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Constitutive modelling approach forevaluating the triggering of flow slides
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Citation Buscarnera, Giuseppe, and Andrew J. Whittle. “ConstitutiveModelling Approach for Evaluating the Triggering of Flow Slides.”Can. Geotech. J. 49, no. 5 (May 2012): 499–511.
As Published http://dx.doi.org/10.1139/t2012-010
Publisher Canadian Science Publishing
Version Author's final manuscript
Citable link http://hdl.handle.net/1721.1/89650
Terms of Use Creative Commons Attribution-Noncommercial-Share Alike
Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/
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Constitutive modelling approach for evaluating the triggering of flow slides 3
Giuseppe Buscarnera† and Andrew J. Whittle†† 4 5
† Politecnico di Milano – Department of Structural Engineering 6 Piazza Leonardo da Vinci, 32 – 20132 – Milan (Italy) 7
†† Massachusetts Institute of Technology (MIT) – Civil and Environmental Engineering Department 8 Massachusetts Avenue, 77 – Cambridge (MA) - USA 9
10 11
ABSTRACT 12
13
The paper presents a methodology to evaluate flow slide susceptibility in potentially liquefiable sandy slopes. The 14
proposed approach accounts for both contractive and dilative volumetric behaviour during shearing using the MIT-S1 15
constitutive model. As a result, it is possible to distinguish among different types of undrained response induced by a 16
rapid shear perturbation. The first part of the paper describes the general methodology for infinite slopes, providing an 17
index of stability for incipient static liquefaction in shallow deposits. The methodology accounts for anisotropy due to 18
the initial stress state within the slope and uses simple shear simulations to assess instability conditions as a function of 19
slope angle, stress state and density of the soil. The resulting stability charts define the margin of safety against static 20
liquefaction and the depths likely to be affected by the propagation of an instability. The second part of the paper 21
applies the methodology to the well known series of flow failures in a berm at the Nerlerk site. The MIT-S1 model is 22
calibrated using published data on Nerlerk sands and in situ CPT data. The analyses show that in situ slope angles 23
α=10°-13° are less than the critical slope angle needed for incipient instability. The analyses show that liquefaction and 24
flow failures are likely for small perturbations in shear stresses that could be generated by rapid deposition of hydraulic 25
fill. 26
27
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KEY WORDS: Static liquefaction, slope stability, flow slide, constitutive modelling, soil instability. 29
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1
INTRODUCTION 2
3
Landslides and slope failures are widely recognized as an important class of natural hazards that 4
has relevance at a range of scales, from the design of earthworks to the management of land use in 5
densely populated areas. The wide distribution of these phenomena represents a continuing 6
challenge for the geotechnical community to develop appropriate tools of analysis, explain complex 7
failure mechanisms, evaluate and mitigate current hazards and define reliable design criteria. Within 8
the general class of slope failures, runaway instabilities associated with flow slides in cohesionless 9
soils are particularly impressive phenomena that involve several unanswered research questions. 10
The geotechnical literature reports several case histories of large submarine flow slides [Koppejan 11
et al., 1948; Terzaghi, 1957; Andersen and Bjerrum, 1968]. Flow slides in submerged artificial 12
sandy slopes can also represent a major threat in coastal environments, where deposition, dredging 13
and excavation can produce rapid shear perturbations in the soil mass [Sladen et al., 1985-b; Hight 14
et al., 1999; Yoshimine et al. 1999]. 15
One of the first interpretations of these slope failures was due to Terzaghi (1957). In order to 16
characterize the observed phenomenon, Terzaghi introduced the term spontaneous liquefaction, 17
relating this typology of slope instability to the metastable state of the deposits involved. Most of 18
the attempts to define quantitatively the triggering conditions for a flow slide have been based either 19
on semi-empirical frameworks relying on the concept of steady state of deformation [Castro, 1969; 20
Poulos, 1981; Poulos et al., 1985] or on the definition of instability boundaries in effective stress 21
space [Sladen et al., 1985-a; Lade 1992]. However, none of these approaches is sufficiently general 22
for a practical implementation into triggering analyses. 23
Experimental observations and analyses of case studies have shown that many different factors 24
can affect both the necessary perturbation to induce an instability and the post-failure behaviour 25
(e.g., drainage and test control conditions, relative density and stress level, anisotropy etc.). Recent 26
3
advances in soil constitutive modelling can provide powerful tools to shed light on this complex 1
issue. One of the first and most interesting modelling approaches to address the problem of flow 2
slide triggering using a thorough description of soil behaviour was proposed by di Prisco et al. 3
(1995), with particular reference to the simple case of an infinite slope. 4
This paper presents a methodology to evaluate flow slide susceptibility in a potentially 5
liquefiable sandy slope based on the original idea suggested by di Prisco et al. (1995), but tries to 6
link more directly the model predictions to the framework of critical state for cohesionless materials 7
and to in situ observations. The key contribution is the ability to predict transitions between 8
contractive and dilative volumetric behaviour upon shearing. As a result, the approach is able to 9
distinguish among different types of sand response induced by an undrained perturbation (complete 10
liquefaction, partial liquefaction, etc.), which is an essential aspect to define the expected post-11
failure behaviour of a sliding mass. The MIT-S1 model (Pestana and Whittle, 1999) is used for this 12
purpose. The model accounts for some of the most relevant factors affecting the undrained response 13
of sands (e.g., density dependence, pressure dependence, initial and evolving anisotropy etc.). Here 14
it is combined with an appropriate stability criterion for shallow slopes. In this way, the influence of 15
slope angle, stress state and density of the deposit are investigated synthetically, evaluating the 16
magnitude of the stress perturbation necessary to trigger liquefaction. This is done by producing 17
stability charts for any depth in the slope that identify the margin of safety from static liquefaction 18
