Liquefaction characteristics of gap-graded gravelly soils in K0 condition

A series of undrained cyclic direct simple shear tests, which used a soil container with a membrane reinforced with stack rings to maintain the K₀ condition and integrated bender elements for shear wave velocity measurement, were performed to study the liquefaction characteristics of gap-graded gravelly soils with no fines content. The intergrain state concept was employed to categorize gap-graded sand–gravel mixtures as sand-like, gravel-like, and in-transition soils, which show different liquefaction characteristics. The testing results reveal that a linear relationship exists between the shear wave velocity and the minor fraction content for sand–gravel mixtures at a given skeleton void ratio of the major fraction particles. For gap-graded gravelly sand, the gravel content has a small effect on the liquefaction resistance, and the cyclic resistance ratio (CRR) of gap-graded gravelly sands can be evaluated using current techniques for sands with gravel content corrections. In addition, the results indicate that the current shear wave velocity (V_s) based correlation underestimates the liquefaction resistance for V_s values less than 160 m/s, and different correlations should be proposed for sand-like and gravel-like gravelly soils. Preliminary modifications to the correlations used in current evaluations of liquefaction resistance have thus been proposed.     

Comparing liquefaction evaluation methods using penetration-VS relationships

Three methods that follow the general format of the Seed-Idriss simplified procedure for evaluating liquefaction resistance of soils are compared in this paper. They are compared by constructing relationships between penetration resistance and small-strain shear–wave velocity (V_S) implied from cyclic resistance ratio (CRR) curves for the three methods, and by plotting penetration-V_S data pairs. The penetration-V_S data pairs are from 43 Holocene-age sand layers in California, South Carolina, Canada, and Japan. It is shown that the V_S-based CRR curve is more conservative than CRR curves based on the Standard Penetration Test (SPT) and Cone Penetration Test (CPT), for the compiled Holocene data. This result agrees with the findings of a recent probability study where the SPT-, CPT-, and V_S-based CRR curves were characterized as curves with average probability of liquefaction of 31, 50, and 26%, respectively. New SPT- and CPT-based CRR equations are proposed that provide more consistent assessments of liquefaction potential for the Holocene sand layers considered.     

Cyclic resistance and liquefaction behavior of silt and sandy silt soils

The liquefaction behavior and cyclic resistance ratio (CRR) of reconstituted samples of non-plastic silt and sandy silts with 50% and 75% silt content are examined using constant-volume cyclic and monotonic ring shear tests along with bender element shear wave velocity (V_s) measurements. Liquefaction occurred at excess pore water pressure ratios (r_u) between 0.6 and 0.7 associated with cumulative cyclic shear strains (γ) of 4% to 7%, after which cyclic liquefaction ensued with very large shear strains and excess pore water pressure ratio (r_u>0.8). The cyclic ring shear tests demonstrate that cyclic resistance ratio of silt and sandy silts decreases with increasing void ratio, or with decreasing silt content at a certain void ratio. The results also show good agreement with those from cyclic direct simple shear tests on silts and sandy silts. A unique correlation is developed for estimating CRR of silts and sandy silts (with more than 50% silt content) from stress-normalized shear wave velocity measurements (V_s1) with negligible effect of silt content. The results indicate that the existing CRR–V_s1 correlations would underestimate the liquefaction resistance of silts and sandy silt soils.     

Correlation of shear wave velocity with liquefaction resistance based on laboratory tests

According to the results of cyclic triaxial tests on Hangzhou sands, a correlation is presented between liquefaction resistance and elastic shear modulus. Material-dependent but independent of confining stress, shows the linear relation of (σ_d/2)^1/2 with G_max. For its application to different soils, a method proposed by Tokimatsu [Tokimatsu K, Uchida A. Correlation between liquefaction resistance and shear wave velocity. Soils Found 1990:30(2):33–42] is utilized to normalize the shear modulus with respect to minimum void ratio. A simplified equation is established to evaluate the liquefaction potential by shear-wave velocity. The critical shear-wave velocity of liquefaction is in linear relation with 1/4 power of depth and the peak horizontal ground surface acceleration during earthquakes. The equation proposed in this paper is compared with previous methods especially the procedure proposed by Andrus [RD Andrus, KH Stokoe. Liquefaction resistance of soils from shear-wave velocity. J Geotech Geoenviron Eng 2000:126(11):1015–25]. The results show its simplicity and effectiveness when applied to sands, but more validation or modification is needed for its application to sand with higher fines content.     

