Evaluation of the relative density based on flat dilatometer test

To check the compaction of noncohesive soils present in the embankment and its base, as well as the deformation and strength parameters of noncohesive and organic soils, DPL testing and DMT were conducted at six selected locations in pairs (i.e., DPL testing with DMT at each location). The use of a DPL to assess the relative density of soil is a well-known method employed in engineering practice for decades (e.g., Meardi, 1971; Borowczyk and Frankowski, 1981; Pinheiro et al., 2018; Gruchot, 2019). Interpreting the results of DPL tests based on the standards issued in Poland can raise several doubts. The value estimated for the relative density D_r may significantly differ depending on the interpretation method applied (Borowczyk and Frankowski, 1981; Hawrysz and Stróżyk, 2015). For the purposes of this study, data from DPL test have been interpreted using the relationship shown in Eq. 5. This formula originating from the Polish standard (PN-B-04452) has been repeatedly verified under local conditions and has become quite firmly established in the awareness of geotechnical engineers who are engaged in in situ research and interpretation: (5) Dr=0.429⋅logN10+0.071 {{\rm{D}}_{\rm{r}}} = 0.429 \cdot {\rm{log}}{{\rm{N}}_{10}} + 0.071 where D_r is the relative density (-) and N₁₀ is the number of blows (-).

DMT requires a little more attention, even though it is already a very popular research tool and engineers have been using it for almost half a century (e.g., Marchetti, 1980; Totani et al., 2001; Rabarijoely, 2018; Nepelski, 2020; Virsis et al., 2023). It consists of measuring the gas pressure acting on the diaphragm of a dilatometer blade (Fig. 1a) at selected subsoil depths. In soil tests, two pressures are usually measured (A and B); they force the center of the membrane to move 0.05 mm to the ground (reading A) and deflect the center of the membrane toward the ground by approximately 1.05 mm (reading B). To extend the dilatometer testing, pressure measurements are sometimes taken as the membrane returns to ground contact (C reading). Readings A, B, and C are corrected for the stiffness of the diaphragm and marked as p0, p1, and p₂, respectively. Pressures p₀ and p₁ and the value of the vertical effective stress σ’_v0 are used to determine the following dilatometer indexes: material index (I_D), horizontal stress index (K_D), and dilatometer modulus (E_D) and pore pressure index (U_D) (Marchetti, 1980). (6) ID[−]=f(A,B,u0)=p1−p0p0−u0 {I_D}[ - ] = f(A,B,{u_0}) = {{{p_1} - {p_0}} \over {{p_0} - {u_0}}} (7) KD[−]=f(A,u0,σv0′,B)=p0−u0σv0′ {{\rm{K}}_{\rm{D}}}[ - ] = {\rm{f}}({\rm{A}},{{\rm{u}}_0},\sigma _{{\rm{v}}0}^{'},{\rm{B}}) = {{{{\rm{p}}_0} - {{\rm{u}}_0}} \over {\sigma _{{\rm{v}}0}^{'}}} (8) ED[MPa]=f(A,B)=34.7⋅(p1−p0) {{\rm{E}}_{\rm{D}}}[{\rm{MPa}}] = {\rm{f}}({\rm{A}},{\rm{B}}) = 34.7 \cdot ({{\rm{p}}_1} - {{\rm{p}}_0}) (9) UD[−]=f(A,C,u0,B)=p2−p0p0−u0 {{\rm{U}}_{\rm{D}}}[ - ] = {\rm{f}}({\rm{A}},{\rm{C}},{{\rm{u}}_0},{\rm{B}}) = {{{{\rm{p}}_2} - {{\rm{p}}_0}} \over {{{\rm{p}}_0} - {{\rm{u}}_0}}} where: A, B, C are the pressure readings (bar), p₀, p₁, p₂ the pressures (MPa), σ′_vo the in situ overburden stress (MPa), and u₀ is the pore water pressure acting in the center of the membrane before insertion of the DMT blade (often assumed as hydrostatic below the groundwater table) (MPa).

Figure 1:

The DMT unit control during the test (a) and geophysical investigation (b).

