Evaluating hydraulic parameters in clays based on in situ tests

1 Introduction

The properties of fine-grained soils are of interest to many researchers involved in the study of the influence of factors related to the properties of the flowing fluid (e.g., viscosity and density) and the soil medium (e.g., void ratio, effective stress, and degree of water saturation) on hydraulic permeability. Hydraulic parameters of the soil medium are used in environmental and geotechnical studies [1,2,3], to assess the impermeability of filtration diaphragms in hydrotechnical structures [4,5], and the prediction of ground settlement under engineering structures [6]. Thus, the evaluation of the hydraulic parameters and the assessment of the speed of water flow in the soil medium in many cases are crucial.

Soil permeability may be obtained from direct methods, such as field studies [5,7,8,9] and laboratory investigations [10,11], as well as indirect ones. The latter include, e.g., determining hydraulic permeability from grain size distribution curves [12,13,14], consolidation tests [15], based on the analysis of the dissipation time of excess pore water pressure [16,17,18,19,20] and dissipation time of the A or C readings in Marchetti’s dilatometer tests [21,22,23].

One of the commonly used methods to evaluate hydraulic parameters is the CPTU test (cone penetration test with pore pressure measurements – general information on the design and methodology of the CPTU tests is widely reported in the literature [16,17,18] and is briefly described in Section 2.3). Large values of excess pore pressures (Δu) are generated during this test. The soil hydraulic parameters can be determined from peak fluid pressure recorded on-the-fly [24] or by measuring the time at which the excess pore water pressure is dissipated [16,17,18].

The results of dissipation tests from CPTU analysis are presented in the form of a relationship between the logarithm or square root of time and normalized pore pressure. Dissipation curves obtained during the investigations may be standard (monotonic), when the excess pore pressure disappears from the moment when the probe stops. The coefficient of permeability can be determined based on time t ₅₀ directly from Parez and Faureil equation [25] or with measured time for each degree of consolidation and the corresponding time factor (T) derived from the two main analytical approaches: cavity expansion theory and strain path method, if the observed dissipation curve matches the theoretical models [26,27,28].

Non-standard dissipation curves are characterized by further increase of the excess pore pressure to a maximal value (Δu _2max), followed by its decrease [16,17,29,30,31]. This type of dilatory response is observed, e.g., in heavily overconsolidated soils, and as has been already described and discussed by Ha et al. [32], in soils in higher over consolidation ratio (OCR) values, a higher excess pore pressure is expected to propagate and dissipate. In the case of dilatory dissipation, the standard approach for interpreting dissipation results in normally consolidated soils cannot be applied, since dissipation does not follow the theoretical response, i.e., monotonic reduction with time. To approximately assess coefficient of consolidation (c _h) from the dilatory dissipation curve, empirical data modification techniques, such as the offset method and the square root of the time plot correction method, have been suggested [30,33,34]. Chai et al. [34] carried out a numerical simulation of piezocone penetration and dissipation employing the theory of contact mechanics and proposed an empirical equation for correcting the value of t ₅₀ to interpret the dilatory dissipation curve as used in the calculations in this article.

Performing dissipation analysis during CPTU tests and interpretation of the obtained results are linked with numerous issues. They include correct air removal from the measurement system of the cone [28,35], restricted test duration [36], assessment and interpretation method of the dissipation results – e.g., incomplete dissipation curves [19,20] or correct determination of time t ₅₀ from non-standard curves [20,34].

There are very few solutions for determining the permeability coefficient based on CPTU tests presented in the literature omitting parameters obtained from dissipation tests. These on-the-fly methods offer an alternative approach in which hydraulic parameters are directly linked to CPTU penetration measurements. Examples of such solutions are empirical relationships [35,37] for assessing the permeability coefficient based on soil behavior-type index, normalized cone resistance and normalized friction ratio which are calculated as follows:

where Q _t is the normalized cone resistance (−), F _r is the normalized friction ratio (%), q _t is the corrected cone resistance (MPa), σ v0 ′ is the in situ effective vertical stress (MPa), and σ _v0 is the in situ vertical stress (MPa).

One of the methods that allows us to calculate the permeability is based on combining dislocation and cavity expansion analysis [24,38] (further developed by Shen et al. [39] and Monforte et al. [40]). Elsworth and Lee proposed the following relation:

where Δu is the excess water pressure at u ₂ position (MPa), v is the rate of cone advance (m/s), r is the radius of the cone (m), γ _w is the water unit weight (MN/m³), k is the coefficient of permeability (m/s), and K _D is the dimensionless permeability (−).

