Creep behaviour of intact and remoulded fibrous peat

Transcription

1 DOI /s RESEARCH PAPER Creep behaviour of intact and remoulded fibrous peat Mohan P. Acharya 1 Michael T. Hendry 1 C. Derek Martin 1 Received: 12 February 2016 / Accepted: 23 March 2017 Ó Springer-Verlag Berlin Heidelberg 2017 Abstract This paper presents the creep behaviour of intact and remoulded specimens of fibrous peat obtained from a field site near Anzac, Alberta, Canada. The creep behaviour was investigated by means of long-term drained and undrained triaxial tests. The development of volumetric, axial, and undrained axial strain and strain rate during drained and undrained creep tests under variable stress conditions is presented. The stress strain strain rate (p 0 e v _e v ) relationship is found to be unique for different stress and loading durations. The p 0 e v _e v relationship is analysed and represented by creep isotaches. The applicability of different creep models developed for normally consolidated clay is discussed and applied to define the development of creep strain in fibrous peat under varying isotropic and deviator stresses. The secondary consolidation coefficient for evaluating the volumetric strain rate of peat is found to be applicable with some limits. The drained creep behaviour of remoulded peat specimens differs from the behaviour shown by Shelby tube specimens, whereas the undrained creep behaviour in remoulded and Shelby tube specimens is similar. Electronic supplementary material The online version of this article (doi: /s ) contains supplementary material, which is available to authorized users. & Mohan P. Acharya mpachary@ualberta.ca Michael T. Hendry hendry@ualberta.ca C. Derek Martin derek.martin@ualberta.ca 1 Markin/CNRL Natural Resources Engineering Facility, University of Alberta, Edmonton, AB T6G 2W2, Canada Keywords Creep test Fibrous peat Strain and strain rate Stress Triaxial test List of symbol C c Coefficient of compression C a Coefficient of secondary compression 1D One-dimensional compression p 0 0 Preconsolidation pressure p 0 Mean confining pressure _p0 Rate of effective stress q Deviator stress ðr 1 r 3 Þ q 0 First deviator stress applied (kpa) Dq Deviator stress increment r 0 3 Effective confining stress Dr 0 3 Confining stress increment Dr 0 v Stress increment in 1D compression SIR Stress increment ratio (Dq/q or Dr 0 3/r 0 3) w 0 Initial water content of specimen w f Water content at the end of the creep tests q 0 Density of specimen (g/cm 3 ) e vp Volumetric strain at the end of the pre-consolidation e 0 Initial void ratio e v Volumetric strain _e v Volumetric strain rate e a Axial strain _e a Axial strain rate e ad Undrained axial strain _e ad Undrained strain rate u Increase in pore pressure a, b Creep parameters m Slope of log _e v - log t plot (the rate of decrease in strain rate) e r Lateral strain m Poisson s ratio

2 1 Introduction The long-term deformation behaviour of peat has been the subject of several studies [6, 8, 9, 24 26]. These studies investigated and modelled the consolidation behaviour of peat based on one-dimensional (1D) consolidation, doing so using coefficients of primary consolidation and secondary compression (C c and C a, respectively) derived from oedometer tests [4, 8, 24, 26]. Measured field settlements often vary notably from those predicted from the models based on laboratory oedometer tests [15, 19, 30, 34]. This discrepancy is attributed to the variability of peat, the three-dimensional nature of settlement, and the tendency of C c and C a to increase with time [19, 20, 30]. Other studies focus on the mechanisms behind this deformation and describe a more complex process of consolidation consisting of structural creep and a sequential or concurrent pressure-driven expulsion of water from between (inter-particle) and within (intraparticle) the organic structures that compose the particles [4, 5, 19]. Published field and laboratory findings consistently show that the secondary deformations in peat are significantly larger than those from primary consolidation [13, 24, 25, 33]. Viscoplastic models based on 1D deformation behaviour define the secondary compression or creep of peat using creep functions developed for clays or otherwise define the creep functions in terms of parameters developed for similar 1D behaviour in clay [5, 6, 8]. This approach is taken because clays as well as soft sedimentary rocks have undergone more intense investigation than peat, with creep behaviour studied under more complex stress state including 1D and triaxial stress [7, 12, 22, 31 33, 36]. Such investigations have produced a general relationship between stress, strain, strain rate, and time and provided a robust framework for the development of one- and three-dimensional viscoplastic models [17, 18, 37, 38]. The purpose of this study was to expand the understanding of the long-term deformation behaviour of peat in triaxial stress conditions, develop the stress-strain-strain rate (p 0 e v _e v ) relationships [7, 22, 33] for peat, at different stress states, and evaluate the applicability of the creep models developed for normally consolidated clay. 2 Peat samples and classification The peat samples were retrieved from a site located on the Canadian National Railway s (CN) Lac la Biche Subdivision near Anzac, Alberta ( N, W), where a railway embankment crosses a large expanse of peat bog. Peat samples were taken from the 2.6- to 3.5-mthick peat subgrade that underlies a 2- to 3-m-thick embankment. Peat samples were collected both in Shelby tubes and as highly disturbed material from auger cuttings. The peat is classified as fibrous peat, with light yellowish, highly coarse fibres in the top layer and finer fibres at greater depths. The water content ranges from 800% for the coarse fibres and 400% for the fine fibrous layers. The degree of humification was determined to be insignificant, with the plant structures within the peat appearing to be intact. The classification of the peat as per Hobbs [15] and the von Post peat classification [21] system is H2B3F1R3W1N4. 3 Laboratory testing methodology 3.1 Specimen preparation The specimens consisted of relatively intact peat trimmed from Shelby tube (SBT) samples as well as remoulded specimens prepared from auger cuttings clean of root and stones. For the latter, cuttings were placed inside a 38-mmdiameter steel tube up to a height of 130 ± 3 mm and subjected to a vertical stress (r 0 v) of 55 kpa until the settlement-versus-time curve flattened, usually after 24 h. The vertical strain at the end of compression varied from 5 to 26%. The compressed samples were extruded from the steel tube and trimmed to a length of 76 ± 4 mm for triaxial creep testing. The density of the remoulded specimens ranged from 0.97 to 1.09 g/cm 3, and the initial water content varied between 363 and 505%. SBT samples were trimmed to generate four peat specimens 72 ± 2mmin diameter and 150 ± 15 mm in length, and one specimen 38 ± 2 mm in diameter and 76 ± 2 mm in length. The resulting specimens appeared relatively smooth and free from defects and large roots. Two SBT specimens (SD2, SU2) had relatively shorter fibres (\2 mm). The density of these specimens varied between 0.94 and 1.08 g/cm 3, and the water content varied between 440 and 730%. The physical properties of the specimens are summarized in Table Laboratory creep tests Two remoulded and three Shelby tube peat specimens were subjected to a triaxial consolidated drained (CD) creep test, and two remoulded and two SBT specimens were subjected to a triaxial consolidated undrained (CU) creep test. Figure 1 is a schematic diagram of the triaxial testing appa-

