This document compares the Apeiron Liquefaction Calculator against Cliq v3.5.2.22.
Summary
This study provides a detailed comparison of CPT-based liquefaction susceptibility and triggering calculations between Apeiron and Cliq. For this benchmarking exercise, we selected 65 CPTs from across New Zealand, representing diverse conditions including varying PGA (peak ground acceleration), Mw (magnitude), user-defined Ic (soil behaviour index), and cut/fill scenarios.
Damage indicators up to 15 m below ground level (m.b.g.l.) are used to quantify the differences between Apeiron and Cliq. These indicators include sv1d (liquefaction-induced volumetric settlement), LSN (Liquefaction Severity Number), LPI (Liquefaction Potential Index), and LD (Lateral displacement). The results are provided in Appendix A.
Results suggest that Apeiron and Cliq results match closely. There's a difference in assumption on how the relative density is estimated from CPT data, which resulted in some differences in the LD results. The document demonstrates that if the same assumptions are adopted for relative density estimation, the results show a very close match in the LD values.
Overall, Apeiron and Cliq results are matching well.
Objective
- Document all test cases for comparison
- Identify the differences in assumptions made in Apeiron and Cliq.
Methodology
All test cases in this documentation were assessed using the methodologies summarised in the table below.
| Analysis | Methodology |
|---|---|
| Liquefaction Triggering | Boulanger and Idriss (2014) |
| Settlement analysis | Zhang et al. (2002) |
| Lateral displacement | Zhang et al. (2004) |
| Ic calculation | Robertson and Wright (1998) |
Settings in Cliq
The following options are adjusted from the default values in Cliq in order to match the assumptions adopted in Apeiron. The assumptions adopted in Apeiron are listed here.
- The liquefaction methodology is set to ‘Boulanger and Idriss (2014)’.
- In ‘Basic Parameters’, the ‘Average Results Interval’ is set to ‘1’ (default value is ‘3’). This means no rolling average is calculated after the analysis.
- In ‘Basic Parameters’, the option to ‘automatically calculate unit weight’ is disabled.
- In ‘Advanced Parameters’, the option to use ‘factor of 2 in dry settlement’ is disabled.
- In ‘I&B (2008)’, the option to ‘calculate settlement according to Zhang et al. (2002)’ is enabled. Although ‘I&B 2008’ is not used in our analysis, this setting also applies to ‘B&I 2014’ in Cliq.
- When a cut is specified, the applied load is set to 0 kPa.
- The analysis limit is set to 15 m in both Cliq and Apeiron, so that differences in cumulative damage indicators can be compared.
Analysis Input Parameters
The test cases input and CPTs used in the analysis are summarised here.
| Cases | PGA | Magnitude (Mw) | Investigation GWL | Design GWL | Cut / Fill | Ic cut-off | Unit weight | Slope (%) |
|---|---|---|---|---|---|---|---|---|
| 1 | 0.24 | 7.0 | 2 | 1 | Not applied | 2.6 | 19 | 1 |
| 2 | 0.2 | 5.5 | 3 | 1 | 2m cut | 2.6 | 19 | 2 |
| 3 | 0.3 | 6.5 | 2 | 0.5 | 2m fill | 2.9 | 19 | 1 |
| 4 | 0.5 | 8.0 | 2 | 0.5 | Not applied | 2.4 | 19 | 2 |
Investigations used for testing
All investigations used are publicly available CPT’s in New Zealand.
