# Correction Method for Hydraulic Conductivity Measurements Made Using a Fixed Wall Permeameter

Authors: Qiang Luo; Mengshi Liu; Tengfei Wang; Peng Wu
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

Hydraulic conductivity measurement through a fixed wall permeameter is a common practice to obtain the fluid transmissibility characteristics of soil matrix; however, sidewall leakage due to rigid wall effect may significantly influence the observed values for coarse-grained soils. In this study, the boundary flow error was identified through characterizing the geometrical properties of voids adjacent to the sidewall, and a parameter known as the boundary void ratio (eb) was proposed to account for this effect. The findings suggest that a fixed wall cell containing coarse soils would unavoidably generate extra voids at the interface between soil grains and inner rigid wall, contributing to a larger eb at the wall than void ratio within the soil bed; the measured hydraulic conductivity is increased primarily due to the apparatus-induced error. A two-dimensional geometric model was then established to estimate the eb value for uniformly sized coarse soils confined by a rigid permeameter wall, based on which a method was obtained for eliminating the boundary flow error from a fixed wall cell. The mathematical method was finally validated against experimental data from existing literature. It can be concluded that the boundary condition at sidewall featuring unwanted gaps lead to overestimation of the coefficient of permeability; however, the proposed correction method could adequately eliminate the boundary flow error for uniformly sized coarse-grained soils tested within a rigid wall cell.


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## Body

## 1. Introduction

Soil mass made up of solid particles with necessary voids can allow water to pass through [1, 2]. Hydraulic conductivity (also referred to as the permeability coefficient) defined by Darcy’s law is an essential parameter for identifying the permeability of soils under the laminar flow region. Currently, there are two typical types of permeameter used for measuring the hydraulic conductivity in the laboratory, namely, fixed wall permeameter [3] and flexible-wall permeameter [4]. Fixed wall cell mainly consists of a rigid cylindrical tube and offers the benefits, such as simplicity, low cost, and the convenience for specimen preparation. At the same time, the shortcoming is obvious since the wall effect for particles packing adjacent to the wall might lead to potential sidewall leakage and flow maldistribution and an exaggerated permeability of laboratory test as well; i.e., the hydraulic conductivity value for finite bed is greater than that for infinite bed [5, 6]. A flexible-wall device comprises a triaxial cell, in which the bed is enclosed by a flexible membrane and subjected to controlled confining pressure. It can effectively eliminate boundary flow issue, and the measured data are close to the real hydraulic conductivity of unconfined bed. Thus, more researchers were focused on employing flexible-wall permeameter for hydraulic conductivity measurements [7–9]. However, complicated operations and high cost set limits for a widespread use [10].Concerning a fixed wall cell, the boundary effect has long been investigated. Franzini [11] demonstrated that the porosity in the vicinity of sidewall is greater than within the bed packed with grains because the grains close to the wall cannot be packed as tightly as those inside soil bed. The bed can be divided into two zones, namely, the outer shell near the wall and the core whose porosity is free from the boundary effect.Meanwhile, Roblee et al. [12] and Ridgway and Tarbuck [13] conducted several elaborate measurements of the porosity on uniformly sized grains contained in a rigid cylindrical tube, through pouring the wax into the bed to fix them in position. By analyzing variation law of porosity with the distance away from sidewall, Cohen and Metzner [14] suggested using a triregional model to partition the cross section of confined bed, namely, a wall region, a transition region, and a bulk region, each with a different porosity. Moreover, based on the capillary model from Carman [15], the flow distribution in each region was considered, and they concluded that the boundary influence on water flow could be ignored when the ratio of tube diameter to grains diameter is greater than approximately 30 for Newtonian fluids and 50 for non-Newtonian fluids. de Klerk [16] established a mathematical model with an exponential decay function for describing the porosity variation in the radial direction and predicted the average porosity of confined bed.More recently, Allen et al. [17], Yadav [18], and Larsson et al. [19] reached an agreement on the effect of permeameter boundary on water flow primarily displayed in two contradictory aspects: (1) the increased porosity near the wall would reduce the resistance to flow; therefore, sidewall leakage occurs; (2) the presence of shearing stress due to a larger surface area at the wall increases flow resistance, inducing reduction in hydraulic conductivity of confined bed. Kango et al. [20] carried out a series of permeability tests for natural soils with different permeameters to particle size ratios (i.e., Dp/dg, where Dp is the permeameter diameter and dg is the particle diameter) and found that the influence of increasing porosity is more pronounced than surface are at the wall for Dp/dg<40, and thus the hydraulic conductivity of confined bed (k) would be greater than unconfined conditions (k∗). However, there would be a reversal phenomenon for Dp/dg ranging between 40 and 120, and the wall effect is negligible provided that Dp/dg>120.In summary, small-scale fixed wall permeameter does not require excessive soil samples and high water flow from permeability apparatus that make it difficult to conduct in the laboratory [21]. However, the related boundary flow issue in a permeability test shall be carefully dealt with. In this paper, the underlying mechanism of the wall effect was firstly elucidated by analyzing boundary void characteristics in the confined bed. Second, within the 2D theoretical framework, a geometric model was proposed to estimate the boundary void ratio of coarse-grained soils adjacent to the wall. Finally, based on the relationship between void ratio and hydraulic conductivity, a correction method was developed for hydraulic conductivity measured in a fixed wall cell and verified against test data from the existing literature. It should be emphasized that this is only a simplistic approach for uniformly sized coarse-grained soils. Further investigation is required to extend its application to soils having different grain dimensions.