3 Table 1 Summary of physical properties of peat specimens Specimen type Specimen ID Diameter (mm) Height (mm) w 0 (%) q 0 (g/cm 3 ) e 0 p 0 0 (kpa) e vp (%) w f (%) Intact SD SD SD SU SU Remoulded RD RD OD OD RU RU Fig. 1 Schematic diagram of triaxial setup for creep tests ratus used in these tests. The pore pressure, axial displacements, and volume changes were, respectively, measured with multiple pore pressure transducers, a linear variable differential transformer (LVDT), and Teledyne ISCO pumps. The pumps were also used to apply backpressure. Water was used as a cell fluid. All specimens were saturated using a backpressure of 190 kpa and a cell pressure of 200 kpa. Skempton s B value was found to be greater than 0.97 for all specimens. The specimens were then consolidated to the desired effective confining pressure (p 0 0), which varied between 10 and 40 kpa. The consolidation was continued for a few days to a few weeks until the volume change verses time curve flattened. After consolidation, deviator stresses (q) and effective confining stresses (r 0 3) were applied in increments (Dq and Dr 0 3, respectively). The tests and analysis were conducted based on the methods presented in Tavenas et al. [33] and Leroueil et al. [22]. The application of constant loads was due to its simplicity and the similarity of the load application to the real world conditions to which the resulting model will ultimately be applied. The Dq increments were applied with weights placed to act on the loading piston (Fig. 1). The Dr 0 3 increments were applied by increasing the cell pressure while keeping the back pressure constant. Each Dq and Dr 0 3 was applied sequentially; thus, q or r 0 3 was the sum of all previous increments. For example, specimen SD1 was isotropically consolidated with p 0 0 = 30 kpa, then a q = 20 kpa load was applied, and the specimen was allowed to deform until the axial strain rate was less than 10-4 %/min. A second stress increment of 10 kpa was added, and the specimen was allowed to deform under q = 30 kpa until the axial strain rate was less than 10-4 %/min. The same process was followed for three subsequent increments of 10 kpa. The stress increment ratio (SIR = Dq/q) varied from 0.5 for the first increment and 0.33, 0.25, and 0.2 for next three increments, respectively. The stress increment ratio (SIR) for both Dq and Dr 0 3 ranged from 0.2 to 1. A small SIR was used for the CD tests to minimize the magnitude of the pore pressure (u) response due to the stress increment and thus the duration of elevated u, as this results in an increase rate of volumetric strain driven by the hydraulic gradient between the specimens and the back pressure boundary conditions (primary consolidation) (Barden [5], Hobbs [15]). A higher increment ratio (SIR = 1) such as in standard oedometer tests was used to study the development of strain not affected by the previous load, e.g. [5, 39]. Each Dq or Dr 0 3 was maintained until the strain rate slowed near to 10-4 %/ min. The tests were stopped when either the specimens failed or the axial strain exceeded 25%. The total duration

4 Table 2 Summary of CD, CU, and 1D tests Specimen type Tests Specimen ID Type of stress q, r 3, and r 0 v (kpa) Dq or Dr 3 (kpa) SIR Intact CD SD1 D q = 20, 30, 40, 50, 60 Dq = SD2 D q = 5, 10, 20, 30, 40 Dq = 5, 10, 20 1 SD3 I r 0 3 = 33.5, 37.0, 40.5, 44.0, 47.5, 51.0, Dp = 3.5, 10, 20, 40, , 64.5, 84.5, 124.5, UD SU1 D q = 5, 10, 20, 40 Dq = 5, 10 1 SU2 D q = 5, 10, 20, 40 Dq = 5, Remoulded CD RD1 D q = 10, 20 Dq = 10 1 RD2 D q = 10, 20, 30, 40, 50, 60 Dq = OD1 1D r 0 v = 6.25, 12.5, 25, 50, 100 Dr 0 v = 6.25, 12.5, 25, 50 1 OD2 1D r 0 v = 25, 50, 100, 200 Dr 0 v = 25, 50, UD RU1 D q = 20, 30, 40, 50, 60, Dq = RU2 D q = 10, 20, 30,40, 50, 60, 70, 80 Dq = D deviator, I isotropic, 1D one dimensional to 200 kpa, respectively, to compare the creep behaviour of peat under triaxial and one-dimensional (1D) compression. These 1D tests are similar to an Oedometer test but with differing specimen dimensions (Table 1). The SIR was kept equal to 1. Each increment was held for 24 h, and drainage was allowed from both ends. The vertical displacement was measured using LVDTs. 4 CD test results and analysis 4.1 Development of volumetric strain during CD tests Fig. 2 Plot of the effective stress states of the specimens after the application of each stress increment for a CU creep tests (remoulded), b CD creep tests (remoulded), and c CU and CD creep tests (SBT) of these tests ranged from 4 to 17 weeks. Table 2 presents the summary of the test program, including the details of the q and r 0 3 stresses applied during the tests and the SIRs used. The stress paths followed by the specimens during the CD and CU creep tests are presented in Fig. 2. Each circular shape in Fig. 2 represents the stress state of the specimen in the q p 0 space just after the application of each stress increment. Additionally, two remoulded specimens (OD1 and OD2) were horizontally confined within a cylindrical mould and subjected to vertical stress ranging from 6.5 to 105 and 25 Figure 3 presents the volumetric strain (e v ) and volumetric strain rate ( _e v ) developed in three SBT specimens during CD tests from the beginning of the first stress increment. The e v was calculated relative to the initial volume of the specimen, and the _e v was calculated relative to the strain at the beginning of each stress increment. Figure 3a presents the e v log t curves for specimen SD1 corresponding to deviator stresses (q) of kpa (Table 2) at small SIRs ( ). The resulting e v log t curves are all similar in shape. The highest e v developed under the first deviator stress increment (Dq) (i.e. q = 20 kpa) (9.28%). The net e v generated under the next four Dq, each 10 kpa, were 1.80, 1.94, 3.07, and 2.56%, respectively. No sign of failure was detected even after a e v of 18.5%. The initial _e v was highest under the first Dq (i.e. q = 20 kpa). However, the _e v decreased rapidly under the smaller q and slowly under the higher q. This trend indicates that, over the long term, the _e v under the higher q could be higher than the _e v under the smaller q. The creep test in specimen SD2 began with a small Dq of 5 kpa (Table 2), and the SIR was kept equal to 1. The resulting e v log t curves (Fig. 3b) are similar in shape to

