Petrochemical Steel Pipe Rack: Critical Assessment of Existing Design Code Provisions and a Case Study

The behaviour factor is defined as the ratio of the strength demand if the structure were to respond elastically under the design earthquake to the inelastic strength demand, where the structure behaves beyond the elastic range but within the specified ductility limits. More specifically, if the elastic strength demand is defined as F_e and the inelastic strength one as F_d, it follows that:

According to (Elnashai and Di Sarno 2015), the value of q pertains to the ductility of the structure (the ductility is strongly related with the detailing of structural members), the overstrength of individual members (the redundancy plays an important role in the strength that a structure reserves) and the damping of the structure—the last is not in a straightforward relationship with the q-factors, thus most of the time it is omitted. The way in which the behaviour factor is defined in EN varies primarily as a function of the material of construction and the lateral resisting system utilized; thus, different q-factors are provided, for instance, for reinforced concrete and steel frames. The difference lies mainly in the overstrength ratio a_u/a₁, which is given in the following equation:where q_o is the basic value of behaviour factor; a₁ is the value by which the horizontal seismic action is multiplied in order for any member to reach its flexural resistance and a_u is the value by which the horizontal seismic design action is multiplied in order for plastic hinges to be formed able to cause an overall structural instability. The ratio a_u/a₁ can be obtained either by analysis calculations or by default values proposed by the (EN1998-1 2004) for different steel frame systems. The values of q-factors that the last code determines for steel frame systems with Medium or High Ductility Class (DCM and DCH) and irregular in elevation are shown in the Table 1.

The values shown in the table above come after a reduction by 20% of the relevant values for regular structures as the code specifies. The values have decreased deliberately so as the comparison with the values proposed in the following by the AM code to be feasible, making the assumption that petrochemical steel pipe racks are usually irregular along the height. The overstrength ratio a_u/a₁ is introduced for DCH. The value of overstrength ratio varies between 1.1 and 1.3 for MRF and is equal to 1.1 for CBF. Greater values of the overstrength ratio can be adopted in case nonlinear pushover analysis is used, however, the value cannot be higher than 1.6.

The results of analytical calculations upon the behaviour factor estimation have proved that the value of q-factor proposed by the EN is quite smaller than the product of ductility and overstrength reduction factor. Structures have to withstand seismic forces that correspond to higher seismic intensity than that of 475 years return period, and this is why the codes propose conservatively lower values of the factor in order to keep structures safe enough. However, when it comes to structures of higher importance e.g. oil refinery pipe racks, the values prescribed by the codes could be non-risk related and thus unjustifiable. Recently, a new risk-targeted design method has been introduced (Celano et al. 2018; Dolšek et al. 2017a, b) that accounts for different limit states in order to take the seismic risk in a more justifiable way into account. The method introduces a risk-targeted safety factor (γ_im), which is equal to the ratio of seismic intensity corresponding to a designated return period (e.g. T_LR = 713 yrs in the following case-study) and the mean value of seismic intensity that causes collapse; although, the first value can be found in seismic hazard maps, the second one is calculated numerically from the risk-equation by considering the hazard curve H(S_a) at a site and the target risk P_c. Finally, the risk-targeted behaviour factor is given by:where r_s is the overstrength factor, r_μ is the ductility factor and C_p pertains to the correction factor due to the risk-targeted definition being equal to the inverse of safety factor (γ_im). The Eq. 3 has been included in the new generation of EN codes.

The response modification factor (R)—it is recognized that this term offers a better indication of the role that this factor represents—is defined in the American codes in a similar way:

The factor R_μ corresponds to the ductility factor, whereas the factor Ω to the overstrength. As mentioned above, attention should be given when the AM codes are followed during the design process considering that the values of R-factor proposed refer to the highest possible recurrence period of earthquake, which is 2475 years (probability of occurrence 2% in 50 years), whereas the multinational EN codes or the national Italian code (NTC 2008) consider return period equal to 475 years (probability of occurrence 10% in 50 years).