and the location of the soil masses likely to be affected by the propagation of an instability. 19
Finally, the approach is applied to a well known series of flow failures at the Nerlerk berm 20
(Sladen et al., 1985-b), in which sand liquefaction is likely to have played a relevant role. 21
Experimental data relative to both laboratory tests and CPT in situ tests available in the literature 22
are used and interpreted, in an attempt of providing a consistent mechanical interpretation of the 23
phenomenon. 24
25
26
4
REVIEW OF DEVELOPMENTS IN TRIGGERING OF FLOW SLIDES 1
2
Several authors in the past addressed the problem of flow slides induced by static liquefaction. 3
The first approaches were essentially focused on the experimental definition of liquefaction 4
conditions under undrained loading [Castro, 1969] and the introduction of the steady state strength 5
in classical limit equilibrium analyses [Poulos, 1981; Poulos et al., 1985]. Although the steady 6
state strength can be used to evaluate soil liquefaction potential at very large strains, it does not 7
address the initial triggering conditions for a flow failure. In addition, there are circumstances in 8
which the use of the steady state strength can be misleading. Liquefaction instabilities can also be 9
triggered in soils experiencing dilation at large strains, provided that the excess pore pressures 10
induced prior to shearing is large enough to induce a structural soil collapse (partial liquefaction). 11
In this case a proper instability is still possible, but with a marked change in the post-failure 12
response of the slope [Beezuijen and Mastbergen, 1989]. 13
A more general understanding of the flow slide triggering was achieved when it was fully 14
recognized that potential instability conditions can be attained even when the soil is loaded along 15
drained stress paths, provided that certain shear stress levels were achieved after drained loading. 16
This new perspective led to interpretative frameworks based on the definition of instability 17
boundaries in the effective stress space. Important examples of theories of this kind are the 18
collapse surface concept [Sladen et al., 1985-a] and the instability line concept [Lade, 1992], as 19
shown in Fig. 1. These loci in the effective stress space represent a limit of stability under 20
undrained conditions, therefore instability can be initiated when the stress path reaches such loci 21
during either drained or undrained shearing. However, the stress state is not bounded to lie within 22
the limits described by these instability boundaries. Under drained loading the state of stress can 23
cross the boundary without experiencing any collapse, but spontaneous collapse can occur if 24
undrained shearing conditions prevail. 25
5
Although these theories favor a relevant improvement in recognizing static liquefaction as a 1
proper soil instability phenomenon, they do not constitute a general interpretation framework. 2
Their development was in fact based almost exclusively on experimental observations derived 3
from triaxial testing, and in most cases the evaluation of the deviatoric stresses triggering 4
liquefaction was estimated for the unlikely conditions of an initial isotropic state of stress. This 5
disregards the influence of different static and kinematic boundary conditions (e.g. plane strain, 6
simple shear conditions etc.), and the influence of the initial anisotropy within the slope. As a 7
result, the adoption of instability parameters estimated from undrained triaxial shear tests is ad hoc 8
and is not predictive for evaluating flow slide triggering under field boundary conditions. 9
More refined predictive frameworks based on comprehensive constitutive models have been 10
proposed in the literature (Nova, 1989, 1994; Imposimato and Nova 1998; Borja, 2006). The goal 11
of these contributions was to apply the theory of material instability to static liquefaction, 12
providing a mechanical explanation for the phenomenon. Further generalizations of these 13
approaches have been recently developed, disclosing the importance of the current state of stress 14
and density on the liquefaction potential (Andrade, 2009; Buscarnera and Whittle, 2011) and 15
showing practical applications of the theory to finite element analyses (Ellison and Andrade, 2009; 16
Pinheiro and Wan, 2010). 17
One of the first approaches to consider these notions for the triggering analyses of flow slides 18
was that suggested by di Prisco et al. (1995). In order to study the onset of a flow slide, the authors 19
considered the geometry of an infinite slope and modelled sand behaviour through simple shear 20
simulations. This approach was able to combin the accuracy given by advanced constitutive 21
models with a reduced cost of analysis, and similar approximations to address slope behaviour 22
have been used more recently by other authors to study the onset of subaqueous slides in low 23
permeability clays under cyclic loading (Pestana et al,. 2000; Biscontin et al., 2004) or the 24
tsunamigenic triggering of a shallow underwater slide through energy principles (Puzrin et al., 25
2004). 26
6
The kinematic constraints for the infinite slope geometry (Fig. 2-a) impose plane strain 1
conditions, implying that the out-of-plane strain rate components must be zero (i.e., 2
0χ χξ χηε γ γ= = = ). The assumption of infinite slope also constrains the extensional strain 3
component parallel to the slope, 0ηε = . Finally, if undrained shearing occurs, the isochoric 4
constraint implies a zero value for the strain component normal to the slope, 0ξε = . As a result, 5
the only strain contribution governing the undrained behaviour of an infinite slope is the shear 6
strain ξηγ (i.e., the material points at any depth are subject to undrained simple shear mode). 7
Therefore, provided that suitable initial test conditions are defined in simple shear test simulations, 8
a description for the undrained response of the slope can be predicted by material point analyses. 9
Following these assumptions, di Prisco et al. (1995) described the response of any point in the 10
slope by performing simple shear test simulations, with the initial state corresponding to 11
equilibrium in the slope. Fig. 2b summarizes typical charts of shear perturbations obtained through 12
undrained simple shear simulations. The chart shows the shear stress increment, τΔ , necessary to 13
trigger a flow slide as a function of the slope angle. Given the conventional assumption that stress-14
strain-strength properties can be normalized with respect to the mean effective stress, there is 15
almost no variation of liquefaction susceptibility within the soil mass. As a result, a single 16
