Technical manual - v1.1IntroductionNotationsQuantification of liquefaction hazardPhenomenological remindersSoil sensitivity against liquefactionSimplified "NCEER" procedureDomain of validityPrinciples of calculationNormalized equivalent cyclic shear stressNormalized cyclic resistance ratioGeneral assumptions of calculationStress states in the soil Taking into account project seismic magnitudesAdditional corrections correction factor for NCEER-SPT for NCEER-CPT Correction FactorEvaluation of the cyclic resistance ratioAssessment based on standard penetration tests (SPT)Principle of the SPT testInput parameters - SPTFormulation of based on the SPT testsStep n°1: Normalizing the number of blowsStep n°2: Correction for fines content to get a "clean-sand" equivalentStep n°3: Expression of cyclic resistance ratioAssessment based on cone penetration tests (CPT et CPTu)Principle of the CPT(u) testInput parameters - CPT(u)Formulation of based on CPT(u) testsStep n°1: Normalization of Cone Penetration parameters CPT(u)Step n°2: Correction for fines content to get a "clean sand" equivalentStep n°3: Expression of cyclic resistance ratio Additional notes on the soil behaviour type index Evaluation of earthquake-induced settlementsPrinciples of calculationEstimation of volumetric strains Zhang, Robertson and Brachman (2002) Correlations From CPT(u) testsFrom SPT testsIdriss and Boulanger (2008) Correlations From CPT(u) testsFrom SPT testsAdditional indicatorsCumulative liquefiable thicknessesLiquefaction Potential Index LPIReferences
Slake is intended for the complete carry out of quantification analyses of liquefaction hazard of soils subjected to seismic loading in open field by the direct semi-empirical method known as "NCEER" (Youd and Idriss, 2001)(1), using SPT (standard penetration test) and/or CPT(u) (cone penetration test with or without pore-water pressure measurement) data. By simplification, these analyses are called NCEER-SPT and NCEER-CPT in the following.
(1) Slake v1.1 also features an additional calculation option derived from the simplified "NCEER" procedure, taking into account certain adaptations resulting from the recommendations of the AFPS Technical Notebook n°45 "Assessment of the risk of soil liquefaction under the effect of earthquakes - Practical knowledge and applications to geotechnical projects" (NCEER/CT45-AFPS(2020) calculation option).
The determination of factors of safety against liquefaction is coupled with a strain analysis, allowing the estimation of post-liquefaction settlements under a water table according to the correlations proposed by different authors and derived from the charts of Ishihara and Yoshimine (1992).
Thereafter, the following notations are adopted:
|Parameter or acronym||Unit||Description|
|-||Geometric factor for taking pore-water pressure into account in tests with piezocone|
|Peak Ground Acceleration, noted also as PGA|
|Clay content ; defined as the percentage by weight passing through a 2 µm sieve (according to NF P 11-300)|
|Silt content ; defined as the percentage by weight passing through a 63 µm sieve (according to NF P 11-300)|
|-||Cone Penetration Test|
|-||Cone Penetration Test with pore-water pressure measurement thanks to electrical point (piezocone)|
|Relative density of a granular material|
|Fines content defined as the percentage of passing by weight through the 75 µm sieve according to USCS classification (the most similar sieve in France is 80 µm)|
|-||Factor of safety against liquefaction|
|Acceleration of gravity|
|Unit weight of the fill materials if any|
|Saturated unit weight of the material|
|Unsaturated unit weight of the material|
|-||Soil Behaviour Type Index (Robertson)|
|-||Threshold above which soils tested by cone penetration test CPT(u) and qualified by the soil behaviour type index are deemed too fine or too plastic to liquefy|
|Plasticity index ; determined from consistency indices :|
|-||Moment magnitude of earthquake|
|-||Surface-wave magnitude of earthquake|
|-||Magnitude Scaling Factor, correction factor on the project earthquake magnitude compared to magnitude 7.5|
|-||Correction factor (magnitude scaling factor) on the project earthquake magnitude determined from the lower bound of the range proposed by the "NCEER" procedure|
|-||Correction factor (magnitude scaling factor) on the project earthquake magnitude determined from the upper bound of the range proposed by the "NCEER" procedure|
|-||Correction factor (magnitude scaling factor) on the project earthquake magnitude corresponding to the average between the upper and lower bounds of the range proposed by the "NCEER" procedure|
|Reference pressure taken equal to atmospheric pressure, approximately 100 kPa|
|-||Reference coordinate system (for example: NGF, NVP, ...); allowing to link the investigation depths (relative) to elevations (absolute)|
|Total vertical stress in project conditions|
|Effective vertical stress in project conditions|