Shear wave velocity-based evaluation and design of stone column improved ground for liquefaction mitigation

The evaluation and design of stone column improvement ground for liquefaction mitigation is a challenging issue for the state of practice. In this paper, a shear wave velocity-based approach is proposed based on the well-defined correlations of liquefaction resistance (CRR)-shear wave velocity (V _s)-void ratio (e) of sandy soils, and the values of parameters in this approach are recommended for preliminary design purpose when site specific values are not available. The detailed procedures of pre- and post-improvement liquefaction evaluations and stone column design are given. According to this approach, the required level of ground improvement will be met once the target V _s of soil is raised high enough (i.e., no less than the critical velocity) to resist the given earthquake loading according to the CRR-V _s relationship, and then this requirement is transferred to the control of target void ratio (i.e., the critical e) according to the V _s-e relationship. As this approach relies on the densification of the surrounding soil instead of the whole improved ground and is conservative by nature, specific considerations of the densification mechanism and effect are given, and the effects of drainage and reinforcement of stone columns are also discussed. A case study of a thermal power plant in Indonesia is introduced, where the effectiveness of stone column improved ground was evaluated by the proposed V _s-based method and compared with the SPT-based evaluation. This improved ground performed well and experienced no liquefaction during subsequent strong earthquakes.     

Non-plastic silty sand liquefaction,screening, and remediation

Assessing liquefaction potential, in situ screening using cone penetration resistance, and liquefaction-remediation of non-plastic silty soils are difficult problems. Presence of silt particles among the sand grains in silty soils alter the moduli, shear strength, and flow characteristics of silty soils compared to clean host sand at the same global void ratio. Cyclic resistance (CRR) and normalized cone penetration resistance (q_c1N) are each affected by silt content in a different way. Therefore, a unique correlation between cyclic resistance and cone resistance is not possible for sands and silty sands. Likewise, the response of silty soils subjected to traditional deep dynamic compaction (DC) and vibro-stone column (SC) densification techniques is influenced by the presence of silt particles, compared to the response in sand. Silty soils require drainage-modifications to make them amenable for dynamic densification techniques. The first part of this paper addresses the effects of silt content on cyclic resistance CRR, hydraulic conductivity k, and coefficient of consolidation C_v of silty soils compared to clean sand. The second part of the paper assesses the effectiveness of equivalent intergranular void ratio (e_c)_eq concept to approximately account for the effects of silt content on CRR. The third part of the paper explores the combined effects of silt content (viz effects of (e_c)_eq, k, and C_v) on q_c1N using laboratory model cone tests and preliminary numerical simulation experiments. A possible inter-relationship between q_c1N, CRR, accommodating the different degrees of influence of (e_c)_eq, k, and C_v on q_c1N and CRR, is discussed. The fourth part of the paper focuses on the detrimental effects of silt content on the effectiveness of DC and SC techniques to densify silty soils for liquefaction-mitigation. Finally, the effectiveness of supplemental wick drains to aid drainage and facilitate densification and liquefaction mitigation of silty sands using DC and SC techniques is discussed.     

Liquefaction potential and strain dependent dynamic properties of Kasai River sand

The availability of efficient numerical techniques and high speed computation facilities for carrying out the nonlinear dynamic analysis of soil-structure interaction problems and the analysis of ground response due to earthquake loading increase the demand for proper estimation of dynamic properties of soil at small strain as well as at large strain levels. Accurate evaluation of strain dependent dynamic properties of soil such as shear modulus and damping characteristics along with the liquefaction potential are the most important criteria for the assessments of geotechnical problems involving dynamic loading. In this paper the results of resonant column tests and undrained cyclic triaxial tests are presented for Kasai River sand. A new correlation for dynamic shear damping (D_s) and maximum dynamic shear modulus (G_max) are proposed for the sand at small strain. The proposed relationships and the observed experimental data match quite well. The proposed relationships are also compared with the published relationships for other sands. The liquefaction potential of the sand is estimated at different relative densities and the damping characteristics at large strain level is also reported. An attempt has been made to correlate the G_max with the cyclic strength of the soil and also with the deviator stress (at 1% strain) from static triaxial tests.     

