4th International Conference on Earthquake Engineering

4th International Conference on Earthquake Engineering Taipei, Taiwan October 12-13, 2006 Paper No. 115

VULNERABILITY OF CODE-COMPLIANT RC BUILDINGS UNDER MULTI-AXIAL EARTHQUAKE LOADING Aman Mwafy 1 and Amr Elnashai 2 ABSTRACT In the vicinity of the source of moderate-to-strong earthquakes, the ratio of peak vertical to horizontal acceleration (V/H) often exceeds the values around 2/3rd adopted in design codes. The difference in frequency content between the vertical and horizontal ground motions (VGM and HGM, respectively), when coupled with difference between the vertical and horizontal dynamic characteristics of structures, cast doubt regarding the adequacy of the simplified approach adopted in seismic design codes. There are also increasing field evidences confirming the significance of VGM. These evidences were even observed in regions where state-of-the-art in earthquake design practice is applied, such as Japan and the USA. The objective of this paper is to investigate the effect of VGM on seismic response and force reduction factors ‘supply’ of multi-storey RC buildings located in the vicinity of active faults and designed to modern seismic codes employing capacity design principles. A comprehensive set of local and global response parameters is selected to assess the building response under multi-axial earthquake loading (HGM and VGM). These include assessment of the shear supply-demand response of structural members using a realistic ductility- and axial forcesensitive shear strength approach. Near-field earthquake records with moderate-to-high V/H ratios are selected to provide realistic conclusions regarding the effect of VGM. The wide range of buildings and performance criteria selected and the state-of-the-art modeling approaches adopted render the results of this study indicative of response trends. It is concluded that the lower the contribution of horizontal seismic forces to the seismic response, the higher is the significance of vertical motion. The fluctuation of axial force in vertical structural members significantly increases when including VGM. This not only has direct consequences on tension and compression response but also has considerable impact on the shear capacity. Although the investigated buildings are designed and detailed according to modern seismic codes, the importance of including VGM in seismic design and assessment of RC buildings in the vicinity of active faults is emphasized. Keywords: Vertical ground motion, RC buildings, seismic codes, shear failure, near-field records

INTRODUCTION Since the vertical ground motion (VGM) attenuates faster than its horizontal counterparts, the average vertical-to-horizontal PGA (V/H) ratio will be lower than the values conventionally assumed in design at some distance from the epicentre. Conversely, there is a considerable body of evidence (e.g. Ambraseys and Simpson, 1996; Bozorgnia and Campbell, 2004; Papazouglou and Elnashai, 1996; Elgamal et al., 2004) that in the vicinity of the causative fault of moderate-to-strong earthquakes the V/H ratio exceeds unity and hence exceeds the values assumed in design. For instance, for the Imperial Valley ‘EO6’, U.S., 1979 and Morgan Hill ‘G07’, U.S., 1984, events, the V/H ratio was 3.70 1 2

Senior Post-Doctoral Research Scholar, University of Illinois at Urbana-Champaign, USA. Assistant Professor, University of Zagazig, Egypt (on leave). Email: [email protected]. Bill and Elaine Hall Endowed Professor of Civil Engineering, Director of the Mid-America Earthquake Centre, University of Illinois at Urbana-Champaign, USA. Email: [email protected].

