1 Introduction

Structures, e.g., tanks, vessels, reactors, chimneys, flares, pipelines etc., in oil refineries constitute critical infrastructure for economy and environment. Failure, usually non-anticipated or even considered as unprecedented, of such infrastructure can be accompanied with severe losses, extensive damage or even a number of casualties. Therefore, the design, construction, inspection, maintenance and repair of such infrastructure is of outmost importance especially for the cases of extreme loading conditions, such as that caused by floods, tsunamis, blasts and earthquakes. In many places worldwide, oil refineries have been constructed in earthquake-prone areas, raising, thus, skepticism and public awareness towards potential seismic risk issues. The examples of extensive damages to the oil refineries of Japan after the 2003 Tokachi-Oki (Zama et al. 2008) and the 2011 Tohoku earthquakes (Hatayama 2015) and to those of Turkey after the 1999 Kocaeli (Suzuki 2002) earthquake, are perhaps the most serious ones in the modern history of oil industry.

On the basis of the damages induced by the aforementioned earthquake events and by other ones as well, the engineering community has shifted towards a seismic performance assessment of existing refinery facilities. In this sense, the most common assessment studies are focused on estimating the behavior of any type of structure (including secondary ones like equipment, piping etc.) met in such facilities and on categorizing damage per type of structure, e.g. (Karagiannakis et al. 2022). On the other hand, other studies have explored the possibility of applying seismic isolation or other energy-dissipating devices as a measure of seismic risk reduction in oil refineries, e.g. (Drosos et al. 2019; Gabbianelli et al. 2023).

In general, studies related to the seismic evaluation of refinery facilities are of outmost importance if one realizes the variation in design and construction practices applied in various countries. Nevertheless, this variation is justified due to the geologic, geotechnical, seismic, environmental and structural conditions. Therefore, it seems natural that most petrochemical operating companies rely on their self-developed seismic guidelines.

Not only tanks or piping, but also several other structures in oil refineries can be seriously damaged if stricken by an earthquake beyond the design basis one. Within the refinery facilities there are large-scale building structures, which are mainly used to support bulky mechanical equipment and long pipelines. Among such structures are high-rise stacks (Moharrami 2014; Zhou et al. 2015; Karaferis et al. 2022) and tall frames, made of reinforced concrete (RC) or steel. The latter support catalytic reactors and are seldom constructed as vertically mixed structures, i.e., RC frames are constructed up to some elevation and steel braced frames continue. It is recalled that modern seismic codes, do not provide specific recommendations for the seismic design of vertically mixed RC-steel structures, but rely instead on the seismic design performed separately for their RC and steel parts.

Such a mixed RC-steel structure that supports a reactor is studied herein. In particular, a 3D numerical model of this structure is created and static pushover and dynamic non-linear (NLTH) analyses are conducted in order to investigate the seismic response of the structure as well as to verify its seismic design and possible failure issues. The design and integrity of the mixed RC-steel structure is assessed by specific response metrics, i.e., the base shear, the maximum displacement and acceleration at specific points of the structure, and the stresses induced to the shell of the reactor.

The structure under study bears several installations including piping and mechanical ones. Therefore, it is should be stressed that seismic analyses conducted herein can only provide an assessment and not a real safety evaluation of the structure. The latter is affected by the actual condition of the installations at the time of the assessment, i.e., the seismic response of the structure strongly depends on the operating status of the installation at the time that the earthquake occurs.

2 Design and description of structure

2.1 Geometry and materials

Figure 1a presents the structure under study. The novelty behind this structure is that it is a vertically mixed one, i.e., it consists of both steel and RC members, contrary to the common practice of employing exclusively steel or RC members. The structure has been designed to support mainly a naphtha reactor but also all the necessary piping system and service platforms around it. Figure 1b displays the whole structure, including the equipment and piping systems. The total height of structure is 64.90 m in which RC moment frames elevate from + 0.00 m to + 23.175 m, and steel braced frames continue up to + 64.90 m. The longitudinal dimension of the frames is 8.00 m, whereas their transverse dimension is 7.80 m.

Fig. 1
figure 1

a The mixed RC-steel structure; b The whole structure including its equipment and piping systems; c Detail of the reactor and concrete slab

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The dimensions of the four columns of the RC frame are 1.40 m × 1.40 m, whereas those of the beams have as follows: 0.70 m × 0.90 m at elevation + 5.75 m, 1.20 m × 1.20 m at elevation + 10.025 m, and 0.80 m × 1.00 m at elevation 16.025 m. At elevation + 20.57 m there is a concrete slab of 1.20 m thickness and constitutes the anchoring elevation of the reactor. The anchorage is achieved by 32 anchor bolts. In the middle of the slab, there is a hole of 2.60 m diameter, permitting the installation of the reactor and at elevation + 23.175 m is the anchoring elevation of the steel structure. Figure 1c presents a detail of the reactor and the concrete slab.