In Table 2, values of R-factors for three different ductility classes and two structural types of steel pipe racks are illustrated. The values have been converted to refer to earthquake event with the same occurrence as per EN codes; in doing so, the comparison between them is made feasible. The values of reduction factors are comparable being greater or lower in one code compared to the other. The AM code does not specify values of R-factor for intermediate ductility CBFs. Also, it is worth mentioning that, in contrast with the EN code, the AM one proposes R-factor for ordinary pipe racks; this is reasonable considering the low ductility demand for this type of structure. The R-factor values shown in Table 2 do not consider increase of pipe rack height, since it is not considered in EN1998-1 (2004), however, they do account for the overstrength factor included in the pertinent table of AM code, which is equal to 3 and 2 for MRF and CBF, respectively.

A piping system can be modelled by using beam elements as specified in EN13480-3 (2012) and ASME B31.3 (2008). A critical issue that arises when using beam elements for the modelling of pipes pertains to the nonlinear geometry of pipe bend. To take the higher flexibility of those critical components into account, the thickness of the straight beam that substitutes the curved pipe decreases according to a rough code-related rule as specified in EN13480-3 (2012) and Bursi et al. (2016). Another way of modelling the pipe bent that has been adopted and assessed herein by using beam elements is proposed by Bursi et al. (2015). The method attempts to form an ‘Equivalent Straight Elbow, ESE’ (straight beam) that has the same flexibility with the original one by using the Euler–Bernoulli theory. In particular, the stiffness of the original elbow (see Fig. 3a for the modelling of elbow on ABAQUS) is set equal to the one of a straight beam by subjecting the elbow into axial, shear and bending loading. In fact, the only parameter that changes in the end is the pipe thickness of the straight element. The reader who is interested in this methodology can find more info in Bursi et al. (2015). It is emphasized that beam elements proposed by the codes are not accurate and definitely inappropriate to capture the nonlinear deformation of the pipe (the so-called ovalisation phenomenon), however, neither EN nor AM codes deal with shell elements.

The use of beam elements instead of shell ones should be treated with care given that the former type of elements may be incapable of estimating all the fundamental frequencies of the pipeline, which can be found, though, by shell elements or experimental tests. A modal analysis has been conducted on ABAQUS software (ABAQUS 2017) for the pipeline shown in Fig. 2b by using shell elements. As it is illustrated in the first row of Table 4, the beam elements that have been examined in Bursi et al. (2015) lose the first fundamental frequency of the pipeline, whereas the results from the experimental (DeGrassi et al. 2008) and ABAQUS analyses seem quite similar. Further assessment of shell and beam elements response has been done by exciting the piping system with a suite of 7 time-histories on ABAQUS software. The outcomes of such assessment prove that beam elements cannot capture all the peak values of stress–strain response (one out of 7 time-histories is shown in Fig. 3b), constituting the accuracy of beam elements questionable, and thus the response of pipes will be examined exclusively with shell elements hereafter.

Furthermore, modelling issues that pertain to the interaction of piping system on the pipe rack are crucial for these types of structures and could change significantly the global seismic response. The European codes do not treat the problem of non-building structure–nonstructural component interaction, whereas the American code ASCE/SEI 7-16 (2017) or the guideline ASCE (2011) (the latter makes reference specifically to petrochemical plants) specify a rough rule based upon the rigidity of connection and the weight of each system. If the non-building structure not similar to building and nonstructural components weight W_p is less than 25% of the weight of the entire system W_t, then the interaction could be neglected, and each structure could be designed and analysed separately. On the contrary, if the supported system weighs more than 25%, then, the coupled system should be considered either by considering the nonbuilding structure only as a rigid element with appropriate distribution of each seismic weight (rigid response with T < 0.06 s) or modelling the whole system in the same model (flexible response with T > 0. 06 s). The above statement indicates that not only the mass of the nonstructural component but also the type of connection rigid/flexible should be given due consideration for the seismic analysis. This conclusion comes in agreement with the research outcome mentioned above (Azizpour and Hosseini 2009) in which the type of connection (e.g. diameter of ring elements) affected the frequency of the system. However, this issue has not received much attention in the literature and additional loading effects should be considered e.g. thermal and pressure. Usually, rigid mechanical supports are considered for the pipes. Also, it is common most of the degrees of freedom of steel supports to be unrestrained in order to avoid excessive sizing of beams cross sections. The analysis of pipes and pipe supports independently of the rack could yield in considerable underestimation of pipes response e.g. displacements.