## 2. Boundary Void Characterization

Several techniques (SEM, MIP, and X-ray computed microtomography) have been developed to reveal the inner structure of compacted soils. There are not only intraparticle voids but also interparticles, and the voids present a wide range of dimensions, varying with different conditions such as loading and compaction [22]. They jointly contribute to the real complexity of the inner structure, which cannot be fully accounted for in this study. Some simplifications have been made before characterizing boundary voids of coarse-grained soils. Figure 1 shows a plane view of composition characteristics of voids near the sidewall within a fixed wall cell, where soil voids are of two general types: typical void among the matrix particles, V0, and boundary void adjacent to rigid wall, Vb. In order to further distinguish V0 and Vb, a few hypothetical matrix particles, which have the same packing characteristics as the existing matrix particles, are assigned along with the boundary voids, as specified in Figure 1. Thus, Vb consists of two parts: Vv refers to the volume of voids encircled by the hypothetical matrix particle and existing matrix particles next to it, equaling to V0; Vp denotes the overlap fraction of the hypothetical matrix particle plus Vb.Figure 1
Schematic of plane distribution of soil voids adjacent to rigid wall.As demonstrated in Figure1, it is also reasonable to assume that Vv consists of V1 and V2, where V1 represents the volume associated with the existing matrix particles surrounding Vv and V2 refers to a volume formed by the hypothetical matrix particle next to it. This implies that some extra voids would exist around the surface of the wall when compared to those in the interior of the bed since the soil solids are not essentially contacting the rigid wall. The extra void (i.e., Vf) caused by sidewall can be expressed as follows:(1)Vf=Vb−V1=Vp+V2.As shown in Figure1, V2 in equation (1) is associated with the grain size as well as the compaction level of the bed and is independent of permeameter diameter. Vp in equation (1), however, is connected to all the factors mentioned above. Besides, a larger permeameter diameter D leads to a smaller volume of hypothetical matrix particle that is placed next to boundary particles, as well as a reduction in Vp.Hence, it can be concluded thatVb can also be treated as the sum of V1 and Vf, which are related to the existing matrix particles surrounding Vb and the permeameter wall, respectively. Referring to the definition of void ratio from soil mechanics, boundary void ratio (BVR, eb) at the inner wall for confined bed can be accordingly defined as follows:(2)eb=VbVs=V1+VfVs=e+VfVs,where Vs is the partial volume of the existing matrix particles near the wall, which contributes to the void V1 (i.e., the shaded area in Figure 1) and e denotes the void ratio of the soil bed.The presence of extra void,Vf, would produce a larger eb than e, increase the seepage velocity in the vicinity of wall, and ultimately induce sidewall leakage. It should be noted that the measured hydraulic conductivity would be overestimated when Vf is ignored.