Concrete and steel reinforcement grades are C25/30 and B500c, respectively according to EC2 (Εurocode 2, 2005) material classification. The diameter/grade of the anchor bolts used for anchoring the reactor (embedded in slab) are hot dip galvanized M56/8.8 (see Appendix), whereas those for anchoring the steel structure are hot dip galvanized M48/8.8. The grade of the structural steel material is S275 JR/J0 according to Eurocode 3, 2009, having, thus, a minimum yield stress fy = 275 N/mm2. Standard steel sections (Androic et al. 2000) are used and have as follows: HEA, HEB, HEM for columns, IPE for main and secondary beams, HEA for the vertical braces, etc. The steel material of the shell of the reactor is SA 387 GR.22 CL.2 which corresponds to fy = 310 N/mm2 and tensile strength fu = 515 N/mm2. This material type is commonly used in petrochemical industry for equipment operating in high temperatures and the allowable strength values are evaluated according to ASME BPVC Section VIII (Bpvc Sect. and VIII, Division 1, 2019). The design temperatures for the shell of the are 549–580 °C.

The design details of all RC and steel members of the structure are presented in Appendix (Figs. 25, 26, 27, 28, 29). Referring to the steel part of the structure, in order to handle stability issues, the steel frames are braced at both horizontal directions, except at elevation from + 58.50 m to + 64.90 m, where moment frames exist on the longitudinal direction of the structure.

2.2 Modeling & assumptions

A detailed linear elastic numerical model of the structure was developed in computer software SAP 2000 to carry out the design checks. The same software is then used for the purposes of the non-linear analyses conducted, offering direct visualization and post-processing of the numerical results.

Steel and RC members are modelled as centerline frame elements. The RC members are modeled as typical beam-column elements, whereas the concrete slab is modeled using shell elements. The RC columns are considered as fixed at their base (foundation level). The reactor has been assumed as pinned to the slab in order to take into consideration the most unfavorable case for displacements. However, a fixed-connection was considered for the actual design of the connection of the reactor to the slab (Fig. 25 in Appendix). Due to the presence of vertical steel braces, steel columns are modeled as pinned to the RC columns at the point of transition from the RC part to the steel part of the mixed structure. Similarly to the connection of the reactor to the slab, a fixed-connection was considered for the actual design of the connection of the steel columns (Fig. 29 in Appendix). Moreover, being part of braced frames, steel beams are also modelled as pinned. Vertical and floor steel braces are modeled as truss elements with pinned ends. Modeling of gusset plates and column splices is omitted.

As shown in Fig. 2b, the steel reactor is modeled using shell elements with variable thickness (from 90 to 45 mm). With reference to Fig. 3, steel sections that are utilized as “guides” exist at elevations + 41.40 m and + 49.40 m, in order to prevent the lateral displacement of the reactor. These guides are modeled using link elements (of only-compression type (SAP 2000)) that rigidly connect the nodes of the reactor with those of steel structure. As shown in Fig. 3, there is a gap of 10 mm between the reactor and the steel plate. This gap is necessary for the free thermal expansion of reactor from ambient temperature to design temperature. The design temperature of the reactor is 549 ºC, therefore, the 10 mm gap is considered to be filled due to thermal expansion of reactor. Thus, the steel plate is assumed to be constantly in touch with the reactor in the model.

Fig. 2
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a Detailed model of structure in (SAP 2000). b Detail of shell elements of reactor in (SAP 2000)

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Fig. 3
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Typical plan detail for guides, elevations + 41.40 m and 49.40 m

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2.3 Loads analysis & loading combinations

For the analysis of the structure under study dead, live, wind, equipment, thermal, maintenance and seismic loads are considered by performing the required loading combinations. Details with respect to the type and values of the aforementioned loads are provided in the following paragraphs.

2.3.1 Dead loads (DL)

The self-weight of all members is considered on the basis of the values given below. The nominal value of self-weight for the steel members is increased by 10% in order to take into account the actual connections between members.

  • Concrete density 25.0 kN/m3.

  • Steel density 78.5 kN/m3.

