Comparison of Vs and SPT Soil Liquefaction Assessments of NCEER: Including Hypothesis Testing

Min-Hao Wu¹, Jui-Pin Wang^2*, Chih-Kun Liao²

¹Department of Civil and Environmental Engineering, National University of Kaohsiung, Kaohsiung.
²Department of Civil Engineering, National Central University, Taoyuan.

DOI: 10.4236/ijg.2023.1411055                

Abstract

Soil liquefaction is one of the complex research topics in geotechnical engineering and engineering geology. Especially after the 1964 Niigata earthquake (Japan) induced many soil liquefaction incidents, a variety of soil liquefaction studies were conducted and reported, including the liquefaction potential assessment methods utilizing the shear wave velocity (V_s) or SPT-N profiles (SPT: standard penetration test). This study used the V_s and SPT methods recommended by the National Center for Earthquake Engineering Research (NCEER) to examine which is more conservative according to the assessment results on 41 liquefiable soil layers at sites in two major cities in Taiwan. Statistical hypothesis testing was used to make the analysis more quantitative and objective. Based on three sets of hypothesis tests, it shows that the hypothesis—the SPT method is more conservative than the V_s method—was not rejected on a 5% level of significance.

Keywords

Soil Liquefaction, Standard Penetration Test, Shear Wave Velocity, Hypothesis Testing

1. Introduction

Soil liquefaction is one of the complex research topics in earthquake engineering and engineering geology. In 1964, the Niigata earthquake induced many soil liquefaction incidents in the fields, subsequently causing hazards like failures of structural foundations, excessive ground settlements, and flotation of pipelines [1] . Afterward, the topic caught our attention, and many soil liquefaction studies have been conducted and reported in the past decades. Such studies include soil liquefaction assessment methods [2] - [9] , liquefaction potential case studies [10] - [15] , and soil liquefaction occurrence mechanisms [16] [17] [18] , among others [19] - [27] .

In engineering geology and geotechnical engineering, it is common to encounter the situation: multiple methods or empirical models are available for solving an exact problem. For example, there are more than ten empirical models [28] - [37] available for estimating the soil’s shear wave velocity (V_s) based on the SPT-N value (SPT: standard penetration test). Such difference was generally called “epistemic uncertainty” owing to our imperfect knowledge of the subject [38] [39] .

In the 1990s, the National Center for Earthquake Engineering Research (NCEER) convened workshops with the invited participants who specialized in soil liquefaction research (e.g., Professor T. L. Youd of Brigham Young University, Professor I. M. Idriss of the University of California at Davis, Professor R. D. Andrus of Clemson University). It reached several consensuses about soil liquefaction potential assessments [40] . The agreements include the recommended V_s and SPT methods for calculating the liquefaction factor of safety. Without a doubt, although the same institute recommended the two methods, the outcome must be different regardless. As a result, this also leads to an “epistemic uncertainty” situation as in other geotechnical studies.

This novel study compared the two methods of NCEER, utilizing statistical hypothesis testing to investigate which one is more conservative in an objective manner. The study was based on 41 liquefiable soil layers in two major cities in Taiwan, calculating their liquefaction safety factors using the NCEER’s V_s and SPT methods. Then, we conducted statistical hypothesis testing on the outcomes and obtained new statistical inferences, which are the most distinguished novelty and contribution to soil liquefaction research.

2. Methodology

2.1. Simplified Method

The simplified method proposed by [2] is one of the most distinguished works in soil liquefaction study. It is the foundation of the current in-situ soil liquefaction assessment methods widely used in site-specific liquefaction potential studies.

The simplified procedure calculates the liquefaction factor of safety (FS) with the following formulation:

$\text{FS}=\frac{{\text{CRR}}_{7.5}}{\text{CSR}}\times \text{MSF}$ (1)

where CRR_7.5 is the soil’s “cyclic resistance ratio” on the condition of earthquake moment magnitude = 7.5, CSR is the “cyclic stress ratio” induced by earthquake ground motions, and MSF is the “magnitude scaling factor” required in the analysis when the earthquake magnitude is not equal to 7.5.

To be more specific, the formulations of CSR and MSF are as follows:

$\text{CSR}=0.65\frac{\text{PGA}}{g}\frac{\sigma }{{\sigma }^{\prime }}{r}_d$ (2)

where r_d is the stress reduction factor, which decreases with depth (Figure 1); σ and σ' are the total and effective vertical earth pressures at the middle of the liquefiable layers. As to MSF, it is:

$\text{MSF}={\left(\frac{M_W}{7.5}\right)}^{-2.56}$ (3)

Note that in addition to Equation (3) proposed by NCEER, several other MSF formulations have been proposed by different researchers [41] [42] [43] [44] . Note that although different MSFs were proposed, they were recommended for magnitudes 5.5 - 8.5.

