Ferrari, A. et al. (2013). Ge
´
otechnique 63, No. 16, 1433–1446 [http://dx.doi.org/10.1680/geot.13.P.041]
1433
Hydromechanical behaviour of a volcanic ash
A. FERRARI
, J. EICHENBERGER
and L. LALOUI
This paper presents experimental analysis and numerical modelling aimed at improved understanding
and prediction of the hydromechanical behaviour of volcanic ash at various states of saturation.
Results from a comprehensive experimental programme are presented in order to characterise the
response of the material in terms of matric suction and confining stress changes. The evolution of the
yield stress at different suction levels has been quantified. The volumetric response with suction
variations allowed the analysis of the collapse-upon-wetting behaviour. Water retention and permeabil-
ity are also addressed. Tests results are used to calibrate a constitutive model based on the effective
stress concept extended to partially saturated conditions. The ability of the model to reproduce and
anticipate the ash behaviour is tested with an articulated stress path.
KEYWORDS: collapsed settlement; constitutive relations; laboratory tests; partial saturation; suction
INTRODUCTION
Volcanic ash soils cover approximately 0
.
84% of the world’s
land surface (Leamy, 1984). Air-fall and colluvial deposits
have variable thicknesses between 0
.
5 m and 7 m, depending
on the slope angle, and up to 50 m in morphological
concavities and slope toes (Bilotta et al., 2005). Landslides
in steep pyroclastic deposits induced by intense rainfall
events have been observed around the world. These have
caused severe destruction and loss of life. Examples are the
Sarno landslide in Italy in 1998 (e.g. Crosta & Dal Negro,
2003; Cascini et al., 2008) and the thousands of landslides in
1998 caused by Hurricane Mitch throughout much of Central
America, with more than 9000 casualties (USAID, 1998).
The failure of volcanic deposit soil masses is often
reported to turn into rapid flow slides or debris flows, with
catastrophic consequences in the run-out zones (Picarelli et
al., 2008). The physical mechanisms leading to sudden
acceleration and the transition to flow-type behaviour, parti-
cularly in volcanic ashes, are still not fully understood.
Several possible causes are detailed in the literature and
summarised by Cascini et al. (2010), who cite as possible
causes the volumetric collapse of loose unsaturated soils,
static liquefaction in loose saturated soils, or local failures
caused by transient, localised pore water pressures due to
particular hydraulic boundary conditions and stratigraphic
settings. In the beginning, the soils involved are mostly in a
state of partial saturation, and they eventually saturate before
failure or later in the failure stage, depending on the
material properties and the morphological aspects of the
slope. Any such changes in the degree of saturation are
assumed to have a fundamental impact on the behaviour of
volcanic ashes.
Recent studies have provided data for the seasonal suction
measurements found in natural deposits of pyroclastic soils
(e.g. Damiano et al., 2012), and criteria for early warning
systems in volcanic ash slopes have recently been proposed
by Eichenberger et al. (2013). However, systematic experi-
mental programmes for the analysis of the geomechanical
behaviour of volcanic ashes under partially saturated condi-
tions are limited. Ng & Chiu (2001) reported experiments
for a compacted, unsaturated volcanic soil, and Sorbino &
Foresta (2002) analysed the hydraulic characteristics of
pyroclastic soils. Olivares & Picarelli (2003) and Olivares &
Damiano (2007) performed undrained triaxial tests and
triaxial wetting tests to demonstrate the liquefaction potential
of saturated volcanic ash, and the occurrence of undrained
conditions at failure upon reaching a fully saturated state.
The shear strength of undisturbed and remoulded volcanic
ash in variably saturated states was investigated by Bilotta et
al. (2005) using conventional direct shear tests with volcanic
ash specimens at different levels of matric suction. Addition-
ally, suction-controlled tests were carried out on undisturbed
pyroclastic soils to highlight the effects of suction on the
stiffness and the volumetric behaviour (Bilotta et al., 2006).
