Evaluation of dynamic behavior of varved clays from the Warsaw ice-dammed lake, Poland

2.1 Material origin and properties

Varved clay originates in specific conditions, including existence of ice sheet front, periglacial climate, variation in material supply due to the seasonal conditions, and variation in sedimentation rate. Varved clay occurs in many locations in the northern hemisphere (USA, Poland, Sweden, Estonia, etc.), and the description of their geological properties has been presented by many researchers, e.g., Merta [20], Młynarek and Horvath [21], De Groot and Lutenegger [22], Lu et al. [23], Tankiewicz and Kawa [24], Kalvāns et al. [25], Johnson et al. [26], etc.

Varved clay of the Warsaw ice-dammed basin (Figure 1) is of heterogeneous provenance, structure, and properties which demonstrate substantial variability in both the vertical and horizontal directions [9,16,17,18,19,20]. The Warsaw ice-dammed basin was formed at the younger Pleistocene and covered most of the Mazovia Lowland. The basin was supplied with the material from the south and east (directions opposite to the glaciated area). This means that the basin was fed by extraglacial rivers from these directions (and not by the proglacial waters). The sediment is a type of extraglacial varved deposits [20].

Figure 1

Location of the sample collection (marked in red) against the extent of Warsaw ice-dammed lake (© OpenStreetMap contributors https://www.openstreetmap.org/copyright) (Myślińska [27] after Różycki [28], modified).

The specific structure of the varved clay is a result of variation in seasonal conditions at the front of the Vistulian Glaciation ice sheet. Each varve is composed from two alternating layers: the light one (silt) – deposited during the warm period, and the dark one (clay) – deposited during the cold period. Varved clay of the Warsaw ice-dammed lake is also characterized by significant variation in terms of facies. Three types of varves are indicated, each corresponding to different sedimentary zone, depending on the location in the sedimentary basin [20].

1. Proximal zone – This zone consists of A-type varves (with indistinct gradual boundaries, light layers thicker than dark ones, and total thickness of a varve above 4.0 cm), which is the environment adjacent to the river mouth. Sandy sediments are dominating (with current structures, and without wave ripples), but there are also clayey layers, provided by subglacial streams. This environment is intermediate between fluviatile and basin regime.

2. Transitional (intermediate) zone – This zone is characterized by the existence of B-type varves (with contrasting sharp boundaries, light and dark layers of equal thickness, and total thickness of a varve in the range of 2.0–4.0 cm), located between the proximal and distal zones. Both current and wave structures can be found on the surface of varves.

3. Distal zone – This zone consists of C-type varves (with contrasting sharp boundaries, light layers thinner than dark ones, and total thickness of a varve below 2.0 cm), located far from the river mouth. It is characterized by a small amount of sandy-silty sediment and those layers are thinner than in previous zones. Turbidity currents were a main factor of deposition (greater water depths, no wave ripples).

The significant difference between dark and light layers is a proof of the different conditions of the environmental energy. The current and wave activities with bottom suspension currents were the characteristics of the light layers, while quiet sedimentations were the characteristics of the dark ones. The B- and C-type varves are suspected to be a product of suspension currents, while A-type ones are more characteristic of environments close to fluvial [20]. Many of the varves are highly variable in terms of thickness, even within the same type of varve (supernormal varves). Variability does not show any regularity. Changes in thickness are independent between light and dark layers and the clay content is more uniformly dispersed than sandy-silty sediments [20].

In some areas, in the eastern part of the Warsaw ice-dammed lake, the varved clay is covered by a thin, 1–3 m layer of Holocene sand of aeolian origin.

Varved clay is one of the most important units of the subsoil in towns located northeast from Warsaw: Radzymin, Kobyłka, and Zielonka (Figure 1). That is why soil samples for laboratory tests were collected in Kobyłka town (Figure 1). Two parallel drills at a distance of 5 m were executed. The material was collected using Shelby’s thin-walled tubes, from the depth of 1.3–2.6 m. Collected soil corresponds mainly to the A-type type of varves (as described by Merta [20]). Mean values of index properties of silty and clayey layers are presented in Table 1.

