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Experimental and analytical framework for modelling soil compaction
Engineering Geology 175 (2014) 22–34
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Engineering Geology journal homepage: www.elsevier.com/locate/enggeo
Experimental and analytical framework for modelling soil compaction Bernardo Caicedo a,⁎, Julián Tristancho b,1, Luc Thorel c,2, Serge Leroueil d,3 a
Universidad de Los Andes, Cra. 1 Este No. 19 A-40, Bogotá, D.C., Colombia Universidad Distrital Francisco José de Caldas, Cra. 7 No. 40B-53, Bogotá, D.C., Colombia c LUNAM University, IFSTTAR, GER Department, Physical Modelling in Geotechnics, Route de Bouaye, BP4129, 44341 Bouguenais cedex, France d Département de génie civil, Université Laval, Pavillon Adrien-Pouliot-1065, av. de la Médecine, Québec, Québec G1V 0A6, Canada b
a r t i c l e
i n f o
Article history: Received 17 April 2013 Received in revised form 8 January 2014 Accepted 24 March 2014 Available online 3 April 2014 Keywords: Compaction Laboratory tests Constitutive relations Anisotropy Partial saturation Deformation
a b s t r a c t Compacted materials are fundamentally unsaturated soils whose behaviour can be expansive or collapsible depending upon changes in water content or stresses. Their behaviour is strongly dependent upon matric suction, water content, and stress history. This paper presents a methodology for investigating the stress/strain, and suction/water content paths during one dimensional compaction of unsaturated soils. It focuses on anisotropic behaviour. The testing programme was carried out in a new automated oedometer apparatus that allows measurement of axial strain, radial and axial stresses, suction, and water content during tests. The laboratory component used in this study involves kaolin compacted with different water contents. After compaction, the soil was subjected to wetting while the volumetric changes and stress paths were being examined. The results were interpreted within an anisotropic elasto-plastic framework. The proposed methodology provides new insights into the behaviour of unsaturated soils during compaction and wetting. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Throughout the world compacted soils are used as construction materials in numerous geotechnical contexts. In spite of huge advances in unsaturated soil mechanics in the last 20 years, there continues to be a disconnection between the current design of geotechnical earthworks based on Proctor's ideas and the fundamental principles of unsaturated soil mechanics. Two reasons may explain this disconnection: (i) the simplicity of Proctor's tests compared to the high complexity of tests on unsaturated soils with controlled suction; and (ii) the absence of well-understood constitutive laws of how stress and suction during compaction are related to the post compaction behaviour of soils. These two difficulties could be overcome by combining the development of new laboratory apparatuses which would allow the study of compaction by measuring the state variables of the unsaturated soil (including stresses, matric suction, water content and void ratio) with the use of constitutive models adapted to compacted soils.
⁎ Corresponding author at: Universidad de los Andes, Cra. 1 Este No. 19 A-40, Bogotá, Colombia. Tel.: +57 1 3324312; fax: +57 1 3324313. E-mail addresses: [email protected] (B. Caicedo), [email protected] (J. Tristancho), [email protected] (L. Thorel), [email protected] (S. Leroueil). 1 Tel.: +57 1 3239300. 2 Tel.: +33 240845808; fax: +33 240845997. 3 Tel.: +1 418 656 2206; fax: +1 418 656 2928.
http://dx.doi.org/10.1016/j.enggeo.2014.03.014 0013-7952/© 2014 Elsevier B.V. All rights reserved.
To include unsaturated characteristics in the understanding of compacted soils, Toll (1988), Schreiner (1988), Maswoswe et al. (1992), Li (1995), Delage and Graham (1996) and Alonso (1998), among others, have characterised the post-compaction suction and microstructure of soils compacted using oedometric paths. However, most of these works were carried out after compaction without controlling the history of stresses and phase variables during compaction. The possibility of following the stress and phase variables paths during compaction has recently become possible with the development of suction measurement systems based on psychrometers (Zerhouni, 1995; Blatz and Graham, 2000, 2003; Caicedo et al., 2008) or on high capacity tensiometers (Ridley and Burland, 1993; Jotisankasa et al., 2007; Tarantino and Tombolato, 2008). Concerning constitutive laws for compacted soils, Cui and Delage (1996), Leroueil and Barbosa (2000) and Ghorbel and Leroueil (2006) have all shown the essentially anisotropic behaviour of compacted soils, in particular in terms of yielding. Moreover, Tarantino and De Col (2008) studied the microstructure of compacted soils at different water contents and presented a one dimensional mechanical model adapted to reproducing soil behaviour during compaction. The purpose of this paper is to present a methodology to investigate the stress/strain, and suction/water content paths during oedometric compaction of unsaturated soils. The results are interpreted in an anisotropic elastoplastic framework combining the characteristics of the models presented by Cui and Delage (1996), Leroueil and Barbosa (2000) and Ghorbel and Leroueil (2006). The proposed methodology
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provides new insights into the behaviour of unsaturated soils during compaction and subsequent wetting. 2. Compaction interpreted within the framework of unsaturated soil mechanics Fig. 1 presents the description of the stress path of a soil subjected to oedometric compaction in a plane of radial total vs axial total stresses (σr, σa), Alonso (1998). It shows the critical state lines, CSLs, in compression and in extension for zero and positive suction value, and it shows the K0 line, which is defined as the relationship between radial and axial stresses during one dimensional compression under zero radial strain. Oedometric compaction could be described as follows. First the soil is mixed and prepared in unsaturated conditions. In this initial state the soil is represented by an unsaturated yield surface (F1). Next, if an axial stress is applied, radial stress increases within the elastic domain to the surface F1 (paths A to B). After the stress path continues in the plastic domain following the anisotropy line up to a second yield surface (F2) (paths B to C). If the soil is then unloaded, the axial and radial stresses decrease in the elastic domain and the CSL in extension may be attained. If it is, the path will follow this CSL until the axial stress equals zero (paths C, D, E). It is important to note that when zero axial stress is reached, a radial stress remains within the unsaturated soil (point E). On reloading, the stress path remains within the elastic domain up to the F2 yield surface; afterwards the path follows the anisotropy line and defines a new and larger yield surface. On the other hand, if after unloading there is a change in suction, as for example saturation of the soil under zero axial stress, the radial stress goes to zero (paths E to O), and swelling or collapse occurs, depending on the position of the loading collapse surface. It is important to keep in mind that the previous explanation is a simplified approach to in situ compaction. In fact, oedometric compaction allows obtaining similar compaction curves than the Proctor's procedure, Biarez (1980). However, moving loads due to in situ compaction produces cyclic loads and rotation of stresses that create stress paths different from the oedometric stress path used in this study, Caicedo et al. (2012). These effects must be included in further researches.
compression while measuring the axial and radial stresses, suction, void ratio and water content during compaction. To accomplish this, the cell includes the following features (see Figure 2): (1) The compression piston in the cell has a large displacement capacity. This allows it to perform compaction tests starting with soils in a loose state and finishing with soils having dry unit weights similar to those obtained in Proctor's tests (The initial size of the sample is 78 mm in height and 70 mm in diameter, the final height of compacted samples varies between 53 mm and 43 mm depending on the water content). (2) The large displacement of the soil produced by one moving piston can result in significant variation in dry density across the sample due to the friction between the soil and the mould. This friction can be reduced either including two moving pistons or reducing friction with an internal Teflon cylinder. The second option has been included in the oedometric cell. The effectiveness of this solution was confirmed verifying that the dry density for samples located at the top and the bottom of the soil varies in less than 2%. (3) The cell is equipped with a capacitive sensor to measure the water content in the soil during compaction. For this reason plastic materials were used in most of the cell design. However, to avoid undesirable radial displacement the cell was conceived with a thick cylinder wall (32 mm) of composite material (phenolic resin reinforced with glass fibres).
3. Materials and equipment 3.1. Oedometric cell for K0 measurement The oedometric cell used in this research was designed to reproduce soil compaction by increasing the axial stress under one dimensional
Fig. 1. Stress path during oedometric compaction.
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Fig. 2. Layout of the instrumented oedometric cell.
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(4) The cell has three Teflon pistons equipped with miniature load cells to measure the radial stress. (5) Three Peltier psychrometers, in contact with the soil, are located in the wall of the cell at the same level as the Teflon plugs. (6) A capacitive water content sensor is located in the centre of the sample. The measuring electrodes are located at the same level as the psychrometers and the radial load cells. 3.2. Radial stress measurement system Previous studies on the measurement of radial stress in oedometric cells have used two different methods. One method is to use an apparatus with a steel membrane equipped with strain gauges, with pressurized oil behind the membrane to compensate for the strains (Hendron, 1963; Brooker and Ireland, 1965; Komornik and Zeitlen, 1965; Saxena et al., 1978; Elif et al., 2009). The other method which has been used includes small load cells fitted into the wall of the cylinder (Thompson, 1963; Abdelhamid and Krizek, 1976; Schreiner, 1988; Schreiner and Burland, 1991). This second method is used in this research. A set of three low compliance load cells were installed into holes in the thick cylinder wall (Figure 2b). These load cells act on three Teflon pistons in contact with the soil and react upon a rigid steel ring. The compliance of the whole system was evaluated by direct measurements and F.E. analysis, this analysis show that the relative displacement between the wall of the oedometer and the set piston-load cell is about 20 μm at the maximum radial load achieved during tests. 3.3. Thermocouple psychrometers Three commercially available thermocouple psychrometers (Wescor PST-55) are utilised to measure suction during testing. The psychrometers were installed in three holes in the thick wall and then the holes were filled with soil to insure adequate contact between the soil and the screens of the psychrometers. The psychrometers were monitored using a Psypro Wescor data acquisition system. Peltier psychrometers permit the measure of total suction through the measure of two thermocouples: the reference thermocouple and the measurement thermocouple. However temperature affects the psychrometric readings in two ways: one is the effect in the measurement thermocouple and the other one is the effect of the temperature gradient between the reference and measurement junctions. To correct the first effect an adjustment equation, cf. Wescor (1998), can be used. The second effect is controlled verifying the difference of temperature between the two junctions before the measure (offset measurement). This offset should be less than 3 μV for meaningful measurements; higher offsets are evidence of excessive thermal gradients. Due to the influence of temperature on the psychrometric readings, the best procedure to perform psychometric measurements is to carry out the tests in a temperature controlled room. In the case of this research, the recorded variation of temperature in the room was less than 2 °C; however a room with better controlled temperature is necessary to have more valid measures. In addition, the effect of temperature was reduced using for the structure of the oedometer a material having low thermal conductivity. It is important to note that psychrometers are useful for laboratory studies in a controlled temperature room; however are unpractical for in situ studies because of the high temperature variations.