|Total vertical stress in initial conditions at the time of the tests|
|Effective vertical stress in initial conditions at the time of the tests|
|-||Standard Penetration Test|
|Pore-water pressure measured by the pressure sensor u2 (on the sleeve at the back of the cone) in the case of test with piezocone|
|Elevation of the water-table in initial conditions at the time of testing expressed in the chosen coordinate referencing system|
|Elevation of the water-table in the conditions of project (concomitant with the earthquake) expressed in the chosen coordinate referencing system|
|Initial elevation of natural ground (initial conditions)|
|Final elevation of the ground (project condition)|
Liquefaction is a characteristic instability of contracting saturated sands (granular materials in a very loose to loose state) that can develop increased pore-water pressures as a result of cyclic stress in undrained conditions. These large pore-water pressures are responsible for the loss of resistance by reducing - or even canceling - the effective stress in the soil. Under certain conditions, this phenomenon can also take place under a monotonous loading, which is called static liquefaction.
The phenomenon of liquefaction is to be distinguished from the cyclic mobility, also characterized by a behaviour at constant or nearly constant volume (saturated materials in undrained conditions) and which affects the dilative sands (granular materials in a moderately dense to very dense state). For the latter, the generation of excess pore-water pressures during loading leads to temporary losses of resistance and significant cyclic deformation, but the tendency to dilatancy that occurs during shear prevents overall loss of resistance and significant permanent deformation.
Soft clays are prone to another phenomenon, cyclic softening, which causes a loss of stiffness due to the potentially large accumulation of irreversible deformations under cyclic loading.
The simplified semi-empirical calculation method implemented in Slake allows the quantification of hazard only within the strict framework of the liquefaction phenomenon as defined above, apart from the instabilities associated with cyclic mobility and cyclic softening.
Soil physical properties were the first characteristics used to estimate their susceptibility against liquefaction. Different criteria for sensitivity analysis have been proposed, historically based on the limits of consistency, granulometric properties and water content, or combinations of these properties.
Slake featers a Liquefaction Sensitivity Assessment Wizard that complies with the current requirements of Eurocode 8 Part 5 (EC8-5). This wizard is independent from the quantitative hazard analysis, which can be examined locally using SPT and/or CPT(u) surveys using different methods. At a specific measurement point, and based on the analysis of the Eurocode criteria detailed below, the Wizard determines "the need for a quantitative hazard analysis", or on the contrary "the possibility of ruling out the risk of liquefaction".
This assessment is based on the examination of one main condition concerning the seismic assumptions of the project, plus three additional criteria derived from laboratory and in situ test results: granulometry, plasticity, normalized SPT test results. The verification of the main condition and, simultaneously, of at least one of the three additional criteria, allows the risk of liquefaction in the sense of EC8-5 to be neglected. If not, the risk of liquefaction must be quantified.
|**Main condition: the coefficient of horizontal acceleration at the surface () is strictly less than 0,15|
|Additional criterion : sands contain clay in a proportion strictly superior to 20%, with a plasticity index strictly superior to 10%||and|
|Additional criterion : the sands contain silts in a proportion strictly higher than 35% and, at the same time, the SPT blow count normalized for the effect of overburden and the energy ratio is strictly higher than 20||and|
|Additional criterion : the sands are clean, with the value of the number of SPT blows, normalized for the effect of overburden and the energy ratio is strictly higher than 30||and|
Note: it shall be reminded that there is no consensus on the use of sensitivity criteria, particularly with regard to risk exclusion criteria. Nevertheless, the criteria offer a practical entry point (at least qualitatively) for assessing the sensitivity of soil against liquefaction.
Slake is based on the implementation of the simplified analysis procedure formalized by Youd and Idriss in 2001 following the consensus reached at the working seminars on soil resistance to liquefaction organized by the NCEER research in 1996 and jointly NCEER/NSF in 1998 (published in the ASCE journal JGGE in April 2001). By simplification, this methodology is noted as the "NCEER" procedure in the following.
