} = \int_{A} E_{i} [H] {d} d A_{i} = \int_{A} E_{i} [H] d A_{i} {d}

(7)

M_{y} = \int_{A} σ_{i} z_{i} d A_{i} = \int_{A} E_{i} ε_{i} z_{i} d A_{i} = \int_{A} E_{i} [H] {d} z_{i} d A_{i} = \int_{A} E_{i} [H] z_{i} d A_{i} {d}

(8)

M_{z} = \int_{A} σ_{i} y_{i} d A_{i} = \int_{A} E_{i} ε_{i} y_{i} d A_{i} = \int_{A} E_{i} [H] {d} y_{i} d A_{i} = \int_{A} E_{i} [H] y_{i} d A_{i} {d}

(9)

Set the force vector of the fiber section to ${p^{*}} = {\begin{matrix} N & M_{y} & M_{z} \end{matrix}}^{T}$ , and the following equation is derived

{p^{*}} = [\begin{matrix} \int_{A} E_{i} [H] d A_{i} \\ \int_{A} E_{i} [H] z_{i} d A_{i} \\ \int_{A} E_{i} [H] y_{i} d A_{i} \end{matrix}] \cdot {d^{*}} = \int_{A} {[H]}^{T} E (y, z) [H] d A \cdot {d^{*}}

(10)

Stiffness matrix of the fiber section is as follows

\begin{matrix} G = \int_{A} {[H]}^{T} E (y, z) [H] dA \\ = [\begin{matrix} \int_{A} E (y, z) dA & - \int_{A} E (y, z) zdA & \int_{A} E (y, z) ydA \\ \int_{A} E (y, z) zdA & - \int_{A} E (y, z) z^{2} dA & \int_{A} E (y, z) yzdA \\ \int_{A} E (y, z) ydA & - \int_{A} E (y, z) yzdA & \int_{A} E (y, z) y^{2} dA \end{matrix}] \end{matrix}

(11)

Submatrix S can be determined by the section-based shear hysteric curves for column with construction joints obtained through test

S = [\begin{matrix} \frac{d V_{y} (γ)}{d γ} & 0 \\ 0 & \frac{d V_{z} (γ)}{d γ} \end{matrix}]

(12)

Given the above, the element stiffness matrix of the construction joint model is as follows

[k_{s}] = [\begin{matrix} \begin{matrix} \int_{A} E_{i} d A_{i} & - \int_{A} E_{i} z_{i} d A_{i} & \int_{A} E_{i} y_{i} d A_{i} \\ \int_{A} E_{i} z_{i} d A_{i} & - \int_{A} E_{i} z_{i}^{2} d A_{i} & \int_{A} E_{i} y_{i} z_{i} d A_{i} \\ \int_{A} E_{i} y_{i} d A_{i} & - \int_{A} E_{i} y_{i} z_{i} d A_{i} & \int_{A} E_{i} y_{i}^{2} d A_{i} \end{matrix} & 0 \\ 0 & \begin{matrix} \frac{d V_{y} (γ)}{d γ} & 0 \\ 0 & \frac{d V_{z} (γ)}{d γ} \end{matrix} \end{matrix}]

(13)

In order to verify the correctness and effectiveness of the model, numerical simulation of pseudo-static tests on four columns with construction joint and two RC plane structures has been performed. The simulation results show a good agreement between the data calculated from the model and the test data. For more information about the validation procedure, please refer Yu (2011).

Dynamics analysis of seismic behavior of RC frame structures in different intensity regions

Numerical models

Four-story RC frames in intensity regions 7–9 were designed according to the Chinese Code. The materials used include HRB400 longitudinal bars (marked as Φ, f_yk = 400 N/mm²) and HRB335 stirrups (f_yk = 335 N/mm²) for beams and columns. The strength concrete is C30 (f_ck = 20.1 N/mm², f_tk = 2.01 N/mm²), and the thickness of floor slab is 120 mm. Information such as the sectional dimension of the component and the longitudinal reinforcement are shown in Figure 3. The stirrup ratio and stirrup spacing of columns and beams meet the minimum requirements of the Chinese Code. The purpose of this article is to design structures that meet the minimum requirements of the specification.

Figure 3.