The dimensionless permeability can be determined directly from the CPTU metrics: normalized cone resistance and pore pressure ratio according to:

where B _q is the pore pressure ratio (−).

Elsworth and Lee’s proposal to use on-the-fly method based on K _D ratio according to some researchers [24], does not allow us to estimate the coefficient of permeability in overconsolidated cohesive soils which are the subject of this research.

This article focuses on the evaluation of the consolidation and permeability coefficients of soils based on monotonic and dilatory dissipation results of piezocone tests in overconsolidated clays as well as those cemented. The calculations were based on various empirical relationships proposed by Torstensson [26], Teh and Houlsby [27], Parez and Faureil [25], and Robertson and Cabal [41]. Non-standard dissipation curves have been corrected according to the recommendations of Sully et al. [30] and Chai et al. [34]. Due to the difference between the various approaches, the authors proposed to evaluate the permeability directly from the CPTU metrics. First to be proposed is a formula for determining the coefficient of permeability based on the soil behavior-type index I _c. Results of CPTU tests were verified using data from the BAT groundwater monitoring system. Values of the permeability coefficient obtained from BAT soundings were treated as reference ones.

2 Methods

2.1 Location and characteristics of the test sites

The first test site – SGGW Campus – is located in the southern part of Warsaw, Poland (Figure 1). It covers the margin of a denudated moraine plateau in the marginal zone of the Vistula River valley. In the Ursynów district, its deposits form a continuous, distinct layer, consisting mostly of fine sands. Above the fluvioglacial sediments occur glacial deposits from the Odranian Glaciation, represented by grey boulder clays. The thickness of the clay layer is from several to tens of meters and in the case of the SGGW Campus it is between 6 and 10 m. In some places, the Odranian boulder clays are covered by fluvioglacial sands and gravels and/or ice-dammed silts. Above them or directly on the boulder clays, occur glacial tills from the Wartanian Glaciation (the last glaciation in this area).

Figure 1

Location of the SGGW campus and the Stegny site.

Considering the physical and mechanical soil properties in the SGGW Campus test site, there are four geotechnical layers. The first layer, with a thickness of about 3 m, consists of fluvioglacial sediments of the Wartanian Glaciation: medium and fine sands (MSa, FSa), with a relative density D _r = 0.35–0.55. The second layer (about 3 m thick) comprises brown glacial boulder clays (sisaCl) of the Wartanian Glaciation and sandy clays (saCl), with a consistency index I _c = 0.9–1.0. The third layer (about 4 m thick) includes grey glacial boulder clays (sisaCl) of the Odranian Glaciation and saCl with boulders, with a consistency index I _c = 0.88–1.0. The last layer underlies the fluvial deposits of the Mazovian Interglacial: fine and medium-grained sands in the top of a very dense layer with relative density D _r = 0.8–0.9.

In situ investigations were conducted at four localities on the SGGW Campus site and included CPTU, SCPT (seismic cone penetration test), and BAT (groundwater monitoring system [7]) tests. The position of these localities and the survey points is shown in Figure 1. Moreover, the chart proposed by Robertson based on CPTU test results was used to verify the soil types obtained in the profile. This nomogram clearly illustrates the differences between the brown and grey boulder clays. It indicates significant overconsolidation and cementation of the brown clay (Figure 2).

Figure 2

Typical borehole profiles and the chart of Robertson based on CPTU tests.

The second test site – the Stegny site – is located northeast of SGGW campus in a Vistula River (Figure 1). For several years, an extensive research program has been carried out here by the Warsaw University of Life Sciences and other research institutions. The main purpose of this study was to evaluate the clay parameters and to protect the water intake located at the site. The stratigraphy consists of Quaternary deposits developed as fine and medium dense sand up to a depth of 4.5 m. The underlying layers consist of high plasticity clays with random traces of silt.

The three CPTU tests and the closest BAT measurements were used to interpret the data. The Robertson’s chart (Figure 2) indicates that the investigated cohesive soils are overconsolidated clays (Cl) and silty clays (siCl).

