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sand mixtures for underground waste repository sealing
Applied Clay Science 49 (2010) 394–399
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Applied Clay Science j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c l a y
Geotechnical characterization and performance assessment of bentonite/sand mixtures for underground waste repository sealing Haluk Akgün ⁎ Faculty of Engineering, Department of Geological Engineering, Middle East Technical University, Ankara 06531, Turkey
a r t i c l e
i n f o
Article history: Received 24 September 2008 Received in revised form 12 August 2009 Accepted 17 August 2009 Available online 24 August 2009 Keywords: Bentonite/sand seal Geotechnical seal design Seal/rock mechanical interaction Underground waste repository sealing Proposed Akkuyu Nuclear Power Plant
a b s t r a c t The objective of this study is to assess the performance of a bentonite/sand mixture for the sealing of underground waste repositories through performing geotechnical laboratory tests such as compaction and flow tests. Swelling, mechanical and shear strength tests along with analyses of seal/rock mechanical interactions of an axially loaded seal in rock have been conducted to recommend an optimum compacted bentonite/sand mixture and a suitable bentonite/sand seal length-to-radius ratio (L/a) as a function of water load. The bentonite used in this study was a natural sodium based non-treated bentonite possessing a high swelling potential and containing at least 90% montmorillonite. The results of the compaction permeameter tests led to a recommendation to select a mixture with a bentonite content of about 30% since it possessed the lowest hydraulic conductivity. Analysis of seal/rock mechanical interaction to reduce the possibility of seal slip was performed as a function of the axial load generated from a water column on the seal for seal length-to-radius ratios (L/a) ranging from 2.0 to 20. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Sealing of boreholes, shafts, mine drifts, and tunnels may be required for a variety of reasons. Penetrations of and near a high-level nuclear waste repository need to be sealed reliably to retard any radionuclide migration to the accessible environment (e.g., Hoffman, 2004; USEPA, 1995; US Nuclear Regulatory Commission, 1983; 1985). Sealing may prove necessary to prevent flooding of underground operations (e.g., Akgün and Daemen, 1999). Sealing of diversion tunnels is often required on hydro-electric projects (e.g., Pettman, 1984). Sealing of mine openings is a growing concern in order to control mine effluents (e.g., Einarson and Abel, 1990). There is an increased conviction that geotechnical exploratory boreholes need to be sealed reliably in order to prevent groundwater contamination (e.g., Fuenkajorn and Daemen, 1996). The most extensive practice, experience, and investigations of borehole sealing have been developed in the oil and gas industry (e.g., Halliburton Services, undated). Bentonite and bentonite/sand mixtures are considered as buffer and backfill materials for repositories of high-level nuclear waste in Sweden, Switzerland, Canada, Germany and France (e.g., Coulon et al., 1987; IAEA, 1990; Pusch, 1994) and for sealing of shafts emplaced in the vicinity of the Waste Isolation Pilot Plant (WIPP) site in southeastern New Mexico (e.g., Daemen and Ran, 1996; USDOE/
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WIPP, 1995). It is possible that bentonite and bentonite/sand mixtures may be utilized for sealing repositories of high-level nuclear waste that is expected to be generated from the proposed Akkuyu Nuclear Power Plant in the near future. The proposed plant site is located on the southern Mediterranean coast of Turkey, 45 km southwest of the city of Silifke, directly inshore from Cyprus. Chapius (1990), Dixon et al. (1985), Kenney et al. (1992), Komine (2004), Kjartanson et al. (1996), Ouyang and Daemen (1996), Papp (1996), Pusch (1978, 1983), Sivapullaiah et al. (2000) and Yong et al. (1986) have performed sealing studies with bentonite/sand, bentonite, bentonite/crushed rock or soil mixture plugs in the laboratory as well as insitu. Akgün et al. (2006) have investigated the sealing performance of bentonite/sand mixtures with bentonite contents ranging from 15% to 20% for sealing boreholes in the vicinity of the Yucca Mountain tuff site in Nevada. Axial loads on seals emplaced in openings in the vicinity of a highlevel nuclear waste repository may be due to water, drilling mud, gas or backfill pressures. Axial loads induce shear stresses along the contact between the seal and host rock which, under extreme conditions, could cause dislodging or slipping of seals, leading to increased permeability through the seal (Akgün and Daemen, 1999). Hence, repository sealing requires that the sealing barrier possess adequate interface strength, a low permeability, a long lifetime, a high resistance to erosion, mechanical and chemical stability, and compatibility with host rocks or materials (Pusch, 1978). Bentonite and its soil mixtures have an extremely low hydraulic conductivity, are self-healing and have good chemical stability that would provide effective long-term sealing (Gnirk, 1988).
H. Akgün / Applied Clay Science 49 (2010) 394–399
The objective of this study is to investigate the sealing performance of bentonite/sand mixtures possessing bentonite contents ranging from 22.5% to 30% and to find a suitable compacted bentonite/sand mixture for the sealing of underground nuclear waste repositories situated in the vicinity of the proposed Akkuyu Nuclear Power Plant in Southern Turkey through performing geotechnical laboratory tests such as compaction permeameter, swelling, mechanical and shear strength tests. Analysis of seal/rock mechanical interaction in regard to reduce the possibility of seal slip has been performed as a function of the axial load generated from a water column on the seal for seal length-to-radius ratios (L/a) ranging from 2.0 to 20.
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Table 2 Results of standard proctor compaction tests. Bentonite content (%)
wopt
15a 17.5a 20a 22.5 25 27.5 30
15.82 15.41 15.10 14.72 14.00 13.59 13.29
(%)
γdmax (kN/m3) 16.01 16.24 16.29 16.42 16.54 16.62 16.73
Mean values of the optimum moisture content (wopt) and maximum dry unit weight (γdmax) of compacted bentonite/sand mixtures possessing 15% through 30% bentonite. a Data from Akgün et al. (2006).
2. Geotechnical evaluation and compaction permeameter testing of bentonite/sand mixtures The bentonite used was KAR-BEN, a natural sodium based nontreated bentonite possessing a high swelling potential and containing at least 90% montmorillonite (Karakaya, 2009). Table 1 presents the geotechnical index properties and the engineering characteristics of the KAR-BEN bentonite. The specific gravity of the solids and Atterberg limits, namely, the liquid limit (LL), plastic limit (PL) and plasticity index (PI) reported in Table 1 were determined according to standard practice (ASTM D 854-06 e1 and D 4318-05)). The wellgraded lean sand used in this study consisted of about 99% of quartz minerals and possessed a hydraulic conductivity at maximum compacted density of about 10−4 m/s, specific gravity (Gs) of 2.64, void ratio (e) of 0.45 and a maximum compacted dry density (γdmax) of about 18 kN/m3. Akgün et al. (2006) present gradation information for the well-graded sand possessing a particle size ranging from 1.18 mm to 0.075 mm, and a particle shape generally ranging from subrounded to rounded. The bentonite and sand specimens were kept in plastic bags under ambient room conditions (22 ± 2 °C, 30% ± 1% relative humidity) in the Engineering Geology Laboratory of the METU Department of Geological Engineering prior to being mixed for standard compaction and falling head permeability testing. The Standard Proctor compaction apparatus was used to compact four different bentonite/sand mixtures, namely, mixtures possessing 22.5%, 25%, 27.5% and 30% bentonite content at various molding water contents, respectively, according to ASTM D 698-07 e1. The results of the standard compaction tests are summarized in Table 2. Table 2 also contains compaction data on samples with bentonite contents of 15%, 17.5% and 20% that have been reported by Akgün et al. (2006). The compacted bentonite/sand specimens were placed in rigidwall permeameters for hydraulic conductivity testing in accordance
with ASTM D 5856-07. Fig. 1 shows the falling head compaction permeameter setup. The test apparatus consists mainly of four compaction permeameters, de-airing tank, four burettes, a distilled water tank and a vacuum pump so that four tests may be performed concurrently. Each test took place for a period of about 1.5 to 2 months which was the approximate length of time required for the compacted samples to attain full saturation prior to permeability testing. Full sample saturation was confirmed by water coming out of the water outlet portal of the compaction permeameter equipment.
