Particle breakage and the critical state of sand

Soils and Foundations 2014;54(3):451–461 The Japanese Geotechnical Society Soils and Foundations www.sciencedirect.com journal homepage: www.elsevier.com/locate/sandf Particle breakage and the critical state of sand M. Ghafghazia,n, D.A. Shuttleb, J.T. DeJonga a Department of Civil and Environmental Engineering, University of California, Davis, One Shields Ave., Davis, CA 95616, USA b Klohn Crippen Berger, 500–2618 Hopewell Place NE, Calgary, AB, Canada T1Y 7J7 Received 21 January 2013; received in revised form 1 October 2013; accepted 30 January 2014 Available online 21 May 2014 Abstract Soil particles break during shear, with the intensity of the breakage depending on the stress level amongst other factors. Particle breakage has important implications for the soil's critical state, which is an input to the majority of advanced constitutive models. This work examines a micromechanical framework where particle breakage shifts down the critical state locus in void ratio versus mean effective stress space without changing its slope. The framework assumes that detectable particle breakage in sand does not occur unless the contraction potential of the material, solely by the sliding and the rolling of the particles, is exhausted and a soil specific stress level threshold is surpassed. A series of triaxial compression tests conducted to investigate the validity of the framework is presented. It is shown that particle breakage is a factor, working alongside dilatancy, imposing additional compressibility on the soil. & 2014 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved. Keywords: Particle breakage; Particle crushing; Critical state; Sand; Compressibility; Constitutive relations; Deformation; State parameter 1. Introduction In critical state soil mechanics, shearing drives particulate soils towards a state of constant volume and constant shear stress at a constant mean effective stress, termed the critical state (Roscoe et al., 1958). At high stress levels, however, particles undergo breakage that results in a continuous change of soil gradation. The breakage causes additional compressibility n Corresponding author. Tel.: þ1 415 235 1974. E-mail addresses: mohsenghaf@yahoo.com (M. Ghafghazi), dawn_shuttle@hotmail.com, dshuttle@klohn.com (D.A. Shuttle), jdejong@ucdavis.edu (J.T. DeJong). Peer review under responsibility of The Japanese Geotechnical Society. and volume change, resulting in uncertainty in defining the critical state condition. In practice, stress levels sufficient for particle breakage occur in deep penetration problems, such as pile driving and cone penetration testing (Russell and Khalili, 2002), as well as below large earth-fill dams. Grain crushing has also been related to sanding in oil wells (Marketos and Bolton, 2007). Hence, the effect of particle breakage becomes important for understanding and analysing such problems within the critical state framework. Traditionally, a two- or three-segment linear Critical State Locus (CSL) in e log p0 space (where e is the void ratio and 0 p is the mean effective stress), similar to the one shown in Fig. 1, has been adopted for the full range of p0 . This is consistent with the three zones of behaviour identified by Vesić and Clough (1968): very low stress where dilatancy controls behaviour and breakage is negligible; elevated stress where breakage becomes more pronounced and suppresses dilatancy effects; and very high stress where the effects of http://dx.doi.org/10.1016/j.sandf.2014.04.016 0038-0806/& 2014 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved. 452 M. Ghafghazi et al. / Soils and Foundations 54 (2014) 451–461 Nomenclature D50, D10 grain size larger than 50% and 10% (by mass) of the soil particles, respectively e void ratio critical state void ratio ec emin, emax minimum and maximum void ratios, respectively FC fines content Gs specific gravity p0 mean effective stress (s1 þ s2 þ s3)/3 q deviator stress in triaxial compression, s1 s3 u pore pressure initial density vanish, very little void space remains within the material, and soil behaves like an elastic material. Difficulties are encountered with the three-segment CSL when considering particle breakage; these can be illustrated using the state parameter concept (Been and Jefferies, 1985). The evolution of the state parameter towards the three-segment CSL becomes logically questionable for stress paths that undergo a reduction in p0 from a positive initial state. For the test shown in Fig. 1, the specimen starts at an initial state parameter, ψ0, which is defined as the difference between the initial void ratio and the CSL void ratio at the same initial p0 . If that specimen is now taken to the critical state, for example, under undrained conditions, then the implication is that the specimen has gone from a condition associated with a certain amount of breakage (since it is at a stress level within the second segment of the CSL), to one with less, or no, breakage (i.e., to the first segment of the CSL). This contradicts the fact that breakage is an entropic phenomenon which, of course, cannot be reversed by further shearing. The elevated stress range (typically about 1 MPa o p' o 30 MPa associated with the second segment of the CSL in Fig. 1), which covers the higher end of effective stress of interest in most geotechnical problems, has been less studied. To date, there is no consensus on whether a unique CSL exists for this Fig. 1. Full stress range CSL in e–log p0 space and a schematic undrained triaxial test. Δ Δeb Δesr ε1 εv Γ λ10 ψ ψ0 denotes the increment of a variable increment (reduction) of void ratio due to particle breakage increment of void ratio caused by sliding and rolling axial strain volumetric strain, ε1 þ ε2 þ ε3 intercept of CSL in e log p' space measured at p' ¼ 1 kPa slope of CSL in e log10( p') space state parameter, e ec initial state parameter, e0 ec stress range or on how