normalized chart can represent triggering conditions at all depths within the slope. It is evident that 17
spontaneous flow will occur for slopes having inclinations greater that the angle of spontaneous 18
liquefaction SLα . In other words, slopes with inclinations greater than SLα can suffer a runaway 19
instability even if an infinitesimal triggering perturbation is applied to the slope. This result 20
provides a theoretical basis consistent with Terzaghi’s notions of spontaneous liquefaction and 21
incipient instability. 22
These simplifications imply that slope instability can be fully defined by a single stability chart. 23
As a consequence, the calculation of charts similar to Figure 2-b requires a procedure for depth-24
averaged undrained shear properties. This is clearly an approximation for real granular materials 25
7
whose properties depend on stress level and density, and are not adequately described using 1
averaged parameters. 2
The following sections present a more refined modelling approach that tries to overcome these 3
limitations and describes more realistically triggering conditions for infinite slopes. The goal is to 4
provide a framework that can predict liquefaction susceptibility based on in situ and laboratory 5
data. 6
7
MODELLING APPROACH FOR FLOW SLIDE TRIGGERING 8
9
The modelling framework presented in this paper is based on the MIT-S1 constitutive model 10
[Pestana and Whittle 1999]. MIT-S1 is a model developed to predict the rate-independent 11
anisotropic behaviour for a broad range of soils (uncemented sands, clays and silts). The model 12
describes the stress-strain-strength properties of cohesionless sands that are deposited at different 13
initial formation densities as functions of both the stress state and current density (void ratio), 14
using a single set of model parameters, i.e. it accounts for both barotropic and pycnotropic effects. 15
Table I summarizes the model parameters which will be used hereafter. A complete description of 16
both model formulation and material parameters is available in Pestana and Whittle (1999). 17
The current analyses assume that flow slide triggering conditions in infinite slopes can be 18
evaluated by considering the stress-strain properties in an undrained simple shear mode of shearing 19
at a given depth. The initial stress state at the depth of interest is the outcome of complex 20
deposition processes which could be by themselves the subject of separate investigations (di Prisco 21
et al. 1995; Pestana and Whittle, 1995). For the sake of simplicity, the initial stress state can be 22
approximated by calculating 0ξσ ′ and 0ξητ based on equilibrium (as shown in Fig. 2-a) and 23
assuming 0 0 0Kη ξσ σ′ ′= . This assumption is adequate for low slope angles (Lade, 1993), and it will 24
be adopted hereafter, restricting the analyses to gentle slopes ( 15α ≤ ° ). The MIT-S1 model also 25
8
requires the definition of initial directions of material anisotropy. These are introduced through a 1
tensorial internal variable, b , that governs the orientation of the yield surface and evolves as a 2
result of mixed isotropic-kinematic hardening rules. The current analyses assume that the initial 3
stress state coincides with the tip of the yield surface (consistent with prior applications of the 4
model for K0-consolidation). 5
Fig. 3 illustrates MIT-S1 simulations of undrained simple shear response at the same level of 6
initial vertical effective stress but with different magnitudes of initial shear stresses τ 7
(representing different slope angles). The simulations have been performed using the model 8
calibration for a reference material (Toyoura sand; see Table I, after Pestana et al., 2002), with 9
vertical stress 0vσ ′ =150 kPa and e=0.93. The results show how the initial state of stress 10
significantly affects the magnitude of the shear perturbation required to induce instability ( 1τΔ vs 11
2τΔ ). The onset of a mechanical instability coincides with the peak in the shear stress, that is 12
readily apparent from the stress-strain response pictured in Fig. 3-b. Consistent predictions of this 13
circumstance can be obtained from the mathematical notion of controllability (Nova, 1994), 14
according to which any instability mode under mixed stress-strain control is associated with the 15
singularity of the constitutive matrix governing the incremental response. In particular, it can be 16
proved that for elastoplastic strain-hardening models controllability conditions can be evaluated 17
from a critical value of the hardening modulus, H (Klisinski et al., 1992; Buscarnera et al., 2011). 18
For undrained simple shear conditions the critical hardening modulus must be evaluated in 19
accordance with the kinematic constraints outlined in the previous section, and is given by: 20
21
LSS Cf gH H Gξη ξητ τ
∂ ∂= +
∂ ∂ (1) 22
23
9
where ξητ is the shear stress acting along the slope direction, G is the elastic shear modulus, f 1
the yield surface and g the plastic potential (di Prisco and Nova, 1994). The term CH in Eq. (1) is 2
the critical hardening modulus for pure strain control than can be expressed in matrix notation as: 3
4
Cf gH ∂ ∂
= −∂ ∂
eDσ σ
(2) 5
6
where eD is the elastic constitutive stiffness matrix and the tilde indicates a transposed vector 7
(Maier and Hueckel, 1979). 8
The assessment of stability conditions for infinite slopes is then straightforward, and can be 9
conducted by adapting to undrained simple shear conditions the procedure outlined by Buscarnera 10
and Whittle (2011). Starting from Eq. (1), a stability index for undrained simple shear loading can 11
be defined as: 12
13
LSS LSSH HΛ = − (3) 14 15
In particular, a stable incremental undrained response is predicted for a positive stability index 16
( 0)LSSΛ > , while a non positive value for LSSΛ marks the conditions necessary for incipient 17
instability. As a result, the initiation of static liquefaction is predicted when the stability index 18
given by Eq. (2) vanishes ( 0)LSSΛ = , as shown in Fig. 3-c. 19
If the same type of simulation is performed for a range of slope angles, it is possible to evaluate 20
the influence of the slope inclination on the susceptibility to liquefaction instability. Fig. 4 presents 21
further results showing the undrained stress paths at constant normal stress and variable in-situ 22
shear stress tanVτ σ α′= . These simulations are then used to define the triggering relationship 23
between τΔ and the slope angle α , with triggering shear stresses identified by using the condition 24
0LSSΛ = . The progressive approach towards a less stable condition with increasing slope angle is 25
10
reflected by the reduction in both the triggering shear perturbation and the stability index prior to 1
shearing (Fig. 4-b). 2