Table 1 Geotechnical index and engineering characteristics of the natural bentonite component of the compacted bentonite/sand mixtures (Karakaya, 2009). Index or engineering property
Value
Specific gravity (Gs) Liquid limit, LL (%) Plastic limit, PL (%) Plasticity index, PI (%) Positive cation exchange capacity (mequiv/100 g) 350 ml of distilled water suspension test results: 600 rpm reading by Fann 35 Viscometer (min) Maximum filtration volume (cm3) Minimum yield (bbl) Maximum moisture content by weight (%) Maximum residue retained by weight on 200 mesh wet screen analysis (%) Maximum yield point plastic viscosity ratio (Yp/Pv) Minimum dispersed plastic viscosity (cp) Aged Yp/Pv to normal Yp/Pv ratio Maximum normal Yp/Pv to dispersed Yp/Pv ratio
2.74 450 35 415 100 30 12.5 80 10 2.5 1.5 10 1.5 3.0
Fig. 1. Schematic drawing of compaction permeameter setup. (modified from Met et al. 2005).
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Distilled and de-aired water was used as the permeant. The hydraulic conductivity (k) values were calculated through Eq. (1): k=
aL h ln 1 h2 Aðt2 −t1 Þ
ð1Þ
where a is the inside cross-sectional area of the burette, L is the length of the specimen, A is the cross-sectional area of the compacted soil specimen, h1 is the head at time t1, and h2 is the head at time t2 (Fig. 1). The hydraulic conductivity tests were performed on bentonite/ sand samples compacted at about 2% on the wet side of their optimum moisture contents since as pointed out for example by Daniel and Benson (1990) and Lambe (1954), compacting clayey soils on the wet sides of the line of optimums permits greater remolding of clods, elimination of large interclod voids and preferential re-orientation of clay particles, all of which result in decreased hydraulic conductivity values. The results of the hydraulic conductivity tests measured at about 2% wet of the optimum moisture contents of samples with bentonite contents of 22.5%, 25%, 27.5% and 30% are summarized in Table 3. Table 3 also contains hydraulic conductivity data on samples with bentonite contents of 15%, 17.5% and 20% that have been reported by Akgün et al. (2006). These results lead to a recommendation to select a compacted bentonite/sand mixture possessing a bentonite content of about 30% since this mixture possesses the lowest hydraulic conductivity value (i.e., 8.9 × 10− 12 m/s) and since there is no set regulatory criterion for a minimum hydraulic conductivity value in nuclear waste repository sealing. The results of the compaction and flow tests on samples possessing 15 to 30% bentonite content reported in Tables 2 and 3 showed that the maximum dry unit weight (γdmax) tended to increase, while the corresponding optimum moisture content (wopt) and hydraulic conductivity (k) tended to decrease with increased bentonite content of the bentonite/sand mixtures. Upon selecting the mixture possessing a bentonite content of 30%, swelling, unconfined compression and direct shear testing was performed on this mixture to determine the swelling pressure, elastic constants and shear strength parameters in accordance with ASTM D 4546-08, D 2166-06 and D 6528-07, respectively. The swelling pressure generated by the mixture after a period of one week was determined to be 0.27 MPa. The Young's modulus, cohesion (c) and the angle of internal friction (ϕ) were determined to be 64.2 MPa, 104 kPa and 26.9°, respectively. The Poisson's ratio was assumed to be 0.30. Fig. 2 gives the result of the direct shear test performed on the bentonite/sand mixture with a bentonite content of 30%.
Fig. 2. The result of the direct shear test performed on a bentonite/sand mixture containing 30% bentonite.
ratio (L/a) as a function of the water column acting on the seal. Analysis of seal/rock mechanical interaction to reduce the risk of seal slip is performed as a function of the axial load generated from the water column on the seal for seal length-to-radius ratios (L/a) ranging from 2.0 to 20. The geotechnical properties of the mixture with a bentonite content of 30% reported in the previous section are utilized in the stability analysis.
3. Analysis of seal/rock mechanical interaction and stability assessment Analyzed in this section is the stability of an axially loaded compacted bentonite/sand seal that is emplaced in boreholes or shafts. The stability of the seal is analyzed as a function of the water column in an attempt to determine the required seal length-to-radius
Table 3 Mean hydraulic conductivity values of compacted bentonite/sand samples at about 2% wet of the optimum moisture content. Bentonite content (%)
Hydraulic Conductivity (m/s)
15a 17.5a 20a 22.5 25 27.5 30
6.4 × 10− 9 1.7 × 10− 9 3.0 × 10− 10 8.6 × 10− 11 4.8 × 10− 11 1.3 × 10− 11 8.9 × 10− 12
a
Data from Akgün et al. (2006).
Fig. 3. Stresses acting on a seal/rock system. σz = axial stress applied to the seal, τ = shear stress at seal/rock interface, z = axial distance from initial location of the loaded end of the seal, a = seal radius, R = rock cylinder outside radius, L = seal length, rc = critical radius, wp, wp′ = axial seal displacement, dσz = axial stress increment over diametral seal slice ABCD of thickness dz.
H. Akgün / Applied Clay Science 49 (2010) 394–399
Composite materials, reinforced concrete, rock-socketed piers, piles and rock bolts are mechanistically similar to an axially stressed seal emplaced within a borehole or shaft in rock (Akgün and Daemen, 1991, 1999). In all structures of these types, the applied axial stress is transferred from the inclusion to the host or vice versa in the form of shear stresses along the interface. Fig. 3 gives the geometry and coordinate system utilized for stress calculations for an axially loaded seal in rock. As an axial stress (σz) is applied to the seal, load transfer occurs through shear stresses, τ, along the interface between the seal and rock. This results in differential compression of the seal leading to an axial seal displacement wp at the loaded end of the seal and wp′ at a distance z from the initial location of the loaded end of the seal. Consideration of the axial force equilibrium of element ABCD in Fig. 3 leads to the solution of the interface shear stress τ. The three-dimensional exponential elastic shear stress distribution along the seal/rock interface (τ) due to an axial stress applied to the seal (σz) is presented by Eq. (2) (Akgün and Daemen, 1999): σ β cosh½βðL−zÞ = a τ= z 2 sinh½βðL = aÞ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1−2νs λ β= ð1 + νr ÞðEs = Er Þlnðrc = aÞ
λ=
ð2Þ
ð2aÞ
νs ð1−ða =RÞ2 Þ ð2bÞ ð1−νs Þð1−ða= RÞ Þ + ðEs = Er Þð1 + νr Þ½ð1−2νr Þða=RÞ2 + 1 2
−0:18ðEs = Er Þ
rl = a + 2:07Le
ð2cÞ
rc = rl ; if R >rl
ð2dÞ
rc = R; if R≤rl
ð2eÞ
where λ and β are dimensionless parameters, z is the axial distance from the initial location of the loaded end (top) of the seal (z = 0 at the top of the seal and z = seal length, L, at the seal bottom), Es/Er is the ratio of the Young's moduli of seal and rock, νs and νr are the Poisson's ratios of seal and rock, rc is the critical radius beyond which the shear stresses and axial displacements in the rock are considered negligible, rl is the limiting critical radius which accounts for seal emplacement in a laboratory-sized specimen or in-situ, a and R are the seal and rock cylinder outside radii, respectively. Fig. 3 gives the geometry and coordinate system utilized for stress calculations. It follows from Eq. (2) that the peak shear stress induced by axial loading (τp) occurs at the loaded end (z = 0) of the seal/rock interface: σz β τp = 2tanh½βðL = aÞ
ð3Þ
The peak shear stress induced by axial loading (τp∞) for an in-situ seal in rock (e.g., R/a = ∞) also occurs at the loaded end of the seal/ rock interface and follows from using R/a = ∞ in Eq. (3): τp∞ =
σz γ 2tanh½γðL = aÞ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1−2νs α γ= ð1 + νr ÞðEs = Er Þlnðrc = aÞ α=
νp ð1−νp Þ + ðEs = Er Þð1 + νr Þ
where all the other parameters of Eq. (4) are given by Eq. (2).