In the present case study, both the nonbuilding-nonstructural components and supporting structure are modelled and analysed together since W_p > 25% and T > 0.06 (the analysis for estimating the fundamental frequency of the vessels and piping system includes the towers on which are supported on).

The structural type to be used for modelling pipe racks depends on the single case and should always be compatible with design code provisions; for instance, the use of modular pipe racks is extensive in oil and gas industry due to financial reasons and the type of connections is strongly related with the distribution of pipes and/or vessels weight as well as fabrication cost. Pinned connections are typically utilized for beams in the longitudinal direction (struts) and shear tabs for the transverse (bent) beams. Also, the type and location of bracing is essential for the transportation, lifting and support of permanent and operating loads. As an example, vertical bracing could be used to support side overhang cantilevers that are necessary for pipelines that run out of the main pipe rack frame (Bedair 2015). In the present case-study, the petrochemical steel pipe rack is considered first as an Ordinary Concentrically Braced Frame (OCBF) with horizontal and vertical bracing (more info about this structural type can be found in Imanpour et al. (2011) and is modelled on ABAQUS software. The assumption of the low ductility class (ordinary structure) comes after the low deformation demand for pipe racks. The rack is placed in a high seismic-prone area in the north-eastern part of Sicily (near Milazzo city), in Southern Italy, where an oil refinery is located, and designed according to the Italian NTC (2018) and the two European codes EN 1993-1-1 (2005) and EN1998-1 (2004) for the Safe Life Limit State (SLLS) with recurrence period equal to 712 years (or probability of exceedance 7% within 50 years as per NTC (2018). The design parameters of the pipe rack can be found in Table 5.

The piping system is designed according to the Allowable Stress Method (ASM) as specified in EN13480-3 (2012) and ASME B31.3 (2008) and analysed taking both inertial effects and differential movements of the supports into account (coupled case). It is emphasised that in case of decoupled system, which is out of the scope of this case-study, only the inertia effects of pipes can be evaluated. Furthermore, the EN13480-3 (2012) code makes reference to two seismic levels, viz Operating Basis Earthquake (OBE) and Safe Shutdown Earthquake (SSE), whereas the latter one only to OBE (or occasional loads as they are defined in the code). It is emphasized that the ASCE/SEI 7-16 (2017) proposes additional seismic acceptance criteria for nonstructural components e.g. allowable peak spectral acceleration at attachment points or relative displacement between attachment points that are not included in EN13480-3 (2012) and ASME B31.3 (2008). The latter codes pertain mainly to the design of pipelines itself without considering dynamic interaction with attachment structures. Following this design methodology, other acceptance criteria could be assessed in order to enhance the design methodology in future publications. Also, it is pointed out that the lower q-factor value between the piping system and the supporting structure is adopted, since the coupled case is considered. This assumption and the reduction factor come after the ASCE/SEI 7-16 (2017) (see also Table 2), considering that EN code still does not specify values of q-factor for pipe racks yet only for irregular structures, which may be unsafe due to the pipe rack—nonstructural components interaction as well as the high risk existing in oil industry.

Finally, a modal analysis has also been conducted and the first two fundamental mode shapes excite the 42% and 26% of the total mass of the structure in the Y- and X-direction (Fig. 4), respectively.

In contrast with the common building structures, the highest modal participating mass ratio is observed at higher modes e.g. 6th mode, and that makes the use of common design and assessment methodologies questionable. Also, the interaction of nonstructural components and building structure could be affected by higher modes.

