Yet Another Update of Limitations of Simplified Methods for Evaluating Earthquake-Induced Liquefaction and its Consequences

Also available on ResearchGate.net and SlideShare.net and can be downloaded from either of these sites with proper subscripts.

February 20, 2025

This note originated as a two-page document that summarized the main limitations of simplified methods for evaluating earthquake-induced liquefaction and its consequences. These consequences include loss of bearing capacity, uplift of structures embedded below the water table, settlement that occurs when excess pore pressures are dissipated, and lateral spreading. Most of these limitations also apply to simplified methods for estimating earthquake-induced settlements of dry or moist sands. Some of the same limitations also apply to simplified methods for estimating earthquake-induced displacement of slopes, but those methods also involve other issues which were not covered in my original note and are not addressed here. The original note also assumed that the reader was familiar with the methods that were being discussed and focused mostly on their limitations. Various updates have described some of the history of development of these simplified methods in order both to place some context around their current use and to note the significant approximations that are involved. This latest update adds more detail about the limitations of simplified methods for predicting the magnitude of lateral spreading displacements and emphasizes the fact that if the initial evaluation for triggering of liquefaction is conservative, then the predicted settlements and the predicted lateral spreading displacements will also be conservative.

The Origin of Simplified Methods

The basis of the original “simplified procedure for evaluating soil liquefaction potential” described by Seed and Idriss (1971) was that the average cyclic shear stress on a horizontal plane, τav, could be obtained as a function of the peak ground surface acceleration by the following equation:

τav = 0.65 ? amax/g ? σv ? rd

where amax is the peak ground surface acceleration, g is the acceleration due to gravity, σv is the total vertical stress at the depth in question, and rd is an empirical factor that accounts for the fact that the soil column above the depth in question is not rigid. The average, that is uniform, cyclic shear stress for a number of cycles of loading, taken to be a function of the earthquake magnitude, can then be compared to the uniform cyclic shear stress that causes “initial liquefaction”, or 100 percent excess pore pressure, in the same number of cycles. This combination of the uniform cyclic shear stress and number of cycles that triggers initial liquefaction was originally obtained from cyclic triaxial tests and were subsequently “corrected” to simple shear conditions.

The original simplified procedure was a brilliant way of making it possible for engineers to better understand and to make preliminary evaluations of the potential for liquefaction at a time when there were only a few people who could run even equivalent linear one-dimensional site response analyses. However, times change, and fifty years later, there are many more geotechnical engineers with graduate education who are capable of running nonlinear effective stress site response analyses in order to obtain better estimates of the cyclic shear stresses and strains in critical layers. In addition, the importance of the depositional history and soil fabric to the behavior of real soils under cyclic loading is now better understood and there should be more emphasis on taking this into account.

In any case the original simplified procedure caught on and evolved into a variety of more complex but still simplified procedures that are available today. One of the first steps was that both sides of the above equation were divided by the initial vertical effective stress, σv', at the depth in question and the value τav / σv' became known as the cyclic stress ratio (CSR). Likewise, the cyclic shear stress causing initial liquefaction, or a prescribed single or double amplitude cyclic shear strain, was “normalized” by dividing it by the vertical effective stress and became referred to as the cyclic resistance ratio (CRR). However, because the cyclic shear stress causing initial liquefaction does not vary linearly with the initial vertical effective stress, this was an imperfect normalization and an overburden correction factor, Kσ, later had to be added in order to address this issue.

Then, rather than basing the cyclic stress ratio causing liquefaction in a given number of cycles on laboratory test data, practice shifted to using correlations between the observation of the occurrence, or non-occurrence, of liquefaction in various earthquakes and Standard Penetration Test (SPT) blowcounts and Cone Penetration Test (CPT) tip resistances. These correlations were normally developed for magnitude 7.5 earthquakes, so that then a magnitude scaling factor was introduced to provide for other magnitudes. Variations of the depth reduction curve that were magnitude dependent were also developed. Thus, the simplified procedure for “triggering” of liquefaction, that is reaching 100 percent excess pore pressure, became based on a series of charts like this:

Unfortunately, as one of my colleagues has put it, academics then spent about two decades shifting these curves around the page rather than focusing on the overall limitations of the procedure.

Extensions of the procedure developed for “triggering” liquefaction were also developed for evaluating settlement of both saturated and non-saturated sands and for predicting the magnitude of possible lateral spreading. These extensions, as well as the interpretation of SPT and CPT data, generally involve a number of correlations which are both very approximate and poorly understood. Most, if not all, of these correlations are based on laboratory tests, including calibration chamber tests, conducted on washed and screened clean sands that have not been subjected to pre-straining or overconsolidation, what Professor Michele Jamiolkowski referred to as “baby” sands. The behavior of real soils may be different. Thus, the simplified procedures gradually became more complicated, so that few, if any, practicing engineers fully understand each step in the various procedures, the limits of applicability of that step and whether the site in question fits within the limits of the overall applicability of the method. The current procedures have ended up being both over-simplified and too complicated to understand!

