Low Peak Ground Acceleration Research Articles

Investigation of the effects of mainshock-aftershock sequences on the dynamic responses of pipeline considering soil-pipeline interaction

Pipelines are important structural elements that are frequently used today to meet many infrastructures needs such as drainage, natural gas or water transmission. In this context, the usability of such structures, which are important elements of infrastructure systems, especially after disasters such as earthquakes, is of great importance. For this reason, within the scope of this study, a parametric investigation of the seismic behaviors of a natural gas pipeline system under mainshock-aftershock sequences have been carried out, specifically taking into account the soil-natural gas pipeline interaction (SNGPI) in the help of finite element model (FEM) proposed. Before developing the model of SNGPI system proposed using solid element, the fundamental mode frequencies of the pipeline system modeled using the solid element for the verification have been compared with those of obtained from the pipeline system modeled using the beam element and the analytical solutions. After verification of proposed model is demonstrated, SNGPI system has been modeled and its fundamental modes have been compared with mode frequencies of soil stratum obtained from well-known simple analytic solutions. After this stage, the dynamic analyses of natural gas pipeline (NGP) system in the time domain have been carried out using four different soil systems and four different mainshock-aftershock sequences. The results of the nonlinear time-history analyses have been investigated in terms of the stress and the displacement responses. Parametric evaluations show that the greatest displacements and the stresses occurring at the considered nodes of NGP system may be importantly affected from mainshock-aftershock sequences and soil stiffness changes. As the soil stiffness decreases, both the peak stresses and displacements increased significantly. On the other hand, the same responses obtained under mainshock loadings, which have relatively lower peak ground acceleration (PGA)/peak ground velocity (PGV) ratio compared to aftershock loadings, are generally larger than those obtained under aftershock loadings.

A systematic review of hybrid passive energy dissipating devices

Once earthquakes occur, they release a considerable amount of elastic strain energy, which is measured by Peak Ground Acceleration (PGA). To reduce the impact of this energy, buildings can be fitted with dampers. These include passive energy dissipation devices, which are effective in mitigating the effects of both high and low PGA. Hybrid dampers, which combine multiple devices, enhance strengths and minimize weaknesses, significantly improving a building’s seismic resilience by reducing roof displacement, drift, inter-story, floor acceleration, and base shear. These dampers are the focus of extensive research, emphasizing their role in seismic performance enhancement. Despite numerous studies, their application in concrete structures remains underexplored, presenting a vast scope for advancement in the design, development, and implementation of hybrid damping devices. These devices are particularly valued for their superior vibration control capabilities, offering a promising avenue for bolstering structural stability.

Shaking table tests for seismic response of jack-up platform with pile leg-mat foundation on sandy seabed

The pile leg-mat foundation is a novel composite foundation designed for jack-up offshore platforms. The seismic response of such foundations in sandy seabeds is an issue that requires significant attention. In this study, shaking table tests were conducted under various input seismic waves to investigate the dynamic response of a seabed platform system subjected to seismic loads. The effects of the peak ground acceleration (PGA), seismic wave frequency, wave type, pile leg insertion depth, and pile length on the response of the seabed platform system were investigated. The results indicated that as the PGA increased, the acceleration response of the soil and platform model increased, increasing the accumulation of excess pore water pressure and the horizontal displacement of the platform model. The acceleration and horizontal displacement responses of the seismic wave with lower frequencies were higher than those with higher frequencies. The peak acceleration amplification factors under the measured and regular seismic waves showed significant differences, with the dynamic response of regular waves to the platform model being pronounced. Under seismic waves with low PGAs, the horizontal displacement of the platform model decreased with increasing pile leg insertion depth or pile length.

Effect of attached outlets on the dynamic response of arch dams

Attached outlets are integral components of arch dams to discharge flood. However, they are usually neglected in the current seismic analysis of arch dams for simplicity. This paper aims to analyze the effect of attached outlets on the nonlinear seismic response of arch dams. For this purpose, a 235 m high arch dam is analyzed as a case study. The results indicate that the effect of attached outlets on the seismic response of arch dams depends on the ground motion intensity. For the ground motions with a low peak ground acceleration (PGA), the effect of attached outlets on the concrete damage is slight and local, which is consistent with the existing perception. However, as the ground motion intensity increases, their effect extends to the entire dam body. In contrast, the influence of attached outlets on the joint opening is typically observed at the middle contraction joints. Furthermore, the model analysis demonstrates that the inertia effect of attached structures is the primary contribution to these phenomena. Finally, a simplified simulation approach is used for incorporating the influence of attached outlets by coalescing the mass to the dam surface.