Due to the high irregularity of the pipe rack and high uncertainty of the effects of pipe rack–piping system interaction, the evaluation of system performance factor (q) is considered necessary. In doing so, the reliability of the factor proposed by the codes can be assessed and design parameters that are commonly adopted for common buildings can be highlighted. According to ASCE/SEI 7-16 (2017) and the guideline ASCE (2011), the selection of analysis method depends on design category, structural system, dynamic properties and regularity of the structure. The equivalent later force and dynamic analysis methods are commonly used for petrochemical plant structures. Considering the mass and stiffness irregularities of the rack along the height, the dynamic analysis is arguably the best choice, however,in the framework of this case-study, the conventional PA is used first to estimate the behaviour factor of the pipe rack considering the inertia forces concentrated at each floor (uniform distribution). Furthemore, the Incremental Dynamic Analysis (IDA) follows in order to assess the accuracy of the previous method for pipe racks. Seismic codes encourage both methods to be used for making comparisons e.g. in terms of base shear. Since there is no slab at the third floor to ensure a diphragmatic behaviour (see also Fig. 2a), the response is monitored at different control points along the perimeter of the third floor of the pipe rack to examine possible variation of the seismic behaviour; in the following only the worst case -point with the highest IDR- is presented, though. The substantial reduction of rack lateral resistance considering the force–deformation curve is adopted as global collapse limit state for each direction (Mwafy and Elnashai 2001). Also, the criterion used to define the global yield threshold, which is necessary for the behaviour factor estimation, is selected as the yield displacement at 75% of the maximum strength of the original force–displacement curve compared to the equivalent elasto-plastic system. The ductility factor is estimated by using the equal displacement method. In more details, the ductility fuctor (r_μ, see also Eq. 3) was calculated first by deviding the maximum elastic force F_e with the yeilding one (F_y = 0.75·F_max). Furthermore, the ductility factor was multiplied with the ovestrength r_s (= F_y/F_d, where F_d is the design base shear obtained by the response spectrum analysis) to acquire the non-risk related q-factor. More information about the ductility and behaviour factor estimation can be found in Elnashai and Di Sarno (2015).

The assessment of the rack with the nonlinear time-history analysis is conducted using a suite of 7 seismic records that refer to near-field conditions with epicentral distance smaller than 15 kms (Table 6 and Fig. 5). It is worth mentioning that, although that distance threshold was generally accepted in the past (Chopra and Chintanapakdee 2001; Heydari and Mousavi 2015) for differentiating far-field and near-field records, nowadays, the epicentral distance is not the only parameter to be considered; parameters such as the fault directivity and fling-step are also accounted for. More information can be found among others in Iervolino et al. (2017) and Pacor et al. (2018). To be consistent with the pushover analysis, the same criterion is adopted for defining global collapse and yielding of the system (Fig. 6). The seismic records are scaled up to collapse based upon the maximum Peak Ground Acceleration (PGA) in the two horizontal directions, however, the vertical component is scaled as well in order to keep the V/H ratio constant (Mwafy and Elnashai 2001).

Comparing the seismic response based upon the two analysis methodologies, it is obvious that the PA overestimates the rack resistance, and thus makes the use of PA analysis questionable. The overestimation seems to be considerably high in the Y direction since for IDR = 0.8%, when the maximum resistance is achieved according to PA, the pertinent value for IDA is 1.86 times lower. Also, the pipe rack is considerably more ductile in the Y-than in the X-direction since the ductility factor occurred 45% higher in the former direction, and this might be due to the tank response considering that there is no slab in order to support the weight in a utterly uniform manner and the longitudinal direction of it runs in the Y-direction making the tank to be more rigidly restrained in the other direction. Most probably, this is the reason why the PA method overestimates the behaviour factor as shown in Table 7, since the last method is not capable of activating the tank mass and cause torsional effects in the entire system. What is also of interest pertains to the outcome of the factor in the Y direction when comparing the two methodologies; the value yielded by the PA is almost 29% higher than IDA.