I am not sure how or why it became common practice to rely so much on simplified methods of analysis, especially for evaluating the consequences of liquefaction such as settlement and lateral spreading, but likely the paper by Youd et al. (2001), which reported the conclusions of two academic / industry workshops, and the subsequent paper by Seed et al. (2003) and monograph by Idriss and Boulanger (2008), all of which focused more on the triggering of initial liquefaction, had at least something to do with it. I wrote a critical discussion of the Youd et al. paper and my discussion and the authors’ closure, which largely agreed with my comments, were published as Pyke (2003). However, I suspect that most graduate students and practicing geotechnical engineers have read the original Youd et al. paper and not my discussion! Readers of this note might like to read my discussion and the authors’ closure, but the six points that I made at that time are still valid and are covered in the following text. However, practicing geotechnical engineers should not have to read my previous writings or this note to understand that the simplified methods are not very accurate. It is just wrong if you calculate 30 feet of lateral spreading of a levee built on a sandy, but relatively dense, foundation, or if you calculate 10-15 inches of settlement for a profile that lacks horizontally continuous sand or silty sand layers, and that kind of profile has never been known to exhibit any consequences of liquefaction. If that happens you should seek a better method of evaluation if the project has any importance at all.

The Critical First Step

The first step in any evaluation of liquefaction and its consequences should in fact be answering the question “is there any evidence of earthquake-induced liquefaction and settlement or lateral spreading of similar soils in a similar tectonic environment?” - see for instance Pyke (1995, 2003, 2015) and Semple (2013). While there are rare instances of liquefaction being reported in Pleistocene-age sands, the vast majority of well-documented case histories have occurred in geologically recent cohesionless soils and man-made fills, particularly hydraulically placed fills. A significant early contribution on the susceptibility of various types of sedimentary deposits to liquefaction was made by Youd and Perkins (1978) and excellent recent contributions on this subject are provided by Kayen (2024) and Abayo et al. (2023).

Do You Always Need to Show a Calculation?

The widespread use of simplified methods of analysis has been driven in part by the belief that “one has to show a calculation.” However, that belief does not promote better geotechnical engineering practice, and often leads to the opposite, which is worse practice. The policy of having to show a calculation promotes the use of computer programs which the user may not understand and can lead to blind acceptance of the output of computer programs, rather than checking the results of calculations against common sense and experience. A good screening analysis, for example, should emphasize common sense and experience rather than calculations. It did not require any analyses to conclude that the Marina District in San Francisco was susceptible to liquefaction prior to the 1989 Loma Prieta earthquake, or that the areas with recent alluvium and a high water table along the Avon River in Christchurch NZ were susceptible to liquefaction prior to the 2010-11 Christchurch earthquakes.

Common Sense Rules

But, if you have to do a quick simplified analysis, here are some common sense rules that should be applied:

1. All soil layers that have “clayey” descriptors should be tested as necessary to confirm that description and should be excluded. (The question of the effect of silty and clayey fines on liquefaction is discussed in more detail below.)

2. Soils that are older than several thousand years or are known to be over-consolidated should be excluded. See for instance Arango et al. (2000).

3. Sand and silty sand layers with measured shear wave velocities exceeding about 720 fps should also be excluded, see Andrus et al. (2009). However, gravelly soils which contain sufficient sand to be susceptible to liquefaction may have shear wave velocities up to about 1050 fps, see Rollins et al. (2022). Broadly speaking, gravels with less than about 30 percent sand are not susceptible to liquefaction because, unless they are confined by impermeable layers, any excess pore pressures that tend to develop will dissipate too quickly, but gravels that contain more than 30 percent sand or are otherwise confined should not be excluded unless the shear wave velocity exceeds 1050 fps. If measured shear wave velocities are not available, layers that would be otherwise characterized as “dense” or “very dense” should be excluded. Layers that are characterized as “dense” may still be susceptible to excess pore pressure development under strong shaking, but few if any adverse consequences of liquefaction have been observed when the normalized clean sand SPT blowcount exceeds 15. See for instance Ishihara (1993) and Youd et al. (2002).

4. Finally, a clayey or otherwise non-liquefiable crust overlying a potentially liquefiable layer will limit any adverse consequences of liquefaction. See for instance Ishihara (1985) and Youd and Garris (1995). While lateral spreads triggered by liquefaction of layers under a crust as thick as 10 m are not totally unknown, they are limited to very large earthquakes such as have occurred off the coasts of Alaska, Chile and Japan.