Sectional dimension of the component and the reinforcement of frames in different intensity regions: (a) frame in 7 intensity region (FR7), (b) frame in 8 intensity region (FR8), and (c) frame in 9 intensity region (FR9).

Two kinds of numerical models are adopted for each frame structure. One is the “jointed frame” (marked as “-f” in the Table 2), with construction joint model attaching to the column bottom of all stories (i.e. the elevation of top beam surface), as shown in Figure 3(a), the construction joints are marked as “CJ.” The other is the “monolithic frame” (marked as “-z” in the Table 2), which is the conventional method of modeling frame structure, as shown in Figure 3(b) or (c). The calculations were completed on the open system for earthquake engineering simulation (OpenSEES) platform (Mazzoni et al., 2009). Beams and columns are simulated using nonlinear beam–column elements, while floor slabs are simulated through assumption of rigidity.

A uniform division approach is used for discretization of cross-section fiber. Only when the number of section fibers reaches a certain level, we can assume the results of numerical integration meet the accuracy requirement. In the analysis presented herein, core concrete fiber of the column section is divided into 10 × 10, and that of the beam section is divided into 4 (width) × 20 (height). It is believed to assure good calculation accuracy. The fiber section division of the construction joint model is identical to that of the corresponding column section.

Selection of ground motion records

Selecting input ground motion records is essential to NTHA. The Chinese Code requires the ground motion records selected with a statistical significance match case with the design spectrum. In this calculation, five ground motion records, including three actual ground motion records and two artificial ground motions, were selected for each frame. The ground motion records were selected according to the input ground motion scheme for two frequency domains of response spectra in accordance with the design spectra in a statistical sense (Yang et al., 2000). The two frequency domains correspond to the flat range of design spectra and the natural period of structure. The natural periods of frames designed in 7, 8, and 9 intensity regions are 0.85, 0.78, and 0.50 s, respectively. The ground motion records selected are listed in Table 1, and the elastic response spectrums are shown in Figure 4.

Table 1.

Ground motion records selected.

No.	Earthquake	Occurrence time	Recording station	Direction	Magnitude
USA98	Northridge	1994.1.17	Carson, CA	S90E	6.7
USA05	Northwest California	1951.10.7	City Hall, Ferndale, CA	N46W	6.0
USA74	Helena Montana	1935.10.31	Montana Carroll College	S90W	6.0
USA97	Northridge	1994.1.17	Water, Carson, CA	S00W	6.7
PRC83	Long Ling Aftershock	1976.6.9	Longlin, Yunan, China	NS	6.2
USA55	Mammoth Lakes	1980.5.25	Convict Creek	180	6.0
USA19	Imperial Valley	1979.10.15	El Centro Array 12, CA	140	6.9
USA02	Northridge	1994.1.17	14801 Osage Ave, CA	S02W	6.7
AF1–10	Several artificial ground motions fitting class II site for different frames
Results	FR7: USA05, USA74, USA98, AF1, AF2; FR8/kj-4: USA05, USA74, USA98, AF3, AF4; FR9: USA97, USA74, USA98, AF5, AF6; kj-2: USA07, PRC83, USA19, AF7, AF8; kj-8: USA05, USA55, USA02, AF9, AF10

Figure 4.

Elastic response spectrums of ground motion records selected for frames in different intensity regions: (a) for FR7, (b) for FR8, and (c) for FR9.

Calculation results and analysis

The selected ground motion records were input for NTHA by building two kinds of numerical models of RC frames in intensity regions 7, 8, and 9. The impact of construction joint on seismic behavior of RC frame was described through comparing the parameters of the maximum top displacements (MTDs), the maximum inter-story drift (MSD), the plastic hinge distribution (PHD), and the moment–curvature relationship (MCR) of key structural member. Considering the impact of random factors, the average values of multiple ground motions are taken as the final result for every parameter.

MTD could reflect the comprehensive response of structure in the earthquake. The horizontal ground motion input was performed, so, the MTD in this paper refers to the lateral maximum top displacement of frame. For comparison, two kinds of numerical model for the same frame were performed. The calculation results are shown in Table 2. “FR7-z-minor” refers to “monolithic frame in the intensity region 7 subjected to minor earthquake,”“FR7-f-major” refers to “jointed frame in the intensity region 7 subjected to major earthquake,” and so on. It can be seen that the MTD of jointed frames is almost always larger than that of monolithic frames, especially in the major earthquake. However, the impact varies from different intensity regions, that is, frames in intensity region 7 are affected most, while the effects of frames in intensity regions 8 and 9 are decreased in turn. The time-history curves of the top displacement of frame in intensity region 7 are shown in Figure 5. It can be seen that with the increase in earthquake magnitude, the influence of the construction joint is more and more obvious. And it shows the similar rules in other two intensity regions.