  • Galvanized steel gratings as uniform distributed area load of 0.40 kN/m2.

  • Galvanized steel handrails as linearly distributed load of 0.30 kN/m

2.3.2 Live loads (LL)

The live loads considered refer to persons for maintenance and repair operations, portable machinery, tools, furniture, business machines, archive materials, materials temporarily stored during maintenance as well as materials normally stored during operation such as tools, maintenance equipment, catalysts and chemicals. In particular, the live loads assumed are: 2.50 kN/m2 for operating floors, 5.00 kN/m2 for stairs and exit ways, 6.00 kN/m2 for control rooms and 0.45 kN/m for vertical ladders. As typically required, for the calculation of seismic mass, 30% of live loads are considered in conjunction with the dead loads.

2.3.3 Piping loads

In this load category, all kind of loads that are acting on structure and are produced by the operation of the equipment and pipes are included. It should be noted that a special study by piping and mechanical engineer experts is required in order to specify the values of these loads. More specifically, there are three types of such loads: a) the operating piping loads (EO), b) the erection piping loads (EE) and c) the test piping loads (ET). These loads are modeled as concentrated vertical forces on the beam elements of the structure. Moreover, for the erection piping loads, the equipment and pipes are considered as empty, whereas an ‘‘under pressure condition’’ is assumed for the operating and test piping loads. Figure 4 shows representative values of the operating piping (a) and test piping (b) loads on the structure at elevation + 41.40 m.

Fig. 4
figure 4

a operating piping loads (kN) and b test piping loads (kN) at elevation + 41.40 m

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2.3.4 Thermal loads

They refer to horizontal loads that are caused by temperature variations and include three different types: a) loads caused by variation of ambient temperature (TLT). For all steel members of the structure, a uniform temperature component ± 20 ºC is applied; b) Pipe anchor loads (TLS) caused by varying pressure per pipe size and liquid and c) friction loads (FRL) caused by thermal expansion of equipment and pipes. The values for the b) and c) types of thermal loads are provided by mechanical engineer experts.

2.3.5 Maintenance loads (ΜL)

Correspond to all operating floors of structure and refer to persons for maintenance and repair operations, portable machinery, tools, furniture, business machines, archive materials, materials temporarily stored during maintenance as well as materials normally stored during operation such as tools, maintenance equipment, catalysts and chemicals. Maintenance loads are similar to live loads, referring to general maintenance activities of piping and/or equipment on structure that occur periodically. These loads are considered as uniform area loads equal to 5.00 kN/m2.

2.3.6 Wind loads (WL)

Wind actions are calculated in accordance with EC1 (Eurocode 1, 2005) considering the structure as open. In particular, the fundamental value of the basic wind velocity is Vb,0 = 33 m/s, where cdir is the directional factor equal to 1.0 and cseason is the season factor equal to 1.0. Thus, the basic wind velocity is: Vb = cdir·cseason·vb,0 = 33 m/s. Furthermore, the values Z0 = 0.01 m and Zmin = 1.00 m corresponding to Terrain Category “I” are assumed, and the peak velocity pressure is given by:

$$ q_{p} \left( {z_{{}} } \right) = \left[ {1 + 7I_{v} \left( z \right)} \right] \cdot \frac{1}{2}\rho_{{}} {\text{v}}_{{\text{m}}}^{{2}} \left( z \right) = c_{e}^{{}} \left( z \right) \cdot q_{b}^{{}} $$

in which the mean wind velocity vm(z) should be determined using the formula vm(z) = cr(ze)·co(ze)·vb. In this formula, co(ze) is the orography factor (equals 1.0) and cr(ze) is the roughness factor given as:

\({C}_{r}\left({Z}_{e}\right)={k}_{r}\times ln\left(\frac{{Z}_{e}}{{Z}_{0}}\right)\), where \({k}_{r}=0.19\times {\left(\frac{{z}_{0}}{{z}_{0,II}}\right)}^{0.07} and\, {z}_{o,II}=0.05 m\)

The wind turbulence intensity is equal to:

$${I}_{v}\left(z\right)=\frac{{\sigma }_{\nu }}{{v}_{m}(z)}=\frac{{k}_{1}}{{c}_{o}\left(z\right)\times \text{ln}(z/{z}_{0})} $$

for zmin ≤ z ≤ zmax.

$${I}_{v}\left(z\right)={I}_{v}({z}_{min})$$

for z ≥ zmin. where kl turbulence factor is equal to 1.0, Co(Z) is the orography factor (equal to 1.0) and ρ = 1.25 kg/m3 is the air density. The wind pressure acting on surfaces, evaluated at height “Z”, is calculated by the following equation (Eurocode 1, 2005):

$$ W = q_{p} (z) \cdot C $$

where qp (z) is peak velocity pressure at reference height z, and C is the pressure coefficient and equals 2.0. The wind loads for the structural members are modeled as distributed loads while those for equipment and piping as concentrated forces.