5 Fig. 3 Development of e v a SD1 (p 0 0 = 30 kpa), b SD2 (p 0 0 = 20 kpa), and c SD3 (p 0 0 = 30 kpa) and _e v, d SD1, e SD2, and f SD3, for three SBT peat specimens subjected to drained triaxial creep testing those of specimen SD1 (Fig. 3a), but a higher e v was measured under larger q. The initial _e v peaked under the first Dq irrespective of the higher SIR used. The _e v decreased sharply with time under the smaller q and slowly under the larger q (Fig. 3e). At the end of the test, the highest _e v was measured under the largest q (40 kpa). This result agrees with the conclusions presented in Barden [5] that the _e v is not effected by loading history if the current stress increment is kept for sufficiently long time. Specimen SD3 was isotropically compressed under r 0 3 ranging from 33.5 to kpa at SIRs varying from 0.2 to 1 (Table 2). For small SIR and r 0 3 ( kpa), the shapes of the e v - log t plots (Fig. 3c) are quite similar and the magnitude of e v is about 1%. A higher e v, ranging from 0.6 to 12.3%, is generated under larger r 0 3 ( kpa) (SIR = 1). The shapes of _e v - log t plots (Fig. 3f) under smaller r 0 3 (\54.5 kpa) are similar to each other. A faster decrease in _e v occurred under the smaller r 0 3 and a slower decrease in _e v under higher r 0 3. Under the larger r 0 3 ([54.5 kpa), the slope of the _e v - log t plots is almost parallel and a higher _e v is generated under the higher r 0 3 (Fig. 3f).

6 Fig. 4 Development of e v, a RD1 (p 0 0 = 40 kpa), b RD2 (p 0 0 = 20 kpa) and _e v, c RD1, d RD2 for two remoulded peat specimens under different q increments Figure 4 presents the development of e v and _e v on two remoulded peat specimens under varying q increments and SIRs (0.2 1) (Table 2). The development of e v was not gradual (Fig. 4), and a number of sharp increases in volume change are evident. In specimen RD1 (SIR = 1), higher e v and _e v were measured under the second stress increment (Fig. 4a, c). Specimen RD2 went through a series of compressions and dilations. Consequently, the e v - log t plots are not smooth (Fig. 4b). The cumulative e v developed under all stress increments was 4.14%, which is much smaller than the e v developed in the SBT specimen under similar Dq. The _e v was slightly higher under the first Dq and almost the same under all subsequent Dq. The _e v became negative under q values above 50 kpa (Fig. 4d). 4.2 Development of pore pressure during CD tests Figure 5 presents the pore pressure (u) developed in excess of the applied back pressure in three SBT specimens during the CD creep tests. u increased to the maximum value instantly after the application of each stress increment. The magnitude of the u generated depends on the SIR and the magnitude of Dq or Dr 0 3. In specimen SD1 (SIR \ 0.5), the highest u (18 kpa) was generated under the first Dq (20 kpa) (Fig. 5a); in SD2 (SIR = 1), the highest u (16 kpa) was recorded under larger Dq (10 and 20 kpa) (Fig. 5b). This u decreased significantly after 24 h and remained below 5 kpa after 1 week (10 4 min). In specimen SD3, the u increased up to 5.5 kpa under every Dr 0 3 and either remained constant near 5 kpa or decreased to a lower magnitude after 24 h. This small u generation is attributed to the application of Dr 0 3 \ 3.5 kpa and SIR \ 0.5. In general, higher u are generated under the higher stress increments and SIR. Under the same magnitude of q, higher u were observed in SBT specimens than in remoulded peat specimens. 4.3 Volumetric creep strain and strain rate The log _e v - log t plots from CD creep tests in SBT specimens (Fig. 3d f) are not linear, except for some stress with smaller SIR. These plots show that, after some time elapsed following loading, a significant decrease occurred in the _e v. This deviation of _e v, which occurred together with the decrease in u, was not seen in remoulded specimens (Fig. 4c, d). Such deviations in log _e v - log t plots have been reported in 1D consolidation test results in Canadian peat [35]. The initial slope of the log _e v - log t curve is consistent with primary consolidation. The later stage of straining that