## 3. Mathematical Formulation

Figure2 illustrates an overview of uniformly sized disks packing in a 2D problem. The regular triangle packing (Figure 2(a)) and the square packing (Figure 2(c)) can produce the densest and loosest states, respectively. Therefore, the density of other rhombus packing falls within this range (Figure 2(b)). By connecting the centers of adjacent four disks, e.g., o1o2o3o4 in Figure 2, and defining the packing angle as ∠o2o1o3=α(π/3 ≤ α ≤ π/2), the plane void ratio (PVR) e′ can be expressed as follows:(3)e′=4sinαπ−1.Figure 2
Uniformly sized disks packing in a plane: (a)α = π/3; (b) π/3 < α < π/2; (c) α = π/2.
(a)
(b)
(c)Asα increases, the void size in a packing unit o1o2o3o4 and e′ would monotonously increase, leading to a reduction in density. In particular, if α equals to π/3 or π/2, the minimum emin′=0.103 and the maximum emax′=0.273 can be thus obtained, respectively [23].Owing to numerous factors affecting the boundary void, some necessary simplifications are made before establishing a theoretical model. In this paper, the soil mass in a permeameter cell are assumed to be composed of uniform circular disks in a plane with packing angleα as an indication of packing density. Through replacing partial disks of a packing unit o1o2o3o4 with the permeameter wall, a simplified geometric model is developed to estimate eb, as shown in Figure 3.Figure 3
Computational model for 2D void ratio determination at sidewall: (a) Type I-1 (π/3 < α ≤ π/2); (b) Type I-2 (α = π/3); (c) Type II (π/3 < α ≤ π/2); (d) Type III (π/3 ≤ α ≤ π/2).
(a)
(b)
(c)
(d)In this model, the inner wall of permeameter has a radius ofD/2, and the disks having a uniform diameter of d next to the wall represent the soil particles. Moreover, the blank area between the wall and the particles refers to the boundary void Vb, around which are two tangent points between the wall and the particles. Within the framework of the computational model, a disk refers to soil particle, while the gap between the wall and the particles represents the boundary void. The thickness of sidewall has thus been ignored.In the packing unito1o2o3o4 where π/3 < α ≤ π/2, three boundary-packing types are clarified for Vb, with multiple disks removed and replaced by the wall. Thereafter, the plane boundary void ratio (PBVR, eb′) is proposed, which can be determined for certain boundary-packing types.Type I:Vb is surrounded by any two tangent particles of unit o1o2o3o4 and permeameter wall. For instance, as shown in Figure 3(a), o3 and o4 are assumed to be replaced by the wall; Hence, the wall is tangent to the particles o1 and o2, and the corresponding θ1 can be calculated as(4)θ1=2arcsindD−d.The areaA1B1C1 excluding disks in Figure 3(a) represents Vb, which can be easily inferred:(5)SA1B1C1=θ18D−dD+d−d4D−dcosθ12−πd28.A complete void for unito1o2o3o4 corresponds to an area of an individual particle. Vb is surrounded by two particles in Figure 3(a), based on the adjacent complementation law of the interior angles for rhombus, and the disk Vs corresponding to void V1 in Figure 1 shall be(6)Ss1=12×πd24=πd28.Combining Equations (2), (5), and (6), the PBVR eb1′ for Type I can be obtained as follows:(7)eb1′=SA1B1C1Ss1=2πd2D−dD+darcsindD−d−2πdD2−2Dd−1.Type II:Vb is jointly surrounded by any three particles in unit o1o2o3o4 and permeameter wall. In addition, the lines connecting the centers of these particles generate a triangle (e.g., when α = π/2, a right triangle will be). For instance, by replacing particle o4 with the wall in Figure 3(c), θ2 can be calculated