Chapter 5:
Liquefaction of Saturated Granular Materials
This chapter is devoted to the investigation of liquefaction phenomena, which usually appear in saturated granular materials after dynamic excitation. This includes definitions and descriptions of liquefaction mechanisms, factors affecting saturated soil behaviour and an in-situ example of seismic-induced liquefaction. Moreover, the elasto-viscoplastic constitutive model, as introduced in Section 3.2, is used to capture the basic features of liquefaction events, such as the pore-fluid pressure accumulation and softening of the granular structure.
σ0 σ0 σ0
τ
τ τ
γ1
γ2 γ0
1 initial state
2 contraction εVS <0
3 dilation εVS >0
τ
εVS
γ γ γ1
γ1
γ2
γ2 γ0
γ0
critical state
dense dense
loose loose
phase
transformation
Figure 5.1: Contraction and dilation due reordering of the grains in a shear test of cohe-sionless dry sand (left) and a schematic illustration of the shear stress τ versus the shear strainγ and the volumetric strainεVS versusγ of a sand in a dense and a loose state (right) Concerning the undrained behaviour of granular materials, it is assumed in the undrained experiments that the samples are 100% saturated with a materially incompressible fluid and no drainage occurs. Consequently, the volumetric strains almost vanish and become no longer interesting outputs, and instead, the focus is laid on the pore-pressure devel-opment. Herein, an increase in the pore pressure is expected if the soil behaviour is contractive, whereas a decrease in the pore pressure occurs for dilative soil behaviour.
In order to explain the influence of the initial density (or the initial void ratio) and the initial mean effective stress (after consolidation) on the behaviour of saturated porous media in a schematic way, Figure 5.2 shows the variation of the mean effective stress p′ (p′ := −13Iσ) and the void ratio e (e(nF) := nF/(1−nF)) in drained and undrained triaxial compression tests (cf. Manzari & Dafalias [122]). In this case, the shear stress (called ‘deviatoric stress’) is applied by varying the principal stresses of the triaxial cell.
CSL λ
a
ad ac
b
bc 1
2 e (nF)
lnp′= ln(−13Iσ) loose,
contractive
dense, delative
perfectly drained
CSL λ
ad a
ac bc b
1 2 e (nF)
lnp′= ln(−13Iσ) loose
dense
perfectly undrained
Figure 5.2: A schematic illustration of sand behaviour in drained (right) and undrained (left) triaxial tests with dense and loose initial densities
5.1 Preface and Definitions 89
Within the framework of the Critical State Soil Mechanics (CSSM), the critical state line (CSL) with slope λ defines the state at which the deformations continue for almost fixed shear stress and zero volumetric strain rate. At the CSL, the void ratio of the drained test reaches a critical value (ec), which meets in the undrained test a critical mean effective stress (p′c) .
In Figure 5.2, one distinguishes between two cases of material density:
(1) A dense material with an initial density higher than a critical value (point a). In the drained case under deviatoric stress (Figure 5.2, left), the specimen initially tends to contract with decreasing void ratio until reaching the state ad (path 1). Thereafter, the behaviour switches to dilation with increasing void ratio (path2). Under undrained conditions (Figure 5.2, right), the contractive tendency leads to an increase in the pore pressure and a reduction in the effective stress (path 1 ). Thereafter, the behaviour changes and the dilative trend causes an increase of the mean effective stress until the state reaches a point ac with p′ =p′c (path2), where a critical collapse takes place.
(2) A loose granular material has an initial density less than a critical value, cf. Figure 5.2, point b. Here, the expected drained behaviour under shear stress is contraction, which leads to an increase in the pore pressure under undrained conditions. In this case, the collapse might occur when reaching the state bc, or alternatively, a further increase in p′ leads to cross the CSL to a bounding limit and then the state turns back to bc to fail, cf.
Manzari & Dafalias [122] for more details.
For the treatment of liquefaction mechanisms in this monograph, some basic concepts of soil mechanics are recalled. Here, the effective stress relations (3.18)1,2 and the overall volume balance (3.45)4, which results in the macroscopic filter law can be rewritten as
TS + TF = TSE − pI, nFwF = − kF
γF R gradp + kF g
hb−(vF)′Si
. (5.1)
Herein, (5.1)1 shows that the total applied stress to a saturated porous medium is carried by the solid skeleton via the effective solid stress TSE and the pore fluid via the pore-fluid pressure p. In the absence of sudden loading (as under quasi-static loads), each grain of the soil particles assemblage is found in a contact with a number of neighbouring particles, which allows for the solid skeleton to carry most of the applied external total stress (TS ≈TSE and p≈0), cf. Figure 5.3, left.
low p highp
dynamic load static load
Figure 5.3: Saturated granular assemblage under static and dynamic loadings
Under rapidly applied loading, the pore pressure suddenly increases leading to a collapse in the loose, saturated granular structure, and consequently, solid particles try to move
into a denser configuration, cf. Figure 5.3, right. Thereafter, the excess pore-fluid pressure tends to dissipate, which causes an adverse motion of the solid and the pore fluid phases.