7 Fig. 5 Measured pore pressure during CD creep tests on SBT peat specimens a SD1, b SD2, and c SD3 under applied q and r 0 3 increments occurred under minimum constant u is creep strain, which developed under constant stress conditions. At this stage, the _e v in all peat specimens under most of the stress increments was less than 10-3 %/min. The _e v generated at the later stages in SBT specimens can be expressed in terms of Eq. (1), which represents the linear decrease of log _e v with log t, such that _e v ¼ b t i m: ð1þ t The parameter b is the ordinate value of the strain rate at the beginning of creep and includes a stress function that defines the development of _e v at different stress conditions. b is a function of the magnitude of p 0 and stress condition. t i and t are the current and reference time, respectively. m is the slope of a log _e v - log t plot. According to the classical approach of volumetric creep, this parameter should be equal to 1.0 in 1D compression if _e v is only a function of time [33]. However, the test results indicate much lower values varying between 0.6 to 0.2 under q increments and values of about 0.70 under all Dr 0 3 increments. Higher m values ( ) are observed for remoulded specimens. The smaller m values are also related to the calculation of _e v corresponding to e v at the beginning of stress increment. The m value represents the rate of decrease in _e v with time. Higher m represents a faster decrease in _e v, and smaller m represents a slower decrease in _e v. The small values of m for the SBT specimens might account for the presence of highly compressible layers of peat fibres with gas bubbles [2]. These layers are continuously compressed without decreasing the strain rate. Thus, the development of strain was gradual in SBT specimens, whereas the e v developed instantly in remoulded peat specimens after the placement of the stress increment and considerably decreased later. The value of m is dependent on the magnitude of Dq or Dr 0 3, SIR, and the difference between the current mean pressure (p 0 ) and p 0 0. Higher initial stress increments generated higher e v, but the _e v decreased rapidly and, consequently, the m value is higher. A comparatively longer time was needed to achieve the same decrease in _e v under the higher q and e v and resulted in a smaller m. Equal magnitude decreases of _e v in log _e v - log t plots under different q or r 0 3 may take the same amount of time but will generate lower or higher e v unless the slopes of the log e v - log t plots are parallel. Figure 6 presents the e v - log _e v plot for different stress increments from specimens SD1, SD2, and SD3. The plot shows an initial rapid decrease in _e v at small values of e v followed by a sharp increase in the e v and progressive decrease in _e v. In specimens SD1 and SD2, 1 10% of the e v developed with a decrease in _e v from to %/min (Fig. 6a). In specimen SD3, the e v is 0.5 6% and corresponds to a decrease in the strain rate from to %/min (Fig. 6b). From these portions of the e v - log _e v plots, the development of creep rate ( _e v ) at different stress can be defined. Figure 7 presents the e v developed at a constant _e v under multiple stress increments. These e v - log p 0 plots for both q (Fig. 7a) and r 0 3 loading (Fig. 7b) produce a series of parallel lines. These constant _e v lines are the creep isotaches in the strain stress (e v - p 0 ) plane. Creep isotaches for specimens SD1 and SD2 plot parallel to each other regardless of the different SIRs and loading durations used. The creep isotaches under r 0 3 (specimen SD3) (Fig. 7b) have a lower slope than the creep isotaches produced under q loading (specimens SD1 and SD2). Together with the isotaches, Fig. 7b presents the plot of strain measured

8 Fig. 6 Development of e v with _e v under a q and b r 0 3 increments Fig. 7 Development of e v with p 0 at constant _e v under a q and b r 0 3 increments during 1D consolidation tests (OD1 and OD2) under 1D stress increments (Dr 0 v) varying between 25 and 100 kpa. The lines joining the strains measured 24 h after the beginning of loading, i.e. normal consolidation lines (NCL), are plotted parallel to the isotaches for SD3. As the slopes of the isotropic consolidation lines (Iso-NCL) and NCL plots are parallel [3], this implies that, in the e v - p 0 plane, the isotaches derived for r 0 3 loading are parallel to both 1D NCLs and Iso-NCLs, respectively, whereas the creep isotaches derived for q loading plot away from the Iso-NCL line. This result is analogous to the variation of specific volume in the e v - p 0 plane during conventional CD tests on normally consolidated soil. Some scatter in the plot of e v with p 0 (Fig. 7a) for specimens SD1 and SD2 was due to the faster decrease in _e v under the first Dq (Fig. 6a). Within the same specimens, the linearity of creep isotaches shows that the slopes of e v - log t plots under different Dr 0 3 and Dq at _e v values smaller than %/min can be considered parallel. At this or smaller _e v, the constant _e v lines presented in Fig. 7 will be identical to the equal duration of loading lines defined by Bjerrum [7]. This implies that the magnitude and number of stress increments (Dr 0 3 or Dq), i.e. the history of loading, do not influence the development of creep strain. Thus, the rheological behaviour of peat can be uniquely expressed in terms of current stress (p 0 ), strain (e v ), and strain rate ( _e v ), similar to that in clay after Leroueil et al. [22], i.e. R ðp 0 ; e v ; _e v Þ¼0 ð2þ This uniqueness of p 0 e v _e v has been used to define the 1D creep behaviour of clay and peat [8, 18]. The isotaches presented in Fig. 7b are equivalent to the creep isotaches presented by den Hann [8] for 1D compression conditions. According to the Taylor Bjerrum model, the NCL and Iso- NCL are also lines of constant _e v [33]. Thus, in both isometric and non-isometric stress conditions, the development of _e v at a particular e v and p 0 can be defined relative to the NCL or Iso-NCL. The vertical distance between two isotaches represents the development of strain at constant p 0 while the _e v decreases with time. The constant gap between creep isotaches, except some scatter