| Cases | Number of CPT |
|---|---|
| Case 1 | 29 |
| Case 2 | 17 |
| Case 3 | 7 |
| Case 4 | 12 |
Glossary
| Parameter | Unit | Description |
|---|---|---|
| sigma’v | kPa | Vertical effective stress during design, after cut, fill or surcharge is applied. |
| delta_qc1N | dimensionless | The equivalent clean sand adjustment for CPT from Eqn 2.22 in Boulanger and Idriss (2014). |
| Qc1N | dimensionless | Normalised cone resistance from Eqn 2.4 in Boulanger and Idriss (2014) |
| Qc1Ncs | dimensionless | Clean sand equivalent normalised cone resistance from Eqn 2.10 in Boulanger and Idriss (2014). |
| Ic | dimensionless | Soil behaviour type index calculated using Robertson and Wride (1998). |
| FC | % | Fines content in percentage. |
| r_d | dimensionless | Shear stress reduction coeficcient from Eqn 2.14a in Boulanger and Idriss (2014). |
| CRR_15 | dimensionless | 15th Percentile Cyclic Resistance Ratio from Boulanger and Idriss (2014). |
| CSR | dimensionless | Cyclic Stress Ratio from Boulanger and Idriss (2014). |
| MSF | dimensionless | Magnitude Scaling Factor from Boulanger and Idriss (2014). |
| LSN | dimensionless | Liquefaction Severity Number |
| LPI | dimensionless | Liquefaction Potential Index |
| LD | mm | Lateral Displacement calculated using Zhang et al. (2004) |
| LDI | mm | Lateral Displacement Index calculated using Zhang et al. (2004) |
| FoS | dimensionless | Factor of Safety agasint liquefaction triggering |
| sv1d | mm | One dimensional volumetric settlement due to liquefaction from Zhang et al. (2002) |
| gamma_max | % | Maximum cyclic shear strain from Zhang et al. (2004) |
| e_v | % | Post-liquefaction volumetric strain from Zhang et al. (2002) |
Summary of results
A typical CPT is presented in the figures below. The red traces are the results from Cliq. The blue traces are the results from Apeiron. In most cases they closely match and overlay each other. The differences are discussed in detail in the next section.
Site 1, CPT 58560 results graph 1
Site 1, CPT 58560 results graph 2
Histogram of percentage and absolute differences
The surface damage indicators are used to quantify the difference between Apeiron and Cliq. Surface damage indicators LSN, LPI, LD and Sv1d for the top 15 m are calculated for each CPT.
Histograms are created to quantify the difference between Apeiron and Cliq for each site.
The absolute difference and percentage difference are calculated using the formula below:
Percentage difference of damage indicators
Site 1 Surface damage indicator histogram - percentage
Site 2 Surface damage indicator histogram - percentage
Site 3 Surface damage indicator histogram - percentage
Site 4 Surface damage indicator histogram - percentage
All histograms use a 5% bin size. For all sites, the differences in surface damage indicators between Apeiron and Cliq are generally within +/- 5%. The only exception is the lateral displacements. The differences are discussed in more detail in the next Section.
Absolute difference of damage indicators
Site 1 Surface damage indicator histogram - absolute values
Site 2 Surface damage indicator histogram - absolute values
Site 3 Surface damage indicator histogram - absolute values
Site 4 Surface damage indicator histogram - absolute values
Differences between Apeiron and Cliq results
The differences come from the following:
- Calculation of Ic, fines content, qc1ncs, CRR at data points where the liquefaction is not susceptible. Note that only the Ic calculation fluctuation affects the damage indicators, as it is used to determine whether a layer is susceptible; the calculation differences in the non-susceptible layers do not affect the damage indicator calculations, as the contribution in layers not susceptible to liquefaction is always zero in Apeiron and Cliq.
- Rounding of gamma_max in Zhang et al. 2004, which is used to calculate the lateral displacement index and lateral displacement.
- In Zhang et al. (2004), Equation 2, Apeiron uses qc1Ncs to estimate the relative density, Cliq uses qc1N to estimate the relative density.
1. Calculation of Ic, fines content, qc1ncs, CRR
The calculation process for layers not susceptible to liquefaction is different between Apeiron and Cliq. If a data point is not susceptible to liquefaction:
| Parameter | Apeiron | Cliq |
|---|---|---|
| Ic at layers where liquefaction is suceptible | Robertson and Wride (1998) | Robertson and Wride (1998) |
| Ic at layers where liquefaction is not suceptible | Robertson and Wride (1998) | Robertson and Wride (1998), but likely using a different initial exponent n value |
| delta_qc1N | Always calculated, whether a layer is susceptible or not | Only calculated for layers that are susceptible to liquefaction |
| qc1Ncs | Always adjusted using delta_qc1N | Adjustments only applied when the layer is susceptible to liquefaction (since delta_qc1N is not calculated for layers not susceptible) |
| CRR | Always calculated based on qc1Ncs | Automatically set to 4.0 for non-susceptible layers |
| CSR | Always calculated | Automatically set to 2.0 for non-susceptible layers |
| FoS | Always calculated, no capping applied | Automatically set to 2.0 for non-susceptible layers, and always capped to a maximum of 2.0 if the calculated FoS is greater than 2.0 |
Apeiron follows Robertson and Wride (1998) and performs a three-step process to calculate Ic. The detailed methodology is available here.