This process is governed by relation (5.1)2 between the seepage velocitywF and the pore-pressure gradient, where the permeability kF in m/s plays a major role in the rapidity of the excess pore-pressure dissipation. If the pore fluid is trapped in the solid matrix, the applied external stress is mostly carried by the pore fluid leading to a poor contact between the solid grains and causes a softening of the granular deposit.
In the following, a number of liquefaction-related definitions and terminologies are given, which are based on pioneering publications in the fields of soil modelling and earthquake engineering, such as the works by Kramer & Elgamal [109], Castro [34], Ishihara [97], Ishihara et al. [98], Verdugo & Ishihara [170] and Zienkiewicz et al. [186].
General definitions of saturated soil liquefaction
1. Liquefaction: A general term used to describe the behaviour of saturated soils, which is characterised by a build-up of the pore pressure and a softening of the granular structure. This comprises a number of physical phenomena such as the ‘flow liquefaction’ and the ‘cyclic mobility’.
2. Flow liquefaction: An instability phenomenon that frequently happens in loose soils with low shear strength. Under undrained conditions, the applied load results in an increase of the pore pressure and an incredible reduction of the effective stress until the residual shear strength cannot sustain the static equilibrium. Consequently, saturated soil looses its nature as a solid and flows like a viscous fluid.
3. Cyclic mobility: A kind of permanent but limited plastic deformation of saturated soil under cyclic shear loading. Therein, an accumulation of the pore pressure takes place after each applied cycle, however, the mean effective stress can never reach a zero value, and the residual shear strength can always maintain the static equilibrium.
4. Phase transformation: A threshold character of liquefiable sands. Here, sand initially shows contractive behaviour, but then exhibits dilation after crossing the phase transformation line.
5. Steady state strength: A critical state character of sands, which refers to the shear strength at which the shear strain increases continuously under constant shear stress and constant effective confining pressure at constant volume.
(5.2)
Remark: Another related phenomenon, known as ‘dry liquefaction’, is introduced in the literature, see, e. g., Kolymbas [107] and Miraet al.[132]. This usually occurs in dry soils of very low density, such as in uncompacted, volcanic fly ashes. In case of sudden loading, the pore air and the soil skeleton coupling plays a paramount role in the stability, where in worst cases, the frictional angle cannot sustain the stability and a collapse might happen.
5.1 Preface and Definitions 91
5.1.1 Earthquake-Induced Field Liquefaction
For a better understanding of the conditions that lead to a seismic-induced saturated soil collapse, an in-situ liquefaction example of saturated silty sand is given in the following, where more details can be found in the works by Zeghal & Elgamal [184] or Kramer &
Elgamal [109]. Here, the liquefaction-prone Wildlife Refuge area of the Imperial Valley in southern California has been instrumented by the U. S. Geological Survey with the necessary equipments to measure different soil properties during an earthquake. The ultimate aim of this investigation was to analyse the relations among the ground motion, the pore-pressure accumulation and the soil shear strength change.
Figure 5.4, left, shows a cross section in the Wildlife Refuge site, which consists of a clayey silt surface layer (≈ 2.7 m, very low permeability), a liquefiable silty sand (≈ 3.3 m) and a layer of stiff clay (≈ 5.0 m).
0.0 m 1.5 m 2.7 m
6.0 m
12.0 m
silt- clayey silt
silty sand
stiff clay
silt
accelerometer
B
Figure 5.4: Wildlife Refuge site layers (left) and the measured surface acceleration together with the excess pore pressure at pointB (right), cf. Zeghal & Elgamal [184]
The ground surface acceleration during Superstition Hills (SH)1 earthquake is plotted in Figure 5.4, right-top. As an index for the initiation of the in-situ liquefaction under seismic shear loading, the excess pore-pressure ratio |ru|or simply ru, which is defined as the ratio of the excess pore pressure to the initial effective vertical stress, is used. The value |ru| = 1 is considered as a threshold referring to a decrease of the effective stress until zero value and an increase of the pore pressure until the whole vertical load is carried by the pore fluid upon collapse (cf. Wu et al. [181] and Tsuji et al. [167]). Figure 5.4, right-bottom, shows the sharp generation of the pore pressure at point B (2.9 m below the ground surface) until the flow liquefaction takes place when ru attains the value 1.0.
1Took place on November 24, 1987, with Richter magnitude M = 6.6 .
In Figure 5.4, right, four stages of seismic response are observed: In stage (1) with t ∈ [0−13.7 s], both the ground acceleration and the pore-pressure build-up are low. Stage (2) with t ∈[13.7−20.6 s] coincides with the strongest shocks and the rapid increase of the pore pressure, where ru reaches the value 0.5 . In stage (3) with t ∈ [20.6−40 s], lower peak accelerations but rapid increase of the pore pressure can be observed, which indicates a continuous contraction tendency. This behaviour is related to the loose nature of the silty sand layer as will be discussed in details in the following section. In stage (4), ru attains the value 1.0 , which corresponds to a flow liquefaction state. Herein, due to the incredible reduction of the effective stress, the saturated sand layer looses its nature as a solid material and flows like a viscous fluid.