This paper presents the results from an experimental and
numerical investigation aimed at analysing and predicting
the geomechanical behaviour of a volcanic ash at various
saturation states. The experimental programme was designed
and carried out in order to collect evidence on the volu-
metric behaviour of the ash when subjected to changes in
matric suction and vertical stress. The fabric of the material
is first presented, and the technique for specimen preparation
is discussed. The initial suction and water retention curves
are then reported, and their dependence on the material
porosity is analysed. The observation that the permeability is
a function of the void ratio and degree of saturation is then
discussed. Controlled-suction oedometric tests are presented
in order to analyse the evolution of the preconsolidation
pressure and the soil stiffness with suction, and to assess the
position of the loading collapse yield limit.
For predicting the behaviour of the ash, the volume
change response is interpreted in the light of a constitutive
model for unsaturated soils. The constitutive model is pre-
sented prior to discussing the numerical simulations that
were performed. The ability of the model to reproduce and
anticipate the volcanic ash behaviour is tested by calibrating
the model with some of the experimental results and validat-
ing it with an articulated stress path.
CHARACTERISATION OF THE TESTED SOIL
Tested material and specimen preparation
The laboratory programme was carried out on a volcanic
ash obtained from the sides of the Irazu
´
Volcano in Costa
Manuscript received 16 March 2013; revised manuscript accepted 23
July 2013. Published online ahead of print 19 September 2013.
Discussion on this paper closes on 1 May 2014, for further details
see p. ii.
Laboratory for Soil Mechanics, School of Architecture, Civil and
Environmental Engineering, Ecole Polytechnique Fe´de´rale de Lau-
sanne, Lausanne, Switzerland.
Rica. The material was sampled using Shelby tubes to a
depth of about 1
.
5 m. The tested soil has a liquid limit
w
l
¼ 0
.
26 and a plastic limit w
p
¼ 0
.
20. The natural water
content for the collected samples was in the range 0
.
22–
0
.
24. The hygroscopic water content is 0
.
02 at the relative
humidity and temperature of the laboratory (approximately
40% at 228C). The specific gravity is G
s
¼ 2
.
61, and the dry
unit weight is in the range 9
.
2–10
.
2 kN/m
3
: The grain-size
distribution presents a sand-size fraction of 48% and a silt-
size fraction of 50%. The soil is classified as a clayey-silty
sand. In order to reproduce the average characteristics of the
delivered samples, specimens for the hydromechanical tests
(controlled-suction oedometric tests and triaxial tests) were
prepared by moist-tamping at a water content of 0
.
24 and at
a dry unit weight of 9
.
9 kN/m
3
(average initial void ratio of
1
.
58).
Description of the fabric
Figure 1(a) is an SEM image of an ash aggregate obtained
from an undisturbed sample of the tested ash. The picture
shows the typical fabric features of a collapsible soil, with
grain–grain contacts encased with silt and clay particles
(Collins & McGown, 1974).
Mercury intrusion porosimetry (MIP) was used to measure
the pore size density (PSD) function of a natural sample of
the volcanic ash, and of two specimens prepared at the
target dry unit weight (9
.
9 kN/m
3
). Specimens were trimmed
and air-dried to remove the pore water. The analysis of the
volumetric response upon drying of the statically compacted
ash specimens showed that limited volume reductions were
induced by drying (see below, under ‘Controlled suction
tests’). Therefore it could be assumed that the air-drying
procedure did not induce significant changes in the soil
structure. The MIP tests were performed in a Thermo
Electron Corporations porosimeter, and attained a maximum
intrusion pressure of 400 MPa, which corresponds to an
entrance pore size dimension of about 2 nm. The pressure
was applied continuously, and the intrusion data (pressure
and volume) were automatically recorded. To reach equili-
brium, an appropriate pressure build-up rate and a long
equalisation period were selected. The apparent pore sizes
were determined by applying corrections for the compressi-
bility changes of the various components of the equipment.