it is affected by the continuous gradation change due to particle breakage. This work focuses on the critical state at the lower end of the elevated stress range (1 MPa o p' o 3 MPa) where breakage gradually becomes dominant over dilatancy. It is well accepted that shearing at high stress changes the gradation of a soil and facilitates volumetric compression (e.g., Lee and Farhoomand, 1967). The critical state is associated with a state of constant volume despite continued shearing. Hence, it is expected that for the soil to reach the critical state, a stable gradation should be reached for a specific stress level (Luzzani and Coop, 2002). This implies that such gradation would be more stable than the original one, and can sustain a higher level of stress without further breakage (despite being formed by particles of exactly the same mineralogical combination). Hypothetically this is a viable proposition, knowing that particle breakage drives the soil towards a less uniformly graded distribution and smaller particles, which will establish more inter-particle contacts (Bishop, 1966) and reduce the particle– particle contact forces for a given global stress. However, experimental evidence demonstrating the formation of a stable gradation related to a particular stress level is not yet available. Been et al. (1991), Konrad (1998), Russell and Khalili (2004), and Vilhar et al. (2013) adopted the three-segment CSL framework illustrated in Fig. 1 and assumed that a continual constant volume state will be achieved once the tests approach the second segment of the CSL. The data presented by Russell and Khalili (2004) suggest that for elevated stress levels (above 1 MPa), tests on loose specimens do not reach a constant volume and continue to contract. Lade and Yamamuro (1996) made the same observation on tests presented in Yamamuro and Lade (1996), and concluded that the critical state conditions can only be achieved at very low stress (the first segment of CSL) or at very high stress after particle breakage has ceased (the third segment of CSL). Both sets of experiments were limited by the levels of shear strain allowed by the triaxial apparatus (up to around 40%). At lower confining stress, loose specimens often reach the critical state at such strain levels. An experimental study on a granitic soil by Lee and Coop (1995) suggested that the amount of particle breakage at the M. Ghafghazi et al. / Soils and Foundations 54 (2014) 451–461 critical state is path independent and solely a function of the value of p0 on the CSL. In a later attempt to investigate whether the critical state can be achieved at higher stress levels, Coop et al. (2004) used ring shear tests to test specimens of a carbonate sand up to shear strains of 100,000%. They concluded that particle breakage continues to very large strains beyond those reached in triaxial tests, but a constant gradation is eventually achieved at very large strains. This constant gradation is dependent not only on the stress level, but also on the uniformity and particle size range of the original gradation. Theoretically, the change in gradation cannot continue indefinitely; conceptually a final gradation where all voids are filled with smaller and smaller particles can be envisioned (as proposed by McDowell et al., 1996). Such a fractal gradation would be linear on a log–log plot of particle gradation. This condition of zero void space in the soil structure has been experimentally obtained by the early work of Bridgman (1918) for very high stresses (up to 300 MPa). But, for the range of stresses, strains, and breakage of interest to this work it appears reasonable to assume that breakage does not completely cease at higher stress. Thus, the idea of a CSL defined as a state of zero total volume change becomes inapplicable for the elevated stress range (1–30 MPa). Daouadji et al. (2001) first suggested that the changing gradation caused by the breakage imposes a downward shift on the CSL. Muir Wood (2007) developed this idea, suggesting that during shearing at higher stresses, the CSL moves down towards a final location associated with the fractal gradation. He proposed a third dimension to the e log p0 space called the “grading state index”, a parameter between 0 and 1 that identifies the soil state on a scale between uniform and fractal gradations. Muir Wood and Maeda (2008) showed, using a discrete element model, that the effect of particle breakage on the CSL location in e log p0 space is essentially a parallel downward shift as a function of the grading state index. Kikumoto et al. (2010) expanded the effects of this parallel downward shift to the strength response of sands pushing it towards a looser type of behaviour. The work presented herein builds upon the concept that the CSL progressively shifts downward as breakage continuously alters the soil gradation with increasing stress. First, a framework outlining a simple conceptual model to explain the shift in the CSL due to breakage is presented. Triaxial test results on specimens of a uniformly graded natural sand before and after breakage are then presented. The stress covered in these tests ranges from 100 kPa to 3 MPa. Finally, the results of the triaxial tests are used to examine the validity of the proposed framework. 