As is well known, the undrained behaviour of sands is significantly influenced by changes in the 3
effective stress and density (Ishihara, 1993). For example, even very loose sands can exhibit a 4
tendency to dilate at low effective stress levels, but will collapse for undrained shearing at high 5
levels of effective stress. Hence, the prediction of liquefaction potential requires a constitutive 6
framework that can simulate realistically the stress-strain properties as functions of stress level and 7
density. 8
Fig. 5 and 6 illustrate MIT-S1 predictions of the undrained simple shear behaviour for Toyoura 9
sand. The figures show how the stability index LSSΛ makes it possible to differentiate between 10
inception of liquefaction ( 0LSSΛ = and 0LSSΛ < ), quasi-steady state conditions ( 0LSSΛ = and 11
0LSSΛ > ) and critical state at large shear strains ( 0LSSΛ = and 0LSSΛ = ). In Fig. 5 the in situ pre-12
shear void ratio varies from 0.87 to 0.94, and the model predicts a sharp transition from a stable 13
behaviour (e0=0.87) to complete collapse (e0=0.94). In Fig. 6, post-peak instabilities in the stress-14
strain behaviour at Vcσ ′ =100 and 200 kPa are followed by metastable conditions and tendency to 15
dilate at large strains, as illustrated by typical laboratory measurements reported by others 16
(Shibuya, 1985). In the following, these two different types of undrained response will be referred 17
to as partial liquefaction and complete liquefaction, respectively. According to this terminology, 18
partial liquefaction indicates an undrained response in which the shear stress at large strains is 19
higher than the initial in situ shear stress 0τ , while complete liquefaction addresses an undrained 20
response in which the post-peak shear stress is lower than 0τ (no recovery of stability at large 21
shear strains). 22
The outcome of pycnotropic and barotropic effects on undrained sand response is that the 23
perturbation shear stress ratio ( ), / Vczτ α σ ′Δ associated with the initiation of liquefaction is not 24
only a function of the slope angle but must be evaluated at the effective stress and density states at 25
11
the depth of interest. Fig. 7 gives a qualitative example of the triggering conditions, based on 1
simulations with Toyoura sand as a reference material. In the first series (Fig. 7-a) the effect of 2
several possible initial densities has been considered, keeping constant the initial level of mean 3
effective stress. In contrast, in the second series (Fig- 7-b) considers different pressure levels at 4
constant void ratio. 5
Once stability charts expressing the shear resistance potential ( ), / Vczτ α σ ′Δ have been 6
obtained, it is possible to define the variation in the triggering perturbation along the profile of a 7
given infinite slope. The transition from liquefiable to non liquefiable response illustrated in Figs. 8
5-6 is crucial to identify the sand layers that are vulnerable to the propagation of an instability. To 9
achieve this type of prediction, the calibration of model parameters has to be related to the in situ 10
density profile for the specific problem at hand. These capabilities are illustrated through a case 11
study in the following section. 12
13
RE-ANALYSIS OF FLOW INSTABILITIES AT THE NERLERK BERM 14
15
The Nerlerk berm case history refers to an impressive series of slope failures that took place in 16
1983 during construction of an artificial island in the Canadian Beaufort Sea. These slope 17
instabilities occurred within a hydraulically placed sand (from a local borrow source). Details on 18
the construction methods, equipment and materials are given by Mitchell (1984). Based on 19
detailed studies of the slide morphology, Sladen et al. (1985-b) classified the slope instabilities as 20
flow slides. 21
The case of the Nerlerk berm failures represents one of the best documented examples of slope 22
failures in which static liquefaction is considered to have played a relevant role. The underlying 23
causes of the slides have attracted an intense scientific discussion, since the first attempts to back-24
analyse the phenomenon [Sladen et al., 1985-b; Been et al., 1987; Sladen et al. 1987]. Two main 25
lines of thought were developed. The first considered static liquefaction as the most plausible 26
12
cause of the flow failure, while the second focused on the role of a possible shear failure involving 1
the seabed soft clay. 2
Many authors tried to back-analyse Nerlerk slides using a variety of different methodologies, 3
including (i) limit equilibrium analyses to investigate the type of failure mechanism (Rogers et al., 4
1991), (ii) modified versions of the classical critical state framework for sands (Konrad, 1991), 5
(iii) the use of the notion of incipient instability (Lade 1993) and also (iv) non-linear finite element 6
analyses of the entire berm as a boundary value problem (Hicks and Boughrarou, 1998). Hicks and 7
Boughrarou (1998) present a detailed review of the previous works. 8
This paper uses the MIT-S1 model to investigate potential static liquefaction mechanisms in the 9
Nerlek berm. The proposed methodology is hereafter applied assuming that the local behaviour of 10
the sides of the berm can be studied through the scheme of infinite slope. Of course, this choice 11
represents an important simplification of the real geometry. However, it is an assumption that 12
enables an immediate evaluation of possible incipient instability within the fill and the type of 13
expected undrained response. Although this type of analysis is conceptually similar to earlier 14
studies based on the notion of incipient instability (Lade, 1993), the current approach relies on the 15
predictions of a constitutive model that are calibrated to site specific properties of the Nerlerk 16
sands. 17
18
Calibration of MIT-S1 for Nerlerk Sand 19
20
The calibration of the MIT-S1 model for the prediction of instabilities in the Nerlerk berm has 21
required a number of approximations. Although Nerlerk sand has been extensively studied through 22
laboratory tests, there are no published data regarding the 1-D compression behaviour. As a 23
consequence, some model parameters (Table I) have been selected making reference to another 24
Arctic region sand, Erksak. Erksak sand (Been and Jefferies, 1991; Jefferies, 1993) is a clean 25
quartzitic granular material (0.7 % fines content), having D50=330 mm and Cu=1.8. The Nerlerk 26
13
sand has similar mineralogy and particle size characteristics, with D50=280 mm and Cu=2.0, but 1
with in situ non plastic fines content that ranges from 2% to 15%. Laboratory studies on Nerlerk 2
sands (Sladen et al. 1985-a) have focused on the shear behaviour of specimens with fines contents 3
0%, 2% and 12%. Additional data on these sands, and a comparison of the grain size distributions 4