Clay content shows significant variation which is noticeable macroscopically. This may cause unusual differentiation of mechanical properties, as the horizontal shear strength along the clayey layer may be lower than the vertical shear strength of varved clay. Thus, it is of particular importance to apply adequate methods for predicting the behavior of the varved clay under different loading conditions [9].

In respect of the history of geological loads, Zawrzykraj [17] proved that varved clay of the Warsaw ice-dammed lake are normally consolidated soils, and have not been covered by either the ice sheet or the large amount of younger deposits. But these deposits can demonstrate behavior comparable to some overconsolidated soils because of the post-sedimentary chemical cementation process, occurring in conditions of lowering of water table.

2.2 Test procedure

The aim of the investigation was to study the dynamic behavior of the varved clay in conditions corresponding to in situ conditions of typical construction in Kobyłka: subsoil loaded by the construction of unit stress of 100 kPa at the foundation level and additionally subjected to intermittent vibrations due to traffic. The dynamic behavior of the samples was compared to their static behavior, thus the laboratory test program included two types of triaxial CU (consolidated undrained) tests: under static conditions (monotonic loading) and under dynamic conditions (cyclic loading). All tests were conducted in GDS Ltd dynamic triaxial testing apparatus under the CU conditions (CU tests) according to the following procedure:

• The samples were oriented in the direction corresponding to their orientation in natural conditions. The specimens were trimmed to an average dimension of D = 35.0–38.4 mm and H/D = 1.83–2.65

• Prior shearing, each test consisted of the following stages: initial loading under effective stress, three saturation steps with three B-checks, consolidation stage, initial deviator stress increase, three dynamic stages, and final static shearing

• Initial effective stress applied on each sample was equal to 50 kPa, in case of preventing swelling

• After that, the back-pressure saturation was undertaken, average B-value for all the samples was 0.93

• Next stage was isotropic consolidation under effective confining pressure, respectively, σ c ′ = 100, 200, or 400 kPa

• After consolidation, samples were subjected to an increase in the initial deviator stress to 100 kPa to reflect the vertical stress that is applied to the soil due to the construction load

• Then, axial loading was applied under undrained conditions

• For samples tested under static conditions, monotonic loading with constant rate of strain of 0.01 mm/min were executed

• For samples tested under dynamic conditions, three consecutive stages of ADC tests were performed (Table 2)

1. Dynamic stage I – high amplitude vibration: displacement amplitude A = 0.1 mm, frequency f = 5 Hz, and number of cycles N = 1,000

2. Dynamic stage II – low amplitude vibration: A = 0.01 mm, f = 5 Hz, and N = 10,000

3. Dynamic stage III – high amplitude vibration: A = 0.1 mm, f = 5 Hz, and N = 1,000

Vibration parameters were designed with regards to correspond to the different traffic conditions in site, and the technical limitations of the triaxial apparatus.

After each dynamic stage, samples were subjected to mid-phase loadings, so that each dynamic stage started from 100 kPa of initial deviator stress. General conditions of dynamic phases were presented on the schematic graphs (Figure 2).

Figure 2

Scheme of cyclic loadings.

Since no shear failure was observed during dynamic loading, after the dynamic stage III, the monotonic shearing was executed with a constant rate of strain of 0.01 mm/min to determine the post-dynamic shear strength.

In total, 24 tests were conducted. Under dynamic conditions, 17 samples were tested: 4 samples consolidated under σ c ′ = 100 kPa, 7 samples under σ c ′ = 200 kPa, and 6 samples under σ c ′ = 400 kPa. Under static conditions 7 samples were tested: 2 samples under σ c ′ = 100 kPa, 2 samples under σ c ′ = 200 kPa, and 3 samples under σ c ′ = 400 kPa.

3.1 Shear modulus parameter

Modulus of deformation was calculated on the basis of the following equation (Figure 3):

where E _N is the modulus of deformation at the Nth cycle; dev _N,max and dev _N,min are the maximum and minimum deviator stress at the Nth cycle; and ε _N,max and ε _N,min are the maximum and minimum axial strains at the Nth cycle, respectively.