Measurement of small strain shear modulus of clean and natural sands in saturated condition using bender element test

Bender element (BE) tests of saturated sand have increased interest to researchers currently. However, the measurement of small strain modulus from BE tests shows large difference between saturated and dry conditions. In this study, BE tests of a type of clean sand (Fujian sand) and two types of natural sands (Hangzhou sand and Nanjing sand) were performed. For the purposes of comparison, resonant column (RC) test and torsional shear (TS) test were also carried out on the same specimen. The factors that influence the determination of the travel time of shear wave in BE tests are discussed and a reliable method for the determination of the shear-wave velocity is obtained. It is found that the shear-wave velocities V_s of saturated Fujian sand (clean sand) and Hangzhou sand (natural sand) obtained from BE tests are 5–10% greater than those obtained from RC and TS tests. However, the V_s of saturated Nanjing sand (natural sand) obtained from BE, RC and TS tests show good agreement with a maximum difference of about 3%. Sands with various fines contents were also tested in an attempt to explain the differences between the two saturated natural sands. Biot׳s theory accounting for the dispersion of shear wave was employed to interpret the results of BE tests. The results indicate that the fines content of natural sand plays an important effect on the hydraulic conductivity, which affects the relative motion between soil particles and fluid when a high frequency shear wave propagates in the specimen. Based on this, a method for the determination of small strain shear modulus in BE test was proposed for both saturated clean sands and natural sands.     

Experimental and conceptual evidence about the limitations of shear wave velocity to predict liquefaction

Based on the liquefaction performance of sites with seismic activity, the normalized shear wave velocity, V_s1, has been proposed as a field parameter for liquefaction prediction. Because shear wave velocity, V_s, can be measured in the field with less effort and difficulty than other field tests, its use by practitioners is highly attractive. However, considering that its measurement is associated with small strain levels, of the order of 10⁻⁴–10⁻³%, V_s reflects the elastic stiffness of a granular material, hence, it is mainly affected by soil type, confining pressure and soil density, but it is insensitive to factors such as overconsolidation and pre-shaking, which have a strong influence on the liquefaction resistance. Therefore, without taking account of the important factors mentioned above, the correlation between shear wave velocity and liquefaction resistance is weak.In this paper, laboratory test results are presented in order to demonstrate the significant way in which OCR (overconsolidation ratio) affects both shear wave velocity and liquefaction resistance. While V_s is insensitive to OCR, the liquefaction resistance increases significantly with OCR. In addition, the experimental results also confirm that V_s correlates linearly with void ratio, regardless of the maximum and minimum void ratios, which means that V_s is unable to give information about the relative density. Therefore, if shear wave velocity is used to predict liquefaction potential, it is recommended that the limitations presented in this paper be taken into account.     

3rd Ishihara Lecture: An investigation into why liquefaction charts work: A necessary step toward integrating the states of art and practice

This paper is a systematic effort to clarify why field liquefaction charts based on Seed and Idriss׳ Simplified Procedure work so well. This is a necessary step toward integrating the states of the art (SOA) and practice (SOP) for evaluating liquefaction and its effects. The SOA relies mostly on laboratory measurements and correlations with void ratio and relative density of the sand. The SOP is based on field measurements of penetration resistance and shear wave velocity coupled with empirical or semi-empirical correlations. This gap slows down further progress in both SOP and SOA. The paper accomplishes its objective through: a literature review of relevant aspects of the SOA including factors influencing threshold shear strain and pore pressure buildup during cyclic strain-controlled tests; a discussion of factors influencing field penetration resistance and shear wave velocity; and a discussion of the meaning of the curves in the liquefaction charts separating liquefaction from no liquefaction, helped by recent full-scale and centrifuge results. It is concluded that the charts are curves of constant cyclic strain at the lower end (V_s1<160 m/s), with this strain being about 0.03–0.05% for earthquake magnitude, M_w≈7. It is also concluded, in a more speculative way, that the curves at the upper end probably correspond to a variable increasing cyclic strain and K_o, with this upper end controlled by overconsolidated and preshaken sands, and with cyclic strains needed to cause liquefaction being as high as 0.1–0.3%. These conclusions are validated by application to case histories corresponding to M_w≈7, mostly in the San Francisco Bay Area of California during the 1989 Loma Prieta earthquake.     