2.2 Site investigation methods

CPTU soundings are commonly applied in engineering practice for many years. The methodology and interpretation of the results, including assessment of hydraulic parameters, have been widely discussed in numerous reports [17,29,41,42]. Data from dissipation tests in CPTU analysis are interpreted using empirical relationships and nomograms commonly applied in engineering practice and based on the correlation between data measured in the field and data from laboratory investigations. BAT tests, as opposed to dissipation of excess pore water pressure, are based on actual measurements of the volume of water flowing into the medium. Analysis of hydraulic permeability includes injecting water from the measurement unit to the surrounding soil through a filtering gage (outflow test) or by groundwater uptake from the surrounding soil (inflow test). Pressure change in the measurement device allows us to calculate the permeability coefficient according to the formula proposed by Torstensson [7].

Table 1 presents the schemes, description, and application of the described probes, whereas Table 2 lists the relationships allowing us to calculate the consolidation and permeability coefficients based on CPTU and BAT tests.

Table 1

Schemes of geotechnical probes used in the tests

Scheme	Description	Application
	CPTU	Identification of the soil type Determination of geotechnical soil parameters (based on empirical relationships):
	1 – Friction sleeve
	2 – Filter
	3 – Cone
	CPTU sounding consists in pushing the cone penetrometer into subsoil at the rate of penetration about 20 mm/s. The standard cone installed at the end of the rods has an apex angle of 60° and a 10 or 15 cm2 base area
		relative density (D r), consistency index (I c), undrained shear strength (s u = τ fu), effective vertical stress (σ v0′), OCR, coefficient of earth pressure at rest (K 0), constrained deformation modulus (M), Young’s modulus (E), initial shear modulus (G 0), coefficient of permeability (k), coefficient of consolidation (c h), shear wave velocity measurements (V s), electrical resistivity measurements (SCPTU and RCPTU cones)
	During the CPTU test, the following data are recorded: depth, cone resistance (q c), sleeve friction resistance (f s), and pore pressure behind the cone (u 2)
	BAT System	Sampling of ground water or gas; Measurement of pore water pressure; In situ testing of coefficient of permeability; Tracer test for monitoring ground water flow
	1 – Pressure transducer
	2 – Transfer nipple with hypodermic needle
	3 – Extension adapter
	4 – Test container
	5 – Quick coupling sleeve
	6 – Filter tips – with a diameter of 30 mm and a height of 100 mm
	The BAT system enables the monitoring of the water-soil environment and the determination of the parameters of water flow in in situ conditions. The measuring unit is a set of membranes, needles, glass test containers and a pressure transducer. Installation of the BAT groundwater monitoring system is similar to a CPTU cone and uses rods of very similar size (rods differ only in internal diameter)

Table 2

Relationships determining the hydraulic parameters used in the calculations

	Empirical relationship	Author	Explanations of symbols
CPTU	c h = T 50 ⋅ r 0 2 t 50	Torstensson [26]	c h – coefficient of consolidation (m2/s)
			k – coefficient of permeability (m/s)
			t 50 – measured time for 50% dissipation (s)
			T 50 – theoretical time factor (−), (u 2 − T 50 = 1.2)
	k = 1 ( 251 t 50 ) 1.25	Parez and Fauriel [25]
			T* – modified time factor (−), (T* = 0.245)
			I r – rigidity index (I r = G/s u)
	c h = T ⁎ ⋅ r 0 2 ⋅ I r t 50	Teh and Houlsby [27]
			r 0 – penetrometer radius (m), (r 0 = 0.0178)
	c h = ( 1.67 ⋅ 10 − 6 ) ⋅ 10 1 − log t 50	Robertson [43]
BAT	k = P 0 ⋅ V 0 F ⋅ t ⋅ 1 P 1 ⋅ P 0 − 1 P 1 ⋅ P t + 1 P 1 2 ⋅ ln P 0 ⋅ P 1 P 0 ⋅ P t P t − P 1		k – coefficient of permeability (m/s)
			P 0 – initial container pressure (m)
	Torstensson [7]
			t – time (s)
			u 0 – hydraulic pore pressure (m)
			P t – container pressure in time (m)
			F – filter constant (−)

2.3 Saturation of piezocones

Measurement of correct pore pressure values requires appropriate preparation of all elements of the measuring system. To achieve good pore pressure response during a piezocone test, it is necessary to have a very rigid pore pressure measuring system and a fully saturated system. The fluids used to saturate usually include de-aired water, silicone oil, or glycerine.

Historically, de-aired water was a commonly used saturating fluid, although water presents problems at low temperatures; maintaining saturation before penetration below the groundwater level may also be difficult [28]. It may also lead to loss of filter saturation, especially when testing heavily overconsolidated soils. In contrast, silicone oil and glycerine are characterized by high density and high surface tension, which makes them less susceptible to being sucked out of the filter during testing. However, these characteristics may also pose issues to the equipment and personnel.

