MIP AND GAS PERMEABILITY MEASUREMENT ON INJECTED SOILS
A. Ait Alaiwa, N. Saiyouri and P-Y. Hicher
Research Institute of civil and mechanical engineering - GeM
Ecole Centrale de Nantes
Nantes, F- 44321
ABSTRACT
Over the past twenty years, grouting technology has evolved to treat a wide range of subsurface conditions for construction.
When a properly designed cement grout is injected into sand soils, homogeneous grout bulbs are formed that densify and thus
strengthen the surrounding soil. For successful grouting, the knowledge of subsurface conditions is important. Ground
improvement can be assessed by permeability testing and mercury porosimetry testing. Laboratory experiments were
conducted to examine grout injection through Loire sand columns under saturation conditions. They were performed in order to
highlight the effect of some key factors: cement-to-water ratio, relative density of the granular skeleton on the permeability of
the grouted sands. Subsequent Mercury Intrusion Porosimetry tests showed that both porosity and its distribution are modified.
Besides, the intrinsic permeability was measured by gas permeability. Then, an evaluation of intrinsic permeability using the
Katz-Thompson equation on theses tests is proposed and compared to gas permeability which is still commonly used in civil
engineering to measure this intrinsic parameter.
Introduction
To improve soil properties, various techniques were developed. They allow modifying underground flows modification by
reducing their permeability. One of these techniques is cement grout injection process. This treatment consists in introducing
under pressure, through a sleeve pipe, various materials intended to fill the void space available in the soil. To evaluate the
effectiveness of this operation, the intrinsic permeability coefficient (Kv) is measured.
In soil mechanics, water permeability measurements are generally carried out. This test consists in saturating with water a
sample, then to apply a constant head on this sample and to measure the quantity of water crossing the specimen when flow
is steady.
For the injected grounds, this method, also applicable, is more delicate because of difficult preliminary saturation. Besides a
high water pressure must be imposed to obtain measurable flows, which can damage the studied medium. To avoid this
difficulty, we select gas permeability using gases such as oxygen or nitrogen. These ones are inert with respect to materials. In
addition, we measure porosity by mercury intrusion porosimetry tests (MIP). Gas permeability allows estimating intrinsic
coefficient of permeability Kv which can also be obtained by Katz-Thompson equation using MIP results. This coefficient
depends on several parameters which will be discussed in this paper.
Gas permeability
The main research objective is to understand the mechanisms of ultrafine cement grout propagation in granular media (Loire
sand at fixed densities). We focus on filtration phenomenon during the grout propagation. For that, we follow an indicator of the
void space filling: the permeability coefficient of an injected soil when the grout hardens and gains strength (after the setting of
the grout). In 1856, Darcy proposed an application of the Hagen-Poiseuille law for the calculation of the permeability of a
porous medium using a fluid. The permeability of the medium is connected with the flow of the fluid according to the formula
Q=
K ∆p
µ L
(1)
where Q is the laminar stationary flow of the fluid through a cylindrical tube of constant cross section, ∆p is the drop of
pressure, µ is the dynamic viscosity of the fluid, L is the length of the tube and K is the permeability
Darcy also notices that the permeability depends on the percolant fluid nature and can be related to an intrinsic permeability
which only considers the material by the following relation:
K=
ρg
K
µ v
(2)
where K, Kv, ρ, µ and G are respectively the permeability of porous material respect to the percolant fluid (generally water), the
intrinsic permeability, the density and the viscosity of the percolant fluid, finally the acceleration of gravity.
The equation (1) is based in the following hypotheses:
the flow is laminar,
the flow is under isothermal conditions,
the fluid is incompressible,
the fluid flow is dominant viscous i.e.: the forces of inertia are insignificant in relation to the viscous forces.
In these conditions and for liquids as water the Darcy's law can be used directly.
The general principle of the test is to carry out a continuous gas flow through the sample under steady conditions. The
pressure cell was designed to subject the sample to a constant gas pressure Pinj at the bottom of the sample and atmospheric
pressure Patm at its head (up).
Thanks to digital acquisition system, we can monitor gas injection pressure, atmospheric pressure, flow rate, and temperature
in real time.
Permeability is given by using the Hagen-Poiseuille equation (3) using mass conservation in the steady state between the
inner and the outer sides of the specimen.