of Erksak sand and Nerlerk sands at different fines content are reported in Fig. 8. The following 5
paragraphs summarize the procedure used to calibrate MIT-S1 material parameters for Nerlerk 6
sand with 2% and 12% of fines contents (selected variables are listed in Table I). 7
Input parameters describing the compression behaviour ( cρ , /ref ap p′ and θ in Table I) are 8
obtained by fitting low pressure data for Erksak sand (from Jefferies and Been, 1993). This is 9
accomplished using the approximate approach proposed by Pestana and Whittle (1995). Fig. 9 10
shows the resulting compression behaviour and the Limiting Compression Curve (LCC) that 11
defines high pressure behaviour in the model. The same model parameters are used for Nerlerk 12
sand with 2% and 12% fines, with the exception of θ and /ref ap p′ , that have been estimated by 13
means of empirical correlations (Pestana and Whittle, 1995). 14
Fig. 10 reports the critical states (CSL) for Erksak sand and Nerlerk sands (2% and 12% fines 15
content). There is considerable judgment involved in the interpretation of the CSL data presented 16
by Sladen et al. (1985-a). The data are fitted using an analytical expression for the CSL that is 17
defined using three model input parameters ( mrφ , m and p ; Table I), as proposed by Pestana et al. 18
(2005). The results show significant differences in the CSL for all the sands and also in the 19
corresponding model input parameters (Table I). 20
Fig. 11 compares the computed and measured effective stress paths and shows stress-strain 21
behaviour for Nerlerk 2% in undrained triaxial compression shear tests. These data have been used 22
to define some of the remaining model parameters, notably sω and ψ (Table I). Fig. 12 confirms 23
that the selected parameters are able to describe reasonably also the drained shear behaviour. Fig. 24
13 shows similar comparisons of undrained behaviour for Nerlerk-12%. The model captures first 25
14
order features in the measured behaviour but underestimates the peak shear strength mobilized in 1
these tests. 2
3
In situ states and stability charts 4
5
In order to apply the MIT-S1 model for the Nerlerk berms it is necessary: a) to define the in situ 6
initial void ratios along the slope profile and b) to evaluate the stability charts of the Nerlerk berm 7
for several depths within the slope. 8
The first step is largely dependent on a reliable interpretation of the available in situ tests. 9
Several CPT tests were performed on the hydraulic fills at Nerlerk, with the aim of extimating the 10
in situ density. The interpretation of these CPT tests has always represented a matter of debate in 11
prior studies of the Nerlerk berm (e.g., Been et al., 1987; Sladen et al., 1987). 12
It is clear that the choice of a specific interpretation method for CPT test results will affect the 13
estimation of relative density (and, in turn, the model predictions). This uncertainty is probably 14
unavoidable in any method of interpretation. 15
The current analyses assume that relative density can be estimated using the empirical 16
correlation proposed by Baldi et al. (1982). Fig. 14-a shows that Dr ranges from 30 to 55 %. This 17
approach makes no distinction on the influence of fines content. Fig. 14-b shows the distribution of 18
these initial states relative to the CSL of Nerlerk-12%. 19
Fig. 15 shows the computed instability curves ( ), /z zτ α γ ′Δ at selected depths for infinite 20
slopes in Nerlerk sand with 12% fines content. The results show that the magnitude of the shear 21
perturbation needed to cause instability can be significantly affected by the specific depth within 22
the slope profile. 23
This result defines the initial stability state of the Nerlerk berm slopes in a proper mechanical 24
sense, providing a prediction of the critical geometry for incipient instability. The Nerlerk berm 25
was constructed at slope angles in the range α =10°-13° and, hence, required additional shear 26
15
stress to trigger flow failures. In other locations where steeper slopes were recorded, only very 1
small perturbations in shear stress could have triggered failure. 2
Fig. 16 shows the undrained effective stress paths predicted by MIT-S1 for the same depths 3
investigated in Fig. 15, and for a slope angle 13α = ° . These results show stable (i.e., potentially 4
dilative) behaviour at z =1 m, partial liquefaction at z =3 m, 8 m (i.e., large strain strength is 5
larger than the initial shear stress) and complete liquefaction at z =5 m, 10 m and 13 m. These 6
results provide predictions of the depths where flow slides are most likely to be triggered. In this 7
case, two different zones in the range z = 5 - 8 m or z ≥ 10 m are more susceptible to static 8
liquefaction. This result is consistent with what was reported on the basis of bathymetric surveys 9
by Sladen et al. (1985-b), which stated that “the depth of the failed mass varied between 5 and 12 10
m and the prefailure slope gradients were typically between 10°-12°”. 11
Fig. 17-a and 17-b illustrate the depth profile of the triggering shear stress for liquefaction based 12
on the stability curves presented in Fig. 15 for slopes having α =10° and 13°, respectively. The 13
results are compared with those that would be obtained for depth-averaged assessment (in this case 14
based on MIT-S1 simulation at z = 8 m and 0e = 0.73). This average could represent the optimal 15
calibration of a simpler model where the effects of confining pressure and density are not 16
considered. From the picture it is evident that such an averaging procedure can overestimate the 17
liquefaction resistance in some parts of the slope and is not able to distinguish important 18
differences in undrained shear behaviour that make the slope vulnerable to flow failure. 19
It is clear from Fig. 17 that an undrained perturbation of the shear stress was necessary to trigger 20
flow slides in the Nerlerk berm. A possible source for this stress perturbation could be associated 21
with the rapid deposition of sand at the top of the slope. Assuming uniform filling along the 22
infinite slope, the shear stress perturbation is given by 23
24
sinSAT hτ γ αΔ = Δ (4) 25 26
16
where hΔ is the thickness of the deposited sand layer and SATγ is its total unit weight (here assumed 1
to be equal to 19.4 kN/m3). 2
From the above equation and from the limit shear stress given by Fig. 17 it is possible to obtain 3
an estimate of the critical values of additional surcharge required to trigger liquefaction for rapid 4
filling. According to this analysis, failure for a slope with α =10° will be triggered for a rapid fill 5
with hΔ = 0.52 - 0.76 m, reducing to hΔ = 0.25 - 0.37 m at α =13°. 6
7
Discussion 8
9
The current analysis of the Nerlerk Berm slides has focused on the possible role played by static 10
