A site-specific geotechnical engineering approach was proposed as part of a seismic retrofit design of a multi-storey building in Christchurch CBD (Central Business District). Various analytical techniques were utilized including Probabilistic Seismic Hazard Analysis (PSHA), development of time histories, Site Specific Response Analysis (SSRA), and Soil Foundation-Structure Interaction (SFSI). Miyamoto’s New Zealand seismic hazard model was used as the basis for computing PSHA and deaggregation. The hazard model is developed using open-source Seismic Hazard Analysis (SHA) software (OpenQuake 2.1.0). This model includes active faults, area sources, and time-dependent point source model based on the modified-Oomori Law. It was compared with the New Zealand National Seismic Hazard Model (NZSHM) which form the basis for NZS 1170.5:2004. A suite of eleven spectrally-matched, single-component horizontal earthquake acceleration time histories, was developed for each of the 25-year and 500-year return period loading conditions. Then, the time histories were propagated from Riccarton Gravel to ground surface using non-linear, one dimensional (1D) total stress analysis in DEEPSOIL 6.1. A medium-rise multi-storey building with a 3.0m deep basement was modelled and analysed in ETABS software using non-linear elements. Dynamic soil properties were derived from the analysis of geotechnical data acquired from the site, this included shear wave velocity (Vs) profiles from downhole tests. The result from the geotechnical analysis can be used as the input for models incorporating soil foundation-structure interaction with further refinement and verification. This approach requires more effort but does provide an improved and realistic result of the building’s behaviour including considerations of the influence of soil foundation-structure interaction.
For the majority of practices in New Zealand, the most widely adopted methodology to calculate earthquake demand to building structures involves using the hazard factor, Z in combination with site classification as per NZS 1170.5:2004. The elastic site spectra for horizontal loading as per NZS 1170.5 is simplified using spectral shape coefficient based on site classification of Soils A, B, C, D, and E without considering site specific effect, i.e. non-linear behaviour of the soil and liquefaction. The Z factor map in NZS 1170.5 is generalised in an effort to cover all New Zealand but limited to an earthquake database up to the year 2000 while several mid to high-rise buildings in Christchurch were damaged from earthquake shaking and/or soil liquefaction during the 2010-2011 Canterbury Earthquake Sequence (CES). In a lot of designs, the geotechnical and the structural engineer fail to work in a collaborative manner, and ultimately, the intricacies in soil foundation-structural-interaction are not captured and/or explored.
An example of the current application of site-specific geotechnical earthquake engineering is illustrated in Figure 1. The Probabilistic Seismic Hazard Analysis (PSHA), development of time histories, seismic 1D Site Specific Response Analysis (SSRA), and Soil Foundation-Structure Interaction (SFSI) are typically used in important/critical infrastructure projects, i.e. nuclear powerplants, tall buildings, large dams, and long-span bridges. However, with the development of increasingly powerful and affordable personal computers in modern times, combined with the availability of reasonably priced and open-source software alternatives, advanced analytical methods have never been more accessible and cost effective even with small to medium sized projects.
This paper presents an example to demonstrate how the method can be applied to small-medium engineering design projects for New Zealand engineering practice. Most of the analysis is not included in this paper due to space constraint.
Figure 1: Advance geotechnical earthquake engineering: (1) Probabilistic seismic hazard analysis; (2) time histories development; (3) seismic ground response analysis; (4) soil foundation-structure interaction
BUILDING AND SITE DESCRIPTION
The example case is an eight-storey reinforced concrete-framed commercial building with the upper two storeys being smaller in plan and the final storey built as a lightweight penthouse. The building extends into the ground to 1 basement level, covering footprint of approximately 300m². The foundation is a reinforced concrete mat foundation. The concrete structure was built around 1958. The building consists of six concrete frames in the east-west (transverse) direction and four concrete frames in the north-south (longitudinal) direction, Each floor has a 115mm thick suspended concrete slab and beams. Beam sizes are consistent throughout the building, and column sizes gradually reduce from ground to the upper floors.
The west elevation contains masonry infill walls, and there is a full-height opening on the west side of the building, where a lift and concrete stairs are located. At the first-floor level, a 2.4 m concrete canopy overhangs the street on the east and south sides and is supported by a deep beam. Low height walls up to sill level and brick infill walls are located between the perimeter columns at each level. The building foundation, north, and east elevation are shown in Figure 2.