2. Framework The framework proposed herein explains how breakage affects the CSL in e log p0 space, when breakage can occur, and how it contributes to the soil's compressibility. The framework is based on two assumptions. First, for small amounts of particle breakage, the finer particles generated by 453 breakage do not contribute to the soil's load carrying skeleton nor does the breakage affect the overall characteristics of the particles forming the soil's load carrying skeleton. Second, detectable particle breakage (measurable change in gradation) in a particulate material does not occur unless the following two conditions are satisfied: (1) the contraction potential of the material, solely by the sliding and rolling of the particles, is exhausted, and (2) a soil-specific stress threshold is surpassed. The first assumption is fairly intuitive provided only a relatively small number of soil particle asperities break off during shearing. Breakage starts with the particles with the largest contact forces (Marketos and Bolton, 2007; Russell et al., 2009). The smallest load carrying particles (Lee and Farhoomand, 1967; McDowell and Daniell, 2001) and asperities (Nakata et al., 2001; Altuhafi and Coop, 2011) are typically the ones developing the largest internal stress due to their dimensions, and undergo breakage first. As long as the number of particles that have undergone breakage remains small, the finer particles generated by the breakage do not contribute to the soil's load carrying skeleton; instead, they remain unloaded by falling into the void space. The concept that particle breakage does not commence until all sliding and rolling compressibility is suppressed is hypothesised as follows. Particle rolling is likely to be the first prevailing mechanism as it requires the least amount of energy to mobilise. Once rolling is suppressed by an increase in confinement (increased stress and/or reduced void space) sliding begins to dominate (Skinner, 1969). Negligible breakage may occur when particles have the opportunity to avoid loading by moving into voids by merely rolling or sliding (compression). In low density specimens, the end of compression coincides with the critical state, while for dense specimens, it is followed by a tendency for dilation. At this stage, breakage initiates if the stress is sufficient. The assumption then continues as the finer particles produced by breakage are capable of sliding and rolling into the voids, thus further reducing the specimen volume. The most fundamental implication of the first assumption, that the finer particles generated by breakage do not contribute to the soil's load carrying skeleton, is its effect on the CSL in the e log p0 space. A sheared specimen will reach the critical state at a certain void ratio, ec. If a specimen undergoes a finite amount of breakage, the particles formed during breakage reduce the specimen's void ratio (herein the discussion is limited to drained conditions, considering the undrained condition a boundary constraint). This reduction in void ratio due to breakage is denoted as Δeb. For small amounts of breakage the load bearing skeleton will still reach the critical state at the expected “skeleton void ratio”, but the specimen's overall void ratio will be lower by Δeb. The locus of the critical state void ratio of the soil skeleton is a function of the current stress level, (on the CSL) defined here by intercept Γ and slope λ10 (the CSL shape is an arbitrary choice and does not affect the argument) and is independent of the history of the specimen. Conversely, the Δeb generated is not related to the current stress level and instead is a function of the soil's breakage history. Hence, if the amount of breakage 454 M. Ghafghazi et al. / Soils and Foundations 54 (2014) 451–461 remains constant, the effect of breakage for the whole specimen would be a parallel shift in the CSL (ΔΓ). Eq. (1) follows from this argument: ΔΓ ¼ Δeb ð1Þ To expand the second assumption regarding conditions needed for particle breakage to occur, the soil's expected behaviour under different loading situations is considered. For a low density specimen under high initial stress, the CSL remains practically unchanged as the soil particles preferentially roll and slide as the applied stress increases until the specimen approaches the critical state. As the critical state is approached, the capacity for contraction decreases and particle breakage starts to shift the CSL downwards, and the specimen follows it by a further reduction in volume. For a dense specimen at higher initial stress, the CSL remains unchanged until the initial contraction phase (related to sliding and rolling) ceases. As contraction transitions to dilation, breakage initiates and the CSL moves downward, increasing the total contraction. Hence, the contraction continues to higher strains than expected in the absence of breakage, and some breakage may occur before the overall contraction is replaced by dilation. The dilation phase consists of a simultaneous volume increase caused by sliding and rolling and volume reduction caused by breakage. Eventually the volume reduction caused by breakage and the volume increase due to sliding and rolling balance each other. Usually researchers have stopped shearing at this stage, considering the specimen to be at the critical state (e.g., Russell and Khalili, 2004; Yamamuro and Lade, 1996). However, this may not necessarily be the case as breakage may continue with additional shearing, further reducing the specimen's volume. This transient constant volume stage could more accurately be referred to as an “apparent critical state”. Additional insight into the influence of breakage can be gained by focusing on the state parameter and how it changes with regard to a CSL whose position is dependent on the extent of breakage. The state parameter is defined as ψ ¼ e ec ð2Þ where ec is the critical void ratio for the current CSL and at the current mean stress (Been and Jefferies, 1985). Differentiating both sides of Eq. (2) results in Δψ ¼ Δe Δec ð3Þ 0 Differentiating the CSL (ec ¼ Γ λ10 logðp Þ) by assuming a constant λ10 and variable Γ gives Δec ¼ ΔΓ λ10 Δ log p0 ð4Þ Combining Eqs. (3) and (4) we can write Δψ ¼ Δe ΔΓ þ λ10 Δ log p0 ð5Þ Separating the change in void ratio into two parts Δe ¼ Δesr þ Δeb ð6Þ where Δesr is the change in void ratio caused by sliding and rolling. From Eqs. (1), (5), and (6), we obtain Δψ ¼ Δesr þ λ10 Δ log p0 ð7Þ Fig. 2. Microscopic picture of FRS grains. Fig. 3. Gradation curve (log–log scale) for specimens of Fraser river sand before and after shearing. Eq. (7) is