2.3.7 Earthquake loads (EL)

Earthquake loads on structure has been evaluated in accordance with the Greek Seismic Code (EAK 2000). In particular, the horizontal elastic response spectrum employed is described by the following equations:

$$ {\Phi }_{d} \left( T \right) = \gamma_{1} \cdot A \cdot \left[ {1 + \frac{T}{{T_{1} }} \cdot \left( {\frac{{n \cdot \theta \cdot \beta_{o} }}{q} - 1} \right)} \right]\, for \,0 \le T < T_{1} $$
$$ {\Phi }_{d} \left( T \right) = \gamma_{1} \cdot A \cdot \left( {\frac{{n \cdot \theta \cdot \beta_{o} }}{q}} \right) for T_{1} \le T < T_{2} $$
$$ \Phi_{d} \left( T \right) = \gamma_{1} \cdot A \cdot \left( {\frac{{n \cdot \theta \cdot \beta_{o} }}{q}} \right) \cdot \left( {\frac{{T_{2} }}{T}} \right)^{{{\raise0.5ex\hbox{$\scriptstyle 2$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}}} for\, T > T_{2} $$

where \({\Phi }_{d}\left(T\right)\) is the design spectral acceleration, A is the ground seismic acceleration calculated as α x g (α = 0.24 g for seismic hazard zone II), q is the behavior factor (taken as 1.5 for both directions, η is the correction factor relevant to damping ratio, \({\gamma }_{1}\) is the importance factor (equals 1.3), T is the fundamental period of the structure, T1 and T2 are the characteristic periods (0.15 s and 0.60 s, respectively), \(\theta \) is the foundation coefficient (equals 1.0) and \({\beta }_{o}\) is the spectrum amplification factor (taken as 2.5 for all types of ground and structures). The damping correction factor η is calculated by the formula:

$$\eta =\sqrt{\frac{7}{2+\zeta }}\ge 0.7$$

where \(\zeta \) is the critical damping ratio (2.0% for welded steel structures, 4.0% for bolted steel structures and 5.0% for RC structures according to EAK (2000); Eurocode 8, 2004)). For the structure under study, the critical damping ratio is 2.0%, because with respect to the total mass of the structure the steel members are dominant and between 2.0% and 4.0%, the lowest ratio is selected.

2.3.8 Loading combinations

The loading combinations are defined in accordance with Eurocode 1, 2005 and PIP STC01015 (2017), and are associated with specific limit states. More specifically,

  • The elevated structures (RC & steel parts) and foundations shall be designed for the Ultimate Limit State (ULS).

  • Static equilibrium check shall be done for Ultimate Limit State (EQU) loading combination.

  • The maximum deflections in the structure shall be checked for the Serviceability Limit State (SLS).

All loading combinations needed for ULS and SLS are presented in Appendix, in Tables 5 and 6, respectively. In these tables, the specific loading combinations associated with different states, i.e., erection and construction, erection and accidental earthquake, operating, accidental operating, hydraulic test, and maintenance, are also provided.

Table 1 The first three natural periods of structure
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2.4 Design checks

2.4.1 Design checks for steel members

The steel members of the structure are checked according to Eurocode 3 (2009) under ULS loading combinations and their utility (stress) ratio is found to be under 1.0. Buckling checks were performed for all steel members. For the majority of steel elements, the governing combinations are those of Operating & Accidental Earthquake load combinations (see Appendix). Furthermore, the steel frames are checked under the ULS loading combinations against global (sway) imperfections (Eurocode 3, 2009). For steel frames sway imperfections may be disregarded if (Eurocode 3, 2009): HED ≥ 0.15VED, where HED and VED are the total design horizontal load transferred by the storey (storey shear) and the total design vertical load on the frame transferred by the storey (storey thrust), respectively. On the basis of the HED and VED values found, the aforementioned inequality is satisfied and sway imperfections are disregarded.

