Performance-based seismic assessment of a large concrete framed structure supporting multi-units of heavy compressors

Song Fong Jan1

1Principal Engineer, Bechtel Corporation, Houston, Texas, USA

Journal of Vibroengineering, Vol. 20, Issue 1, 2018, p. 494-502. https://doi.org/10.21595/jve.2017.19325
Received 15 August 2017; received in revised form 19 October 2017; accepted 28 October 2017; published 15 February 2018

Copyright © 2018 JVE International Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Abstract.

In a liquefied nature gas (LNG) plant, a large concrete framed structure supporting multi-units of heavy compressors was designed in accordance with ACI 318-08 code requirements and ASCE 7-05seismic loads. When applied to new structures, provisions of ACI 318 are intended to provide Life Safety (LS) performance for the Design Basis Earthquake (DBE). Due to the important function of the compressors, this study will perform a seismic assessment of the Table Top Pedestal to assure adequate capacity of preventing collapse from Maximum Considered Earthquake (MCE) and only having limited structural damage under a moderate (MOD) 20%@50 years earthquake event. In this study, the Linear Dynamic Procedure (LDP) of ASCE 41-13 is used for the seismic performance evaluation of the table top structure. The structural modeling parameters and acceptance criteria of structural performances are based on Chapter 10 of ASCE 41-13. Soil-structural interaction and P-Delta effects are considered in the analysis process. The response spectra of the three levels of seismic hazards of DBE, MCE and MOD earthquake were developed for response spectra analysis. The procedures presented in this study can be used as a general guideline for Performance-Based Design of most reinforced concrete structures located in industrial plants.

Keywords: performance-based, seismic, maximum considered earthquake, design based earthquake, compressor, reinforced concrete structure, linear dynamic procedure, industrial plants, P-Delta analysis, soil-structural interaction, life safety performance.

1. Introduction

In a liquefied nature gas (LNG) plant, it requires multiple compressor units of methane, ethylene and propane compressors in order to convert natural gas to LNG by cooling the liquid temperature to –270 °F. A typical concrete framed structure (also referred to as Table Top |Pedestal) supporting two trains of methane compressors as shown in Fig. 1 has been designed by Jan [1] in accordance with ACI 318-08[2] and ASCE 7-05 [3] code requirements. The maximum considered earthquake (MCE) in the plant site has a 2 % probability of exceedance in 50 years (a return period of 2475 years). The design base earthquake (DBE) is two-thirds of the of MCE. It is equivalent to an earthquake having a 10 % probability in 50 years (a return period of 475 years). For ordinary structures, life safety under a DBE hazard event are ensured by designing the structure for the effects of code-prescribed earthquake forces and by conforming to material design and detailing requirement set forth in the code. Due to the important function of the compressors, this study will perform a seismic assessment of the Table Top Pedestal to assure adequate capacity of preventing collapse from MCE and only having limited structural damage under a moderate (MOD) earthquake event of 20%@50 years (a return period of 225 years). The ground response spectra of the three levels of earthquake MCE, DBE and MOD are shown in Fig. 2.

Structural analysis of the Table Top Pedestal may be performed by using either linear dynamic procedure (LDP) or nonlinear dynamic analysis procedure (NDP) as provided in ASCE 41-13 [4] for performance-based seismic evaluations of structures. NDP is normally required for a tall building whose height exceeding the limit of building code (ASCE 7). Extensive international research and developments have been carried out on the tall building design in USA [5], Canada [6], Japan [7], China [8], Turkey [9] and Greece [10]. The structural response obtained from the nonlinear dynamic analysis results represent true structural performances under the earthquake event. However, NDP requires considerable efforts in mathematic modelling and tedious analysis process and interpretation of analysis results. An industrial structure such as the table top pedestal has little irregularity in the structure layout in general, thus the linear dynamic procedure is appropriate to be used for seismic performance evaluation of the structure. In general, LDP yields a more conservative design result than NDP design result as presented in Reference [11]. Mathematical modelling and analysis process for the linear dynamic procedure can be accomplished efficiently by using commercial available general finite element programs. Therefore, the linear dynamic procedure is adopted in this paper for carrying out the seismic performance assessment of the pedestal. The LDP is a practical and efficient approach for seismic performance based retrofitting of existing structures and is recommended to be used for analysis of new structures in the industrial plants.