Fig. 3. Calibration of the water content sensor.
Fig. 3 shows the calibration of the sensor for the kaolin compacted at different volumetric water contents. As observed, good linear calibration is obtained over a large range of water contents (r2 = 0.97, and accuracy ± 2%). However the measures of the sensor during loading and unloading shows that the stress level has a slight effect on the calibration (around 2%), as the calibration made for this study avoid this effect, the water content used in the analysis before soaking is the theoretical water content assuming constant weight of water. 3.5. Loading device A loading device was designed to perform compaction under controlled rates of strain or stress. This device has a servomotor coupled to a mechanical actuator. The servomotor can be controlled in load or displacement modes using a load cell (20 kN capacity) or an optical encoder. As a result, the loading device can perform stress or strain controlled compaction tests with an accuracy of 10 N (2.60 kPa) in the stress controlled mode or 1 μm (1.3 ∗ 10−3%) in the strain controlled mode. In this study, the compaction is carried out for controlled rate of strain (CRS tests), followed by stress controlled periods. However, as the test starts with the soil in a loose state and the compaction requires large displacements, the rate of displacement is calculated at each second to take the changing height of the sample and the imposed rate of strain into consideration. In addition an LVDT transducer a 50 mm stroke makes complementary measurements of displacement. 4. Materials and specimen installation The soil used in this study is commercially available kaolin whose properties are presented in Table 1. The liquid and plastic limits are 55% and 30% respectively. The soil was prepared in a mixing machine starting with dry powder. It was gradually sprayed with water to avoid the formation of lumps. Afterwards the soil was sieved at 1 mm to eliminate the presence of large aggregates (Tarantino and de Col, 2008). The mixed soil was then enclosed in a plastic bag and stored in a wet room for one week to guarantee good moisture equilibration and homogeneity. For the compaction tests loose soil was poured into the oedometer cell. Then a mini-hammer applied 5% of the Proctor Standard energy to compact the soil slightly. Next, excess soil was removed to set the Table 1 Characteristics of the kaolin used in the investigation.
3.4. Water content sensor The method used to measure the water content during testing is based on a combination of the resistive method (Matlin, 1975) and the capacitive method (Dupas et al., 2000; Günzel et al., 2003). These methods take advantage of variation in the relative dielectric permittivity and resistivity of the soil with water content.
Liquid limit, wL (%) Plastic limit, wP (%) Particles d at 30% (%) Particles d at 50% (%) Particles d at 90% (%) rρs (g/cm3) Drained friction angle ϕ′, (Bolton and Powrie, 1987)
55 30 1.5 μm 3 μm 9 μm 2.65 23.7° to 25.6°
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sample height at 78 mm for all tests. This procedure was implemented to obtain loose soils with controlled initial conditions. Afterwards a thin walled 19 mm tube was inserted into the middle of the sample to create a cavity in which to place the water content sensor (see Figure 2). 5. Compaction tests The compaction tests were performed in five loading/unloading cycles at a controlled rate of strain. Once the axial stress reaches the maximum or minimum value for each cycle it was maintained constant for another 30 min. The range of axial stress for oedometric compaction has been determined bearing in mind that for kaolin a vertical stress of around 1000 kPa leads to similar compaction curves than Proctor Standard tests, Biarez (1980). The axial stress was increased by an increment of 300 kPa in each loading cycle starting at 300 and increasing in steps to 600, 900, 1200, and finally 1500 kPa, each loading stage continues with unloading to 20 kPa (Figure 4). The strain rate in the first compression stage is 40 μstrain/s. It is higher than in the other cycles because the first compression stage needs a large axial strain to reach the first axial stress limit. However, this larger strain rate does not affect the equilibration of air pressure since the initial soil state is loose. A lower strain rate of 20 μstrain/s was chosen for subsequent cycles. The air pressure was measured in two tests (15% and 25% water content), the results shown that the variations in air pressure were lower than 500 Pa, this value suggest that air pressure could be assumed as zero without significant error. However this variation could have an important effect on the psychrometric measurements, mainly for low suction values. Fig. 4 shows the final state of the sample after each loading stage on a Proctor plot, a comparison with the standard Proctor curve shows that the maximum standard dry density corresponds to a vertical stress between 900 kPa and 1200 kPa, just as stated by Biarez (1980). Once the five cycles were completed the sample was subjected to soaking by introducing water at a pressure of 10 kPa at the base of the sample. For these subsequent loading/unloading cycles five tests were performed at constant, but different, water contents with soaking during the final unloading stage. One additional test was performed at 10% water content with soaking the sample at the maximum axial stress (see Table 2).
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Table 2 Test characteristics. Test
Water content (%)
Axial stress during wetting (kPa)
1 2 3 4 5 6
5 10 15 20 25 10
20 20 20 20 20 1500
Fig. 5 shows axial strain versus time for the test carried out at 20% water content. The loading/unloading cycles are clearly identified as are the stages of constant axial stress. Upon wetting the axial strain decreases as a result of axial expansion (bearing in mind that compression strains are considered positive). Figs. 6 and 7 show the evolution of axial strain (Figures 6a and 7a) and the axial and radial stresses during the tests performed on two samples compacted at 10% water. Yielding stress is clearly noticeable
through a slope variation during loading mainly in axial stress. For the sample wetted under an axial stress of 20 kPa (Figure 6), there is axial swelling associated with a decrease in radial stress. On the other hand, for the sample wetted under an axial stress of 1500 kPa (Figure 7), there is axial collapse associated with a significant increase in radial stress. This is a clear evidence of anisotropic behaviour during wetting as it will be clarified later. In addition, concerning radial stress during wetting, a non-monotonic trend is observed in Figs. 6(c) and 7(c). However, this tendency appears during the transient wetting phase, for which the soil in the oedometer has not homogeneous conditions. The evolution of radial and axial stresses during loading/unloading cycles is presented in Fig. 8. The results show two types of behaviour. One is a tangential relationship along which the stress paths gather after reaching the yield stress in each cycle. The other behaviour occurs when axial and radial stresses in each cycle are lower than the maximum values previously reached. The results show that the second behaviour depends on stresses, whereas the tangential behaviour is essentially independent of stresses. On soaking, radial stresses decreases in all the cases for which soaking is performed at the minimum vertical stress (σa = 20 kPa), whereas the radial stress increases when soaking is performed after final loading (σa = 1500 kPa); Table 3 shows radial stresses achieved at the final stage of compaction, before and after soaking. Fig. 9 shows the stress path cycles for the various tests in the s, t plane, in which s = (σa + σr) / 2, and t = (σa − σr) / 2. Except for the last test (Figure 9f), all the unloading paths finished at a stress point within a line corresponding to a constant axial stress of σa = 20 kPa. Under these conditions radial stress is positive, however when samples are wetted the radial stress decreases significantly. On the other hand, when wetting is performed at the maximum axial stress of σa = 1.5 MPa (Figure 9f), radial stress increases. Similar behaviour has been identified by Schreiner and Burland (1991) for single stage compaction. Although psychrometers measure total suction, comparative measures of suction made by Tarantino and De Col (2008), and Tarantino (2009), using high capacity tensiometers and transistor psychrometers, shown that for kaolin mixed with demineralised water the osmotic component of suction is negligible, so measured suction can be considered to be close to matric suction.
Fig. 4. Comparison between proctor standard curve and final state of the samples after each loading stage.
Fig. 5. Loading and unloading cycles measured during the test carried out at 20% water content.
6. Results
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Some of the measurements made with psychrometers shown extreme suction, these readings were interpreted as invalid measurements because: (i) the time necessary for the equilibration between the humidity of air in soil and the humidity of air in the psychrometer is about 20 min but maintaining constant air pressure. (ii) a small variation of air pressure, as a result of loading and unloading, affects the relative humidity of the air in the psychrometer: relative humidity grows as air pressure grows and vice-versa, consequently under these conditions the variation of suction measured with psychrometers could be amplified; in fact if air pressure doubles, the psychrometric constant doubles (Rawlins and Campbell, 1986). As a consequence of these difficulties, to choose the valid psychrometer readings an additional criterion to the conventional offset criterion must be applied. Variations from the initial suction higher than 1.5 the standard deviation of the whole measurements for any water content
Fig. 7. Evolution of the axial strain, and axial and radial stresses during loading for the soil compacted at 10% water content and wetted under an axial stress of 1500 kPa.
Fig. 6. Evolution of the axial strain, and axial and radial stresses during loading for the soil compacted at 10% water content and wetted under an axial stress of 20 kPa.
has been chosen as criterion to eliminate extreme suctions. This criterion is not physically based criterion, however it is wide enough to conserve the suction variations due to soil behaviour and tighter to eliminate spurious values. The variation of suction during tests, considering only the valid measures, in terms of radial and axial stresses is presented in Fig. 10, this figure shows some variation of suction during loading and unloading, however it is difficult to assess any hydraulic path due to the discontinuous characteristic of the psychrometric measurements. On the other hand, for the high suction values or low water contents explored in this paper, the suction is not significantly influenced by the change in void ratio. The variation of suction during tests in terms of degree of saturation Sr plotted against suction (ua − uw) is presented in Fig. 11. Despite the difficulties in suction measurement using psychrometers, the results presented in Fig. 11 show an increase in the degree of saturation with compaction and a general decrease in suction when water content increases. Furthermore, when considering the extreme values during loading and unloading it is possible to identify two
B. Caicedo et al. / Engineering Geology 175 (2014) 22–34
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presented by Leroueil and Barbosa (2000). The slope of the normal compression lines in Fig. 14 are roughly similar (parallel lines in the range 0.2 MPa b p b 1 MPa). This could correspond to an intermediate behaviour between: decreasing slope as the suction increases; or steeper compression lines at higher suctions reported by Alonso et al. (1990) and Wheeler and Sivakumar (1995) respectively; however it is important to keep in mind that the results presented in Fig. 14 are obtained at constant water content and not at constant suction like the results presented in these researches. On the other hand the evolution of void ratios during unloading follows lines having the same slope for all water contents, just as described by Alonso et al. (1990). 7. A constitutive model for soil compaction The behaviour of compacted soils is noticeably anisotropic, as demonstrated by Cui and Delage (1996). This stress induced anisotropy appears to be a result of the distribution of contacts between particles that reflects the forces applied. Most constitutive models for unsaturated soils were developed for isotropic soils (Alonso et al., 1990). In models developed for anisotropic unsaturated soils, anisotropy remains constant (Cui and Delage, 1996; Leroueil and Barbosa, 2000; Ghorbel and Leroueil, 2006). This characteristic reduces the capacity of these models to capture the evolution of anisotropy during compaction. The constitutive model proposed in this paper is however based on the GFY model (Given Fabric Yielding) proposed by Leroueil and Barbosa (2000), and Ghorbel and Leroueil (2006). This model was developed based on the yield curves proposed by Larsson (1977) for natural clays. When this model is applied to unsaturated compacted soils, it permits to model the change in anisotropy during loading. 7.1. Stress variables
Fig. 8. Evolution of radial and axial stresses during the loading/unloading cycles.
