Stability Analysis of HSD Tank Against Dynamic Response

. The existing HSD tank F-6302 has suffered damage in the form of corrosion which has caused the plate thickness to decrease. Developments in analysis methods and tank design standards have an effect on determining the stable capacity of the tank, so it is suspected that this tank is unstable. This study aims to analyze the stability of the existing HSD tank F-6302 to seismic response. The analysis was carried out by collecting structural property data of the tank, modelling the tank in FEM with a combination approach of finite element model and auxiliary mass, and evaluating the stability value of the tank using the equation issued by API 650:2020 to assess whether the tank is stable or not. The analysis results confirmed that the tank was unstable to earthquake loading. This is shown by the tank anchorage ratio values of 2.59 for the empty condition and 3.21 for the full condition. Both are greater than the stable limit value of 1.54. In the future, it is recommended to perform tank shell design and anchorage design on the tank.


Introduction
High Speed Diesel (HSD) storage tanks play a crucial role for the industrialized world in fulfilling the world's fuel supply.The importance of this facility is aligned with the vulnerability of the risks and hazards posed in the event of failure.These failures are generally caused by degradation of tank structural strength in the form of corrosion of plates and lack of maintenance.In addition, changing standards for tank analysis and design have indirectly contributed to the failure of these facilities, particularly on the topic of seismicity.A study describes some of the severe damage to some dominant tanks caused by earthquakes, where damage is commonly found in the form of vertical roll of the structure, inverted roll of the structure, falling equipment with crushing or damage to tank instruments, damage to the roof and roof supports, tilting or deformation of the tank foundation, buckling of the tank shell [1].The types of damage to this tank include corrosion, leakage, and paint damage.This damage is caused by the fact that this tank has been in operation for a long time, and has been shaken by the 2004 Aceh earthquake.In order to be reused, the tank must be thoroughly analyzed, starting in terms of utilization, strength, tank stability, up to the feasibility of supporting equipment for the tank.Research from [2] proves that the tank structure is not able to withstand earthquake loads, both when empty and when filled.
Other study describes the procedure for seismic analysis of tanks.Several methods are applied using various approaches that consider the tank structure -fluid system interaction, including: 1. the collected single mass method proposed by Chandrasekaran and Khrisna, 2. the simplified method (equivalent spring mass) raised by Housner, and 3. the added mass method proposed by Westergard.The observed results are the behaviour of the tank structure, i.e., the period and base shear force of the tank [3].The study concluded that the period in the first approach produced the largest results compared to the other two methods, but the largest base shear force arose with the last two approaches.Study presented the seismic spectral analysis of the tank using a simple method and a complex method.The simple method was performed analytically using standardized equations, while the complex method was performed by numerical simulation [4].The results of this study compare the results of both methods on the structural behaviour of the tank in terms of period, base shear force, and tank moment.It was found that the period values of the two methods showed good agreement, although there were differences in the results for shear force and moment.Study describes the analysis of storage tanks against seismic response, namely structural or modal vibration response and earthquake response [5].The results presented the modal response viz: Vibration modes and vibration frequencies of the tank for 30 modes, while the earthquake response is the maximum displacement which is generally the maximum value on the roof.Other study was observed in numerically analyzing the tank vibration by modelling the water in the tank as well [6].In addition to the above analytical methods, studies on tank behaviour were conducted experimentally.This was done by [7] who conducted experiments on a tank model scaled 1/10 of the actual tank to confirm the suitability of the tank's dynamic behaviour to the simulation results.From this study, it was understood that the seismic responses such as vibration, shock pattern, and buckling of the tank were confirmed in accordance with the results of the finite element method-based tank simulation by applying the constraints and inputs of the tank standard.Based on these studies, it is known that various methods have been published to observe the seismic behaviour of tanks and have been tested both by analytical, simulation, and experimental testing.
In addition, developments related to HSD tank analysis and design are progressing.The latest standard for tank design is [8].As for the Indonesian region, tank design also refers to this standard, while loading generally refers to [9], [10].It is very important to apply this regulation to any facility or building in Indonesia, this is influenced by the Indonesian region which is prone to earthquakes and induces loads on the tank later.Also, to create a structure that is safe, durable, and able to function optimally.A study concluded that the dynamic analysis of the tank is influenced by the location and site class of the tank location, where the softer the soil, the greater the response given by the structure [11].
The seismic response of the tank has a significant impact on stability analysis, as it can trigger changes in load distribution, deformation, center-of-mass shifts, overturning, and risk of tank collapse.Study described that the stability of the tank is inseparable from the material limit state, and the material limit state is inseparable from the stability of the tank, when the tank is subjected to significant horizontal acceleration, the seismic response in the form of impulsive force and convective force on the tank causes shear force which is converted into overturning force and then overturning moment [12].The study results state that uplift at the bottom and walls of the tank occurs when there is a large shear force which eventually results in tank overturning.The overturning of the tank is affected by the bending stiffness of the base plate and the tank wall shell.Furthermore, study from [13] applied the standard API 650:2020 to calculate the stability magnitude of the tank.The results of the finite element method computation, especially the base shear force, are useful for stability analysis.Some studies describe the base shear force results of the finite element method that adopts the mass centered on the tank as an additional convective mass or water mass [14]- [16].
Based on the above problems, this study was developed to analyze the stability of the existing HSD tank F-6302 against seismic response.Stability analysis involves assessing the stability of the tank against received loads, such as wind and earthquake, both when the tank is empty and in operational condition.