identical to the change in the state parameter in the lack of breakage suggesting that breakage, and the change in the void ratio it induces, do not affect how the state parameter evolves. This implies that the volume reduction caused by the breakage may be superimposed on the volume change controlled by stress-dilatancy. The shearing of a sample at high stress constantly changes the gradation due to breakage, thus changing the CSL as defined in the absence of any breakage. As breakage is associated with an additional reduction in void volume (compressibility), reaching the critical state requires breakage to cease. To understand how the CSL evolves with breakage, it is necessary to eliminate the breakage from a specimen undergoing shearing at high stress. For such a specimen, this would only be possible if the particles became instantaneously unbreakable at the moment of interest during shearing. Since this is physically impossible, a compromise was to remould and retest specimens at a stress level where essentially no breakage happens and determine the CSL for a soil which has already undergone particle breakage in a prior test. This is the rationale behind the testing program presented in this work and that reported by Bandini and Coop (2011). 455 M. Ghafghazi et al. / Soils and Foundations 54 (2014) 451–461 Table 1 Summary of triaxial compression tests used for determining the virgin critical state line of fraser River sand (Figs. 4 and 5). Test namen Initial conditions End of test Remarks p' (kPa) e ψ0nn Statusnnn ε1 (%) p' (kPa) q (kPa) e CIU-M 200 CIU-D 200 CIU-D 390 CIU-M 400 200.2 196.4 388.4 393.3 0.897 0.820 0.906 0.832 −0.005 −0.083 0.044 −0.030 Dil. Dil. Dil. Dil. 10.2 5.1 24.3 19.6 184.6 334.6 186.0 613.6 273.5 504.7 266.4 896.5 0.897 0.820 0.906 0.832 CID-L 100 † CID-D 115 CID-L 300 102.1 113.9 302.9 0.946 0.668 1.005 0.005 −0.268 0.128 CS Dil. Con. 34.8 21.7 29.1 193.7 226.0 585.9 274.2 336.9 847.1 0.909 0.794 0.868 CID-D 410†† CID-D 515†† 409.6 514.5 0.634 0.689 Dil. CS 24.3 28.4 811.1 984.3 1196.6 1405.1 0.728 0.742 †† −0.225 −0.156 CID-L 1600††† CID-L #6 100††† 1601.4 104.4 0.867 1.004 0.089 0.063 Con. CS 8.3 5.8 545.5 189.7 744.3 255.3 0.843 0.902 ††† CID-L 190 UR CID-D 200 UR 190.0 198.0 0.902 0.730 −0.004 −0.173 CS Dil. 23.6 26.2 356.0 399.2 496.1 601.3 0.870 0.804 Un/Re-load cycles applied † Void ratio calculated from reconstitution density Some particle breakage expected Specimens confirmed to be virgin n CIU, consolidated undrained test; CID, consolidated drained test; L, loose; M, medium dense; and D dense specimen. The state parameter is obtained with respect to the virgin Critical State Line defined in Figure 5. nnn Con., contracting; CS, no change in volume or pore pressure i.e. at the critical state; and Dil., dilating. nn 3. Materials and methods The tested material, Fraser River Sand (FRS), is an alluvial deposit widely spread in the Fraser River delta in the Lower Mainland of British Columbia, Canada. FRS is a uniform, angular to sub-angular with low to medium sphericity, medium grained clean sand. Fig. 2 shows a microscopic picture of FRS grains. The gradation used in this research contains 0.8% fines content and has D50 and D10 of 0.271 mm and 0.161 mm, respectively. Fig. 3 presents the gradation curve of virgin FRS. emin and emax are 0.627 and 0.989, respectively, and Gs ¼ 2.719 (Shozen, 1991). emin was measured according to ASTM D2049 while emax was reported as the initial deposition void ratio in the loosest state. The average mineral composition based on a petrographic examination is 25% quartz, 19% feldspar, 35% metamorphic rocks, 16% granites, and 5% miscellaneous detritus. The test program included 28 drained and 11 undrained triaxial tests (Ghafghazi, 2011), 26 of which are reported and discussed here for brevity. All specimens were 142 mm in height and 71 mm in diameter, and were prepared using the moist tamping technique. Lubricated end platens were used to reduce stress non-uniformity within the specimens. The specimens were flushed with CO2 and de-aired water and back pressurised until a B value of 0.95 or greater was obtained. They were then consolidated and sheared under constant confining stress until a steady state was reached, apparent shear localisation was observed, or the equipment limitations were met. The strain controlled shearing was applied at a constant rate of 5% per hour and the void ratio was calculated by obtaining the specimen's water content at the end of the test. Special attention was paid to the accurate measurement of the void ratios considering its significance to the arguments made. At the end of the shearing phase, the drainage valves were closed. The triaxial cell was then taken apart and the cell base, membrane, and cap were dried before putting the setting containing the specimen in a freezer for 24 h. The frozen specimen was then extracted with care, making sure that no water or grains were lost during the process. This technique (Sladen and Handford, 1987) effectively eliminated the loss of water during specimen extraction, enabling accurate determination of the water content. A repeatability of 0.01 or better was obtained in void ratio measurement for three pairs of tests that were targeted to start from identical conditions. Corrections were applied for membrane penetration (Vaid and Negussey, 1984) and membrane force (Kuerbis and Vaid, 1990). The initial stage of the testing program was aimed at measuring the CSL of FRS at low stress levels expected not to have particle breakage. Table 1 summarises these 13 tests. To investigate the effect of particle breakage on CSL, four additional specimens were sheared at elevated levels of stress (up to 1.4 MPa) and sieved post-test. Table 2 provides details of these tests, referred to as the “parent tests” (identified in the table by bold font). Information provided includes initial and final stress levels and void ratios, status of the specimen with regards to the critical state at the end of the test, and the percentage fines following shearing. The four specimens all showed an increase in their fines content following shearing. After being sieved, they were used to prepare specimens for testing at lower stress levels to investigate the change in CSL due to breakage. Table 2 also provides details of the nine subsequent tests performed on presheared specimens at lower stress levels. 