Applied Energy 75 (2003) 137–144 www.elsevier.com/locate/apenergy
Salt-mudstones and rock-salt suitabilities for radioactive-waste storage systems: rheological properties J. S´lizowski*, L. Lankof Mineral & Energy Research Economy Institute, Cracow, Poland Accepted 26 January 2003
Abstract Rheological properties of salt massif are crucial factors deciding about its tightness. The purpose of this article is the comparison of stationary creep rate of salt-mudstones with salt rock. The object of the research was brown and red salt-mudstone containing 20–30% of insoluble parts. It was found that the content of insoluble parts has no significant rheological influence. On the basis of the calculated coefficients for the Norton creep law, we may state that salt-mudstone’s creep rate strongly depends on the temperature and on the effective stress in the same manner as for rock salt. The boundary values of relaxation also depend on temperature. Salt-mudstone with a considerable content of rock salt is a medium suitable for the construction of a radioactive waste repository. # 2003 Elsevier Science Ltd. All rights reserved. Keywords: Creep; Relaxation; Salty mudstones; Rock salt
1. Introduction Tightness is the crucial propriety of rock massif which is decisive about its usefulness for the storage of radioactive waste. In the case of rock salt, sufficient tightness is assured by its rheological proprieties, i.e. creep leading to the closure of micro-fissures and the inverse phenomenon-relaxation causing a compensation of the salt massif stress state components. The purpose of the present pilot research was the comparison of the rheological properties of salt-mudstones and rock salt. Two types of salt-mudstones, derived from the Kodawa mine were examined [6]: * Corresponding author. Fax: +48-12-632-3524. E-mail address:
[email protected] (J. S´lizowski). 0306-2619/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0306-2619(03)00026-6
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young, brown salt-mudstone (Z3) with an average content of insoluble parts—20.9%, the youngest, red salt-mudstone (Z4) with an average content of insoluble parts—30.2%. The statistical distribution of insoluble parts in both examined populations was close to normal. Both creep and relaxation tests were carried. The relaxation tests were supplemented by experiments that had been carried out earlier on rock salt derived from Polish salt-domes.
2. Results of creep and relaxation tests In the case of creep, the most essential test is the determination of the stationary phase rate of this process depending on applied stress and temperature. The simplest method is an examination of a large number of samples under varied stress and thermal conditions. The results obtained depend on petrophysical structure of each sample. In extreme cases, we obtained results which are the inverse from general tendency, e.g. a lower rate of creep under higher stress or temperature conditions. Representative results may be obtained only in the case of a large series of tests. In the mentioned pilot experiments, the temperature and stress were changed. This makes it possible to define the influence of these factors on the creep rate of each sample’s petrophysical structure. It demands, however, sufficiently long periods of time between the changes of stress or temperature. Eight tests of creep in the triaxial stress state were carried out, four for each kind of salt-mudstone. The same conditions were applied in the first phase of tests for each sample—axial stress p1 =15 MPa and confining stress p2=5 MPa. The initial temperature was 22 C or 60 C (295 K or 333 K). Constant conditions were applied for the two samples, but, in the case of other samples, the stress or temperature or both parameters were changed. The resulting creep curves are presented in Fig. 1 and the values of rate of creep presented in Table 1. The relaxation tests were carried on four samples of brown salt-mudstone and on four samples of the older white salt at room temperature and a temperature of 333 K. The initial stress was the same for each sample: axial stress p1=30 MPa and confining stress p2 =5 MPa. The curves obtained for axial stress versus time are shown in Fig. 2. The value of stress at which the process of relaxation was terminated is essential for the storage of radioactive waste. This is the boundary value below which the phenomenon of creep does not occur. These values are shown in Table 2.
3. Determination of the creep-law coefficients The Norton creep law is : Q=RT B " cr ef ef ¼ Ae
ð1Þ
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Fig. 1. Creep curves of salt-mudstone in triaxial stress conditions.