A surface seismic approach to liquefaction

The liquefaction potential of soils is traditionally assessed through geotechnical approaches based on the calculation of the cyclical stress ratio (CSR) induced by the expected earthquake and the ‘resistance’ provided by the soil, which is quantified through standard penetration (SPT), cone penetration (CPT), or similar tests. In more recent years, attempts to assess the liquefaction potential have also been made through measurement of shear wave velocity (V_S) in boreholes or from the surface. The latter approach has the advantage of being non-invasive and low cost and of surveying lines rather than single points. However, the resolution of seismic surface techniques is lower than that of borehole techniques and it is still debated whether it is sufficient to assess the liquefaction potential.In this paper we focus our attention on surface seismic techniques (specifically the popular passive and active seismic techniques based on the correlation of surface waves such as ReMi^TM, MASW, ESAC, SSAP, etc.) and explore their performance in assessing the liquefaction susceptibility of soils. The experimental dataset is provided by the two main seismic events of M_L=5.9 and 5.8 (M_W=6.1, M_W=6.0) that struck the Emilia-Romagna region (Northern Italy) on May 20 and 29, 2012, after which extensive liquefaction phenomena were documented in an area of 1200 km².The CPT and drillings available in the area allow us to classify the soils into four classes: A) shallow liquefied sandy soils, B) shallow non-liquefied sandy soils, C) deep non-liquefied sandy soils, and D) clayey–silty soils, and to determine that on average class A soils presented a higher sand content at the depth of 5–8 m compared to class B soils, where sand was dominant in the upper 5 m. Surface wave active–passive surveys were performed at 84 sites, and it was found that they were capable of discriminating among only three soil classes, since class A and B soils showed exactly the same V_S distribution, and it is possible to show both experimentally and theoretically that they appear not to have sufficient resolution to address the seismic liquefaction issue.As a last step, we applied the state-of-the art CSR–V_S method to assess the liquefaction potential of sandy deposits and we found that it failed in the studied area. This might be due to the insufficient resolution of the surface wave methods in assessing the Vs of thin layers and to the fact that Vs scales with the square root of the shear modulus, which implies an intrinsic lower sensitivity of Vs to the shear resistance of the soil compared to parameters traditionally measured with the penetration tests. However, it also emerged that the pure observation of the surface wave dispersion curves at their simplest level (i.e. in the frequency domain, with no inversion) is still potentially informative and can be used to identify the sites where more detailed surveys to assess the liquefaction potential are recommended.     

Analysis of the liquefaction phenomena in the village of Vittorito (L��Aquila)

This paper describes a case-history of liquefaction occurred near the village of Vittorito after the April 6, 2009 L’Aquila earthquake (moment magnitude M_w = 6.3), approximately 45 km far from the epicentre. In the document, first, an estimation of the seismic motion in the area has been made. Thereafter, the performed geotechnical investigation is described, followed by the application of some fast assessment criteria for the occurrence of liquefaction, recently proposed by the new Italian Building Code. A careful assessment of all the parameters involved in conventional Seed and Idriss (1971) liquefaction analyses is considered. The cyclic resistance ratio CRR is evaluated by cone penetration tests CPT and by in situ seismic dilatometer tests SMDT; in the latter case CRR is evaluated by different empirical correlations with shear wave velocity V_s and horizontal stress index K_D. Analytical data confirmed the observed occurrence of the liquefaction in Vittorito, even if the acceleration field in the area, produced by the L’Aquila earthquake, was very low.     

Probabilistic correlation between laboratory and field liquefaction potentials using relative state parameter index (ξR)

Cyclic triaxial tests on reconstituted sand samples are broadly employed in practice while they ignore the inherent characteristics of soil in field condition such as aging, fabric, and prior strain history. Relative state parameter index, ξ_R, is utilized in a probabilistic framework to adjust the cyclic triaxial resistance ratio of sands at 15 uniform cycles (CRR_tx,15) to field condition. A wide-ranging database containing the results of cyclic triaxial tests conducted on reconstituted samples has been compiled to derive a correlation between relative state parameter index (ξ_R) and triaxial cyclic resistance ratio. The adjustment coefficients proposed by researchers are employed to correct CRR_tx,15−ξ_R relationship for actual field condition. The adjusted CRR_tx,15−ξ_R relationships are applied to a database of field liquefaction case histories composed of both SPT and CPT based data and their performances in field condition are evaluated. It is demonstrated that constant triaxial-to-field adjusting coefficients cannot ever predict conservative results. Logistic regression method is employed to derive a field probabilistic criterion that obtains the likelihood of liquefaction initiation in terms of ξ_R. The ξ_R-based boundary curve standing for 20% likelihood of liquefaction initiation is found to be the most conservative limit state boundary to be used in field conditions. Finally, the triaxial and field CRR−ξ_R relationships are composed and a probabilistic triaxial-to-field adjustment coefficient is proposed in terms of ξ_R and a given liquefaction probability. It is anticipated that the proposed relationship could reasonably correct the results of cyclic triaxial testing on freshly reconstituted sand samples.     