ð4Þ
ð4aÞ
ð4bÞ
397
The shear strength of the interface (|τ|) is given by the Coulomb criterion as: j τj = c + σn tan ϕ
ð5Þ
where c is the cohesion (adhesion), ϕ is the angle of internal friction and σn is the total normal stress across the plug–rock interface. The total normal stress across the interface (σn) of an axially loaded expansive bentonite/sand seal is given by Akgün (2000) as: σn = σr + σs
ð6Þ
where σr is the radial (contact) normal stress induced by axial loading along the seal/rock interface due to an axial stress σz applied to the bentonite/sand seal and σs is the seal swelling pressure that is assumed constant along the interface. σr is derived by Akgün (2000) as follows: sinh½βðL−zÞ = a σr = σz λ sinh½βðL = aÞ
ð7Þ
where all the parameters of Eq. (7) are given by Eq. (2). Utilizing Eq. (6) in Eq. (5) and inspecting the resultant equation reveal that the peak normal stress across the interface (σnp) occurs at the loaded end of the seal (i.e., at z = 0) and follows from using z = 0 in Eqs. (6) and (7): σnp = σz λ + σs
ð8Þ
The peak normal stress across the interface (σnp∞) for an in-situ seal in rock (e.g., R/a = ∞) also occurs at the loaded end of the seal/ rock interface (z = 0) and follows from using R/a = ∞ in Eq. (6): σnp∞ = σz α + σs
ð9Þ
where α is given by Eq. (4b). The peak shear strength across the interface for an in-situ seal emplaced in rock (|τp∞|) follows from using Eq. (9) in Eq. (5): jτp∞ j = c + σnp∞ tan ϕ
ð10Þ
where σnp∞ is the peak normal stress across the seal/rock interface for an in-situ seal in rock. The factor of safety (F) of an in-situ seal in rock against slipping may be expressed by the following equation (e.g., Wyllie, 1999): F=
j τp∞ j ∑Resisting forces Shear strength = = τp∞ Shear stress ∑Driving forces
ð11Þ
where |τp∞| and τp∞ are the peak shear strength and peak shear stress across the interface for an axially loaded and expansive (swelling) insitu seal in rock given by Eqs. (10) and (4), respectively. 4. Geotechnical seal design and discussion The stability of bentonite/sand seals emplaced in boreholes or shafts in the vicinity of a high-level radioactive waste repository, such as that to be located in the proximity of the proposed Akkuyu Nuclear Power Plant in southern Turkey is analyzed for seals emplaced at a possible depth of for example 100 m in the relatively low permeable levels (i.e., shale/mudrock levels of the Akdere formation, which consists of alternations of limestone, sandstone, mudstone and shale) (Demirtaşlı, 1985). The stability of the seals is analyzed as a function of the water column acting on the seal in an attempt to determine the required seal length-to-radius ratio (L/a) as a function of water head. The geotechnical properties of the mixture with a bentonite content of 30% reported in the previous section are utilized in the stability analysis. The geotechnical properties of the shale/mudrock and of the
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seal considered in the stability analysis are as follows: the average Young's modulus (Er) and Poisson's ratio (νr) of the shale/mudrock are 364.4 MPa and 0.26, respectively (EİE (Turkish General Directorate of Electrical Power Resources Survey and Development Administration), 1985; METU Earthquake Engineering Research Center, 1984); the swelling pressure (σs), Young's modulus (Es), Poisson's ratio (νs), cohesion (c) and angle of internal friction (ϕ) of the seal as reported previously are 0.27 MPa, 64.2 MPa, 0.30, 104 kPa and 26.9°, respectively. A seal radius (a) of 3.0 m is used. Fig. 4 gives the minimum required seal length-to-radius ratios (L/a) as a function of the water column acting on the seal (hw) in order to reduce the possibility of seal slip for a factor of safety (F; Eq. (11)) of 1.0 (i.e., for the condition where the peak shear stress given by Eq. (4) equals the peak shear strength given by Eq. (10)). Inspection of Fig. 4 shows that a seal length-to-radius ratio (L/a) of 20 could support a maximum water column (hw) of about 75 m. For a 3 m radius shaft/ borehole seal having L/a of 20 with the base emplaced at a possible depth of for example 100 m in the relatively low permeable levels (i.e., shale/mudrock), this would lead to a maximum water column (hw) of about 40 m and an increase in the factor of safety (F) to 1.58 (Eq. (11)). It should be noted that the stresses do not distribute over the entire length of a longer seal, such as one with an L/a of 20 that is recommended by this study. The advantage of a longer seal is realized at slip initiation. When slip occurs, the interface no longer behaves elastically. If the interface has residual strength, some of the load in the seal will be transferred to the rock in this slip zone and the value of the maximum shear stress will decrease (e.g., Hollingshead, 1971; Akgün and Daemen, 1991, 1999). Hence, local failure does not imply total seal failure if the seal is long enough to dissipate, through residual strength, the maximum shear stress to a value below the shear strength. Strength is therefore increased upon local failure if the seal is longer than that required for the pre-failure elastic shear stress distribution. In other words, the portion of the interface that fails still transfers some load to the rock through residual shear strength, and the maximum shear stress drops below the shear strength at some point along the interface. The intact seal–rock interface below this particular point transfers the remainder of the load by an elastic, exponential shear stress distribution with a reduced peak shear stress. Therefore, the elastic analysis performed herein is conservative for seal design. 5. Summary, conclusions, discussion and recommendations The objective of this study is to assess the performance of a bentonite/sand mixture through performing geotechnical laboratory tests such as compaction and flow tests. Swelling, mechanical and shear strength tests along with analyses of seal/rock mechanical
Fig. 4. Minimum required seal length-to-radius ratios (L/a) as a function of the water column acting on the seal (hw) for a factor of safety (F) of 1.0 against seal slip.
interactions of an axially loaded seal in rock have been conducted to recommend an optimum compacted bentonite/sand mixture and a suitable bentonite/sand seal length-to-radius ratio (L/a) as a function of water column load. The bentonite used was KAR-BEN, a natural non-treated bentonite possessing a high swelling potential and containing at least 90% montmorillonite. The lean sand component of the sand/bentonite mixture used is classified as “well-graded”. The results of the compaction permeameter tests on mixtures ranging from 15 to 30% bentonite content showed that the hydraulic conductivity decreased with increased bentonite content obeying a power law and led to a recommendation to select a mixture with a bentonite content of about 30% since it possessed the lowest hydraulic conductivity of 8.9 × 10− 12 m/s. The sample with 30% bentonite content possessed an optimum water content (wopt) of 13.29% and a corresponding maximum dry unit weight (γdmax) of 16.73 kN/m3. The swelling pressure (σs), Young's modulus (Es), Poisson's ratio (νs), cohesion (c) and angle of internal friction (ϕ) of this optimum mixture were determined to be 0.27 MPa, 64.2 MPa, 0.30, 104 kPa and 26.9°, respectively. Analysis of seal/rock mechanical interaction to reduce the possibility of seal slip was performed as a function of the axial load generated from the water column on the seal for seal length-to-radius ratios (L/a) ranging from 2.0 to 20. The recommendation was to utilize the seal length-to-radius ratio of at least 20 to resist a water column of about 75 m. For a 3 m radius shaft/borehole seal having an L/a of 20 with the base emplaced at a possible depth of for example 100 m in the relatively low permeable levels of Akdere formation (i.e., shale/mudrock), this would lead to a maximum water column (hw) of about 40 m and a factor of safety (F) of 1.58. It should be noted that the results of the compaction permeameter tests led to a recommendation to select a compacted bentonite/sand mixture possessing a bentonite content of 30% since this mixture possesses the lowest hydraulic conductivity value (i.e., 8.9 × 10−12 m/s) and since there is no set regulatory criterion for a minimum hydraulic conductivity value in nuclear waste repository sealing. However, for a more thorough understanding of the performance and the hydraulic conductivity of the bentonite/sand mixtures, it may be worthwhile to test mixtures possessing a higher bentonite content, preferably in a range between 30 and 50% for a