Ka =
2µLP0 Q
2
Pinj2 − Patm
S
(
)
(3)
2
2
3
Here Ka is the apparent permeability [m ], S is the section subjected to flow [m ], Q the volumetric flow rate [m /s], L the
sample thickness in the direction of the flow [m], µ the dynamic viscosity of the test gas N2 [Pa⋅s] (at 20 °C for nitrogen: µ =
-5
1,76 10 Pa⋅s), Pinj absolute injection pressure at the bottom [Pa], Patm absolute atmospheric pressure at the top [Pa] and P0
the pressure to which the flow is measured [Pa]; usually: P0 = Patm.
Actually the apparent permeability depends on the pressure gradient, temperature, water saturation and material
microstructure. The permeability given by Eq. (3) assumes that a laminar flow is established during the test but in fact a no
viscous contribution due to the pore fineness in cement based material is observed (slip flow phenomenon). This contribution
and pressure dependence have been studied by Klinkenberg [1]. He also proposed the following law (4) giving the intrinsic
permeability:
⎛
β ⎞
⎟
K a = K v ⎜⎜1 +
Pm ⎟⎠
⎝
(4)
2
where β, Kv, Pm are respectively the Klinkenberg coefficient [Pa], the intrinsic permeability [m ] and the average pressure
(Pinj+Patm)/2 [Pa] (i.e. the mean of the absolute injection pressure and absolute atmospheric pressure).
Apparent permeability Ka (m2)
x 10
-14
exp
linear
5.5
Ka = 4.7e-009*(1/Pm) + 1.4e-014
R2 = 0.996
5
4.5
4
6.5
7
7.5
8
1/Pm (Pa-1)
8.5
9
x 10
-6
Figure 1. Evolution of apparent permeability versus the inverse of the average pressure
Thus, from a set of apparent permeabilities measured at different injection pressures, we can obtain the intrinsic permeability
(transfer property representative of the viscous flow within material) combining Eq. (4) and linear regression.
Mecury intrusion porosimetry
Mercury Intrusion Porosimetry (MIP) is a technique used to measure pore size distribution, and has an advantage in that it is
able to span the measurement of pore sizes ranging from a few nanometers, to several hundred micrometers. As injected soil
has a distribution of pore sizes ranging from sub-nanometer to many millimeters, MIP has formed an important tool in the
characterization of pore size distribution and total volume of porosity.
Mercury is a non-wetting liquid for almost all substances and consequently it has to be forced into the pores of these materials.
Pore size and volume quantification are accomplished by submerging the sample under a confined quantity of mercury and
then increasing the pressure of the mercury hydraulically. The detection of the free mercury diminution in the penetrometer
stem (a glass container with a sealable lid which is used to hold the sample during testing) is based on a capacitance system
and is equal to that filling the pores. As the applied pressure is increased the radius of the pores which can be filled with
mercury decreases and consequently the total amount of mercury intruded increases. The data obtained give the pore volume
distribution directly and with the aid of a pore physical model, allow a simple calculation of the dimensional distribution of the
pore size. Determination of the pore size by mercury penetration is based on the behavior of non-wetting liquids in capillaries.
A liquid cannot spontaneously enter a small pore which has a wetting angle of more than 90 degrees because of the surface
tension (capillary depression), however this resistance may be overcome by exerting a certain external pressure. The pressure
P required is a function of the pore size D, the relationship between pore size exerted when the pore is considered to be
cylindrical is commonly known as the Washburn equation [2]. This one is expressed as:
D=
− 4σ cos θ
P
(5)
Where θ is the angle of contact between mercury and the solid phase and σ is the interfacial tension air-mercury. Placed in an
air-conditioned room with regulated temperature 20 ± 2°C, the mercury porosimeter (Micromeritics Autopore 9500) used for
our measurements can provide a maximum intrusion pressure of 414 MPa. Only the pores whose diameters are between 3nm
and 360µm are accessible with this apparatus.
Evaluation of intrinsic permeability by Katz-Thompson theory
There have been many attempts over the years to relate permeability to some relevant microstructurally defined length scale.
Katz and Thompson works [3] provide an important contribution to mass transport studies in facilitating the prediction of fluid
permeability of materials from mercury injection data. The equation was derived from percolation theory [4].
k=
1 2 lmax
⋅ lc ⋅
⋅ n ⋅ S (l max ) where l max = 0.34 ⋅ lc
226
lc
(6)
where lc is the characteristic pore diameter of the porous medium which is the smallest pore diameter necessarily filled to
initiate a flow through the porous medium, lmax is the value of the length (pore size) at which hydraulic conductance is
maximum, n is total porosity and S is the fraction of total porosity filled at lmax. This parameter includes information on the
connectivity of the porous network.