Seismic vulnerability of shallow tunnels subjected to far-field long-period ground motions

Extensive documentation and research have highlighted the destructive impact of near-field earthquakes on underground structures, while the effects of far-field earthquakes remain relatively less explored. In regions such as Bangkok and Singapore, where active seismic faults are located at a significant distance, the influence of far-field motions on tunnels tends to be ignored. However, far-field earthquakes are generally less destructive than near-field motions due to their low peak ground acceleration, peak ground velocity, and Arias intensity, resulting in lower energy. Conversely, far-field earthquakes tend to have a longer duration than near-field and a higher probability of containing long-period waves, which can lead to higher responses in the low-frequency region of the response spectrum. When these far-field ground motions are applied to thick layers of soft natural clays, a common geological feature in Bangkok, they can undergo significant amplification in the long-period range, resulting in large soil displacements and shear strains. Consequently, this induces significant forces in the tunnel lining comparable to those generated by near-field earthquakes. This paper presents a comprehensive study of this rarely investigated topic, using advanced numerical simulations to analyse the seismic behaviour of a shallow circular tunnel in Bangkok soft clays subjected to long-period earthquakes. The results show that far-field earthquakes have the potential to generate forces in the tunnel lining that are equally destructive as those induced by near-field motions. Therefore, these far-field effects should be accounted for in the seismic design of tunnels.

Ground motion characteristics of the 2015 central Nepal (Gorkha-Dolakha) Earthquake and 2023 SE Turkey Earthquake doublets

The Alpine-Himalayan orogenic belt, the well-identified seismically active region in the world, has been evidenced by the occurrence of recent two devastating earthquake doublets in 2015 in central Nepal (MW 7.8 and MW 7.3) and in 2023 in southeastern Turkey(MW 7.8 and MW 7.5). In this study, seismic ground motion characteristics of two damaging earthquakes namely the 2015 central Nepal earthquake doublet that occurred in the central Himalaya and the 2023 southeastern Turkey earthquake doublet that occurred in the eastern Mediterranean has been investigated. The observed strong-motion recordings indicate that the peak ground acceleration (PGA) values are about 152.61–154.96 cm/s2 of the 2015 central Nepal earthquake doublet at KATNP station and about 451.834–842.924 cm/s2 of the 2023 southeastern Turkey earthquake doublet at station 3137. The seismic ground motion of both the 2015 central Nepal and the 2023 SE Turkey earthquakes doublet shows that the 2015 central Nepal doublet produced much lower peak ground acceleration than the 2023 southeastern Turkey earthquake doublet.

Seismic Performance Assessment of the 18th Century Jesuit College in Dubrovnik’s Old City

The seismic performance assessment of heritage architecture presents many challenges due to the restrictions set forth by the conservation principles to protect the associated social and cultural values. These buildings are typically characterized by unreinforced masonry walls connected by tie-rods, vaults, and wooden floors. The era of construction dates to the time when seismic design regulations were largely unknown, making heritage structures potentially vulnerable to earthquake damage. This study presents the seismic performance assessment of the Jesuit College located in the southern part of the Old City of Dubrovnik. A series of field surveys were conducted to qualitatively examine the material composition and obtain geometrical details in part of the Croatian Science Foundation research project IP-2020-02-3531 entitled “Seismic Risk Assessment of Cultural Heritage in Croatia—SeisRICHerCRO”. The structural response is thoroughly investigated by means of a complex finite element model calibrated using the frequencies determined from ambient vibration measurements and material characteristics obtained from the literature review of representative cultural heritage buildings. The seismic performance is evaluated using linear static and response spectrum analysis in accordance with Eurocode 8 guidelines for the demand seismic action level. The numerical analysis indicates several structural components in the building exhibiting high shear stress concentration and exceeding the elastic tensile limit under the demand ground acceleration level. The assessment further reveals substantial out-of-plane bending of vulnerable wall components (identified by local mode shapes) at low peak ground acceleration levels. The stress concentration in numerous structural components leads to the identification of vulnerable zones where retrofitting measures are essentially required.