General Limitations

More specifically the following eight factors limit the accuracy of simplified methods of analysis and tend to make the results very conservative:

1. The “cyclic stress ratio” computed working down from the peak ground surface acceleration assuming no liquefaction is invariably much greater than that computed using a nonlinear effective stress site response analysis which takes into account the specific layering and properties of the site. Pyke (2019) and Crawford et al. (2019) show examples of the comparison of the cyclic stress ratios computed using the simplified and more accurate methods and found that the cyclic stress ratio computed using site response analyses can be as low as one half that computed using the simplified method. This reduction also results from the fact that triggering liquefaction in any one layer reduces the amplitudes of the ground motion above that layer.

2. Duration varies with the type of source and the distance as well as with magnitude. Site specific ground motions have to be much more accurate than using averages of worldwide data. See item 7 below for additional advantages of using site-specific input motions.

3. The correction of penetration resistance measured using either the SPT or the CPT for fines content is generally inadequate. Fines, and especially clayey fines, can dramatically reduce the penetration resistance while improving the resistance to developing excess pore pressures under cyclic loadings. If simplified analyses suggest that there are significant consequences of liquefaction, it is desirable to take samples and run hydrometer tests in order to obtain the full particle size distribution. Measurement of the PI is not unimportant but viewing the full particle size distribution is even more informative. Because the interpretation of soil type from CPTs is not foolproof, it is good practice to always conduct at least several CPT / boring pairs at the outset of an investigation whenever liquefaction is a possibility. The CPTs should be advanced first, and then SPT blowcounts can be targeted in the upper portion of any sufficiently thick sandy layers. Regardless of whether the weighted average shear wave velocity is required in order to determine the site class according to the building code, measurement of the shear wave velocities in seismic CPTs is always valuable because the shear wave velocity also serves as a good index test.

4. The correction of penetration resistance measured using either the SPT or the CPT for “transition”, “thin layer”, “multiple thin layer”, and “underlying soft layer” effects is also generally inadequate. Recent work by Boulanger and DeJong (2018) and Yost et al. (2021) provides some guidance on these effects, but they are rarely accounted for in practice.

5. Penetration resistance also does not fully reflect the effect of ageing, including cementation, pre-straining, and over-consolidation on improving the soil response to cyclic loading.

6. There is growing evidence that the cyclic stress ratios that trigger liquefaction in a given number of cycles that are obtained as a function of the penetration resistance from the standard charts that are used in simplified methods may be overly conservative - see for instance Stokoe (2023). Stokoe’s team conducted relatively well-controlled studies of silty sands following the earthquakes in Christchurch NZ. By comparison, the soil profiles and properties in the case histories on which the standard curves are based are not so well documented.

7. There is also a growing consensus that the occurrence of liquefaction can only be understood by conducting nonlinear effective-stress site response analyses in which excess pore pressure development, redistribution and dissipation are tracked. See Ntritsos et al. (2018), Cubrinovski (2019), Hutabarat and Bray (2019), Kramer (2019), Olson et al. (2020) and Cubrinovski and Ntritsos (2023). It further turns out that such analyses are needed to determine which intervals in the deposit are most susceptible to liquefaction and to properly understand the case histories on which the simplified, empirical methods are based.

8. Nonlinear effective-stress site response analyses also use site-specific acceleration histories as input so that the overall duration and the number of cycles of loading are much better represented than they are in simplified analyses. And, because settlement and excess pore pressure development are a function of the prior loading up to the current point in time, these quantities can be calculated much more accurately using site-specific acceleration histories as input, rather than assuming a number of cycles of a uniform loading. Just as equivalent linear site response analyses were a brilliant idea at the time, so was the concept of a number of uniform cycles being equivalent to an irregular loading, but that was more than fifty years ago!

While nonlinear effective-stress site response analyses are usually considered to be more difficult to perform than simplified methods of analysis, and may require more detailed field and laboratory studies, they are actually easier to understand and they can provide the engineer with more insight into both liquefaction issues and design ground motions.

9. Analyses based on a single boring or CPT may include what are logged as “layers” but are in fact lenses or portions of a sinuous backfilled channel. Such lenses or segments of a channel cannot respond to earthquake ground motions independently as is assumed in simplified analyses or even in standard one-dimensional site response analyses. If such “layers” do tend to develop excess pore pressures, they become “soft inclusions” and the shear strains and hence the shear stresses are controlled by the response of the surrounding materials (see Pyke (2003)).