Figure 3

Shear modulus on the basis of hysteresis loop of Nth cycle.

Then, shear modulus (G) was calculated from the following equations [29]:

where ν is the Poisson coefficient; Δε is the axial strain amplitude; Δγ is the shear strain amplitude; and G _N is the shear modulus at the Nth cycle.

The Poisson coefficient equal to 0.5 was taken into calculations, as the soil samples were fully saturated prior to triaxial loading.

Characteristic loops for 1, 100, 1,000, and 10,000 cycles of dynamic stages were selected to determine the values of G (Table 3). The results of G values (Table 3) were analyzed with regards to vibration amplitude A, number of cycles N, and effective confining pressure (effective stress at consolidation) σ c ′ .

3.2 Vibration amplitude

The results can indicate two qualitatively different ways of soil response to dynamic loading applied at the same frequency of vibrations but with different amplitudes:

• In the dynamic stages I and III, when the amplitude was higher (A = 0.1 mm) after 1,000 cycles, G _av values decreases c.a. 25%;

• While in the dynamic stage II, when the amplitude was lower (A = 0.01 mm), an increase in G _av value by several percentage was registered.

This may indicate that a slight strengthening of soil is possible at lower vibration amplitudes, while higher vibration amplitudes cause weakening of the structure, which is expressed by the decrease in G _av due to dynamic loading.

3.3 Number of cycles

The changes in G _av values during dynamic loading are not linear. The dependence of G _av value on the number of cycles was approximated by a logarithmic function (Figure 4a–c).

where G _av is the average value of shear modulus, N is the number of Nth cycle, α is the gradient of logarithmic curve, and G _avN=1 is the G _av value at 1st cycle of a particular dynamic stage.

Figure 4

Shear modulus changes during: (a) the dynamic stage I, (b) the dynamic stage II, and (c) the dynamic stage III.

The value of α coefficient is an indicator of the trend of G _av changes during the dynamic loading: negative values (α < 0) correspond to the decrease in G _av which indicate soil weakening, while positive values (α > 0) correspond to the increase in G _av which indicates soil strengthening.

Comparison of α values allows for a quantitative evaluation of G _av changes. The most significant reduction in G _av value (from −0.70 to −0.91) was observed in the dynamic stage I – in the samples where no dynamic loads were applied so far. The soil weakened after dynamic stage I, and the soil was then subjected to dynamic stage II with vibrations of significantly lower amplitude but much higher number of cycles. This resulted in an increase in G-value, which is expressed in positive α values (from 0.11 to 0.21). This slight strengthening influenced the quantitative changes in soil response when dynamic loads of high amplitude were applied again (dynamic stage III). Although a further reduction in G _av value during the dynamic stage III was observed, the quantitative indicators of this reduction were slightly smaller (α values range from −0.48 to −0.84) compared to those observed in the dynamic stage I.

The changes in G _av values were analyzed in the two intervals: during the initial cycles and during the subsequent cycles of dynamical loading. It was assumed that for the dynamic stages I and III, the initial cycles are cycles from N = 1 to N = 100, and for the dynamic stage II the initial cycles are from N = 1 to N = 1,000. The subsequent cycles are, respectively, from N = 100 to N = 1,000, and from N = 1,000 to N = 10,000. The initially rapid changes in G _av values during the initial cycles and smaller changes during the subsequent cycles of each dynamic phase (Figure 4a–c) are indicated not only by the parameters of the logarithmic model G _av = f(N), but also by comparisons of values of absolute changes in ΔG _av/ΔN gradients.

In the dynamic stage I, ΔG _av/ΔN determined in the initial cycles decreased 27–30 times faster compared to the smaller ΔG _av/ΔN changes noted during the subsequent cycles.

In the dynamic stage II, the increase in ΔG _av/ΔN determined in the initial cycles was only 7–19 times greater compared to much smaller increase during the subsequent cycles.

