ABSTRACT

System response using dynamic effective stress modelling can capture the holistic behaviour of a potentially liquefiable soil deposit, including interaction between different soil layers. Compared to a conventional liquefaction triggering analysis, a system response assessment can either predict more or less damage depending on the characteristics of the soil profile. This paper describes a case study where considering the system response resulted in a more realistic prediction of liquefaction effects than a simplified CPT based triggering assessment.

The soil profile at the site comprises upper loose to medium dense sand (from 0-9 m depth), overlying silt (9-12.5 m), and overlying a lower loose sand layer (12.5-19.5 m). A simplified liquefaction triggering analysis predicted liquefaction occurring from 2 to 6 m depth and 12.5 m to 19.5 m in an Ultimate Limit State (ULS) earthquake event.

Several large diameter tanks are to be constructed at the site. Using a simplified liquefaction analysis, ground improvement was required to 8 m depth to improve bearing capacity and mitigate differential settlements.

A liquefaction system response analysis was carried out using an effective stress time history analysis of a 1D soil column. The model was created in FLAC with a PM4Sand constitutive model for the liquefiable sand layers. The results showed that liquefaction would first occur in the very loose sand layer from 12 to 19.5 m depth, reducing accelerations in the soil column above by approximately 50%. Because of this “base isolation” effect, liquefaction was not triggered in the loose to medium dense sand above 9 m depth in the ULS event. From this result it was concluded that ground improvement is not required to support the tank.

Introduction

Simplified liquefaction triggering analysis using MBIE Module 3 (2016) is common practice in New Zealand when completing geotechnical assessments for residential, commercial, industrial and infrastructure projects. Boulanger and Idriss (2014) is currently the most common triggering analysis to use, which is based on the case history response of soil overall, and the observed liquefaction severity. This analysis assesses liquefaction triggering based on soil type and parameters at individual depths. It does not account for the interaction between different soil layers, which is often referred to as a system response.

Cubrinovski, M. et al. (2017) has assessed system response effects at a number of sites from the Canterbury earthquake sequence and completed effective stress analyses to demonstrate key system response mechanisms. Cubrinovski identifies a response where a loose soil at depth liquefies and reduces the extent and severity of liquefaction / softening in the soils above this layer. In this paper we describe this as a natural “base isolation” effect. This paper explains the process we went through to evaluate this effect on an industry project with the objective of obtaining a more accurate understanding of the seismic performance of the tanks at the site, and assess the need for ground improvements.

This project involved the geotechnical assessment of several 12 m diameter, 15 m height oil storage tanks. The soil profile has been simplified into three units for the purposes of this paper as these are considered the most important units, which are controlling the system response at the site. An upper loose sand layer exists from 0 to 9 m depth, overlying silt at 9 to 12.5 m depth, overlying a lower sand layer which is loose between 12.5 m and 19.5 m depth. Below this depth the density of sandy deposits increases. A summary of the soil profile is provided below in Figure 1 along with a liquefaction triggering plot using Boulanger & Idriss (2014).

Figure 1: CPT results, I_c and liquefaction triggering assessment using simplified liquefaction analysis – red is where FoS_Liq < 1.0 and green is where FoS_Liq > 1.0 (when using the CRR_PL<15% curve) for Mw = 6 and PGA = 0.25g.

Ground model and simplified liquefaction results

A simplified liquefaction triggering assessment was completed using Boulanger & Idriss (2014) to provide an initial understanding of the liquefaction risk and potential damage to the tanks at the site.

Table 1 (below) summarises the ground model, susceptibility, triggering and consequences as a result of the simplified analysis. A median groundwater table of 1.5 m below ground level (bgl) was used.

The simplified method identified that further analysis and/or liquefaction mitigation will need to consider the following geotechnical issues:

1. Potential for liquefaction of the upper sand resulting in bearing failure of the foundations and large differential settlements.
2. Liquefaction of the lower loose sand layer resulting in large total settlements. However, global bearing failure of the tank foundation is unlikely as a result of this lower layer.