by(8)θ2=2arcsin2dsinα/2D−d.Similarly, the areaA2B2C2J2 standing for Vb equals to(9)SA2B2C2J2=θ28D−dD+d+2sinα−π4d2−18D−d2sinθ2.As can be seen in Figures2(b) and 3(c), the particle o4 is replaced by a wall; therefore, the disk area Ss2 representing Vs can be obtained:(10)Ss2=1−α2ππd24.To sum up, the PBVReb2′ for Type II is(11)eb2′=SA2B2C2J2Ss2=12π−αd2/82sinα−π4d2+14D−dD+darcsin2dsinα/2D−d−18D−d2sin2arcsin2dsinα/2D−d.Type III:Vb is jointly surrounded by any three particles of unit o1o2o3o4 and the permeameter wall. It should be noted that the lines connecting the centers of these particles create an obtuse triangle (when α = π/2, it will then be a right triangle). If so, replacing particle o2 with the wall in Figure 3(d), θ3 will be expressed by(12)θ3=2arcsin2dsinπ−α/2D−d.Following the same procedure for Type II, the areaA3B3C3J3 representing Vb and the PBVR eb3′ for Type III are calculated as follows:(13)SA3B3C3J3=θ38D−dD+d+2sinπ−α−π4d2−18D−d2sinθ3,(14)eb3′=8π+αd22sinπ−α−π4d2+14D−dD+darcsin2dsinπ−α/2D−d−18D−d2sin2arcsin2dsinπ−α/2D−d.Among all the boundary-packing types mentioned above, it is apparent that PBVRs for Type I, Type II, and Type III are in the ascending order, primarily due to the increased representative area ofVb.To be more specific, the particleo2 contacts the particle O3 when α = π/3 (Figure 2(a)). More importantly, it also serves as a boundary between Type II and Type I in Figure 3. Hence, there are two general boundary-packing types for the particles adjacent to the wall, namely, Type I and Type III. As shown in Figure 2(a), it is three particles that surround a single pore of unit o1o2o3o4, so that a pore corresponds to half of a particular area that is different from Figures 2(b) and 2(c). Because the wall replaces one particle and combines the other two particles to form such a boundary void in Type I (Figure 3(b)), based on the sum of the interior angles of a triangle, the disk area of Vs is given as follows:(15)Ss1,α=π/3=23×πd28=πd212.Substituting equations (5) and (15) into equation (2) yields(16)eb1,α=π/3′=3πd2D−dD+darcsindD−d−dD2−2Dd−πd22.Moreover, another boundary-packing type (i.e., Type III) is the same as that in Figure3(d); then, PBVR eb3,α=π/3′ for Type III remains unchanged when compared to eb3′, indicating that it can be calculated by equation (14).On the premise of thatα is a constant, with the various numbers and locations of particles within a certain unit o1o2o3o4 replaced by a sidewall, the number of combinations of the residual particles to form the boundary void should be 8 (referring to Table 1). Assuming that all the combinations follow the principle of random events, the probability of boundary-packing types, namely, P1, P2, and P3 corresponding to Types I, II, and III, respectively, have been tabulated in Table 1, including such particular conditions as π/3 < α ≤ π/2 and α = π/3. When π/3 < α ≤ π/2, there are four particle combinations for Type I-1, two for Type II, and two for Type III; when α = π/3, there are six particles combinations in total for Type I-2 and just two for Type III.Table 1
Probability summary of boundary-packing types in the PBVR geometric model.
Packing angleα
Boundary-packing type
Particle combination
Probability
PBVR
π/3 < α ≤ π/2
Type I
O
1
O
2, O1O3, O2O4, O3O4
P
1 = 0.50
Equation (7)
Type II
O
1
O
2
O
3, O2O3O4
P
2 = 0.25
Equation (11)
Type III
O
1
O
2
O
4, O1O3O4
P
3 = 0.25
Equation (14)
α = π/3
Type I
O
1
O
2, O1O3, O3O4, O2O4, O1O2O3, O2O3O4
P
1 = 0.75
Equation (16)
Type II
N/A
P
2 = 0
N/A
Type III
O
1
O
2
O
4, O1O3O4
P
3 = 0.25
Equation (14)