more complete performance assessment. In addition, it may be noted that the bentonite/sand mixture tested herein could be utilized as a part of a multi-component sealing system to reduce the hydraulic conductivity which is surrounded by reinforcing abutments or other more rigid sealing components such as cement or concrete seals to mechanically stabilize the sealing system. A single material sealing system, such as the bentonite/sand system defined herein has the disadvantage of forming a compromise between hydrologic and strength requirements. The compacted bentonite/sand mixture recommended in this study is based on geotechnical testing and analyses. However, since a nuclear waste containment study is rather complex and involves multiple subjects, for a more complete study, it is warranted that the geotechnical testing and evaluation of the seal and buffer materials be supported by geochemical, physicochemical, kinetical, thermodynamical and textural characterization of the bentonite/sand barriers. For long-term performance of the bentonite/sand seals, the influence of creep strain and groundwater chemistry needs to be considered. The hydraulic conductivity testing performed herein involved the use of distilled water as the permeant. Coagulation that increases the hydraulic conductivity and decreases the swelling pressure and the shear strength may take place if the percolate is electrolyte-rich, particularly where Ca is the dominant cation. In order to minimize the effect of coagulation, further investigation needs to be carried out in regard to determining the increase of the proportion of bentonite and/or ways to improve bentonite–sand mixing to yield a homogeneous mixture (Pusch, 1994). Other failure modes such as piping (e.g., ASCE Task Committee on Instrumentation and
H. Akgün / Applied Clay Science 49 (2010) 394–399
Monitoring Dam Performance, 2000; Fell et al., 1992; Rosewell, 1977; Sherard et al., 1972) need to be considered besides slippage along the seal/rock interface for the design of such seals. Acknowledgements This work is supported by the Middle East Technical University (METU) Research Fund Project no. AFP-2001-03-09-02. Thanks are due to Dr. Mustafa K. Koçkar for his kind assistance in the laboratory work and in drafting the illustrations. The author would like to express his gratitude to Professor Jaak J.K. Daemen, Mining Engineering Department, University of Nevada-Reno for his constructive and invaluable comments regarding the analysis presented in this manuscript. The author would like to extend his appreciation to the anonymous Reviewers for their excellent review comments and constructive criticisms of the manuscript. References Akgün, H., 2000. Shear strength of cement-grout borehole plug. In Situ 24, 107–137. Akgün, H., Daemen, J.J.K., 1991. Bond strength of cementitious borehole plugs in welded tuff. Technical Report NUREG/CR-4295. In U.S. Nuclear Regulatory Commission, Washington, D.C. Akgün, H., Daemen, J.J.K., 1999. Design implications of analytical and laboratory studies of permanent abandonment plugs. Canadian Geotechnical Journal 36, 21–38. Akgün, H., Koçkar, M.K., Aktürk, Ö., 2006. Evaluation of a compacted bentonite/sand seal for underground waste repository isolation. Environmental Geology 50, 331–337. ASCE Task Committee on Instrumentation and Monitoring Dam Performance, 2000. Guidelines for Instrumentation and Measurements for Monitoring Dam Performance. ASCE, Reston, VA. Sponsored by Hydropower Committee of the Energy Division of the American Society of Civil Engineers. ASTM D 698-07 e1. Standard test methods for laboratory compaction characteristics of soil using standard effort (12 400 ft-lbf/ft3 (600 kN-m/m3)). Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. ASTM D 854-06 e1. Standard test methods for specific gravity of soil solids by water pycnometer. Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. ASTM D 2166-06. Standard test method for unconfined compressive strength of cohesive soil. Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. ASTM D 4318-05. Standard test methods for liquid limit, plasticity limit, and plasticity index of soils. Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. ASTM D 4546-08. Standard test methods for one-dimensional swell or settlement potential of cohesive soils. Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. ASTM D 5856-07. Standard test method for measurement of hydraulic conductivity of porous material using a rigid-wall, compaction-mold permeameter. Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. ASTM D 6528-07. Standard test method for consolidated undrained direct simple shear testing of cohesive soils. Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. Chapius, R.P., 1990. Sand-bentonite liners: predicting permeability from laboratory tests. Canadian Geotechnical Journal 27, 47–57. Coulon, H., Lajudie, A., Debrabant, P., Atabek, R., Jorda, M., Andre-Jehan, R., 1987. Choice of French clays as engineered barrier components for waste disposal. In: Bates, J.K., Seefeldt, W.B. (Eds.), Scientific Basis for Nuclear Waste Management X, Materials Research Society Symposium Proceedings, Boston, MA, December 1–4, 1986: Materials Research Society, Pittsburgh, PA, 84, pp. 813–824. Daemen, J.J.K., Ran, C., 1996. Bentonite as a Waste Isolation Pilot Plant Shaft Sealing Material. Contractor Report SAND96-1968. Sandia National Laboratories, Albuquerque, NM. Daniel, D.E., Benson, C., 1990. Water content-density criteria for compacted soil liners. Journal of Geotechnical Engineering ASCE 116, 1811–1830. Dixon, D.A., Gray, M.N., Thomas, A.W., 1985. A study of the compaction properties of potential clay–sand buffer mixtures for use in nuclear fuel waste disposal. Engineering Geology 21, 247–255. Demirtaşlı, E., 1985. Final report on the geology of the Çamalanı Nuclear Power Plant. MTA. 102 pp. Ankara (in Turkish). EİE (Turkish General Directorate of Electrical Power Resources Survey and Development Administration), 1985. Report on the results of the pressuremeter tests
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performed at the Akkuyu II (Çamalanı) Nuclear Power Plant location, EİE. July, 30 pp. + attachments (in Turkish). Einarson, D.S., Abel, J.F., 1990. Tunnel bulkheads for acid mine drainage. Proceedings International Symposium on Unique Underground Structures, Denver, Colorado, Vol. II, Chapter 71. Fell, R., MacGregor, P., Stapledon, D. (Eds.), 1992. Geotechnical Engineering of Embankment Dams. A.A. Balkema, Rotterdam. Fuenkajorn, K., Daemen, J.J.K. (Eds.), 1996. Sealing of Boreholes and Underground Excavations in Rock. Chapman and Hall, London. Gnirk, P., 1988. State-of-the-art evaluation of repository sealing materials and techniques. In: Apted, M.J., Westerman, R.E. (Eds.), Scientific Basis for Nuclear Waste Management XI. In: Materials Research Society Symposium Proceedings, Boston, MA, November 30-December 3, 112. Materials Research Society, Pittsburgh, PA, pp. 219–231. Halliburton Services, Undated. Cement plug studies. Halliburton Cement, Halliburton Services, A Halliburton Company, Houston, Texas. Hoffman, C., 2004. Nuclear Waste Repository: Long-term Storage. Popular Science, Tampa, FL. April (http://www.popsci.com/scitech/article/2004-04/nuclear-waste-repository. Hollingshead, G.W., 1971. Stress distributions in rock anchors. Canadian Geotechnical Journal 8, 588–592. IAEA, 1990. Sealing of underground repositories for radioactive wastes. In: Gray, M., Gera, F., Wiley, J.R., Dlouhy, Z., Squires, D. (Eds.), Technical Reports Series No. 319, International Atomic Energy Agency, Vienna, Unipub, Lanham, MD. Karakaya, 2009. Properties of KAR-BEN natural bentonite. Karakaya Bentonite Manifacture and Trade Co, Ankara, Turkey. www. karakaya.com.tr. Kenney, T.C., Van Veen, W.A., Swallow, M.A., Sungaila, M.A., 1992. Hydraulic conductivity of compacted bentonite–sand mixtures. Canadian Geotechnical Journal 29, 364–374. Komine, H., 2004. Simplified evaluation on hydraulic conductivities of sand–bentonite mixture backfill. Applied Clay Science 26, 13–19. Kjartanson, B.H., Chandler, N.A., Wan, A.W.L., 1996. In situ performance of a clay based barrier. In: Fuenkajorn, K., Daemen, J.J.K. (Eds.), Sealing of Boreholes and Underground Excavations in Rock. Chapman and Hall, London, pp. 96–125. Lambe, T., 1954. The permeability of compacted bentonite fine-grained soils. Special Technical Publication No. 163. ASTM, Philadelphia, pp. 56–67. Met, İ., Akgün, H., Türkmenoğlu, A.G., 2005. Environmental geological and geotechnical investigations related to the potential use of Ankara clay as a compacted landfill liner material, Turkey. Environmental Geology 47, 225–236. METU Earthquake Engineering Research Center, 1984. Akkuyu II (Çamalanı) Nuclear Power Plant geological and geotechnical investigations. Progress Report No. 1. 