Table 1: Ground model, liquefaction susceptibility and triggering

*LSN = Liquefaction Severity Number, ** Sv1d = 1 dimensional free field settlement without tank loading

Opportunity identification using a system response approach

The simplified method described above does not account for a system response (Cubrinovski, M. et al. (2017)). In taking this approach, there are three key units expected to control the effects of liquefaction on the tank structure at this site:

• Liquefaction is triggered in the lower loose sand layer at around 0.1 to 0.15g using the simplified approach.
• The middle unit is a silt, which is expected to provide a “cap” to the lower sand and prevent excess pore pressure migration between upper and lower sand layers.
• Liquefaction is triggered in the upper sand layer at around 0.15 to 0.3g using the simplified approach.

When considering the system response, the lower loose sand is expected to liquefy at a lower PGA than the upper sand and therefore liquefy earlier in the earthquake. As a result of this, the lower loose sand can cause a “base isolation” effect, reducing the PGA and the potential of liquefaction triggering within the upper sand layers. It was therefore recognised that the simplified approach may be providing a more severe consequence than what would be expected if considering the soil layers as a system. This was also consistent with the analysis and observations in Cubrinovski, M. et al. (2017). Detailed modelling was needed to justify this approach for the project.

An opportunity was recognised to obtain a more accurate response of the structure by completing more detailed numerical modelling which considers a system response (or inter-layer effects). This was considered compelling for the client as it would allow them to:

• Understand more about the seismic performance of their existing tank structures on the site.
• Reduce the uncertainty and risk in relation to liquefaction at their site.
• Create an opportunity to reduce or remove ground improvement from the foundation design for future tanks.

System response analysis

To simulate the soil system response, numerical simulations were undertaken using FLAC 8.0 (produced by Itasca Consulting Group). The model was run seven times with different earthquake time histories scaled to meet the target spectra for the site. The following sections discuss the modelling approach and aspects of the model which may be refined in future design phases. In general, we consider the model output to be sufficiently accurate for a preliminary study.

Figure 2: Geometry and boundary conditions implemented in the FLAC model

Constitutive models

The soil layers judged most susceptible to liquefaction based on Boulanger and Idriss triggering procedures were modelled using the PM4Sand constitutive model developed by Boulanger & Ziotopoulou (2017). PM4Sand is a stress-ratio controlled, critical state compatible, bounding surface plasticity model for sand. The model was developed and implemented to approximate stress-strain responses of specific importance to geotechnical earthquake engineering and liquefaction problems.

For soil layers less susceptible to liquefaction, Mohr-Coulomb behaviour was assumed.

Boundary conditions

The input ground motion was applied at the base of the model where a viscous boundary was employed to avoid the reflection of seismic waves. Input motions were defined through a velocity time-history applied at the base in terms of shear stresses. Free-field boundaries were used at the sides of the model to minimize the seismic wave reflection. We note that the free-field boundary condition has yet to be validated for the PM4Sand model. However, alternative boundary conditions were observed to lead to unrealistic results.

Material properties

Material properties for Mohr-Coulomb materials were developed from the results of geotechnical investigations comprising boreholes and CPTs from across the site. Shear wave velocities estimated from CPT results were approximately 130 m/s for the lower loose sand layer and 200 m/s for the upper medium dense sand layer.

PM4Sand input parameters were calibrated following the recommendations of Boulanger & Idriss (2014). This entailed matching the number of cycles to trigger liquefaction in a simulated cyclic shear test () with predicted from CPT based correlations (Cubrinovski et al., 2017). Calibrations were undertaken under the effective stress corresponding to mid-depth of each PM4Sand layer.

Permeability testing has not been completed at the site. Instead, soil permeability was assumed based on the available investigation data. Importantly, the silt layer at approximately 10 m depth was assigned low permeability relative to the over- and underlying sand. This effectively prevented the migration of excess pore pressures between upper and lower sand layers.