9 at smaller initial stress increments, indicates the development of almost constant e v under different p 0 at the same rate of decrease in _e v. Some variation in the development of e v under p 0 higher than 100 kpa is noted for specimen SD3. For the same decrease in _e v, a higher e v developed. This indicates a slower decrease in _e v under higher p 0, which means the coefficient of secondary consolidation (C a ) is stress dependent at higher stress. C a is almost constant for the loading range applied in specimens SD1 and SD2. There is a notable difference in the e v developed at a constant _e v due to the effect of stress conditions in specimens SD1, SD2, and SD3 (Fig. 7). Under the same p 0 and same magnitude of decrease in _e v, a smaller amount of e v developed under r 0 3 increments (specimen SD3), which is evident from the smallest gap between isotaches (Fig. 7b). A larger e v developed in specimen SD2 than in specimen SD1. The loading of specimens SD2 and SD1 began at p 0 0 = 20 and 30 kpa, respectively. Thus, in q - p 0 space, the stress condition in SD2 is near the tension line, resulting in the development of higher strain (Fig. 2c). Figure 8 plots the variation in _e v with p 0 at various loading durations (t) for specimens SD1, SD2, and SD3. For specimen SD3, the _e v only from r 0 3 increments with larger SIR ([0.5) are considered. These log _e v - p 0 plots are different from the equal duration of loading lines, e.g. [7] mentioned previously. At any given time and stress condition, a linear relationship exists between log _e v and p 0. For any of the loading durations and range of p 0 applied, _e v is smaller under r 0 3 increments (specimen SD3) (Fig. 8b). The highest _e v values were recorded in specimen SD2. In spite of the smaller SIR applied to specimen SD1, the _e v developed between t = 5000 to 15,000 min (Fig. 8a) is larger than that in specimen SD3. For the time range considered, a faster decrease occurs in the _e v in specimen SD3 (r 0 3 increments). The slight decrease in gap between log _e v - p 0 lines at larger duration indicates small decrease in C a with time. The relationship proposed by Singh and Mitchel [31] to describe the axial and deviatoric strain can be used to describe the development of _e v in fibrous peat. This correlation has also been used to express _e v [33]. The development of _e v in peat is expressed in terms of p 0 and time (t) in combination with Eq. (1): _e v ¼ be t m ap0 i ð3þ t The parameter a, which is the slope of the log _e v - p 0 lines, increases slightly with time and is higher under the isotropic stress than under the deviator stress. Figure 9 presents a plot of the variation of _e v with p 0 at various e v in specimens SD2 and SD3. The _e v considered in SD3 are those under q with larger SIR values ([0.5) and which are not influenced by stress history. The linear relationship between log _e v and p 0 presented in Fig. 9 can be expressed in terms of axial strain and shear stress, as proposed by Murayama and Shibata [27] and used by Berry and Poskitt [6] to describe the rate of secondary consolidation in fibrous peat, such that _e v ¼ bp 0 ap0 0 sinh p 0 ð4þ 0 b and a, the slope of the log _e v - p 0 line (Fig. 9) decrease with increasing strain but remain constant for different stress. The limitation of using this approach to express _e v is that this relationship can only be verified for small e v. 4.4 Development of axial strain during CD test Figure 10 presents the development of e a and _e a on two SBT specimens, SD1 and SD2, under different Dq. The shapes of the e a - log t curves are similar to those of the e v - log t curves presented in Fig. 3. Similar to e v, the development of e a depends on Dq and SIR. The e a measured in specimens SD1 and SD2 is about 18 and 15% higher, respectively, than the magnitude of e v. Fig. 8 Development of _e v at constant t with p 0 under a q and b r 0 3 increments

10 Fig. 9 Development of _e v at constant e v with p 0 under a q and b r 0 3 increments Fig. 10 Development of e a in specimens a SD1 and b SD2 and _e a in specimens c SD1 and d SD2 with time under different q increments The _e a - log t plots (Figs. 10c,10d) vary slightly from the _e v - log t plots presented in Fig. 3 but again their shape depends on the Dq and SIR. In specimen SD1 (SIR \ 0.5), the _e a was highest under the first Dq (Fig. 10c). At the end of the tests, a higher rate of decrease of _e a was noted under the first Dq than under subsequent Dq (higher q). In specimen SD2 (SIR = 1), the _e a increased under larger Dq (higher q) (Fig. 10d) and was largest under 40 kpa (largest q). A slight decrease in _e a was noticed after 24 h. During the final stage of the test, the slopes of the _e a - log t plots under each Dq are almost parallel, suggesting a constant decrease in _e a. Figure 11 presents the development of e a and _e a on two remoulded specimens. Except for some sharp increases in e a, the e a - log t plots are smooth and have similar shapes (Fig. 11a, b). In specimen RD1 (SIR = 1), higher e a and _e a developed under the second Dq (Fig. 11a, c). In specimen RD2, larger e a developed under the higher q irrespective of lower SIR (\0.5). The cumulative e a developed under all Dq was 12%, nearly three times the

11 cumulative e v generated (Figs. 4b, 11b). This is attributed to the dilation of the specimen under subsequent loading. At the initial stage of loading, the maximum _e a developed under the first Dq (q = 10 kpa) but at the later stage _e a peaked for q = 50 kpa (Fig. 11d). 4.5 Axial creep strain and strain rate The log _e a - log t plots (Figs. 10c, d, 11c, d) are not linear except under subsequent Dq with smaller SIR in the SBT specimens. Similar to _e v (Fig. 3), the _e a in SBT specimens decreased with u (Fig. 10c, d). In remoulded peat specimens, the decrease in _e a slowed due to dilation of the specimen (Fig. 11c, d). Similar to e v, e a developed after a decrease in pore pressure and at _e a values less than %/min as axial creep strain developed at constant stress. The development of _e a with time can again be represented by Eq. (1), as _e a ¼ b t m i ð5þ t The m value, the slope of the log _e a - log t plots, varies between 0.45 and 0.7 for SBT specimens and between 0.55 and 0.95 for remoulded specimens. The higher value of m in the log _e a - log t plots compared to the log _e v - log t plots corresponds to the development of higher initial e a under higher q increments. The e a - log _e a plots (Fig. 12a) from specimens SD1 and SD2 are similar to the e v - log _e v plots. The progressive decrease in _e a at higher e a is clearly visible. The e a developed at constant _e a plotted with q produces constant _e a lines (Fig. 12b). Similar to the constant _e v lines (Fig. 7b), constant _e a lines produce a series of parallel lines or creep isotaches for e a irrespective of the magnitude of the Dq and SIR applied. The linearity of constant _e a lines shows that history of loading does not influence the development of e a and that Eq. (2) is equally valid for the development of axial creep strain in fibrous peat. Similar to e v, a larger magnitude e a developed in specimen SD2 for the same decrease in _e a. Figure 12c presents the plots _e a with q at various t in specimen SD2. At any given time, a linear relationship exists between log _e a and q. The relationship presented in Eq. (3) can be modified to describe _e a by replacing p 0 by q, as follows: _e a ¼ be aq t m i ð6þ t For the time considered in this correlation, a, the slope of the log _e a - q lines, increases with time. Similarly, the linearity between log _e a and q at various _e a (Fig. 12d) can be described by equation (4), replacing p 0 by q such that: Fig. 11 Development of e a in specimen a RD1 and b RD2 and _e a in c RD1 and d RD2 with time