As of 2021, the "NCEER" procedure is still considered to be the international reference for quantifying liquefaction hazard of soils (sole consensus). The methods proposed by Idriss and Boulanger in particular are variations of the latter, but do not reach consensus.
Note: in its current version (v1.1), Slake features an additional calculation option : NCEER/CT45-AFPS(2020).
This alternative calculation option takes up the general principles of the "NCEER" procedure (detailed in the following paragraphs) with subtle adaptations/modifications to certain clearly identified calculation parameters, in accordance with the recommendations made in the appendices of Technical Notebook n°45 "Assessment of the risk of soil liquefaction under the effect of earthquakes - Practical knowledge and applications to geotechnical projects" (to be published in 2021) by the "Liquefaction" Sub-Working Group of the AFPS (french association for earthquake engineering).
When applicable, these modifications are detailed in the relevant paragraphs. Wherever this is not expressly stated, the "NCEER/CT45-AFPS(2020)" calculation option strictly follows the calculation assumptions of the "NCEER" procedure.
The "NCEER" procedure is a deterministic approach, in total stress, and considering the hypothesis of open field site conditions, i.e. assuming the spatially unconstrained liquefiable layers(s) and susceptible(s) to be freely set in motion (one-dimensional calculation).
It was developed empirically from the compilation of field data (in situ tests of different types) and laboratory tests performed on samples composed of siliceous alluvial materials (silty sands), of Holocene age, collected at shallow depths and from sites mainly in California, under level to gently sloping ground having liquefied or not liquefied as a result of earthquakes of magnitude equal to 7.5.
The results of any analysis conducted outside the strict assumptions of the "NCEER" method's validity domain must be subject to critical analysis by the geotechnical engineer.
These considerations are also valid when the calculation option "NCEER/CT45-AFPS(2020)" is selected.
For an earthquake of any magnitude, the method consists in the assess of a factor of safety against liquefaction defined as the ratio between the normalized cyclic resistance ratio (Cyclic Resistance Ratio) of the ground for a reference earthquake of magnitude of 7.5 on the one hand, and the equivalent normalized shear stress generated by the earthquake (Cyclic Stress Ratio) on the other hand, at any point where measurements are available in the tested soil column.
This ratio is then corrected by the term (Magnitude Scaling Factor) which allows to take into account the project magnitude of the earthquake under consideration, and by the possibly combined effects of confining pressure () and inclination of stress ().
The factor of safety against liquefaction is then expressed as follows:
Theoretically, liquefaction occurs when the factor of safety is less than the unit (local cancellation of the vertical effective stress). The accumulation of irreversible volumetric strains associated with a significant reduction in vertical effective stress may nevertheless develop due to excess pore-water pressures for computation points with factors of safety greater than the unit.
In Slake, the threshold of the stability domain is thus limited by the limit factor of safety , while the lower limit of the safety domain is bounded by the targeted factor of safety noted directly inputed by the user with respect to a pre-defined level of safety.
As an indication, Eurocode 8 currently sets the minimum safety threshold at 1.25, a value associated with the development of excess pore-water pressures in the order of 60% of the vertical effective stress. This threshold can be increased according to the nature and sensitivity of the studied structure, being implicitly understood that beyond this value the earthquake-induced post-liquefaction deformations are negligible and therefore acceptable by the supported structure.
Slake presents the FS calculation results only at points where the following double condition is verified:
The calculation point (ie the test point) is below the project water-table level: ;
The normalized measurement at the point of the test (depending on the type of test) does not exceed the threshold values beyond which it is conventionally accepted that the materials tested are too dense to be liquefiable:
In the case of CTP(u) analyses, an additional criterion applies on the basis of the behaviour type index . Soils with a behaviour type index greater than or equal to a threshold value are considered too fine and/or plastic to liquefy:
Usually, is set at 2.6. However, it is possible to change the threshold value on the behaviour type index in Slake. The threshold should then be calibrated from cyclic laboratory tests. Changing this threshold value is strongly discouraged.
The process for safety factor determination against liquefaction is synthesized in the following logigram.