Ground motion selection

Seven earthquake time history records were selected and scaled to be used as input ground motions to the FLAC model. These time history records are representative of the design ‘outcrop’ ground motions for the reference ground conditions at the base of the FLAC model.

The target acceleration response spectrum has been determined using the recommended spectrum in NZS1170.5:2004 for a ‘Class D – deep soil site’, a 500 year design earthquake return period with M_w 6 and PGA 0.25g. This is because the soil layers below the base of the FLAC model are consistent with Class D – deep soils. The tank structures are considered to be analogous to Importance Level 2 structures in terms of NZS1170.0:2002 (equivalent to seismic use group 1 in API650).

The selection and scaling of time history records has been carried out in general accordance with the recommendations of the PEER (2014) guidelines for Ground Response Analysis (GRA). The selection process considered the following factors:

1. The target acceleration response spectrum for the reference ground conditions underlying the base of the GRA model and the ULS level of shaking under consideration.
2. The period range of importance for the GRA analysis.
3. The seismological signature of the site (i.e. likely earthquake magnitude, fault mechanism, source-to-site distance and duration).

The time history records have been sourced from the Pacific Earthquake Engineering Research Centre (PEER) ground motion database.

Results

For the seven scaled ground motions, the simulated response shows significant variability. This is reflected in Figure 3 where maximum acceleration, excess pore pressure and shear strain are shown as a function of depth. However, there are several behaviours that are common to all the simulated motions:

• Liquefaction (Ru = 1) only occurs at the upper extent of the lower sand layer.
• Excess pore pressures within the upper sand layer are typically less than 0.3
• Peak horizontal accelerations are generally lower in the upper sand layer compared to the lower sand layer.
• Shear strains are localized close to the interface between the silt and lower sand layers.

Figure 3: Summary of FLAC output (all 7 ground motions)

Figure 4: Time histories of acceleration and excess pore pressure ratio for a single ground motion.

Combined, the simulated ground motions indicate that the upper sand layer is to a large degree isolated due to softening / liquefaction of the lower sand layer. More detailed results of a single scaled ground motion are presented in Figure 4.

For the ground motion shown in Figure 4, the base isolation effect is particularly clear with reduced horizontal accelerations in the upper sand layer following triggering of liquefaction lower in the soil column.

Impact on the tank foundation

The response of the structure was analysed using a 2D axisymmetric model in Plaxis (2018). Two models were prepared to compare the simplified approach and the system response approach. The differences are described below:

• Model 1: based on the simplified approach, assuming full liquefaction within both upper and lower sand layers, with liquefied soil parameters based on Idriss and Boulanger (2008).
• Model 2: based on the system response approach using the maximum excess pore water pressure ratio (Ru) from numerical analysis for soils susceptible to liquefaction. For the upper sand layer, where soil was shown to soften, soil stiffness and strength parameters were reduced by a factor Ru corresponding to the maximum excess pore pressure ratio from the seven simulations. Liquefied soil parameters for the lower sand layer were based on Idriss and Boulanger (2008).

Table 2 below provides a comparison of effects on the tank foundation between the two approaches.

Table 2: Comparison to simplified analysis and system response approach for a ULS Event

*LSN = Liquefaction severity number, Sv1d = Free field settlement. Both these values have been obtained from the simplified liquefaction analysis. For Model 2 the values have been determined assuming the upper sand layer does not liquefy, taking the contribution only from the lower layer.

As can be seen in the table, with a simplified analysis, the factor of safety is predicted to be less than 1.0 which is unacceptable. Large uncontrolled displacements are estimated.

However, with the system response approach, the tank stability (API650, 2012) was considered acceptable for a seismic ULS event. Provided the client and structural engineer could accept the predicted settlements, ground improvement was not considered necessary. If the settlements were unacceptable, then less ground improvement was considered necessary when taking a system response approach, compared to a simplified approach.