Displacement and deflection are checked for the SLS loading combinations. More specifically, a total horizontal displacement check for the structure is firstly performed. The admissible horizontal displacement (corresponding to the damage limit state) should be less than H/300, where H is the total height of structure), for frames supporting industrial equipment. Then, an interstorey drift check (or equivalently a displacement check) at both horizontal directions, x and y, is performed at each elevation of the structure. For this check, the admissible horizontal displacement should be less than h/150 (h is the interstorey height). Regarding the damage limitation check under the operating and accidental earthquake loading combinations of SLS, the admissible displacement should satisfy the 0.0075∙h limit for both x and y directions.

The vertical deflection for beams should not exceed: i) L/500 for floor beams supporting equipment; ii) L/250 for floor beams not supporting equipment and iii) L/150 for cantilevers not supporting equipment, where L is the length of the beam.

The allowable values for the displacement and deflection checks mentioned above, are those required by industrial practices and guidelines for equipment structures at refineries (PIP STC01015 2017; Guidelines for Seismic Evaluation and Design of Petrochemical Facilities 2011).

2.4.2 Design checks for RC members and anchor bolts

RC members, i.e., columns, beams and slabs are verified according to Εurocode 2 (2005) and EKOS (2000) under the ULS loading combinations for biaxial bending, axial and shear forces for columns, bending and shear for beams and punching shear for slabs. The damage limit state of the RC part of the structure is checked under the SLS accidental operating loading combinations (see Table 6) at both horizontal X and Y directions and the interstorey drift has should satisfy the 0.0075·h limit. Finally, the anchor bolts are checked according to Εurocode 2 (2005) ans Mallée et al. (2013) against failure in tension, pull-out failure and concrete cone failure.

Table 2 Base shear and ratio of shear resistance to base shear
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3 Analysis for seismic assessment

3.1 Modal analysis results

Dead loads, operating equipment and piping loads and 30% of live loads are taking into account for the computation of seismic mass. Modal response spectrum analysis of the structure is performed and the number of modes required to achieve 90% mass participation in each direction as well as the cumulative modal mass participation are presented in Appendix (Table 7). It should be noted that the seismic load of equipment is automatically calculated in SAP (2000) by distributing the masses on the shell elements.

The first three natural periods of structure as well as the mass participation (including the cumulative one) for each direction are presented at Table 1. The first three significant modes are displayed in Fig. 5.

Fig. 5
figure 5

a 1st, b 2nd and c 3rd mode of the structure

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3.2 Pushover analysis results

Static non-linear analysis (pushover) of the structure is performed in SAP (2000) in order to determine the overall post-yielding behavior and trace the formation of plastic hinges in route to progressive collapse. A uniform load pattern was performed, proportional to mass, regardless of elevation, according to Eurocode 8, 2004. The inelastic behavior of these members is modeled by using point plastic hinges at the member ends. In particular, for plastic hinges pertaining to steel or RC columns the axial force-bending moment interaction is taken into account, whereas for plastic hinges pertaining to steel or RC beams and to steel braces, bending moment and axial force is considered, respectively. The moment-rotation (M-θ) pattern describing the inelastic behavior of the aforementioned plastic hinges for specific seismic performance levels can be found in ASCE 41–13 (2013), and it is schematically shown in Fig. 6. Non-linearities (material and geometrical) are considered in all steel and RC frame elements. However, taking into account that the reactor is not a bearing-type element and must remain elastic, non-linearities are not considered at the shell elements used for modelling the reactor. Thus, the material of the shell is modeled as elastic. Shell imperfections are also omitted.

Fig. 6
figure 6

Force–deformation diagram for typical plastic hinge

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Two pushover analyses are performed, one in each horizontal direction, i.e., + x and + y. The structure is symmetric, thus, directions -x and –y, are not considered. For the aforementioned two pushover analyses, the base shear versus top displacement curves, i.e., pushover capacity curves, are extracted and displayed in Fig. 7.

Fig. 7
figure 7

Pushover capacity curves of the structure for a x direction and b y direction

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From the plots of Fig. 7, it is observed that structure exhibits almost similar base shear capacity at both x and y directions. In particular, the yield strength of the structure in the x and y directions is 13,021 kN and 12,362 kN, respectively, whereas the maximum strength is 15,006 kN in x direction and 14,592 kN in y direction. Moreover, the residual strength at a lateral top displacement of 300 mm, after the first vertical drop of the lateral strength, was found to be 11,365 kN and 12,135 kN in the x and y directions, respectively. This strength reduction is nearly at 20% to 25% and is based on the hinge behaviour defined in Fig. 6. For comparison purposes, the design base shear VEd (5,924 kN) and the design value of shear resistance VRd (Εurocode 2, 2005; Eurocode 8, 2004) (9,572 kN) on the basis of the actual steel reinforcement placed at the four RC columns (see Fig. 26, Appendix) are also provided in the plots of Fig. 7. The latter shear value indicates the significant overdesign provided to the RC columns as well as the additional overstrength provided by the overall frame behavior.