The lens / sinuous channel issue can now be simulated in my own site response analysis program, TESS2, by applying the displacement histories generated by running the site response calculation representing the general site conditions to a column that includes the potentially liquefiable “layer.” This level of effort is not justified for all projects as knowledge of the depositional environment and common sense should be sufficient on most projects, but where regulators require a “calculation”, it is possible to provide a meaningful calculation without running two or three-dimensional response analyses.

Particular Limitations

It is not possible in a relatively short note to spell out all the particular limitations of individual simplified methods of analysis, but there are many of them and it is not easy for practicing engineers to be fully cognizant of them or to evaluate their impact on any given project. It is important that practicing engineers understand that not everything that is published in a journal is correct for every situation, and that simplified analyses of some sites may never be accurate enough to be useful. Some of the more important limitations are discussed below.

Settlement

Neither Harry Seed nor I thought that settlements of non-saturated sands was a major problem, but I nonetheless completed my Ph.D. thesis on this subject for other reasons, including achieving a better general understanding of the behavior of sands under cyclic loadings, as explained in Pyke (2022).

The conservatism of simplified methods for evaluating settlements of non-saturated sands results from the use of inappropriate laboratory test results, as well as the limitations associated with working down from the peak ground surface acceleration. Tokimatsu and Seed (1987) used data from Silver and Seed (1971), who had used a particularly angular sand which might be expected to settle much more than natural soils. Tokimatsu and Seed also recommended doubling the computed settlements of non-saturated sands based on Pyke et al. (1975). But that is a conservative interpretation of the Pyke et al. paper and doubling the computed settlements when they are already conservative is unnecessary. More accurate estimation of earthquake-induced excess pore pressures and settlements requires use of bi-directional nonlinear effective stress site response analyses in which two horizontal input motions are applied simultaneously and the increments in excess pore pressures and latent or immediate settlements are then calculated each half cycle for the motions in each of the two horizontal directions and added to the total.

The computer program CLiq includes a procedure for estimating settlements of dry, that is non-saturated sands, due to Robertson and Shao (2010). This is a legitimate, although very approximate procedure, which is based on Pradel (1998), which in turn is based on Tokimatsu and Seed (1987), thus the results are likely quite conservative.

There is no hard limit on the total amount of settlement that can occur, but it can be seen from data presented in Pyke (2020) and Pyke (2022) that additional settlements will be small once the accumulated settlement reaches a value on the order of 0.5 percent of the layer thickness under uni-directional loading. Since the settlements caused by each component of motion are additive, once the accumulated settlement reaches about 0.5 percent of the layer thickness, additional settlements caused by motion in either direction will also be small. In other words, accounting for the second component of motion increases the rate at which settlements or latent settlement accumulate but does not have much effect on the maximum settlement.

For saturated sands the problem is more complicated because, as noted for instance by Macedo and Bray (2018), there are three possible contributors to ground surface or building settlements: the settlement that occurs when excess pore pressures are dissipated during or after the earthquake; the settlement that occurs as a result of material being ejected by excess pore pressures; and the settlement under or adjacent to buildings and other structures that results from rocking of the building adding to the cyclic shear stresses and strains in the soil.

For the first of these mechanisms, that is free-field settlement that occurs when excess pore pressures are dissipated during or after the earthquake, excessive conservatism again results partly from the use of conservative laboratory data. Tokimatsu and Seed (1987) used old data from Lee and Albaisa (1974), obtained from cyclic triaxial tests, which are inappropriate for this purpose. Ishihara and Yoshimine (1992) used a variety of laboratory tests, but as noted subsequently by Ishihara et al. (2016), they tested only freshly placed washed sands instead of naturally occurring soils. But simplified analyses of the settlement of saturated sands are even more conservative because they are both conservative with respect to reaching the point of initial liquefaction in a particular layer, and conservative regarding the depth of sand that reaches the point of initial liquefaction. Both these factors lead to larger settlements on reconsolidation. A nonlinear effective stress site response analysis will generally indicate both slower development of excess pore pressures and a much more limited depth of liquefaction. See Crawford et al (2019) and Pyke (2020) for examples of this issue.