Fig. 1. Finite element model – table top pedestal

 Finite element model – table top pedestal

Fig. 2. Earthquake ground response spectra

 Earthquake ground response spectra

2. The existing compressor table top structure

The three-dimensional finite element model of the concrete table top pedestal is shown in Fig. 1. The mathematic model consists of 1230 plate elements for deck slab, 2400 plate elements for mat and 80 line elements for 40 columns. The soil stiffness is represented by Winkler spring elements. In order to consider the effects of concrete cracking, shrinkage, and reinforcement slip, the effective component stiffness is reduced per Table 10-5 of ASCE 41. In this study, the modulus of elasticity of concrete Ec for all columns and deck slab are reduced to 0.3Ec. The structural design parameters in the original structural design [1] are summarized as follows:

Concrete structure:

– Mat: 93 ft×164 ft×4 ft, with #9 @ 12” top/bottom, total weight = 9200 kips,

– Deck size: 87 ft×128 ft×3.3 ft with #9 @8” top/bottom, total weight = 5500 kips,

– Columns: 40-3.3 ft squares, total weight = 1200 kips,

– Concrete maximum compressive strength f'c= 4ksi,

– Yield strength of reinforcing steel = 60 ksi,

– Critical damping ratio of concrete structure βc= 4 %.

Equipment:

– The table top supports two trains of methane compressors. Each train has one compressor and one gas turbine.

– Compressor: weight = 522 kips/unit, operating speed =104.5 cps,

– Gas turbine: weight = 370 kip/unit, operating speed = 64.7 cps.

Soil properties:

– Allowable soil bearing pressure = 2.5 ksf,

– Ultimate soil bearing pressure = 5 ksf,

– Critical damping ratio of soil βc= 10 %.

Seismic design parameters used in the original structural design:

– Soil site class “D”,

– Occupancy category III,

– Seismic design category “D”,

– Occupancy important factor of structure I= 1.25,

– Response modification factor R= 8 for special reinforced concrete moment frame per ASCE 7.

– Mapped Acceleration parameters:

• At short period (0.2 s) Ss= 1.12,

• At one second period S1= 0.48.

– Design spectral acceleration parameters:

• At short period (0.2 s) SDS= 0.79,

• At 1-second period SD1= 0.49.

3. Linear dynamic analysis procedure (LDP)

In this study, the modal response spectrum method was used to evaluate structural responses. The linearly elastic response spectra shown in Fig. 2 are not modified to account for anticipated nonlinear response. It is expected that the LDP will produce displacements that approximate maximum displacements expected during the selected Seismic Hazard Level but will produce internal forces that exceed those that would be obtained in a yielding building. Calculated internal forces typically exceed those that the building can sustain because of anticipated inelastic response of components. These forces are evaluated through the acceptance criteria of ASCE 41-13 Section 7.5.2, which include modification factors to account for anticipated inelastic response demands and capacities. In the criteria, a component is classified as either deformation controlled (ductile) or force controlled (non-ductile) elements. Moreover, structural elements are categorized as primary or secondary components. A primary component resists earthquake forces while a structural component not designed to resist earthquake forces is categorized as secondary component. In LDP, deformation and force controlled actions are evaluated using following criteria:

Deformation-controlled actions: mkQCEQUD,

Force-controlled actions: kQCLQUF,

where: m is the component demand modification factor to account for the expected ductility related to this action at the selected structural performance level, k is the knowledge factor to account for the uncertainty of collection of as-built data per 6.2.4 of ASCE 41-13, QCE is the expected strength of a component at the deformation level under consideration for deformation-controlled actions, QUD is the deformation-controlled design action due to gravity loads (QG) and earthquake loads (QE), QCL is the lower-bound strength of a component at the deformation level under consideration for force-controlled actions, QUF is force controlled design action determined by:

Q U F = Q G ± Q E C 1 C 2 J ,

where: C1 is the modification factor that relates the expected maximum inelastic displacements to displacements calculated using linear elastic response, C2 is a modification factor that considers the effect of pinched hysteresis shapes, cyclic stiffness degradation, and strength deterioration on maximum displacement response, J is the force delivery reduction factor, calculated as the smallest demand capacity ratio (DCR = QUD/QCE) of all components in the load path delivering forces to the component being examined.