Figure 2: Foundation plan view (with ground investigation locations) and elevation view of its north and east oriented frame
Two well-boreholes (M1 and M2), and two machine boreholes to a maximum depth of 33 m below ground level (bgl) were downloaded from Environmental Canterbury and New Zealand Geotechnical Database website. The three Piezocone Penetration Test (CPT) was undertaken by ENGEO to a maximum depth of 15.0 m, and the raw data was provided to Miyamoto International NZ (MINZ). Further to the above MINZ undertook (1) a 30m borehole for the installation of a grouted PVC pipe; (2) laboratory testing on retrieved disturbed soil samples (fines content and plasticity indexes); and (3) downhole shear (Vs) and compressional (Vp) wave velocity surveys down to 30 m and 5 m respectively. The ground profile and geotechnical properties have been developed following a detailed evaluation of existing and new geotechnical data, the resulting ground model and parameters are shown in Figure 3. Small strain shear modulus, Gmax, is a fundamental parameter for SSRA and DSFSI. Gmax for the soils underlying the site was determined from shear wave velocity, Vs, as
where ρ is the total density of the soil.
Vs were derived from the downhole shear test and CPT data using a Christchurch-specific correlation proposed by McGann et al. (2014). The measured and calculated Vs for each of the CPTs to a depth of 15.0m are included in Figure 3. The calculated Vs from CPT of the sandy and silty soils correlate well with measured Vs from the downhole test (correlation coefficient = 0.7 – 0.9). The base of the SSRA model (Riccarton gravels) is set at a depth of 30m bgl and was assigned an average Vs of 450m/s. The Vs profile for seismic ground response analysis is also shown in Figure 3. The estimated site period of the ground is between 0.55s to 0.65s from Riccarton Gravel.
Figure 3: Ground profile at the site with measured, calculated, and SSRA model of Vs, and laboratory test result
SEISMIC SOURCE MODEL
The seismic source model has been developed from the available published geological, tectonic and seismological information. The sources model includes active faults, area sources, and time-dependent point source model based on modified Oomori Law, as describe below:
1. Existing active fault and area seismic sources throughout New Zealand have been characterised and incorporated into the 2010 New Zealand National Seismic Hazard Model (NZSHM). Details of the data for the NZSHM can be found in Stirling et al. (2012) and can be downloaded through GNS website.
2. The fault database has been updated based on the data compiled by Langridge et al. (2016) as shown in the New Zealand active faults database (http://data.gns.cri.nz/af/).
3. The fault trace has been re-traced using the Light Detection and Ranging (LIDAR). The data was downloaded from Land Information New Zealand (LINZ) website (https://data.linz.govt.nz/layers/) and incorporated to open-source software called QGIS version 2.18 as shown in Figure 4.
4. Seismic hazard parameters presented in this paper are based on the NZSHM seismic source models uploaded to open-source SHA software (OpenQuake 2.1.0) and updated to the latest study.
5. The maximum magnitudes of faults were updated based on scaling relations suggested by Stirling et al. (2013).
6. The area sources using gridded (smoothed) seismicity model was updated using an earthquake catalogue before 2016. The earthquake catalogue is downloaded from GeoNet and ISC-GEM (Storchak et al., 2013) website.
7. The earthquake magnitude recorded in local magnitude (ML) and body wave magnitude (Mb) recorded in earthquake catalogue were converted to moment magnitude (Mw) using relationship proposed by Ristau (2009).
8. After combining two individual catalogues, duplicate earthquake events were removed with GNS catalogue as a primary source.
9. The full catalogue was declustered using the algorithm proposed by Gardner and Knopoff (1974).
10. The earthquake records within the declustered catalogue were evaluated for completeness.
11. A free Python and R programming were used during the process above.
12. A 50km Gaussian kernel as proposed by Frankel (1995) was used. A Fortran programming script developed by Frankel (1995) for 1996, 2002 and 2008 USGS seismic hazard map was used in this study. The region was divided into cells of 0.1° in latitude and 0.1° in longitude.
13. The Ground Motion Prediction Equation (GMPEs) presents earthquake ground motion attenuations where different from NZSHM and shown in Figure 5. New Zealand site-specific Ground Motion Prediction Equation (GMPE) by Bradley (2013) and McVerry et al. (2006) have been used.
14. Logic tree analyses were used to account for epistemic uncertainty in the magnitude and GMPE as shown in Figure 5.
Figure 4: Fault database and declustered earthquake catalogue used in this study
Figure 5: The example output of gridded (smoothed) seismicity model and logic tree model used in this study
TIME-DEPENDENT MODEL USING MODIFIED OOMORI LAW
A key assumption of the standard PSHA model is that earthquake occurrences can be modelled as a Poisson time independent process. However, standard PSHA does not model hazard decay, resulting from and event(s) such as the CES, over the typical 50-year design life of future buildings and structures. The time-dependent model in this study follows the procedure proposed by Bradley (2014, 2016) with the following modifications:
1. The activity rate was modelled as 55 points sources on 0.1° x 0.1° grid over an area of -43.75° to -43.25° Latitudes and 172° to 173° Longitude as shown in Figure 6.