Research Methodology
The object of this research is the existing HSD tank F-6302.This tank is classified as an aboveground tank based on its location, an atmospheric tank based on its internal pressure or a tank without internal pressure.The roof type of the tank is closed with a cone shape fixed roof tank.And the tank bottom type is a flat bottom tank.The tank geometry data is presented in the following Table 1.In analyzing the stability of the tank, a finite element method simulation was carried out with the help of SAP2000 V.20.where the tank part was modeled as a shell element, the support or foundation was modeled as a pinch, and the base plate was given a soil stiffness number of 20.000 kN/m 2 referred from the stiffness correlation for medium soil by Bowles (see Fig. 1.)The analysis was run to solve the differential equations of dynamic motion of the tank system, which were written as follows.
Where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, and Ü, U ̇, and U are the structural response matrices, namely acceleration, velocity, and displacement, respectively, Üg is the ground spectral acceleration response matrix.The mass in the tank, in addition to the contribution from the tank structure itself, in this study the fluid is modeled as an additional centered mass or convective mass at height whose magnitude is calculated according to API 650:2020 as follows.
Where W c is the convective mass, W f is the fluid weight, D is the nominal diameter of the tank, h is the fluid height of the tank, X c is the center of convective mass measured from the bottom of the tank.To connect the centered mass with the tank body, a gap element is used which is calculated by the general dynamic stiffness formula.The period of the gap element is represented as the convective period (T c ) of the tank which is calculated as follows.The tank material is A285M Grade C steel with a yield strength of 205 MPa and a tensile strength of 380 MPa.The thickness of the tank plate or shell is the thickness in the existing condition, which is the thickness obtained from the results of the tank plate thickness measurement report in the field using the UTM (Ultrasonic Thickness Measurement) system shown in Table 2.The loading patterns applied to the tank include: self-weight of the structure, weight of HSD oil (ρ = 870 kg/m 3 ) which becomes hydrostatic pressure on the entire submerged surface of the tank walls and bottom, wind load, and earthquake load.The wind load of the tank refers to the procedure published by SNI 1727:2020 with the input parameters shown in Table 3. Below.While the tank earthquake load adopts the standard SNI 1726:2019 with the modal response spectrum dynamic analysis method.Modal analysis is a structural response analysis technique that combines the results of response spectrum and vibration mode analysis using the superposition method (SRSS or CQC) of various vibration modes.In contrast, a response spectrum is an empirical graph of the relationship between the vibration period and the maximum spectral acceleration response of a structure based on a specified damping ratio and earthquake.The requirements for the number of vibration modes and force scaling must be met to ensure that the seismic analysis results are compatible.For the number of variations, the result of the variational analysis must achieve a combined variational mass participation of 100%.For force scaling, the ratio of the dynamic analysis seismic force to the static analysis seismic force must achieve a goal of 100%.The response spectrum of this tank is shown in Fig. 2.