4. Seismic performance objectives

As previous discussed, there are three seismic hazard levels considered in this paper. The corresponding structural performance levels per ASCE 43-13 guidelines are as followings:

Severe overall structural damage occurs under 2%@50 years (MCE) seismic hazard event. It is corresponding to the Collapse Prevention (CP) Structural Performance Level.

Moderate overall structural damage occurs under 10%@50 years (DBE) seismic hazard event. It is corresponding to the Life Safety (LS) Structural Performance Level.

Light overall structural damage occurs under 20%@50 years (MOD) seismic hazard event. It is corresponding to the Immediate Occupancy (IO) Structural Performance Level.

The 5 % damped acceleration spectra for the three seismic hazards are shown in Fig. 2. The component demand modification factors corresponding to the three structural performance levels are evaluated per ASCE 41-13.

5. Dynamic analysis and analysis results

The linear dynamic analysis procedure described in Section 3 is used in this study. The elastic response spectrum analyses for horizontal excitations in the orthogonal X and Y axes are performed for the three levels of earthquake events MCE, DBE and MOD. The seismic responses in the X and Y direction, QEx and QEy, are then combined with gravity load QG as:

Deformation-controlled actions:

Q U D = Q G + 1.0 Q E x + 0.3 Q E y ,
Q U D = Q G + 0.3 Q E x + 1.0 Q E y .

Force-controlled actions:

(1)
Q U F = Q G + 1.0 Q E x C 1 C 2 J + 0.3 Q E y C 1 C 2 J ,
(2)
Q U F = Q G + 0.3 Q E x C 1 C 2 J + 1.0 Q E y C 1 C 2 J ,

where: C1C2= 1.1 from Table 7-3 of ASCE 41 for period T between 0.3 and 1.0 seconds, J= 2.0 for MCE, 1.5 for DBE and 1.0 for MOD earthquake event based on section 7.5.2.1.2 of ASCE 41-13.

The following two gravity load conditions are considered in all above load combinations:

QG= 1.1(QD+QL) (Notes: QD= Dead loads, QL= Live loads),

QG= 0.9QD.

Based on the analysis results, the capacity demands of columns and deck slab under gravity loads are less than 80 % of nominal capacity of the components. Therefore, the vertical seismic effects are not considered in this study.

The fundamental natural frequencies of the soil supported table top structure are 2.57 cps and 2.80 cps in the two horizontal directions and 4.43 cps in the vertical direction. From the response spectra analysis, the maximum accelerations at the top deck slab are shown in Table 1. All acceleration responses are within 150 % of peak spectra accelerations. They appear to be within the acceptable floor acceleration limits for non-structural components.

Table 1. Acceleration responses at top deck slab

Peak Spectra Accel. (g)
Earthquake X-Excitation
Earthquake Y-Excitation
X -Horiz. Accel. (g)
Y -Horiz. Accel. (g)
Z -Vertical Accel. (g)
X -Horiz. Accel. (g)
Y -Horiz. Accel. (g)
Z -Vertical Accel. (g)
DBE
0.79
0.94
0.41
0.38
0.38
1.16
0.50
MCE
1.18
1.41
0.61
0.54
0.69
1.75
0.73
MOD
0.39
0.47
0.20
0.19
0.23
0.58
0.28

The maximum displacement at the top deck slab are shown in Table 2. The story height between the top of deck slab to the top of mat is 23 ft. The allowable drifts are set to be 3 %, 2 % and 1 % of story height for MCE, DBE and MOD earthquake levels, respectively. All displacements shown in Table 2 are within the allowable limits.