4. Results The triaxial test results are presented in terms of deviator stress, excess pore water pressure, and volumetric strains versus axial strain in Fig. 4 and summarised in Table 1. A specimen is considered at the critical state (CS in the status 456 M. Ghafghazi et al. / Soils and Foundations 54 (2014) 451–461 Table 2 Summary of triaxial compression tests done at high stresses to generate breakage (parent tests) and the subsequent tests on pre-sheared specimens of Fraser River sand (Figs. 6–8). Test name Initial conditions p′ (kPa) e ψ End of Test nn FC (%) Sieve Test Remarks Reference Status ε1 (%) p′ (kPa) q (kPa) e CID-L 1400 CID-M #3 200† 1396.2 204.6 0.839 – Con. 0.824 0.044 CS 10.7 43.0 2718.7 392.2 3950.5 560.9 0.600 7.0 0.746 6.3 #3 CID-M #3 600 CID-L #3 150 614.9 155.9 0.780 0.065 CS 0.831 0.059 CS 25.9 28.4 1193.0 274.4 1760.6 363.5 0.657 7.8 0.739 #3a CID-L 1400-2 CID-L #4 100 CID-L #4 300 1403.5 103.6 303.6 0.849 – Con. 0.999 0.087 CS 0.938 0.091 CS 39.4 9.8 35.0 2325.5 186.5 563.5 2744.7 249.3 780.4 0.736 1.9 0.883 0.809 #4 CID-D 1000-peak†† 1003.4 0.666 – 31.3 2019.6 3027.3 0.643 1.0 #7 CID-L #7 100 CID-L #7 300 105.2 302.7 1.005 0.074 CS 0.954 0.086 CS 23.1 38.8 187.2 570.6 246.0 802.4 0.898 0.823 CID-D 1000 CID-L #8 100 CID-L #8 300 1014.6 104.1 304.1 0.663 – Con. 0.982 0.095 CS 0.924 0.102 CS 36.3 6.0 34.4 1880.8 187.6 559.5 2633.7 250.2 765.6 0.657 3.1 0.854 0.788 Con. Figs. 10% of the specimen weight Figs. virgin FRS was added to the specimen, reducing FC to 6.3% Figs. Figs. † 6a and 8b 6b and 8b 6b and 8b 6b and 8b Figs. 6a and 8a Figs. 6b and 8a Figs. 6b and 8a †† Sheared to near peak strength or end of compression phase Figs. 6a and 7a Figs. 6b and 7a Figs. 6b and 7a #8 Figs. 6a and 7b Figs. 6b and 7b Figs. 6b and 7b n Tests shown in bold provide the “parent” specimens for the following tests after being sieved for gradation. nn The initial state parameter not stated for the “parent” specimens as Critical State Line may have changed during consolidation due to particle breakage. column of Table 1) if the stress ratio and the volumetric strain (drained) or pore pressure (undrained) have reached a steady value. The virgin CSL is approximated with Γ ¼ 1.22 and λ10 ¼ 0.138 between 100 kPa and 800 kPa in the typical semi-log space idealisation shown in Fig. 5. The dataset includes three tests that ended on the proposed CSL. An additional eight tests bound the CSL between specimens that were contracting or dilating at the end of shearing. Two tests ended at higher stress levels where breakage could occur; these tests were not considered when estimating the virgin CSL. Above a ‘breakage threshold’ stress level particle breakage occurs. The approximate threshold is indicated by the hatched zone between 800 kPa and 1 MPa in Fig. 5. This is a reasonable range considering the mineral composition of FRS and that the range is between that of silica (harder) and calcareous (weaker) sands. The initiation of breakage is related to soil mineralogy, angularity, and density as well as the loading direction. This indicates that the threshold is in reality non-vertical in the e log p0 space. Defining the breakage threshold more precisely is not critical to the current work as tests were performed at stress levels sufficiently below the threshold such that breakage did not occur or sufficiently above where breakage was clearly present. The occurrence of breakage has been confirmed by comparison of gradation measurements before and after each test. The initial (parent) tests to induce particle breakage in FRS are presented in Fig. 6a. At the end of each parent test, the specimen was sieved and then retested in the triaxial apparatus at lower levels of stress where further breakage was not expected to occur (conditions summarised in Table 2). Fig. 3 illustrates the gradation curves for the virgin FRS and specimens #3, #4, #7, and #8 after shearing induced breakage under higher stress. For simplicity, the fines content has been used here to quantify particle breakage, although more detailed indices are available (e.g., Hardin, 1985; Miura and O-Hara, 1979). Results from pre-sheared specimens (containing breakage from the initial test) at lower stress levels where additional breakage during the second shearing test is not expected are presented in Fig. 6b. These test results have been presented along with their parent test (shown in bold) in Figs. 7 and 8 in order to identify the effect of particle breakage on the CSL. The sequence of testing is indicated beside each state path in these figures. The tests performed at lower stress levels point to a CSL that is parallel to that of virgin FRS with differing offsets (ΔΓ values). Results of a series of triaxial tests on two initially identical dense specimens, consolidated to 1000 kPa, are presented in Fig. 7 to examine when breakage initiates during shearing. The parent test CID-D 1000-peak in Fig. 7a was stopped near its peak stress before the dilation phase. Gradation testing showed very little increase in its fines content (from 0.8% to 1.0%). The sheared specimen was then re-constituted as new specimens and addition triaxial tests were performed at consolidation stress levels of 100 and 300 kPa (within a stress range where further breakage did not occur; state paths 2 and 3) indicating only a small shift in the CSL. In the second testing scheme, the parent test CID-D 1000 was sheared to larger strains until dilation ended and the specimen started to contract again (see Fig. 6a). This resulted in significant