2.2. NCEER’s V_s and SPT Methods

As mentioned, the NCEER convened soil liquefaction workshops in the 1990s and proposed the V_s and SPT methods for calculating the liquefaction factor of safety. Note that the two were developed within the framework of the simplified procedure proposed by [2] . The technical details of the two methods are shown in Figures 2-5. Specifically, Figure 2 and Figure 3 are the analytical flowcharts when using the two methods to calculate liquefaction safety factors. Figure 4 shows the empirical plot to obtain CRR_7.5 based on V_s1, the normalized V_s considering the vertical earth pressure the target soil layer is subject to. Similarly, Figure 5 is the empirical plot to obtain CRR_7.5 based on the soil’s normalized SPT-N value (i.e., (N₁)₆₀).

Figure 1. Stress reduction factor vs. depth.

Figure 2. Flowchart for the SPT method.

2.3. Data

To examine whether the V_s method is more conservative than the SPT method (both recommended by NCEER), we applied both to exact soil layers. Suppose the safety factor obtained with the V_s method is always more significant than that via the SPT method for exact soil layers. In that case, the hypothesis—that the SPT method is more conservative than the V_s method—might be accepted.

As a result, the next critical task of this study is to gather liquefiable soil data. In this study, we utilized the database established by the National Center for Research on Earthquake Engineering (NCREE) of Taiwan. The database includes the soil profiles with the information like soil unit weights, fines content, USCS soil classifications (USCS: Unified Soil Classification System), as well as the V_s and SPT-N profiles of ~800 sites in Taiwan. The data set is adequate for us to calculate total stress, effective stress, stress reduction factor, etc., which are

Figure 3. Flowchart for the V_s method.

Figure 4. V_s1 vs. CRR_7.5 of the NCEER’s V_s procedure.

Figure 5. (N₁)₆₀ vs. CRR_7.5 of the NCEER’s SPT procedure.

required for calculating the liquefaction safety factor using the two methods above. Many investigators have used such a database for their research [45] [46] [47] [48] . Nevertheless, it is noted that NCREE only provided us with some of the data of the ~800 sites for some reason. The data we were provided are associated with the sites in Taipei and Kaohsiung areas of Taiwan.

2.4. Selecting Criteria and “Qualified” Soil Layers

The NCEER workshops [40] also concluded what types of soil are prone to liquefaction. The criteria are:

➢ The soil’s shear wave velocity in 100 - 200 m/s;

➢ The soil’s SPT-N value less than 30;

➢ The groundwater table at a depth of 0.5 - 6 m;

➢ The soil no deeper than 10 m below the ground surface;

In addition, we also referred to a similar guideline implemented by the NCREE (Taiwan) for determining liquefiable soil layers [49] . Besides the thresholds of SPT-N value, depth, etc., they considered the soil’s plasticity index (PI) threshold of 7 as far as soil liquefaction is concerned, or a soil layer with PI > 7 is considered non-liquefiable. As a result, the resultant criteria used in this study comprise the five thresholds. When a soil layer fails to fulfill one of them, the data will be excluded from our analysis.

2.5. Statistical Hypothesis Test

Many statistical hypothesis tests have been developed, such as the one testing or comparing whether the mean values of the two populations are equal. Such a hypothesis test is exactly what we need and use in this research, and its technical details are elaborated in the following.

The null hypothesis (H₀) of such a hypothesis test is set as μ₁ = μ₂ (where μ denotes the population mean), with the alternative hypothesis as μ₁ > μ₂. By definition, this is a right-tail hypothesis test. In addition, such a hypothesis test uses “Z” as the fundamental statistic, a random variable following the standard normal distribution.

As a result, the first calculation when conducting such a hypothesis test is to compute the Z value (denoted as Z_test) based on the information from the sample, including the respective sample mean, sample variance, and sample size. Specifically, it is equal to:

$Z_{\text{test}}=\frac{{\bar{X}}_1-{\bar{X}}_2}{\sqrt{\frac{S_1^2}{n_1}+\frac{S_2^2}{n_2}}}$ (4)

where ${\bar{X}}_1$ and ${\bar{X}}_2$ are the respective sample mean, $S_1^2$ and $S_2^2$ are the respective sample variance, $n_1$ and $n_2$ are the respective sample size.

Next, the hypothesis test calculates the critical value given a significance level (usually 5%) and determines the rejection region accordingly. Figure 6 shows the relationship between the two for a right-tail test. Specifically, since Z (following the standard normal distribution) is the statistic used by this test, the critical value equals 1.64 on a 5% significance level. Hence, the rejection region of this right-tail test is Z > 1.64. Then, when the Z_test value is located in the rejection region, the null hypothesis is rejected, and the alternative hypothesis is accepted.

3. Results

3.1. Factor of Safety

Figure 7 shows the factors of safety (FS) for the 41 target soil layers using the SPT and V_s methods recommended by the NCEER. Understandably, the deviation in the result (in FS) is due to the different site conditions. It shows that the variation of FS calculated with the V_s method is more significant than that with the SPT method. Nevertheless, there is no noticeable trend that the FS calculated by the V_s method is greater than that of the SPT counterpart. In some cases, the V_s method was found to be more conservative (with a smaller FS) than the SPT method, while the outcome was the opposite in others. Table 1 summarizes the mean value and variance (square of standard deviation) of the liquefaction safety factor from the 41 liquefiable layers.