The dynamic analysis results of internal forces of columns and deck slab are summarized in Tables 3 and 4.

Table 2. Displacement responses at top deck slab

Allowable drift (in)
Earthquake X-excitation
Earthquake Y-excitation
X -horiz. disp (in)
Y -horiz. disp (in)
Z -vertical disp (in)
X -horiz. disp (in)
Y -horiz. disp (in)
Z -vertical disp (in)
DBE
5.52
1.15
0.46
0.34
0.61
1.68
0.38
MCE
8.28
1.75
0.68
0.51
0.92
2.52
0.58
MOD
2.76
0.58
0.23
0.17
0.31
0.84
0.19

Table 3. Column internal forces

Loads
P (kips)
M x (kips-ft)
M y (kips-ft)
V x (kips)
V y (kips)
Remarks
DBE
1.1 QD+L
401
13
5
9
18
P m a x
1.1 QD+L+E
260
3275
1776
140
262
Flexural
682
2181
1966
161
171
P m a x
0.9 QD+E
18
2801
1863
144
214
Flexural
D + E /C1C2J
461
921
2201
203
86
Flexural
571
1407
1144
94
110
P m a x
0.9 D+E/C1C2J
94
1412
1331
108
110
Flexural
MCE
1.1 QD+L+E
291
4963
2441
192
398
Flexural
822
3164
3011
245
247
P m a x
0.9 QD+E
–69
4266
2618
202
327
Flexural
D + E /C1C2J
478
1009
2456
227
98
Flexural
592
1557
1303
107
122
P m a x
0.9 D+E/C1C2J
71
1612
1475
120
126
Flexural
MOD
1.1 QD+L+E
231
1584
1109
88
127
Flexural
541
1198
923
76
94
P m a x
0.9 QD+E
104
1334
1106
87
102
Flexural
D + E /C1C2J
401
832
1072
86
65
Flexural
540
1407
1198
76
94
P m a x
0.9 D+E/C1C2J
126
1134
1131
92
88
Flexural

Table 4. Top deck slab element stress resultants

Loads
M x (kips-ft/ft)
M y (kips-ft/ft)
M x y (kips-ft/ft)
V x (kips/ft)
V y (kips/ft)
Remarks
DBE
1.1 QD+L+E
100
140
60
90
90
Flexural
0.9 QD+E
90
90
50
75
120
Flexural
D + E /C1C2J
60
90
30
50
50
Flexural
0.9 D+E/C1C2J
60
60
25
40
40
Flexural
MCE
1.1 QD+L+E
120
180
70
100
100
Flexural
0.9 QD+E
100
150
60
120
120
Flexural
D + E /C1C2J
80
100
40
60
60
Flexural
0.9 D+E/C1C2J
70
80
30
45
45
Flexural
MOD
1.1 QD+L+E
75
70
25
55
50
Flexural
0.9 QD+E
60
60
20
50
45
Flexural
D + E /C1C2J
50
60
24
35
35
Flexural
0.9 D+E/C1C2J
40
50
20
30
30
Flexural

6. Seismic performance assessments

The steps for seismic performance evaluation of the concrete structural components in the linear dynamic analysis procedure are as following:

Step 1: Classify components as a Primary or Secondary components.

All columns and the deck slab of the table top structure are considered as primary components. They are required to resist seismic forces and accommodate deformations for the structure to achieve the selected Performed Level.

Step 2: Classify components as deformation-controlled or force-controlled actions.

Different actions for a same element can be classified in different category. For instance, shears in beams and columns are considered as force-controlled actions. However, bending moments in columns and beams can be considered as force or deformation-controlled actions depending on the amplitude of the axial force.

Step 3: Determine component properties.