The method of Ishihara and Yoshimine (1992) is also conservative for other another reason. Based on earlier studies by Ishihara’s students, Ishihara and Yoshimine (1992) developed a relationship between volumetric strain on reconsolidation and the maximum amplitude of the shear strain as a function of relative density on the basis of various stress-controlled cyclic tests with uniform cycles of loading. They then settled on a definition of the “factor of safety” against liquefaction defined as 5 percent double amplitude axial strain in 20 cycles, and, following a complicated process which I doubt any practitioners have ever read, constructed relationships between this factor of safety and the maximum amplitude of the shear strain as a function of relative density. They then concluded that “if the factor of safety is known by means of the conventional method of liquefaction analysis, it will be possible to circumvent the determination of the maximum shear strain and to directly estimate the amount of post-liquefaction volumetric strain.” They cite references from that time on how to evaluate the conventional factor of safety against liquefaction, but who knows how this is implemented in current spreadsheets and computer programs and whether it is consistent with how the settlement data was processed. Moreover, fundamentally the concept of a factor of safety against liquefaction makes no sense. The value of the expected excess pore pressures as a percentage of the initial vertical effective stress (the excess pore pressure ratio) makes sense and might be of some value, but the processes of settlement on reconsolidation after liquefaction or lateral spreading do not lend themselves to a single value of the factor of safety. Back when laboratory tests were generally conducted using stress-controlled cyclic tests with uniform cycles and irregular shear stress histories were converted to an equivalent number of uniform cycles, it was understandable that Ishihara and Yoshimine (1992) developed this procedure, but Pyke (1973), Pyke et al. (1975) and Pyke (2022) describe a much better way of computing the accumulation of latent settlement for irregular cyclic loadings. These procedures compute latent settlements every half cycle as a function of the peak strain in that half cycle and the accumulated latent settlement to that point. The accumulated settlement is used as a measure of the extent of previous cyclic loading as suggested by Martin et al. (1975) and Seed et al. (1978).

As a simple example of the limitations of the Ishihara and Yoshimine (1992) procedure, let me summarize part of a recent analysis conducted for a site in San Jose, California, focusing on a deep sand layer which is about 20 feet thick. This sand layer showed tip resistances ranging from 200 to 600 tsf, which convert to interpreted normalized SPT blow counts in order of 25 to 50 and had measured shear wave velocities in the order of 1200 to 1300 fps. But even though “transitions” were excluded and an Ic cutoff of 2.05 was applied, the computed “factors of safety”, while they are above 2.0 in some parts of this layer, drop to as little as 0.25 in other parts of the layer, so that volumetric strains in the order of 2 percent and settlement on reconsolidation of 2 inches were computed. While it would be possible to just ignore this result because of the depth of the layer, the high measured shear wave velocities, and also the facts that in this case there is a 20-foot-deep clay cap and no history of liquefaction at similar sites, the computed factors of safety make no sense, and the engineer should reject the analysis on that basis alone.

Further examples of the excessive conservatism of the Ishihara and Yoshimine (1992) procedure are illustrated in the papers by Pyke (2019) and Crawford et al. (2019) in which settlements of saturated sands computed using Ishihara and Yoshimine (1992) are directly compared with those computed using a bi-directional, nonlinear, effective stress site response analysis, as described in Pyke (2019) and Pyke (2022). In these two examples, computed settlements of 10 and 16 inches using Ishihara and Yoshimine (1992) were reduced to what are still believed to be conservative estimates of 1 to 2 and 2 to 3 inches, that is by a factor of 5 or more! Similar reductions have also been achieved in several dozen unpublished consulting studies.

The method of Zhang et al. (2002), which uses CPT data, basically relies on Ishihara and Yoshimine (1992) and is conservative for the same reasons, but it does have the advantage of offering a correction for fines due to Robertson and Wride (1998), which is one of the better corrections for fines content.

A good example of the over-conservatism of simplified methods in predicting seismic settlements is given by Geyin and Maurer (2019) using data from Christchurch NZ, as shown in Figure 2. This data is for saturated sands in which there was widespread liquefaction, including ejection of sands and silts which should add to the observed settlements, however use of the method of Zhang et al. (2002) grossly over-predicts the observed settlements. Because they used a straight-line regression to fit the data, the published paper states that settlements were underpredicted when the settlements were very small, although this is a questionable interpretation and has no practical significance. Note that for the larger estimated settlements of 0.4 m or 1.3 feet, the error is typically 0.3 m or 0.99 feet, that is, a 75% overprediction.

Two final comments regarding estimating settlements:

Cetin et al. (2009) recommended a “correction” for the settlement of saturated sands on reconsolidation which is unconservative. While this work was well-intentioned, the basis for the authors’ “linear weighting scheme” is not well supported and should not be used. If the computed settlements are thought to be excessive, there are better ways to get a more accurate estimate.

Prediction of the exact amount of settlement that may results from the second and third mechanisms described by Macedo and Bray (2018), namely, the settlement that occurs as a result of material being ejected by excess pore pressures and the settlement under or adjacent to buildings and other structures that results from rocking of the building adding to the cyclic shear stresses and strains in the soil, is quite difficult. There is no question that these mechanisms are real, but these problems are best avoided by not using shallow foundations on sites that are highly susceptible to liquefaction.