Geophysical studies were also conducted with the aim of assessing the homogeneity of the embankment in terms of the material from which it was constructed (Fig. 1b). The research was conducted in a selected cross section determined based on soundings, supplemented with macroscopic assessment of soil after removing the breakstone, and by performing a research trench at the base of the embankment (Fig. 2). Electrical tomography (ERT) using 32 electrodes in the Wenner array, which was applied in the present study, has been thoroughly described in numerous literature sources such as Reynolds (2011), Koda et al. (2017), and Lech et al. (2020), for example.

Figure 2:

An overall view of the embankment (a), a view after removing the breakstone layer (b), and an excavation at the base of the embankment (c).

The area where the research was conducted is a renovated section of a railway embankment located to the north of Warsaw. It is situated within the Warsaw Basin, between the Vistula and Narew rivers. The terrain in the basin consists mainly of flat, relatively folded surfaces that form a part of the floodplain terrace. The morphology of the terrain is closely related to its geological structure, particularly the type of near-surface deposits. The area consists mainly of sandy and sandy-gravel deposits, as well as alluvial clay deposits of the floodplain terrace, with peat and silt locally found in low-lying areas.

The section under study has an embankment with a height of up to 6.5 m and is built of noncohesive soils, mainly medium and fine sands in a medium dense condition (D_r = 0.35 ÷ 0.65) and also, as shown by DPL investigations, in a loose condition (D_r < 0.35). Only in the upper part, the embankment soils to a depth of about 1 m are dense (D_r = 0.65 ÷ 0.8). In Figure 2, an overall view of the examined section of the embankment is presented, as well as a view after removing the top layer of breakstone.

Beneath the embankment are organic soils (peats and sandy and clayey silts) with a maximum thickness of 1.8 m to a depth of 8.2 m, characterized by particularly low strength parameters and low deformation parameters. Organic and mineral soils found in the embankment base should be classified as soft soils. The groundwater level is approximately 0.6 m below the embankment's base (Figure 2c).

To assess the construction of the embankment, the electrical resistivity tomography (ERT) tests were also conducted, which show its cross-sectional structure. The results of geophysical measurements are presented in Figure 3. Analyzing these studies, we can conclude that the body of the embankment consists of noncohesive soils (sands) and the structure of the embankment is homogeneous, without visible soil lenses. Zones with increased electrical resistivity in the upper layer result from the presence of a breakstone layer, while zones with low electrical resistivity at the base of the embankment are due to the presence of water in the residual soils and the presence of organic or clayey materials.

Figure 3:

Geoelectrical cross section across the railway fill.

The geoelectric cross section in conjunction with the material index I_D from DMT at the classification chart (Fig. 4) allows to conclude that sandy soils with occasional presence of silty (clayey) and organic soils at the base of the embankment are present throughout the entire profile.

Figure 4:

Soil classification chart by DMT.

From the results of the DPL tests (Fig. 5), it can be stated that both the embankment and the subsoil beneath the embankment exhibit a medium-dense condition throughout the entire profile. From the ground surface (or more precisely, from 1 m, as the in situ test results are analyzed from this depth), up to approximately 1.5 m deep, the relative density of the embankment exceeds the value of 0.65 and even reaches 0.8. The embankment's loose zone, where the relative density falls below the value of 0.35, occurs from a depth of 3.2 m and depends on the cross section where the test was conducted. Profile 6 is an exception, where the embankment's loose zone and dry density fall below the value of 0.35 at a depth of approximately 4.4 m. These results provide a background for the values of this parameter according to the newly proposed relationship.

Figure 5:

Relative density of sands based on DPL tests.

Figure 6 shows the results of DMT in the form of profiles of DMT index changes. The change in the material index I_D confirms that the soils are noncohesive. An exception is observed in DMT-1, DMT-2, and DMT-6, where lenses of cohesive soils are found – the index value drops below 1.8.

Figure 6:

DMT results.

Horizontal stress index (K_D), according to what Larsson observed (1989), assumes significantly higher values up to a depth of 2 m (in our case, 2.4 m) than deeper in the profile. Since most formulas in the literature base the value of relative density precisely on the K_D index, this results in a significant overestimation of soil compaction in this layer.