The cyclic shear stress induced by the earthquake normalized by the vertical effective stress is assessed from the following equation (Seed & Idriss, 1971):
The coefficient is a coefficient of stress reduction based on the depth resulting from soil flexibility; it is defined in Slake according to Blake's formula (1996):
Where z is the depth. This formulation of the term is strictly valid only up to 15 m deep, and is no longer applicable beyond 20 m. It is implicitly accepted in Slake that the user provides in situ test results to depths deemed compatible with the development and surface expansion of liquefaction effects. Attention is drawn to the fact that the factor is therefore not limited and is extrapolated to any depth following this formulation by the software.
The term (Cyclic Resistance Ratio), thus the normalized cyclic resistance ratio offered by the examined soils, is estimated by post-processing of the results of in situ SPT and/or CPT(u) tests. The definition of the term is detailed in the paragraphs relating to the computation of each test category.
Liquefaction analyses are conducted by defining two distinct multilayer geotechnical models to distinguish the calculation of stress states relating to the cyclic resistance term (CRR) and the term of earthquake action (CSR). The first one is representative of the context prevailing at the time of the surveys, while the second one must be representative of the conditions projected in the operational phase and concurrent with the considered seismic actions.
These models take into account:
The "NCEER" procedure recommends a range for estimating the correcting factor based on seismic magnitudes . The latter are to be distinguished from the magnitudes of surface waves (). As an indication, it is shown below the transformation of a magnitude measure to another that can be made according to the bilinear relations of Scordilis (2006), valid for shallow earthquakes (less than 70 km).
It is commonly accepted that below a magnitude of 5.0 the energy released by seismic waves is not sufficient to initiate the phenomenon of liquefaction (lack of counter-examples referenced as of 2019). It should be noted that Slake determines MSF values by extrapolation beyond the limits defined by the "NCEER" procedure ( and ).
The MSF range recommended by the "NCEER" procedure as well as the equations of the lower () and upper () bounds are shown below.
|Lower bound of "NCEER" range||Upper bound of "NCEER" range|
|(Idriss corrected 1982)||(Andrus and Stokoe 1997)|
Note 1: Slake provides an intermediate option for the determination of the magnitude scaling factor directly corresponding to the arithmetic mean, for a given magnitude of seismic moment, between the values associated with the lower and upper bounds of the recommended range : .
Note 2: it is possible to manually insert into Slake any value of . However, it is recalled here that the and parameters are strictly linked; it is therefore not recommended to input correction factors outside of the proposed range as part of analyses conducted strictly according to the "NCEER" procedure (nor the “NCEER/CT45-AFPS(2020)” option).
The equation (1) involves two complementary correction factors and which are outside the framework of the simplified "NCEER" procedure.
Laboratory cyclic loading tests indicate that liquefaction resistance increases with increasing confining stress, but not linearly (the normalized resistance CRR decreases as the effective confining stress increases). In order to extrapolate the normalized resistance CRR (obtained by simplified method for a vertical stress of 100 kPa) to layers where the effective stress are greater than 100 kPa taking into account this non-linearity, Seed (1983) introduced a corrective factor. The values were obtained from cyclic triaxial tests on clean-sands with various relative densities and consolidated under stress between 100 kPa and 600 kPa.
The use of this correction factor may be justified in potentially liquefiable sandy soils located at a deep depth, or in the case of a deep water-table.
In the 2001 paper, the formulation of Hynes and Olsen (1999) defines the parameter as the vertical effective stress normalized by atmospheric pressure (approximately 100 kPa) and then raised to the power depending on site conditions: relative density, age of deposits, level of overconsolidation.
In practice, the definition of the exponent is reduced to a correlation based on relative density . The values chosen for are summarized in the table below.
|Condition on the relative density of granular materials||Exponent|
|linear variation between 0.8 and 0.7|
|linear variation between 0.7 and 0.6|
Precaution: The relative density is a notion only relevant to granular materials, with a fine content 1 strictly less than 15%. To correct this problematic definition, because it is not independent of the nature of the soils, Slake does not take into account by default the correcting factor (). However, the user can force the calculation of this correction term, if he wishes, by activating the option in the advanced calculation parameters. If so, the calculation is systematically limited to a unit value:
1 Strictly speaking, the fine content () used to establish these correlations must be consistent with the USCS, and therefore corresponds to the percentage of passing by weight through the 75 µm sieve. This sieve is not used in the French standards of sieve analyses (in the old NF P 94-056 standard, the fine content is defined by the percentage of passing by weight through a sieve of 80 µm; in the new NF P 94-512-4 standard it is defined by the passing through a 63 µm sieve). It is therefore important that the definition of chosen is compatible with the strict application of the NCEER-SPT procedure, i.e. a passing through a 75 µm sieve, or, failing that, 80 µm sieve.