liquefaction in the failure mechanism and on the conditions necessary to trigger instability. The 11
quantitative results are clearly related to the assumptions regarding the in situ density of the 12
hydraulic fill and the hypothesis that a rapid deposition during construction could have produced 13
undrained shear perturbations sufficient to trigger instability. While neither of these assumptions is 14
validated by this work, the main purpose is to verify the possible role of liquefaction instability in 15
the triggering of flow slides. Our results, obtained using a site specific calibration of the MIT-S1 16
model with established empirical correlations for relative density from CPT tests, show that static 17
liquefaction is likely to have played a relevant role in the failure mechanism. 18
This conclusion is consistent with earlier findings (Sladen et al. 1985-b; Lade 1993). The 19
current analysis provide a more detailed predictive framework that shows critical zones of flow 20
failure may have been located in the range in the range z =5÷8 m or z ≥ 10 m. 21
The Nerlerk berm slopes were likely not in an incipient unstable state, and an undrained 22
triggering perturbation was a necessary condition for a flow failure. A central point of possible 23
future investigation would therefore have to be focused on the likelihood of temporary undrained 24
conditions during construction. 25
17
Although many additional aspects could have been considered in this re-analysis of the Nerlerk 1
slides (e.g., the variability of the in situ density, the role of the fines content and its spatial 2
distribution, the rate of sand deposition, etc.), the present approach captures most of the first order 3
features affecting the liquefaction potential and is able to link in a fairly simple way model 4
predictions at material point level to the in situ response observed at the Nerlerk site. 5
6
CONCLUSIONS 7
8
This paper presents a framework for evaluating the triggering of flow slides in infinite slopes by 9
modelling the undrained shear behaviour using the anisotropic MIT-S1 model. Stability charts are 10
derived from simulations of undrained simple shear behaviour at a series of material points. 11
The current approach follows the same kinematic assumptions previously used by di Prisco et 12
al. (1995), but introduces predictive capabilities for simulating instability as a function of the in 13
situ stress and density within the slope. The selected soil model (MIT-S1 model), in fact, is able to 14
simulate realistic transitions in the contractive/dilative response of sands. 15
Thus, a more complete description of sand behaviour is a key issue in predicting not only the 16
shear perturbations able to induce instability, but also the location within the soil masses and the 17
potential for propagation of a flow failure (static liquefaction). In practice the model needs to be 18
calibrated for the site specific properties of the soil, and requires reliable data on in situ density in 19
order to make predictions of liquefaction potential. 20
The proposed methodology has been applied to the well known case of slope failures in the 21
Nerlerk berm. A general picture of the distribution of liquefaction susceptibility on the Nerlerk 22
slope profile has been obtained. The analysis are based on the calibration of model input 23
parameters based on published laboratory tests results and empirical correlations for Dr based on 24
CPT data. The results show that there are two zones within the slope that are vulnerable to flow 25
failure (complete liquefaction). Although some sections of the berm slope were oversteepened, 26
18
most were deposited with α =10°-13°. For these slope angles, the current analyses show that 1
instability can be triggered by rapid deposition of 0.2-0.5 m of hydraulic fill. Thus, static 2
liquefaction is likely to have contributed to the observed failures, confirming earlier hypothesis by 3
Sladen et al. (1985-b). 4
The current analysis offers a simple, consistent and complete mechanical framework for 5
interpreting and predicting the triggering of flow slides in sands that can be easily applied to other 6
similar engineering cases. 7
8
ACKNOWLEDGMENTS 9
The first author gratefully acknowledges the Rocca Fellowship program, that provided support 10
for his research studies at MIT. The authors are also grateful to Professor Roberto Nova for the 11
useful suggestions during the editing of the manuscript and to Professor Michael Hicks for his 12
assistance in providing laboratory data for the Nerlerk sands. 13
14
References 15
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[4] Been, K., Conlin, B. H., Crooks, J. H. A., Fitzpatrick, S. W., Jefferies, M. G., Rogers, B. T., Shinde, S. (1987). 21
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4, 211–224, 2006. 2
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submerged slopes, Géotechnique , 45, 479-496. 12
[14] Ellison, K.C., Andrade, J.E. (2009). Liquefaction mapping in finite-element simulations. J. Geotech. 13
Geoenviron. Eng. ASCE, Vol. 135, No. 11, 1693-1701. 14
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[16] Hight D.W., Georgiannou V.N., Martin P.L. and Mundegar A.K. (1999) “Flow Slides in Micaceous Sands”, 17
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Sendai, Japan, pp. 945- 958. 19
[17] Imposimato S, Nova R. (1998). An investigation on the uniqueness of the incremental response of elastoplastic 20
models for virgin sand, Mechanics of Cohesive-Frictional Materials, 3: 65-87. 21
[18] Ishihara, K. (1993). Liquefaction and flow failure during earthquakes. Géotechnique 43, No. 3, 351-415. 22
[19] Jefferies M.G.(1993). Nor-Sand: a simple critical state model for sand. Géotechnique 43, 91-103. 23
[20] Jefferies M.G., Been K. (1991). Implications for critical state theory from isotropic compression of sand. 24
Géotechnique 50:44, 419-429. 25
[21] Jefferies M.G. Been K. (2006). Soil Liquefaction: a critical state approach. Taylor and Francis Ed., New York. 26
[22] Klisinski M, Mroz Z, Runesson K. (1992). Structure of constitutive equations in plasticity for different choices 27
of state and control variables. International Journal of Plasticity, 3, 221-243. 28
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Can. Geotech. J. 28(4): 601–612. 30
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[24] Koppejan A.W., Wamelen B.M., Weinberg L.J.H (1948). Coastal flow slides in the Dutch province of Zeland. 1
Proc. II ICSMFE, Rotterdam, Holland, Vol. 5, 89-96. 2
[25] Lade P. (1992). Static Instability and Liquefaction of Loose Fine Sandy Slopes. Journal of Geotechnical 3
Engineering. Vol. 118, No. 1, pp. 51-71. 4
[26] Lade P. V. (1993). Initiation of static instability in the submarine Nerlerk berm. Can. Geotech. J. 30, 895-904. 5