As the pressure is increased, mercury is forced to invade smaller and smaller pore openings in the permeable medium.
Ultimately, a critical pressure is reached at which the mercury spans the sample. This conduction path is composed of pores of
diameter equal to and larger than the diameter calculated from the Washburn equation for the critical pressure. This diameter,
lc in equation (6), is a unique transport length scale and dominates the magnitude of the permeability. To obtain this
characteristic length lc from the mercury intrusion data set, pressure is determined at the point of inflection in the rapidly rising
range of the cumulative intrusion curve (figure 2).
Cumulative intrusion Volume (mL/g)
0.1
0.09
0.08
0.07
0.06
Inflexion point
0.05
0.04
0.03
0.02
0.01
0 0
10
Lc
2
4
10
10
Equivalent pore diameter (nm)
10
6
Figure 2. Pore distribution of an injected Loire sand sample
This inflection point was determined experimentally by Katz and Thompson to correspond closely to the pressure at which
mercury first spans the sample and the point at which percolation begins. The value of lc is the pore diameter calculated from
the Washburn equation.
Results
The samples are cylinders of 50 mm in diameter and 50 mm high. They are cored from larger cylinders ∅100x300 mm then
rectified to obtain a perfect geometry (two coplanar sections). Circumferential surface is sealed by a heat-shrinkable sleeve
which prevents gas leakage during measurement.
As the permeability test is based on measurement of the intrinsic permeability by gas injection, the samples must be dried
before the test to allow gases to move freely through the open voids and spaces. Partial removal of moisture will not result in a
truly open pore-structure through which gases are able to move, and measurements made of any flow or penetration through
the material will not reflect the actual nature of the pore-structure, which may vary between being open and well
interconnected or restrictive and of low interconnectivity.
The most commonly used method is to place specimens in a regulated oven for a pre-determined period of time until a
constant weight is achieved. It indicates that all available moisture which is able to escape from the pore-structure has done
so. However, the temperature of the oven is often quite high (105°C ± 5°C) as a result of the conventions imposed by various
test standards. Although this is an effective way to remove moisture from the specimen, it is not without its drawbacks, as
microcracking may be induced into the specimen. This can be a result of differing thermal expansion and contraction of various
components during the drying cycle. A compromise on this is to use lower temperatures (~60°C). Specimens may be left for
longer than normal to attain constant weight. The procedure assumes that the drying process only leads to superficial
microcracking, which does not reach the sample heart and has no influence on permeability measurements [5].
Just before the test, the sample is stored during 24 hours in a desiccator settled in an air-conditioned room at 20°C. The
apparent permeability measurements for different injection pressures respectively 0.05, 0.1, 0.2, 0.3 and 0.4 MPa are realized
using Cembureau method [6-7]. Upstream flow is measured with a digital mass flowmeter which directly calculates the volume
flow at normal pressure and temperature conditions (expressed in normal milliliters per minute) in the range 0-1000 mln/min.
Atmospheric pressure and temperature are also monitored during the test using a digital barometer and a thermohygrometer.
Table 1 presents, for each sample (1 to 3) the main parameters of 3 columns respectively named K, N and C: the initial
densities (γd), the grout Cement to Water (C/W) ratio used for the injection, the intrinsic permeabilities measured with water (K)
before the injection and the gas ones (Kmes) after cement grout injection. We point out the gas permeability for injected soils
with similar initial densities, is all the more large as their C/W ratio is weak (Table 1). Indeed, it can be explained by the
localized cement microagregates formation which induces lower permeability.
We observe in Table 1 that the relative variation of porosity decreases with the density and the cement grout concentration.
Actually, filling void space of the medium by the grout is all the more difficult as the initial sand density is high. We can show
the same effect when C/W ratio increases.
Besides, in figure 2, the porosity spectrum reveals two main classes of pores delimited by the values of diameter poral 0.4µm
and 6µm [8]:
- Microporosity: pores whose diameter is lower than 0.4µm, which characterize the fine phase of the injected sand due to fine
component agglomerations.
- Mesoporosity: pores between 0.4µm to 6µm due to the assembly of coarse elements and micro-aggregates.