## 4. Correction Method

As discussed above, if extra void contributing to potential sidewall leakage is known, the error of measured hydraulic conductivity through fixed wall permeameter can be corrected accordingly. Based on a plane-geometric model for calculating PBVR, the main computation procedure to correct the hydraulic conductivity of uniformly sized coarse-grained soils is given as follows.Step 1.
determining the average grain size of the material tested. The disks diameter (d) in the PBVR geometric model is regarded as the geometric-equivalent diameter of poorly graded coarse soils obtained from standard sieve analysis. The applicability of this correction method in well graded soils has not been fully discussed and illuminated.Step 2.
determining the correction factor for PBVR. Following the assumption that the uniform disks withα = π/3, π/2 corresponds to the densest or the loosest state of the soil sample, respectively. Thus, the soil bed in the permeameter with any given compaction level can be reproduced by the plane packing of uniform disks in Figure 2 with a specific packing angle α ranging from π/3 to π/2.
Since the soil particles are simplified as mono-sized 2D disks in the model development, it cannot fully reflect the real packing characteristics under 3D conditions, under the effect of grain shape, spatial dimension, and the variability between the overlapping 2D disks. Assuming that the compaction levels for the uniformly sized disks in a plane and compacted soil bed are controlled as the same, the difference between PVR (e′) and the real void ratio should be accordingly modified, given by(17)e=ξe′,where ξ is the correction factor for PVR.
For the densest scenario, the corresponding correction factorξmin is calculated through comparing emin′ to the minimum void ratio emin as follows:(18)ξmin=eminemin′=9.71emin.
Likewise, the correction factorξmax for the loosest scenario shall be(19)ξmax=emaxemax′=3.66emax,where emax denotes the maximum void ratio.
Therefore, the correction factorξ for the confined bed with any given compaction level corresponding to the void ratio e could be obtained through linear interpolation between ξmin and ξmax, and thus,(20)ξ=ξmin+e−eminξmax−ξminemax−emin=9.71emin+3.66emax−9.71emine−eminemax−emin.Step 3.
determining the packing angle. It can be seen from equation (17) that e is dependent on e′. Also, e′ is positively related to α in equation (3). Hence, in order to reflect the compaction level of the confined bed in plane whose void ratio is e, α for uniform disks packing in plane is expressed from equation (21) by considering equations (3) and (17):(21)α=arcsinπ4eξ+1.Step 4.
calculating the area ratio of wall region and PBVR. Employing the measurement of water flow rateQt at the permeameter outlet and hydraulic gradient J across the test length of the soil bed for certain period, the observed value of hydraulic conductivity for confined bed in a fixed wall cell, i.e., kt, could be obtained by Darcy’s law:(22)kt=QtAtJ,where At is the clearance cross-sectional area of permeameter, At = πD2/4.
It is reasonable to assume thatQt is divided into two parts, i.e., Qc flows through the interior region of the bed and Qw flows through the wall region, consistent with the assumption of [11]. If the water flow near the wall still obeys Darcy’s law and has the same hydraulic gradient as the interior one, equation (22) can be transformed into(23)kt=Qc+QwAtJ=kcAcJ+kwAwJAtJ=kcAcAt+kbAwAt=kc1−AwAt+kwAwAt,where kc is the hydraulic conductivity for the interior region, which equals to the hydraulic conductivity without confinement; kw is the hydraulic conductivity for the wall region; and Ac and Aw represent the cross section areas of the interior region and the wall region, respectively. In addition, Aw+Ac=At.
As illustrated in equation (23), only when the area ratio of wall region λ (where λ=Aw/At) is small enough that it can be ignored. In other words, the interior region is much larger than the wall region; kt would approximate the unconfined value, kc. Owing to the empirical equation proposed by Liu [24, 25], which revealed a third-order nonlinear relationship between porosity and hydraulic conductivity of cohesionless soil shown in equation (24), a relationship between kt and kc thus is deduced in equation (25) by the combination of equations (23) and (24):(24)k=βn3=βe1+e3,where n is the porosity of soils and β refers to the coefficient for the influence of particle graduation.(25)kt=kc1+λeb+e⋅eb/e+e⋅eb3−1.
According to the geometric model in a plane used for calculating PBVR, the area of the wall region in Type I, Type II, and Type III, namely,Aw1, Aw2, and Aw3, respectively, are inferred as follows:(26)Aw1=1+1eb1′SA1B1C1,Aw2=1+1eb2′SA2B2C2J2,Aw3=1+1eb3′SA3B3C3J3,where eb1′, eb2′, and eb3′ can be calculated in Table 1; the expression of SA1B1C1, SA2B2C2J2, and SA3B3C3J3 can be found from equations (5), (9), and (13), respectively.