The Lower-Bound material properties of the table top structure are concrete compressive strength fc'= 4 ksi and reinforcing steel yield strength fy= 60 ksi. The expected strength properties are fce'= 1.5·4 = 6 ksi and fye= 1.25·60 = 75 ksi per Table 10-1 of ASCE 41-13. Where evaluating the behavior of deformation-controlled actions, the expected material strengths are used. Where evaluating the force-controlled actions, the lower-bound material strengths are used. Calculations of component design strength are in accordance with ACI 318-08 with an exception that the strength reduction factor φ is taken as unity.

All column cross-sections are 40 in squares with 28-#9 longitudinal reinforcement and 6-#4 shear tie legs with 135° seismic hooks. The spacing of transvers reinforcement so is 5 in. The effective depth of column dc= 36 in. The following are calculated column properties and strength:

– Gross area Ag= 1600 in2, Total longitudinal reinforcing area = 28 in2,

– Nominal axial load strength at zero eccentricity Po= 1600·4 = 6400 kips,

– Flexural reinforcement ratio ρs= 0.0175,

– Arear of shear reinforcement Av= 6·0.2 = 1.2 in2,

– Shear reinforcement ratio ρv= 1.2/(40·5) = 0.006.

– Shear strength of column: Vs=Av·fy·dc/so= 1.2·60·36/5 = 605 kips, Vc=f'c·40·36 = 182 kips,

– Total shear strength Vo=Vc+Vs= 787 kips,

The deck slab has a uniforms thickness t= 40 in. It was provided with #9 @ 8 in longitudinal reinforcements at top and bottom faces. The following are calculated slab properties and strength:

– Longitudinal reinforcing area = 1.33 in2/ft top and bottom,

– Flexural reinforcement ratio ρs= 0.0031.

Step 4: Determine component demand modification factor m for deformation-controlled actions.

Determination of m-factors for columns are based on the criteria provided in Tables 10-9 of ASCE 41-13. The failure mode of columns is considered as condition i (flexure failure) since the column transvers reinforcement ratio ρv= 0.0065 > 0.002 and the ratio of shear ties spacing to column depth so/dc= 5/37 = 0.135 < 0.5. The evaluated m-factors are shown in Table 5. In the table, P is the axial force action.

Table 5. Column m-modification factors

P (kips)
P / A g f ' c
p v
m -factors
DBE
682
0.107
0.006
2.49
MCE
822
0.128
0.006
2.94
MOD
540
0.084
0.006
2.02

Determination of m-factors for deck slab are based on the criteria provided in Table 10-16 of ASCE 41. The evaluated m-factors are shown in Table 6. In the table, Vg is the gravity shear acting on the critical shear sections and Vo is the direct punching shear strength defined by ACI 318.

Step 5: Check component capacities for deformation-controlled actions.

The acceptance criteria for deformation-controlled actions is:

m k Q C E Q U D .

For the table top structure, the knowledge factor is 1.0 since the structural design meets the benchmark requirement of Tables 4 and 5 ASCE 41-13. Calculations of component strength are based on the expected strength material properties. The allowable m-modification factors for columns and slab are calculated in Tables 5 and 6. The deformation-controlled actions caused by the combination of gravity load QG and earthquake forces QE are presented in Tables 3 and 4. The expected strength QE of component deformation-controlled action of an element are determined considering all coexisting actions on the component from load combinations as discussed in Section 3. The component capacity checks are summarized in the Tables 7 and 8. In Table 7, P is column axial force and Mu is algebra sum of the biaxial bending moments for the square columns. In Table 8, Mu is bending moments with consideration of twisting moment in the slab. All components demand capacity ratios (DCR) are less than the allowable m-modification factors and therefore, achieve the seismic performance objectives.