breakage and M. Ghafghazi et al. / Soils and Foundations 54 (2014) 451–461 457 Fig. 4. Deviator stress, pore pressure and volumetric strain plotted against the axial strain for tests aimed at determining the critical state line for virgin FRS. (a) Undrained triaxial compression tests. (b) Drained triaxial compression tests. Fig. 5. e log p0 lot of triaxial compression tests and the critical state line of virgin Fraser River sand. the fines content increased from 0.8% to 3.1%. This specimen (with breakage) was then used to test two additional specimens under lower stress conditions (state paths 2 and 3 in Fig. 7b). As evident in Fig. 7b, the change in gradation resulted in a larger downward shift in the CSL. A second set of tests performed following the same approach, but on initially loose specimens, is presented in Fig. 8. The parent test CID-D 1400-2 was sheared to 10% axial strain (see Fig. 6a). The gradation test post-shearing indicated that the fines content had increased from 0.8% to 1.9%. The two test results on re-constituted specimens performed at 100 and 300 kPa consolidation stress indicated a modest, but clear shift in the CSL (Fig. 8a). The second parent test CID-D 1400 was performed to a larger strain of 43% in order to induce significant breakage (see Fig. 6a). As expected for such large axial strains, towards the end of the test excessive bulging and shear localisation was observed, along with a decrease in the measured deviator stress. After testing, the fines had increased to 7.0%. This specimen was then mixed with about 10% by weight of virgin sand (resulting in 6.3% overall fines content) to produce enough material for the following tests. Additional tests were performed starting at isotropic consolidation stress levels of 200 kPa and 600 kPa with the new material (Fig. 8b). The modified CSL was inferred based on test CID-M #3 200. Test CID-M #3 600 consolidated to 600 kPa and then sheared and sieved post-test and found to have an increase in fines content from 6.3% to 7.8%. This additional breakage resulted in the final state being below the CSL determined from test CID-M #3 200. To determine the additional shift in the CSL due to this further breakage, another test was conducted at 150 kPa confirming a further drop (ΔΓn) in the CSL. 5. Discussion 5.1. Influence of breakage on CSL The data presented indicate that changes in gradation towards a more well-graded condition, due to particle 458 M. Ghafghazi et al. / Soils and Foundations 54 (2014) 451–461 Fig. 6. Deviator stress and volumetric strain plotted against the axial strain for tests at higher stress levels and the subsequent tests performed on pre-sheared specimens to determine the change in the critical state line. (a) Parent tests. (b) Follow up tests on pre-shared specimens. Fig. 7. e log p0 plots of tests on dense specimens starting at 1000 MPa (thick lines) and the subsequent tests performed on pre-sheared specimens to determine the change in the critical state line of Fraser River sand. (a) CID-D 1000-peak. (b) CID-D 1000. breakage, moves the CSL down (reducing Γ) without changing the slope (constant λ10). This is in agreement with the discrete element modelling of Muir Wood and Maeda (2008) who found that the change in λ10 is negligible in comparison to the change in Γ. Test results on drained loose specimens (Fig. 8) indicate that extrapolation of the CSL determined from tests at low stress levels to higher stress levels passes through (or is slightly lower than) the final state of the parent test. This is evident in the test series presented in Fig. 8a. It is also evident, but less clear, in the test series presented in Fig. 8b due to the complications of having to add virgin FRS in the later tests. The end points of loose samples undergoing particle breakage are coincident with the CSL obtained from subsequent tests at lower stress levels. Hence, it can be inferred that samples undergoing particle breakage at higher stress are at or near their CSL from a sliding and rolling point of view. In other words, contraction of a loose specimen such that the state path moves below the virgin critical state is almost entirely caused by the M. Ghafghazi et al. / Soils and Foundations 54 (2014) 451–461 459 Fig. 8. e log p0 plots of tests on loose specimens starting at 1400 MPa (thick lines) and the subsequent tests performed on pre-sheared specimens to determine the change in the critical state line of Fraser River sand. (a) CID-L 1400Kpa-2. (b) CID-L 1400. breakage phenomenon. This is the concept captured by Eq. (1). The data presented suggests that Eq. 1 holds true some time after the specimen has passed the original CSL. The relation between the end point of parent tests and the shifting CSL is not as clear for the dense specimens (e.g., Fig. 7b) due to localisation occurring post peak in dense specimens, affecting both the volume change and the amount of breakage measured in the parent test. With localisation, the specimen has a smaller measured global void ratio at the end of the test than it would have if the entire specimen had dilated to the critical state. The same mechanism applies to particle breakage (Luzzani and Coop, 2002), resulting in a specimen which is not only nonuniform in straining, but also in gradation and extent of breakage. The pre-sheared specimen is thus a mixture of materials with different degrees of breakage, resulting in a higher CSL. This makes correlating the CSL with the specimen's state at high stress more difficult for dense specimens. on dense specimens shown in Fig. 7a and b were taken to different levels of strain in order to investigate the initiation of breakage. Test CID-D 1000-peak was stopped around its peak strength after it had undergone the initial contraction expected from a dense specimen. The consequent gradation tests showed only a small increase in the fines content and a very small shift in the CSL. In contrast, test CID-D 1000, which was sheared until dilation was completely suppressed, showed a considerable amount of particle breakage. This confirms that particle breakage primarily occurs after sliding and rolling compressibility is exhausted. This is consistent with the Hyodo et al. (1999) findings for undrained tests on sands, namely, that particle breakage accelerates after the phase transformation point. It is also a confirmation of the findings of Ueng and Chen (2000) that the rate of particle breakage increases beyond the peak strength. 