34 pp. Ankara. Ouyang, S., Daemen, J.J.K., 1996. Performance of bentonite and bentonite/crushed rock borehole seals. In: Fuenkajorn, K., Daemen, J.J.K. (Eds.), Sealing of Boreholes and Underground Excavations in Rock. Chapman and Hall, London, pp. 65–95. Papp, J.E., 1996. Sodium bentonite as a borehole sealant. In: Fuenkajorn, K., Daemen, J.J.K. (Eds.), Sealing of Boreholes and Underground Excavations in Rock. Chapman and Hall, London, pp. 280–297. Pettman, E.R., 1984. Tunnel plugs in recent H.E.C. Practice. 5th Australian Tunnelling Conference, Sydney, pp. 207–212. Pusch, R., 1978. Small-scale bentonite injection test on rock. KBS Report 75, Stockholm. Pusch, R., 1983. Borehole sealing for underground waste storage. ASCE Journal of Geotechnical Engineering 109, 113–119. Pusch, R., 1994. Waste disposal in rock. Developments in Geotechnical Engineering, 76. Elsevier, Amsterdam. Rosewell, C.J., 1977. Identification of susceptible soils and control of tunnelling failure in small earth dams. Dispersive Clays, Related Piping, and Erosion in Geotechnical Projects, ASTM STP 623. ASTM, West Conshohocken, PA. Sivapullaiah, P.V., Sridharan, A., Stalin, V.K., 2000. Hydraulic conductivity of bentonite– sand mixtures. Canadian Geotechnical Journal 37, 406–413. Sherard, J.L., Decker, R.S., Ryker, N.L., 1972. Piping in earth dams of dispersive clay. Proc. ASCE Special Conference on Performance Earth and Earth-Supported Structures 1, 589–626. USDOE/WIPP, 1995. Waste isolation pilot plant sealing system design report. DOE/WIPP95-3117. U.S. Department of Energy, Waste Isolation Pilot Plant, Carlsbad, NM. USEPA, 1995. Environmental radiation protection standards for management and disposal of spent nuclear fuel, high-level and transuranic radioactive wastes. CFR 40, Part 191, Washington, D.C. US Nuclear Regulatory Commission, 1983. Disposal of high-level radioactive wastes in geologic repositories. Final rule 10 CFR 60. Federal Register, Vol. 48, No. 120, June 30, Washington, D.C. US Nuclear Regulatory Commission, 1985. Disposal of high-level radioactive wastes in geologic repositories, Final rule, unsaturated zone amendment. Federal Register, Vol. 50, No. 140, July 22, Washington, D.C. Yong, R.N., Boonsinsuk, P., Wong, G., 1986. Formulation of backfill material for a nuclear fuel waste disposal vault. Canadian Geotechnical Journal 23, 216–228. Wyllie, D.C., 1999. Foundations on Rock, Second ed. E&FN Spon, London.
Contents lists available at ScienceDirect
Applied Clay Science j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c l a y
Geotechnical characterization and performance assessment of bentonite/sand mixtures for underground waste repository sealing Haluk Akgün ⁎ Faculty of Engineering, Department of Geological Engineering, Middle East Technical University, Ankara 06531, Turkey
a r t i c l e
i n f o
Article history: Received 24 September 2008 Received in revised form 12 August 2009 Accepted 17 August 2009 Available online 24 August 2009 Keywords: Bentonite/sand seal Geotechnical seal design Seal/rock mechanical interaction Underground waste repository sealing Proposed Akkuyu Nuclear Power Plant
a b s t r a c t The objective of this study is to assess the performance of a bentonite/sand mixture for the sealing of underground waste repositories through performing geotechnical laboratory tests such as compaction and flow tests. Swelling, mechanical and shear strength tests along with analyses of seal/rock mechanical interactions of an axially loaded seal in rock have been conducted to recommend an optimum compacted bentonite/sand mixture and a suitable bentonite/sand seal length-to-radius ratio (L/a) as a function of water load. The bentonite used in this study was a natural sodium based non-treated bentonite possessing a high swelling potential and containing at least 90% montmorillonite. The results of the compaction permeameter tests led to a recommendation to select a mixture with a bentonite content of about 30% since it possessed the lowest hydraulic conductivity. Analysis of seal/rock mechanical interaction to reduce the possibility of seal slip was performed as a function of the axial load generated from a water column on the seal for seal length-to-radius ratios (L/a) ranging from 2.0 to 20. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Sealing of boreholes, shafts, mine drifts, and tunnels may be required for a variety of reasons. Penetrations of and near a high-level nuclear waste repository need to be sealed reliably to retard any radionuclide migration to the accessible environment (e.g., Hoffman, 2004; USEPA, 1995; US Nuclear Regulatory Commission, 1983; 1985). Sealing may prove necessary to prevent flooding of underground operations (e.g., Akgün and Daemen, 1999). Sealing of diversion tunnels is often required on hydro-electric projects (e.g., Pettman, 1984). Sealing of mine openings is a growing concern in order to control mine effluents (e.g., Einarson and Abel, 1990). There is an increased conviction that geotechnical exploratory boreholes need to be sealed reliably in order to prevent groundwater contamination (e.g., Fuenkajorn and Daemen, 1996). The most extensive practice, experience, and investigations of borehole sealing have been developed in the oil and gas industry (e.g., Halliburton Services, undated). Bentonite and bentonite/sand mixtures are considered as buffer and backfill materials for repositories of high-level nuclear waste in Sweden, Switzerland, Canada, Germany and France (e.g., Coulon et al., 1987; IAEA, 1990; Pusch, 1994) and for sealing of shafts emplaced in the vicinity of the Waste Isolation Pilot Plant (WIPP) site in southeastern New Mexico (e.g., Daemen and Ran, 1996; USDOE/
⁎ Tel.: +90 312 210 5727; fax: +90 312 210 5750. E-mail address: [email protected]. 0169-1317/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.clay.2009.08.020
WIPP, 1995). It is possible that bentonite and bentonite/sand mixtures may be utilized for sealing repositories of high-level nuclear waste that is expected to be generated from the proposed Akkuyu Nuclear Power Plant in the near future. The proposed plant site is located on the southern Mediterranean coast of Turkey, 45 km southwest of the city of Silifke, directly inshore from Cyprus. Chapius (1990), Dixon et al. (1985), Kenney et al. (1992), Komine (2004), Kjartanson et al. (1996), Ouyang and Daemen (1996), Papp (1996), Pusch (1978, 1983), Sivapullaiah et al. (2000) and Yong et al. (1986) have performed sealing studies with bentonite/sand, bentonite, bentonite/crushed rock or soil mixture plugs in the laboratory as well as insitu. Akgün et al. (2006) have investigated the sealing performance of bentonite/sand mixtures with bentonite contents ranging from 15% to 20% for sealing boreholes in the vicinity of the Yucca Mountain tuff site in Nevada. Axial loads on seals emplaced in openings in the vicinity of a highlevel nuclear waste repository may be due to water, drilling mud, gas or backfill pressures. Axial loads induce shear stresses along the contact between the seal and host rock which, under extreme conditions, could cause dislodging or slipping of seals, leading to increased permeability through the seal (Akgün and Daemen, 1999). Hence, repository sealing requires that the sealing barrier possess adequate interface strength, a low permeability, a long lifetime, a high resistance to erosion, mechanical and chemical stability, and compatibility with host rocks or materials (Pusch, 1978). Bentonite and its soil mixtures have an extremely low hydraulic conductivity, are self-healing and have good chemical stability that would provide effective long-term sealing (Gnirk, 1988).
H. Akgün / Applied Clay Science 49 (2010) 394–399
The objective of this study is to investigate the sealing performance of bentonite/sand mixtures possessing bentonite contents ranging from 22.5% to 30% and to find a suitable compacted bentonite/sand mixture for the sealing of underground nuclear waste repositories situated in the vicinity of the proposed Akkuyu Nuclear Power Plant in Southern Turkey through performing geotechnical laboratory tests such as compaction permeameter, swelling, mechanical and shear strength tests. Analysis of seal/rock mechanical interaction in regard to reduce the possibility of seal slip has been performed as a function of the axial load generated from a water column on the seal for seal length-to-radius ratios (L/a) ranging from 2.0 to 20.