The formation and state (shown by colors) of plastic hinges in the two horizontal directions, is displayed in Fig. 8. On the basis of Fig. 8, plastic hinges are observed only at reinforced concrete elements and critical for collapse are those hinges (with cyan and red colors) at the bottom end of the columns of the base (see Fig. 6). Nevertheless, even though the structure has been designed with q = 1.5, i.e., no capacity design is required, the plastic hinge formation appears to follow the desirable pattern, i.e., at the ends of the beams and at the bottom end of the bottom RC columns.

Fig. 8
figure 8

Deformed shapes derived by pushover analysis in a direction x and b direction y

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3.3 Time history analysis

3.3.1 Ground motions

The structure is now subjected to nonlinear time-history (NLTH) analyses, taking into account the superiority of such analyses in comparison to static non-linear ones. Therefore, the three translational components (two horizontal and one vertical) of seismic motions recorded in the broader region of the structure are employed. These regional seismic motions were recorded from the Alkionides (1981), Aigio (1995) and Parnitha (1999) earthquakes in Greece and have been downloaded from the ITSAK strong motion database (ITSAK 2023). The three components, i.e., the transverse (T), the longitudinal (L) and the vertical (V), of these seismic motions are displayed in Fig. 9.

Fig. 9
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The three components of Aigio a, Alkionides b, and Parnitha c seismic motions

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The response spectra of the records considered intend to represent the frequent earthquake event and not the design-basis one. Figure 10 displays the response spectra of the two horizontal components of the Aigio, Alkionides and Parnitha seismic motions as well as, for comparison purposes, the elastic design spectrum of EAK (2000) and the fundamental period of structure. The design spectrum for the frequent-basis earthquake is assumed to be represented by 0.4 times the elastic design spectrum of EAK (2000), where the value of 0.4 takes into account the importance class of the structure under study (Eurocode 8, 2004). In order to obtain the actual seismic response of the structure, no scaling has been applied to the components of the aforementioned seismic motions. However, at the fundamental period of interest, the spectral ordinate of the response spectra is almost equal or higher (only for the L component of Aigio seismic motion) than that of the design spectrum.

Fig. 10
figure 10

Horizontal components of natural seismic records

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In total, by exchanging the two horizontal components of the seismic motions with respect to the two horizontal directions of the structure, six NLTH analyses are performed. For each analysis the time step is 0.005 s. In the plots that follow:

  • Combination 1 corresponds to the analysis in which the longitudinal and transverse components of the seismic motions are applied to the x and y directions of the structure, respectively.

  • Combination 2 corresponds to the analysis in which the longitudinal and transverse components of the seismic motions are applied to the y and x directions of the structure, respectively.

3.3.2 Plastic hinges of the structure

The plastic hinge distribution derived by NLTH analyses is presented in Fig. 11. More specifically, for Aigio seismic motion (Fig. 11a and b), for both Combinations 1 and 2, in addition to the plastic hinges appear at the bottom end of the RC part of the structure, plastic hinges (mainly yielding of the sections—green color as defined in Fig. 6) are observed in steel beams of the top floor, steel braces of the intermediate part of the structure and in some steel columns. This failure mechanism has not been identified by the pushover analysis where damages were found only in the RC part of the structure (Fig. 8), perhaps due to the neglection of the higher mode effects. Therefore, contrary to the pushover analyses, NLTH analyses revealed that the seismic motions considered herein can lead to the development of plastic hinges, hence damage, at critical structural members. Considering the importance of the structure, such failures need to be avoided and design codes should be stricter. Nevertheless, the developed plastic hinges do not follow the desirable pattern. This can be attributed to the absence of adequate ductility-based design requirements. For the case of Parnitha seismic motion the structure did not exhibit plastic hinges, whereas only one plastic hinge at the bottom end of one column was formed for the Alkionides seismic motion as shown in Fig. 11c and d.