Lateral Spreading

The relationships for lateral spreading developed by Les Youd and his colleagues - Bartlett and Youd (1995) and Youd et al. (2002) are the best of the simplified methods if applied with respect for the geology of the site as illustrated in Youd (2018). Youd (2018) also discusses checks that should be applied to each layer in the soil profile which includes the exclusion of sand layers under 1 m in thickness and those having a normalized clean sand SPT blowcount of greater than 15. The importance of ruling out sites with significant fines is also noted: “only nonplastic granular sediments (gravelly sands through sandy silts) are contained in liquefiable layers compiled in the MLR database and in the liquefiable layers used to confirm the Zhang et al. (2004) procedure. Inclusion of finer- grained or more plastic soils in T15 adds uncertainty to predictions and a tendency to overpredict.” See also Youd et al. (2009) for three case histories involving sites where lateral spreading might have been anticipated but where significant deformations did not in fact develop: “The absence of detectable lateral spread displacement at the Cark Canal and Cumhuriyet Avenue sites indicate that the fine-grained sediments at those sites, although liquefiable by the criteria of Bray and Sancio (2006 ), were not susceptible to seismically induced lateral spread deformation.” Both Youd et al. (2009) and Youd (2018), as well as Chu et al. (2006), note other reasons that the MLR procedure might overpredict lateral spreading deformations but omit to mention the fact that if simplified methods are used to determine the cumulative depth of soils that might liquefy, that depth is likely to be very conservative because those methods tend to be very conservative - just as happens when the Ishihara and Yoshimine (1992) method is used to predict post-earthquake settlements of saturated soils. Overpredict the cumulative depth of soils that liquefy and you will overpredict the magnitudes of both settlement and lateral spreading!

The large scatter in the empirical data, which is not unexpected given the sensitivity of lateral spreading displacements on the character of the ground motions and the inherent variability of ground motions, suggests that more advanced analyses, such as that described by Pyke (2019b), which use site-specific input motions, may be justified on more critical or high value projects. But this requires use of a soil model that correctly accumulates permanent displacements when a cyclic shear stress is applied to an element of soil that is subjected to an initial shear stress. While such analyses generally require more detailed field and laboratory investigations, another benefit is that the possible occurrence of liquefaction is determined more accurately, and this will limit the lateral spreading displacements.

The method of Zhang et al. (2004) is flawed because it relies on an inappropriate correlation between cyclic strains in tests conducted without initial shear stresses and permanent strains developed in the field where there are initial shear stresses, which is what causes permanent deformations. These are two quite different mechanisms, and the method of Zhang et al. (2004) should not be used. The fact that it sometimes gives reasonable results does not offset the fact that it often gives crazy results!

Summary comment

It is for all these reasons that Dr. Peter Robertson, the technical advisor to the developer of the program CLiq, has suggested to me that such tools should be used primarily for screening and should not be used to obtain the final answer on “high value” projects.

A Shocking Misunderstanding

Notwithstanding the plentiful misunderstandings about simplified methods which are in the conservative direction, there is an even more shocking misunderstanding in the unconservative direction. I have recently seen some engineers, presumably trying to offset the conservatism of simplified methods of analysis, argue that sands which are dilative under static loadings, as indicated by either laboratory tests or CPT-based correlations, do not exhibit any consequences of earthquake-induced liquefaction. This is simply not correct. It is true that such sands are likely not susceptible to “static liquefaction” and the generation of flow slides, but it was clearly established by the original studies by Seed and Lee, and many subsequent studies and field observations, that under cyclic loading otherwise dilative sands could develop excess pore pressures and at least reach the point of initial liquefaction, or 100% excess pore pressure development. However, as noted above, the consequences of this excess pore pressure development diminish with increasing density, and other factors such as ageing and pre-straining. Ishihara (1993) suggested that clean sands are dilative above a normalized SPT blowcount of about 9 and do not exhibit significant consequences of liquefaction above a normalized SPT blowcount of about 15, at which point sands at normal confining pressures are strongly dilative. Development of any significant excess pore pressures is unlikely for sands with normalized SPT blowcounts above 30. But simply assuming that clean sands which are dilative under static loadings are not susceptible to earthquake-induced liquefaction and its consequences is unconservative!

A Good Example

A good example of the limitations of simplified analyses of liquefaction and its effects is provided by Jon Bray in his 2022 Seed Lecture. Much of that lecture is based on studies conducted in Christchurch, New Zealand, following the 2010 and 2011 earthquakes. Most of those studies were conducted along the Avon River whose floodplain is underlain by quite recent alluvial deposits.

Those studies did not add a great deal of practical value to existing knowledge because most of these alluvial deposits were clear examples of soils that would be susceptible to liquefaction in even moderate earthquakes. However, there were some sites that showed no surface manifestations of liquefaction, and in particular no ejecta. The sites that did show surface effects of liquefaction, which are shown in red in Figure 3, were found to contain thick deposits of clean sands that had a typical value of Ic, the soil behavior index obtained from cone penetration tests, of consistently less than 1.8. The sites that did not show surface effects of liquefaction, shown in blue, may have contained some cleaner sand layers but were generally finer grained and typically had Ic values greater than 1.8.