Fig. 1(b) depicts the measured pore size density functions of
the three specimens tested. The PSD is obtained according
to the expression PSD ¼[˜e
Hg
/˜(log r)], where r is the
entrance pore radius and e
Hg
represents the void ratio
intruded at each increment of mercury pressure. The three
specimens showed very similar PSDs, with dominant pore
radii in the range 10–50 m, which corresponds sufficiently
well to the intergrain pores observed in Fig. 1(a). The small
differences in the PSD could be explained by considering
that the exact dry density is not known for the natural
specimen. The similarity of the PSD functions demonstrated
that the moist-tamping technique used to prepare the speci-
mens resulted in a soil fabric similar to that of the natural
material.
Initial suction and water retention curve
The initial matric suction was measured using contact
filter paper. Leong et al. (2002) pointed out several factors
affecting the method, and discussed existing calibration
curves. In this study, an ad hoc calibration curve was
determined on initially oven-dried Schleicher and Schuell
No. 589 filter paper, in order to use the method for the
measurement of low matric suction values. The initial oven-
dried condition ensured that there was an adequate transfer
of water from the specimen to the paper during the measure-
ment. The calibration was carried out by applying matric
suction (s) to the filter paper, in the range 20–100 kPa, by
means of the axis-translation technique in a specially de-
signed set-up. An equalisation time of 2 weeks was selected
for both the calibration and the measurements. Fig. 2(a)
shows the results of the calibration. The initial suction of
the volcanic ash was measured on several specimens pre-
pared at different water contents (in the range 0
.
18–0
.
25)
and dry unit weights (8
.
0, 9
.
8 and 11
.
4 kN/m
3
), and these
results are shown in Fig. 2(b). The plot allows an assessment
of the initial suction in the range 20–45 kPa for the natural
water content of the samples in their ‘as delivered’ condi-
tion. It is worth noticing that, in the suction ranges consid-
ered, the dry unit weight has a marginal effect on the
relationship between suction and water content.
Water retention curves were obtained using a controlled-
suction pressure plate apparatus, employing the axis-
translation technique at zero vertical stress. This method is
associated with the matric suction component, in which the
soil water potential is controlled predominantly by liquid
phase transfer through an interface that is permeable to
dissolved salts. The procedure involves translation of the
reference air pressure by inducing an artificial increase in
1·6
1·2
0·8
0·4
0
Pore size density function
Prepared
Prepared
Natural
0·001 0·01 0·1 1 10 100 1000 10 000
Pore radius: m
(b)
μ
80 mμ
(a)
Fig. 1. Microstructural features of the tested volcanic ash: (a) SEM
image of a natural ash aggregate; (b) results of MIP tests on natural
and compacted specimens
1434 FERRARI, EICHENBERGER AND LALOUI
the atmospheric pressure in the apparatus. Water pressure
was kept constant, and supplied through a pressure/volume
controller by means of a high-air-entry value ceramic disc
(bubbling pressure 0
.
5 MPa). The air pressure was applied in
steps, and adjusted in order to impose suction values in the
range 0–180 kPa. The specimens were prepared at different
initial void ratios in confining rings (35 mm in diameter and
4 mm high), and subsequently saturated. In a preliminary
testing phase, the specimens were periodically weighed to
assess the time required for a complete equalisation at the
imposed suction; this was found to be 3 days. At the end of
each suction step, the specimens were weighed and their
volume measured. Solid weights were measured at the end
of the test, and the water content and degree of saturation
were back-calculated for each specimen. There was limited
volumetric deformation during complete drying paths; in
experiments on volcanic ash from the Vesuvian area, Sorbino
& Foresta (2002) observed similar behaviour during suction
increments at low vertical stresses. The experimental results
obtained for the suction and degree of saturation at three
different values of the void ratio are depicted in Fig. 3. The
experimental data obtained on the main drying and wetting
paths are represented. The point corresponding to the hygro-
scopic water content is also represented (suction 80 MPa).
It was observed that there was no significant dependence of
the retention properties on the void ratio in the range
considered. Also, there was no indication of any significant
hysteretic effects during wetting and drying. The experimen-
tal points were fitted using the expression (van Genuchten,
1980)
S
r
¼ S
r,res
þ
1 S
r,res
1 þ (Æs)
n
½
m
(1)
where S
r,res
is the residual degree of saturation (equal to
0
.
03); Æ is a parameter related to the inverse of the air-entry
value; and n and m are fitting parameters. Optimal curve-
fitting was obtained for the parameters Æ ¼ 0
.
91 m
1
,
n ¼ 2
.
19 and m ¼ 0
.
42. Information on the water retention
properties of the volcanic ash was also gained from the
mercury intrusion test. The injection of non-wetting mercury
was assumed to be equivalent to the ejection of water from
the pores by the non-wetting front advance of air (Romero
et al., 1999). The void ratio not intruded by mercury was
used to evaluate the degree of saturation corresponding to
the equivalent imposed suction. The pressure of the mercury
intrusion, p, and the suction, s, for the same pore diameter
are related by the expression
s ¼
w
cos Ł
w
Hg
cos Ł
nw
p
¼ 0
:
196p
(2)
where
w
and
Hg
are the water and mercury surface
tensions, Ł
w
is the contact angle of the air/water interface
(08), and Ł
nw
is the non-wetting contact angle between the
mercury and the soil grain (taken as equal to 1408). Fig. 3
presents the estimated water retention curve based on MIP
data, which is compared with the curve obtained by the
axis-translation technique. A good agreement is observed.
Both experimental methods suggest that the air-entry
value of the material (the suction value at which the material
starts to desaturate) is approximately 2 kPa. This value is
assumed to be constant in the range of void ratios being
considered.
Permeability
The permeability of the volcanic ash samples in a satur-
ated condition (k
w,sat
) was measured by constant-head per-
meability tests carried out in a triaxial cell at different
1
10
100
40 60 80 100
Matric suction: kPa
Water content: %
(a)
1
10
100
15 20 25 30
Matric suction: kPa
Water content: %
(b)
sw
R
15·972
0·967
⫽
⫽
⫺3·002
2
γ
d
3
: kN/m
8·0
9·8
11·4
Fig. 2. Initial suction determination by contact Schleicher and Schuell No. 589 filter paper:
(a) calibration of filter paper for matric suction measurement; (b) initial suction of volcanic
ash as a function of water content for different values of dry unit weight
0
0·2
0·4
0·6
0·8
1·0
Degree of saturation
0·1 1 10 100 1000 10 000 100 000
Suction: kPa
Drying Wetting
e 1·65⬇
e 1·50⬇
e 1·35⬇
From MIP results
Fitting
Fig. 3. Water retention behaviour of volcanic ash at different void
ratios, and comparison with water retention curve based on MIP
results
HYDROMECHANICAL BEHAVIOUR OF A VOLCANIC ASH 1435
confining isotropic pressures. The applied radial stresses
allowed good contact between the specimen and the latex
membrane, and avoided preferential flow paths along the
lateral surface of the specimen. The void ratio at the end of
the consolidation phase was measured; in this way it was
possible to establish the relationship between the coefficient
of permeability and the void ratio.
The dependence of the permeability on the degree of
saturation was assessed through back-analysis of the transi-
ent water exchange (V
w
(t)) registered in the tests for the
volumetric response with suction variation (see below, under
‘Controlled-suction tests’) (Kunze & Kirkham, 1962;
Romero et al., 2002),
V
w
(t) ¼ 1
X
1
n¼1
2 exp (Æ
2
n
D
w
tL
2
)
Æ
2
n
(A þ csc
2
Æ
n
)
"#
V
0
(3)
where V
0
is the total inflow volume for a water pressure
increment u
w
; L is the soil height; D
w
is the capillary
diffusivity, which is dependent on the water permeability; A
is the ratio of the impedance of the ceramic disc to that of
the soil (A ¼ k
w
t
d
/Lk
d
, where t
d
is the ceramic disc thick-
ness, and k
d
is its water permeability); and Æ
n
is the nth
solution of the equation aÆ
n
¼ cot Æ
n
(for n ¼ 1, 2,...). The
ceramic disc had a thickness t
d
¼ 4
.
