Sensitivity evaluation of Krakowiec clay based on time-dependent behavior

2.1 Study area

To validate the application of time-dependent behavior assessed by the time resistance concept for the evaluation of sensitivity, an extensive testing programme was conducted. The chosen test site was the "Chmielów I" clay deposit in Chmielów village (Figure 1). Geographically, the deposit area is located in the northern part of the Fore-Carpathian Basin, in Sandomierz Lowland, Poland on the right bank of the Vistula river.

Figure 1

Location of soil sampling.

2.2 Material overview

The material for the laboratory analysis was taken from the clay formation of Miocene age (Sarmatian stage) of the Fore-Carpathian Basin. These soils are represented by gray or slightly green clays, locally with inserts of sandy layers. The physical properties of soil used in the study are listed in the Table 1. The time dependent behaviour of reconstituted Krakowiec clay as well as the intact clay have been in the focus of interest. Reconstituted samples were obtained by remolding the natural Krakowiec clay material. The aim of the remolding procedure is to erase the initial soil structure. Remolding was performed by mixing the natural Krakowiec clay material with water to produce slurry having water content approaching the liquid limit (wn ≈ LL). To obtain clear insight into time dependent behaviour and creep characteristics of Krakowiec clay we performed incrementally loaded (IL) oedometer tests. The consolidation cell used a fixed-type ring setup with single drainage at the top of the specimen.

2.3 Time dependent behavior of cohesive soils

Since the late 1940s, the interest of many research centres on time-dependent mechanical properties of soil has increased. The determination of a delay in deformation as a function of time was of fundamental importance for the description of these properties. Bjerrum [7], observing long-term settlements of foundations, suggested distinguishing instant and delayed compression and introduced the so-called time lines (isochrones) (Figure 2) to model the reduced creep rates resulting from changes in loading time. Instant compression occurs simultaneously with an increase of effective stresses and reduces the pore space at which the structure is able to transfer the load completely. Delayed compression represents the reduction of the pore space at which the structure completely transfers the load. Delayed compression includes both the stages of consolidation: primary and secondary consolidation. Their course can be presented using the concept of fixed time lines (isochrones) (Figure 2). The AB line represents “immediate” compression during a conventional oedometer test, while BC line shows a change in the porosity or strain index at constant effective stress due to secondary consolidation. If the soil at point C is loaded, the obtained new CD curve, with a clear effect of apparent preconsolidation pressure, will represent instant compression. The CE curve represents the behaviour corresponding to the time-dependent compression. The course of the time line in terms of Bjerrum is directly related to the creep hypothesis B, which was formally proposed by Ladd et al. [8]. The hypothesis B concerns •the occurrence of creep during primary compression and is based on the assumption that the void ratio e_EOP or strain at the end of the primary compression ϵ_EOP increases and the apparent preconsolidation pressure σ^′_c decreases together with the duration of the primary compression.

Figure 2

Bjerrum’s isotaches model for incremental 1-D loading. Series of parallel time lines describing the compressibility and shear strength of clay, which shows delayed consolidation.

The justification for B hypothesis is the occurrence of delayed deformation during the entire consolidation process [6, 9, 10, 11]. The creep of the soil skeleton is often considered as secondary consolidation. However, this view is not entirely correct. The distinctions between these two concepts were made by Tavenas et al. [12] who recognised that secondary consolidation was caused only by creeping. However, creep may also occur before the secondary consolidation stage. Ex definitione creep is a process when soil deformation in a function of time is observed and creep rate is controlled by viscous resistance. Using the concept of time resistance proposed by Janbu (1969) and successively developed in later works [13, 14, 15], the occurrence of the creeping factor both in the primary and secondary consolidation stage was also observed and presented in the analysis.