Table 6. Top deck slab m-modification factors

Column locations
Seismic levels
V g (kips)
V o (kips)
DCR Vg/Vo
Continuity reinforcement
m -factors
Corner
DBE
312
906
0.34
yes
2.15
MCE
312
906
0.34
yes
2.48
MOD
312
906
0.34
yes
1.15
Side
DBE
380
1750
0.22
yes
2.45
MCE
380
1750
0.22
yes
2.93
MOD
380
1750
0.22
yes
1.45
Interior
DBE
401
2331
0.17
yes
2.54
MCE
401
2331
0.17
yes
3.08
LOW
401
2331
0.17
yes
1.58

Table 7. Summary of column capacity check for deformation-controlled actions

°
Load combinations
P (kips)
M u (Mx+My)
(kips-ft)
M o (kips-ft)
DCR (Mu/Mo)
Allowable m-factor
Remarks
DBE (LS)
1.1D+E
260
5051
3300
1.53
2.49
Acceptable
0.9D+E
18
4767
2900
1.64
2.49
Acceptable
MCE (CP)
1.1D+E
294
7404
3500
2.12
2.94
Acceptable
0.9D+E
–194
6884
2800
2.46
2.94
Acceptable
MOD (IO)
1.1D+E
303
2693
3500
0.77
2.02
Acceptable
0.9D+E
187
2440
3100
0.79
2.02
Acceptable

Table 8. Summary of top deck slab capacity check for deformation-controlled actions units

Load
combinations
M u (My+Mxy)
(kips-ft/ft)
M n
(kips-ft/ft)
DCR
M u /Mn
m -factor
Remarks
DBE (LS)
1.1D+E
200
432
0.46
2.15
Acceptable
0.9D+E
140
432
0.32
2.15
Acceptable
MCE (CP)
1.1D+E
250
432
0.58
2.48
Acceptable
0.9D+E
210
432
0.49
2.48
Acceptable
MOD (IO)
1.1D+E
95
432
0.22
1.15
Acceptable
0.9D+E
80
432
0.19
1.15
Acceptable

Step 6: Check component capacities for force-controlled actions.

The acceptance criteria for force-controlled actions is:

k Q C L Q U F .

Axial forces and shears in columns and slabs are force-controlled actions. Calculations of component strength are based on the lower bound material properties. Tables 9 and 10 present summaries of capacity checks for columns and top deck slab, respectively. The demand capacity ratios (DCR) are less than 1.0. Therefore, the capacity of the table top pedestal meets the seismic performance objectives.

Table 9. Summary of column capacity check for force-controlled actions

Loads
P (kips)
P o (kips)
D C R = P / P o
V (kips)
V o (kips)
D C R = V / V o
D + E C 1 C 2 J
DBE
571
6000
0.095
145
189
0.77
MCE
564
6000
0.094
162
189
0.86
MOD
540
6000
0.090
121
189
0.64

Table 10. Summary of top deck slab capacity check for force-controlled actions

Loads
Beam shear (kips/ft)
Punching shear (kips)
V (kips)
V o (kips)
D C R = V / V o
V u
V o
D C R = V u / V o
D+E/C1C2J
DBE
71
162
0.44
571
906
0.63
MCE
141
162
0.87
592
906
0.65
MOD
64
162
0.39
540
906
0.60

Per ASCE 41-13, the capacity of soil bearing pressure shall be evaluated as force-controlled actions. The calculated soil bearing pressure are in allowable limits as shown in Table 11.

Table 11. Foundation bearing capacity

Loads
Soil bearing pressure (ksf)
Allowable bearing pressure (ksf)
Gravity
Gravity
1.75
2.5
D+E/C1C2J
DBE
2.75
5.0
MCE
2.90
5.0
MOD
2.56
5.0

7. Conclusions

Based on the assessment of seismic performance presented in this study, it is concluded that the concrete compressor table top structure can provide life safety structure performances under a design basis earthquake event, has adequate capacity of preventing collapse from a maximum considered earthquake event, and has only limited structural damage under a moderate earthquake event.

The Linear Dynamic Procedure provided in ASCE 41-13 is a practical procedure for seismic performance assessment of industrial plant structures. This procedure can achieve performance-based seismic design without requiring highly sophisticated non-linear dynamic analysis program which is still under research and development. The analysis steps presented in this study for using linear dynamic analysis procedure can be applied for seismic performance-based retrofitting of reinforced concrete structures.

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