and 3.52, respectively. However, these high values do not imply that a structure will suffer severe damage under these records since either or both of the two components may be insignificantly small or they may not coincide in time to cause strong interaction effects. The simplification adopted by design codes is therefore not commensurate with the complexity of the problem and the numerous observations from field studies of earthquakes. It was concluded in a number of investigations that structural failure modes from past earthquakes might be attributed to underestimating the effect of VGM in design (e.g. Bozorgnia et al., 1998; Ghobarah and Elnashai, 1998; Papazouglou and Elnashai, 1996; amongst others). Recently, new approaches have been suggested to rationally account for VGM (Elnashai and Papazouglou, 1997; Collier and Elnashai, 2001; Elgamal et al, 2004), which lead to the adoption of more realistic VGM spectra in design (EC8, 2004). The objectives of the present study is to investigate the effect of VGM on seismic response and force reduction factor of RC buildings designed to modern seismic codes and located near active faults. An extensive list of local and global structural response parameters is monitored for twelve multi-story RC buildings. This includes assessment of structural members shear response using a realistic ductility- and axial force-sensitive shear strength approach. Natural ground motions are applied with and without VGM. Natural earthquake records with moderate-to-high V/H ratio were selected and accelerograms with unusual features were avoided. The latter considerations are aimed to arrive at practical, rather than extreme, conclusions regarding the effect of VGM. Although the employed set of input ground motions (four input combinations of the Kobe ‘KBU’, Japan, 1995 and Loma Prieta ‘SAR’, U.S., 1989 events) are rather limited, the wide range of buildings and performance criteria as well as the rigorous analytical models and analysis approach (incremental dynamic collapse analysis) adopted in this study render the results indicative of response trends. It is also important to emphasize that the main objective of this study is not to quantify numerical design values. The objective is rather to focus on the importance or otherwise of including VGM in design of RC buildings and its impact on the member and the structure levels. SELECTION AND MODELING OF STRUCTURAL SYSTEMS Twelve buildings are selected in the current study to represent characteristics of contemporary medium-rise RC buildings designed to modern seismic codes. Different building heights (24 - 36 m) and structural systems (moment-resisting frames and frame-wall systems) as well as structural regularity are taken into consideration. The buildings are split into three sets based on their structural system, as shown in Table 1. Combinations of three design ductility classes (High, Medium and Low) and two design ground accelerations (0.15g and 0.30g) lead to the four investigated cases within each group. This selection was motivated by the desire to investigate the effect VGM on structures designed to different ductility requirements and ground acceleration levels. The buildings were designed and detailed in accordance with Eurocode 2 and 8 (Fardis, 1994). Characteristic cylinder strength for concrete and yield strength for steel of 25 N/mm2 and 500 N/ mm2, respectively, were used. The elastic fundamental periods ‘Telastic’, obtained from free vibration analyses confirm that the horizontal periods of the selected buildings (0.53 - 0.92) cover a wide range of spectral amplifications. The geometric characteristics of the structures and sample reinforcement details of an 8-story irregular building designed to ductility ‘Medium’ for a PGA of 0.30g are given in Fig. 1. Assessment of the seismic behavior of RC structures subjected to strong multi-axial ground motions requires the resolution of some fundamental difficulties. VGM mainly increases the fluctuation of axial forces in columns, which is superimposed on the forces generated from overturning. Since flexural and shear behavior of structural elements are strongly dependent on the axial force level, the fluctuation in axial forces may cause a significant variation in stiffness and strength. Therefore, refined analytical models and verified tools are needed. The finite element analysis platform used in this study has been developed and thoroughly verified at Imperial College, UK, and University Illinois at Urbana-Champaign, USA (Elnashai et al., 2006). Refined three-dimensional fiber modeling approach of the entire buildings was adopted for inelastic analysis. Each structural member is assembled using a number of cubic elasto-plastic elements capable of representing the spread of inelasticity within the member cross-section and along the member length. The latter rigorous modeling approach explicitly

accounts for the interaction between axial force and bending moment and monitors the shear supplydemand ratio during the multi-step analysis. Table 1. Characteristics of the investigated structural systems Group

Design PGA 0.30 0.15 0.30 0.15 0.30 0.15

IF RF FW

Design ductility H&M M&L H&M M&L H&M M&L

TH: Elastic period in horizontal direction.

0.70 m

Lc

LC

3 O 18 3 O 18

Eight Twelve Eight

TV: Elastic period in vertical direction.

0.70 m

0.50 m LC

5 O 20 3 O 18

No. of stories

LC

LC

4 O 18 3 O 18

TV (sec) 0.075 & 0.073 0.086 & 0.087 0.089 & 0.089 0.088 & 0.088 0.070 & 0.070 0.082 & 0.082

H: Design ductility high; M: Medium; L: Low.

0.70 m LC

7 O 16 3 O 18

TH (sec) 0.674 & 0.654 0.719 & 0.723 0.857 & 0.893 0.920 & 0.913 0.538 & 0.533 0.592 & 0.588