As Professor Bray correctly says in his lecture, it all goes back to geology. The sites that generally had Ic values greater than 1.8 had been deposited in back-water swamps. While these soils were often characterized as silty sands, they in fact tended to have clean sand layers separated by silt or even clay layers. For some years I have advised clients that they should not rely on simplified analyses if the values of Ic generally exceed 2.05, the generally accepted upper limit for clean sands (see Pyke and North (2019)), rather than the value of 2.6, which is the conventional point of separation of sandy and clayey soils. This does not necessarily mean that there is no problem at sites that include silty soils that have Ic values greater than 1.8 or 2.05, but it does mean that you should not automatically accept the results of simplified analyses and that more detailed site investigations or more advanced analyses are called for on high-value or critical projects. Further support for Bray’s limiting value of Ic of 1.8 for classic liquefaction with surface effects was provided by Robertson and Wride (1998) who found that the need to correct penetration resistances to “clean sand” values started at an Ic value of 1.7, and by the case history described by Boulanger et al. (2016), so that applying even a limit on Ic of 2.05 in simplified analyses may be too conservative.

Further Support for Using a Lower Ic Cutoff

Figure 4 shows a typical pattern of SPT blowcounts interpreted from the results of CPTs in the San Francisco Bay Area where the Bayshore deposits typically result from overlapping alluvial fans with occasional creek and levee deposits cutting through them. This results in lenses or pockets of cleaner sands within layers of more silty and clayey materials that are not continuous over a wide area. This kind of variability is also seen in relatively recent alluvial deposits in which cleaner sands are interposed with clayey sands and silts.

Deposits like the one shown in Figure 4 have rarely if ever exhibited historic liquefaction, but simplified methods often predict liquefaction and significant seismic settlements. It may be seen in Figure 4a that below an Ic value of about 1.8 the interpreted SPT blowcounts are between about 15 and 30. These materials, which are cleaner sands, may develop some excess pore pressures under cyclic loading but are most unlikely to produce consequences of engineering significance because, as noted previously, engineering consequences are unlikely above a normalized clean sand blowcount of 15. For Ic values greater than about 1.8, the interpreted SPT blowcounts fall off as a function of the Ic value, but this reflects increasing fines content and lower penetration resistance rather than increased susceptibility to adverse performance under cyclic loadings.

Additional Factors to Consider

Additional factors that should be considered, even in screening analyses, include greater emphasis on the method of deposition, and the significance of complete saturation. The method of deposition is critical for both natural and man-made deposits. As illustrated in Pyke (1973) and in basic texts on sedimentary geology, a denser rain of particles leads to looser packing and lower densities. Conversely a less dense rain of particles leads to tighter packing. Some of the effects of this are reflected in penetration resistance, but not all of the effects. The impact of the method of deposition can be seen for instance in the difference in the behavior of older hydraulic fills, which were largely dumped, or otherwise deposited with a dense rain of particles, compared with newer hydraulically placed fills in which the placement is more distributed and there is some compactive effort applied by spreading and grading operations using heavy equipment once the fill is above water - see Pyke et al. (1978) for an example.

Also, it should not be assumed that sands below the current water table are “fully saturated”. In the laboratory it takes quite high back pressures to obtain a B factor approaching unity. This can easily be checked in the field by measuring the compression wave velocity – see Stokoe (2023) for an example. And see Banister et al. (1976) for an example where simplified analyses had predicted liquefaction in a large-scale field experiment, but liquefaction did not occur. This was attributed in part at least to seasonal fluctuations in the water table and the need for longer-term saturation, ideally with some flow of water, to obtain complete saturation.

Criteria for Eliminating Soils with Silty and Clayey Fines

It should be noted that the academic criteria for delineating soils that are susceptible to liquefaction are likely very conservative. These criteria define soils that might develop significant excess pore pressures under the worst conditions, such as those under buildings constructed on shallow foundations on loose sands or silts with a high water table, where rocking of the building can add to the cyclic shear stresses and strains in the soil. Although the criteria of Bray and Sancio (2006) are widely cited and used, there are important points made in their conclusions which should be emphasized: “Moreover, some soils with PI < 12 may not be susceptible to liquefaction. Other factors such as soil minerology, void ratio, overconsolidation ratio, age, etc. are also contributing factors to liquefaction susceptibility”, and “the proposed criteria should be applied with engineering judgment.”