Fig. 11
figure 11

Plastic hinges of structure for a Aigio—Combination 1, b Aigio—Combination 2, c Alkionides—Combination 1 and d Alkionides—Combination 2 ground motions

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3.3.3 Base shear versus top displacement of the structure

In Figs. 12, 13, 14 representative plots of base shear versus top displacement are presented as computed by NLTH analyses for the aforementioned two combinations and horizontal directions:

Fig. 12
figure 12

Base shear versus top displacement plots for the Aigio seismic motion: a in direction x—Combination 2; b in direction y—Combination 1

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Fig. 13
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Base shear versus top displacement plots for the Alkionides seismic motion: a in direction x—Combination 2; b in direction y—Combination 1

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Fig. 14
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Base shear versus top displacement plots for the Parnitha seismic motion: a in direction x—Combination 2; b in direction y—Combination 1

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From the plots in Figs. 12, 13, 14, it is evident that the Aigio seismic motion led to the maximum base shear force and top displacements. Table 2 presents the maximum base shear for all combinations and directions, as derived by NLTH analyses as well as the ratio of the design value of shear resistance over this maximum base shear. On the basis of the ratios presented, it is concluded that the base shear demand for the case of Aigio seismic motion exceeds the design value of shear resistance (9,572 kN) of the structure. As presented in Fig. 10, the spectral ordinate of the response spectra for the L component of Aigio seismic motion is higher than that of the design spectrum at the fundamental period of interest.

3.3.4 Top displacement time-histories of the structure

A critical point of the overall seismic performance of the structure is the top horizontal displacement (corresponding to damage limit state) found for each combination and direction. As mentioned in a previous section, the maximum admissible top displacement umax (in mm) is calculated according to the following formula: umax = Htot/300, where Htot is the total height of the structure. This formula is empirical but it is recommended by international guidelines specializing in oil and gas industriy (PIP STC01015 2017; Guidelines for Seismic Evaluation and Design of Petrochemical Facilities 2011). Top displacement must be below a threshold value, ensuring, thus, not only the servicability of the members of structure but the operational status of equipment as well. In the following, Figs. 15, 16, 17 provide representative plots of the top displacement time histories, seeking excursions with respect to the minimum and maximum admissible top displacement.

Fig. 15
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Top displacement time histories for Aigio seismic motion-Combination 2

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Fig. 16
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Top displacement time histories for Alkionides seismic motion-Combination 1

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Fig. 17
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Top displacement time histories for Parnitha seismic motion-Combination 1

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From the displacement responses involving the Aigio seismic motion, the admissible top displacement is exceeded in four occasions for Combination 2, as shown in Fig. 15. The Alkionides seismic motions also lead to significant top displacements, but the admissible top displacement is exceeded only once and for Combination 1. Therefore, in these cases the top displacement exceeds the admissible value corresponding to the damage limit state. Table 3 presents the maximum top displacement as derived by NLTH analyses as well as the ratio of the maximum displacements over the admissible top displacement.

Table 3 Comparative results for top displacement of structure
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3.3.5 Acceleration time-histories of the structure

Of special importance are the absolute accelerations of the structure. Figures 18, 19, 20 display representatively, the acceleration time histories at two positions of structure, i.e., on the 1st and 2nd guide, and for the x and y directions. It is important to note that these two positions are considered critical for the structure since they constitute points of interaction between the structure and the reactor.

Fig. 18
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Acceleration time histories for Aigio seismic motion at the position of the 1st and 2nd guide of the structure for Combination 1

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Fig. 19
figure 19

Acceleration time histories for Alkionides seismic motion at the position of the 1st and 2nd guide of the structure for Combination 2

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Fig. 20
figure 20

Acceleration time histories for Parnitha seismic motion at the position of the 1st and 2nd guide of the structure for the: a Combination 2

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Table 4 presents the maximum acceleration values at the two guides in both horizontal directions as derived by NLTH analyses. On the basis of the values presented in Table 4, it is concluded that the maximum accelerations occur at upper elevation (2nd guide, + 49.40 m) and for the Aigio seismic motion. Taking into account that the maximum ground acceleration of the Aigio seismic motion is 5.6 m/s2 (0.57 g) an acceleration amplification between 1.75–2.62 is observed at both guides. Under such high accelerations, there is severe possibility of failure of equipment and piping systems supported on the structure (Hosseini et al. 2020; Blasi et al. 2023; Kazantzi et al. 2022).

Table 4 Comparative results for recorded accelerations on guides
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3.3.6 Stress analysis of the reactor

To investigate the stress state of the reactor, maximum von Mises stresses are provided in Figs. 21, 22, 23. Note that based on the thermal analysis, the 10 mm gap (see Fig. 3) will be filled due to thermal expansion of reactor and the steel plate will be in touch with reactor.