Probabilistic Damage Analysis of Isolated Steel Tub Girder Bridge Excited by Near and Far Fault Ground Motions

Friction Pendulum Bearing (FPB) has emerged as a popular solution for damage protection of bridges under seismic events. The study presents the probabilistic damage analysis for the isolated tub girder continuous bridge under the near and the far fault earthquakes using fragility analysis. The steel tub girder continuous bridge is considered with friction pendulum isolator as the seismic isolation mechanism. In order to represent the hysteretic behavior of friction pendulum isolators, a bilinear force-deformation model was used. Fragility curves are developed for various damage measures namely rotational ductility of pier and girder displacement with the peak ground acceleration (PGA) as an intensity measure (IM). Incremental dynamic analyses (IDA) were performed to develop the fragility curves and probabilistic damage model considering the four threshold damage states. The results suggest that in the case of low PGA level, the near fault earthquake leads to the high probability of exceedance in the case of isolated tub girder bridge. Damage model for piers and girder were developed to correlate component responses levels to overall bridge deterioration states. Finally, recommendations for the bridge developers in the stage of the early bridge seismic isolation design utilizing friction pendulum isolators are discussed.

Sensitivity analysis of input ground motion on surface motion parameters in high seismic regions: a case of Bhutan Himalaya

Abstract. Historical earthquakes demonstrate that strong motion characteristics and local soil condition, when coupled, significantly influence seismic site response. Interestingly, most of the Himalayan earthquakes depicted anomalous behavior per the site conditions historically. Being one of the most active seismic regions on earth, the eastern fringe of the Himalaya has observed many devastating earthquakes together with non-uniform damage scenarios. To quantify such anomalies, we evaluate surface motion parameters for a soft soil deposit located in the city of Phuentsholing in western Bhutan. Using one-dimensional site response analysis, the sensitivity of ground motion variation is estimated. This study accounts for the earthquakes of moment magnitudes 6.6 to 7.5 with a wide variation in peak ground acceleration (PGA). To dissect the characteristics of six inputted ground motions on eight local ground conditions, a sensitivity analysis is performed statistically. The statistical correlation of the response datasets and the linear regression model of the bedrock outcrop and the surface motion spectral acceleration along the stratified depth are examined to quantify the variation in surface motion parameters. The results highlight that the strong motions with PGA greater than 0.34 g demonstrate greater sensitivity, leading to some anomalies in response parameters, especially amplification. Similar results were obtained for the low PGA range (<0.1 g).

Stability analysis of a closed underground hard rock metal mine using Finite Element Method

Active deep hard rock metal mines with long mining history come with inherent problems of stability and mining induced issues. These hard rock mines once closed, still pose even greater environmental risks and stability concerns. The issues of post-mining impact on environment are usually undervalued and disregarded. It is very essential to give utmost importance to these mines by following standard mine closure methods and remediations using post-mining management plans for long-term monitoring and risk assessments associated with the mine for the safety of life and structures above. The area identified for the study is Kolar Gold Fields mine located in Karnataka, India. The mine was completely closed in 2000. The underground mine has been posing post-mining induced seismicity even today. Due to the complexity of the underground mine and the inaccessibility to the mine post closure, the Finite Element Method of approach has been used. The approach is developed to simulate a model similar to actual field conditions, subjecting them to the seismic loads, varying the parameters which play a significant role, assessing the entire Kolar Gold Fields mines for vulnerable zones subjected to post-mining induced effects and finally making it possible to evaluate the stability conditions of the deep hard rock underground metal mine. The simulations were carried out for the three cases with varying the peak ground acceleration (PGA) for a low PGA of 0.06g, for an intermediate PGA of 0.1g and high value of 0.2g. It can be inferred that as the acceleration is increased from 0.06g to 0.22g, there is a corresponding increase in ground acceleration observed at the ground surface for each case. The maximum acceleration for PGA of 0.06g is 0.071g, for PGA of 0.10g, it is 0.170g and for PGA of 0.22g it is 0.266g. The results were validated with the field observations (data of seismicity from installed seismic monitoring systems). The Finite Element Method of approach has aided in quick assessment of stability of the underground closed mine.