lines: compression lines showing decreasing suction as the saturation increases, and post compaction lines limiting the values of suction during unloading. However more valid measurements are required to draw these lines more precisely. The stress ratio K = σr / σa observed during the loading stages of the tests is shown as a function of σa in Fig. 12. Except at relatively low stresses where the soil may be in its pre-yield domain, the K values are relatively constant. These values are strongly influenced by water content: the higher the water content, the higher the value of K, except for the lower water contents (10%, 5%) for which the stress ratio K tend to the same value. These results indicate that K decreases when suction increases but tends to a constant value for higher suctions as shown in Fig. 13. Fig. 14 shows the normal compression lines obtained at different water contents. It can be seen that, at a given void ratio, the lower the compaction water content (thus the higher the suction) the larger is the mean stress. This is consistent with the oedometer test results
To ensure a continuous transition from saturated to unsaturated conditions Ghorbel and Leroueil (2006) proposed using “modified net stress” and matric suction as stress variables. The coefficient ζ⁎, and modified net stress σ⁎ are defined as follows:
σ ¼ σ −ua þ ζ ðua −uw Þ
ð1Þ
with
ζ ¼ 1 for
ð2Þ
ðua −uw Þ≤ ðua −uw Þb
and
ζ ¼
ðua −uw Þb ðua −uw Þ
for
ðua −uw ÞNðua −uw Þb
ð3Þ
where (ua − uw)b is the matric suction corresponding to the air entry value of the soil, defined as the suction value below which the soil remains saturated.
Table 3 Radial stress change after final compaction, unloading and soaking. Water content %
5 10 15 20 25 10
Vertical stress on soaking
Radial stress final loading
Radial stress before soaking
Radial stress after soaking
(kMPa)
(kPa)
(kPa)
(kPa)
20 20 20 20 20 1500
501 504 526 554 667 502
213 215 196 218 225 502
⬇ ⬇ ⬇ ⬇ ⬇ ⬆
8 68 52 103 195 554
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Fig. 9. Stress path followed in the s, t plane.
7.2. Water retention model
reloading cycles (scanning behaviour) proposed by Tarantino and De Col (2008) is as follows:
Romero and Vaunat (2000), Gallipolli et al. (2003), and Tarantino (2009) proposed a water retention model for deformable soils. The equation following equation was proposed by Gallipolli et al. (2003):
Sr ¼ Sr0 −ks ðua −uw Þ−ðua −uw Þ0 :
( Sr ¼
1 n 1 þ ϕðua −uw Þeψ
)m ð4Þ
where e is the void ratio, and φ, ψ, n and m are the parameters of the model. The expression for matric suction during the unloading/
Fig. 10. Variation of suction measured during tests plotted in terms of axial and radial stresses.
ð5Þ
Here (ua − uw)0 and Sr0 are the suction and degree of saturation when unloading begins, and ks is the slope of the scanning curve in the space relating matric suction with degree of saturation. 7.3. Yield surface and loading collapse functions The stress path soils follow during compaction is comparable to the stress path followed by soft clays during normal consolidation. As
Fig. 11. Degree of saturation–suction measured during tests at compaction with different water contents.
B. Caicedo et al. / Engineering Geology 175 (2014) 22–34
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Fig. 12. Stress ratio, K = σr / σa, calculated from the results of the tests.
Larsson (1977) hypothesised for such materials, they cannot be subjected to stresses in any direction larger than the maximum stresses already applied. Under these circumstances the yield curves can be schematized by four segments: two corresponding to the strength envelopes in compression and in extension; and two corresponding to the maximum axial and radial stresses previously applied to the soil. Leroueil and Barbosa (2000), and Ghorbel and Leroueil (2006) expand this concept to unsaturated soils (Figure 15). Anisotropic behaviour can be represented using the stress variables s and t defined under modified net stress as s* and t*, where s* = (σ⁎a + σ⁎r) / 2, and t* = (σ⁎a − σ⁎r) / 2. In the plane s*, t*, a soil in saturated conditions has a yield curve of the type OB0A0D0. A given suction should extend the saturated cap B0A0D0 to an unsaturated cap BsAsDs with an increase in axial yield stress from σ⁎ay0 to σ⁎ays, and an increase in radial yield stress from σ⁎ry0 to σ⁎rys. The variation of the axial and radial stresses with suction corresponds to two loading collapse curves, LCa in the axial and LCr in the radial directions (Figure 15b). By increasing the axial yield stress from σ⁎ay0 to σ⁎ays matric suction increases the shear strength of the soil under compression from point B0 to point Bs, or from B0 to B′. According to Ghorbel and Leroueil (2006), the increase in shear strength in compression due to suction is Δτ fc ¼
i sinϕ0 cosϕ0 h σ ays −σ ayb 0 1 þ sinϕ
ð6Þ
Fig. 14. Compression curves in the void ratio vs. mean stress plane.
Vanapalli et al. (1996) proposed an equation for predicting shear strength as a function of matric suction and volumetric water content. Expressed in terms of the water ratio ew, this equation is as follows (Ghorbel and Leroueil, 2006): e −e 0 Δτ f ¼ ðua −uw Þ w wr −ðua −uw Þb tanϕ : ews −ewr
From Eqs. (6) and (8), Ghorbel and Leroueil (2006) proposed the following expressions for the LC curves:
σ ays −σ ayb ¼
1− sinϕ0 ew −ewr ðua −uw Þ −ðua −uw Þb for 02 ewsat −ewr cosϕ
LCa ð9Þ
and the increase in shear strength in extension is i sinϕ0 cosϕ0 h σ rys −σ ryb : Δτ fe ¼ 0 1 þ sinϕ
ð8Þ
, and ð7Þ
In Eqs. (6) and (7) σ⁎ayb and σ⁎ryb are the axial and radial modified net yield stresses for a value of matric suction corresponding to the air entry value. Δτfc is the contribution of strength due to matric suction in compression, in excess of the air entry value, while Δτfe is the contribution of strength due to matric suction in extension, in excess of the air entry value.
σ rys −σ ryb ¼ K AL
0 1− sinϕ ew −ewr ð u −u Þ ð −u Þ − u a w a w b for LCb ewsat −ewr cosϕ02 ð10Þ
where K⁎AL is the anisotropic parameter defined as
K AL ¼
σ rys : σ ays
ð11Þ
The previous model is conceptual; in reality, yield curve is certainly more rounded than the four segment surface of the GFY model. An elliptic surface has been proposed by Cui and Delage (1996) for anisotropic unsaturated soils. In a parametric form and in the plane (s⁎, t⁎), Fig. 16; the ellipse can be expressed as the path of a point (s⁎(ξ), t⁎(ξ)), where
ð12Þ
ð13Þ
s ðξÞ ¼ sc þ ae cosðξÞ cosðθÞ−be sinðξÞ sinðθÞ
t ðξÞ ¼ t c þ ae cosðξÞ sinðθÞ þ be sinðξÞ cosðθÞ:
Fig. 13. Stress ratio, K = σr / σa, vs. suction.
Here, the point (s⁎c, t*c) is the centre of the ellipse, θ is the angle between the s⁎ − ua axis and the anisotropy line, ae and be are the major and minor semi-axes, and ξ is a variable used to describe the
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ew −ewr 1 0 ss ¼ Δτ f = sinϕ ¼ ðua −uw Þ −ðua −uw Þb cosϕ0 ewsat −ewr
tanθ ¼
ð16Þ
σ ays −σ rys : σ ays þ σ rys
ð17Þ
As a result, the centre of the ellipse and the major semi axis are
sc ¼
sk þ ss 2
ð18Þ
t c ¼ tanðθÞsc
ae ¼
ð19Þ
sk −ss 1 : 2 cosθ
ð20Þ
The angle α in the centre of the ellipse between the anisotropy line and the line linking the point (s⁎0, 0) and the centre is α ¼ cos
−1
s0 −sc −t c tanθ ae ð sinθ tanθ þ cosθÞ
ð21Þ
and the minor semi-axis is be ¼
Fig. 15. Yield surface for the GFY model proposed by Leroueil and Barbosa (2000), and Ghorbel and Leroueil (2006).
ellipse in parametrical form. The values of the parameters ae, be, and (s⁎c, t*c) can be derived if three points of the ellipse are known: the maximum and minimum points along the major axes, s⁎k and s⁎s respectively; and the intercept of the ellipse at t⁎ = 0, s⁎0. As the yield curve is more rounded than the four segment surface of the GFY model, unloading paths crosses the axis t⁎ = 0 for a stress value slightly lower than σ⁎rys; a value of s⁎0 = 0.9 σ⁎rys shows good agreement for most of the unloading paths measured experimentally. The values of s⁎0, s⁎s, and s⁎k, and θ can be easily found by fitting the ellipse into the GFY model (Figure 15) as follows:
σ ays þ σ rys 2
sk ¼
s0 ¼ 0:9σ rys
ð14Þ
ð15Þ
sc −s0 þ ae cosð−α Þ cosθ : sinð−α Þ sinθ
ð22Þ
8. Application of the model to experimental results The evolution of suction during cyclic oedometric compaction can be calculated using Eq. (4) that describes the evolution of suction during compression and Eq. (5) describing the variation of suction on unloading. Eq. (4) was adjusted fitting the suction measurements obtained during compression, Fig. 10, with their corresponding saturation degree; this procedure provides an assessment of the constants (m, n, φ, ψ). Afterwards, the parameter ks in Eq. (5) is assessed using the unloading data. The obtained parameters are presented in Table 4, these parameters are different from those presented by Tarantino and De Col (2008) because the kaolin used in both studies have wide differences, particularly in its grain size distribution: 80% of particles with d b 2 μm in Tarantino and De Col (2008), and 40% in this study. Fig. 17 shows the evolution of suction during loading and unloading calculated with Eqs. (4) and (5), and the experimental results, also two extreme suction curves are presented corresponding to two void ratios (e = 1.9, and e = 0.9). The figure shows that the amplitude of the suction cycles corresponds to the amplitude measured experimentally and the calculated suctions are close to the measurements; however no exact matching appears between experimental and calculated suctions, this is associated to the difficulties in the equilibration of psychrometers during cyclic loading. Fig. 18 shows the stress paths determined experimentally during compaction tests and the elliptical yield surfaces obtained from the proposed model. According to the proposed model, compaction by cyclic loading can be described as follows: the loading path in the plane (s⁎, t⁎) starts in the elastic domain corresponding to the previous Table 4 Coefficients used in the model.