Table 2.

MTD of frames in different intensity regions.

Intensity region	Magnitude	Frame	MTD (m)
	Minor	FR7-z	0.0078
		FR7-f	0.0080
7	Major	FR7-z	0.1048
		FR7-f	0.1523
	Minor	FR8-z	0.0096
		FR8-f	0.0090
8	Major	FR8-z	0.0989
		FR8-f	0.1025
	Minor	FR9-z	0.0064
		FR9-f	0.0066
9	Major	FR9-z	0.0603
		FR9-f	0.0632

Figure 5.

Time-history curves of the top displacement of frame in the intensity region 7: (a) in minor earthquake, (b) in medium earthquake, and (c) in major earthquake.

The impact of construction joint varies from different intensity regions can be explained by tracing the force history of the “interface-TC spring” on the top of the column at the ground floor. Assumed the force as F_c, the axial force ratio N_c is defined as N_c = F_c/A · f_c, where A is the section area of the column; f_c is the design value of concrete prismatic compressive strength, for C30, f_c = 14.3 N/mm². The time-history curves of N_c of frames in different intensity regions are shown in Figure 6. Assuming that the pressure is negative and the tension is positive. The values of N_c are always negative and the maximum is −0.25 in the intensity region 7. The maximum values of pressure and tension are −0.23 and 0.04, respectively, in the intensity region 8, while the values are −0.11 and 0.14, respectively, in the intensity region 9. When the value exceeds −0.2, the stiffness and strength of column declined rapidly, and the tensile failure is easy to occur.

Figure 6.

Time-history curves of the axial force ratio of the bottom column of frames in different intensity regions: (a) FR7, (b) FR8, and (c) FR9.

The MSD could reflect the weak parts of the structure. And the MSD of frames in intensity regions 7–9 subjected to different earthquake magnitudes is shown in Table 3. It can be seen that the MSD of jointed frames is normally larger than that of monolithic frames, and it could be increased by 14% at most. The results show little difference when subjected to different earthquake magnitudes. In general, construction joint has little impact on the values and distributions of MSD in minor earthquake, while the impact is more serious in major earthquake. But all of which are not overrun the limit value specified in the Chinese Code. The limit values of minor and major earthquakes are 1/550, 1/50, respectively. It is worth noting that the distribution of MSD may be changed in the intensity region 9.

Table 3.

MSD of frames in different intensity regions.

Intensity region	Magnitude	Frame	MSD	Floor	Overrun
	Minor	FR7-z	1/1250	4	No
	Minor	FR7-f	1/1000	4	No
7	Major	FR7-z	1/54	1	No
		FR7-f	1/52	1	No
	Minor	FR8-z	1/714	4	No
		FR8-f	1/714	4	No
8	Major	FR8-z	1/91	1	No
		FR8-f	1/80	1	No
	Minor	FR9-z	1/1075	4	No
	Minor	FR9-f	1/1000	4	No
9	Major	FR9-z	1/192	2	No
		FR9-f	1/174	4	No

MSD: maximum inter-story drift.

The PHD reflects the failure mode of structure. The results of frame in intensity region 9 excited by artificial ground motion which cause the largest effect are shown in Figure 7 (the hollow circle represents the plastic hinge). It can be seen that construction joint causes the structure to form more plastic hinges, due to the existence of construction joints, plastic hinges are more likely to appear in column ends, and less likely to appear in beam ends, which is in well agreement with the actual earthquake damage. Frames in the intensity regions 7 and 8 almost show the same rule.

Figure 7.

PHD of frame in intensity region 9 under ground motion AF5: (a) FR9-z and (b) FR9-f.