2.4 Time resistance concept

The analysis of the course of creep resistance changes [6] allows to characterize the stress-dependent and time-dependent behaviour of the compressed soil. Graphically, the time resistance of soil creep R can be expressed as tangent to the time-strain curve at the analyzed point (Figure 3A). Creep time resistance is defined as the time necessary to create a unitary value of relative strain:

Figure 3

Time resistance concept: A) Typical strain – time curve from oedometer test; B) Time resistance as a function of time with key parameters for modelling creep behaviour of soil; C) Time resistance as a function of strain for one load step in an oedometer (σ^′_v = constant).

where: dt – increase in time, dϵ – change (increase) of strain

For the majority of cohesive soils, time resistance increases together with the progress of consolidation (Figure 3B). Considering the primary consolidation phase, the R−t curve has a curvilinear shape at an early stage, changing in a further stage after reaching the time t_p into a quasilinear relationship, which should be associated with creep of the soil skeleton. Experiments show [16, 17] that extrapolation of a straight line to a horizontal timeline allows to determine the value of time t_r, which is usually much lower than the duration of the primary consolidation phase, t_p. Based on the R - t curve, three zones can be divided. Initial zone represented by a second degree of parabola, corresponding to primary consolidation for time t ≤ t_c, transitional zone for time t_c ≤ t ≤ t_p and pure creep for time t ≥ t_p. An illustration of this division has been given in Figure 3B. As can be seen after exceeding a certain time t_c, time resistance increases linearly together with time, thus strain can be expressed as follows:

where: ϵ_c is the reference strain for the current effective stress and corresponds to the strain at the end of the primary consolidation, r_s is time resistance number (creep number) and t_r is reference time

The inclination of the linear relationship between time resistance R and time t, at exceeding time t_r, can be described by the creep number:

Typical values of r_s for normally consolidated clays range from 100-500 at natural water content in the range of 30-60%. Assuming that R = r_s(t - t_r) and R_c = r_s(t_c - t_r), the equation (2) can be written in a different way:

where: R_c is a reference value of the time resistance at the time t_c which conforms to the start of secondary consolidation

The reference strain ϵ_c defines the point on the resistance R - t curve from which the equation (4) can be considered as correct (Figure 3C), hence for ϵ ≥ ϵ_c the time resistance R can be presented as a function of the current strain:

The concept of time resistance has been successfully implemented in many constitutive models accounting for the time-dependent response of the soil to changes in the state of stress. These models, developed from the late 1980s take into account, in addition to creep, structural effects occurring in the soil skeleton, such as bonding and structural degradation (destructuration) [18, 19].

2.5 Sensitivity framework

Cotecchia and Chandler [20] presented the sensitivity framework (SF), in which comparisons between parameters referring to intact and remolded soil were made. The aim was to assess the impact of changes in the structure on soil behaviour. The mechanical properties of the soil with a completely disturbed natural structure were defined as intrinsic properties. Structural sensitivity is usually considered as an indicator of the decrease in shear strength of the soil as a result of progressive deformations. Burland [21] related the differences in mechanical characteristics to decreasing strength due to structural disturbances of the natural clay during field sampling.

The sensitivity framework can be applied to show the effect of structure and stress dependency on time resistance number (creep number) in one-dimensional consolidation and compressibility, too. For this purpose, structured and remolded creep behaviour of clay during consolidation were compared, and the initial amount of bonding (structure) was determined as well. In this work the initial amount of bonding was defined through the intrinsic time resistance number and minimum measured time resistance number determined by the IL test conducted on intact (undisturbed) sample. Then, evaluation on the sensitivity of the investigated clay was possible. The sensitivity in this study was related to initial amount of bonding x₀:

The initial amount of bonding x₀ was determined using the time resistance concept and intrinsic creep number [13]:

where: r_si is the intrinsic creep number and r_s,min is the minimum, measured creep number determined by an incremental oedometer test

3.1 Evaluation of the time dependent behavior

The behaviour of the Krakowiec clay under load during the oedometer test was presented using the creep time resistance model. For a comprehensive analysis, it was convenient to track the behaviour related to volumetric creep separately (analysis of the strain-time relationship) and to assess the variability of the parameters together with the consolidation pressure (analysis of creep number-pressure relationship). In this study, only those parts of ϵ – R and R – t curves were considered that characterized the creep phase. In order to check the predictions of the model, the obtained experimental data were compared with a set of theoretical curves with optional values ϵ_c, r_s, t_c, t_r, R_c. For this purpose, equations (2) and (5) were used. In Figure 4 an example of the interpretation of the results of the uniaxial consolidation study of a natural sample of Krakowiec clay at a consolidation pressure of 300 kPa was shown.

Figure 4

Interpretation of the R – t curve for one load step in oedometer test.

