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Creep Rate and Creep Model of Rockfill
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ProcediaProcedia Engineering 00 (2011) Engineering 28 000–000 (2012) 796 – 802
Procedia Engineering www.elsevier.com/locate/procedia
2012 International Conference on Modern Hydraulic Engineering
Creep Rate and Creep Model of Rockfill LI Haifanga, ZHANG Yinqi, a* State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, NO.20, West Chegongzhuang Road,Haidian District, Beijing 100048, China
Abstract Due to the test duration restriction, not only the creep strain but also the creep rate should be considered to establish the creep model of the rockfill. The creep rate decides whether the creep model deviates from the actual strain after the test duration. Both the same confining pressure loading and the constant stress ratio loading ways were adopted in this study. In the creep test, the Lianghekou mixture, the Zuoxiagou rockfill and the Xiaolangdi rockfill were used, and their creep characteristics and the creep rate were analyzed. Both the creep strain and the creep rate of the rockfills followed the linear relationship with the time in a double logarithmic coordinate. Therefore a power function model is suitable to describe the creep.
© © 2012 2011 Published Publishedby byElsevier ElsevierLtd. Ltd.Selection and/or peer-review under responsibility of Society for Resources, Environment and Engineering Keywords: rockfill; creep rate; creep model; stress level; stress ratio; confining pressure
1. Introduction As high rockfill dams were constructed, the dam settlement upon completion became a significant issue and its effect on the dam was concerned. The settlement developed in the constant load was often referred as the creep or rheology. The maximum settlement of the concrete facing rockfill dam of Tianshengqiao First-cascade hydropower station reached 3.38m and YANG Jian [1] considered that the creep was one of the main causes for such a large settlement. In 1991 SHEN Zhujiang et al. [2] researched on the rheological characteristics of rockfill, and proposed creep model of rockfill with three parameters. But there was a deficiency that the model was too flat in the latter stage. SHEN Zhujiang et al. [3] did the feedback analysis on the observed data of 4 dams, and put forward three parameters
* Corresponding author. Tel.:13552823801. E-mail address: [email protected] .
1877-7058 © 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Society for Resources, Environment and Engineering doi:10.1016/j.proeng.2012.01.812
797
LI HaifangAuthor and ZHANG / Procedia Engineering 28 (2012) 796 – 802 name / Yinqi Procedia Engineering 00 (2011) 000–000
2
rheological model which was the exponential decay type. MI Zhankuan et al. [4] improved the creep model proposed by SHEN Zhujiang and calculated the deformation of the dam body and face-plate of Gongboxia concrete facing rockfill Dam. WANG Yong and YIN Zongze [5-7] established a rheology model of the rockfill used in the rheology analysis of the concrete facing rockfill dam. CHENG Zhanlin and DING Hongshun [8] used a large scale stress-controlled triaxial apparatus to study the creep characteristics of the rockfill, proposing nine-parameter mathematical expressions of rockfill creep. The creep model and creep calculation obtained more attention gradually [9-11]. Due to the test duration restriction, not only the creep strain but also the creep rate should be considered to establish the creep model of the rockfill. The creep rate decides whether the creep model deviates from the actual strain after the test duration. The creep characteristics and the creep rate of Lianghekou mixture, Zuoxiagou rockfill and Xiaolangdi rockfill were analyzed through the creep test. Two loading ways, the same confining pressure and constant stress ratio, were adopted in this study. The study provided the basis to establish a reasonable creep model. 2. Test equipment, methods and materials The test used a large scale and high pressure triaxial creep apparatus, and the size of sample was Ф300×700mm. The axial load and the confining pressure were loaded by weight and transmitted to the sample through the hydraulic. The apparatus could meet the requirement of the long-term constant load for the creep test. Lianghekou core dam is 293 meters high and its quarry is a sand alternating slate area. The test materials were the mixture of slate and sandstone of Zuoxiagou. Slate and sandstone accounted for 30 per cent and 70 per cent respectively. Xiaolangdi rockfill came from Shimen borrow area which was megathick layer of siliceous quartz sandstone. Control of dry density of Lianghekou mixture, Zuoxiagou rockfill and Xiaolangdi rockfill were 2.14g/cm3, 2.12g/cm3, 2.13g/cm3 respectively. The gradations of the rockfills were shown in Table1. Table1. Gradations of rockfills (content less than particle size) Particle size / mm Mixture Zuoxiagou Xiaolangdi