The seismic behavior of structure under earthquake is related not only to the overall indicators above, but also to the local response of key structural members, such as the lower end section of column at the ground floor, where the plastic hinge is most likely to form. The MCRs of the lower end section of column at the ground floor were studied, and the results of the frames in intensity region 8 excited by the artificial ground motion AF5 are shown in Figure 8. It is obtained by tracing the mechanics time-history of “interface-shear spring.” It could be seen that there is a linear relationship between the moment and curvature of both monolithic frame and jointed frame when subjected to minor earthquake. This indicates that the structural members are in the elastic stage, when the construction joints have little influence. When subjected to major earthquake, severe plastic deformation occurs, and the MCR appears as a hysteric curve. Both curves of monolithic frame and jointed frame are spindle-shaped and follow a similar pattern, but the monolithic frame shows a better energy dissipation capacity from the area within the hysteretic loop. It was also noted that in intensity region 7, the MCR of two kinds of frames follow a similar pattern (i.e. slip occurs in the same direction), but the slips of jointed frames are larger. In intensity region 9, plastic deformation at a certain level occurs in both types of frames, but no plastic hinges are formed in the bottom of left edge column at the ground floor.

Figure 8.

MCR of the lower end section of column at the ground floor of frame FR8: (a) in minor earthquake and (b) in major earthquake.

By comparing the above calculation results, generally it can be concluded that when subjected to minor earthquake, the structural members are almost in elastic stage, and then the construction joints have little influence and can be neglected; when subjected to medium earthquake, some structural members enter the nonlinear stage and even yield, and then the influence of construction joints becomes more visible, causing a deformation behavior different from the monolithic frame; when subjected to major earthquake, a large number of structural members enter the yielding stage and the construction joints start to play a bigger role.

However, it should be noted that except for the common rules above, the construction joints are not affecting the frames equally in all intensity regions. When subjected to minor earthquake, as the structures are in the elastic stage, construction joints have the same influence on frames of all intensity regions, while the case is different when subjected to medium and major earthquakes, the construction joints have a more obvious impact on frames in intensity regions 7 and 8 than in intensity region 9. The reason is that the seismic design concept adopted by the Chinese Code is inconsistent with the $R - μ - T$ theoretical relation proposed by Newmark based on the “equal displacement rule” and “equal energy rule.” When seismic force reduction factor R is a constant value, the requirement for structure ductility µ should also be constant, regardless of which region the structure is in. While according to the Chinese Code, the seismic configuration requirements are most rigorous in intensity region 9, followed by intensity regions 8 and 7.

It could be inferred that the frames with identical geometry act differently when subjected to rare earthquake due to the adoption of different configuration details in different intensity regions. The safety margin of frame in the intensity region 7 is the lowest and frames in intensity regions 8 and 9 are in ascending order. Therefore, frames in intensity region 7 go into nonlinear stage most seriously and shows the worst affected by construction joints.

Numerical analysis of seismic behavior of RC frame structures with different height-to-width ratios

Determination of calculation parameters

According to the Chinese Code, the RC frames should be designed according to different seismic grades and shall meet corresponding requirements for calculation seismic design details. In order to study the influence of construction joints on the seismic behavior of frames designed according to different seismic grades, frames with three height-to-width ratios, 0.58 (two-story, marked as kj-2), 1.11 (four-story, marked as kj-4), and 2.18 (eight-story, marked as kj-8)), are designed in the intensity region 8. The design principal is the same as above, and the sectional dimension and reinforcement of frames are shown in Table 4. The ground motion records selected are listed in the Table 1.

Table 4.

Dimension and reinforcement of columns and beams.