0.80 m LC

8 O 16 3 O 18

0.60 m

LC

LC

Lc

6 O 20 3 O 18

3 O 18

10 O 18

12 O 18

Lc

5 O 18 2 O 16

2 O 18 2 O 16

5 O 18 2 O 16

8 O 18 2 O 16

Lc

7 O 18 3 O 20

3 O 20

8 O 16 3 O 20

11 O 16 3 O 20

5 O 20

4 O 20

4 O 20

6 O 20

0.60 m

2nd floor beams 2 O 18 1 O 20

3 O 18

Lc

2 O 18 3 O 20

Lc

8 O 18 3 O 20

3 O 20 3 O 20

Lc

4 O 20 2 O 18

2 O 20 2 O 18

LC

LC

4 O 18 3 O 18

4 O 18

LC

6 O 18

LC

LC

2 O 20

2 O 20

6 O 18 2 O 20

7 O 18 2 O 20

2 O 20 1 O 14

2 O 20 1 O 14

3 O 20 1 O 14

2 O 20 4 O 20

LC

0.80 m

2 O 20 1 O 18

2nd Story

Col. 1

Col. 1

1st Story

1st Story

Ext.Col.

Ext.Col.

Ext.Col.

External Frame Col.1

External Frame

Ext.Col.

Ext.Col.

Int.Col.

Ext.Col.

Col.1

- The height of the typical floor is 3.0 m, with the exception of the ground

Ext.Col. 4.0 m

Int.Col.

Ext.Col.

Internal Frame X Int.Col.

Ext.Col.

Int.Col.

Internal Frame

Y

4.0 m

Int.Col.

Ext.Col.

story of the IF set, which is 4.5 m.

- Col.1 is cut-off at the ground story of the IF buildings. - Col.1 has the same cross section of Ext.Col. in the 12-story RF building. - The RC core of the FW buildings, (shown shaded) replaces the four central columns and Col. 1 of the frame structures.

Internal Frame 4.0 m

External Frame 4.0 m

0.80 m

8th Story

2nd Story

Ext.Col.

LC

1st floor beams Lc

8th Story

Ext.Col.

LC

Col.1 4.0 m

Ext.Col. 4.0 m

Ext.Col. 4.0 m

Col.1

Ext.Col.

- Solid slabs of 14 cm thickness are used in the frame buildings, while waffle slabs are employed in the FW structures.

4.0 m

Figure 1. Description of the investigated buildings and sample reinforcement details of IF-M-030 Based on anticipated critical response, dynamic analyses are conducted along the global X-axis for the frame buildings, and along the Y-axis for the frame-wall structures. Three limit state criteria are utilized to monitor global structural failure. These are: (i) an upper limit of the interstory drift (ID) ratio equal to 3%, (ii) formation of a column hinging mechanism and (iii) a drop in the overall lateral resistance by more than 10%. Two additional failure criteria on the member level are employed: (i) exceeding the ultimate curvature or (ii) the force-based shear failure. The latter is evaluated using a realistic ductility- and axial force-sensitive shear strength model (Priestley et al., 1994). The design code shear strength model is also employed for comparison after eliminating associated design-based safety factors. The adopted performance criteria are implemented in a versatile post-processing algorithm to directly monitor capacities and demands of shear and curvature and apply the performance

parameters during the response history analysis. Further information regarding the analytical modeling can be found elsewhere (Elnashai and Mwafy, 2002; Mwafy and Elnashai, 2001 and 2002). Inelastic response history analysis is performed using the above-mentioned natural horizontal ground motions applied with and without VGM. The acceleration response spectra of the natural records used in analysis are compared with the design spectrum in Fig. 2. The spectra are scaled to a PGA of 0.30g. The inelastic fundamental periods of vibration of the twelve buildings investigated herein are also depicted in Fig. 2. These were identified by Mwafy and Elnashai (2001) for eight seismic excitations and at different input ground motion levels. The average inelastic periods for the three groups of structures are 1.40, 1.75 and 0.9 sec, respectively. It is worth noting that a refined normalization approach is adopted in the current study, whereby all records are scaled to possess equal velocity spectrum intensity in the period range of the buildings. One of the advantages of this scaling approach is the reduction in response variability under different excitations, thus allowing the use of fewer input ground motions. It is observed that the spectral acceleration of the longitudinal component of Loma Prieta (SAR) at the period range 0.1-0.5 sec is significantly higher than Kobe (KBU). Amplifications of higher mode effects are therefore anticipated under the Loma Prieta horizontal component. It is also noteworthy that the spectra of the vertical components of Kobe (KBU) and Lome Prieta (SAR) were comparable before normalization. Employing the HGM scale factors to normalize VGM causes an observable reduction in the vertical component spectrum of Kobe (KBU) compared with Loma Prieta (SAR), as shown from Fig. 2. This approach was adopted to avoid changes in the V/H ratio of the records (1.09 and 1.56 for Loma Prieta and Kobe, respectively). The effect of the vertical component of Lome Prieta (SAR) is therefore expected to be more pronounced compared with Kobe (KBU). This is despite the fact that the PGA of the vertical component of Kobe (KBU) is higher than Loma Prieta (SAR). 1.6