5.3. Apparent critical state 5.2. Initiation of breakage The framework requires two conditions to be satisfied for the breakage to start. Detectible breakage will not occur if one of these conditions is not present. Test CID-L 1600 is an example of lack of breakage when the capacity for sliding and rolling is not exhausted in a specimen above the breakage threshold stress. The specimen was isotropically consolidated to 1600 KPa, the highest confining stress in the program (see Table 1). It was sheared to 0.1% strain before the pump controlling the cell pressure failed resulting in a continuously decreasing confining stress; shearing then continued until the specimen approached the CSL; yet no breakage was observed as confirmed by a gradation test. This confirms that breakage did not occur in a specimen that could contract to critical state and reached it below the breakage threshold. In other words, in the initial stage of the test, where the stress condition was present, the capacity for sliding and rolling was not yet exhausted. When this occurred as the sample approached the CSL, the stress condition was no longer present. Test CID-D 1000-peak is another example of lack of breakage when only one of the conditions is present. The drained tests A particularly interesting mechanism may occur during the shearing of dense specimens when they approach the critical state at higher stress. At this stage, the breakage may balance dilation, creating a state of zero volume change or “apparent critical state”. The proposed framework suggests that provided that breakage can continue with further shearing, compression will resume. This was observed in CID-D 1000 as a resumption of contraction beyond 20% strain (shown in Fig. 6a). For dense specimens like CID-D 1000, sheared to the apparent critical state and beyond, the CSL is expected to follow the specimen as it moves towards lower void ratios. Although test CID-D 1000-peak was stopped before the specimen started dilating, some minor breakage was recorded; the fines content increased from 0.8% to 1.0% and a small drop in the CSL was registered (Fig. 7a). It is possible to explain this using Eq. (6). Towards the end of the contraction phase and at the beginning of the dilation phase, Δesr becomes very small while breakage initiates (Δeb r 0). The resulting measured total Δe remains negative. Depending on the stress level, density, and the material, the apparent critical state may be reached and passed or this effect may completely suppress the 460 M. Ghafghazi et al. / Soils and Foundations 54 (2014) 451–461 particle breakage. The framework was examined using a series of triaxial compression tests on Fraser River sand, reaching mean effective stresses up to 3 MPa. The associated increase in the fines content of sheared specimens ranged from zero to 7%. The main conclusions of this work are:    Fig. 9. The change in Γ, (ΔΓ) versus the change in fines content (ΔFC) after shearing at high pressures: comparison between Fraser River sand and Kurnell sand (Russell and Khalili, 2004). dilation phase and cause the specimen to behave like a loose specimen (Vesić and Clough, 1968) despite starting on the dense side of the CSL. 5.4. General observations The variation in Γ, (ΔΓ), is plotted against the change in fines content (ΔFC) for the FRS tests performed herein as well as Kurnell sand (Russell and Khalili, 2004) in Fig. 9. The Kurnell sand data is plotted by applying the conceptual framework presented here to the triaxial compression and gradation test data presented by Russell and Khalili, 2004. The data presented in the figure follow similar trends lending more support to the ideas presented despite the differences between the materials and the testing performed. Although determining the CSL for specimens undergoing breakage requires additional tests to be performed on sheared specimens, the correlation between the shift in the CSL and the fines content produced by breakage is rather promising and once this relation is established the CSL can be estimated for other specimens by performing a sieve test. The proposed framework and the test data presented here result in a different picture of the effects of particle breakage on the CSL than that described by Bandini and Coop (2011). Bandini and Coop (2011) suggested a shift in the CSL of Dog's Bay sand that included both an offset and a rotation. The effect of breakage on the CSL observed here is more pronounced than that speculated by Bandini and Coop (2011) for materials such as Fraser River and Kurnell sands. It is likely that the differences mainly stem from the difference between the carbonate sand used by Bandini and Coop (2011) and the sands used by Russell and Khalili (2004) and in this work. 6. Summary and conclusions The current work presented a simple micromechanical framework to explain the changes to the Critical State Line due to shearing sand at stress levels sufficient to produce Measurable breakage only starts after the soil's contraction capacity is exhausted. Breakage causes a downward parallel shift in the CSL in e log p0 space; a finding in agreement with Daouadji et al. (2001) and Muir Wood and Maeda (2008). The magnitude of the CSL shift is directly correlated with the increase in the fines content. These observations and the framework provide an alternative to the three-segment line often used to model the effect of particle breakage on the CSL. This work instead proposes idealising the CSL as a series of parallel lines each associated with a certain level of particle breakage. The experimental observations also imply that since Δeb ¼ ΔΓ, the evolution of the state parameter is independent of breakage. Hence, the volume reduction caused by the breakage may simply be superimposed on the volume change controlled by stressdilatancy. Acknowledgements The authors would like to thank Golder Associates' Burnaby Laboratory for the use of their facility to carry out the tests presented in this paper, and Mike Jefferies, Roberto Olivera, and Larry Lee for their technical guidance and practical testing support. We also wish to thank Profs. Nasser Khalili and Adrian Russell for providing the Kurnell sand data. References Altuhafi, F.N., Coop, M.R., 2011. The effect of mode of loading on particlescale damage. Soils Found. 