Frame	Floor	Columns				Beams
		Section (mm)	Reinforcement		Section (mm)	Reinforcement
			Side	Middle		Side		Middle
			Side	Middle		Top	Bottom	Top	Bottom
kj-2	1	400 × 400	4Φ25+4Φ22		200 × 400	3Φ22+2Φ18	2Φ25	3Φ22+2Φ18	2Φ25
kj-2	2	400 × 400	4Φ25+4Φ22		200 × 400	3Φ22+2Φ18	2Φ25	3Φ22+2Φ18	2Φ25
kj-4	1	500 × 500	4Φ20+8Φ18		300 × 500	2Φ20+2Φ18	2Φ18+2Φ16	2Φ20+2Φ18	4Φ16
	2		12Φ18			2Φ20+2Φ18	2Φ18+2Φ16	2Φ20+2Φ18	4Φ16
	3		12Φ18			4Φ16	4Φ16	4Φ16	4Φ16
	4		12Φ18			4Φ16	4Φ16	4Φ16	4Φ16
kj-8	1	650 × 650	8Φ25+4Φ22	8Φ25+4Φ22	300 × 500	2Φ25+2Φ22	3Φ25	2Φ25+2Φ22	3Φ25
	2		8Φ22+4Φ25	8Φ22+4Φ25		2Φ25+2Φ22	3Φ25	2Φ25+2Φ22	3Φ25
	3		8Φ22+4Φ25	8Φ22+4Φ25		2Φ25+2Φ22	3Φ25	2Φ25+2Φ22	3Φ25
	4	500 × 500	4Φ22+8Φ18	4Φ22+8Φ20		2Φ20+2Φ18	3Φ22	2Φ25+2Φ22	3Φ22
	5		4Φ22+8Φ18	4Φ22+8Φ20		2Φ25+2Φ22	3Φ22	2Φ25+2Φ22	3Φ22
	6		4Φ18+8Φ16	4Φ22+8Φ20		2Φ25+1Φ22	3Φ22	2Φ25+1Φ22	3Φ22
	7		4Φ18+8Φ16	4Φ18+8Φ16		2Φ25+1Φ22	3Φ22	2Φ25+1Φ22	3Φ22
	8		4Φ18+8Φ16	4Φ18+8Φ16		2Φ25+1Φ22	3Φ22	2Φ25+1Φ22	3Φ22

Calculation results and analysis

Similarly, parameters such as MTD, MSD, maximum inter-story drift distribution (MSDD), and the MCR of key member were analyzed by building the “jointed model” and “monolithic model” separately for each frame and inputting the selected seismic ground motions. The time-history curves of MTD of frame kj-2 subjected to different earthquake magnitudes are shown in Figure 9. It could be seen that the two curves of monolithic and jointed frames are almost overlap under the minor earthquake. The gap between the two curves increases with the increase in earthquake magnitude. It shows that the MTDs of jointed frames are significantly larger than that of monolithic frames under the medium and major earthquakes. The results of frame kj-4 basically follow the same rules. While the frame kj-8 shows some differences, the MTDs are relatively small and no big difference was observed in the curves of both types of frame model. This phenomenon is related to the degree of nonlinearity of the structure. The structure is in elastic state under the minor earthquake, and the effect of construction joint is not shown. As the seismic force increases, the structure begins to enter the plastic state or even yield, and then the influence of construction joints is becoming apparent. The frame kj-8 has a MTD of only 0.045 m under the major earthquake and is in slight elastic stage, so the construction joints have no obvious influence. It can be concluded that frames with different height-to-width ratios behave differently in terms of MTD, which is due to the emergency capacity of frame in design. The MTDs of frame are shown in Table 5.

Figure 9.

Time-history curves of the top displacemen of the two-story frame: (a) kj-2-minor, (b) kj-2-middle, and (c) kj-2-major.

Table 5.

MTD of frames with different height-to-width ratios.

Frame	Earthquake magnitude	Model	MTD (m)
	Minor	Monolithic	0.007
		Jointed	0.007
kj-2	Middle	Monolithic	0.026
		Jointed	0.057
	Major	Monolithic	0.062
		Jointed	0.095
	Minor	Monolithic	0.010
		Jointed	0.009
kj-4	Middle	Monolithic	0.039
		Jointed	0.053
	Major	Monolithic	0.099
		Jointed	0.103
	Minor	Monolithic	0.003
		Jointed	0.003
kj-8	Middle	Monolithic	0.016
		Jointed	0.016
	Major	Monolithic	0.045
		Jointed	0.048

The MSDs of frames are shown in Table 6, and the MSDD of frame kj-4 are shown in Figure 10. Two specific moments were selected in the calculation. One is the moment of MTD reaching the maximum, recorded as “t 1”; the second is the largest inter-story drift reaching the maximum, recorded as “t 2.” It can be seen that the two-story frame and four-story frame almost follow the same rules. Construction joints have no effect on the structure, so two kinds of frame models have no difference in the MSD and MSDD when subjected to the minor earthquake. While the differences were observed when subjected to medium or major earthquake. The values of the jointed frame are larger than that of the monolithic one, and it could be increased by 18% at most. For the eight-story frame, the MSDs of both models are extremely small and almost equal, while the MSDD shows slight difference.