natural gradation
600
400
300
200
100
60
40
20
10
5
100
82.5
69.5
56
41
31.5
26
17
10.5
5
100
80.5
51.3
31.2
14.5
100
92.5
88
77
61.5
51.5
44.5
34
25.5
17.5
100
82.3
60.9
41.3
25.5
45.5
38
29.9
22.5
16.3
100
81.8
59.1
41.9
26.5
gradation of sample natural gradation gradation of sample natural gradation gradation of sample
100
87
80
70
57.8
The sample was vacuumed and water was fed from the sample bottom until overflowed from the top. Then the test adopted hydrostatic head saturation in 4 hours. In order to consider the influence of the stress path, the same confining pressure loading and the constant stress ratio loading ways were adopted, detailed in Table2. The confining pressure and the axial pressure were loaded on a sample. When the creep deformation was steady at one stress state, (1) The same confining pressure method would load next axial pressure until the creep was stable. Axial pressure was loaded stage by stage until the test end; (2) The constant stress ratio method would load next axial pressure and the confining pressure but keep the same stress ratio. The axial pressure and the confining pressure were loaded stage by stage until the test end. The test
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LI Haifang YinqiEngineering / Procedia Engineering 28 (2012) 796 – 802 Author and nameZHANG / Procedia 00 (2011) 000–000
3
duration in every stress state was 7 days. Table2. Test loading programs of rockfill Test methods of loading Same confining pressure
Rockfill
Confining pressure/MPa
Stress level/Stress ratio
Lianghekou mixture
0.5; 1.5; 2.0; 3.0
0.2; 0.4; 0.6; 0.8
Zuoxiagou saturated rockfill
0.5; 1.0; 2.0; 3.0
0.2; 0.4; 0.6; 0.8
Zuoxiagou unsaturated rockfill
0.5; 1.0; 2.0; 3.0
0.2; 0.4; 0.6; 0.8
Lianghekou mixture
0.5; 1.0; 1.5; 2.0; 2.5; 3.0
1.5; 2.0; 3.0; 3.5; 4.0
Xiaolangdi rockfill
1.0; 1.5; 2.0; 2.5; 3.0
1.5; 2.0; 2.5
Constant stress ratio
3. Test results of same confining pressure loading way 3.1. Creep characteristics of rockfill Based on the Lianghekou dam height, the maximum confining pressure in the test was 3.0MPa. Before discussing creep laws, we must separate creep from the elasticoplastic deformation of the rockfill, but there was no a division accepted generally. The creep test showed that in a short time after the axial pressure loading, the deformation increased rapidly, and in an hour, the deformation rate became flat gradually. In the Reference [8], an hour was used as the boundary between the elasticoplastic strain and the creep in the Shuibuya rockfill test. In the creep test on the cushion materials of the Xibeikou facing rockfill dam in the Reference [1], the same boundary was used. It is also used in this study. As shown in Fig.1, the axial and the volume creep of the Lianghekou mixture are in a linear relationship with time in a double logarithmic coordinate when confining pressure is 2.0MPa. The laws are similar in the other confining pressure. Creep characteristics of the Zuoxiagou rockfill are also similar. 10
1
Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.1
0.01
1
10
100
1000
10000
100000
Volume creep /%
Axial creep /%
10
1 Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.1
0.01
1
10
Time/min
100
1000
10000
100000
Time/min
Fig.1. Relationship between creep and time of the mixture (same confining pressure) (a) Axial creep; (b) Volume creep
3.2. Creep rate of rockfill Creep rate can be got in the following ways. The test time is divided into several segments, and then strain increment and time increment of each segment can be calculated. According to the following formula, average rate of the segment can be got. ε =
Δε Δt
(1)
With the end time of segments as the abscissa and the creep rate as the ordinate, the relationship
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LI HaifangAuthor and ZHANG / Procedia Engineering 28 (2012) 796 – 802 name / Yinqi Procedia Engineering 00 (2011) 000–000
4
between the creep rate and the time of the rockfill was obtained. The creep rate is faster at the initial stage of the test, so the segments should be short, and the segments near to the end of the test could be longer. Fig.2 and Fig.3 show that the axial and the volume creep rates of the Lianghekou mixture and the Zuoxiagou rockfill are linear with the time in a double logarithmic coordinate when the confining pressure is 2.0MPa. The characteristics of the axial and the volume creep rates are similar in the other confining pressure. The higher the stress level, the faster the axial creep rate. The volume creep rate is not the fastest at the high stress level, because it is influenced by the compaction and the shearing dilation. This paper also studies the creep characteristics of the Zuoxiagou rockfill at the unsaturated state that are similar to the above. 0.01 Volume creep rate /%/min
Axial creep rate/%/min
0.01 0.001 0.0001
Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.00001
0.000001
0.001 0.0001 0.00001