A commonly used procedure for saturation of the filter element is to place it in the saturation fluid in an airtight container and then subject it to high vacuum for about 2 h [28]. A glycerine was used as the saturation fluid, following the procedures proposed by Robertson and Campanella [44] and Larsson [45], with some modifications.

The method used herein has been tested many times and has already been patented [46]. The filter saturation process consists of two stages. In the first stage, filters immersed in warm glycerine (60°C) are vibrated (at a frequency of about 38 kHz) in an ultrasonic cleaner for 60 min (Figure 3a). In the second stage, the filters and glycerine are placed in a container and vibrated at 50 Hz on a vibrating table for 45 min. The next stage, according to the procedure described by Larsson, consists of placing the filter and cone in a rubber funnel, pouring glycerine over the whole object (Figure 3b and c), assembling the cone and securing it with a protective rubber sleeve (Figure 3d).

Figure 3

De-airing (a), mounting filter element (b and c) and protecting the cone (d) when using glicerine.

3 Results and discussion

Results of CPTU and SCPTU tests carried out at SGGW Campus are presented in Figure 4, i.e., normalized cone resistance – Q _tn, sleeve friction resistance – f _s, friction ratio – R _f, pore pressure – u ₂, normalized soil behavior type index I _c, and shear wave velocity V _s. The results obtained from four different localities in the SGGW Campus test site do not differ significantly, and the values of index I _c and the shear wave velocity V _s indicate the presence of identical soils in the analyzed profile (depth interval 4–10 m) within the entire object. Shear resistance of the brown clay attains values s _u = 250–350 kPa, and of the grey clays s _u = 200–300 kPa. The rigidity index of the analyzed soils oscillates at about I _r ≈ 175 and I _r ≈ 150.

Figure 4

CPTU test results – SGGW Campus.

Dissipation results of excess pore water pressure obtained from the SGGW Campus clays are presented as normalized curves in Figure 5. Dissipation curves of excess pore water pressure in grey boulder clay from depth levels 8.60, 8.62, 8.74, 9.06, and 10.08 m are standard curves. The time required to dissipate 50% of excess pore water pressure was estimated to be 108–198 s (Figure 6).

Figure 5

Dissipation curves for clays from the SGGW Campus test site.

Figure 6

Interpretation of standard curves – grey boulder clay (SGGW Campus).

Dissipation curves for brown boulder clay from depth levels 5.36, 5.52, and 5.98 m are non-standard curves. Sully et al. [30] and Chai et al. [34] suggested three methods of correcting dilation curves. The method proposed by Chai et al. includes the determination of a point on the normalized time curve (t _Nmax), after which excess pressure attains the maximal value (u _max); from this moment the time (t ₅₀) required for dissipation of 50% of the maximal pressure is measured (Figure 7). Based on numerical analysis, the authors of this solution have proposed a formula correcting the obtained t ₅₀ value.

where t _50m is the corrected time for 50% excess pore pressure dissipation (s), t ₅₀ is the time for 50% excess pore pressure dissipation (s), t _Nmax is the time for the measured excess pore pressure to reach its maximum value (s), and I _r – rigidity index (−).

Figure 7

Interpretation of non-standard curves after Chai et al. [34] – brown boulder clay (SGGW Campus).

Moreover, numerical analyses performed by the authors of the formula presented above have indicated that soil rigidity does not essentially influence the value of t _Nmax, but has impact on time t _50m, which decreases with increase in rigidity index I _r. In the case when non-standard curves are interpreted, the t _50m value may be successfully substituted into the equation proposed by Teh and Houlsby [27].

Figure 8 presents the interpretation of dissipation curves proposed by Sully et al. [30]. Values of excess pore water pressure are presented as a square root of time and the interpretation of 50% of pressure dissipation includes setting a tangent to the falling curve and determining the maximal value on the pressure axis – u _max. Based on the u _max and u ₀ values, time t ₅₀ is determined.

Figure 8

Interpretation of non-standard curves after Sully et al. [30] – brown boulder clay (SGGW Campus).

The third method of interpreting non-standard curves consists in drawing a normalized dissipation curve only in the range from the maximal value to the complete dissipation of excess pore water pressure. This method allows for determining time t ₅₀, and the result does not differ significantly from that obtained using the method of Chai et al. [34], the only exception being the lack of t ₅₀ correction.