Therefore, the area ratio of the wall region for three boundary-packing types (λ1, λ2, and λ3) can be accordingly expressed as follows:
Type I:(27)λ1=Aw1SOA1B1=1+1/eb1′SA1B1C1SOA1B1.
Type II:(28)λ2=Aw2SOA2B2=1+1/eb2′SA2B2C2J2SOA2B2.
Type III:(29)λ3=Aw3SOA3B3=1+/1/eb3′SA3B3C3J3SOA3B3,where the section areas of SOA1B1, SOA2B2, and SOA3B3, which denote At in Type I, Type II, and Type III, respectively, are obtained as follows:(30)SOAiBi=D28θi,i=1,2,3.
Hence, considering the probability of boundary-packing types, i.e.,P1, P2, and P3, in Table 1, eb and λ can be expressed by(31)eb=ξ∑j=13ebj′Pj,(32)λ=∑j=13λjPj.Step 5.
correcting hydraulic conductivity. Substituting equations (31) and (32) into equation (25) yields the correction value of hydraulic conductivity for confined bed:(33)kt′=kt1+λeb+e⋅eb/e+e⋅eb3−1.
To verify the rationality of the proposed correction method, the constant falling head experiments conducted by Kango et al. [20] in a fixed wall cell with uniformly sized soils (e.g., sand, marble chips, and gravels) were used as a reference. The collected data of hydraulic conductivities with D/d < 40 are demonstrated in Table 2 because the permeameter boundary predominates over other factors’ influence on the permeability test results under such conditions. Unfortunately, since the values of emax and emin for these soil samples have not been provided in [20], the maximum and minimum void ratio of monodisperse sand in [26] shall be chosen to substitute them during the overall computational process, namely, emax = 0.786 and emin = 0.372. Additionally, kc in Table 2 representing the hydraulic conductivity of unconfined bed is measured with D/d greater than 120, where the wall effect is not significant concerning the permeability test results and the permeameter wall could be assumed to be infinite as well [20, 27].
Thekt/kc value was greater than the allowable error (i.e., 1.25) [3], indicating that the increase in kt is mainly because of extra void Vf in Figure 1 and greater boundary void ratio eb at the wall. After adopting the above procedures to revise these permeability test results, the correction values of hydraulic conductivity are also shown in Table 2. The ratio kt′/kc approximates one, indicating that the corrected hydraulic conductivity of confined bed is consistent with that of unconfined bed in the proposed method.
Though the proposed method can correct hydraulic conductivity to some extent, the limitations of the model lie in that the soil particles in the confined bed are simplified as mono-sized 2D disks, which differs from the natural deposits. As a result, it is desirable to treat the soil particles as 3D balls to establish a computational model for boundary void ratio. Besides, this method can only be applied to uniformly sized soils. Given the real granulometric composition of naturally occurring soil that is composed by grains of various dimensions, further investigations need to be carried out to enhance the method’s capability. It should also be noted that things become much more complex as more than two grain diameters are involved in developing a geometric model.Table 2
Summary of corrected hydraulic conductivities against observed values for confined soil bed.
No.
D (mm)
d (mm)
E
e
max
e
min
ξ
α
e
b
λ
k
c (cm/s)
Test results [20]
Correction value
k
t (cm/s)
δ
1 (%)
k
t
′ (cm/s)
δ
2 (%)
1
50.8
4.00
0.590
0.786
0.372
3.225
1.192
1.688
0.181
7.28
11.60
59.3
6.83
6.2
2
50.8
2.80
0.572
0.786
0.372
3.256
1.177
1.635
0.129
4.00
5.68
42.0
3.76
6.0
3
50.8
1.70
0.565
0.786
0.372
3.269
1.171
1.585
0.079
1.82
2.37
30.2
1.81
0.5
Note: absolute relative errorδ1=kt−kc/kc and δ2=kt′−kc/kc.


## 5. Conclusions

The boundary effect derived from fixed wall cell was investigated by analyzing the composition characteristics of voids close to sidewall, whereby the boundary void ratio (eb) was defined for quantifying the wall effect within confined bed. It appears that the extra void adjacent to rigid wall should depend upon the grain size, compaction level of soil bed, and permeameter diameter. It should be noted that eb is likely greater than the void ratio in the interior of the bed and contributes to the sidewall leakage during a permeameter test. Assuming that the soil particles of compacted bed are uniform disks packing in a plane, a geometric model for estimating eb was established. Based on this model and employing an empirical relationship between void ratio and hydraulic conductivity, a correction method for the measured hydraulic conductivity using a fixed wall permeameter was proposed. The experimental data from published literature verified the feasibility of this method for uniformly sized coarse-grained soils. Further developments regarding the correction method should take gradation characteristics into account and derive a generalized formula. Notwithstanding such limitations, it can be treated as a promising step towards providing reliable references for the application of a fixed wall permeameter in laboratory tests.



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