The analysis of changes in the soil profile of the K_D and E_D indices, as well as wedge resistance – q_D – does not allow for direct conclusions about the relative density of the investigated soils.

The dilatometer indices (I_D, K_D, E_D), wedge resistance (q_D), pressures (p₀ and p₁), and vertical effective stress (’_v0) were investigated to estimate their influence on the relative density of the embankment. For the statistical analysis, measurement results from DMT-1, -2, and -3 were used, that is, data from 107 depths. The table shows Pearson product moment correlations between each pair of variables. These correlation coefficients range between −1 and +1 and measure the strength of the linear relationship between the variables. The second number in each location of the table is a P-value, which tests the statistical significance of the estimated correlations. P-values below 0.05 indicate statistically significant nonzero correlations at the 95% confidence level.

As indicated by the above analysis, the highest correlation of 0.74 was found between relative density and horizontal stress index. Relative density also depends, in sequence, on wedge resistance, dilatometer modulus, and pressures p₀ and p₁, but it does not depend on the material index and vertical effective stress.

Considering the above, using the solver module, an equation has been proposed to determine density based on calculated dilatometer indices. This equation takes the following form: (10) Dr=ln(0.1⋅KD⋅EDPa)0.125 {{\rm{D}}_{\rm{r}}} = {\rm{ln}}{\left( {{{0.1 \cdot {{\rm{K}}_{\rm{D}}} \cdot {{\rm{E}}_{\rm{D}}}} \over {{{\rm{P}}_{\rm{a}}}}}} \right)^{0.125}} where: D_r is the relative density (-), K_D the horizontal stress index (-), E_D the dilatometer modulus (MPa), and P_a is the atmospheric pressure (MPa).

The relationship between the analyzed data on the plane described by the proposed formula is shown in Figure 7a, while the relationship between the reference data from DPL tests and the predicted one is shown in Figure 7b. In accordance with the diagram, the agreement between the parameter calculated based on DMT and the parameter obtained from DPL results is high (coefficient of determination R² = 0.691, mean square relative displacement [MSRD] = 12.7%, and mean relative error [MRE] = 8.8%).

Figure 7:

Plot of D_r = f(K_D, E_D) relationship (a) and predicted versus obtained data on the investigated area.

In Figure 8, the results of relative density are presented according to the new formula proposed in the paper. The relative density is compared against values determined in the field using DPL soundings (these represent reference values) and those calculated based on DMT using the relationships provided in the literature. The first formula for assessing D_r is the Marchetti correlation, which relates it to the wedge resistance (q_D). Here, soil relative density is clearly overestimated not only compared to DPL test, but also compared to other methods – all relationships mentioned in the article were plotted only for the DMT-1 profile (other profiles present only data obtained from DPL, calculated according to the Jamiolkowski formula and according to the proposed one).

Figure 8:

Relative density (D_r) estimated based on the proposed formula (Eq. 10) versus values determined from DPL tests and calculated from literature-based relationships.

On analyzing the relationships proposed by Tanaka (1988), Mayne (2002), and Jamiolkowski et al. (2001), it is found that despite differences in formula forms, the shapes of the graphs are almost identical with a slight shift – this is well illustrated by the results from DMT-1.

In all cases (Eqs 1–4), it is evident that the density is significantly overestimated in the first few meters of the profile, and it is almost a rule that it exceeds the value of 1 up to a depth of 2 m. With increasing depth, density values decrease, and in the case of the proposal provided by Tanaka and Mayne, they underestimate relative density. The D_r values closest to the reference ones are given by the Jamiolkowski correlation.

The change in relative density in the profile according to the newly proposed correlation depends not only on horizontal stress index, but also on dilatometer modulus. It can be observed that the estimated values in this case are closest to DPL values. Moreover, there is no overestimation of density in the first meters of the profile. Measurements from DMT-4, -5, and -6 were not considered in the statistical analysis, and data from these studies were not used in the search for dependencies between relative density and DMT indices, so they serve as a kind of verification of the proposed correlation.

It should be noted that, as with the other relationships mentioned in the article, the one proposed now has a local character and will require further verification and adjustment of the constants present in the equation.