Fig. 16. Elliptical yield surface fitted into the GFY model.
m
n
φ
ψ
0.414
1.243
0.013
1.885
(ua − uw)b
ewr
Fϕ′
0
0
25.6°
B. Caicedo et al. / Engineering Geology 175 (2014) 22–34
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collapse curves calculated with Eqs. (9) and (10). These curves show how the LC curves move towards larger stresses as a result of successive loading cycles. The coefficients of the model used for the elliptical yield surfaces and the LC curves are presented in Table 4. Using this proposed model, the behaviour of the anisotropic soil during wetting can be explained. Figs. 20 and 21 illustrate the behaviour of soil compacted at 10% water content and wetted under an axial stress of 20 kPa (Figure 20), and then wetted under the maximum axial stress of 1500 kPa (Figure 21). In both cases the yield surface at the final loading cycle is the same Fs5. Consequently, the movement of stress paths and yield surfaces as a result of wetting is as follows:
Fig. 17. Modelling the hydraulic paths during compaction tests.
loading cycle and continues up to the yield surface; then the stress path continues towards and finally along the K line which is associated with the water content or, more precisely, which is associated with suction. During unloading, the stress path goes down a more or less linear path in the elastic domain, possibly to the yield surface. Afterwards the stress path follows the elliptical yield surface up to the line corresponding to the minimum axial stress. Fig. 17 shows that the agreement between the model and the test results is reasonably valid for all water contents and all cycles. Fig. 19 shows the suction calculated with Eqs. (4) and (5) as a function of the radial and axial modified net stresses, and the experimental measurements of suction. Good agreement is observed regarding the level of suction for each test, however in some tests the trend of the measures during compression does not agree with the theoretical prevision; this is probably related to the variability on the suction measurements. In addition, this figure shows the axial and radial loading
(i) When wetting is carried out at the minimum axial stress (σa = σa⁎ = 20 kPa), the suction reduces, the stresses σ⁎ays and σ⁎rys reduce, and the yield curve changes from Fs5 to F0. Stress conditions located at point A, on Fs5, must follow the change in the yield curve to B on F0, with a reduction in σr. (ii) When wetting is carried out at the maximum axial stress (σa = σa⁎ = 1.5 MPa), the reduction in suction in the LCa plane produces collapse, and growth in the size of the yield curve (Figure 21c). However, the reduction in suction is associated with an increase in K from a value of 0.337 for a water content of 10% (Figure 12) and a suction of about 1000 kPa, to a value that would be larger than 0.45 at zero suction. Consequently, σr has to increase from point C to point D in Fig. 21a. 9. Conclusions The experimental programme carried out with the suction-monitored instrumented oedometer apparatus provided new information about the behaviour of unsaturated non-active clay during oedometric compaction. The use of the controlled rate of strain procedure allowed
Fig. 18. Stress paths and elliptical yield surfaces given by the model.
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Fig. 19. Modelling the axial and radial loading collapse curves for the different loading cycles and water contents.
a clear identification of the main features of the volumetric changes against stress: the slope of the virgin compression curve decreases as the suction increases, and all the unloading curves are parallel. The measurement of radial stress during oedometric compaction allowed assessment the stress ratio K = σr / σa for unsaturated conditions. The experimental results show that K0nc increases as the suction decreases. In five tests performed at different water contents the soil was subjected to wetting after final unloading. Under these conditions the soil exhibits anisotropic behaviour for all water contents: exhibiting axial expansion and decreasing radial stress. However, when wetting is performed after loading to the maximum axial stress, anisotropic behaviour changes resulting in axial collapse and increasing radial stress. The behaviour of the soil with anisotropy induced as a result of oedometric compaction has been modelled using inclined ellipses whose size increases with suction, and which have two loading collapse surfaces. One is for the axial direction and the other is one for the radial direction. The characteristic points of the inclined ellipses depend on the position of the two LC curves, suction and the axis of symmetry of the ellipses. This later characteristic reflects induced anisotropy. The results show that the loading/unloading cycles are characterised by stress paths that first remain in the elastic domain and then follow with reasonably accuracy the proposed elliptical yield surface. The anisotropic behaviour during wetting is described by the evolution of the proposed yield surfaces as follows:
Fig. 20. Yield surfaces and stress paths during wetting under an axial stress of 20 kPa, soil compacted at 10% water content.
(i) When the soil is wetted at its minimum axial stress the soil experiences axial expansion as a result of the evolution of the axial stress–suction path in the LCa plane. Stress decreases in the radial direction as a result of the reduction of suction leading to a subsequent reduction in size of the ellipse.
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ua pore air pressure uw pore water pressure (ua − uw) suction (ua − uw)b matric suction corresponding to the air entry value of the soil (ua − uw)0 suction value at the beginning of unloading W water content Δτfc, Δτfe contribution of strength due to matric suction in compression and in extension in excess of the air entry value Fϕ′ friction angle θ angle between the s⁎axis and the anisotropy line σr, σa radial total and axial total stresses σ⁎ modified net stress σ⁎r, σ⁎a modified radial and axial net stresses σ⁎ry0, σ⁎ay0 modified radial net stresses corresponding to zero matric suction σ⁎rys, σ⁎ays modified axial net stresses corresponding to suction different than zero σ⁎ryb, σ⁎ayb radial and axial modified net yield stresses at that matric suction which corresponds to the air entry value ξ variable used to describe the elliptical yield surface in parametrical form ζ⁎ parameter modifying net stress.
Acknowledgements
Fig. 21. Yield surfaces and stress paths during wetting under an axial stress of 1500 kPa, soil compacted at 10% water content.
(ii) When the soil is wetted at its maximum axial stress both LC surfaces are mobilized; there is then axial collapse but as the K0nc coefficient increases when suction decreases, wetting induces an increase of the radial stress. Complete prediction of the stress strain curves during compaction and wetting would require implementation of the proposed yield surfaces in a generalized elasto-plastic model with an appropriate flow rule. This will be included in further developments.
Notation ad,w, bd,w, and nd,w parameters of water retention model for drying and wetting ae, be major and minor semi-axes of the elliptical yield surface e void ratio ew water ratio (ew = eSr) ews water ratio at saturation ewr water ratio at the residual water content [(ew − ewr) / (ews − ewr)]0 water ratio at the beginning of unloading K stress ratio K = σr / σa K⁎AL anisotropic parameter ks slope of the scanning segment of the water retention curve Sr degree of saturation Pp⁎ mean modified net stress p* = (σ⁎a + 2σ⁎r) / 3 s stress variable s = (σa + σr) / 2 s* modified stress variable s* = (σ⁎a + σ⁎r) / 2 t* modified stress variable t* = (σ⁎a − σ⁎r) / 2 s⁎k, s⁎s maximum and minimum points along the major axes of the elliptical yield surface s⁎0 intercept of the elliptical yield surface at t⁎ = 0 t stress variable t = (σa − σr) / 2 (s⁎c, t*c) central point of the elliptical yield surface
The writers would like to express their gratitude to Colciencias, the Colombian research organization that supported the first author during his Ph.D. thesis and the cooperation project ECOS-Nord between France and Colombia.
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Jotisankasa, A., Ridley, A., Coop, M., 2007. Collapse behavior of compacted silty clay in suction-monitored oedometer apparatus. J. Geotech. Geoenviron. Eng. ASCE 867–877 (comment). Komornik, A., Zeitlen, J.G., 1965. An apparatus for measuring lateral soil swelling pressure in laboratory. Proc. 6th Int. Conf. Soil Mechanics and Foundation Eng. vol. 1, pp. 278–281. Larsson, R., 1977. Basic behaviour of Scandinavian soft clays. Swedish Geotech. Inst., Report No 4. Leroueil, S., Barbosa, P.S. de A., 2000. Combined effect of fabric, bonding and partial saturation on yielding of soils. In: Rahardjo, Toll, Leong (Eds.), Unsaturated Soils for Asia. Balkema, Rotterdam, pp. 527–532. Li, Z.M., 1995. Compressibility and collapsibility of compacted unsaturated loessial soils. Proc. 1st int. Conf. Unsaturated Soils, pp. 139–144. Maswoswe, J., Burland, J.B., Vaughan, P.R., 1992. Stress path method of predicting compacted soil collapse. Proc. 7th Int. Conf. on Expansive Soils, pp. 61–66. Matlin, C. (1975). Soil Moisture Sensing System. U.S. patent 3,882,383, May 6, 1975. Rawlins, S.L., Campbell, G.S., 1986. Water potential: thermocouple psychrometry, In: Klute, A. (Ed.), Methods of Soil Analysis Part 1, 2nd ed. pp. 597–618. Ridley, A.M., Burland, J.B., 1993. A new instrument for the measurement of soil-moisture suction. Geotechnique 43, 321–324. Romero, E., Vaunat, J., 2000. Retention curves in deformable clays. In: Tarantino, A., Mancuso, C. (Eds.), Experimental Evidence and Theoretical Approaches in Unsaturated Soils. A.A. Balkema, Rotterdam, pp. 91–106. Saxena, S.K., Hedberg, J., Ladd, 1978. Geotechnical properties of Hackensack Valley varved clays of New Jersey. Geotech. Test. J. 1 (3), 148–161.