[27] Maier, G., Hueckel, T., (1979). Non-associated and coupled flow-rules of elastoplasticity for rock-like 6
materials. Int. J. Rock. Mech. Min. Sci. 16, 77-92. 7
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Conf.,Ontario, pp. 141-146. 9
[29] Nova R. (1989). Liquefaction, stability, bifurcations of soil via strain-hardening plasticity. In E.Dembicki, 10
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Int. Works. Gdansk, Technical Univeristy of Gdansk, 117-132. 12
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programmes. J. Mech. Behavior Mater., 5, No. 2, 193–201. 14
[31] Pestana J.M., Whittle A.J. (1995). Compression model for cohessionless soils, Géotechnique, 45 (4), 611-631. 15
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Numer. Anal. Meth. Geomech., 23, 1215-1243. 17
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Sand behavior, Int. J. Numer. Anal. Meth. Geomech., 26, 1097-1121. 19
[34] Pestana, J.M., Nikolinakou, M.A., Whittle, A.J. (2005). Selection of material parameters for sands using the 20
MIT-S1 model, Proceedings of Geofrontiers 2005, ASCE, Austin, TX. 21
[35] Pestana, J.M., Biscontin, G., Nadim, F., Andersen, K. (2000). Modeling cyclic behaviour of lightly 22
overconsolidated clays in simple shear. Soil Dynamics and Earthquake Engineering; 19; 501-519. 23
[36] Pinheiro M., Wan, R.G. (2010). Finite element analysis of diffuse instability using an implicitly integrated 24
pressure-density dependent elastoplastic model. Finite Elements in Analysis and Design, 46, 487-495. 25
[37] Poulos, S.J. (1981). The steady state of deformation. Journal of the Geotechnical Engineering Division, ASCE. 26
107(GT5): 553-562. 27
[38] Poulos, S.J., Castro, G. and France, J. (1985). Liquefaction evaluation procedure. Journal of the Geotechnical 28
Engineering Division, ASCE. 111(6): 772-792. 29
[39] Puzrin, A.M., Germanovich,L.N., Kim, S. (2004). Catastrophic failure of submerged slopes in normally 30
consolidated sediments. Géotechnique, 54 (10), 631-643. 31
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[40] Rogers, B. T., Been, K., Hardy, M. D., Johnson, G. J. & Hachey, J. E. (1990). Re-analysis of Nerlerk B-67 1
berm failures. Proc. 43rd Can. Geotech. Conf., Quebec, pp. 227-237. 2
[41] Shibuya, S. (1985). Undrained behaviour of granular materials under principal stress rotation. PhD Thesis, 3
University of London, 320 pp. 4
[42] Sladen, J. A., D'Hollander, R. D. & Krahn, J. (1985-a). The liquefaction of sands, a collapse surface approach. 5
Can. Geotech. J. 22, 564-578. 6
[43] Sladen, J. A., D'Hollander, R. D., Krahn, J. & Mitchell D. E. (1985-b). Back analysis of the Nerlerk berm 7
Liquefaction slides. Can. Geotech. J. 22, 579-588. 8
[44] Sladen J. A., D'Hollander, R. D., Krahn, J., Mitchell, D. E. (1987). Back analysis of the Nerlerk berm 9
liquefaction slides: Reply. Can. Geotech. J. 24, 179-185. 10
[45] Terzaghi K. (1957). Varieties of submarine slope failures. NGI Publication N. 25, 1-16. 11
[46] Yoshimine, M., Robertson, P. K., (Fear) Wride, C.E. (1999). Undrained shear strength of clean sands to trigger 12
flow liquefaction, Can. Geotech. J. 36(5): 891–906. 13
22
t = (s
' 1 - s'
3)/2
s' = (s'1 + s'
3)/2
Collapse Surface
Typical UndrainedStress Path
Steady StatePoint
PeakShear Stress
tSS
s'SS
aSS
aL
Soil StructureCollapse
p' = (σ'
1 + 2σ'
3)/3
Failure Line
Instability Line
Effective Stress Path
Yield Surface
Top of Yield Surface
Top of Effective Stress Path
q =
s'1 -
s'3
Fig. 1. a) Collapse Surface concept [redrawn after Sladen et al. 1985-a] ;
b) Instability Line concept [redrawn after Lade 1992].
23
0
0.05
0.1
0.15
0.2
0 5 10 15 20 25
Nor
mal
ized
Trig
gerin
g P
ertu
rbat
ion,
(tpe
ak-t
0)/s' x=D
t/s'
x
Slope Inclination, α [°]
Angle of spontaneous liquefaction a
SL
z=16m
z=0.4m
Figure 2. a) Reference system for a submerged infinite slope and initial stress conditions; b) Dependency of the triggering perturbation Δτ on the slope angle (results obtained with an elastoplastic soil model calibrated for loose Hostun sand; redrawn after di Prisco et al. (1995)).
24
Table I. Summary of MIT-S1 model parameters.
25
0
20
40
60
0 20 40 60 80 100 120 140She
ar S
tress
, t [k
Pa]
Vertical Effective Stress, σ'v [kPa]
τ0 = σ'
Vtanα
Δτ2
Δτ1
0°
10°α =
MIT-S1: Toyoura Sande
0 = 0.93; K
0 = 0.49
0 5 10
Shear Strain, γ (%)
Initiation of liquefaction
-1
0
1
2
3
4
5
0 1 2 3 4 5
Shear Strain, γ (%)
Sta
bilit
y in
dex,
LLS
S
Initiation of liquefaction:vanishing of L
LSS
10°α =
0°
Figure 3. Example of simple shear simulations (loose Toyoura Sand):
a) stress path in the σ’V-τ plane; b) stress strain behaviour; c) evolution of the stability index ΛLSS during the two simulations
26
0
20
40
60
0 20 40 60 80 100 120 140 160She
ar S
tress
, τ [k
Pa]
Vertical Effective Stress, σ'v [kPa]
10°
α
5°
0°
15°
MIT-S1: Toyoura Sande
0 = 0.93; K
0 = 0.49
0.00
0.05
0.10
0.15
0.20
0.25
0
5
10
15
20
25
30
0 5 10 15
Shear triggering perturbation
In situ Stability Index
In Situ Stability index, L
LSS
She
ar S
tress
Incr
emen
t, Dt/
s'V
0
Reduction in margin of safety for incipient liquefaction
Slope Inclination, α [°] Figure 4. Effect of the slope angle: a) Stress path; b) Stability chart for an infinite slope made of loose Toyoura Sand
and stability index ΛLSS prior to undrained shearing as a function of the slope angle.
27
0
20
40
60
80
100
0 50 100 150 200
0.87
e0= 0.91
0.94
She
ar S
tress
, t [k
Pa]
Vertical Effective Stress, σ'v [kPa]
MIT-S1: Toyoura Sandσ'
v0= 150kPa; K
0 = 0.49
0 2 4 6 8 10
0.87
e0= 0.91
0.94
Shear Strain, γ (%)
Inception of instability
(LLSS
=0;LLSS
<0)Quasi steady state
(LLSS
=0;LLSS
>0)
Ultimate steady state (L
LSS=0;L
LSS=0)
Figure 5. MIT-S1 predictions: effect of void ratio on undrained simple shear response of Toyoura Sand.
a) stress path in the σ’V-τ plane; b) stress-strain behaviour.
28
0
20
40
60
80
100
0 50 100 150 200 250 300 350
MIT-S1: Toyoura Sande
0 = 0.92; K
0 = 0.49
Vertical Effective Stress, σ'v [kPa]
She
ar S
tress
, t [k
Pa]
Figure 6. MIT-S1 predictions: effect of mean effective pressure on simple shear response of Toyoura Sand. a) stress path in the σ’V-τ plane; stress-strain behaviour.
0 5 10 15 20Shear Strain, γ (%)
Ultimate steady state (L
LSS=0;L
LSS=0)
Inception of instability (L
LSS=0;L
LSS<0)
Quasi steady state (L
LSS=0;L
LSS>0)
29
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 5 10 15
MIT-S1: Toyoura Sandσ'
v0= 150kPa; K
0 = 0.49
e0= 0.90
e0= 0.93
e0= 0.95
e0= 0.98
Slope Inclination, α [°]
Per
turb
atio
n Sh
ear S
tress
Rat
io, D
t/s'
V0
0 5 10 15
MIT-S1: Toyoura Sande
0 = 0.93; K
0 = 0.4915 kPas'
v0=
75 kPas'v0
=
150 kPas'v0
=
300 kPas'v0
=
Slope Inclination, α [°]
Figure 7. a) Effect of void ratio on stability charts for a given vertical effective stress; b) Effect of vertical effective stress on stability charts for a given void ratio.