Table 1. Parameters of injected samples
Reference
1
3
γd (kN/m )
C/W
K2 (10-11m2)
Kmes (10-16m2)
n03 (%)
nf 4 (%)
1K1
17.24
0.42
2.53
1,33
34.2
20.6
2K2
17.24
0.42
2.53
1.47
34.2
21.4
3K1
17.24
0.42
2.53
6,28
34.2
20.1
1N
17.3
0.28
2.51
22,7
34.0
26.8
2N2
17.3
0.28
2.51
104
34.0
27.2
3N
17.3
0.28
2.51
310
34.0
25.6
1C1
18.03
0.42
1.93
140
31.2
21.7
2C3
18.03
0.42
1.93
181
31.2
21.8
2C2
18.03
0.42
1.93
490
31.2
24.5
We notice, in all the cases, a typical bimodal porosity spectrum characteristic of the media finely aggregate when C/W ration is
weak (figure 3a) and microagregated medium for high charged cement grout (figure 3b, 3c). We can also highlight that the
mesoporosity disappears in aid of microporosity when the initial density of the injected soil grows.
0.1
0.09
1N
3N
2N2
0.07
dV/dlogD Pore Volume (mL/g)
dV/dlogD Pore Volume (mL/g)
0.08
0.06
0.05
0.04
0.03
0.02
0.01
0 0
10
1K1
3K1
2K2
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
2
4
10
10
Equivalent Pore Diameter (nm)
10
0 0
10
6
(3a) γd = 17,3kN/m3, C/W = 0,28
2
(3b) γd = 17,24kN/m3, C/W = 0,42
0.08
2C3
1C1
2C2
dV/dlogD Pore Volume (mL/g)
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0 0
10
2
4
10
10
Equivalent Pore Diameter (nm)
10
6
(3c) γd = 18,03kN/m3, C/W= 0,42
Figure 3. Pore distribution of an injected Loire sand sample
1
γd is the dry density of non injected soil.
K is the initial intrinsic permeability of non injected sand.
3
n0 is the initial total porosity.
4
nf is the total porosity estimated by MIP tests.
2
4
10
10
Equivalent Pore Diameter (nm)
10
6
Several authors [3-8] indicated that such samples, with this typical porosity spectrum, represent a complex porous network.
Consequently, the interpretation of the distributions calculated by the Washburn model, containing various significant pores
does not match to the gas permeability measurements. That means total porosity is underestimated by measurement.
Table 2 presents the results of the permeability calculation using Katz-Thompson formulation (Kcalc) and those measured by
the gas permeability (Kmes). Finally we underscore the gas permeability (Kmes) is three orders of magnitude higher than the one
calculated (Kcalc) based on MIP tests (Table 2). Permeabilities calculated using Katz-Thompson equation (Eq. 6) does not
correspond to the experimental data for this type of material.
To improve this prediction,, we derive from Katz-Thompson formulation the equation (7) to include the initial density effect
upon intrinsic permeability.
γd
2−
1 2
k=
⋅ lc ⋅10 γ max ⋅ n ⋅ S (lc )
226
(7)
where lc is the characteristic pore diameter of the porous medium, γd is the initial apparent density, γmax the maximal initial
density obtained using NF P 94-059 standard, n is total porosity and S is the fraction of total porosity filled at lc. This parameter
includes information on the connectivity of the porous network. Table 2 shows the intrinsic permeability Km calculated by the
modified Katz-Thompson formulation. Using this enhancement, we can obtain the same order of magnitude.
Table 2. Intrinsic permeabilities of injected samples
Reference
lc (nm)
Kmes (10-16m2)
Kcal (10-19m2)
Km (10-16m2)
1K1
40
1,33
4,81
442
2K2
40
1.47
4,93
121
3K1
40
6,28
4,61
26
1N
337
22,7
316
56
2N2
393
104
469
137
3N
364
310
385
970
1C1
40
140
5,11
279
2C3
40
181
5,11
264
2C2
40
490
5,46
1893
Conclusions
In this paper, we presented results of the intrinsic permeability measurements and the porosity evolution of injected sand using
MIP tests. The variation of porosity is inversely proportional to the initial soil density. The permeability reduction grows with the
density and C/W ratio of the grout injection. The Katz-Thompson theory underestimates, at first sight, the intrinsic permeability.
A modified formulation slightly allows estimating the intrinsic permeability for an injected soil. However it requires further
studies of the relevant parameters of this formulation for this type of ground. Lastly, the gas permeability results are coherent
and satisfactory. The measurement method, initially tested on the mortars and concretes, seems to adapt completely to this
type of material.
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