Spectral Acceleration (g)

1.4 1.2

Design code elastic spectrum

Design code elastic spectrum

Loma Prieta (SAR) - H

Kobe (KBU) - H Kobe (KBU) - V

Loma Prieta (SAR) - V

Inelastic period range of the buildings

1 FW

FW

IF

0.8

Inelastic period range of the buildings IF

RF

RF

0.6 0.4 0.2

Period (sec)

0 0

0.5

1

1.5

2 0

0.5

1

1.5

2

Figure 2. Elastic response spectra (5% damping) of input ground motions scaled to a PGA of 0.30g along with the average inelastic period of the three groups of buildings IF, RF and FW VERTICAL PERIODS OF RC BUILDINGS Papazoglou and Elnashai (1996) suggested that the ratio of horizontal-to-vertical fundamental period of RC moment resisting frames up to an 8-story height varies from 2.5 to 7.0. Bozorgnia et al. (1998) reviewed and reported on the vertical response of twelve instrumented buildings recorded during the Northridge earthquake. Moderate vertical ground accelerations were recorded at the base of the buildings, ranging from 0.02 to 0.22g. The structures included steel, RC and base-isolated buildings with heights ranging from 2 to 14 stories. The identified vertical periods of the buildings were 0.075 to 0.26 sec. The period range of conventional RC buildings should be lower than the upper limit of 0.26 seconds observed in the latter study since the instrumented buildings included steel and base-isolated structures, which are more susceptible to the vertical vibrations. The results of the present study indicate that the ratio of horizontal-to-vertical ‘elastic’ period of the three groups of buildings investigated here are 8.6, 10.1 and 7.4, respectively. The periods of vibration of the buildings are given in Table 1. It is clear that this ratio is related to the height and the vertical stiffness of the structure. The maximum ratio and the longest vertical period are for the tallest buildings (the 12-story group of buildings), whilst the minimum ratio and shortest period is for the stiffest and lowest structural system (the 8-story FW structures). These results are consistent with previous studies reported above.

Comparison of the ratio of the horizontal-to-vertical fundamental period for the first and the third groups investigated here, which exhibit the lowest and the highest stiffness, indicates that this ratio is not significantly influenced by building characteristics. This implies that a wide range of buildings experiences approximately the same dynamic amplification during vertical excitation. Papazoglou and Elnashai (1996) concluded that the periods corresponding to the highest amplification range for vertical strong-motion records is 0.05 - 0.15 sec. The vertical periods of the twelve buildings investigated here and those reported in previous studies suggest that the period range for the majority of conventional RC buildings is less than 0.20 sec. This observation further suggests that the effect of VGM in the near-field is likely to be significant for a wide range of buildings. Therefore, as a practical and safe solution, RC buildings should be designed according to the maximum amplification of VGM. EFFECT OF VERTICAL GROUND MOTION ON SEISMIC RESPONSE Global Response Global response results of the twelve buildings investigated in the current study are compared for the cases of analysis with and without VGM at different levels of PGA. A large increase in top displacement, interstory drift and base shear is observed in several cases. The maximum increase in the latter response parameters at the design intensity is 14%, 22% and 15%, whilst at twice the design PGA it is 12%, 12% and 13%, respectively. The maximum effect of VGM is observed on the global response of the FW buildings when subjected to Loma Prieta (SAR). This is justified by the lower contribution of the lateral seismic loads to the global response of this group of buildings, particularly to deformations. Including VGM in analysis does not though show a clear trend in increasing or decreasing the global response. As expected, Loma Pieta (SAR) causes higher response compared with Kobe (KBU), particularly for the second and the third groups of building. It is confirmed that the V/H ratio does not reflect the actual contribution of VGM, which depends on characteristics of the structure and the vertical and horizontal ground motion. The extensive incremental dynamic collapse analysis undertaken in the current study yields several interesting observations. For instance, the interstory drift collapse limit state is frequently exceeded under a lower PGA level when employing VGM and HGM in analysis. This is coupled in several cases with an increase in the roof displacement and the base shear by up to 20%. The incremental dynamic analyses also enable tracing the effect of VGM at different PGA levels. Figs. 3 and 4 depict the relationship between PGA level and global response parameters (roof displacement, interstory drift and base shear) with and without VGM. These are presented for a sample building under the effect of the Loma Prieta record. The conclusions drawn above regarding the effect of VGM are confirmed from these figures. Including VGM in analysis does not result in a consistent trend. Notwithstanding, it is observed that VGM may lead to a reduction in global response parameters at a certain PGA level, while a significant increase in deformation demands results at higher intensities due to the increase in second order (P-Δ) moment, as shown from Fig. 3. It is confirmed that for medium and high-rise buildings, P-Δ effects may be significant in the presence of high vertical dynamic forces. It is also observed that the effect of VGM is not significant at lower PGA levels. The variability in the response at higher levels of seismic forces is due to the elongation in the horizontal and vertical periods of the buildings, which results in changes in the contribution of both VGM and HGM to the overall response according to the shape of the input motion spectra. The results confirmed that the common belief that the effect of VGM on global seismic response in insignificant may lead to considerable errors in estimating seismic demand. The response of the dual structural system shown in Fig. 4 is different than that of the frame structures. It is observed that the relationship between PGA and global response is almost linear. Clearly this is due to the conservatism of the design code for this type of structural systems since inelasticity is allowed only at the base of the wall and the response of the system remains nearly elastic. The behavior of the walls dominates the response of these buildings due to their higher stiffness compared