Results of calculating the consolidation and permeability coefficients for clays from the SGGW Campus site are presented in Table 3 (standard dissipation) and Table 4 (non-standard dissipation).

The obtained values of the permeability coefficient are most consistent in the case of the relationships indicated by Teh and Houlsby [27] and Robertson and Cabal [41], both for standard and non-standard curves. Figure 9 illustrates the permeability values calculated according to these relationships and those calculated from the Torstensson [7] relationship against the values determined from the BAT studies. Values of the permeability coefficient vary from 8.43 × 10⁻¹⁰ to 1.55 × 10⁻⁹ m/s for brown clays, and 4.31 × 10⁻¹⁰ to 6.53 × 10⁻¹⁰ m/s for grey clays. Values for brown clays were obtained following interpretation of non-standard curves and correction of time required for 50% dissipation of excess pore water pressure according to the recommendations of Chai et al. [34].

Figure 9

Error plot between permeability values determined from empirical relationship and BAT tests.

Interpretation of the results according to the proposal of Sully et al. [30] gave similar results; this proposal may thus be used to interpret dilation curves. Permeability coefficient values calculated with application of the relationships proposed by Torstensson [26] and Parez and Faureil [25] differ by an order of magnitude in both directions in comparison to the remaining ones. Summing up, it may be concluded that the stiffer brown clays display slightly higher values of the permeability coefficient.

In order to verify the obtained results of the permeability coefficient for the analyzed soils, they were correlated with data from the BAT groundwater monitoring system. The permeability coefficient was measured in all four locations and at three depth levels in each test profile. The BAT results are presented in Figure 10, whereas the calculated permeability coefficient values were assumed as reference values.

Figure 10

Results of BAT tests – SGGW Campus.

Analysis of the BAT results indicates that the permeability coefficient for clays from the SGGW Campus test site is in the range of 1.17 × 10⁻⁹ and 4.85 × 10⁻⁹ m/s. Similarly, as in the case of the CPTU sounding, higher values were obtained for brown clays.

Investigations on the Stegny site aimed at verification of the obtained relations between the coefficient of permeability and the soil behavior type index I _c. Detailed analysis of the CPTU tests has shown that the Pliocene clay layer is interlayered with a layer of silty clay at depths between 12.6 and 14.4 m (Figure 11a). The soil behavior-type index I _c in clays attain values between 2.95 and 3.30, while in silty clays the I _c values are between 2.60 and 2.95. Both the former and latter ranges of values do not match those determined for boulder clays in the subsoil of the SGGW Campus. The BAT system results (Figure 11b) indicate that the permeability coefficient:

• for clays are in the range of 1.5 × 10⁻¹¹ and 4.3 × 10⁻¹¹ m/s,

• for silty clays this value is 2.1 × 10⁻¹⁰ m/s.

Figure 11

CPTU (a) and BAT (b) test results – the Stegny test site.

3.1 Determination of permeability based on soil behavior-type index I _c

Correlation between time (t ₅₀) and consolidation (c _h) or permeability (k _h) indexes presented above is based on a specific dataset from in situ studies. There are relatively few simple solutions in the literature, which would definitely allow us to assess the hydraulic parameters of cohesive soils. These solutions have a number of restrictions, as for example in the proposal of Ansari et al. [47]. It focuses on standard and non-standard dissipation curves and includes correction of time t ₅₀ taking account of vertical effective strain and rigidity index I _r, whereas the permeability coefficient is calculated from a simple relationship. The proposal allows us to assess the permeability coefficient for soft clays but in fact can be applied only to soils with OCR < 1.2. Similar is the problem with on-the-fly method proposed by Elsworth and Lee [24], which is not applicable to overconsolidated and highly dilative materials. Experimental work by Chai and Chanmee [48] with reconsolidated clay samples confirmed this limitation.

The proposed method to assess the permeability coefficient directly from CPTU metrics consists of using index I _c according to the concept presented by Robertson and Cabal [41]. According to the calculations, in the analyzed profile of brown and grey boulder clays (depth interval 4 ÷ 10 m), the values of this index vary between 2.1 and 2.5. Values of index I _c presented by Robertson [49] exclude, e.g., heavily overconsolidated and cemented fine-grained soils, such as the brown soils from depth interval 4–6 m in the analyzed profile. Nevertheless, we have agreed to relate the permeability coefficient to index I _c, because, as indicated, the chart is global in nature and provides only a guide to soil behavior type. The overlap in some zones should be expected and the zones should be adjusted somewhat based on local experience.