Cliq follows the same process using the Settings detail above, however, the calculation over layers where liquefaction is not susceptible, there’s a minor difference.
A typical comparison between Apeiron and Cliq results are shown in the plots below.
Site 2, CPT 55603 Results graph 1
Site 2, CPT 55603 Results graph 2
Site 3 has a slightly larger difference compared to the other sites due to a small difference in Ic near the surface. An example is CPT_163663.
Site 3, CPT 163663 Results graph 1
Site 3, CPT 163663 Results graph 2
In the Site 3 example, the difference in Ic between 2 - 3 mbgl is minor, but resulted in a fluctuation of Ic above and below the user-specified Ic cut-off value of 2.9 in this case. This led to a steeper increase in all damage indicators between 2 - 3 m.b.g.l.
The difference in lateral displacement and LDI are discussed in point 3 below.
2. Gamma_max and e_v calculations
In Apeiron, the maximum cyclic shear strain, gamma_max in Zhang et al. (2004) is calculated using the equations in Appendix A. Since these equations are only provided for relative densities equal to 40 - 90 at multiples of 10, when the relative density is not a multiple of 10, linear interpolation is used to estimate gamma_max based on the relative denstiy. In Cliq, some values of gamma_max are rounded based on the relative density, resulting in minor differences in gamma_max.
3. Estimating relative density in Zhang et al. (2004)
Zhang et al. (2004) references Tatsuoka et al. (1990) in Equation 2. Tatsuoka et al. (1990) uses qc1N to estimate relative density D_r, which is later used in Fig 1 in Zhang et al. (2004) (functionalised in Appendix A) to estimate the maximum cyclic shear strain, gamma_max.
Apeiron uses the clean sand equivalent, qc1Ncs, calculated in the liquefaction triggering assessment instead of qc1N to estimate the relative density. Cliq uses the original qc1N to estimate the relative density.
This causes a difference in gamma_max when there’s a large difference in qc1N and qc1Ncs. The difference between qc1N and qc1Ncs is delta_qc1N, which is calculated iteratively in Boulanger and Idriss (2014) using qc1N and fines content (FC).
If qc1N is used to calculate Dr in Apeiron, the results would match. There are still minor rounding differences, but the surface damage indicators are essentially the same.
Take CPT_100468 in Site 1 as an example, the results using qc1Ncs as input to estimate relative density are shown below:
Site 1, CPT 100468 results graph 1, using qc1Ncs to estimate Dr based on Eqn 2 in Zhang et al. (2004)
Site 1, CPT 100468 results graph 1, using qc1Ncs to estimate Dr based on Eqn 2 in Zhang et al. (2004)
The results using qc1N (Cliq’s approach) as input to estimate relative density are shown below:
Site 1, CPT 100468 results graph 1, using qc1N to estimate Dr based on Eqn 2 in Zhang et al. (2004)
Site 1, CPT 100468 results graph 2, using qc1N to estimate Dr based on Eqn 2 in Zhang et al. (2004)
Conclusion
65 CPT investigations across New Zealand were selected for this benchmarking exercise to compare the liquefaction triggering results between Aperion and Cliq. A range of input seismic shaking levels and site conditions, such as cut and fill are included in the test.
Apeiron and Cliq liquefaction analysis results compare well when the same assumptions are adopted. There's a difference in assumption on how the relative density is estimated from CPT data, and how gamma_max is rounded, which resulted in some differences in the LD results. The document demonstrates that if the same assumptions are adopted for relative density estimation, the results show a very close match in the LD values.
Overall, the liquefaction analysis results between Apeiron and Cliq match closely.
The full results for all CPT's can be downloaded here: