A New Method for the Estimation of Hydraulic Permeability, Coefficient of Consolidation, and Soil Fraction Based on the Dilatometer Tests (DMT)

Over the years, the development of geotechnics has begun using devices that allow for more and more accurate in situ testing. An example of such a device is a dilatometer presented in 1975 by Prof. S. Marchetti. A dilatometer is used very often because of its functionality – the measurement is performed in a short time and in an uncomplicated way, and at the same time, the range of results is representative statistics and usually gives a sufficient result, causing the abandonment of additional measuring equipment. Tests made with the use of a dilatometer test became the starting point for the considerations in this article, in which, the technique of their execution and methods of interpretation of the obtained results were discussed in detail.

Flat Marchetti dilatometer is a measuring device first presented in 1975 by Prof. Silvano Marchetti from Italy. The device measured horizontal deformation of the ground and was characterized by an uncomplicated structure – it consisted of a sharpened steel plate and a circular membrane placed at the shoulder. In his scientific work published in 1980, Marchetti described the dilatometer as a device for determining soil properties in situ test and developed empirical correlations between results of the DMT test and soil parameters used for geotechnical design purposes. This original publication, despite the passage of time, is still the basic source for analysing the results of tests carried out with the DMT probe. Further publications have contributed to the popularization of DMT research on a large scale. Currently, they are willingly used for the needs of engineering practice and scientific research activities in over 70 countries.

The study carried out with the Marchetti dilatometer gives three readings: A, B and C, on the basis of which, by making further calculations, geotechnical parameters of the soil are determined. The pressure values measured in the field should be corrected with values of DA and DB. The corrections take into account the stiffness of the diaphragm and the zero pressure gauge, and after their introduction, the pressure values are described by the following formulas:

where: p₀ – the 0.05 corrected pressure reading in DMT, p₁ – B-pressure reading corrected for Z_m and ΔB membrane stiffness at 1.10 mm expansion to give the total soil stress acting normal to the membrane at 1.10 mm membrane expansion, p₂ – C-pressure reading corrected for Z_m and ΔA membrane stiffness at 0.05 mm expansion and used to estimate pore water pressure, σ’vo – vertical effective in situ overburden stress at the centre of the membrane before insertion of the DMT blade, u₀ – pore water pressure acting at the centre of the membrane before insertion of the DMT blade (often assumed as hydrostatic below the water table), Z_m – gage pressure deviation from zero when vented to atmospheric pressure (an offset used to correct pressure readings to the true gage pressure).

The material index (I_D) is related to the soil behaviour type and not directly to the grain size (Marchetti, [1]). Marchetti observed that in the case of clays, the pressures p₀ and p₁ reach similar values, whereas for sands, these values diverge significantly. On this basis, the subsoil was divided into types depending on the value of the material index I_D.

Several methods have been developed to estimate the horizontal consolidation coefficient c_h using DMT pressure dissipation tests. The first method was developed by Robertson and Schmertmann in 1988; in response to their publication, Marchetti and Totani published their study in 1989 (e.g., Marchetti, [1]; Lutenegger and Kabir, [2]; Młynarek et al., [3]; Schmertmann, [4]; Marchetti and Totani, [5]; Lechowicz and Rabarijoely, [6]; Bałachowski, [7]; Młynarek et al., [8]; Młynarek et al., [9][10]; Long et al., [11]; Bihs et al., [12];Mayne, [13]; Zawrzykraj et al., [14]). The pressure dissipation tests proposed by the researchers use individual pressure measurements from DMT probing, which have been described in detail earlier. It should be mentioned that only total horizontal stress is measured during dissipation, and not effective stress.

The DMTA dissipation curves were published by Marchetti as early as in 1986, as part of a publication on the prediction of friction values on a blade of a dilatometer embedded in clays. An evident conclusion after this publication was that the decay rate of A dissipation in soils vary greatly depending on the permeability of the tested soil. In plasticity clays, a large part of the horizontal stresses affecting the dilatometer blade is the water pore pressure. It was easier to calculate as it is not necessary to measure the pore water pressure to determine later the horizontal coefficient of consolidation. The Robertson et al. in 1988^[15] DMTC method is based on the measurement of the p₂ closing pressure, while the Marchetti and Totani in 1989^[16] proposal uses a series of readings for the p₀ pressure. By determining the horizontal coefficient of consolidation, it is possible to later determine the hydraulic permeability of the tested soils.

2.1

DMTA method

The dissipation pressure curves A (DMTA) were published by Marchetti as early as in 1986, as part of a publication on the prediction pressure value in clay around the dilatometer blade. The distribution of horizontal stresses largely corresponds to the distribution of pore water pressure; therefore, a logical conclusion was that the approximate relationship would show horizontal stresses and a coefficient of consolidation in horizontal direction. In addition, the simplification of calculations was the fact that it is not necessary to measure the pore water pressure to determine later the coefficient of consolidation in horizontal direction (e.g., Totani et al., [17]; Schnaid et al., [18]).

The procedure necessary to determine the coefficient of consolidation in horizontal direction by the DMTA method is to measure the dissipation pressure A over time. The dilatometer’s blade is stopped at a given depth and a series of A readings is performed at the appropriate time interval. Most often, pressure A is measured in minutes 0.5, 1, 2, 4, 8, 15, 30 and 60. The measurement series are placed on a graph. An example of the DMTA decay curve from the Stegny site is shown in Figure 1 A-T, which shows the time distribution of pressure A. The classification is used to later determine the t_flex time, and the time is read at the inflexion point of the curve (e.g., Marchetti and Totani, [5]).

Figure 1

The coefficient of consolidation in horizontal direction c_h can be calculated as follows:

(8)Ch=7cm2tflex,m2yr$${{C}_{h}}=\frac{7c{{m}^{2}}}{{{t}_{flex}}},\left[ \frac{{{m}^{2}}}{yr} \right]$$(9)kh=chγwMh,cms$${{k}_{h}}=\frac{{{c}_{h}}{{\gamma }_{w}}}{{{M}_{h}}},\left[ \frac{cm}{s} \right]$$

where: t_flex – the time to reach the contraflexure point in the A-log t curve, k_h – coefficient of permeability, M_h – constrained modulus in horizontal direction, γ_w – water unit weight.

2.3

SASK-2 method

In the SASK-2 method proposed for the determination of hydraulic conductivity of soils, time varying pressures measured by DMT during the return of the deformed membrane to the position of the plane blade (pressures C) are used. The return of the DMT membrane is caused by groundwater pressure (Figure 2). The stream of groundwater flow at a variable pressure gradient depends on the deflection of the membrane geometry and time. To calculate hydraulic conductivity (k), the following formula is proposed:

Figure 2

(11)k=Qp1−p2⋅lA⋅t2⋅lnp1p,cms$$k=\frac{\frac{Q}{{{p}_{1}}-{{p}_{2}}}\cdot l}{A\cdot {{t}_{2}}}\cdot ln\frac{{{p}_{1}}}{p},\left[ \frac{cm}{s} \right]$$

where: Q – volume of groundwater flow equal to the volume of a sphere section formed from the deformed membrane (cm³), p₁, p₂ – the maximum pressure needed to deform a membrane of 1.1 mm and the pressure at the return of the membrane to the plane of the blade (cm H₂O), respectively, l – average range of the ground involved in the groundwater flow (cm), A – average cross-sectional area of the ground involved in the flow of water (cm²), t₂ – time of groundwater flow (suggested t₂ = t_flex).

The most important assumption is that during the return of the DMT membrane, the groundwater flow is variable depending on the changes in the hydraulic gradient. Therefore, the total volume of groundwater (Q) and the time varying hydraulic gradient should be determined. The course of changes in the water volume due to the deflection of the membrane was determined from dilatometer tests used in the spherical soil space (Figure 2).

As a result of membrane deformation, a solid similar to the segment of a sphere is formed; its volume can be calculated from the formula:

(12)Qk=π⋅h233R−h0,cm3$${{Q}_{k}}=\frac{\pi \cdot {{h}^{2}}}{3}\left( 3R-{{h}_{0}} \right),\left[ c{{m}^{3}} \right]$$

where: Q_k – volume of the sphere segment (cm³), h – deflection of the membrane (cm), R – radius of the sphere (cm) calculated from the formula:

(13)R=r2−h022h,cm$$R=\frac{{{r}^{2}}-h_{0}^{2}}{2h},\left[ cm \right]$$

r – radius of the membrane (cm), h0 – membrane deflection.

The dilatometer’s membrane radius is 3 cm; therefore, Q_k is 1.56 cm³. The value of membrane surface A is 28.27 cm².

This paper presents the test results of mineral and organic subsoils obtained from the Nielisz site located in the Wieprz river valley in the Lublin province, the SGGW Campus site with the Department of Geotechnical Engineering SGGW, and the Stegny site located in Warsaw, where a laboratory and field testing programme was performed. The location of all analysed objects is shown in Figure 3. The index properties of mineral and organic soils and the grain size distribution curve obtained from laboratory tests for mineral soil from the described sites is presented in Table 1 and Figure 4 (Interim reports^[22]).

Figure 3

Figure 4

The test results of p_o, p₁, p₂, I_D, K_D and E_D profiles from DMT investigations were used to determine later the practical usefulness of the created chart (Figures 5, 6 and 7). These studies were carried out in the Geoengineering

Figure 5

Figure 6

Figure 7

Department of the Warsaw University of Life Sciences, concerning sites located at the Nielisz dam, the Stegny site and the SGGW Campus, Warsaw University of Life Sciences.

Obtaining the value of the cv coefficient of vertical consolidation is usually done by performing a standard one-dimensional test, where the time factor of soil compression is obtained. After data acquisition, further analysis is carried out in the curve fitting procedure. The one-dimensional consolidation test is an experimental method and does not entirely coincide with Therzaghi’s theory of consolidation, on which the curve selection procedure is based (Sridharan and Nagaraj, [23]). The coefficient of vertical consolidation cv was determined according to the following formula (Terzaghi et al., [24]).

where: h – length of the filtration path [m], t₅₀ – time required for 50% consolidation to occur.

It is possible to determine the coefficient of consolidation cv using the effective vertical overburden stress and the material index (I_D) values. Based on these parameters, a formula was constructed. The advantage of this formula is the fact that it depends, among others, on the material index (I_D) and the effective vertical stress σ’_vo, where the tested soils may have the same state but a different s undrained shear strength at different stress histories. Therefore, the relationship is proposed as follows:

where: A = -1.72; B = 0.4; C = 0.17; D = 0.81; E = -0.39; F = 1143; G = -0.2; H = 1.5; I_D [-] – material index; σ′v${{{\sigma }'}_{v}}$– vertical effective overburden stress [kPa].

Using formula (15), a proposition of the empirical formula enabling the calculation of the vertical coefficient of consolidation (cv) is presented. The original of an empirical dependence requires comparison of its results with the results obtained on the basis of already performed studies. The results of tests, to which the results from the proposed model will be compared, were taken from the archives of the Department of Geoengineering SGGW in Warsaw. Results of tests carried out at the Nielisz dam were analysed. Calculations for the empirical correlation were made in the Solver modulus. Formula (15) has been optimized to describe the results from the comparative tests as close as possible. For this purpose, calculations of relative deviations based on formulas were used.

Maximal Relative Deviation (MRD):

Mean Square Relative Deviation (MSRD):

For this purpose, the calculations of relative deviations were based on the formulas for which mean square relative deviation MSRD = 11% and the maximum relative deviation MRD = 17 % were used.

Based on the extrapolation of vertical displacement results (geodesy measurements), total settlement S100 (resulting from the initial consolidation) was determined, which allowed to estimate the value of S50 constituting 50% of the total settlement value and time t₅₀. The calculated values of the coefficient of consolidation (cv) on the basis of field measurements of vertical displacements and the length of the filtration path h and t₅₀ were determined according to formula 14.