06 mm and a water
permeability k
d
¼ 1
.
93 3 10
10
m/s. In order to apply this
method, a number of assumptions have to be satisfied: there
should be no significant volume change during the suction
change (true for the volcanic ash in drying paths); the water
flow is isothermal and one-dimensional; the fluid is homo-
geneous and incompressible; and the flow of air in the
porous medium is neglected, or considered as instantaneous.
A non-linear, least-squares optimisation procedure was used
to fit the test readings (time evolution of inflow data, V
w
(t))
to the predictions of the model, in order to obtain the D
w
parameter. Water permeability k
w
was calculated from the
expression (Romero et al., 2002)
k
w
¼
D
w
ª
w
V
0
V u
w
(4)
where V is the volume of the specimen, and ª
w
is the specific
weight of water. Water permeability values are depicted in
Fig. 4 as a function of the degrees of saturation for different
values of the void ratio. As a consequence of the experimen-
tal method, data were obtained only for the range of degree
of saturation investigated with the controlled-suction oedo-
metric tests. Experimental points are fitted using the expres-
sion
k
w
(S
r
, e) ¼ k
w,sat
k
w,r
(5)
where k
w,r
is the relative permeability function. k
w,sat
(in
m/s) is expressed as a function of the void ratio as
k
w,sat
(e) ¼ k
0
w,sat
e
c
k
(6)
where k
0
w,sat
is the saturated coefficient of permeability for a
reference void ratio, and c
k
is a fitting parameter. The
relative permeability function is expressed through the rela-
tionship (Brooks & Corey, 1964)
k
w,r
(S
r
, e) ¼ S
º
r
(7)
where the dependence on the void ratio is accounted for
with the exponent º, and
º ¼ c
l
e þ c
m
(8)
where c
l
and c
m
are fitting parameters.
The fitting parameters for the permeability function and
their values are summarised in Table 1.
EXPERIMENTAL PROGRAMME
Controlled-suction oedometric tests
Controlled-suction tests were planned and carried out in
order to analyse the volumetric response of the unsaturated
volcanic ash when it is subjected to variations in the degree
of saturation.
Tests were carried out in a controlled-suction oedometer
cell operating with the axis-translation technique on speci-
mens with a diameter of 63
.
4 mm and a height of
16
.
30 mm. Matric suction was controlled by keeping the
air pressure constant and varying the water pressure applied
to the specimen. Air pressure was controlled by means of
a pressure–volume controller that pressurised the cell. The
specimen rested on a ceramic disc (air-entry value of
0
.
5 MPa), through which the pore water pressure was
controlled with a pressure–volume controller (operative
accuracies for pressure and volume 1 kPa and 10 mm
3
10
⫺12
10
⫺11
10
⫺10
10
⫺9
10
⫺8
10
⫺7
10
⫺6
10
⫺5
10
⫺4
10
⫺3
0 0·2 0·4 0·6 0·8 1·0
Coefficient of permeability: m/s
Degree of saturation
e 1·1⬇
e 1·3⬇
e 1·5⬇
e 1·7⬇
1·7
1·5
1·3
e 1·1⫽
Fig. 4. Coefficient of permeability as a function of degree of
saturation for different values of void ratio
Table 1. Parameters for water retention and permeability function
Parameter Value
First VG parameter, Æ:m
1
0
.
91
Second VG parameter, n 2
.
19
Third VG parameter, m 0
.
42
Residual degree of saturation, S
res
0
.
03
Coefficient of permeability in saturated conditions for reference void ratio, k
0
w,sat
: m/s 4
.
8 3 10
6
Fitting parameter for dependence of coefficient of permeability in saturated conditions on void ratio, c
k
6
First fitting parameter for relative permeability function, c
m
53
Second fitting parameter for relative permeability function, c
l
25
.
