Original article
Stability of expansive cement grout borehole seals emplaced in the vicinity of underground radioactive waste repositories H. Akgu¨n Æ J. J. K. Daemen
Abstract An expansive cementitious borehole plug emplaced in an underground opening in the vicinity of an underground nuclear waste repository may generate radial stresses on the walls of the opening due to an axial stress applied to the borehole plug and due to plug swelling. As these radial stresses may lead to the tensile fracturing of the rock, minimizing or preferably eliminating tensile stresses in rock is particularly important to preserve waste containment. Presented in this paper are the theoretical radial (normal) stress distribution and tensile strength in a borehole plug–rock system due to combined axial, thermal and lateral loading, along with analyses of plug–rock mechanical interactions in regards to borehole stability against tensile fracturing. Keywords Tensile strength Æ Cement swelling Æ Repository sealing Æ Radioactive waste disposal Æ Arizona
Introduction Sealing of man-made openings (e.g., boreholes, shafts, mine drifts and tunnels) in the vicinity of a high-level nuclear waste repository is required to retard any radionuclide migration to the accessible environment (US Nuclear Regulatory Commission 1983, 1985). The
Received: 28 July 2003 / Accepted: 6 January 2004 Published online: 26 February 2004 ª Springer-Verlag 2004 H. Akgu¨n (&) Department of Geological Engineering, Faculty of Engineering, Middle East Technical University, 06531 Ankara, Turkey E-mail:
[email protected] Tel.: +90-312-2105727 Fax: +90-312-2101263 J. J. K. Daemen Mining Engineering Department, Mackay School of Mines, University of Nevada-Reno, Reno, NV 89557-0139, USA
most likely sources of axial loading on plugs or seals in an underground repository is hydrostatic pressure due to a water column, and axial loading due to the heat generated subsequent to waste and plug emplacement. An expansive cementitious borehole plug emplaced in an underground opening may generate radial stresses on the walls of the opening due to an axial stress applied to the borehole plug and due to plug swelling. As these radial stresses create tension in the rock and may lead to tensile fracturing of the rock, minimizing or preferably eliminating tensile stresses in rock is particularly important for permanent sealing of openings through enhancing the durability or longevity of plugs. The work described herein is part of a research effort on sealing man-made openings at an underground radioactive waste repository in welded tuff, in which the initial objective was to study the bond strength of axially loaded, expansive cement grout borehole plugs cast in welded tuff cylinders through push-out testing. Push-out testing involves a steel rod to dislodge a cement grout plug emplaced within the coaxial borehole of a hollow rock cylinder. Figure 1 gives the push-out test setup. A cylindrical steel rod applies an axial load to a cement grout plug installed in a rock cylinder. The LVDT and dial gage that measure the vertical displacement of the plug are mounted on horizontal arms connected to the loading rod. Push-out testing was performed as a function of elevated temperature and degree of saturation of the push-out sample to simulate the effects of plug emplacement in a partially saturated environment, and the effects of elevated temperature originating from the radioactive waste. Tensile fracturing of the rock cylinders of the push-out samples during testing gave an opportunity to study the tensile strength of samples and to investigate the stability of expansive cement plugged boreholes against tensile fracturing. The rock samples were obtained from the densely welded brown unit of Apache Leap tuff near Superior, Arizona. The push-out tested tuff cylinders had inside radii (a) of 25.4 and 50.80 mm, outside radii (R) of 76.2 mm and 93.66 mm, and length-to-radius ratios (L/a) of approximately 2.0. The tuff cores were plugged with nearly centered, Self-Stress II expansive cement grout plugs. The push-out samples were cured and tested at temperatures of 36 C under dry saturation condition (i.e., average sample degree of saturation of 24.51%), and
DOI 10.1007/s00254-004-0984-5 Environmental Geology (2004) 45:1167–1171
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Fig. 1 Schematic drawing of push-out test setup
at 44 and 70 C under low saturation condition (i.e., average sample degree of saturation of 34.83%). The cement plugs of the push-out specimens were initially loaded to 4,450 N (1,000 lbf). The load was kept approximately constant and incremented 4,450 N every 2 min until the sample failed. The load and displacements were recorded every 30 s. Akgu¨n and Daemen (2000a, 2000b) give details on rock cylinder and cement grout preparation, along with the push-out test experimental apparatus and sample loading. The paper presents the results of the push-out tests, cement grout swelling pressure measurements, and analyses of plug–rock mechanical interactions in regards to borehole stability against tensile fracturing.
stress at failure (rz,f) of the tensile-fractured push-out specimens. The results show that samples cured and tested at 36, 44 and 70 C have tensile fractured at an average applied axial stress at failure (rz,f) of about 20.0, 17.9 and 11.0 MPa, respectively.