Figure 8 shows the coefficient of vertical consolidation values calculated from equations (14) and (15) in order to compare the values obtained by various calculation methods. It is recommended to check the effectiveness of this method in another region of Poland.. A comparison of the results measured and calculated using the proposed method is presented in Figure 8. The highest deviation from the obtained results occurs in the profile on the hectometer of 4 + 50 upstream at an elevation of 192.50 m.a.s.l, while the most similar results were obtained for the profile on the hectometer of 4 + 10 downstream, differing only by 4%.

Figure 8

The last stage of the work was to create a nomogram showing the relationship between hydraulic permeability k_h and time t_flex. The data used to construct the graph were obtained from DMT tests carried out at the Nielisz dam and at Stegny sites. The main purpose of this chart is to show the dependence between the type of soil, whose soil fractions have been plotted on the graph, the hydraulic permeability, and sometimes t_flex, which is an important part of the methods used for determining soil hydraulic permeability parameters with during the exploratory survey tests.

The following equation was used while making the graph

where: pt_flex – normalized p₀ (the 0.05 corrected pressure reading in DMT), σv – vertical total in situ overburden stress

The equation is a relationship between vertical effective stress, vertical total stress and p₀ pressure with an empirical coefficient, expressing the pt_flex function. With basic soil parameters, such as vertical total stress, pore water pressure, and the t_flex time value, hydraulic permeability can be determined. Values of hydraulic permeability presented in Figure 9 were obtained after the proposed DMT tests described in this paper, using the BAT system.

Figure 9

The obtained values of hydraulic permeability from the proposed nomogram chart are comparable to those obtained directly after probing or from the calculation methods. We can see a slight disproportion between the results from the SASK method and the results from the nomogram chart; the values differ by about one order of magnitude. The results obtained for the Stegny site may be slightly inaccurate due to the shortcomings in the t_flex time data for all the measuring depths (Rabarijoely, [25]).

The nomogram can be used in several ways depending on the data available to the user. With t_flex time and the tested soil, the engineer can read the approximate hydraulic permeability (on the nomogram chart moving from point A to B, then to C), or knowing the hydraulic permeability and the thickness of the soil, can read the approximate t_flex time (moving around the nomogram chart from point C to B, then to A). Another application may be the possibility to determine in a given area of the main division of soil fractions and its type, knowing the value of hydraulic permeability and t_flex time. The calculation method for using the nomogram chart is to apply the Pt_flex function by means of the effective and total vertical stress of the soil, and the pressure p₀. The nomogram chart is applied in the case of specifying characteristics for clays or silts, such as those in the sites studied, and soils with a very small grain size. The proposed nomogram chart was used to compare the values of hydraulic permeability obtained from the tests by several methods (Figure 10).

Figure 10

The dilatometer test (DMT) is widely used for determining the characteristics of soil permeability and the soil fractions content. On the basis of soil analysis performed in three sites (Nielisz, Stegny and WULS-SGGW Campus), the following conclusions may be drawn.

The aim of the article was to provide information on the methods of obtaining soil hydraulic permeability parameters. Largest attention was devoted to the DMTA and DMTC methods and the SASK method, which were used in the computational part of the work. The proposed relationship between DMT, t_flex and soil hydraulic permeability parameters, and normalized pressure, p₀ was based on the results of dilatometer tests derived from DMT research under the Nielisz dam and in the Stegny site, which has been optimized accordingly. The obtained results are satisfying. The nomogram chart can be used for organic mud, mud, clays, silts or fine sands. The results derived from the archives of the Department of Geoengineering, SGGW were compared with the results read from the proposed nomogram chart. The proposed relationships show features of compliance with geotechnical conditions prevailing in reality.

A proposal of nomogram charts for determining the percentage of each fraction was created based on p₀, p₁. These nomogram charts are aimed at obtaining the approximate value of the fraction using the results of dilatometer pressures (DMT). These charts may limit to some extent the number of additional laboratory tests. Thanks to the empirical method established, the excessive amount of research needed to assess soil fraction may be reduced.