Table 1 Results of salt-mudstone creep test in different temperature and stress conditions Number of sample
Creep stage
Brown salt-mudstone 1 I I 2 II III 3 I I 4 II III Red salt-mudstone 5 I II 6 I II 7 I II 8 I II
Time interval (days)
Effective stress ef ¼ ðp1 p2 Þ (MPa)
Temperature (K)
Stationary creep (axial strain) rate : " (%/day)
0–201 0–92 92–371 371–421 0–201 0–92 92–371 371–421
10 10 10 7.5 10 10 10 12.5
295 333 308 308 295 333 308 308
0.0057 0.1550 0.0406 0.0134 0.0037 0.0508 0.0137 0.0524
0–371 371–421 0–90 90–201 0–92 92–201 0–371 371–421
10 7.5 10 10 10 10 10 12.5
295 295 333 308 333 308 295 295
0.0065 0.0013 0.0173 0.0023 0.0889 0.0325 0.0022 0.0085
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Fig. 2. Relaxation curves of brown salt-mudstone and white rock salt in the triaxial stress condition.
Table 2 Minimal values of the axial stress obtained in the relaxation test Number of sample Brown salt-mudstone 9 10 11 12 Rock salt 13 14 15 16
Temperature (K)
Duration (days)
Minimum axial stress (MPa)
295 295 333 333
83 108 97 112
11.8 11.0 8.5 8.5
295 295 333 333
103 96 87 98
12.3 10.8 9.7 8.5
pffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð"1 "2 Þ2 þð"2 "3 Þ2 þð"3 "1 Þ2 3 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ef ¼ pffiffiffi ð1 2 Þ2 þð2 3 Þ2 þð3 1 Þ2 2
"ef ¼
ð2Þ ð3Þ
d"cr : ef where: "ef=effective strain, ef=effective stress, "cr =rate of effective strain of ef ¼ dt creep, "1, "2, "3=principal strains, 1, 2, 3=principal stresses, Q=free activation energy, R=8.3144 J.mol1K1=1.987 cal.mol1K1=gas constant, T=temperature
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[K], A, B=constant coefficients, the law is widely applied to describe the stationary creep rate in rock-salt [1–5]. In the case of creep tests under triaxial stress conditions, where 1 6¼ 2 ¼ 3 effective stress is equal to the difference of axial and confining stresses ef ¼ p1 p2 and the effective strain, in the case of creep-strain dilatancy=0, is equal to the axial cr strain "cr ef ¼ " . This indicates that the measurement of axial strain is sufficient to determine the rate of creep strain. The values of coefficients Q/R and B were determined in a selective manner, via tests during which the temperature, stress or both parameters were changed. In the case of brown salt-mudstone, samples Nos. 2 and 4, and in the case of red saltmudstone samples Nos. 6 and 7 were used to determine the values of coefficient Q/R. Samples Nos. 5 and 8 were used to determine the values of coefficient B. From a transformation of formula (1), : "cr ef ð1Þ ln : cr "ef ð2Þ Q=R ¼ ð4Þ 1 1 T2 T1 : : where: "cr ef ð1Þ ¼ " ð1Þ =rate of axial strain at temperature T1, : cr "ef ð2Þ ¼ "ð2Þ =rate of axial strain at temperature T2. : : cr ln"cr ef ð1Þ =" ef ð2Þ B¼ ef ð1Þ ln ef ð2Þ
ð5Þ
: : cr : where: "cr ef ð1Þ ¼ " ð1Þ =rate of axial strain at stress ef(1), " ef ð2Þ ¼ "ð2Þ =rate of axial strain at stress ef(2). The obtained values are shown in Table 3. Table 3 Values of coefficient Q/R obtained in temperature range from 333 K to 308 K and values of the coefficient B obtained for an effective stress change from 10 MPa to 7.5 or 12.5 MPa Number of sample
Q/R (K)
B
1 2 3 4 5 6
5496.0 5382.4 8341.0 4128.3 – –
3.85 6.02 – – 5.67 6.05
Average values of coefficients Q/R and B: Brown salt-mudstone Red salt-mudstone Both
Q/R=5439.2 K; Q/R=6234.7 K; Q/R=5439.2 K;
B=4.94 B=5.86 B=5.4
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The values of coefficient A were determined by transforming formula (1) to the values of creep rate presented in Table 1, then applying the determined values of coefficients Q/R and B. They are expressed by formula: : "j Aj ¼ Q ð6Þ eTj jB : where " j ; Tj ; j are respectively: rate of creep, temperature and effective stress of the samples. The values of coefficient A are shown in Table 4. Average values of coefficient A: Brown salt-mudstone Brown salt-mudstone Both
A=13.56 (%/day) A=10.84 (%/day) A=12.89 (%/day)