with perimeter columns. The effect of VGM is higher for the buildings designed to a PGA of 0.30g, particularly on the top displacement and interstory drift, which increase by 20% at a PGA of 0.80g. 1000

(a)

Top displacement (mm)

900

Building: RF-M030 Record: Loma Prieta (SAR)

800 700 600 500 400

[1] Loma Prieta (H) [2] Loma Prieta (H+V) Polynomial Fit of [1] Polynomial Fit of [2]

300 200 100

PGA (g)

0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

4.5

(c)

16000

3.5

14000

Base shear (kN)

Interstorey drift (%)

18000

(b)

4.0

3.0 2.5 2.0 1.5 1.0 0.5 0.2

0.4

0.6

0.8

1.0

10000 8000 6000 4000 2000

PGA (g)

0.0 0.0

12000

PGA (g)

0 0.0

1.2

0.2

0.4

0.6

0.8

1.0

1.2

Figure 3. Tracing the effect of VGM on the global response of the RF-M-030 building using incremental dynamic analysis: (a) top displacement; (b) interstory drift; (c) base shear 800

(a)

Top displacement (mm)

700

Building: FW-M030 Record: Loma Prieta (SAR)

600 500 400 300

Loma Prieta (H) Loma Prieta (H+V) Polynomial Fit of [1] Polynomial Fit of [2]

200 100

PGA (g)

0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

28000

4.0

24000

3.0

Base shear (kN)

Interstorey drift (%)

3.5

(b)

2.5 2.0 1.5 1.0 0.5 0.0 0.0

PGA (g) 0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

(c)

20000 16000 12000 8000 4000 0 0.0

PGA (g) 0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Figure 4. Tracing the effect of VGM on the global response of the FW-M-030 building using incremental dynamic analysis: (a) top displacement; (b) interstory drift; (c) base shear Member Response Earthquake forces may be applied upwards as well as downwards, thus subjecting structural members to unaccounted-for action if the naturally existing VGM is neglected in design. Columns may be

adversely affected if high compressive forces are developed or if axial forces changed to tension. In the presence of high vertical forces, the ductility demand also increases due to second order moments. Additionally, the ductility supply is significantly reduced by the presence of high compressive axial forces; hence extensive damage may result due to increased demand and reduced supply. The shear supply may be significantly affected by the variation in column axial forces, which may cause loss or reduction of the axial load contribution to shear strength. Sample results of the effect of VGM on a planted column are shown in Fig. 5. It is observed that maximum axial compressive forces increase by 35% at twice the design intensity. The deterioration in the response of this column under cyclic loading is clear from the axial force response history. It is confirmed from previous studies on the investigated set of buildings (Mwafy and Elnashai, 2001 and 2002; Mwafy, 2001) that the planted columns of irregular buildings exhibit very high curvature ductility demands, reflecting the high energy dissipated in these structural members. Although VGM slightly increases the variation in shear supply, it does not significantly influence the shear demand-supply response for these columns. Variation of axial force : (H)