Schreiner, H.D., 1988. Volume Change of Compacted African Clays. (PhD thesis) Imperial College of Science, Medicine and Technology, University of London. Schreiner, H.D., Burland, J.B., 1991. A comparison of three swell test procedures. In: Blight, et al. (Eds.), Geotechnics in the African Environment. Balkema, pp. 259–266. Tarantino, A., De Col, E., 2008. Compaction behavior of clay. Geotechnique 58 (3), 199–213. Tarantino, A., Tombolato, S., 2008. Boundary surfaces and yield loci in unsaturated compacted clay. In: Toll, et al. (Eds.), Proc. Unsaturated Soils Advances in GeoEngineering. Taylor & Francis, pp. 603–608. Tarantino, A., 2009. A water retention model for deformable soils. Geotechnique 59 (9), 751–762. Thompson, W.J., 1963. Lateral pressures in one-dimensional consolidation. Proc. 2nd Asian regional Conference on, Soil Mechanics and Foundation Engineering, pp. 26–31. Toll, D.G., 1988. The Behaviour of Unsaturated Compacted Naturally Occurring Gravel. (PhD thesis) Imperial College of Science, Medicine and Technology, University of London. Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E., Clifton, A.W., 1996. Model for the prediction of shear strength with respect to soil suction. Can. Geotech. J. 33 (3), 379–392. WESCOR, 1998. Water potential systems. Wescor Scientific Products Catalog (www. wescor.com). Wheeler, S.J., Sivakumar, V., 1995. An elasto-plastic critical state framework for unsaturated soil. Geotechnique 45 (1), 35–53. Zerhouni, 1995. Triaxial testing using psychrometers. (In French) Proc. 1st int. Conf. Unsaturated Soils, pp. 673–678.
Contents lists available at ScienceDirect
Engineering Geology journal homepage: www.elsevier.com/locate/enggeo
Experimental and analytical framework for modelling soil compaction Bernardo Caicedo a,⁎, Julián Tristancho b,1, Luc Thorel c,2, Serge Leroueil d,3 a
Universidad de Los Andes, Cra. 1 Este No. 19 A-40, Bogotá, D.C., Colombia Universidad Distrital Francisco José de Caldas, Cra. 7 No. 40B-53, Bogotá, D.C., Colombia c LUNAM University, IFSTTAR, GER Department, Physical Modelling in Geotechnics, Route de Bouaye, BP4129, 44341 Bouguenais cedex, France d Département de génie civil, Université Laval, Pavillon Adrien-Pouliot-1065, av. de la Médecine, Québec, Québec G1V 0A6, Canada b
a r t i c l e
i n f o
Article history: Received 17 April 2013 Received in revised form 8 January 2014 Accepted 24 March 2014 Available online 3 April 2014 Keywords: Compaction Laboratory tests Constitutive relations Anisotropy Partial saturation Deformation
a b s t r a c t Compacted materials are fundamentally unsaturated soils whose behaviour can be expansive or collapsible depending upon changes in water content or stresses. Their behaviour is strongly dependent upon matric suction, water content, and stress history. This paper presents a methodology for investigating the stress/strain, and suction/water content paths during one dimensional compaction of unsaturated soils. It focuses on anisotropic behaviour. The testing programme was carried out in a new automated oedometer apparatus that allows measurement of axial strain, radial and axial stresses, suction, and water content during tests. The laboratory component used in this study involves kaolin compacted with different water contents. After compaction, the soil was subjected to wetting while the volumetric changes and stress paths were being examined. The results were interpreted within an anisotropic elasto-plastic framework. The proposed methodology provides new insights into the behaviour of unsaturated soils during compaction and wetting. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Throughout the world compacted soils are used as construction materials in numerous geotechnical contexts. In spite of huge advances in unsaturated soil mechanics in the last 20 years, there continues to be a disconnection between the current design of geotechnical earthworks based on Proctor's ideas and the fundamental principles of unsaturated soil mechanics. Two reasons may explain this disconnection: (i) the simplicity of Proctor's tests compared to the high complexity of tests on unsaturated soils with controlled suction; and (ii) the absence of well-understood constitutive laws of how stress and suction during compaction are related to the post compaction behaviour of soils. These two difficulties could be overcome by combining the development of new laboratory apparatuses which would allow the study of compaction by measuring the state variables of the unsaturated soil (including stresses, matric suction, water content and void ratio) with the use of constitutive models adapted to compacted soils.
⁎ Corresponding author at: Universidad de los Andes, Cra. 1 Este No. 19 A-40, Bogotá, Colombia. Tel.: +57 1 3324312; fax: +57 1 3324313. E-mail addresses: [email protected] (B. Caicedo), [email protected] (J. Tristancho), [email protected] (L. Thorel), [email protected] (S. Leroueil). 1 Tel.: +57 1 3239300. 2 Tel.: +33 240845808; fax: +33 240845997. 3 Tel.: +1 418 656 2206; fax: +1 418 656 2928.
http://dx.doi.org/10.1016/j.enggeo.2014.03.014 0013-7952/© 2014 Elsevier B.V. All rights reserved.
To include unsaturated characteristics in the understanding of compacted soils, Toll (1988), Schreiner (1988), Maswoswe et al. (1992), Li (1995), Delage and Graham (1996) and Alonso (1998), among others, have characterised the post-compaction suction and microstructure of soils compacted using oedometric paths. However, most of these works were carried out after compaction without controlling the history of stresses and phase variables during compaction. The possibility of following the stress and phase variables paths during compaction has recently become possible with the development of suction measurement systems based on psychrometers (Zerhouni, 1995; Blatz and Graham, 2000, 2003; Caicedo et al., 2008) or on high capacity tensiometers (Ridley and Burland, 1993; Jotisankasa et al., 2007; Tarantino and Tombolato, 2008). Concerning constitutive laws for compacted soils, Cui and Delage (1996), Leroueil and Barbosa (2000) and Ghorbel and Leroueil (2006) have all shown the essentially anisotropic behaviour of compacted soils, in particular in terms of yielding. Moreover, Tarantino and De Col (2008) studied the microstructure of compacted soils at different water contents and presented a one dimensional mechanical model adapted to reproducing soil behaviour during compaction. The purpose of this paper is to present a methodology to investigate the stress/strain, and suction/water content paths during oedometric compaction of unsaturated soils. The results are interpreted in an anisotropic elastoplastic framework combining the characteristics of the models presented by Cui and Delage (1996), Leroueil and Barbosa (2000) and Ghorbel and Leroueil (2006). The proposed methodology
B. Caicedo et al. / Engineering Geology 175 (2014) 22–34
provides new insights into the behaviour of unsaturated soils during compaction and subsequent wetting. 2. Compaction interpreted within the framework of unsaturated soil mechanics Fig. 1 presents the description of the stress path of a soil subjected to oedometric compaction in a plane of radial total vs axial total stresses (σr, σa), Alonso (1998). It shows the critical state lines, CSLs, in compression and in extension for zero and positive suction value, and it shows the K0 line, which is defined as the relationship between radial and axial stresses during one dimensional compression under zero radial strain. Oedometric compaction could be described as follows. First the soil is mixed and prepared in unsaturated conditions. In this initial state the soil is represented by an unsaturated yield surface (F1). Next, if an axial stress is applied, radial stress increases within the elastic domain to the surface F1 (paths A to B). After the stress path continues in the plastic domain following the anisotropy line up to a second yield surface (F2) (paths B to C). If the soil is then unloaded, the axial and radial stresses decrease in the elastic domain and the CSL in extension may be attained. If it is, the path will follow this CSL until the axial stress equals zero (paths C, D, E). It is important to note that when zero axial stress is reached, a radial stress remains within the unsaturated soil (point E). On reloading, the stress path remains within the elastic domain up to the F2 yield surface; afterwards the path follows the anisotropy line and defines a new and larger yield surface. On the other hand, if after unloading there is a change in suction, as for example saturation of the soil under zero axial stress, the radial stress goes to zero (paths E to O), and swelling or collapse occurs, depending on the position of the loading collapse surface. It is important to keep in mind that the previous explanation is a simplified approach to in situ compaction. In fact, oedometric compaction allows obtaining similar compaction curves than the Proctor's procedure, Biarez (1980). However, moving loads due to in situ compaction produces cyclic loads and rotation of stresses that create stress paths different from the oedometric stress path used in this study, Caicedo et al. (2012). These effects must be included in further researches.
compression while measuring the axial and radial stresses, suction, void ratio and water content during compaction. To accomplish this, the cell includes the following features (see Figure 2): (1) The compression piston in the cell has a large displacement capacity. This allows it to perform compaction tests starting with soils in a loose state and finishing with soils having dry unit weights similar to those obtained in Proctor's tests (The initial size of the sample is 78 mm in height and 70 mm in diameter, the final height of compacted samples varies between 53 mm and 43 mm depending on the water content). (2) The large displacement of the soil produced by one moving piston can result in significant variation in dry density across the sample due to the friction between the soil and the mould. This friction can be reduced either including two moving pistons or reducing friction with an internal Teflon cylinder. The second option has been included in the oedometric cell. The effectiveness of this solution was confirmed verifying that the dry density for samples located at the top and the bottom of the soil varies in less than 2%. (3) The cell is equipped with a capacitive sensor to measure the water content in the soil during compaction. For this reason plastic materials were used in most of the cell design. However, to avoid undesirable radial displacement the cell was conceived with a thick cylinder wall (32 mm) of composite material (phenolic resin reinforced with glass fibres).
3. Materials and equipment 3.1. Oedometric cell for K0 measurement The oedometric cell used in this research was designed to reproduce soil compaction by increasing the axial stress under one dimensional
Fig. 1. Stress path during oedometric compaction.
23
Fig. 2. Layout of the instrumented oedometric cell.