12 Fig. 12 Development of a e a with _e a, b e a at constant _e a, c _e a at constant t, and d _e a at constant e a in SBT specimens under different q increments _e a ¼ bq 0 sinh aq : ð7þ q 0 a and b decrease with increasing e a. b is again the ordinate value of the strain rate at the beginning of creep, and a is the slope of log _e a - q line. 4.6 Poisson s ratio Figure 13 plots e v versus e a for two SBT specimens (Fig. 13a) and two remoulded specimens (Fig. 13b). Irrespective of the number of stress increments, different SIR values, and the unequal duration of loading, the e v - e a plots are linear for the SBT specimens and linear to an extent for the remoulded specimens. In specimen RD2, some scatter in the plot coincides with when the specimen went through a series of compressions and dilations. After 4.5% of e v, the generation of e a is almost at a constant volume. The slopes (e v /e a ) of the e v - e a plots are 0.85 and 0.82 for specimens SD1 and SD2 and 0.58 and 0.62 for specimens RD1 and RD2, respectively. A slope (e v /e a ) near unity represents the straining for the 1D condition with a negligible deviatoric strain. The e v /e a also represents the ratio of change in a cross-sectional area of specimens relative to the cross-sectional area at the beginning of the tests. The calculated ratios are consistent with the measured dimensions of the specimens after the tests. Figure 14 presents the calculated lateral strain (e r ) and drained Poisson s ratio (m) for SBT (Fig. 14a, c) and remoulded (Fig. 14b, d) peat specimens. The CD test specimens underwent slightly bulging under q increments, essentially undergoing 1D compression. The calculated value of m ranges from 0.08 to 0.13 for the SBT specimens and 0.19 to 0.27 for the remoulded specimens. The m for constant volume straining at the later stage of the tests of specimen RD2 varies between 0.4 and These values of m for fibrous peat from northern Canada are within the range reported in the literature [28, 29]. 5 CU test results and analysis 5.1 Development of undrained creep strains Figures 15 and 16, respectively, present the measured undrained axial strains (e ad ) and axial strain rate ( _e ad )in two SBT (SU1 and SU2) and two remoulded (RD1 and RD2) peat specimens. Each specimen was subjected to four to seven q increments (Dq) at different SIRs (0.15 1) (Table 2).

13 Fig. 13 Plot of cumulative e v verses e a developed during CD creep tests on a SBT and b remoulded peat specimens under the applied stress increments Fig. 14 Calculated e r versus measured e a on a SBT and b remoulded peat specimens and m versus e a on c SBT and d remoulded peat specimens In both the SBT and remoulded specimens, the shapes of the e ad - log t curves (Figs. 15a, b, 16a, c) and log _e ad - log t curves (Figs. 15c, d, 16c, d) are identical and similar to those of the e a - log t curves (Fig. 10) except at the time of failure. The log _e ad - log t curves are similar to reports for undrained tests on clay [33, 39]. Large

14 Fig. 15 Development of e ad in SBT peat specimens a SU1 (p 0 0 = 30 kpa) and b SU2 (p 0 0 = 20 kpa) and _e ad in specimens c SU1 and d SU2 with time deformation occurs at q greater than 20 kpa in SBT specimens but only above 50 kpa in remoulded specimens. Irrespective of SIR, larger e ad and _e ad develop under a higher q, and the highest _e ad is measured under the Dq causing the failure of the specimen. Some periodic sharp rises in e ad and _e ad are evident for both remoulded and SBT specimens. These rises are more significant under small q. Due to these sharp increases in _e ad, the slope of the log _e ad - log t plot decreases in the later stages of the tests. 5.2 Development of pore pressure during CU test Figure 17 presents the measured increase in pore pressure (u) during the CU creep tests. u instantly increased after the placement of stress increments and is independent of SIR and magnitude of Dq. This u is maximum under the first Dq; larger than the magnitude of Dq in SBT (Fig. 17a, b) and nearly two-thirds of the magnitude of Dq (Fig. 17c, d) in remoulded specimens, respectively. Under the subsequent increments, there is a gradual increase in u to a maximum value equal to (Fig. 17a d) or even larger than (Fig. 17b) the p 0 0. In specimen SU2, the u is higher than the p 0 0 by 7 kpa. Previous studies report the development of u higher or equal to the applied Dq during undrained tests in peat [11, 14]. Some of the given reasons for the higher u include: (1) the anisotropic nature of peat specimens with higher stiffness in the horizontal direction [13] and (2) the compression of gas bubbles existing within the peat fibres [2]. The higher u measured in SBT specimens supports both of these explanations. The SBT specimens have intact horizontally oriented fibres and might have higher gas content. Some periodic sharp increases in u were observed in both remoulded and SBT peat specimens and are associated with the sharp increase in e ad (Fig. 17). These sharp increases in u under the constant q dissipated gradually to the lower value, and then the next cycle starts. The duration of the dissipation is proportional to the magnitude of sharp rise in u. These sharp rises in u are attributed to the release of gas bubbles from the peat fibre to the pore voids of the peat [2]. The failure of the specimens started when the u value approached the effective confining pressure (e ad = 10 15%). The _e ad developed rapidly and reached its maximum value within 30 min to 2 h. The failure of specimens is attributed to bulking, and at least one specimen (SU2)

15 Fig. 16 Development of e ad in remoulded peat specimens a RU1 (p 0 0 = 30 kpa) and b RU2 (p 0 0 = 40 kpa) and _e ad in specimens c RU1 and d RU2 with time failed under shear. The pattern of failure might have some correlation with the length of the fibres. Specimen SU2, a SBT specimen, had finer fibres (\2 mm), which might be why it could develop a shear plane. 5.3 Undrained strain and strain rate The log _e ad - log t plots for both SBT and remoulded specimens (Figs. 15c, d, 16c, d) are mostly linear except at the time of failure. The increase in _e ad occurs together with increases in e ad and u under the higher q. As it is difficult to conclude whether failure occurred due to the shearing or buckling of specimens, the _e ad at the time of failure of the specimens is not considered to be due to shearing alone. Similar to _e a, the _e ad developed during the CU tests except at failure can be expressed by Eq. (1), _e ad ¼ b t m i ð8þ t b is the value of _e ad at the beginning of creep and depends on q. The slope of the log _e ad - log t plots, m, varies between 0.75 and 0.95 in the SBT and between 0.6 and 0.95 in the remoulded peat specimens. Smaller m values (\0.6) are associated with a sharp increase in _e ad at the later stages of the tests. The value of m is independent of the magnitude of Dq and the SIR. For _e ad below %/min, the log _e ad - log t plots for under all q increments (except at failure) can be considered parallel. In this range of _e ad, the log _e ad - q curves representing _e ad based on two SBT specimens at different q and various t are linear and parallel (Fig. 18). Equation (3) can again be used to describe the _e ad in terms of q and t in combination with Eq. (9): _e ad ¼ be aq t m i ð9þ t For the time considered in this correlation, a (the slope of the log _e ad - log t plot) increases with t and b (the reference strain rate) is assumed to be %/min. 6 Discussion The present investigation considered the time-dependent development of volumetric, axial, and shear strain in fibrous peat from northern Canada. Peat itself is