395
Table 2 Results of standard proctor compaction tests. Bentonite content (%)
wopt
15a 17.5a 20a 22.5 25 27.5 30
15.82 15.41 15.10 14.72 14.00 13.59 13.29
(%)
γdmax (kN/m3) 16.01 16.24 16.29 16.42 16.54 16.62 16.73
Mean values of the optimum moisture content (wopt) and maximum dry unit weight (γdmax) of compacted bentonite/sand mixtures possessing 15% through 30% bentonite. a Data from Akgün et al. (2006).
2. Geotechnical evaluation and compaction permeameter testing of bentonite/sand mixtures The bentonite used was KAR-BEN, a natural sodium based nontreated bentonite possessing a high swelling potential and containing at least 90% montmorillonite (Karakaya, 2009). Table 1 presents the geotechnical index properties and the engineering characteristics of the KAR-BEN bentonite. The specific gravity of the solids and Atterberg limits, namely, the liquid limit (LL), plastic limit (PL) and plasticity index (PI) reported in Table 1 were determined according to standard practice (ASTM D 854-06 e1 and D 4318-05)). The wellgraded lean sand used in this study consisted of about 99% of quartz minerals and possessed a hydraulic conductivity at maximum compacted density of about 10−4 m/s, specific gravity (Gs) of 2.64, void ratio (e) of 0.45 and a maximum compacted dry density (γdmax) of about 18 kN/m3. Akgün et al. (2006) present gradation information for the well-graded sand possessing a particle size ranging from 1.18 mm to 0.075 mm, and a particle shape generally ranging from subrounded to rounded. The bentonite and sand specimens were kept in plastic bags under ambient room conditions (22 ± 2 °C, 30% ± 1% relative humidity) in the Engineering Geology Laboratory of the METU Department of Geological Engineering prior to being mixed for standard compaction and falling head permeability testing. The Standard Proctor compaction apparatus was used to compact four different bentonite/sand mixtures, namely, mixtures possessing 22.5%, 25%, 27.5% and 30% bentonite content at various molding water contents, respectively, according to ASTM D 698-07 e1. The results of the standard compaction tests are summarized in Table 2. Table 2 also contains compaction data on samples with bentonite contents of 15%, 17.5% and 20% that have been reported by Akgün et al. (2006). The compacted bentonite/sand specimens were placed in rigidwall permeameters for hydraulic conductivity testing in accordance
with ASTM D 5856-07. Fig. 1 shows the falling head compaction permeameter setup. The test apparatus consists mainly of four compaction permeameters, de-airing tank, four burettes, a distilled water tank and a vacuum pump so that four tests may be performed concurrently. Each test took place for a period of about 1.5 to 2 months which was the approximate length of time required for the compacted samples to attain full saturation prior to permeability testing. Full sample saturation was confirmed by water coming out of the water outlet portal of the compaction permeameter equipment.
Table 1 Geotechnical index and engineering characteristics of the natural bentonite component of the compacted bentonite/sand mixtures (Karakaya, 2009). Index or engineering property
Value
Specific gravity (Gs) Liquid limit, LL (%) Plastic limit, PL (%) Plasticity index, PI (%) Positive cation exchange capacity (mequiv/100 g) 350 ml of distilled water suspension test results: 600 rpm reading by Fann 35 Viscometer (min) Maximum filtration volume (cm3) Minimum yield (bbl) Maximum moisture content by weight (%) Maximum residue retained by weight on 200 mesh wet screen analysis (%) Maximum yield point plastic viscosity ratio (Yp/Pv) Minimum dispersed plastic viscosity (cp) Aged Yp/Pv to normal Yp/Pv ratio Maximum normal Yp/Pv to dispersed Yp/Pv ratio
2.74 450 35 415 100 30 12.5 80 10 2.5 1.5 10 1.5 3.0
Fig. 1. Schematic drawing of compaction permeameter setup. (modified from Met et al. 2005).
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H. Akgün / Applied Clay Science 49 (2010) 394–399
Distilled and de-aired water was used as the permeant. The hydraulic conductivity (k) values were calculated through Eq. (1): k=
aL h ln 1 h2 Aðt2 −t1 Þ
ð1Þ
where a is the inside cross-sectional area of the burette, L is the length of the specimen, A is the cross-sectional area of the compacted soil specimen, h1 is the head at time t1, and h2 is the head at time t2 (Fig. 1). The hydraulic conductivity tests were performed on bentonite/ sand samples compacted at about 2% on the wet side of their optimum moisture contents since as pointed out for example by Daniel and Benson (1990) and Lambe (1954), compacting clayey soils on the wet sides of the line of optimums permits greater remolding of clods, elimination of large interclod voids and preferential re-orientation of clay particles, all of which result in decreased hydraulic conductivity values. The results of the hydraulic conductivity tests measured at about 2% wet of the optimum moisture contents of samples with bentonite contents of 22.5%, 25%, 27.5% and 30% are summarized in Table 3. Table 3 also contains hydraulic conductivity data on samples with bentonite contents of 15%, 17.5% and 20% that have been reported by Akgün et al. (2006). These results lead to a recommendation to select a compacted bentonite/sand mixture possessing a bentonite content of about 30% since this mixture possesses the lowest hydraulic conductivity value (i.e., 8.9 × 10− 12 m/s) and since there is no set regulatory criterion for a minimum hydraulic conductivity value in nuclear waste repository sealing. The results of the compaction and flow tests on samples possessing 15 to 30% bentonite content reported in Tables 2 and 3 showed that the maximum dry unit weight (γdmax) tended to increase, while the corresponding optimum moisture content (wopt) and hydraulic conductivity (k) tended to decrease with increased bentonite content of the bentonite/sand mixtures. Upon selecting the mixture possessing a bentonite content of 30%, swelling, unconfined compression and direct shear testing was performed on this mixture to determine the swelling pressure, elastic constants and shear strength parameters in accordance with ASTM D 4546-08, D 2166-06 and D 6528-07, respectively. The swelling pressure generated by the mixture after a period of one week was determined to be 0.27 MPa. The Young's modulus, cohesion (c) and the angle of internal friction (ϕ) were determined to be 64.2 MPa, 104 kPa and 26.9°, respectively. The Poisson's ratio was assumed to be 0.30. Fig. 2 gives the result of the direct shear test performed on the bentonite/sand mixture with a bentonite content of 30%.
Fig. 2. The result of the direct shear test performed on a bentonite/sand mixture containing 30% bentonite.
ratio (L/a) as a function of the water column acting on the seal. Analysis of seal/rock mechanical interaction to reduce the risk of seal slip is performed as a function of the axial load generated from the water column on the seal for seal length-to-radius ratios (L/a) ranging from 2.0 to 20. The geotechnical properties of the mixture with a bentonite content of 30% reported in the previous section are utilized in the stability analysis.
3. Analysis of seal/rock mechanical interaction and stability assessment Analyzed in this section is the stability of an axially loaded compacted bentonite/sand seal that is emplaced in boreholes or shafts. The stability of the seal is analyzed as a function of the water column in an attempt to determine the required seal length-to-radius
Table 3 Mean hydraulic conductivity values of compacted bentonite/sand samples at about 2% wet of the optimum moisture content. Bentonite content (%)
Hydraulic Conductivity (m/s)
15a 17.5a 20a 22.5 25 27.5 30
6.4 × 10− 9 1.7 × 10− 9 3.0 × 10− 10 8.6 × 10− 11 4.8 × 10− 11 1.3 × 10− 11 8.9 × 10− 12
a
Data from Akgün et al. (2006).
Fig. 3. Stresses acting on a seal/rock system. σz = axial stress applied to the seal, τ = shear stress at seal/rock interface, z = axial distance from initial location of the loaded end of the seal, a = seal radius, R = rock cylinder outside radius, L = seal length, rc = critical radius, wp, wp′ = axial seal displacement, dσz = axial stress increment over diametral seal slice ABCD of thickness dz.