Next steps at future design stages

The analysis described above was completed as part of the project concept design phase for the purpose of preparation of construction cost estimates. During future design phases it is proposed to complete the following analysis in order to refine the accuracy of the settlement predictions:

1. Introduce tank loading into the FLAC model to better consider soil-structure-interaction.
2. For preliminary analysis a free-field boundary condition was applied to the vertical boundaries of the model. Validation of the PM4Sand model with a free field boundary is yet to be undertaken.
3. Extension of areas modelled using PM4Sand to greater depths within the lower sand layer. This may require extending the base of the model to prevent reflections within Mohr-Coulomb soil.
4. Consider tank “sloshing” effects with input from the structural engineer on this behaviour.

Limitations and uncertainties

When comparing system response analysis with empirical methods it is important to recognise the two methods are often complimentary and that one method is not necessarily better than the other. The system response method has a few limitations and uncertainties, including:

1. System response analysis does not capture the complete picture of the dynamic response of the soil. For example, it only considers vertically propagating horizontal shear waves, and does not incorporate aspects such as vertical accelerations and surface waves which may affect the response.
2. System response analysis is still subject to significant uncertainties, for example ground motions and soil conditions. The accuracy of the analysis is still dependent on the quality of the seismic hazard assessment and the site investigation data.
3. In the absence of cyclic laboratory testing on undisturbed samples, the system response method is still reliant on empirical methods to calibrate liquefaction triggering parameters.

Conclusion

This assessment has drawn the following conclusions and discussion points:

• This paper has shown the identification of an opportunity and its implementation to obtain a more accurate soil to structure interaction response as a result of earthquake induced liquefaction.
• The simplified method of Boulanger & Idriss (2014) is appropriate as an initial assessment to understand the response of individual layers, and it may be appropriate for regional liquefaction assessments or assessment of assets of low importance or value. However, consideration should always be given as to the potential for system response effects, and more advanced techniques may be more appropriate to determine the overall system response.
• In this case study, consideration of the system response showed reduced demand at the ground surface. However, this is unlikely to be the case universally. Analysis of the system response should be considered where simplified methods may result in an incorrect response, and the outcome of the analysis is critical to the seismic performance of the asset.
• This study shows the successful application of the system response approach (Cubrinovski, M. et al. (2017)) within industry. This approach is not reserved for academic study and should be used more regularly for practical application within industry.
• It would beneficial to form a working group tasked with developing a guide for application of liquefaction system response within industry. This guide would provide a consistent approach to be used and support our industry in completing this type of assessment.

References

API650. 2012. American Petroleum Institute, Welded Tanks for Oil Storage, Effective from 1 February 2012.

• Boulanger, R. W., and Ziotopoulou, K. 2017. PM4Sand (version 3.1): A sand plasticity model for earthquake engineering applications. Report No. UCD/CGM-17/01, Center for Geotechnical Modelling, Department of Civil and Environmental Engineering, University of California, Davis, CA.

Cubrinovski, M., Rhodes A., Ntritsos, N., Van Ballegooy, S. 2017. System response of liquefiable deposits, Proceedings, 3^rd International Conference on Performance-Based Design in Earthquake Geotechnical Engineering, PBDIII, Vancouver, Canada, July 16-19, 2017.

• Idriss, I. M., and Boulanger, R. W. 2008. Soil liquefaction during earthquakes. Monograph MNO-12, Earthquake Engineering Research Institute, Oakland, CA, 261 pp.
• Ministry of Business Innovation and Employment (MBIE). 2016. Module 3: Identification, assessment, and mitigation of liquefaction hazards
• Standards New Zealand. 2004. NZS1170.5:2004. Structural Design Actions, Part 5: Earthquake actions – New Zealand
• Pacific Earthquake Engineering Research Center. 2014. Guidelines for Performing Hazard-Consistent One-Dimensional Ground Response Analysis for Ground Motion Prediction. PEER Report 2014/16.

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