In the case of an NCEER-SPT analysis, the user can choose to impose the correction factor calculation by activating the dedicated switch in the advanced calculation settings. If so, the following should be provided:
At calculation points included in the interval (or intervals) defined by the selected stratigraphic layer(s) where the condition on the fine content is verified (), the relative density is estimated thanks to the Skempton (1986) correlation:
At calculation points where , no relative density is calculated and the factor is automatically taken equal to .
The correction factor is then calculated from the equation (4).
Important note: Skempton's correlation was established for medium to coarse, clean quartz sands of relative densities between 0.35 and 0.85, under stress between 50 kPa and 250 kPa. Outside the validity domain of this correlation, and in general, the user is asked to control the calculation results. In the result tables, Slake highlights the calculation results where the relative density estimated by correlation is outside the range .
Case of the "NCEER/CT45-AFPS(2020)" calculation option
When selected, the definition of correction factor for SPT based analysis remains an "advanced" calculation option to be set manually. However, the calculation conditions differ on the following points:
The default value of the fines content threshold below which the calculation is performed is arbitrarily raised to 100% (although it can be modified by the user), with the effect of "forcing" (a priori) the calculation at any measurement point of a layer where the option has been selected;
The upper bound of , equation (5)) is no longer locked to the unit but is to be filled in by the user; by default its value is taken to be equal to ;
The value of the exponent f is no longer directly calculated by correlation with the relative density , and is considered constant even in the case of a multilayer. It must be filled in by the user. By default, the exponent is taken equal to 0.7 (conservative approach);
At the calculation points contained in the interval(s) defined by the selected stratigraphic layer(s) where the condition on the fine fraction is verified , equation (4) is replaced by the following expression :
This approach aims at simplifying the calculation of the correction factor without setting conditions on the relative density of the soils on a flat-rate basis.
In the case of an NCEER-CPT analysis, the user can choose to impose the correction factor calculation by activating the dedicated switch in the advanced calculation settings. If so, the following should be provided:
At calculation points included in the interval (or intervals) defined by the selected stratigraphic layer(s) where the condition on the soil behaviour type index is verified (), the relative density is estimated thanks to the Baldi (1986) correlation:
At the calculation points where no relative density is calculated and the factor is automatically taken equal to .
The correction factor is then calculated from the equation (4).
Important note: Baldi's correlation is strictly applicable only in the case of fine to medium clean siliceous sands, homogeneous and uncemented, normally consolidated and moderately compressible. Moreover this relationship is not valid at shallow depth of penetration: the calculation of in Slake is therefore fixed to carry out only beyond 3.0 m deep. Outside the validity domain of this correlation, and in general, the user is asked to control the calculation results. In the result tables, Slake highlights the calculation results where the relative density estimated by correlation is outside the range.
Case of the "NCEER/CT45-AFPS(2020)" calculation option
When selected, the definition of correction factor for CPT(u) based analysis remains an "advanced" calculation option to be set manually. However, the calculation conditions differ on the following points:
This approach aims at simplifying the calculation of the correction factor without setting conditions on the relative density of the soils on a flat-rate basis.
Theoretically, the development of static shear stress in a sloping soil mass influences its ability to withstand liquefaction. This influence - positive or negative - depends in particular on the nature, density and confining state of soil. Some authors propose to express it using a specific correction factor,, without the latter being the subject of a consensus as of the date (2019).
Slake does not allow the correction factor to be taken into account in the execution of routine liquefaction analyses ().
The Standard Penetration Test (SPT) is a standardized dynamic in situ test that also allows the collect of disturbed samples. It is framed by the American standard ASTM-D-1586-11, and partially included in the French application standard NF EN ISO 22476-3.
In a pre-drilled borehole, the test involves pushing a casing following a standardized driving device and counting in successive stages the number of blows needed for a specific penetration of the casing into the ground. Conventionally, and in the absence of refusal, the "SPT resistance" corresponds to the number of blows needed to penetrate 15 cm of the second () and third () driving increments after a first priming penetration () of 15 cm:
Ideally, the energy actually delivered to the rod string by the driving device is measured with an analyzer, via an instrumented rod.