16 Fig. 17 Undrained u developed in specimens a SU1, b SU2, c RU1, and d RU2 Fig. 18 Development of _e ad a SD1 and b SU2 at a constant t with q on specimens characterized by physical variability. The specimens studied varied in terms of homogeneity, density, water content, and fibre content (Table 1). By saturating and consolidating all of the specimens at a similar total or effective stress, it is assumed that all specimens achieved homogeneity. However, significant variability in the test results was expected. At the end of pre-consolidation, the SBT specimens underwent a larger volume change than the remoulded specimens. This is attributed to the higher water and air content in the intact peat and irregularities in the shape of the specimens. Specimens with relatively fine fibres were smooth and underwent faster consolidation but produced a smaller strain (SD2, SU2). The smaller volume change during consolidation of remoulded specimens might be related to the use of higher vertical stress (55 kpa) during the time of preparation. Specimen SD1 was consolidated for a significantly longer time, which resulted in 15.1% volumetric strain (e vp ) at the end of pre-consolidation. Due to this consolidation, less variability was noted in the measured deformation, volume change, and pore pressure. Fibre effects in fibrous peat are believed to provide better stability through higher lateral resistance [20]. For peats with low fibre content, fibre reinforcement effects are insignificant and shear failure may be expected [23]. In this study, the axial strain developed continuously with no signs of failure even at e a [ 30% in specimens with both

17 significantly longer (SD1) and finer fibres (SD2). This result agrees with the conclusion of Farrell [11] that fibrous peat specimens generally do not fail in CD compression tests because of the continual compression of the peat fibre. Under some q increments, the shear strain developed due to transitional obstruction of drainage of gas bubbles [2] followed by an increase in pore pressure (Fig. 5a, b). This development was transient, and the volume change occurred rapidly after the dissipation of pore pressure (Fig. 3b). This pore pressure behaviour has also been observed in field conditions and is not simply the result of the laboratory experiment design [1]. This suggests that the continual compression of fibres in the vertical direction [11] during CD creep tests is more dominant than the reinforcing effect of peat fibres to limit the shear strain [10, 29]. During the CD creep tests, both the axial and volumetric strain developed continuously due to the continuous expulsion of pore water. No distinct boundary between the primary and secondary compression as devised for clay was observed. Consequently, no distinction could be found between deformation due to the expulsion of inter-particle and intra-particle water, as previously considered [5, 6]. This result supports the conclusion of Landva [19] that the intra-particle and inter-particle water drain at the same time due to the highly porous nature of peat fibres. Only under very high r 0 3 ([200 kpa) and e v [ 30% (Fig. 3c) was a rapid increase in the _e v and u observed. This behaviour is attributed to the breaking of fibres, which increases in the compressibility of the peat specimens [20]. Observations of peat specimens at the end of the creep tests indicated that the peat fibres were broken into very fine peat particles. CD creep tests on remoulded specimens resulted in significantly smaller e v and e a under the same magnitude of q. One specimen (RD2) deformed almost at a constant volume when the axial strain exceeded 5% (Fig. 5b). This might be due to a disturbance in the fibre layout, loss of moisture, and a change in the compressibility of the peat fibres. Due to these differences in compression behaviour, remoulded peat specimens may not be suitable for CD tests. Unlike the CD creep tests, CU creep tests on both remoulded and SBT specimens produced similar e a, _e ad, and u (Figs. 15, 16, 17 respectively). The fibres inside the specimens were mostly intact at the end of the tests, which suggests that the failure of the fibrous peat in the CU tests was not associated with the breaking or shearing of fibres. Thus, CU creep tests are not useful for studying the shear creep behaviour of peat. The small v ( ) for SBT specimens and relatively larger v ( ) for remoulded peat specimens reflect the horizontally laid fabric layer in the SBT and disoriented fibres in the remoulded specimens [28]. The similarity of the v value from the two SBT specimens with long and fine fibres (SD1 and SD2) indicates that the reinforcing effect of peat fibres is not dominant during CD compression. The slight increase in the v value in SD2 compared to specimen SD1 is analogous to the increase in v with the decreasing effective confining pressure [16]. 7 Conclusions This paper presented the results from five triaxial consolidated drained and four consolidated undrained creep tests conducted under deviator and isotropic stress increments on remoulded and SBT fibrous peat specimens. The creep behaviour of peat can be explained based on the framework developed for soft, normally consolidated clay. The uniqueness of the p 0 e v _e v relationship devised for clay was also applicable to peat. For the applied stress range, this uniqueness held true regardless of the number and magnitude of stress increments applied. Moreover, the development of volumetric creep rate can be defined with respect to the Iso-NCL or NCL. At the same volumetric strain rate ( _e v ), the development of volumetric strain (e v ) depended on the applied stress condition. At any _e v and at the same mean pressure (p 0 ), higher e v developed under deviator stress (q) than under isotropic stress (r 0 3) increments. Similarly, at any constant p 0 and loading duration (t), the _e v were higher under the q increments. This hardening behaviour of specimen under r 0 3 increments was attributed to the anisotropic nature of peat related to the layering of peat fibres in a horizontal direction while the peat fibres were continuously compressed in a vertical direction. This implies that the widely used assumption in creep deformation of clay, i.e. the development of volumetric creep rate is independent of the stress condition, might not be valid for fibrous peat. Singh and Mitchell s [31] creep equation proposed for clay was used to represent the development of volumetric and axial creep strain in fibrous peat. Compared to that in normally consolidated clay, the measured strain rate was higher and the decrease in strain rate was slower in peat, and this resulted in the considerable difference in the value of the fitted creep parameters. The CD creep tests on fibrous peat also verified the validity of using C a for a range of stress. Slight decrease in C a is observed at the later stage of tests. For the SBT specimens, the average Poisson s ratio (m) calculated from CD tests ranged from 0.8 to 0.14, resulting in almost 1D compression; slightly higher values (0.19 and 0.27) were found in the remoulded peat specimens. The m was dependent on confining pressure and was smaller under higher confining pressures. The small value of m indicates that the development of shear strain is less