Figure 5 was sent to me by Jim Gingery of Keller North America in response to a question that I asked during a presentation to CalGeo. Jim’s accompanying text said: “There is a domain of soil types that are liquefiable but not densifiable. This is generally non-plastic to low-plasticity silty sands and sandy silts. I tried to illustrate this in the figure above from Armstrong and

Malvick (2016) by overlaying zones of compactable (green hatch - small rectangle in bottom left-hand corner), marginal (orange hatch – longer rectangle in bottom left-hand corner) and not compactible (red hatch). The figure’s proportions make it look like the domain for compactible and marginally compactible liquefiable soils is small, but there are plenty of such soils.” Jim’s statement that there are soils that are liquefiable but not densifiable, is likely correct in a general sense, but it might be more correct to say that such soils can still develop some excess-pore pressures and show “cyclic mobility”, but they are unlikely to exhibit significant consequences of this behavior unless, for instance, they are under buildings with shallow foundations, or are adjacent to large diameter piles or piers, which apply additional cyclic shear stresses and strains to the underlying or adjacent soils. Case histories which show larger earthquake-induced settlements usually involve lateral spreading or pumping under buildings with shallow foundations that have been built on loose saturated sands and silts. Analysis of these case histories is of legitimate academic interest but the most important lesson for practicing engineers is to spend the money on a deep foundation!

Methods of Analysis

There are basically four kinds of geotechnical analysis:

1. One that does not involve any calculations but relies on common sense and experience. Experience includes both the engineer’s personal experience and the collected experience of the profession including observations of behavior in past earthquakes.

2. “Back of the envelope” calculations, that is a simple calculation that gives the engineer a sense of the expected behavior.

3. Simplified analyses, which might involve more calculations and require a spreadsheet or a computer program.

4. More complete analyses which include more detailed modeling of the geometry and all the relevant variables. These can be 1, 2 or 3D models.

In many cases I believe that Option 1 is all that is necessary, although a simple “back of the envelope” calculation such as the Youd et al. procedure for estimating lateral spreads, or my suggestion that settlement of non-saturated sands will not exceed about 0.5 percent of the layer height, may help quantify the potential problem. The late Professor Bob Whitman was of the opinion that beyond Options 1 and 2, there was no point in running a simplified analysis and that you should try to model the problem as accurately as possible in a more complete analysis. I concur with that but note that a more complete analysis will still involve a number of approximations, so one should not assume that the numerical answer will be precisely correct. However, the engineer should obtain a much better understanding of the problem and obtain answers that are “in the ballpark” if adequate field and laboratory data are available.

Concluding Remarks

When I was a graduate student in the early nineteen-seventies it was possible to read essentially all the relevant published papers on any topic of interest, but that is impossible for practicing engineers today. Further, the published papers are largely written by academics who have to publish or perish. And both research funding and publication processes tend to favor new findings and problems, rather than consolidation of existing knowledge and focusing on practical engineering solutions. For example, the big lesson from the Niigata and Kocaeli earthquakes is not so much the details of the liquefaction processes that were involved, but that it is not a good idea to construct apartment blocks with shallow foundations on loose sands or silts, especially when there is a high water table! But in this note I have tried to pull together some important findings that come out of both research papers and observations of performance in earthquakes over a period of 50 years.

These can be broadly summarized as follows:

? It’s the geology stupid!

Or, more specifically, the method of deposition and the resulting soil fabric. And don’t forget to ask: “is there any evidence of earthquake-induced liquefaction and settlement or lateral spreading of similar soils in a similar tectonic environment?

? It is not wise to completely rely on automated processes involving spreadsheets or computer programs in geotechnical engineering. The variability in the depositional history and current geometry of soil deposits necessarily calls for some judgment to be exercised by the responsible engineer who should always ask, “does this answer make any sense?”

? The simplified methods for evaluating liquefaction, settlement and lateral spreading are at best screening tools. Ideally, no responsible engineer should rely on any of the simplified methods for evaluating liquefaction and its consequences unless they have some familiarity with each step in the procedure, the limits of applicability of that step and whether the site in question fits within the limits of the overall applicability of the method. And reviewers should not automatically either accept or reject the results of simplified analyses on projects of any importance.

? The simplified methods for evaluating liquefaction, settlement and lateral spreading are particularly inappropriate in the context of risk-informed decision making, which is increasingly being adopted worldwide. It makes no sense to conduct quantitative risk analyses using analytical methods that are both not very accurate and have a built-in conservative bias.

? More detailed site investigations and more advanced analyses may be called for on high-value or critical projects. Even for simplified analyses it is good practice to initially conduct seismic CPTs and, if there are any potentially liquefiable layers, to follow-up with companion borings in which SPTs are targeted towards the top of those layers and full grain size curves are obtained.

oOo

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