Correlation Between Wavelet-Based Energy Parameter and Observational Damage Degrees for Gravity Design Building During the May 2018 Mayotte Seismic Crisis

Mayotte seismic crisis started on 10 May 2018, with a first felt earthquake, quickly followed by many others, that surprised inhabitants. Before 10 May 2018, Mayotte Island, part of the volcanic Comoros archipelago in the North Mozambique Channel of the Indian Ocean was not considered as a significantly seismically active area, and hence the structures were designed without or very recently with a low seismic code. In this study, we pay particular attention to existing seismic records of earthquakes with a magnitude greater than 5, and we try to establish their dangerousness for existing buildings. As the magnitude is not very large, it is difficult to observe and classify the slight to moderate damages using the drift parameter. It is for this reason that in this study we try to consider the shift of the inelastic period and the dissipated energy, estimated using wavelet transform, in order to estimate the damage. We have modeled a target building and calculated its dynamic response using the recordings of the 46 strongest earthquakes of the current crisis as the input. The dynamic calculations were performed using open source finite element software, Opensees © Berkeley. We analyzed the dynamic response at the top of the building in terms of the period of vibration, energy dissipated, and drift. We used the aforementioned 46 recordings from two different seismological stations in terms of site effects: YTMZ station, considered as rock, and MILA station, which shows strong site effects and therefore the strongest recordings in terms of acceleration. We try to find a correlation between the wavelet energy dissipation and the observational damage degree or drift-based damage degrees. We found out that about 25% of the 46 earthquakes selected on soils with site effects (MILA station) have building response parameters corresponding to degrees of damage D1 and D2 of the EMS-98 scale: negligible to light damage (no structural damage and slight non-structural damage) and moderate damage (light structural damage and moderate non-structural damage). This damage can appear for relatively low peak ground acceleration values (e.g., about 0.3 m/s2 for some earthquakes). Furthermore, the damage assessment results from the three damage parameters for the target gravity design building are compared and discussed.

Performance of RC elevated liquid storage tanks installed with semi‐active pseudo‐negative stiffness dampers

The effect of semi-active pseudo-negative stiffness dampers (SAPNSDs) on the seismic response mitigation in the reinforced concrete (RC) elevated liquid storage tanks is investigated. The SAPNSDs are operated in two modes: Passive-ON and Passive-OFF. The effect of placement (location) of the dampers is also studied by placing the dampers in three different configurations. Two aspect ratios of the tanks, viz., 0.5 and 2.0, are considered to study the effect of the variable level of the liquid in the container. Time history analysis is carried out for total of 18 different earthquake ground motions. The differential equations of motion are solved by the state-space approach. The response quantities such as peak base shear, overturning moment, container level displacements, and bracing level displacements, along with the damper forces, are obtained. It is found that the SAPNSDs (Passive-ON) effectively control the response of the RC elevated liquid storage tanks. Further, seismic energy input to the structure without SAPNSDs and the percentage energy dissipated by SAPNSDs is obtained. The placement of the dampers plays a significant role in response reduction during ground motion with high peak ground acceleration (PGA) than that with low PGA. The SAPNSDs installed at alternate levels (Configuration II) is the most efficient configuration for response control of the RC elevated liquid storage tank installed with the SAPNSDs. The seismic input energy reduces considerably by the installation of the semi-active pseudo-negative stiffness dampers (SAPNSDs).

Cost Estimate and Input Energy of Floor Systems in Low Seismic Regions

Reinforced concrete (RC) as a material is most commonly used for buildings construction. Several floor systems are available following the structural and architectural requirements. The current research study provides cost and input energy comparisons of RC office buildings of different floor systems. Conventional solid, ribbed, flat plate and flat slab systems are considered in the study. Building models in three-dimensional using extended three-dimensional analysis of building systems (ETABS) and in two-dimensional using slab analysis by the finite element (SAFE) are developed for analysis purposes. Analysis and design using both software packages and manual calculations are employed to obtain the optimum sections and reinforcements to fit cities of low seismic intensities for all the considered building systems. Two ground motion records of low peak ground acceleration (PGA) levels are used to excite the models to measure the input energies. Uniformat cost estimating system is adopted to categorize building components according to 12 divisions. Also, Microsoft (MS) Project is utilized to identify the construction cost and duration of each building system. The study shows that floor system significantly causes changes in the input energy to structures. In addition, the slight increase in the PGA increases the amount of input energy particularly flat plate system. Estimated cost of the flat plate system that the flat slab system is of higher value as compared to ribbed and conventional slab systems. The use of drop panels increases this value as well. Moreover, the estimated cost of the ribbed slab system exceeds that of conventional system.