30
0
20
40
60
80
100
0.1 1 10
Erksak SandNerlerk Sand -0%Nerlerk Sand -2%Nerlerk Sand -12%
Per
cent
age
finer
, [%
]
Grain Size Diameter, d [mm]
Angularity(emax
; emin
)Sand
Sub-rounded(0.808;0.614)ErksakSub-angular(0.890;0.660)Nerlerk-0%
-(0.940;0.620)Nerlerk-2%-(0.960;0.430)Nerlerk-12%
Figure 8. Grain size distribution curves for Erksak Sand and Nerlerk Sand at different fines percentages.
31
Erksak Sand(Jefferies & Been , 1991)
Linee0
0.840.700.650.60
MIT-S1ρ
c = 0.44, p'
ref/p
a = 40, θ = 0.3
0.4
0.5
0.6
0.7
0.8
0.9
10 100 1000 104
Voi
d R
atio
, e
Mean Effective Stress, p' [kPa]
LCC
Figure 9. Simulation of Erksak sand compression behaviour: definition of the LCC curve.
32
10 100 1000 1040.4
0.5
0.6
0.7
0.8
0.9
Mean Effective Stress, p' [kPa]
Interpreted CSL DataSladen et al., (1985)
Jefferies & Been (1991)Erksak
Nerlerk 2% FinesNerlerk 12% Fines
pmφ'mrMIT-S1 Model
2.70.4921Erksak2.30.4225°Nerlerk-2%2.60.2121°Nerlerk-12%
Nerlerk LCC
Erksak LCC
Void
Rat
io, e
Figure 10. Comparison of CSL and LCC curves for Erksak sand and Nerlerk sand with 2% of fines
33
0
100
200
300
400
500
600
0 200 400 600 800 1000
(e=0.804; p'0=900 kPa)
(e=0.792; p'0=750 kPa)
Mean Effective Stress, p' [kPa]
Dev
iato
r Stre
ss, q
[kP
a]
0 5 10 15 20 25 30
(e=0.792; p'0=750 kPa)
(e=0.804; p'0=900 kPa)
MIT-S1Experimental Data
(after Jefferies and Been, 2008)
Axial Strain, e1 (%)
Figure 11. Calibration of undrained behaviour of Nerlerk Sand 2%: a) undrained stress paths; b) stress-strain response
34
0
500
1000
1500
(e0=0.714; p'
0=200 kPa)
(e0=0.758; p'
0=50 kPa)
(e0=0.639; p'
0=500 kPa)
(e0=0.578; p'
0=200 kPa)
Dev
iato
r Stre
ss, q
[kP
a]
MIT-S1Experimental Data
(after Jefferies and Been, 2008)
-10
-5
0
50 5 10 15 20 25
(e0=0.714; p'
0=200 kPa)
(e0=0.758; p'
0=50 kPa)
(e0=0.639; p'
0=500 kPa)
(e0=0.578; p'
0=200 kPa)
Axial Strain, e1 (%)
Vol
umet
ric S
train
, eV (%
)
Figure 12. Calibration of the drained behaviour for Nerlerk Sand 2%: a) stress strain response; b) volumetric response
35
0
100
200
300
400
500
600
700
0 200 400 600 800 1000
(e=0.745; p'0=200 kPa)
(e=0.734; p'0=300 kPa)
(e=0.638; p'0=900 kPa)
Mean Effective Stress, p' [kPa]
Dev
iato
r Stre
ss, q
[kP
a]
0 5 10 15 20 25 30
(e=0.745; p'0=200 kPa)
(e=0.734; p'0=300 kPa)
(e=0.638; p'0=900 kPa)
MIT-S1Experimental Data
(after Jefferies and Been, 2008)
Axial Strain, e1 (%)
Figure 13. Comparison of computed and measured undrained shear behaviour for Nerlerk Sand 12%.
36
0
2
4
6
8
10
12
14
160 10 20 30 40 50 60
Dr from Baldi et al. (1982)
Depth Averaged Dr
Vrti
cal D
epth
, z [m
]
Relative Density, Dr [%]
Dr [%]z [m]
44.8343.75548.9845.581033.51333.8215
0.5
0.55
0.6
0.65
0.7
0.75
0.8
1 10 100 1000
In Situ State
CSL data
MIT-S1 CSL
Void
Rat
io, e
Mean Effective Stress, p' [kPa]
MIT-S1 CSLCSL Data
(after Sladen et al., 1985-b)Initial State within the Nerlerk slopes
(after Sladen et al., 1985-b)
Figure 14. a) In situ relative density from CPT tests (Baldi et al. 1982); b) Location of in situ state on the CSL plane.
37
0
0.05
0.1
0.15
0.2
0 5 10 15
z=3.0m
z=8.0m
z=13.0m and z=15.0m
z=5.0mz=10.0m
Slope Inclination, α [°]
Partial LiquefctionComplete Liquefaction
MIT-S1 - Nerlerk 12%
Per
turb
atio
n S
hear
Stre
ss R
atio
, Dt/
g'z
γ'z - vertical overburden pressure
Figure 15. Stability charts for the Nerlerk berm.
38
0
2
4
6
8
10
0 5 10 15 20
z=1m
Normal Effective Stress, σ'x [kPa]
MIT-S1Nerlerk 12%
a
s'x
txh
05
101520253035
0 20 40 60 80
z=3m
z=8m
Normal Effective Stress, σ'x [kPa]
05
101520253035
0 20 40 60 80 100 120
z=5mz=10m
z=13m
Normal Effective Stress, σ'x [kPa]
Figure 16. Example of undrained responses along the Nerlerk berm section (α=13°);
a) No Liquefaction: b) Partial Liquefaction; c) Complete Liquefaction.
She
ar S
tress
, txh
[kP
a]
39
Real Density ProfileDepth Averaged Density
Ver
tical
Dep
th, z
[m]
Triggering Shear Stress, Dt [kPa]
0
2
4
6
8
10
12
14
160 1 2 3 4 5 6 7
α= 10°
Real Density ProfileDepth Averaged Density
Triggering Shear Stress, Dt [kPa]0 1 2 3 4 5
α= 13°
Figure 17. Variation with depth of undrained shear perturbation triggering liquefaction: a) Slope angle α=10°; b) Slope
angle α=13° (NL stands for non liquefiable, PL for partial liquefaction and FL for full liquefaction).