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(4) The cell has three Teflon pistons equipped with miniature load cells to measure the radial stress. (5) Three Peltier psychrometers, in contact with the soil, are located in the wall of the cell at the same level as the Teflon plugs. (6) A capacitive water content sensor is located in the centre of the sample. The measuring electrodes are located at the same level as the psychrometers and the radial load cells. 3.2. Radial stress measurement system Previous studies on the measurement of radial stress in oedometric cells have used two different methods. One method is to use an apparatus with a steel membrane equipped with strain gauges, with pressurized oil behind the membrane to compensate for the strains (Hendron, 1963; Brooker and Ireland, 1965; Komornik and Zeitlen, 1965; Saxena et al., 1978; Elif et al., 2009). The other method which has been used includes small load cells fitted into the wall of the cylinder (Thompson, 1963; Abdelhamid and Krizek, 1976; Schreiner, 1988; Schreiner and Burland, 1991). This second method is used in this research. A set of three low compliance load cells were installed into holes in the thick cylinder wall (Figure 2b). These load cells act on three Teflon pistons in contact with the soil and react upon a rigid steel ring. The compliance of the whole system was evaluated by direct measurements and F.E. analysis, this analysis show that the relative displacement between the wall of the oedometer and the set piston-load cell is about 20 μm at the maximum radial load achieved during tests. 3.3. Thermocouple psychrometers Three commercially available thermocouple psychrometers (Wescor PST-55) are utilised to measure suction during testing. The psychrometers were installed in three holes in the thick wall and then the holes were filled with soil to insure adequate contact between the soil and the screens of the psychrometers. The psychrometers were monitored using a Psypro Wescor data acquisition system. Peltier psychrometers permit the measure of total suction through the measure of two thermocouples: the reference thermocouple and the measurement thermocouple. However temperature affects the psychrometric readings in two ways: one is the effect in the measurement thermocouple and the other one is the effect of the temperature gradient between the reference and measurement junctions. To correct the first effect an adjustment equation, cf. Wescor (1998), can be used. The second effect is controlled verifying the difference of temperature between the two junctions before the measure (offset measurement). This offset should be less than 3 μV for meaningful measurements; higher offsets are evidence of excessive thermal gradients. Due to the influence of temperature on the psychrometric readings, the best procedure to perform psychometric measurements is to carry out the tests in a temperature controlled room. In the case of this research, the recorded variation of temperature in the room was less than 2 °C; however a room with better controlled temperature is necessary to have more valid measures. In addition, the effect of temperature was reduced using for the structure of the oedometer a material having low thermal conductivity. It is important to note that psychrometers are useful for laboratory studies in a controlled temperature room; however are unpractical for in situ studies because of the high temperature variations.
Fig. 3. Calibration of the water content sensor.
Fig. 3 shows the calibration of the sensor for the kaolin compacted at different volumetric water contents. As observed, good linear calibration is obtained over a large range of water contents (r2 = 0.97, and accuracy ± 2%). However the measures of the sensor during loading and unloading shows that the stress level has a slight effect on the calibration (around 2%), as the calibration made for this study avoid this effect, the water content used in the analysis before soaking is the theoretical water content assuming constant weight of water. 3.5. Loading device A loading device was designed to perform compaction under controlled rates of strain or stress. This device has a servomotor coupled to a mechanical actuator. The servomotor can be controlled in load or displacement modes using a load cell (20 kN capacity) or an optical encoder. As a result, the loading device can perform stress or strain controlled compaction tests with an accuracy of 10 N (2.60 kPa) in the stress controlled mode or 1 μm (1.3 ∗ 10−3%) in the strain controlled mode. In this study, the compaction is carried out for controlled rate of strain (CRS tests), followed by stress controlled periods. However, as the test starts with the soil in a loose state and the compaction requires large displacements, the rate of displacement is calculated at each second to take the changing height of the sample and the imposed rate of strain into consideration. In addition an LVDT transducer a 50 mm stroke makes complementary measurements of displacement. 4. Materials and specimen installation The soil used in this study is commercially available kaolin whose properties are presented in Table 1. The liquid and plastic limits are 55% and 30% respectively. The soil was prepared in a mixing machine starting with dry powder. It was gradually sprayed with water to avoid the formation of lumps. Afterwards the soil was sieved at 1 mm to eliminate the presence of large aggregates (Tarantino and de Col, 2008). The mixed soil was then enclosed in a plastic bag and stored in a wet room for one week to guarantee good moisture equilibration and homogeneity. For the compaction tests loose soil was poured into the oedometer cell. Then a mini-hammer applied 5% of the Proctor Standard energy to compact the soil slightly. Next, excess soil was removed to set the Table 1 Characteristics of the kaolin used in the investigation.
3.4. Water content sensor The method used to measure the water content during testing is based on a combination of the resistive method (Matlin, 1975) and the capacitive method (Dupas et al., 2000; Günzel et al., 2003). These methods take advantage of variation in the relative dielectric permittivity and resistivity of the soil with water content.
Liquid limit, wL (%) Plastic limit, wP (%) Particles d at 30% (%) Particles d at 50% (%) Particles d at 90% (%) rρs (g/cm3) Drained friction angle ϕ′, (Bolton and Powrie, 1987)
55 30 1.5 μm 3 μm 9 μm 2.65 23.7° to 25.6°
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sample height at 78 mm for all tests. This procedure was implemented to obtain loose soils with controlled initial conditions. Afterwards a thin walled 19 mm tube was inserted into the middle of the sample to create a cavity in which to place the water content sensor (see Figure 2). 5. Compaction tests The compaction tests were performed in five loading/unloading cycles at a controlled rate of strain. Once the axial stress reaches the maximum or minimum value for each cycle it was maintained constant for another 30 min. The range of axial stress for oedometric compaction has been determined bearing in mind that for kaolin a vertical stress of around 1000 kPa leads to similar compaction curves than Proctor Standard tests, Biarez (1980). The axial stress was increased by an increment of 300 kPa in each loading cycle starting at 300 and increasing in steps to 600, 900, 1200, and finally 1500 kPa, each loading stage continues with unloading to 20 kPa (Figure 4). The strain rate in the first compression stage is 40 μstrain/s. It is higher than in the other cycles because the first compression stage needs a large axial strain to reach the first axial stress limit. However, this larger strain rate does not affect the equilibration of air pressure since the initial soil state is loose. A lower strain rate of 20 μstrain/s was chosen for subsequent cycles. The air pressure was measured in two tests (15% and 25% water content), the results shown that the variations in air pressure were lower than 500 Pa, this value suggest that air pressure could be assumed as zero without significant error. However this variation could have an important effect on the psychrometric measurements, mainly for low suction values. Fig. 4 shows the final state of the sample after each loading stage on a Proctor plot, a comparison with the standard Proctor curve shows that the maximum standard dry density corresponds to a vertical stress between 900 kPa and 1200 kPa, just as stated by Biarez (1980). Once the five cycles were completed the sample was subjected to soaking by introducing water at a pressure of 10 kPa at the base of the sample. For these subsequent loading/unloading cycles five tests were performed at constant, but different, water contents with soaking during the final unloading stage. One additional test was performed at 10% water content with soaking the sample at the maximum axial stress (see Table 2).
25
Table 2 Test characteristics. Test
Water content (%)
Axial stress during wetting (kPa)
1 2 3 4 5 6
5 10 15 20 25 10
20 20 20 20 20 1500
Fig. 5 shows axial strain versus time for the test carried out at 20% water content. The loading/unloading cycles are clearly identified as are the stages of constant axial stress. Upon wetting the axial strain decreases as a result of axial expansion (bearing in mind that compression strains are considered positive). Figs. 6 and 7 show the evolution of axial strain (Figures 6a and 7a) and the axial and radial stresses during the tests performed on two samples compacted at 10% water. Yielding stress is clearly noticeable
through a slope variation during loading mainly in axial stress. For the sample wetted under an axial stress of 20 kPa (Figure 6), there is axial swelling associated with a decrease in radial stress. On the other hand, for the sample wetted under an axial stress of 1500 kPa (Figure 7), there is axial collapse associated with a significant increase in radial stress. This is a clear evidence of anisotropic behaviour during wetting as it will be clarified later. In addition, concerning radial stress during wetting, a non-monotonic trend is observed in Figs. 6(c) and 7(c). However, this tendency appears during the transient wetting phase, for which the soil in the oedometer has not homogeneous conditions. The evolution of radial and axial stresses during loading/unloading cycles is presented in Fig. 8. The results show two types of behaviour. One is a tangential relationship along which the stress paths gather after reaching the yield stress in each cycle. The other behaviour occurs when axial and radial stresses in each cycle are lower than the maximum values previously reached. The results show that the second behaviour depends on stresses, whereas the tangential behaviour is essentially independent of stresses. On soaking, radial stresses decreases in all the cases for which soaking is performed at the minimum vertical stress (σa = 20 kPa), whereas the radial stress increases when soaking is performed after final loading (σa = 1500 kPa); Table 3 shows radial stresses achieved at the final stage of compaction, before and after soaking. Fig. 9 shows the stress path cycles for the various tests in the s, t plane, in which s = (σa + σr) / 2, and t = (σa − σr) / 2. Except for the last test (Figure 9f), all the unloading paths finished at a stress point within a line corresponding to a constant axial stress of σa = 20 kPa. Under these conditions radial stress is positive, however when samples are wetted the radial stress decreases significantly. On the other hand, when wetting is performed at the maximum axial stress of σa = 1.5 MPa (Figure 9f), radial stress increases. Similar behaviour has been identified by Schreiner and Burland (1991) for single stage compaction. Although psychrometers measure total suction, comparative measures of suction made by Tarantino and De Col (2008), and Tarantino (2009), using high capacity tensiometers and transistor psychrometers, shown that for kaolin mixed with demineralised water the osmotic component of suction is negligible, so measured suction can be considered to be close to matric suction.
Fig. 4. Comparison between proctor standard curve and final state of the samples after each loading stage.
Fig. 5. Loading and unloading cycles measured during the test carried out at 20% water content.
6. Results
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Some of the measurements made with psychrometers shown extreme suction, these readings were interpreted as invalid measurements because: (i) the time necessary for the equilibration between the humidity of air in soil and the humidity of air in the psychrometer is about 20 min but maintaining constant air pressure. (ii) a small variation of air pressure, as a result of loading and unloading, affects the relative humidity of the air in the psychrometer: relative humidity grows as air pressure grows and vice-versa, consequently under these conditions the variation of suction measured with psychrometers could be amplified; in fact if air pressure doubles, the psychrometric constant doubles (Rawlins and Campbell, 1986). As a consequence of these difficulties, to choose the valid psychrometer readings an additional criterion to the conventional offset criterion must be applied. Variations from the initial suction higher than 1.5 the standard deviation of the whole measurements for any water content
Fig. 7. Evolution of the axial strain, and axial and radial stresses during loading for the soil compacted at 10% water content and wetted under an axial stress of 1500 kPa.