In the dynamic stage III, in the initial cycles, decreases in ΔG _av/ΔN values were only 3–19 times higher than during the subsequent cycles.

Thus, varying dynamic loading conditions in subsequent dynamic stages result in less intense changes in the mechanical soil parameters.

3.4 Effective confining stress

Soil response to dynamic loading is also significantly dependent on effective confining stress at consolidation σ c ′ (Figure 5a and b). In a particular dynamic phase, G _av values increase with the increase in the effective confining pressure σ c ′ . This relationship is well represented by the following equation:

where G _av is the average value of shear modulus, σ c ′ is the consolidation effective stress, β is the gradient of logarithmic curve, and b is the intercept of logarithmic curve

Figure 5

G _av variation as a function of consolidation effective stress: (a) in the dynamic stages I and III and (b) in the dynamic stage II.

Coefficient of determination (R ²) ranged from 0.994 to 0.999. G _av values for samples consolidated under σ c ′ = 200 kPa and σ c ′ = 400 kPa were, respectively, 44% and almost 100% higher than for samples consolidated under σ c ′ = 100 kPa.

G _av values are thus conditioned by the following:

• the value of effective confining pressure σ c ′

• parameters of dynamic loading in successive stages (dynamic stages I, II, and III)

• the number of cycles for which G _av values are determined

The characteristics of the variation in G _av values determined as a function of σ c ′ are illustrated in Figure 5a and b. In all analyzed cycles, G _av/ σ c ′ gradient in the range 100–200 kPa was higher and decreased in the range 200–400 kPa. This confirms the reduced response to dynamic loadings for samples consolidated at higher effective pressure.

Increase in G _av value as a function of σ c ′ is observed at both conditions when higher amplitude of vibration leads to structural weakening of the soil material, and at lower amplitude of vibration resulting in soil strengthening. G _av values in the dynamic stages I and III, where the structural weakening was observed, were smaller than G _av values obtained in the dynamic stage II where the soil strengthening was observed. The increase in G _av = f( σ c ′ ) in the dynamic stage II is characterized by β values ranging from 12.3 to 12.9 (Figure 5b), whereas in the dynamic stage I, by significantly smaller β values (from 7.6 to 8.7). In the dynamic stage III, the effects of the previous varying loading conditions most probably got accumulated and β values were slightly higher (from 8.2 to 10.1) than in the dynamic stage I (Figure 5a). These quantitative comparisons show how the loading history may indicate the dependence of G _av values on stress in the soil mass.

The comparison of factors influencing G _av changes takes into account dynamic stages for samples consolidated under particular effective confining pressure (Figure 6). The ratio of ΔG _av/G _avi−1, where ΔG _av = G _avi-G _avi−1, was assumed as an indicator of the changes. ΔG _av/G _avi−1 ratio was analyzed in the two periods of each dynamic stage: the initial cycles and the subsequent cycles. The most significant changes in ΔG _av/G _avi−1 ratio were observed during the initial cycles, and thus when a given dynamic loading is applied to soil straight after the “deviatoric loading.” During subsequent cycles, much smaller changes were observed (several percent smaller than during the initial cycles). This indicates that the trend of rapidly decreasing ΔG _av/G _avi−1 change is continued and confirms that it is reasonable to analyze them for a larger number of cycles.

Figure 6

Change in average shear modulus in relation to effective confining pressure at each dynamic stage.

The use of vibration with different amplitudes is also reflected in the changes in ΔG _avi/G _avi−1 ratio. During the dynamic stage I, the initial cycles cause the most significant changes in ΔG _av/G _avi−1 proportional to the effective pressure at consolidation σ c ′ . During the dynamic stage II, ΔG _av/G _avi−1 ratio decreases (up to few %) at higher values of effective pressure at consolidation. The least significant changes in ΔG _av/G _avi−1 ratio are observed during the dynamic stage III. Also, in the dynamic stage III, ΔG _av/G _avi−1 changes are similar in the samples consolidated at 200 and 400 kPa, thus it may indicate the unification of material characteristics of soil due to dynamic loading and application of higher values of effective pressure at consolidation σ c ′ .