As part of the liquefaction analyses, the disturbed sample taken from each test is subject to sieve analysis by sieving (NF P 94-056), or at least the measurement of the 80 µm sieve passing.
Conducting liquefaction analyses from the computation of SPT tests requires the following parameters.
|Natural ground elevation survey elevation||General|
|Average piezometric level at the time of testing (preferably measured in a piezometric survey in the immediate vicinity of the SPT survey)||General|
|Test depth||At any point of measurement|
|SPT blow count:||At any point of measurement|
|Fine content of the tested material: percentage (by weight) of passing through 80 µm sieve1||At any point of measurement|
|Driving energy ratio||At any point of measurement|
|Driving device (to provide in case of no direct measurement of driving energy )||General|
|Sampling method 2||General|
1 Strictly speaking, the fine content (FC) given for the implementation of the "NCEER" method complies with the requirements of the ASTM, and therefore corresponds to the percentage by weight of passing through the 75 µm sieve. This sieve is not used in the French standard of granulometric analyses (NF P 94-056), the closest is the 80 µm sieve.
2 The sampling method depends on the type of core used: truncated cone cores (variable inner diameter 35 to 38 mm), cylindrical cores (constant inner diameter of 35 or 38 mm) that may or may not be equipped with sampling liners
The cyclic resistance ratio term is calculated sequentially. The procedure is schematized in the logigram below.
The evaluation criterion of cyclic resistance ratio through analysis based on the computation of SPT results rests on a normalization of the number of blows:
The nature and detail of the corrections made are described in the following table.
|Correction factor||Parameter||Type0||Expression of the correction|
|Overburden pressure1||Automatic||( Liao et Whitman, 1986)|
|Rod string length3||Automatic|
0 For the definition of the "type" of correction, "Automatic" means that it is directly applied by the software, "Manual" means that the correction depends on specific input parameters to be provided by the user.
1 The normalization of the number of SPT blows relative to the stress level is calculated using the formulation of Liao and Whitman (1986). This correction term is automatically limited to . This correction applies to the states of stress prevailing in the studied soil at the time of the execution of the tests; they are normalized by a reference pressure taken equal to the atmospheric pressure (~100 kPa).
2 The driving impact energy is expressed in terms of the energy ratio between the energy actually transmitted to the string of rods (measured with an analyzer, ) and the theoretical maximum potential energy (), i.e. . This ratio should, of course, be positive and less than 100%; it depends on both the type of hammer/driving cap system and the hammer release device. The energy ratio is reduced, via the factor , to a reference value of 60%, which represents in the first approximation the value of restored energy in American practice:
In case the restored energy is not directly measured with an analyzer, i.e. where the ratio is not a direct entry data into the software, average values of are proposed based on the driving system used for the execution of the tests (Robertson and Wride, 1998). Note that if the energy ratios are provided as well as the driving impact device, Slake prioritizes direct measurement.
3 The total length of the rod string must strictly take into account the above-ground part to the cap of the driving device in addition to the depth of the test:
The length of the above-ground rod string varies (depending on the size of the drill rods). Slake considers by default a metric length above ground: , however, it can be adjusted in advanced options.
In the unavailability of accurate data on this subject, it is recommended to neglect this overlength of the rod string and consider only the depth of the test (conservative hypothesis). Note that, strictly speaking, the depth of the test should be increased by 15 cm to take into account the priming penetration.
4 The use of truncated cone cores (a variable inner diameter of 35 to 38 mm) or cylindrical cores with split spoons for a liner, but used without a liner, results in a significant decrease in the number of blows (+10/+30%). If one of these sampling methods is used, Slake applies by default a correction of 20% on the number of SPT blows. On the other hand, no correction is applied for a sampling carried out with cylindrical cores without splits (constant inner diameter of 35 mm), or with splits but equipped with liners.
Case of the "NCEER/SGT-LIQ-AFPS" calculation option
When this calculation option is selected, the determination of the correction factors , and is modified as follows:
|Correction factor||Parameter||Type0||Expression ot the correction|
|Rod string lengths2||Automatic|