Performance-based assessment of permanent displacement of soil slopes using two-dimensional dynamic analysis

ABSTRACT In this paper, a performance-based method is suggested to assess the permanent displacement of a slope using two-dimensional dynamic analysis considering both uncertainties in ground motions and basic soil parameters. In the suggested method, the statistics of the permanent displacement is first analyzed at different peak ground acceleration levels through uncertainty propagation analysis, and regression analysis is then used to derive the fragility curve. A seven-step procedure is suggested to implement the suggested method, and a numerical example is used to illustrate the suggested method. For the slope examined in this paper, the performance-based assessment based on one-dimensional model underestimates the mean of the permanent displacement, and the performance-based assessment based on the empirical model overestimates the uncertainty in the permanent displacement. The uncertainty in soil properties can contribute up to 40% to the uncertainty in the permanent displacement at low peak ground acceleration level.

Seismic performance assessment of structure with hybrid passive energy dissipation device

This study aims at the development of a new hybrid passive energy dissipation device (HPED) which is a combination of X-plate added damping and stiffness damper (XADAS) and friction damper (FD) for improving the seismic performance of structure subjected to earthquakes with different peak ground acceleration values. The advantage of HPED when compared to XADAS and FD of same yield strength as HPED is that only FD dissipates the input seismic energy for earthquakes with low peak ground acceleration value and for earthquakes with high peak ground acceleration value both FD and XADAS works simultaneously to dissipates input seismic energy. Cyclic loading tests were conducted on HPED, XADAS and FD of same yield strength to evaluate their energy dissipation capacity and the tests results shows that HPED dissipated more amount of energy when compared to XADAS and FD. An eight storey reinforced concrete building was retrofitted with HPED and nonlinear time history analysis was used to compare the response of structure with HPED, with XADAS and with FD of same yield strength under eight different earthquake ground motions. In addition to this seismic fragility analysis was also performed. According to nonlinear time history analysis results when the building is retrofitted with XADAS, FD and HPED the percentages of reduction of average of maximum inter-storey drift are 52.9, 58.8 and 66.6 respectively and the percentages of reduction of average of maximum roof displacements are 51.3, 54.5 and 68 respectively and similarly the percentages of reduction of average of maximum base shears are 38, 32.4 and 56 respectively. So HPED is performing better than XADAS and FD in reducing inter-storey drift, roof displacements and base shear. Results also show that HPED is dissipating more amount of seismic input energy when compared to XADAS and FD under earthquakes with different peak ground acceleration values. Fragility analysis results show that probability of reaching the collapse state is reduced by HPED when compared to XADAS and FD.

Seismic fragility analysis of LNG sub-plant accounting for component dynamic interaction

Earthquakes can cause significant damage to liquefied gas terminals, a critical part of lifeline facilities of energy supply networks, failure of which may lead to loss of hazardous material, explosion, environmental contamination, loss of functionality and disruption of business. To date, seismic risk analysis of such facilities mainly focuses at component level, with the inherent dynamic interaction between the supporting structure and non-structural components not receiving the merited attention. In the present study, the seismic performance of an actual facility comprising of a piping system and a reinforced concrete (RC) supporting structure is analyzed through a finite element model in the nonlinear regime, both as coupled and decoupled case. Plastic strains are used as engineering demand parameters (EDP) to define leakage limit state for pipes. Since the RC pipe rack supporting structure is designed for low seismic loads, shear is recognized as the predominant failure mode. The same components are then analyzed in unison, considering coupling due to dynamic interaction. Fragility functions are estimated for both cases using multiple stripe analysis. A set of strong ground motions artificially generated using the specific barrier model, are employed for developing fragility curves. They are expressed with peak ground acceleration (PGA) as an intensity measure. Statistical estimation of the parameters of fragility functions are based on maximum likelihood method. It is inferred that in the decoupled case, pipes show higher vulnerability at lower PGA, at higher PGA pipe rack can fail suddenly resulting in total failure of the system. Moreover, in coupled case the fragility of the pipes and RC rack changes substantially because of the piping system boundary conditions. Thus, concluding that the risk estimation could be erroneous if dynamic interaction is neglected.