Fig. 2. Plot of Design Response Spectrum Curve of Tank F-6302
Based on the seismic response results of the finite element method in the form of base shear force, level shear force, and level force at the tank elevation, a stability analysis was developed.The stability against wind is calculated referring to API 650:2020 and the tank is considered stable when it satisfies the following three cases (if the moment ratio is less than one).6) Where M w is the overturning moment due to vertical and horizontal wind loads, M ws is the overturning moment due to horizontal wind, M pi is the overturning moment due to design internal pressure, M DL is the moment resistance of the tank shell weight, M DLR is the moment resistance of the weight of the roof plate and its support, M F is the moment resistance of the static fluid weight.
Unlike the previous analysis, the earthquake stability analysis is expressed by the tank anchorage ratio criterion according to API 650:2020 calculated by the following equation.
, (8) Where J is the anchorage ratio, M rw is the overturning moment at the base of the tank due to earthquake, W t is the weight of the tank perimeter, A v is the vertical seismic parameter of the tank, W a is the weight of the fluid perimeter, W int is the design lift due to the fluid perimeter, and F p is the combined internal pressure.
The earthquake stability criteria or requirements are presented in Table 4.This figure defines the limits of the stable value of the tank, which are 0,785 and 1,54.

Result and Discussion
The results of the finite element method analysis of the tank are presented in the following Table 5.This table informs about the fulfillment of the requirements for the acceptance of dynamic earthquake forces on the tank as stated in SNI 1726:2019.Based on Table 5. above, it is known that the dynamic analysis of the tank both in empty and full conditions has met the requirements for earthquake forces.This can be seen from the magnitude of the dynamic shear force is 100% greater than the static shear force of SNI 1726:2019.Based on Table 6.above, it is confirmed that the dynamic analysis of the tank for the two load mass conditions has met the requirements for the number of combined varieties.At the 600th mode, the total mass participation ratio of the variations has reached up to 100%.In addition, it is also seen that the period of vibration of the tank structure in the dynamic analysis is greater than the minimum period and smaller than the maximum period required by SNI 1726:2019.
After all acceptance criteria are completed, the seismic response analysis of the tank is continued.However, first analyze the response analysis due to wind loads.Based on the results of the tank stability analysis shown in Table 7. which is visualized with the Fig 5 .diagram. it is known that the existing tank F-6302 is stable against wind loads.This can be seen from the bar diagrams in cases 1, 2, and 3 are still below the stable tank threshold of 1.However, in contrast to earthquakes, it is stated that the tank is unstable to earthquake loads, both when empty and when full of HSD fluid.This is due to the increased earthquake induced on the tank and the dimensions of the tank are not capable of withstanding this load.This can be seen from the bar chart crossing the stable threshold of 1 and 2.

Closure
This research is a numerical simulation and analytical study using secondary data verified in the field.Based on these data, it is stated that this tank has suffered damage in the form of widespread corrosion on the tank shell.Based on the presentation of the results and discussion in this study, it is concluded that the tank is stable to wind (J < 1,00), meeting the stable requirements issued by API 650: 2020.While the tank is declared unstable to seismic or earthquake load responses, both in empty conditions and in operational or full fluid conditions (J > 1,54).And referring to API 650:2020, the initial suggestion for this tank is to change the dimensional configuration of the tank shell to increase the tank's resistance capacity during an empty earthquake and provide a mechanically anchorage system.So that this existing tank can be reused as it should.

Fig. 3 .
Fig. 3. Dynamic Response of Tank Under Wind Load

Fig. 3 .
Fig. 3. (a) shows the results of the tank response analysis in the form of level shear forces for each tank shell.Fig. 3. (b) displays the results of the analysis, namely the level force for each elevation of the top of the shell.And Fig. 3. (c) displays the results of the analysis, namely the overturning moment due to the level force.This value is the static moment of the level force at the bottom of the tank.

Fig 4 .Fig. 4 .
Fig 4. Dynamic Response of Tanks Under Earthquake or Seismic Loads Fig. 4. (a) displays the results of the tank empty earthquake response analysis in the form of level shear forces for each tank shell.Fig. 4. (b) displays the results of the tank full earthquake response analysis in the form of level shear forces for each tank shell.Fig. 4. (c) displays the results of the empty earthquake analysis, namely the level force for each elevation of the top of the shell.Fig. 4. (d) displays the results of the full earthquake analysis

Table 1 .
Tank Structure Properties

Table 3 .
Wind Load Parameters

Table 4 .
Earthquake Tank Stability Criteria J > 1,54Tank is unstable and cannot be self-anchored.Modification with annular ring length control if L < 0.035D or mechanically anchored.

Table 5 .
Earthquake Force Scaling

Table 6 .
Modal Participation Mass Ratio

Table 7 .
Tank Stability Calculation