As shown in Section 4, the results of the coefficient of permeability calculations gave a large scatter of values. Therefore, the results of BAT system measurements were considered as reference values. Based on these quantities, the following solutions are proposed (Table 5).

Table 5

Proposed formulas for evaluating clay permeability in experimental fields

I c	Estimated permeability coefficient (m/s)	Soil description
2.05–2.60	k = 10 − 5.65 I c	sisaCl, saCl (SGGW)
2.60–2.95	k = 10 − 5.80 I c	siCl (Stegny)
2.95–3.30	k = 10 − 5.95 I c	Cl (Stegny)

k is the coefficient of permeability (m/s) and I _c is the soil behavior type index (−).

Figure 12 shows the variability of index I _c in the analyzed profiles, the reference values of the permeability coefficient from BAT investigations, and predicted values based on the proposed relationship. Predicted values of the permeability coefficient at SGGW Campus are slightly higher in brown clays, which is in accordance with the results obtained from dissipation curves. Higher values of the permeability coefficient, in accordance with other observations [34,47], were observed for brown clays for which the rigidity index attains higher values than for grey clays, at I _r ≈ 175. This trend is also observed in the case of BAT data.

Figure 12

Predicted values of the permeability coefficient in the background of BAT system measurements – SGGW Campus and the Stegny sites.

4 Summary and conclusions

The article assesses the hydraulic parameters of heavily overconsolidated clays based on analysis of dissipation of excess pore water pressure from CPTU tests and BAT groundwater monitoring system data. Dissipation curves from piezocone tests were both monotonic and dilatory in character, expressed by initial momentous increase of pore pressure, followed by its decrease. The empirical relationships between time (t ₅₀) and consolidation (c _h) or permeability (k _h) indices presented in the article are widely used, but their practical application requires considering other soil parameters that need to be determined, such as rigidity index, deformation parameters, and stress history. Furthermore, if we add the possibility of obtaining a standard or dilatory dissipation curve and the ability to correct the t ₅₀ time, the resulting permeability values may differ. These differences were observed in our studies when adopting different approaches to interpreting the curves and applying various formulas found in the literature. The analysis of pore water pressure dissipation curves has led to the following conclusions:

• Brown boulder clays, located on Robertson’s chart in the zone of heavily overconsolidated and cemented soils, have dilatory dissipation of excess pore water pressure, whereas grey boulder clays, located on the chart beyond this zone, are characterized by monotonic dissipation.

• With increase of rigidity index I _r for the analyzed soils, the time required for the dissipation of excess pressure t ₅₀ (t _50m) decreased and, in consequence, the value of the permeability coefficient of the analyzed clays increased.

• Analysis of non-standard dissipation curves confirms that a longer time required to achieve the maximal pore pressure (u _max) results in a longer time needed to dissipate its excess.

• Similar values of the permeability coefficient were obtained with application of equations proposed by Teh and Houlsby [27] and Robertson and Cabal [41]. These values differ from the reference values obtained from BAT analyses. Values calculated with the use of equations proposed by Torstensson [26] and Parez and Faureil [25] differ by two orders of magnitude compared to the above.

Taking into account these conclusions and based on the performed investigations, three equations were proposed for the calculation of the permeability coefficient (Table 5). The proposed relationships are simple in form and enables quick assess of the permeability of overconsolidated clays based on the CPTU test. It should be emphasized that the proposed formulas may be applied for overconsolidated cohesive soils with index I _c values in the range of 2.05 ≤ I _c ≤ 3.30 and described in Robertson’s chart as overconsolidated silty clays and heavily overconsolidated and cemented fine-grained soils. For other values of I _c, the equation must be adapted to local conditions.

While observing the differences in obtained results, it should be considered whether the use of empirical relationships and the method of pore water pressure dissipation for assessing the permeability coefficient in cohesive soils should be decisive. In crucial cases, direct measurements should be conducted or undisturbed soil samples should be taken and tested in a laboratory under more controlled conditions. In the literature, there are relatively few straightforward solutions available for assessing the hydraulic parameters in cohesive soils. In simple cases, it may be recommended to estimate the hydraulic parameters based on a simple relationship and in an approximate manner. However, it is important to keep in mind the limitations of empirical formulas and requires verification on a larger dataset from other study sites. However, it is important to bear in mind the limitations of empirical formulas and the necessity of verifying their results using a larger dataset from various study sites.