Furthermore, the risk-targeted behaviour factor is estimated for mean annual frequency of collase (λ_CLS) equal to 2 × 10⁻⁴ that corresponds to a generally accepted value that has been adopted in the development of building codes. As it was expected, the product of ductility and overstrength factor is extremely high. When the results of IDA are considered, the factor fluctuates from 9 to roughly 15 in both directions. To estimate the factor accounting for the designated risk, the risk-equation is used. To this effect, the annual rate of exceedance (λ_IM) of seismic intensity at the site under consideration is evaluated using the REASSES software (Chioccarelli et al. 2018). By assuming that the standard deviation of the fragility function is equal to β = 0.4, which is a generally accepted value in the literature for code-conforming buildings (Dolšek et al. 2017a, b), and changing repetitively the median of IM that causes 50% probability of collapse, the fragility and hazard curves are convoluted till achieving the desirable mean annual frequency of collapse (λ_CLS). A snapshot from the iterative process is given below (Fig. 7). Also, the results of the factor that account for the target-risk are quoted in Table 7 in parentheses. Considering only the values of factor by IDA, the factor was 29% less than the design value in the X-direction and 16% higher in the other direction. The inconsistency of the factor with the design value may indicates that the factors proposed by the code might not be always on the safe side and surely unjustifiable.

Having examined the response of the rack in terms of IDR, it is essential the stress/strain distribution on pipes (local scale) to be checked as well in order to adjudicate the reliability of the design method and compare the pipes response with the IDR values, which were found previously, as well as the maximum Peak Floor Acceleration (PFA) as defined by ASCE/SEI 7-16 (2017). For that purpose, the two seismic levels, OBE and SSE, are considered. The maximum floor acceleration is recorded at multiple points of the third floor of the rack yet only the maximum PFA is considered herein. According to ASCE/SEI 7-16 (2017), the PFA shall not exceed three times the PGA of seismic input (S_e(T=0) = 0.26 g). The first comment on the results shown in Fig. 8 refers to the fact that the piping system stress remains below the yielding value for both seismic levels. It is worth noting that the rack has considerably high overstrength and low ductility, which makes the common IDR values not applicable for the present rack. Additionally, the PFA presents high dispersity among the seven 7 records being even greater than the allowable value proposed by the code (3·S_e(T=0)) and this is an indication that the code ASD method could be unsafe. Usually, the variability around the mean value is expressed in terms of Coefficient of Variation (CV). Regarding the OBE, the CV is equal to 11% for the stress distribution, between 50 and 60% for the IDR in both directions and 36% in case of PFA. The high values of CV, particularly in the last two cases, may signify the complexity of pipe rack–piping system interaction.

To examine further the variation and amplification of PFA, the pipe rack is also analysed in the linear regime. Comparing the Fig. 9a, b, it is obvious that the linear behaviour increases considerably the PFA leading to values greaten than 1.5 times the limit value proposed by ASCE 7-16. This behaviour has also been observed in other steel frame buildings (e.g. Flores et al. 2015). This outcome may signify that the attitude of industrial engineers to analyse pipe racks in the linear range for safety reasons could be detrimental for the seismic safety of nonstructural components.

A common analysis method for nonstructural components pertains to ‘floor response spectra’ where spectra are collected by computing the total acceleration response history at the floor of interest. The spectra for linear and nonlinear material are presented in Fig. 10a, b and regard the median value of response time histories recorded on the third floor. The flexible pipelines should comply with the acceleration demand (0.4·a_p·S_DS·(1 + 2z/h), where a_p is an amplification factor equal to 2.5 for flexible components and S_DS is the design spectral acceleration) implicitly indicated in the formula for the horizontal seismic design force (F_p) for nonstructural components in ASCE 7-16. The maximum spectrum acceleration observed 3.7 and 2.9 times the acceleration demand in the two cases, and obviously, protective measures are required for the seismic safety of piping system such as supporting the tanks more rigidly on the rack and/or bracing, beams and columns reconfiguration. This issue is being investigated by the Authors.