Cement grout swelling measurements The objective of these tests was to determine the radial expansive stresses generated by Self-Stress II cement. The swelling stresses were measured by monitoring the tangential strains on the outside walls of steel pipes in which the cement grout was emplaced and cured. Three pipes each with inside radii of 12.7, 25.4 and 50.8 mm have been monitored. All pipes had wall thickness-to-inside radius ratios of 1/8, and hence, identical confining stiffnesses. The cement grout plugs had length-to-radius ratios (L/a) of approximately 2.0. The cement swelling stresses were Experimental results determined with two tangential strain gages placed 180 apart. Push-out tests Table 1 gives the saturation condition, curing and testing The radial cement grout swelling stress (rs) was calculated temperature, plug radius (a), rock cylinder outside radius from Jaeger and Cook (1979) for a plane strain (R), plug length-to-radius ratio (L/a) and applied axial configuration as follows: Table 1 Saturation condition, curing and testing temperature, plug radius (a), rock cylinder outside radius (R), plug length-to-radius ratio (L/a) and applied axial stress at failure (rz,f) of the tensile-fractured push-out specimens
Sample no.
1 2 3 4 5 6 7 8 9 a
Saturation conditiona Low Low Low Low Low Low Dry Dry Dry
Curing and testing temperature (C)
a
R
(mm)
(mm)
44 44 44 44 44 70 36 36 36
25.4 25.4 50.8 50.8 50.8 50.8 25.4 50.8 50.8
76.2 76.2 93.66 93.66 93.66 93.66 76.2 93.66 93.66
L/a
rz,f (MPa)
2.02 2.02 1.98 1.95 2.04 2.55 2.02 1.85 1.84
20.0 25.0 13.1 10.8 20.6 11.0 30.7 15.5 13.7
The average degree of saturation of the dry and low-saturated samples are determined to be 24.51 and 34.83%, respectively (Akgu¨n and Daemen 2000b)
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Original article
rs ¼
Es ehR ðR2 a2 Þ 2 1 m2s a2
ð1Þ
where Es is the Young’s modulus of the steel pipe, ehR is the measured average induced tangential strain on the steel pipe outside walls, ms is the Poisson’s ratio of the steel pipe, a is the steel pipe internal radius, and R is the steel pipe external radius. Sign conventions used are those where compressive stresses and displacements in the negative directions of the axes are considered positive. Figure 2 presents the measured mean tangential strain on the steel pipe outside walls (ehR) and the calculated cement swelling stress (rs) as a function of time. The results are presented as a function of time for each pipe size, and are for a Young’s modulus (Es) and Poisson’s ratio (ms) of the steel pipe of 207 MPa and 0.27, respectively (Hearn 1977). Swelling tends to increase with time, but at a decreasing rate. The mean swelling stress (rs) measured in the 12.7-, 25.4- and 50.8-mm pipes after 8 days is 2.04, 2.10 and 2.19 MPa, respectively. The mean swelling stress in the 12.7-, 25.4- and 50.8-mm pipes after 335 days is 4.61, 4.81 and 4.97 MPa, respectively. Swelling stresses and tangential strains increase slightly with increasing plug diameter. To study the influence of cement grout swelling on borehole sealing performance, two hollow Apache Leap tuff cylinders with outside radii of 93.66 mm, inside radii of 50.8 mm, and with visible hairline fractures on one side of each sample were plugged with cement and submerged in water. Three points were marked along the dominant fractures to measure the increase in aperture as a function of time (Fig. 3). The samples showed a maximum fracture aperture growth of 0.91 and 0.58 mm after 164 days, respectively. These results show that if plugs are installed in hole sections where joints are present and unfavorably oriented (for example, more or less parallel to the holes, as
Fig. 2 Mean tangential strain on the steel pipe outside walls (ehR) and mean cement grout swelling stress (rs) vs. curing time. The cement grout swelling stress is calculated from Eq. (1). Note that for this figure the radial displacement is considered positive outward
observed by Akgu¨n and Daemen 1986, 1994), excessive cement swelling may be detrimental by enhancing flow paths that allow bypassing of the plug.