(H+V)

(IF-M030)

100

Axial force (kN)

0

Record : Loma Prieta (SAR) PGA : 0.60g

-100

0

-200

15 s

External Frame

Internal Frame

-300 -400 -500 0

3

6

9

Time (sec)

12

15

Figure 5. Effect of VGM on the axial force variation of a planted column at twice the design PGA Fig. 6 depicts the axial and shear force demand-supply response histories of a second story internal column in the RF-M-030 structure when subjected to Loma Prieta (SAR) at twice the design PGA. It is clear that VGM increases the maximum axial compressive forces by 45%. Tensile forces are generated only when VGM is included in the analysis. This has however a marginal effect on the shear strength, which only decreases by 6%. It is clear that the margin of safety, estimated as the supply-todemand ratio using the shear strength model of Priestley et al. (1994), is high. As concluded by Mwafy and Elnashai (2006), columns designed to EC8 (2004) exhibit high overstrength due to the rigorous capacity design provisions imposed by EC8. In frame-wall structures, the effect of VGM on the axial force demand in walls is less significant. This is attributed to the dominant role of the coupled walls in resisting lateral forces for this class of structure, which leads to the attraction of high levels of axial forces towards the walls. Therefore, the contribution of axial forces generated by VGM becomes less significant (similar to the case in external columns). It is also noteworthy that although axial forces in columns are more influenced by VGM at higher stories due to the lower contribution of gravity and seismic forces, no shear failure is observed in these columns. In the design of the buildings investigated here, the cross-sectional dimensions of columns and walls were kept constant along the height to eliminate any potential plastic hinging at intermediate stories due to tapering. Clearly, this increases the margin of safety against shear failure modes and unintentionally protects the columns from shear failure due to vertical vibrations. At higher levels of PGA, the adverse effects of VGM on the response of vertical structural members are more pronounced. As shown in Fig. 7, axial compressive forces increase by 15% and tensile forces develop in an internal ground story column only when VGM is included. The variability of axial force and shear supply increases during the response time window corresponding to the VGM peaks. The susceptibility of vertical structural elements to failure due to the reduction in shear strength and excessive compressive stresses is confirmed. The former is more likely to occur if the instances of minimum axial compressive force and maximum shear demand coincide. It is also observed from the incremental dynamic analysis that neglecting VGM may result in a significant error in predicting

failure modes. The ultimate concrete strain is exceeded first at a PGA of 0.75g when the vertical component of Kobe (KBU) is included in the analysis of IF-L-015, whilst this failure mode is observed at a PGA of 0.97g under HGM only. Moreover, the PGA that causes first shear failure in the FW-M-030 building walls is reduced by 16% when including VGM, as depicted in Fig. 8. Variation of axial force : (H)

(RF-M030)

(H+V)

1000

Axial force (kN)

0


-1000 -2000

0

15 s

-3000

External Frame

Internal Frame

-4000 -5000 -6000 0

3

6

9

Shear force demand:

12

15

Shear force supply (EC2):

Shaer demand & supply (kN)

3200

3200

H

2800

Shear force supply (Priestley et al.): H+V

2800

2400

2400

2000

2000

1600

1600

1200

1200

800

800

400

400

0

0 0

3

6

9

Time (sec)

12

15

0

3

6

9

12

Time (sec)

15

Figure 6. Effect of VGM on shear response of a second story internal column Variation of axial force : (H)

(IF-L015)

(H+V)

1000

Record : Kobe (KBU) PGA : 1.0g

Axial force (kN)

0 -1000

4

19 s

External Frame

Internal Frame

-2000 Maximum vertical acceleration

-3000 -4000

4

4

7

10

13

Shear force demand: Shaer demand & supply (kN)

19 s

16

19


2100

2100

1800

1800

H

1500

Shear force supply (Priestley et al.):

H+V

1500

1200

1200

900

900

600

600

300

300

0

0 4

7

10

13

Time (sec)

16

19

4

7

10

13

Time (sec)

16

Figure 7. Effect of VGM on shear response of a ground story internal column

19

Variation of axial force : (H)

(H+V)

(FW-M030)

8000 6000


4000

Axial force (kN)

2000 0

0

15 s

External Frame

Internal Frame

-2000 -4000 -6000 -8000 -10000 -12000 1

4

7

Shear force demand:

10

13


Shaer demand & supply (kN)