Seismic Fragility Analysis of Poorly Built Timber Buildings in Yangon Slum Areas

In Yangon and the suburbs of Myanmar, timber-framed buildings are the popular choice of construction for residential purposes. Nearly 8% of the total population in Yangon live in the slums and slum-like areas where the dwellings are predominantly made of non-durable materials. Wood, jungle wood, and bamboo are used as the framework and corrugated galvanized iron sheets as walling and sheathing material. The seismic-resistance capacity of timber buildings in slum areas has never been approved based on experimental evidence. Therefore, this study aims to conduct a seismic fragility analysis for poorly built timber buildings by providing a suitable method through numerical and experimental approaches. Pull-over loading tests were conducted on selected buildings to assess their loading-displacement capacity. Further, numerical modeling was done using the Wallstat simulation tool, which is based on the discrete element method. The pushover curve was validated with the curve from the pull-over load test. Once the numerical model was confirmed, dynamic analysis was conducted for different peak ground acceleration (PGA) (g) values until the complete numerical collapse of the building. Three building configurations with three ranges of variable material properties were considered in this study. A primary damage state started at the low PGA value of 0.05 g, and it can be confirmed that the timber buildings that were studied, are vulnerable to earthquakes. The results based on qualitative analysis were accumulated to obtain the damage state matrix, which was then used to obtain the fragility curves.

Empirical fragility functions for Nepali highway bridges affected by the 2015 Gorkha Earthquake

The Gorkha Earthquake Sequence of 2015 affected hundreds of bridges in central, eastern, and part of western Nepal. This paper presents empirical fragility functions of highway bridges affected by the earthquake sequence. The fragility functions are based on the damage data collected during the assessment campaign conducted after the earthquakes. Fragility functions are presented for reinforced concrete and steel bridges based on data collected from 154 bridges. The results show that these highway bridges are very vulnerable to earthquake shaking and sustain damage even at low peak ground acceleration.

Seismological and Hydrogeological Controls on New Zealand-Wide Groundwater Level Changes Induced by the 2016 Mw7.8 Kaikōura Earthquake

The 2016 Mw7.8 Kaikōura earthquake induced groundwater level changes throughout New Zealand. Water level changes were recorded at 433 sites in compositionally diverse, young, shallow aquifers, at distances of between 4 and 850 km from the earthquake epicentre. Water level changes are inconsistent with static stress changes but do correlate with peak ground acceleration (PGA). At PGAs exceeding ~2 m/s2, water level changes were predominantly persistent increases. At lower PGAs, there were approximately equal numbers of persistent water level increases and decreases. Shear-induced consolidation is interpreted to be the predominant mechanism causing groundwater changes at accelerations exceeding ~2 m/s2, whereas permeability enhancement is interpreted to predominate at lower levels of ground acceleration. Water level changes occur more frequently north of the epicentre, as a result of the fault’s northward rupture and resulting directivity effects. Local hydrogeological conditions also contributed to the observed responses, with larger water level changes occurring in deeper wells and in well-consolidated rocks at equivalent PGA levels.

Curved surface sliders with friction damping, linear viscous damping, bow tie friction damping, and semiactively controlled properties

This paper investigates the isolation performance of curved surface sliders (CSSs) with different damping mechanisms. The following passive damping mechanisms are considered: passive friction damping as commonly present in CSSs, linear viscous damping as linear damping mechanism, and bow tie friction as adaptive, that is, position-dependent, but passive approach; CSSs with adaptive behaviour based on different sliding regimes are not considered. From the field of CSSs with semiactive dampers, two control strategies are considered: amplitude proportional friction damping aiming at linearizing the friction damping over one cycle and semiactively controlled damping and stiffness properties to enhance the decoupling between ground and structure by the emulation of zero dynamic stiffness. The CSSs under consideration are assessed in terms of peak structural acceleration, peak CSS horizontal force and displacement, and recentring error as function of peak ground acceleration (PGA) of the accelerograms. The results demonstrate that (a) friction damping can be optimized at one PGA only due to its nonlinearity, (b) the optimization of linear viscous damping does not depend on PGA, (c) optimized bow tie friction improves the isolation at low PGA while the isolation at medium to high PGAs worsens, (d) optimized amplitude proportional friction damping does not improve the isolation compared with optimized linear viscous damping, and (e) zero dynamic stiffness is preferably emulated only for a certain range of CSS relative motion amplitude to keep the recentring error within acceptable limits.