Fig. 6. Evolution of the axial strain, and axial and radial stresses during loading for the soil compacted at 10% water content and wetted under an axial stress of 20 kPa.
has been chosen as criterion to eliminate extreme suctions. This criterion is not physically based criterion, however it is wide enough to conserve the suction variations due to soil behaviour and tighter to eliminate spurious values. The variation of suction during tests, considering only the valid measures, in terms of radial and axial stresses is presented in Fig. 10, this figure shows some variation of suction during loading and unloading, however it is difficult to assess any hydraulic path due to the discontinuous characteristic of the psychrometric measurements. On the other hand, for the high suction values or low water contents explored in this paper, the suction is not significantly influenced by the change in void ratio. The variation of suction during tests in terms of degree of saturation Sr plotted against suction (ua − uw) is presented in Fig. 11. Despite the difficulties in suction measurement using psychrometers, the results presented in Fig. 11 show an increase in the degree of saturation with compaction and a general decrease in suction when water content increases. Furthermore, when considering the extreme values during loading and unloading it is possible to identify two
B. Caicedo et al. / Engineering Geology 175 (2014) 22–34
27
presented by Leroueil and Barbosa (2000). The slope of the normal compression lines in Fig. 14 are roughly similar (parallel lines in the range 0.2 MPa b p b 1 MPa). This could correspond to an intermediate behaviour between: decreasing slope as the suction increases; or steeper compression lines at higher suctions reported by Alonso et al. (1990) and Wheeler and Sivakumar (1995) respectively; however it is important to keep in mind that the results presented in Fig. 14 are obtained at constant water content and not at constant suction like the results presented in these researches. On the other hand the evolution of void ratios during unloading follows lines having the same slope for all water contents, just as described by Alonso et al. (1990). 7. A constitutive model for soil compaction The behaviour of compacted soils is noticeably anisotropic, as demonstrated by Cui and Delage (1996). This stress induced anisotropy appears to be a result of the distribution of contacts between particles that reflects the forces applied. Most constitutive models for unsaturated soils were developed for isotropic soils (Alonso et al., 1990). In models developed for anisotropic unsaturated soils, anisotropy remains constant (Cui and Delage, 1996; Leroueil and Barbosa, 2000; Ghorbel and Leroueil, 2006). This characteristic reduces the capacity of these models to capture the evolution of anisotropy during compaction. The constitutive model proposed in this paper is however based on the GFY model (Given Fabric Yielding) proposed by Leroueil and Barbosa (2000), and Ghorbel and Leroueil (2006). This model was developed based on the yield curves proposed by Larsson (1977) for natural clays. When this model is applied to unsaturated compacted soils, it permits to model the change in anisotropy during loading. 7.1. Stress variables
Fig. 8. Evolution of radial and axial stresses during the loading/unloading cycles.
lines: compression lines showing decreasing suction as the saturation increases, and post compaction lines limiting the values of suction during unloading. However more valid measurements are required to draw these lines more precisely. The stress ratio K = σr / σa observed during the loading stages of the tests is shown as a function of σa in Fig. 12. Except at relatively low stresses where the soil may be in its pre-yield domain, the K values are relatively constant. These values are strongly influenced by water content: the higher the water content, the higher the value of K, except for the lower water contents (10%, 5%) for which the stress ratio K tend to the same value. These results indicate that K decreases when suction increases but tends to a constant value for higher suctions as shown in Fig. 13. Fig. 14 shows the normal compression lines obtained at different water contents. It can be seen that, at a given void ratio, the lower the compaction water content (thus the higher the suction) the larger is the mean stress. This is consistent with the oedometer test results
To ensure a continuous transition from saturated to unsaturated conditions Ghorbel and Leroueil (2006) proposed using “modified net stress” and matric suction as stress variables. The coefficient ζ⁎, and modified net stress σ⁎ are defined as follows:
σ ¼ σ −ua þ ζ ðua −uw Þ
ð1Þ
with
ζ ¼ 1 for
ð2Þ
ðua −uw Þ≤ ðua −uw Þb
and
ζ ¼
ðua −uw Þb ðua −uw Þ
for
ðua −uw ÞNðua −uw Þb
ð3Þ
where (ua − uw)b is the matric suction corresponding to the air entry value of the soil, defined as the suction value below which the soil remains saturated.
Table 3 Radial stress change after final compaction, unloading and soaking. Water content %
5 10 15 20 25 10
Vertical stress on soaking
Radial stress final loading
Radial stress before soaking
Radial stress after soaking
(kMPa)
(kPa)
(kPa)
(kPa)
20 20 20 20 20 1500
501 504 526 554 667 502
213 215 196 218 225 502
⬇ ⬇ ⬇ ⬇ ⬇ ⬆
8 68 52 103 195 554
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B. Caicedo et al. / Engineering Geology 175 (2014) 22–34
Fig. 9. Stress path followed in the s, t plane.
7.2. Water retention model
reloading cycles (scanning behaviour) proposed by Tarantino and De Col (2008) is as follows:
Romero and Vaunat (2000), Gallipolli et al. (2003), and Tarantino (2009) proposed a water retention model for deformable soils. The equation following equation was proposed by Gallipolli et al. (2003):
Sr ¼ Sr0 −ks ðua −uw Þ−ðua −uw Þ0 :
( Sr ¼
1 n 1 þ ϕðua −uw Þeψ
)m ð4Þ
where e is the void ratio, and φ, ψ, n and m are the parameters of the model. The expression for matric suction during the unloading/
Fig. 10. Variation of suction measured during tests plotted in terms of axial and radial stresses.
ð5Þ
Here (ua − uw)0 and Sr0 are the suction and degree of saturation when unloading begins, and ks is the slope of the scanning curve in the space relating matric suction with degree of saturation. 7.3. Yield surface and loading collapse functions The stress path soils follow during compaction is comparable to the stress path followed by soft clays during normal consolidation. As
Fig. 11. Degree of saturation–suction measured during tests at compaction with different water contents.
B. Caicedo et al. / Engineering Geology 175 (2014) 22–34
29
Fig. 12. Stress ratio, K = σr / σa, calculated from the results of the tests.
Larsson (1977) hypothesised for such materials, they cannot be subjected to stresses in any direction larger than the maximum stresses already applied. Under these circumstances the yield curves can be schematized by four segments: two corresponding to the strength envelopes in compression and in extension; and two corresponding to the maximum axial and radial stresses previously applied to the soil. Leroueil and Barbosa (2000), and Ghorbel and Leroueil (2006) expand this concept to unsaturated soils (Figure 15). Anisotropic behaviour can be represented using the stress variables s and t defined under modified net stress as s* and t*, where s* = (σ⁎a + σ⁎r) / 2, and t* = (σ⁎a − σ⁎r) / 2. In the plane s*, t*, a soil in saturated conditions has a yield curve of the type OB0A0D0. A given suction should extend the saturated cap B0A0D0 to an unsaturated cap BsAsDs with an increase in axial yield stress from σ⁎ay0 to σ⁎ays, and an increase in radial yield stress from σ⁎ry0 to σ⁎rys. The variation of the axial and radial stresses with suction corresponds to two loading collapse curves, LCa in the axial and LCr in the radial directions (Figure 15b). By increasing the axial yield stress from σ⁎ay0 to σ⁎ays matric suction increases the shear strength of the soil under compression from point B0 to point Bs, or from B0 to B′. According to Ghorbel and Leroueil (2006), the increase in shear strength in compression due to suction is Δτ fc ¼
i sinϕ0 cosϕ0 h σ ays −σ ayb 0 1 þ sinϕ
ð6Þ
Fig. 14. Compression curves in the void ratio vs. mean stress plane.
Vanapalli et al. (1996) proposed an equation for predicting shear strength as a function of matric suction and volumetric water content. Expressed in terms of the water ratio ew, this equation is as follows (Ghorbel and Leroueil, 2006): e −e 0 Δτ f ¼ ðua −uw Þ w wr −ðua −uw Þb tanϕ : ews −ewr
From Eqs. (6) and (8), Ghorbel and Leroueil (2006) proposed the following expressions for the LC curves:
σ ays −σ ayb ¼
1− sinϕ0 ew −ewr ðua −uw Þ −ðua −uw Þb for 02 ewsat −ewr cosϕ
LCa ð9Þ
and the increase in shear strength in extension is i sinϕ0 cosϕ0 h σ rys −σ ryb : Δτ fe ¼ 0 1 þ sinϕ
ð8Þ
, and ð7Þ
In Eqs. (6) and (7) σ⁎ayb and σ⁎ryb are the axial and radial modified net yield stresses for a value of matric suction corresponding to the air entry value. Δτfc is the contribution of strength due to matric suction in compression, in excess of the air entry value, while Δτfe is the contribution of strength due to matric suction in extension, in excess of the air entry value.
σ rys −σ ryb ¼ K AL
0 1− sinϕ ew −ewr ð u −u Þ ð −u Þ − u a w a w b for LCb ewsat −ewr cosϕ02 ð10Þ
where K⁎AL is the anisotropic parameter defined as
K AL ¼
σ rys : σ ays
ð11Þ
The previous model is conceptual; in reality, yield curve is certainly more rounded than the four segment surface of the GFY model. An elliptic surface has been proposed by Cui and Delage (1996) for anisotropic unsaturated soils. In a parametric form and in the plane (s⁎, t⁎), Fig. 16; the ellipse can be expressed as the path of a point (s⁎(ξ), t⁎(ξ)), where
ð12Þ
ð13Þ
s ðξÞ ¼ sc þ ae cosðξÞ cosðθÞ−be sinðξÞ sinðθÞ
t ðξÞ ¼ t c þ ae cosðξÞ sinðθÞ þ be sinðξÞ cosðθÞ:
Fig. 13. Stress ratio, K = σr / σa, vs. suction.