Table 1. Summary of the hypothesis test for M = 7.5 and PGA = 0.3 g.

*Standard deviation.

Figure 6. Schematic diagram for the hypothesis testing used in this study.

(a)(b)

Figure 7. Liquefaction factor of safety from (a) SPT procedure; (b) V_s procedure.

3.2. Hypothesis Testing

Elaborated in the Methodology of this paper, we used hypothesis testing to examine whether the SPT method is more conservative than the V_s method, based on the information summarized in Table 1 from the (41) samples or soil layers. Accordingly, the Z value (Z_test) was equal to 1.895 based on Equation (4). By contrast, the critical value was 1.645 on a 5% level of significance. Hence, the rejection region is Z > 1.645 for such a right-tail hypothesis test. Then, because the calculated Z statistic was located in the rejection zone, the null hypothesis was rejected, and the alternative hypothesis was accepted: the SPT method is more conservative than the V_s method.

4. Discussion

4.1. More Significant Variation in the Outcome of the V_s Method

For a given soil layer with all other conditions (e.g., PGA, earthquake magnitude, soil unit weight, groundwater table) remained identical, the higher the soil’s shear wave velocity, the higher the soil’s safety factor against soil liquefaction. The same logic is applied to SPT. Nevertheless, the relationship between V_s (or SPT-N) and FS might be highly non-linear, which could be the cause to the more significant variation in the safety factor observed when the V_s method was used.

Figure 8 shows the relationship between the “V_s1 ratio” and “FS ratio” with all other conditions remaining identical. The V_s1 ratio was defined as V_s1 = y* (any value from 100 to 200 m/s) to V_s1 = 100 m/s, while the FS ratio was defined as the FS given V_s1 = y* to the FS given V_s1 = 100 m/s. It shows the curve is highly nonlinear, and when the V_s1 ratio increases twofold to 200 m/s from the base value or lower bound as 100 m/s, the FS ratio increases approximately sevenfold.

Figure 8. V_s1 ratio vs. FS ratio; the baseV_s1 value = 100 m/s.

By contrast, Figure 9 shows the relationship between the “(N₁)₆₀ ratio” and “FS ratio” with all other conditions remaining identical. With the base value of (N₁)₆₀ as 1, it was found that even though the (N₁)₆₀ ratio increased tenfold from 1 to 10, the FS ratio only increased twofold. As a result, because the liquefaction safety factor calculated using the V_s method is much more sensitive to V_s compared to the SPT method, this is the fundamental cause to the more significant variation in the outcome (Figure 8) using the V_s method to assess soil liquefaction potentials.

4.2. Different M-PGA Conditions

So far, the conclusion remark—the SPT method is more conservative than the V_s method—was obtained on the condition of earthquake magnitude (M) = 7.5 and PGA = 0.3 g, and we considered this was a “strong-earthquake” condition. We repeated the calculations and analyses under a “moderate-earthquake” and “weak-earthquake” condition to certify the finding. The respective magnitude and PGA are M = 7 and PGA = 0.2 g (moderate condition) and M = 6.5 and PGA = 0.1 g (weak condition).

Table 2 and Table 3 summarize the results of the additional analyses. For the moderate condition, the Z_test was equal to 1.955. Because it was greater than the critical value of 1.645 on a 5% level of significance, the null hypothesis was also rejected, and the alternative hypothesis was also accepted: the SPT method is more conservative than the V_s method.

On the other hand, the Z_test was found equal to 1.951 for the weak condition. Since it was also greater than the critical value or the Z_test was also located in the rejection region, the exact statistical inference was also obtained from the hypothesis testing: the hypothesis—the SPT method is more conservative than the V_s method—is accepted by the information from the samples.

Figure 9. (N₁)₆₀ vs. FS ratio; the base (N₁)₆₀ value = 1.

Table 2. Summary of the hypothesis test for M = 7 and PGA = 0.2 g.

*Standard deviation.

Table 3. Summary of the hypothesis test for M = 6.5 and PGA = 0.1 g.

*Standard deviation.

5. Conclusions

This study randomly selected 41 liquefiable soil layers at sites in Taipei and Kaohsiung areas of Taiwan. We calculated the liquefaction safety factor for each soil layer using the V_s and SPT methods recommended by the National Center for Earthquake Engineering Research. A series of hypothesis tests show that the hypothesis—the SPT method is more conservative than the V_s method—was accepted based on the information from the samples or the 41 soil layers. In addition, the research also found that the outcome obtained from the V_s method was of more significant variation compared to the SPT method, which should be attributed to the highly nonlinear relationship between the soil’s shear wave velocity and its cyclic resistance ratio against soil liquefaction.

According to this research, we suggest that the more conservative SPT method needs to be included in a case study, especially for the sites where critical structures are located. Besides, because the finding of this study was based on the data in two major cities in Taiwan, similar studies based on different sites in other cities in the world are recommended, examining whether such a fining is universal.

Acknowledgements

The authors appreciate the constructive comments from the Editors and Reviewers. We also thank the National Center for Research on Earthquake Engineering of Taiwan for providing the data.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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