Based on the R - t relationship, it could be noticed that the time resistance starts to increase linearly at R_c = 62604 minutes and time t_c = 840 minutes. Hence reference strain which corresponds to the time at the end of the primary consolidation consolidation, ϵ_c was 0.039. The inclination of this part of the graph was characterized by a creep number of r_s = 150. Extrapolating the resistance line towards the parabolic part of the R – t curve referring to the primary consolidation, a t_r time of 500 minutes was estimated. The obtained parameters gave the opportunity to check how the time resistance model reflected the experimental course of the creep phase. In Figures 5A and 5B example curves ϵ – t and R – ϵ fitted with the best model solution characterized by creep number r_s and time t_r have been presented.

Figure 5

Time dependent behaviour of Krakowiec clay: A) Calculated creep strain in relation to time; B) Calculated time resistance in relation to strain.

In order to better understand how model parameter r_s affects the strain – time curve, additional calculations were made. Also the impact of this parameter on the development and magnitude of deformation was performed. By keeping constant model parameters, it was checked how different values of the creep number affect the characteristics of ϵ – t in the model. The results of this analysis have been illustrated in Figure 6. The solid line indicates the value of the creep number r_s, which was obtained on the basis of the interpretation of experimental data. Dashed lines show the results obtained with the change of r_s parameter. Due to the fact that the creeping number r_s describes the final inclination of the R – t line, the rate of deformation caused by creep could be derived from it. Figure 6 shows the increase of strain associated with the reduction of r_s value. Changes in the r_s value also affected the final inclination of the ϵ – t curve. Summarizing, the higher values of r_s, the smaller values of creep strain and strain rates.

Figure 6

Results from the parametric study of the influence of creep number r_s to the behaviour of the time resistance model.

For each loading stage, the R–t relationships were investigated and the parametric modelling discussed above was performed. The nature of the course of the advanced consolidation stage in case of an undisturbed soil sample was dependent on the values of loads applied during the oedometer test. The values of the creep number r_s were varied, depending on the relationship to the yielding stress σ_vy ,which is determined from log σ – ϵ graph. In the recompression part of curve log σ – ϵ, where σ < σ_vy large R values were obtained, which gradually decreased when approaching to σ = σ_vy. This trend has been illustrated in Figure 7A as a change in the inclination of the graphs at subsequent load steps.

Figure 7

R – t relationships describing time dependent behaviour of Krakowiec Clay for: A – undisturbed samples in wide range of stress; B – remoulded samples just after exceeding preconsolidation pressure.

In the virgin part of curve log σ – ϵ, where σ > σ r_s values increased again, gradually reaching the values observed in the samples of disturbed (remoulded) soil samples. The constant values of r_s for the remoulded soil are show in Figure 7B as the same inclination of the graphs at subsequent load steps. These indicators should be considered as viscoplastic strain component causing irreversible soil deformation. Therefore, the analysis of creep time resistance considered in relation to the subsequent load steps gave the opportunity to assess directly the preconsolidation state of soil.

3.2 Stress dependency on creep number and sensitivity

The creeping phases of 3 remoulded samples showed very similar inclinations, regardless of the applied consolidation stresses in a wide range of values from 300 to 900 kPa. In the analyzed remoulded clays from Chmielów, r_s values in the stabilized range of 680 - 691.5 were obtained. Having the results of consolidation of samples with different structural features resulting from the load history, the initial amount of bonding x₀ from the equation (7) was determined. This value was then used to assess the sensitivity of the tested soil. Figure 8 shows the relationship between the number of creep and the consolidation stress. The initial amount of bonding x₀ for the Krakowiec clay, being a scalar state variable, was 3.57.

Figure 8

Stress dependency of Krakowiec clay.

Using this value in equation (4), on the basis of the time-dependent soil behaviour, the sensitivity S_t = 4.57 was obtained. Comparing sensitivity classification of Rosenquist [22] with the results presented in this paper, the obtained value of sensitivity allowed to consider the structural susceptibility to deformation of clays as medium-sensitive. In turn, in the tests of total and residual strength of Krakowiec clays from different regions of Poland, slightly lower values of structural susceptibility were obtained Olesiak [23, 24] and Pilecka and Zięba [25]. This shows similar values of indicators characterizing the structure impact on the consolidation and strength behaviour of Krakowiec clays. Comparative data has been presented in Table 2.