51 (5), 849–856. Bandini, V., Coop, M.R., 2011. The influence of particle breakage on the location of the critical state line. Soils Found. 51 (4), 591–600. Been, K., Jefferies, M.G., 1985. A state parameter for sands. Géotechnique 35, 99–112. Been, K., Jefferies, M.G., Hachey, J., 1991. The critical state of sands. Géotechnique 41 (3), 365–381. Bishop, A.W., 1966. Strength of soils as engineering materials. 6th Rankine lecture. Géotechnique 16, 89–130. Bridgman, P.W., 1918. The failure of cavities in crystals and rocks under pressure. Am. J. Sci. 45, 243–268. Coop, M.R., Sorensen, K.K., Bodas Freitas, T., Georgoutsos, G., 2004. Particle breakage during shearing of a carbonate sand. Géotechnique 54 (3), 157–163. Daouadji, A., Hicher, P.Y., Rahma, A., 2001. An elastoplastic model for granular materials taking into account grain breakage. Eur. J. Mech. – A/ Solids 20, 113–137. Ghafghazi M., 2011. Towards Comprehensive Interpretation of the State Parameter from Cone Penetration Testing in Cohesionless Soils (Ph.D. Thesis), Department of Civil Engineering, University of British Columbia, Canada. 〈https://circle.ubc.ca/handle/2429/34090〉. Hardin, B.O., 1985. Crushing of soil particles. J. Geotech. Eng. 111 (10), 1177–1192. M. Ghafghazi et al. / Soils and Foundations 54 (2014) 451–461 Hyodo M., Aramaki N., Nakata Y., Inoue S., 1999. Particle crushing and undrained shear behaviour of sand. In: Proceedings of the 9th International Offshore and Polar Engineering Conference, Brest, France, May 30–June 4, 1999.ISBN 1-880653-39-7. Kikumoto, M., Muir Wood, D., Russell, A.R., 2010. Particle crushing and deformation behaviour. Soils Found. 50 (4), 547–563. Konrad, J.M., 1998. Sand state from cone penetrometer tests: a framework considering grain crushing stress. Géotechnique 48 (2), 201–215. Kuerbis, R.H., Vaid, Y.P., 1990. Corrections for membrane strength in the triaxial test. Geotech. Test. J. 13 (4), 361–369. Lade, P.V., Yamamuro, J.A., 1996. Undrained sand behaviour in axisymmetric tests at high pressures. J. Geotech. Eng. 122 (2), 120–129. Lee, I.K., Coop, M.R., 1995. Intrinsic behaviour of a decomposed granite soil. Géotechnique 45 (1), 117–130. Lee, K.L., Farhoomand, I., 1967. Compressibility and crushing of granular soil in anisotropic triaxial compression. Can. Geotech. J. 4 (1), 68–86. Luzzani, L., Coop, M.R., 2002. On the relationship between particle breakage and the critical state of sands. Soils Found. 42 (2), 71–82. Marketos, G., Bolton, M.D., 2007. Quantifying the extent of crushing in granular materials: a probability-based predictive method. J. Mech. Phys. Solids 55 (10), 2142–2156. McDowell, G.R., Bolton, M.D., Robertson, D., 1996. The fractal crushing of granular materials. J. Mech. Phys. Solids 44 (12), 2079–2101. McDowell, G.R., Daniell, C.M., 2001. Fractal compression of soil. Géotechnique 51 (2), 173–176. Miura, N., O-Hara, S., 1979. Particle-crushing of a decomposed granite soil under shear stresses. Soils Found. 19 (3), 1–14. Muir Wood, D., 2007. The magic of sands – The 20th Bjerrum lecture presented in Oslo, 25 November 2005. Can. Geotech. J. 44, 1329–1350. Muir Wood, D., Maeda, K., 2008. Changing grading of soil: effect on critical states. Acta Geotech. 3, 3–14. 461 Nakata, Y., Hyodo, M., Hyde, A.F., Kato, Y., Murata, H., 2001. Microscopic particle crushing of sand subjected to high pressure one-dimensional compression. Soils Found. 41 (1), 69–82. Roscoe, K., Schofield, A.N., Wroth, C.P, 1958. On the yielding of soils. Géotechnique 8 (1), 22–53. Russell, A.R., Khalili, N., 2002. Drained cavity expansion in sands exhibiting particle crushing. Int. J. Numer. Anal. Methods Geomech. 26, 323–340. Russell, A.R., Khalili, N., 2004. A bounding surface plasticity model for sands exhibiting particle crushing. Can. Geotech. J. 41 (6), 1179–1192. Russell, A.R., Muir Wood, D., Kikumoto, M., 2009. Crushing of particles in idealised granular assemblies. J. Mech. Phys. Solids 57 (8), 1293–1313. Shozen T., 1991. Deformation under the Constant Stress State and its Effect on Stress–Strain Behaviour of Fraser River Sand (MASc. thesis), Department of Civil Engineering, University of British Columbia. Skinner, A.E., 1969. A note on the influence of interparticle friction on the shearing strength of a random assembly of spherical particles. Géotechnique 19, 150–157. Sladen, J.A., Handford, G., 1987. A potential systematic error in laboratory testing of very loose sands. Can. Geotech. J. 24, 462–466. Ueng, T.-S., Chen, T.-J., 2000. Energy aspects of particle breakage in drained shear of sands. Géotechnique 50 (1), 65–72. Vaid, Y.P., Negussey, D., 1984. A critical assessment of membrane penetration in the triaxial test. Geotech. Test. J. 7 (2), 70–76. Vesić, A.S., Clough, G.W., 1968. Behavior of granular materials under high stresses. J. Soil Mech. Found. Div. 94 (SM3), 661–688. Vilhar, G., Jovicic, V., Coop, M.R., 2013. The role of particle breakage in the mechanics of a non-plastic silty sand. Soils Found. 53 (1), 91–104. Yamamuro, J.A., Lade, P.V., 1996. Undrained sand behaviour in axisymmetric tests at high pressures. J. Geotech. Eng. 122 (2), 109–119.