4
1436 FERRARI, EICHENBERGER AND LALOUI
respectively). A coarse porous stone was in contact with
the soil at the upper base. A vertical load was applied
using a classical lever for oedometric cells, and vertical
displacements were measured by means of an LVDT with a
resolution of 1 m. Pore water volume changes were
monitored by means of the pressure–volume controller
connected to the ceramic disc. Measurements of pore water
volume changes were corrected to take into account air
diffusion through and water evaporation from the ceramic
disc (Airo` Farulla & Ferrari, 2005).
The stress paths followed in the controlled-suction appara-
tus are depicted in the plane of vertical net stress (difference
between the total vertical stress and the applied air pressure)
against suction in Fig. 5. Loading–unloading cycles at
constant suction were performed to assess the evolution of
the preconsolidation pressure and stiffness with suction
(Ferrari et al., 2012). Suction reduction tests at constant
vertical net stress were carried out to verify the position of
the loading yield limit of the material.
After the reference air pressure translation, all the tested
specimens were allowed to equalise to the initial suction
values registered by the filter paper method (20–40 kPa); a
low vertical net stress (5–7 kPa) was applied in order to
ensure contact between the loading ram and the specimen.
In the loading and unloading oedometer tests the applied
suction was maintained at 80 kPa and 40 kPa respectively
(Figs 5(a) and 5(b)). Starting from the initial value, the
vertical net stress was increased and reduced in steps,
allowing the consolidation process induced by the load
variation at each step to be stabilised. A third test (Fig. 5(c))
was carried out on a specimen dried at 120 kPa of suction,
then loaded at 118 kPa of vertical net stress and wetted in
steps up to a suction value of 1 kPa; the specimen was then
dried at 80 kPa of suction, loaded up to 470 kPa and wetted
a final time.
Triaxial tests
Complementary triaxial tests were performed in controlled-
stress-path triaxial systems, based on the classic Bishop &
Wesley design. Consolidated drained (CD) triaxial tests were
performed under 20 kPa, 50 kPa and 100 kPa initial confining
isotropic effective stress conditions. During the consolidation
phase, pore water volume changes were continuously meas-
ured in order to assess any changes in density. A deviatoric
load was then applied in drained conditions. Before failure
was reached, an unloading–reloading cycle of axial strain
was performed in order to deduce the elastic properties of the
material.
TEST RESULTS
Controlled-suction tests
Figure 6 depicts the results for the stress path shown in
Fig. 5(a) in the planes suction against vertical net stress, void
ratio against vertical net stress, suction against degree of
saturation, and void ratio against degree of saturation. During
the initial drying no significant deformation of the specimen
was recorded, and only a limited reduction in the degree of
saturation was observed (A–B) (in agreement with the reten-
tion curves reported in Fig. 3). The loading path (B–C) at
constant suction clearly defined the transition from a pre-
yield to a post-yield behaviour. The unloading–reloading
path allowed observation of the elastic response of the
material (C–D), and confirmed the position of the normal
compression line (C–E). As a consequence of the reduction
in pore volume, an increase in the degree of saturation was
obtained in the plane suction against degree of saturation;
the path B–E describes a scanning curve. The later wetting
(E–F) induced a small reduction in the void ratio, while the
degree of saturation increased up to 0
.
75; even if the settle-
ment was quite limited, it is worth noting that the wetting of
the material in a normally consolidated condition (E) induced
Suction: kPa
Suction: kPa
Suction: kPa
80
20
1
Two load–unload cycles
at constant suction
Load–unload cycles
at constant suction
Initial
drying
Initial
equalisation
Initial
equalisation
Initial
equalisation
Final
wetting
Final
wetting
Final
wetting
7
44
890 1570
Vertical net stress: kPa
(a)
Vertical net stress: kPa
(b)
Vertical net stress: kPa
(c)
40
1
7
44
923
120
20
1
First drying
Load at constant suction
Drying
Wetting
5
118 470
Fig. 5. Stress paths applied in controlled-suction oedometric tests
HYDROMECHANICAL BEHAVIOUR OF A VOLCANIC ASH 1437