Table 6.

MSD of frames with different height-to-width ratios.

Frame	Earthquake magnitude	Model	MSD	Floor	Overrun
	Minor	Monolithic	1/555	2	No
		Jointed	1/555	2	No
kj-2	Middle	Monolithic	1/204	1	No
		Jointed	1/130	2	No
	Major	Monolithic	1/83	1	No
		Jointed	1/71	1	No
	Minor	Monolithic	1/730	4	No
		Jointed	1/730	4	No
kj-4	Middle	Monolithic	1/262	1	No
		Jointed	1/241	1	No
	Major	Monolithic	1/94	1	No
		Jointed	1/80	1	No
	Minor	Monolithic	1/1000	5	No
		Jointed	1/1000	5	No
kj-8	Middle	Monolithic	1/455	4	No
		Jointed	1/500	1	No
	Major	Monolithic	1/232	4	No
		Jointed	1/232	1	No

Figure 10.

MSDD of the four-story frame: (a) kj-4-minor, (b) kj-4-medium, and (c) kj-4-major.

The MCRs of the lower end section of column at the ground floor were also studied in the NTHA, and the results of the eight-story frame excited by ground motion AF5 are shown in Figure 11. It could be seen that the sections are basically in the elastic stage, and the MCRs are linear, while the influence of construction joints can be neglected; the sections become plastic under major earthquake, while the construction joints have made a certain influence. The calculations of two-story and four-story frames were also carried out and the influence of construction joints shows the same law.

Figure 11.

MCR of lower section of bottom column of the eight-story frame: (a) in minor earthquake and (b) in major earthquake.

In summary, construction joints have little impact on the seismic behavior of frame structures with different height-to-width ratios when subjected to minor earthquake, and thus can be neglected. When subjected to medium and major earthquakes, frames with different height-to-width ratios are affected differently. This is because that the two-story and four-story frames were designed as Seismic Grade II, while the eight-story frame was designed as Seismic Grade I as it is over 24 m high according to the Chinese Code. Therefore, the seismic design details for the eight-story frame are much more rigorous. In addition, the natural period of the two-story frame is around 0.47 s, very close to the characteristic period of Site Class II (0.4 s), which indicates strong seismic action. So, in the event of a fortification intensity earthquake, the frame enters the plastic stage; while when subjected to rare earthquake, it enters strong nonlinear stage. In contrast, the natural period of the eight-story frame is around 1.04 s, a wide difference from the site characteristic period, which indicates a weak seismic action. When suffering rare earthquake, the horizontal seismic action on the first story of the two-story frame structure is about six times of that of the eight-story structure. Accordingly, when suffering rare earthquake, the eight-story frame still has great emergency capacity and the influence of constriction joints can be neglected. The four-story frame falls in between.

Seismic design method for RC frame structures with construction joints

From the summary of the influence of construction joints on the seismic behavior of regular RC frame structures, it is found that if the structures are in the elastic stage, the construction joints have little influence; if the structures go into nonlinear when suffering rare earthquake, the influence of construction joints becomes more visible. Thus, they shall be considered in the seismic design.

At present, the “two-stage and three-level” design method is adopted in the Chinese Code. The MSD of the frame is used as the control index and the adverse impact of construction joints on the seismic resistance of the frame structure can be comprehensively reflected. According to the above calculation data, the value of MSD may increase by no more than 20%. Seismic design method proposed can be executed as Figure 12.

Figure 12.

Seismic design suggestion of RC frame structure with construction joint.

Conclusion

In this article, NTHA of the four-story RC frames in different intensity regions and RC frames with different height-to-width ratios in the intensity region 8 were carried out; two kinds of numerical model, that is, with or without construction joints, were compared and analyzed. Conclusions are as follows:

A new construction joint model was proposed by analyzing its mechanical properties and force transfer mechanisms. It can be used in the numerical calculation of RC frame structure.

NTHA of four-story regular RC frames in intensity regions 7–9 were carried out, and the results show that the structures are slightly affected by construction joints when subjected to frequent earthquake, while the influence becomes more visible when subjected to rare earthquake. The construction joints make plastic hinges more likely appear in the column ends, so the “strong-beam weak-column” failure mode forms more easily, which is in better agreement with the actual earthquake damage.