4. Comparison of rheological proprieties of salt-mudstone and rock salt The characteristic feature of stationary creep-rate measurements of rock salt is a broad scattering of results. From the data shown in Table 1, the values of creep rate range from 0.0023%/day to 0.0406%/day for an effective stress of 10 MPa and a temperature of 308 K. The broad scattering of results is not uncommon and even a much higher one can sometimes be expected. For example, in certain researches of one type of white older rock salt [5], the values of creep rate differ by more than Table 4 Values of coefficient A fitted to the data in Table 1 Sample number
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Aj Q/R=5439.2 B=4.94
Q/R=6234.7 B=5.86
Q/R=5837 B=5.4
6.60 22.15 21.78 29.77 4.26 7.24 7.34 9.34 – – – – – – – –
– – – – – – – – 13.50 14.27 3.23 1.94 4.60 4.80 16.60 27.74
8.81 25.37 27.48 42.88 5.71 8.29 9.26 10.63 10.11 9.37 2.82 1.54 3.45 3.98 14.50 22.00
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Table 5 Coefficients of the Norton creep law accepted for the rock salt from: Gorleben salt-dome, Germany; WIPP (Waste Isolation Pilot Plant); surroundings of one of gas-storage cavern in Mogilno salt-dome, and examined salt-mudstone. Stationary creep-rate for an effective stress ef=10 MPa and temperature T=333 K Model
BGRa [2,3] WIPP [1,4] Mogilno—Cavern K2 [5] Brown salt-mudstone Red salt-mudstone Both (brown and red)
Norton law parameter
Creep rate : "ef (%/day)
A (%/day)
B
Q/R (K)
180 126 1024 13.6 10.8 12.9
5.0 4.9 2.8 4.9 5.9 5.4
6494.7 6039.3 5250.0 5439.2 6234.7 5837.0
0.0609 0.1327 0.0919 0.0871 0.0634 0.0791
20 times. German researches, for different kinds of rock salt derived from the Gorleben salt-dome [2], showed that the values of creep rate differ by more than 100 times. Much more interesting is the comparison of salt-mudstone of creep rate predictions using coefficients obtained with creep laws well known for rock salt. Such a comparison is shown in Table 5. The average values of creep rate are within the interval obtained for rock salt. Taking into account the fact that relaxation rates are similar too, one can ascertain that the rheological properties of salt-mudstone are similar to those of older white salt, i.e. salt with strong rheological proprieties.
5. Conclusions The considerable similarity obtained between rock salt and salt-mudstone creep and relaxation rate determined in pilot researches does not mean of course that their rheological properties are entirely identified. The final estimation of salt-mudstone usefulness for the construction of a high-level radioactive-waste repository requires extending the scope of the research. Tests on samples with distinctively diverse contents of insoluble parts should be carried out in much more variable conditions of stress and temperature. The results obtained should be verified by in situ measurements of convergence in the rock massif, which has been geologically well identified.
References [1] Flack user’s manual app. I. Minneapolis: Itasca Consulting Group Inc.; 1998. [2] Hunsche U. Uniaxial and triaxial creep and failure tests on rock: experimental technique and interpretation. Script of lecture given at the International Centre for Mechanical Geosciences (CISM), Udine, October 1993. [3] Hunshe U, Hampel A. Rock salt—the mechanical properties of the host rock material for a radioactive-waste repository. Engineering Geology 1999:52.
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[4] Matalucci RV, Hunter O. Geomechanical application for the waste isolation pilot plant (WIPP) project. In: The mechanical behavior of salt I, Proc. of First Conf., Pennsylvania State University, 9– 11 November 1981. [5] S´lizowski J. Badania wasnos´ ci reologicznych soli kamiennej przy projektowaniu komo´r magazynowych gazu ziemnego w go´rotworze solnym. Przeglcac˛ d Go´rniczy 2001:5. [6] S´lizowski K. i in. Interpretacja wyniko´w badan´ laboratoryjnych was´ ciwos´ ci zubro´w brunatnych i hematytowych dla oceny ich przydatnos´ ci do skadowania odpado´w promieniotwo´rczych Archiwum IGSMiE PAN, 2001.