Assessment of borehole stability The tensile stress (rh) distribution in a hollow cylinder with an internal radius a and external radius R, subjected to an internal radial stress (rn) at r=a, is presented by Jaeger and Cook (1979) for a plane strain configuration as follows: rn a2 R2 1þ 2 rh ¼ 2 ð2Þ ðR a 2 Þ r It follows from Eq. (2) that the maximum tensile stress in the rock develops at r=a. The total normal stress across the interface (rn) is given by Akgu¨n (2000) as: rn ¼ rr þ rrt þ rri þ rs
ð3Þ
where rr is the peak radial (contact) normal stress induced by axial loading along the plug–rock interface due to an axial stress rz applied to the plug, rrt is the thermally induced radial stress due to thermal axial stress within the plug, rri is the thermally induced radial stress at the plug–rock interface due to the differences in the thermal radial expansions of plug and rock as a result of uniform temperature increase DT, and rs is the cement swelling pressure. rri and rs are assumed constant along the interface. The components of the total normal stress along the plug–rock interface (rn) are derived by Akgu¨n and Daemen (1999), Akgu¨n (2000) and Akgu¨n and Daemen (2000a, 2000b) as follows:
Fig. 3 Plugged push-out sample with hairline fractures on one side. The increase of the aperture width along the dominant fracture due to cement grout swelling was monitored at points marked 1, 2 and 3 as a function of time
Environmental Geology (2004) 45:1167–1171
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rnp
rr ¼ rz k
Ep DT 1 ða=RÞ2 1 þ mp ap ð1 þ mr Þar ð7Þ ¼ rz k þ rs þ 1 2mp 1 þ mp 1 ða=RÞ2 þ ð1 þ mr Þ Ep =Er ð1 2mr Þða=RÞ2 þ 1
sin h ½b ðL zÞ=a sinh ½b ðL=aÞ
ð4Þ
Substituting for rnp and r=a into Eq. (2) gives the maximum tensile stress or the tensile strength of rock ðjrt jÞ:
mp 1 ða=RÞ2 k¼ 1 mp 1 ða=RÞ2 þ Ep =Er ð1 þ mr Þ ð1 2mr Þða=RÞ2 þ 1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2mp k b¼ ð1 þ mr Þ Ep =Er ln ðrc =aÞ
ð4bÞ
h i rl ¼ a þ 2:07e0:18ðEp=ErÞ L
ð4cÞ
rc ¼ rl ; if R > rl
ð4dÞ
ð4eÞ rc ¼ R; if R6rl 2:45ðDT Þ ap ar Ep 1 ða=RÞ2 2 4 rrt ¼ 2 2 k 1 8s þ 16s Ep =Er ða=RÞ þ 1 ða=RÞ ð5Þ
ð4aÞ
jrt j ¼ rnp
1 þ ða=RÞ2 1 ða=RÞ2
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ð8Þ
The mean tensile strengths of the 25.4- and 50.8-mm laboratory-size push-out specimens are calculated from Eqs. (3) and (8) as 9.40 and 9.50 MPa, respectively. Overall, the nine laboratory samples showed a mean tensile strength of 9.47 MPa. The peak normal stress across the interface (rnp) for the ambient-temperature in-situ plugs (DT=0 C; R/a=¥) occurs at the loaded end of the plug–rock interface (z/L=0, zt=)L/2) and follows from using R/a=¥ in Eq. (3):
Ep DT 1 ða=RÞ2 1 þ mp ap ð1 þ mr Þar rri ¼ 1 2mp 1 þ mp 1 ða=RÞ2 þ ð1 þ mr Þ Ep =Er ð1 2mr Þða=RÞ2 þ 1
where k and b are dimensionless parameters, z is the axial distance from the initial location of the loaded end (top) of the plug (z=0 at the top of the plug, and z=plug length, L, at the plug bottom), Ep/Er is the ratio of the Young’s moduli of plug and rock, mp and mr are the Poisson’s ratios of plug and rock, rl is the limiting radius, rc is the critical radius beyond which the shear stresses and axial displacements in the rock are considered negligible, a and R are the plug and rock cylinder outside radii, respectively, DT is uniform temperature increase, ap, ar is the coefficient of linear thermal expansion of the plug and of the rock, and s is equal to zt/L where zt is the coordinate along the axis of the plug of a push-out cylinder with origin at the symmetry plane (i.e., )0.5 £ s £ 0 for )L/2 £ zt £ 0, and 0 £ s £ 0.5 for 0 £ zt £ L/2). Ep=5,254 MPa, mp=0.22, Er=22,600 MPa, mr=0.20, ap=11·10)6/C and ar= 6.9·10)6/C (Akgu¨n and Daemen 2000a). Figure 4 gives the geometry and coordinate system utilized for stress calculations. For laboratory-size push-out specimens, the peak normal stress across the interface (rnp) occurs at the loaded end of the plug and follows from Eq. (3) as follows:
ð6Þ
rnp ¼ rz a þ rs a¼
1 mp
ð9Þ
mp þ Ep =Er ð1 þ mr Þ
ð9aÞ
Fig. 4 Geometry and coordinate system utilized for push-out sample of plug radius a, rock cylinder outside radius R and plug length L. rz is the axial stress applied to the plug
Original article
The peak normal stress across the interface (rnp) for the strengths of rock measured in this study represent low bounds. elevated-temperature in-situ plugs (DT=46 and 66 C; R/a=¥) occurs at the symmetry plane along the plug–rock interface (z/L=0.5, zt=0) and follows from using R/a=¥, z/L=0.5 and zt=0 in Eq. (3): Summary and conclusions sin h ½cðL=2Þa þ 2:45ðDT Þ ap ar Ep a sin h ½cðL=aÞ Ep DT 1 þ mp ap ð1 þ mr Þar þ rs ð10Þ þ 1 2mp 1 þ mp þ ð1 þ mr Þ Ep =Er sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2mp a ð10aÞ c¼ ð1 þ mr Þ Ep =Er ln ðrl =aÞ rnp ¼ rz a
h i rl ¼ a þ 2:07e0:18ðEp=ErÞ L
ð10bÞ
where rz is the axial stress applied to the plug, a (Eq. 9a) and c are dimensionless parameters, DT is uniform temperature increase, ap, ar is the coefficient of linear thermal expansion of the plug and of the rock, Ep is the Young’s modulus of the plug, mp and mr are the Poisson’s ratios of the plug and rock, Ep/Er is the ratio of the Young’s moduli of the plug and rock, rs is the cement swelling stress, rl is the limiting radius, a is the plug radius, and L is the plug length. Substituting R/a=¥ into Eq. (8) gives the maximum tensile stress or the tensile strength of rock ðjrt jÞ hosting in situ borehole plugs: jrt j ¼ rnp
This paper presents the theoretical radial (normal) stress distribution and tensile strength in a borehole plug–rock system due to combined axial, thermal and lateral loading, along with analyses of plug–rock mechanical interactions in regards to the stability of plugged boreholes in the vicinity of radioactive waste repositories. The results of the analysis indicate that the mean tensile strength of rock exceeds the tensile strength of in-situ borehole plugs, and suggest that the rock hosting in-situ borehole plugs is fairly stable against tensile fracturing. The tensile strengths of rock measured in this study represent low bounds due to the absence of confining pressure. Acknowledgements This work is a part of a research effort on rock mass sealing, contract NRC-04-86-113, supported by the Division of Radiation Programs and Earth Sciences, Office of Nuclear Regulatory Research, US Nuclear Regulatory Commission. The authors would like to thank an anonymous reviewer for his/her invaluable review comments and suggestions. Thanks are ¨ nen and M.K. Koc¸kar, Department of Geological due to Dr. A.P. O Engineering, Middle East Technical University, Ankara, Turkey for their assistance in drafting the illustrations.
ð11Þ
The mean tensile strengths of the ambient, 46 C and 66 C in-situ plugs, as calculated from Eq. (11), are 6.60, 8.20 and 8.97 MPa, respectively. Since the mean tensile strength of rock (9.47 MPa) exceeds the tensile strength of in-situ borehole plugs, this suggests that the rock hosting in-situ borehole plugs is fairly stable against tensile fracturing. The tangential stress within the coaxial borehole of a hollow rock cylinder with an internal radius a and external radius R, subjected to any post-plug emplacement change in the confining pressure (ro) at R and a radial internal stress (rnp) at a, for a plane strain configuration is given by Jaeger and Cook (1979): 2ro rnp 1 þ ða=RÞ2 rh ¼ ð12Þ 1 ða=RÞ2 Equation (12) shows that any increase in the confining pressure subsequent to plug emplacement decreases the magnitude of the tangential stress within rock adjacent to the plug–rock interface, and hence, decreases the chance of tensile fracturing. For example, confining pressures of 1.0, 1.5 and 2.0 MPa applied to sample 1 (Table 1) would decrease the chances of tensile fracturing by about 40, 71 and 218%, respectively, which indicates that the tensile
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