18 significant in CD creep tests and a separate analysis for e q is thus not presented. CU tests are routine tests conducted to define the strength parameters of fibrous peat. The problem with CU tests is the rapid growth of pore pressure, which surpasses the cell pressure and results in failure of the specimens due to a lack of lateral confinement. Of the four specimens tested, three failed without developing a shear plane when the axial strain reached 10 15%. Thus, creep strain generated under undrained loading is not only deviatoric creep strain. Moreover, undrained creep tests are not very useful for measuring deviatoric creep strain in peat. Acknowledgement The authors acknowledge the contribution of Canadian National Railways for providing both the project and funding support. This research was made possible through the (Canadian) Railway Ground Hazard Research Program and the Canadian Rail Research Laboratory ( both of which are supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), CPR, CN, American Association of Railroads Transportation Technology Center Inc. (AAR/TTCI) and Transport Canada; and an NSERC Discovery Grant. References 1. Acharya MP, Hendry MT, Martin CD (2015) Thermally induced pore pressure response in peat beneath a railway embankment. Int J Geotech Eng 10(2): Acharya MP, Hendry MT, Martin CD (2016) Effect of the presence and movement of gas bubbles on pore pressure behaviours observed in peat. Can Geotech J 53(5): Atkinson JH (1978) The Mechanics of Soils: An Introduction to Critical State Soil Mechanics. McGraw-Hill University Series in Civil Engineering 4. Barden L (1968) Primary and secondary compression of clay and peat. Géotechnique 18: Barden L (1969) Time dependent deformation of normally consolidated clays and peats. J Soil Mech Found Div 95(1): Berry PL, Poskitt TJ (1972) The consolidation of peat. Géotechnique 22(1): Bjerrum L (1967) Engineering geology of Norwegian normally consolidated marine clays as related to settlements of buildings. Géotechnique 17(2): doi: /geot Den Haan EJ (1996) A compression model for non-brittle soft clays and peat. Géotechnique 46(1): Dhowian AW, Edil TB (1980) Consolidation behaviour of peats. Geotech Test J 3(3): Edil TB, Wang X (2000) Shear strength and Ko of peats and organic soils. In: Edil TB, Fox PJ (eds) Geotechnics of High Water Content Materials, ASTM STP 1374, ASTM International, West Conshohocken, PA: Farrell ER (2012) Organics/peat soils. In: Burland J, Chapman T, Skinner H, Brown M (eds) ICE manual of geotechnical engineering, vol 1. ICE Publishing, London, pp Graham J, Crooks JHA, Bell AL (1983) Time effects on stress strain behaviour of natural soft clays. Géotechnique 3(3): Gunaratne M, Stinnette P, Mullins AG (1998) Compressibility relations for peat and organic soil. J Test Eval 26(1): Hendry MT, Sharma JS, Martin CD, Barbour SL (2012) Effect of fibre content and structure on anisotropic elastic stiffness and shear strength of peat. Can Geotech J 49(4): Hobbs NB (1986) Mire morphology and the properties and behaviour of some British and foreign peats. Q J Eng Geol Hydrogeol 19(1): Hollingshead GW, Raymond GP (1972) Field loading tests on muskeg. Can Geotech J 9(3): Kelln C, Sharma J, Hughes D, Graham J (2008) An improved elastic-viscoplastic soil model. Can Geotech J 45(10): Kim YT, Leroueil S (2001) Modelling the visco plastic behaviour of clays during consolidation: application to Berthierville clay in both laboratory and field conditions. Can Geotech J 38: Landva AO (2007) Characterization of Escuminac peat and construction on peatland. In: Proceedings of the 2nd international workshop on Characterisation and Engineering Properties of Natural Soils, Singapore, pp Landva AO, La Rochelle P (1983) Compressibility and shear characteristics of Radforth peats. American Society for Testing and Materials, Testing of peat and organic soils, STP 820, West Conshohocken, pp Landva AO, Pheeney PE (1980) Peat fabric and structure. Can Geotech J 17(3): Leroueil S, Kabbaj M, Tavenas F, Bouchard R (1985) Stress strain strain rate relation for the compressibility of sensitive natural clays. Géotechnique 35(2): Long M (2005) Review of peat strength, peat characterization and constitutive modelling of peat with reference to landslides. Stud Geotech Mechan 27(3 4): MacFarlane IC (1965) The consolidation of peat: a literature review. National Research Council of Canada Division of Building Research Ottawa, NRC, pp Madaschi A, Gajo A (2015) One-dimensional response of peaty soils subjected to a wide range of oedometric conditions. Géotechnique 65(4): Mesri G, Stark TD, Ajlouni M, Chen CS (1997) Secondary compression of peat with or without surcharging. J Geotech Geoenviron Eng (5): Murayama S, Shibata T (1964) Flow and stress relaxation of clays. International union of theoretical and applied mechanics symposium rheological soil mechanics, Grenoble, France: O Kelly BC, Zhang L (2013) Consolidated-drained triaxial testing of peat. ASTM Geotech Test J 36(3): Rowe RK, MacLean MD, Soderman KL (1984) Analysis of a geotextile reinforced embankment constructed on peat. Can Geotech J 21(3): Samson L, La Rochelle P (1972) Design and performance of an expressway constructed over peat by preloading. Can Geotech J 9: Singh A, Mitchel JK (1968) General stress strain-time functions for soils. ASCE J Soil Mech Found Div 94(SM1): Sukje L (1957) The analysis of the consolidation process by the isotaches method. In: Proceedings, 4th international conference on soil mechanics and foundation engineering, London, England, vol I, pp Tavenas F, Leroueil S, La Rochelle P, Roy M (1978) Creep behaviour of an undisturbed lightly over consolidated clay. Can Geotech J 15: doi: /t Weber WG (1969) Performance of embankments constructed over peat. J Soil Mechan Found Div 95(1): Wilson NE, Radforth NW, MacFarlane IC, Lo MB (1965) The rates of consolidation for peat. Proceedings, 6th international conference. Soil Mechan Montreal 1: Guanlin Ye, Feng Zhang, Kiyokaza Naito, Hla Aung, Atsushi Yashima (2007) Test on soft sedimentary rock under different loading paths and its interpretation. Soils Found 47(5):