H. Akgün / Applied Clay Science 49 (2010) 394–399
Composite materials, reinforced concrete, rock-socketed piers, piles and rock bolts are mechanistically similar to an axially stressed seal emplaced within a borehole or shaft in rock (Akgün and Daemen, 1991, 1999). In all structures of these types, the applied axial stress is transferred from the inclusion to the host or vice versa in the form of shear stresses along the interface. Fig. 3 gives the geometry and coordinate system utilized for stress calculations for an axially loaded seal in rock. As an axial stress (σz) is applied to the seal, load transfer occurs through shear stresses, τ, along the interface between the seal and rock. This results in differential compression of the seal leading to an axial seal displacement wp at the loaded end of the seal and wp′ at a distance z from the initial location of the loaded end of the seal. Consideration of the axial force equilibrium of element ABCD in Fig. 3 leads to the solution of the interface shear stress τ. The three-dimensional exponential elastic shear stress distribution along the seal/rock interface (τ) due to an axial stress applied to the seal (σz) is presented by Eq. (2) (Akgün and Daemen, 1999): σ β cosh½βðL−zÞ = a τ= z 2 sinh½βðL = aÞ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1−2νs λ β= ð1 + νr ÞðEs = Er Þlnðrc = aÞ
λ=
ð2Þ
ð2aÞ
νs ð1−ða =RÞ2 Þ ð2bÞ ð1−νs Þð1−ða= RÞ Þ + ðEs = Er Þð1 + νr Þ½ð1−2νr Þða=RÞ2 + 1 2
−0:18ðEs = Er Þ
rl = a + 2:07Le
ð2cÞ
rc = rl ; if R >rl
ð2dÞ
rc = R; if R≤rl
ð2eÞ
where λ and β are dimensionless parameters, z is the axial distance from the initial location of the loaded end (top) of the seal (z = 0 at the top of the seal and z = seal length, L, at the seal bottom), Es/Er is the ratio of the Young's moduli of seal and rock, νs and νr are the Poisson's ratios of seal and rock, rc is the critical radius beyond which the shear stresses and axial displacements in the rock are considered negligible, rl is the limiting critical radius which accounts for seal emplacement in a laboratory-sized specimen or in-situ, a and R are the seal and rock cylinder outside radii, respectively. Fig. 3 gives the geometry and coordinate system utilized for stress calculations. It follows from Eq. (2) that the peak shear stress induced by axial loading (τp) occurs at the loaded end (z = 0) of the seal/rock interface: σz β τp = 2tanh½βðL = aÞ
ð3Þ
The peak shear stress induced by axial loading (τp∞) for an in-situ seal in rock (e.g., R/a = ∞) also occurs at the loaded end of the seal/ rock interface and follows from using R/a = ∞ in Eq. (3): τp∞ =
σz γ 2tanh½γðL = aÞ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1−2νs α γ= ð1 + νr ÞðEs = Er Þlnðrc = aÞ α=
νp ð1−νp Þ + ðEs = Er Þð1 + νr Þ
where all the other parameters of Eq. (4) are given by Eq. (2).
ð4Þ
ð4aÞ
ð4bÞ
397
The shear strength of the interface (|τ|) is given by the Coulomb criterion as: j τj = c + σn tan ϕ
ð5Þ
where c is the cohesion (adhesion), ϕ is the angle of internal friction and σn is the total normal stress across the plug–rock interface. The total normal stress across the interface (σn) of an axially loaded expansive bentonite/sand seal is given by Akgün (2000) as: σn = σr + σs
ð6Þ
where σr is the radial (contact) normal stress induced by axial loading along the seal/rock interface due to an axial stress σz applied to the bentonite/sand seal and σs is the seal swelling pressure that is assumed constant along the interface. σr is derived by Akgün (2000) as follows: sinh½βðL−zÞ = a σr = σz λ sinh½βðL = aÞ
ð7Þ
where all the parameters of Eq. (7) are given by Eq. (2). Utilizing Eq. (6) in Eq. (5) and inspecting the resultant equation reveal that the peak normal stress across the interface (σnp) occurs at the loaded end of the seal (i.e., at z = 0) and follows from using z = 0 in Eqs. (6) and (7): σnp = σz λ + σs
ð8Þ
The peak normal stress across the interface (σnp∞) for an in-situ seal in rock (e.g., R/a = ∞) also occurs at the loaded end of the seal/ rock interface (z = 0) and follows from using R/a = ∞ in Eq. (6): σnp∞ = σz α + σs
ð9Þ
where α is given by Eq. (4b). The peak shear strength across the interface for an in-situ seal emplaced in rock (|τp∞|) follows from using Eq. (9) in Eq. (5): jτp∞ j = c + σnp∞ tan ϕ
ð10Þ
where σnp∞ is the peak normal stress across the seal/rock interface for an in-situ seal in rock. The factor of safety (F) of an in-situ seal in rock against slipping may be expressed by the following equation (e.g., Wyllie, 1999): F=
j τp∞ j ∑Resisting forces Shear strength = = τp∞ Shear stress ∑Driving forces
ð11Þ
where |τp∞| and τp∞ are the peak shear strength and peak shear stress across the interface for an axially loaded and expansive (swelling) insitu seal in rock given by Eqs. (10) and (4), respectively. 4. Geotechnical seal design and discussion The stability of bentonite/sand seals emplaced in boreholes or shafts in the vicinity of a high-level radioactive waste repository, such as that to be located in the proximity of the proposed Akkuyu Nuclear Power Plant in southern Turkey is analyzed for seals emplaced at a possible depth of for example 100 m in the relatively low permeable levels (i.e., shale/mudrock levels of the Akdere formation, which consists of alternations of limestone, sandstone, mudstone and shale) (Demirtaşlı, 1985). The stability of the seals is analyzed as a function of the water column acting on the seal in an attempt to determine the required seal length-to-radius ratio (L/a) as a function of water head. The geotechnical properties of the mixture with a bentonite content of 30% reported in the previous section are utilized in the stability analysis. The geotechnical properties of the shale/mudrock and of the
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H. Akgün / Applied Clay Science 49 (2010) 394–399
seal considered in the stability analysis are as follows: the average Young's modulus (Er) and Poisson's ratio (νr) of the shale/mudrock are 364.4 MPa and 0.26, respectively (EİE (Turkish General Directorate of Electrical Power Resources Survey and Development Administration), 1985; METU Earthquake Engineering Research Center, 1984); the swelling pressure (σs), Young's modulus (Es), Poisson's ratio (νs), cohesion (c) and angle of internal friction (ϕ) of the seal as reported previously are 0.27 MPa, 64.2 MPa, 0.30, 104 kPa and 26.9°, respectively. A seal radius (a) of 3.0 m is used. Fig. 4 gives the minimum required seal length-to-radius ratios (L/a) as a function of the water column acting on the seal (hw) in order to reduce the possibility of seal slip for a factor of safety (F; Eq. (11)) of 1.0 (i.e., for the condition where the peak shear stress given by Eq. (4) equals the peak shear strength given by Eq. (10)). Inspection of Fig. 4 shows that a seal length-to-radius ratio (L/a) of 20 could support a maximum water column (hw) of about 75 m. For a 3 m radius shaft/ borehole seal having L/a of 20 with the base emplaced at a possible depth of for example 100 m in the relatively low permeable levels (i.e., shale/mudrock), this would lead to a maximum water column (hw) of about 40 m and an increase in the factor of safety (F) to 1.58 (Eq. (11)). It should be noted that the stresses do not distribute over the entire length of a longer seal, such as one with an L/a of 20 that is recommended by this study. The advantage of a longer seal is realized at slip initiation. When slip occurs, the interface no longer behaves elastically. If the interface has residual strength, some of the load in the seal will be transferred to the rock in this slip zone and the value of the maximum shear stress will decrease (e.g., Hollingshead, 1971; Akgün and Daemen, 1991, 1999). Hence, local failure does not imply total seal failure if the seal is long enough to dissipate, through residual strength, the maximum shear stress to a value below the shear strength. Strength is therefore increased upon local failure if the seal is longer than that required for the pre-failure elastic shear stress distribution. In other words, the portion of the interface that fails still transfers some load to the rock through residual shear strength, and the maximum shear stress drops below the shear strength at some point along the interface. The intact seal–rock interface below this particular point transfers the remainder of the load by an elastic, exponential shear stress distribution with a reduced peak shear stress. Therefore, the elastic analysis performed herein is conservative for seal design. 5. Summary, conclusions, discussion and recommendations The objective of this study is to assess the performance of a bentonite/sand mixture through performing geotechnical laboratory tests such as compaction and flow tests. Swelling, mechanical and shear strength tests along with analyses of seal/rock mechanical
Fig. 4. Minimum required seal length-to-radius ratios (L/a) as a function of the water column acting on the seal (hw) for a factor of safety (F) of 1.0 against seal slip.