Here, the point (s⁎c, t*c) is the centre of the ellipse, θ is the angle between the s⁎ − ua axis and the anisotropy line, ae and be are the major and minor semi-axes, and ξ is a variable used to describe the
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B. Caicedo et al. / Engineering Geology 175 (2014) 22–34
ew −ewr 1 0 ss ¼ Δτ f = sinϕ ¼ ðua −uw Þ −ðua −uw Þb cosϕ0 ewsat −ewr
tanθ ¼
ð16Þ
σ ays −σ rys : σ ays þ σ rys
ð17Þ
As a result, the centre of the ellipse and the major semi axis are
sc ¼
sk þ ss 2
ð18Þ
t c ¼ tanðθÞsc
ae ¼
ð19Þ
sk −ss 1 : 2 cosθ
ð20Þ
The angle α in the centre of the ellipse between the anisotropy line and the line linking the point (s⁎0, 0) and the centre is α ¼ cos
−1
s0 −sc −t c tanθ ae ð sinθ tanθ þ cosθÞ
ð21Þ
and the minor semi-axis is be ¼
Fig. 15. Yield surface for the GFY model proposed by Leroueil and Barbosa (2000), and Ghorbel and Leroueil (2006).
ellipse in parametrical form. The values of the parameters ae, be, and (s⁎c, t*c) can be derived if three points of the ellipse are known: the maximum and minimum points along the major axes, s⁎k and s⁎s respectively; and the intercept of the ellipse at t⁎ = 0, s⁎0. As the yield curve is more rounded than the four segment surface of the GFY model, unloading paths crosses the axis t⁎ = 0 for a stress value slightly lower than σ⁎rys; a value of s⁎0 = 0.9 σ⁎rys shows good agreement for most of the unloading paths measured experimentally. The values of s⁎0, s⁎s, and s⁎k, and θ can be easily found by fitting the ellipse into the GFY model (Figure 15) as follows:
σ ays þ σ rys 2
sk ¼
s0 ¼ 0:9σ rys
ð14Þ
ð15Þ
sc −s0 þ ae cosð−α Þ cosθ : sinð−α Þ sinθ
ð22Þ
8. Application of the model to experimental results The evolution of suction during cyclic oedometric compaction can be calculated using Eq. (4) that describes the evolution of suction during compression and Eq. (5) describing the variation of suction on unloading. Eq. (4) was adjusted fitting the suction measurements obtained during compression, Fig. 10, with their corresponding saturation degree; this procedure provides an assessment of the constants (m, n, φ, ψ). Afterwards, the parameter ks in Eq. (5) is assessed using the unloading data. The obtained parameters are presented in Table 4, these parameters are different from those presented by Tarantino and De Col (2008) because the kaolin used in both studies have wide differences, particularly in its grain size distribution: 80% of particles with d b 2 μm in Tarantino and De Col (2008), and 40% in this study. Fig. 17 shows the evolution of suction during loading and unloading calculated with Eqs. (4) and (5), and the experimental results, also two extreme suction curves are presented corresponding to two void ratios (e = 1.9, and e = 0.9). The figure shows that the amplitude of the suction cycles corresponds to the amplitude measured experimentally and the calculated suctions are close to the measurements; however no exact matching appears between experimental and calculated suctions, this is associated to the difficulties in the equilibration of psychrometers during cyclic loading. Fig. 18 shows the stress paths determined experimentally during compaction tests and the elliptical yield surfaces obtained from the proposed model. According to the proposed model, compaction by cyclic loading can be described as follows: the loading path in the plane (s⁎, t⁎) starts in the elastic domain corresponding to the previous Table 4 Coefficients used in the model.
Fig. 16. Elliptical yield surface fitted into the GFY model.
m
n
φ
ψ
0.414
1.243
0.013
1.885
(ua − uw)b
ewr
Fϕ′
0
0
25.6°
B. Caicedo et al. / Engineering Geology 175 (2014) 22–34
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collapse curves calculated with Eqs. (9) and (10). These curves show how the LC curves move towards larger stresses as a result of successive loading cycles. The coefficients of the model used for the elliptical yield surfaces and the LC curves are presented in Table 4. Using this proposed model, the behaviour of the anisotropic soil during wetting can be explained. Figs. 20 and 21 illustrate the behaviour of soil compacted at 10% water content and wetted under an axial stress of 20 kPa (Figure 20), and then wetted under the maximum axial stress of 1500 kPa (Figure 21). In both cases the yield surface at the final loading cycle is the same Fs5. Consequently, the movement of stress paths and yield surfaces as a result of wetting is as follows:
Fig. 17. Modelling the hydraulic paths during compaction tests.
loading cycle and continues up to the yield surface; then the stress path continues towards and finally along the K line which is associated with the water content or, more precisely, which is associated with suction. During unloading, the stress path goes down a more or less linear path in the elastic domain, possibly to the yield surface. Afterwards the stress path follows the elliptical yield surface up to the line corresponding to the minimum axial stress. Fig. 17 shows that the agreement between the model and the test results is reasonably valid for all water contents and all cycles. Fig. 19 shows the suction calculated with Eqs. (4) and (5) as a function of the radial and axial modified net stresses, and the experimental measurements of suction. Good agreement is observed regarding the level of suction for each test, however in some tests the trend of the measures during compression does not agree with the theoretical prevision; this is probably related to the variability on the suction measurements. In addition, this figure shows the axial and radial loading
(i) When wetting is carried out at the minimum axial stress (σa = σa⁎ = 20 kPa), the suction reduces, the stresses σ⁎ays and σ⁎rys reduce, and the yield curve changes from Fs5 to F0. Stress conditions located at point A, on Fs5, must follow the change in the yield curve to B on F0, with a reduction in σr. (ii) When wetting is carried out at the maximum axial stress (σa = σa⁎ = 1.5 MPa), the reduction in suction in the LCa plane produces collapse, and growth in the size of the yield curve (Figure 21c). However, the reduction in suction is associated with an increase in K from a value of 0.337 for a water content of 10% (Figure 12) and a suction of about 1000 kPa, to a value that would be larger than 0.45 at zero suction. Consequently, σr has to increase from point C to point D in Fig. 21a. 9. Conclusions The experimental programme carried out with the suction-monitored instrumented oedometer apparatus provided new information about the behaviour of unsaturated non-active clay during oedometric compaction. The use of the controlled rate of strain procedure allowed
Fig. 18. Stress paths and elliptical yield surfaces given by the model.
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B. Caicedo et al. / Engineering Geology 175 (2014) 22–34
Fig. 19. Modelling the axial and radial loading collapse curves for the different loading cycles and water contents.
a clear identification of the main features of the volumetric changes against stress: the slope of the virgin compression curve decreases as the suction increases, and all the unloading curves are parallel. The measurement of radial stress during oedometric compaction allowed assessment the stress ratio K = σr / σa for unsaturated conditions. The experimental results show that K0nc increases as the suction decreases. In five tests performed at different water contents the soil was subjected to wetting after final unloading. Under these conditions the soil exhibits anisotropic behaviour for all water contents: exhibiting axial expansion and decreasing radial stress. However, when wetting is performed after loading to the maximum axial stress, anisotropic behaviour changes resulting in axial collapse and increasing radial stress. The behaviour of the soil with anisotropy induced as a result of oedometric compaction has been modelled using inclined ellipses whose size increases with suction, and which have two loading collapse surfaces. One is for the axial direction and the other is one for the radial direction. The characteristic points of the inclined ellipses depend on the position of the two LC curves, suction and the axis of symmetry of the ellipses. This later characteristic reflects induced anisotropy. The results show that the loading/unloading cycles are characterised by stress paths that first remain in the elastic domain and then follow with reasonably accuracy the proposed elliptical yield surface. The anisotropic behaviour during wetting is described by the evolution of the proposed yield surfaces as follows:
Fig. 20. Yield surfaces and stress paths during wetting under an axial stress of 20 kPa, soil compacted at 10% water content.
(i) When the soil is wetted at its minimum axial stress the soil experiences axial expansion as a result of the evolution of the axial stress–suction path in the LCa plane. Stress decreases in the radial direction as a result of the reduction of suction leading to a subsequent reduction in size of the ellipse.
B. Caicedo et al. / Engineering Geology 175 (2014) 22–34
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ua pore air pressure uw pore water pressure (ua − uw) suction (ua − uw)b matric suction corresponding to the air entry value of the soil (ua − uw)0 suction value at the beginning of unloading W water content Δτfc, Δτfe contribution of strength due to matric suction in compression and in extension in excess of the air entry value Fϕ′ friction angle θ angle between the s⁎axis and the anisotropy line σr, σa radial total and axial total stresses σ⁎ modified net stress σ⁎r, σ⁎a modified radial and axial net stresses σ⁎ry0, σ⁎ay0 modified radial net stresses corresponding to zero matric suction σ⁎rys, σ⁎ays modified axial net stresses corresponding to suction different than zero σ⁎ryb, σ⁎ayb radial and axial modified net yield stresses at that matric suction which corresponds to the air entry value ξ variable used to describe the elliptical yield surface in parametrical form ζ⁎ parameter modifying net stress.
Acknowledgements
Fig. 21. Yield surfaces and stress paths during wetting under an axial stress of 1500 kPa, soil compacted at 10% water content.
(ii) When the soil is wetted at its maximum axial stress both LC surfaces are mobilized; there is then axial collapse but as the K0nc coefficient increases when suction decreases, wetting induces an increase of the radial stress. Complete prediction of the stress strain curves during compaction and wetting would require implementation of the proposed yield surfaces in a generalized elasto-plastic model with an appropriate flow rule. This will be included in further developments.
Notation ad,w, bd,w, and nd,w parameters of water retention model for drying and wetting ae, be major and minor semi-axes of the elliptical yield surface e void ratio ew water ratio (ew = eSr) ews water ratio at saturation ewr water ratio at the residual water content [(ew − ewr) / (ews − ewr)]0 water ratio at the beginning of unloading K stress ratio K = σr / σa K⁎AL anisotropic parameter ks slope of the scanning segment of the water retention curve Sr degree of saturation Pp⁎ mean modified net stress p* = (σ⁎a + 2σ⁎r) / 3 s stress variable s = (σa + σr) / 2 s* modified stress variable s* = (σ⁎a + σ⁎r) / 2 t* modified stress variable t* = (σ⁎a − σ⁎r) / 2 s⁎k, s⁎s maximum and minimum points along the major axes of the elliptical yield surface s⁎0 intercept of the elliptical yield surface at t⁎ = 0 t stress variable t = (σa − σr) / 2 (s⁎c, t*c) central point of the elliptical yield surface
The writers would like to express their gratitude to Colciencias, the Colombian research organization that supported the first author during his Ph.D. thesis and the cooperation project ECOS-Nord between France and Colombia.
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