Predicting seismic liquefaction potential of sands by optimum seeking method

The feasibility of using the optimum seeking method to assess the seismic liquefaction potential of sands has been investigated. Optimization theory is a very important branch of applied mathematics and has a wide application in the practical world. Using the available field sand liquefaction data, the influence of various factors is quantified using the optimum seeking method. The factors considered are: the earthquake magnitude M, the distance of the site from the source of the earthquake L, the depth of the water table D_w, the depth of the sand deposit D_s, and the standard penetration test (SPT) blow count N. The most important factors have been identified as the earthquake magnitude and the SPT blow count. Prediction results show that the proposed method is effective and feasible. Since neither normalization of the SPT blow count nor calculation of the seismic shear-stress ratio are required, the proposed method is simpler and more direct than the conventional methods of evaluating liquefaction potential.     

A simplified method to determine seismic responses of reinforced concrete moment resisting building frames under influence of soil–structure interaction

As the Iranian seismic code does not address the soil–structure interaction (SSI) explicitly, the effects of SSI on RC-MRFs are studied using the direct method. Four types of structures on three types of soils, with and without the soil interaction, are modeled and subjected to different earthquake records. The results led to a criterion indicating that considering SSI in seismic design, for buildings higher than three and seven stories on soil with V_s<175 m/s and 175<V_s<375 m/s, respectively, is essential. A simplified procedure has been presented, on the basis that lateral displacement increments could be applied to the fixed-base models using simple factors.     

Effects of cross-anisotropic soil behaviour on the wave-induced residual liquefaction in the vicinity of pipeline buried in elasto-plastic seabed foundations

In this paper, a two-dimensional integrated numerical model is developed to examine the influences of cross-anisotropic soil behaviour on the wave-induced residual liquefaction in the vicinity of a pipeline buried in a porous seabed. In the wave model, the RANS (Reynolds Averaged Navier–Stokes) equation is used to govern the wave motion. In the seabed model, the residual soil response in the vicinity of an embedded pipeline is considered with the 2-D elasto-plastic solution, where the phase-resolved shear stress is used as a source for the build-up of residual pore pressure. Classical Biot׳s consolidation equation is used for linking the solid-pore fluid interaction. The validation of the proposed integrated numerical model is conducted by the comparisons with the previous experimental data. Numerical examples show that the pore pressures can accumulate to a large value, thus resulting in a larger area of liquefaction potential in the given anisotropic soil compared to that with isotropic solution. The influences of anisotropic parameters on the wave-induced residual soil response in the vicinity of pipeline are significant. A high rate of pore pressure accumulation and dissipation is observed and the liquefaction potential develops faster as the anisotropic parameters increase. Finally, a simplified approximation based on a detailed parametric investigations is proposed for the evaluation of maximum liquefaction depth (z_L) in engineering application.     

DHI evaluation by combining rock physics simulation and statistical techniques for fluid identification of Cambrian-to-Cretaceous clastic reservoirs in Pakistan