interactions of an axially loaded seal in rock have been conducted to recommend an optimum compacted bentonite/sand mixture and a suitable bentonite/sand seal length-to-radius ratio (L/a) as a function of water column load. The bentonite used was KAR-BEN, a natural non-treated bentonite possessing a high swelling potential and containing at least 90% montmorillonite. The lean sand component of the sand/bentonite mixture used is classified as “well-graded”. The results of the compaction permeameter tests on mixtures ranging from 15 to 30% bentonite content showed that the hydraulic conductivity decreased with increased bentonite content obeying a power law and led to a recommendation to select a mixture with a bentonite content of about 30% since it possessed the lowest hydraulic conductivity of 8.9 × 10− 12 m/s. The sample with 30% bentonite content possessed an optimum water content (wopt) of 13.29% and a corresponding maximum dry unit weight (γdmax) of 16.73 kN/m3. The swelling pressure (σs), Young's modulus (Es), Poisson's ratio (νs), cohesion (c) and angle of internal friction (ϕ) of this optimum mixture were determined to be 0.27 MPa, 64.2 MPa, 0.30, 104 kPa and 26.9°, respectively. Analysis of seal/rock mechanical interaction to reduce the possibility of seal slip was performed as a function of the axial load generated from the water column on the seal for seal length-to-radius ratios (L/a) ranging from 2.0 to 20. The recommendation was to utilize the seal length-to-radius ratio of at least 20 to resist a water column of about 75 m. For a 3 m radius shaft/borehole seal having an L/a of 20 with the base emplaced at a possible depth of for example 100 m in the relatively low permeable levels of Akdere formation (i.e., shale/mudrock), this would lead to a maximum water column (hw) of about 40 m and a factor of safety (F) of 1.58. It should be noted that the results of the compaction permeameter tests led to a recommendation to select a compacted bentonite/sand mixture possessing a bentonite content of 30% since this mixture possesses the lowest hydraulic conductivity value (i.e., 8.9 × 10−12 m/s) and since there is no set regulatory criterion for a minimum hydraulic conductivity value in nuclear waste repository sealing. However, for a more thorough understanding of the performance and the hydraulic conductivity of the bentonite/sand mixtures, it may be worthwhile to test mixtures possessing a higher bentonite content, preferably in a range between 30 and 50% for a more complete performance assessment. In addition, it may be noted that the bentonite/sand mixture tested herein could be utilized as a part of a multi-component sealing system to reduce the hydraulic conductivity which is surrounded by reinforcing abutments or other more rigid sealing components such as cement or concrete seals to mechanically stabilize the sealing system. A single material sealing system, such as the bentonite/sand system defined herein has the disadvantage of forming a compromise between hydrologic and strength requirements. The compacted bentonite/sand mixture recommended in this study is based on geotechnical testing and analyses. However, since a nuclear waste containment study is rather complex and involves multiple subjects, for a more complete study, it is warranted that the geotechnical testing and evaluation of the seal and buffer materials be supported by geochemical, physicochemical, kinetical, thermodynamical and textural characterization of the bentonite/sand barriers. For long-term performance of the bentonite/sand seals, the influence of creep strain and groundwater chemistry needs to be considered. The hydraulic conductivity testing performed herein involved the use of distilled water as the permeant. Coagulation that increases the hydraulic conductivity and decreases the swelling pressure and the shear strength may take place if the percolate is electrolyte-rich, particularly where Ca is the dominant cation. In order to minimize the effect of coagulation, further investigation needs to be carried out in regard to determining the increase of the proportion of bentonite and/or ways to improve bentonite–sand mixing to yield a homogeneous mixture (Pusch, 1994). Other failure modes such as piping (e.g., ASCE Task Committee on Instrumentation and
H. Akgün / Applied Clay Science 49 (2010) 394–399
Monitoring Dam Performance, 2000; Fell et al., 1992; Rosewell, 1977; Sherard et al., 1972) need to be considered besides slippage along the seal/rock interface for the design of such seals. Acknowledgements This work is supported by the Middle East Technical University (METU) Research Fund Project no. AFP-2001-03-09-02. Thanks are due to Dr. Mustafa K. Koçkar for his kind assistance in the laboratory work and in drafting the illustrations. The author would like to express his gratitude to Professor Jaak J.K. Daemen, Mining Engineering Department, University of Nevada-Reno for his constructive and invaluable comments regarding the analysis presented in this manuscript. The author would like to extend his appreciation to the anonymous Reviewers for their excellent review comments and constructive criticisms of the manuscript. References Akgün, H., 2000. Shear strength of cement-grout borehole plug. In Situ 24, 107–137. Akgün, H., Daemen, J.J.K., 1991. Bond strength of cementitious borehole plugs in welded tuff. Technical Report NUREG/CR-4295. In U.S. Nuclear Regulatory Commission, Washington, D.C. Akgün, H., Daemen, J.J.K., 1999. Design implications of analytical and laboratory studies of permanent abandonment plugs. Canadian Geotechnical Journal 36, 21–38. Akgün, H., Koçkar, M.K., Aktürk, Ö., 2006. Evaluation of a compacted bentonite/sand seal for underground waste repository isolation. Environmental Geology 50, 331–337. ASCE Task Committee on Instrumentation and Monitoring Dam Performance, 2000. Guidelines for Instrumentation and Measurements for Monitoring Dam Performance. ASCE, Reston, VA. Sponsored by Hydropower Committee of the Energy Division of the American Society of Civil Engineers. ASTM D 698-07 e1. Standard test methods for laboratory compaction characteristics of soil using standard effort (12 400 ft-lbf/ft3 (600 kN-m/m3)). Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. ASTM D 854-06 e1. Standard test methods for specific gravity of soil solids by water pycnometer. Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. ASTM D 2166-06. Standard test method for unconfined compressive strength of cohesive soil. Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. ASTM D 4318-05. Standard test methods for liquid limit, plasticity limit, and plasticity index of soils. Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. ASTM D 4546-08. Standard test methods for one-dimensional swell or settlement potential of cohesive soils. Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. ASTM D 5856-07. Standard test method for measurement of hydraulic conductivity of porous material using a rigid-wall, compaction-mold permeameter. Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. ASTM D 6528-07. Standard test method for consolidated undrained direct simple shear testing of cohesive soils. Annual Book of ASTM Standards, Section 4, Vol. 04.08, Soil and Rock (I), ASTM, West Conshohocken, PA. Chapius, R.P., 1990. Sand-bentonite liners: predicting permeability from laboratory tests. Canadian Geotechnical Journal 27, 47–57. Coulon, H., Lajudie, A., Debrabant, P., Atabek, R., Jorda, M., Andre-Jehan, R., 1987. Choice of French clays as engineered barrier components for waste disposal. In: Bates, J.K., Seefeldt, W.B. (Eds.), Scientific Basis for Nuclear Waste Management X, Materials Research Society Symposium Proceedings, Boston, MA, December 1–4, 1986: Materials Research Society, Pittsburgh, PA, 84, pp. 813–824. Daemen, J.J.K., Ran, C., 1996. Bentonite as a Waste Isolation Pilot Plant Shaft Sealing Material. Contractor Report SAND96-1968. Sandia National Laboratories, Albuquerque, NM. Daniel, D.E., Benson, C., 1990. Water content-density criteria for compacted soil liners. Journal of Geotechnical Engineering ASCE 116, 1811–1830. Dixon, D.A., Gray, M.N., Thomas, A.W., 1985. A study of the compaction properties of potential clay–sand buffer mixtures for use in nuclear fuel waste disposal. Engineering Geology 21, 247–255. Demirtaşlı, E., 1985. Final report on the geology of the Çamalanı Nuclear Power Plant. MTA. 102 pp. Ankara (in Turkish). EİE (Turkish General Directorate of Electrical Power Resources Survey and Development Administration), 1985. Report on the results of the pressuremeter tests
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