NTHA of regular RC frames with different height-to-width ratios in the intensity region 8 was carried out. The results show that the influence of construction joint is related to the nonlinear level of structural members. If the structure was in elastic state, the influence of the construction joint can be neglected; if the structure was in nonlinear state, the influence of construction joints was more obvious so it cannot be neglected.

Seismic design suggestions of RC regular frames based on the two-stage design method of the Chinese Code were proposed from calculation analysis method.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This article is funded by the National Natural Science Foundation of China (Grant nos 51208407 and 51408464) and also funded by Innovation Team of Xi’an University of Architecture and Technology.

References

Aslani

Nejadi

(2012) Bond behavior of reinforcement in conventional and self-compacting concrete. Advances in Structural Engineering 15(12): 2033–2051.

Clark

Gill

(1985) Shear strength of smooth unreinforced construction joints. Magazine of Concrete Research 37(131): 95–100.

GB50011 (2010) Code for Seismic Design of Buildings. Beijing, China: China Architecture & Building Press.

Goksu

Yilmaz

Chowdhury

. (2014) The effect of lap splice length on the cyclic lateral load behavior of RC members with low-strength concrete and plain bars. Advances in Structural Engineering 17(5): 639–658.

Hassan

Mantawy

Soliman

. (2012) Bond characteristics and shear behavior of concrete beams reinforced with high-strength steel reinforcement. Advances in Structural Engineering 15(2): 303–318.

Huang

Chen

(2009) Experimental research on shear of bonding interface between young and old concrete influenced by constructional reinforcement. Concrete 3: 26–28 (in Chinese).

Hwang

Lee

(2000) Analytical model for predicting shear strengths of interior reinforced concrete beam-column joints for seismic resistance. ACI Structural Journal 97(1): 35–44.

Isao

Noriyoshi

Shigekazu

(1998) Evaluation of mechanical properties of construction joint between new and old concrete under combined tensile and shear stresses. Journal of the Society of Materials Science 47(1): 73–88.

Jensen

(1975) Lines of discontinuity for displacements in the theory of plasticity of plain and reinforced concrete. Magazine of Concrete Research 27(92): 143–150.

10.

Kim

LaFave

Song

(2007) A new statistical approach for joint shear strength determination of RC beam-column connections subjected to lateral earthquake loading. Structural Engineering and Mechanics 27(4): 439–456.

11.

Urukap

. (2012) Seismic behavior of interior RC beam-column joints with additional bars under cyclic loading. Earthquakes and Structures 3(1): 37–57.

12.

Mattock

(1981) Cyclic shear transfer and type of interface. Journal of Structural Division, ASCE 107(10): 1945–1964.

13.

Mazzoni

Kenna

Scott

. (2009) Opensees Users Manual (PEER). Berkeley, CA: University of California.

14.

Monks

(1974) Treatment of construction joints. Concrete 8(2): 28–30.

15.

Sharma

Eligehausen

Reddy

(2011) A new model to simulate joint shear behavior of poorly detailed beam–column connections in RC structures under seismic loads, Part I: exterior joints. Engineering Structures 33(3): 1034–1051.

16.

Unal

Burak

(2012) Joint shear strength prediction for reinforced concrete beam-to-column connections. Structural Engineering and Mechanics 41(3): 421–440.

17.

Waters

(1954) A study of the tensile strength of concrete across construction joints. Magazine of Concrete Research 6(18): 151–153.

18.

Weathersby

(2003) Investigation of bond slip between concrete and steel reinforcement under dynamic loading conditions. PhD Thesis, Louisiana State University, Baton Rouge, LA.

19.

Yang

Lai

(2000) A new method for selecting inputting waves for time-history analysis. Civil Engineering Journal 33(6): 33–37 (in Chinese).

20.

(2011) Study on the construction joint modeling and influence to seismic behavior of RC frame structure. PhD Thesis, Chongqing University, Chongqing, China.

21.

Zhao

Taucer

Rossetto

(2009) Field investigation on the performance of building structures during the 12 May 2008 Wenchuan earthquake in China. Engineering Structures 31(8): 1707–1723.

22.

Zhou

Zhang

(2014) Interaction of internal forces of interior beam-column joints of reinforced concrete frames under seismic action. Structural Engineering and Mechanics 52(2): 427–443.