Fig. 21
figure 21

Maximum Von Mises stresses on the shell of the reactor at time t = 3.635 s of Aigio seismic motion: Combination 1

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Fig. 22
figure 22

Maximum Von Mises stresses on the shell of the reactor at time t = 4.32 s of Alkionides seismic motion: Combination 2

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Fig. 23
figure 23

Maximum Von Mises stresses on the shell of the reactor at time t = 4.67 s of Parnitha seismic motion: Combination 2

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On the basis of the stress distribution shown in Figs. 21, 22, 23, it is observed that Von Mises stresses are greater on guide areas, as expected, since they connect the reactor with the structure and operate during the lateral displacement of the reactor. Moreover, significant stresses are observed on the bottom part of the reactor, i.e., between the base slab and the 1st guide. Figure 24 displays the allowable stresses on the shell of the reactor with increasing temperature (Bpvc Sect. and VIII, Division 1, 2019).

Fig. 24
figure 24

Allowable stresses for reactor’s shell for various temperatures (Bpvc Sect. and VIII, Division 1, 2019)

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Although stresses at high-stress locations of the reactor are low compared to the yield stress of steel (fy = 310 MPa), by comparing the maximum Von Misses stresses from Figs. 21, 22, 23 with the allowable stresses according to ASME (Bpvc Sect. and VIII, Division 1, 2019) for the design temperatures for the shell of the reactor (549–580 °C) as shown in Fig. 24, it is observed that the allowable stresses (45.5–28 MPa) are exceeded at the critical locations (guide areas and bottom part of the reactor) for all seismic motions considered when the reactor is in operation.

4 Conclusions

This study investigates the seismic behaviour of a special mixed RC-steel structure that supports an oil refinery reactor. The structure is 64.90 m tall and consists of three distinct parts: (a) a RC frame basement; (b) a steel braced frame that guides the oil reactor and (c) the steel reactor. More specifically, the study assesses the seismic performance of the novel structure by means of static nonlinear pushover and dynamic NLTH analyses. The main findings of this study are as follows:

  • Based on the results of the seismic analyses conducted herein, it is certified that the use of NLTH analyses has to be mandatory for the structures of the type studied herein. In general, modern seismic codes should enforce the use of NLTH analyses for the final seismic design or seismic assessment purposes of important structures such as those met in oil refineries.

  • Both types of analyses revealed that the structure has limited ductility, something anticipated in view of the fact that has been designed with a behavior factor q (or strength reduction factor) equal to 1.5. The plastic hinge distribution, hence damage, as revealed by the pushover analyses are expected to occur to the RC part of the structure (bottom columns and beam). However, the plastic hinge distribution derived by NLTH analyses reveals that under the frequent earthquake event, undesirable plastic hinge formations in the steel part of the structure in addition to the RC part may be exhibited. This failure mechanism does not follow the desirable pattern and can be attributed to the absence of ductility-based design requirements.

  • Among the three seismic motions, the Aigio seismic motion led to maximum base shear, top displacement and absolute acceleration values. In particular, the top horizontal displacement exceeded the admissible displacement (structure height over 300) about twice (ratio 1.85). The maximum ground acceleration of the Aigio seismic motion was 5.6 m/s2 (0.57 g) with an acceleration amplification between 1.75 and 2.62 to be observed at both supporting guides. Plastic hinges were formed at the bottom ends of all base RC columns, at steel beams of the top floor, and at steel braces and columns of the mid-height of the structure. The Alkionides seismic motion led to top horizontal displacements that exceed the allowable one by 28% but only for one combination (Combination I). Only one plastic hinge was observed, on the bottom end of the base RC column. For Parnitha seismic motion the structure remained elastic, and the top horizontal displacement was well below the admissible one.

  • Due to the maximum displacement and absolute accelerations found for the Aigio seismic motion, there is severe possibility of failure of equipment and piping system supported on the structure.

  • Stress concentration has been observed on guide areas and at the lower part of the reactor near the slab. Although these stresses are low compared to the original yield stress of steel, they were found to be greater than the allowable stresses when the reactor is in operation. Local failure of the high-stress areas of the shell of the reactor may be possible in case of the frequent seismic event (as defined in terms of the relevant seismic code) and localized strengthening of these areas might be necessary to avoid post-earthquake repair works and downtime. Any exceedance of allowable stresses should be viewed with caution in view of not only the importance of the structure but also of the fact that temperatures in the range of 549–580 °C implying a constantly working reactor.