The use of seismic direct hydrocarbon indicators is very common in exploration and reservoir development to minimise exploration risk and to optimise the location of production wells. DHIs can be enhanced using AVO methods to calculate seismic attributes that approximate relative elastic properties. In this study, we analyse the sensitivity to pore fluid changes of a range of elastic properties by combining rock physics studies and statistical techniques and determine which provide the best basis for DHIs. Gassmann fluid substitution is applied to the well log data and various elastic properties are evaluated by measuring the degree of separation that they achieve between gas sands and wet sands. The method has been applied successfully to well log data from proven reservoirs in three different siliciclastic environments of Cambrian, Jurassic, and Cretaceous ages. We have quantified the sensitivity of various elastic properties such as acoustic and extended elastic (EEI) impedances, elastic moduli (K _sat and K _sat–μ), lambda–mu–rho method (λρ and μρ), P-to-S-wave velocity ratio (V _P/V _S), and Poisson’s ratio (σ) at fully gas/water saturation scenarios. The results are strongly dependent on the local geological settings and our modeling demonstrates that for Cambrian and Cretaceous reservoirs, K _sat–μ, EEI, V _P/V _S, and σ are more sensitive to pore fluids (gas/water). For the Jurassic reservoir, the sensitivity of all elastic and seismic properties to pore fluid reduces due to high overburden pressure and the resultant low porosity. Fluid indicators are evaluated using two metrics: a fluid indicator coefficient based on a Gaussian model and an overlap coefficient which makes no assumptions about a distribution model. This study will provide a potential way to identify gas sand zones in future exploration.     

Ground response analysis of Kanpur soil along Indo-Gangetic Plains

The present work deals with 1D and 2D ground response analysis and liquefaction analysis of alluvial soil deposits from Kanpur region along Indo-Gangetic plains. Standard penetration tests and seismic down hole tests have been conducted at four locations namely IITK, Nankari village, Mandhana and Bithoor at 1.5 m interval up to a depth of 30 m below the ground surface to find the variation of penetration blows and the shear wave velocity along the depth. From the selected sites undisturbed as well as representative soil samples have been collected for detailed soil classification. The soil profiles from four sites have been considered for 1D and 2D ground response analysis by applying the free field motions of three Himalayan earthquakes namely Chamba earthquake (M_w—5.1), Chamoli earthquake (M_w—6.4) and Uttarkashi earthquake (M_w—6.5). An average value of Peak Ground Acceleration (PGA) obtained from 1D and 2D analysis is considered for liquefaction analysis and post-liquefaction settlement. The excess pore water pressure ratio is greater than 0.8 at a depth of 24 m from ground surface for IITK, Nankari village, Bithoor sites. More than 50% of post liquefaction settlement is contributed by layers from 21–30 m for all sites. In general, the soil deposits in Kanpur region have silty sand and sand deposits and are prone to liquefaction hazards due to drastic decrease of cyclic resistance ratio (CRR) at four chosen sites in Kanpur.     

Gravelly soils that liquefied during 2008 Wenchuan,China earthquake, Ms=8.0

Field investigations following the 2008 Wenchuan earthquake (M_s=8.0) identified 118 liquefaction sites nearly all of which are underlain by gravelly sediment in the Chengdu Plain and adjacent Mianyang area. Field studies, including core drilling, dynamic penetration tests (DPT), and multiple channel analysis of surface wave velocity tests (MASW) for measurement of shear wave velocities, reveal the following: (1) Sand boils and ground fissures, indicative of liquefaction, occurred across hundreds of square kilometers affecting 120 villages, 8 schools and 5 factories. (2) The Chengdu plain is underlain by sandy gravels ranging in thickness up to 540 m; loose upper layers within the gravels beds liquefied. (3) Mean grain sizes for gravelly layers that liquefied range from 1 mm to more than 30 mm. (4) Shear wave velocities in gravels that liquefied range up to 250 m/s. (5) A 50% probability curve, developed from logistic procedures, correctly bounds all but four data points for the 47 compiled V_s data.     

Assessing CPT-based methods for liquefaction evaluation with emphasis on the cases from the Chi-Chi, Taiwan, earthquake

In the early morning (1:47 Taiwan time) of September 21, 1999, the largest earthquake of the century in Taiwan (M_w=7.6, M_L=7.3) struck this island country. The earthquake killed more than 2400 people and caused great destruction to buildings, bridges, dams, highways, and railways. One of the causes for heavy damages to the structures is soil liquefaction and ground settlement during the earthquake. In this paper, investigation of soil liquefaction and case histories of liquefaction are presented. Three CPT-based simplified methods, the Robertson method, the Olsen method, and the Juang method, are examined using the case histories derived from the Chi-Chi earthquake. The results of the comparison show that the Juang method is more accurate than the two methods in predicting liquefaction potential of soils based on the cases derived from the Chi-Chi earthquake, although all three methods are quite comparable in accuracy.