2. Depth uncertainty was incorporated by weighting the activity rate at depths of 2km (10%), 5km (30%), 10km (40%), and 18km (20%).
3. The earthquake recurrence parameter, b-value of 0.9 is considered conservative value which follow the cumulative number of event as shown in Figure 7.
Figure 6: Spatial distribution of Mw≥3.5 earthquake events in the CES. The considered region of -43.75° to -43.25° Latitude and 172° to 173° Longitude
Figure 7: The predicted rate of aftershocks from 1 January 2017(Mw>3.5 à 38 events, Rate@M5=1.7 for next 50 years
UNIFORM HAZARD SPECTRA (UHS), DEAGGREGATION, DEVELOPMENT OF TIME HISTORIES, SSRA AND DSFSI
A PSHA (Cornell, 1968) was used to assess the target uniform hazard spectra and controlling earthquake rupture scenarios for the site. The PSHA was carried out using open-source software OpenQuake 2.1.0 (Pagani, 2014) to evaluate the site seismic hazard. The PSHA model included a time-independent analysis as per the standard PSHA as well as a time-dependent analysis.
The PSHA was carried out for Riccarton Gravel site conditions with an assumed average shear wave velocity in the upper 30m (Vs30) of 450m/s. Bradley (2015) observed the ground motion records associated with the CES and found that there was a systematic shift between the predicted and observed spectral acceleration at different spectral periods. The authors have applied the proposed correction factor for the Central Business District (CBD) to our PSHA results.
The predominant site periods were estimated as 0.6s, thereby the seismic hazard of 25-year and 500-year return periods are deaggregated at a spectral period of 0.6s as a way to identify the predominant earthquake moment magnitude (M) and source-to-site distance that contributes most to the seismic hazard at the site.
Spectrally-matched, single-component horizontal earthquake acceleration time histories were developed for each of the two return periods, 25-year and 500-year. The time history development follows the standard North American practice of selection time histories and spectral matching.
The authors searched the PEER NGA-West2 earthquake record database and the GeoNet strong motion database (Van Houtte et al., 2017), and selected acceleration time histories whose response spectra, after linear scaling, correlated well with the target spectra close to the fundamental site period. The selected scale factors range from 0.5 to 4. The suite of selected seed time histories generally covers the contributing earthquake magnitudes and source-to-site distances as indicated from deaggregation results.
For the time histories selected in this study, the spectral matching was accomplished using RSPMatch09 software developed by Al Atik and Abrahamson (2010). SSRA was completed using the Christchurch specific silty and sandy soils constitutive model developed by Arefi (2014) as well as the Idaho-US gravelly soil model developed by Menq (2003).
1D nonlinear total stress ground response analysis has been undertaken using Deepsoil v6.1 software (Hashash et al., 2016). The ground profile was subjected to each of the eleven time-histories. The surface ground response spectra are presented in Figure 8.
Figure 8: The surface ground response spectra and ETABS model showing displacement with consideration of SFSI
STRUCTURAL MODEL INCORPORATING SOIL FOUNDATION-STRUCTURE INTERACTION
The model of the building was constructed in ETABS including the basement level.
The soil foundation-structure interaction was modelled as bilinear compression only springs (no uplift capacity), at the base of the external basement walls as shown in Figure 8, using ETABS. The force-displacement curve was averaged from half of the building’s footprint and distributed into a theoretical 1m strip beneath the walls.
The initial result of the modal analysis showed that the building’s fundamental period of vibration to be in excess of 1.5s, in comparison to 0.5s if assuming that the building is fixed at the base. One of the issues in using this approach is that the confining effect of the soil on the side walls was ignored. The period directly from the ETABS model is approaching to the result of pure rocking model whereas in reality the structure behaviour should be in between a full rocking structure and fixed based structure. This is due to the fact that confining effect due the soil acting on the side basement walls were not accounted for. Further verification of the model was completed as a secondary check and refinement. The result reduces the effective period of the building from a full rocking period of 1.5s to around 1.2s.
In addition, an ‘corrected’ forced based method described by B.Sporn and Pampanin (2013) was used to check the base shear. This was completed by iterating the period and stiffness of the structure until convergence. For an assumed ductility of 1.25, the period corresponding was eventually estimated to be 1.2s and agreement with the result.
SUMMARY AND CONCLUSION
The multi-story building in Christchurch CBD constructed around 1958 was assessed by applying a site-specific geotechnical earthquake engineering design approach using open-source software and automatization scripts, resulting in slightly lower spectral acceleration compared to the NZS 11705:2004 spectra. It can be shown that by using the result from site specific geotechnical engineering design approach, combined with further adjustment and verifications, a more realistic prediction of the building’s behaviour can be estimated rather than using a conservative approach of assuming fixed-based model.
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