8000 7000

Shear force supply (Priestley et al.):

8000

H

7000

6000

6000

5000

5000

4000

4000

3000

3000

2000

2000

1000

1000

0

H+V

0 1

4

7

Time (sec)

10

13

1

4

7

Time (sec)

10

13

Figure 8. Effect of VGM at first indication of shear failure in walls Effect of Vertical Ground Motion on Response Modification Factor As shown from the results presented above, yield and collapse may occur under lower PGA when the structure is subjected to HGM and VGM. Based on the definition of the response modification factor (R) proposed by Mwafy and Elnashai (2002) and Mwafy (2001), this may reduce the R factor, leading to higher seismic design forces. The mean values of the response modification factor ‘supply’ for the twelve buildings investigated in the present study are calculated and presented in Table 2. It is clear that the mean R factors are reduced by up to 18% under the effect of VGM. The most observable case is the R factor of IF-M-015, which is reduced by 21% when subjected to Kobe (KBU). The results confirm the inadequacy of the response modification factor calculations in the absence of VGM, especially for reinforced concrete structures. Table 2. Effect of vertical ground motion on the response modification factor (R) Reference IF-H-030 IF-M-030 IF-M-015 IF-L015 RF-H-030 RF-M-030 RF-M-015 RF-L-015 FW-H-030 FW-M-030 FW-M-015 FW-L-015

R (H)

R (H+V)

R (H+V) / R (H)

L

G

F

L

G

F

L

G

F

8.27 4.96 15.22 3.52 13.11 11.76 9.33 6.41 5.47 4.46 5.39 4.59

5.35 3.97 8.81 5.68 8.16 5.23 6.93 6.25 8.69 6.81 8.43 7.59

8.27 4.96 14.23 3.52 13.11 14.58 9.33 6.41 5.47 4.46 5.39 4.59

9.75 5.05 12.53 3.69 13.21 11.13 8.39 6.22 5.83 4.54 4.95 4.33

5.89 4.83 8.91 6.31 7.10 4.90 6.95 6.13 8.50 6.68 9.12 7.76

9.39 5.05 12.53 3.69 13.21 12.85 8.39 6.22 5.83 4.54 4.95 4.33

1.18 1.02 0.82 1.05 1.01 0.95 0.90 0.97 1.07 1.02 0.92 0.94

1.10 1.22 1.01 1.11 0.87 0.94 1.00 0.98 0.98 0.98 1.08 1.02

1.13 1.02 0.88 1.05 1.01 0.88 0.90 0.97 1.07 1.02 0.92 0.94

R= ag(at collapse)/ag(at yield).Ωd (Mwafy and Enashai, 2002) H+V: Horizontal plus vertical ground motions are used G: Global criteria are used

H: Only horizontal component of ground motions is employed L: Local criteria are employed to calculate R F: First observed yield and collapse criteria are employed to calculate R

CONCLUSIONS The effect of vertical ground motion (VGM) on the local and global seismic response and force reduction factor (R or q) of modern code-designed RC buildings in the vicinity of active faults was investigated in the present study. Application to a range of contemporary buildings, using refined analytical modeling, extensive dynamic-to-collapse analyses and rigorously-defined response parameters lend weight to the observations and conclusions of this study. The assessed response parameters included tracing the shear capacity-demand response of all structural members using a realistic time-dependent ductility- and axial force-sensitive assessment approach of instantaneous shear capacity. Natural ground motions with moderate-to-high V/H ratio were selected. Analysis under horizontal-only and horizontal plus vertical motion was undertaken. It is concluded that the VGM has a significant effect on the seismic response on both the member and the structure levels. The V/H ratio does not reflect the anticipated effect of VGM, which mainly depends on the characteristics of HGM and VGM, horizontal and vertical periods of the structure and intensity of both earthquake records. The effect of VGM increases when the contribution of the lateral seismic action is relatively small, such as in low-rise buildings and interior columns of taller structures at higher stories. The situation is even more critical in irregular structures. The results indicate that global response parameters may increase by up to 22% at the design PGA when the effect of VGM is included. The interstory drift collapse limit state was frequently reached at lower earthquake intensities with VGM. The contribution of VGM to global response was not constant at various PGA levels. VGM may reduce the response at lower intensity levels, while significantly increasing it at higher PGAs. The latter observation is more pronounced in taller buildings due to P-Δ effects. 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