0.000001 1
10
1000 100 Time/min
10000
Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
100000
1
10
100 1000 Time/min
10000
100000
Fig.2. Relationship between creep rate and time of the mixture (same confining pressure) (a) Axial creep rate; (b) Volume creep rate
0.01 Volume creep rate/%/min
Axial creep rate /%/min
0.01 0.001 0.0001
Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.00001 0.000001
1
10
100 1000 Time/min
10000
100000
0.001 0.0001 Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.00001 0.000001
1
10
100 1000 Time/min
10000
100000
Fig.3. Relationship between creep rate and time of the Zuoxiagou rockfill (same confining pressure) (a) Axial creep rate; (b) Volume creep rate
4. Test results of constant stress ratio loading way 4.1. Creep characteristics of the rockfill In order to consider the influence of the stress path, the loading method of the constant stress ratio was adopted in the creep test of the Lianghekou mixture and the Xiaolangdi rockfill. The maximum confining pressure is 3.0MPa. Fig. 4 shows the relationship between the creep and the time when the loading way is a constant stress ratio. In the figure, 2005 means that the stress ratio is 2.0 and the confining pressure is 0.5MPa, which is similarly for the others. In the loading condition of the constant stress ratio, the axial and the volume
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LI Haifang YinqiEngineering / Procedia Engineering 28 (2012) 796 – 802 Author and nameZHANG / Procedia 00 (2011) 000–000
5
creep of the Lianghekou mixture are linear with the time in a double logarithmic coordinate. The characteristics of the axial and the volume creep are similar in the other confining pressure and the stress ratio. Creep characteristics of the Xiaolangdi rockfill are also similar. 10 2005 2010 2015 2020 2025 2030
Axail creep/%
1
0.1
0.01
1
10
100 1000 Time/min
10000
Volume creep/%
10
1
0.1
0.01
100000
2005 2010 2015 2020 2025 2030
1
10
100 1000 Time/min
10000
100000
Fig.4. Relationship between creep and time of the mixture (constant stress level) (a) Axial creep; (b) Volume creep
4.2. Creep rate of the rockfill
2005 2010 2015 2020 2025 2030
0.001 0.0001 0.00001
0.000001
1
10
100 1000 Time/min
10000
0.01 Volume creep rate/%/min
Axial creep rate/%/min
0.01
0.001 0.0001 0.00001 0.000001
100000
2005 2010 2015 2020 2025 2030
1
10
100 1000 Time/min
10000
100000
Fig.5. Relationship between creep rate and time of the mixture (constant stress ratio) (a) Axial creep rate; (b) Volume creep rate 0.01 2010 2015 2020 2025 2030
0.001 0.0001 0.00001
0.000001
1
10
100 1000 Time/min
10000
100000
Volume creep rate/%/min
Axial creep rate/%/min
0.01
2010 2015 2020 2025 2030
0.001 0.0001 0.00001 0.000001
1
10
100 1000 Time/min
10000
100000
Fig.6. Relationship between creep rate and time of the Xiaolangdi rockfill (constant stress ratio) (a) Axial creep rate; (b) Volume creep rate
Fig.5 and Fig.6 show that the axial and the volume creep rates of the Lianghekou mixture and the Xiaolangdi rockfill are linear with the time in a double logarithmic coordinate when the stress ratio is 2.0. The higher the confining pressure, the faster the axial creep rate. The characteristics of the volume creep
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LI HaifangAuthor and ZHANG / Procedia Engineering 28 (2012) 796 – 802 name / Yinqi Procedia Engineering 00 (2011) 000–000
6
ratio are complex because they are influenced by the compaction and the shearing dilation. At the other confining pressure and the stress ratio, the creep rate characteristics of the Lianghekou mixture and the Xiaolangdi rockfill are similar. 5. The creep model of the rockfill The creep model is a mathematic method to describe the materials creep. There are two methods to establish the creep model of the rockfill. One is a theoretical model combining elements of Hooke elastomer; Newton Viscous body and Saint-Venant plasticity elements. The other one is an empirical model. The deformation variation of the rockfill with the time is obtained through the test and a mathematical function is selected to fit the test curves. Usually, the relationship between the creep and the time should be described with several functions together, but researchers attempt to use the monomial function for simplicity. Some researchers suggested different functions, and the most popular functions are the index fund, the power type, the logarithmic type and so on. As mentioned previously, the axial creep, the volume creep and their rates of the rockfills are linear with the time in a double logarithmic coordinate. A function that both the function and its first derivative are linier in a double logarithmic coordinate is needed. The power function has these features, so it is adopted to fit the relationship between the creep and the time of the rockfills [12-14]. ε a（
t b ） t0
(2)
In which t0 is a point-in-time of the creep test duration, a is the creep in the point that is called the axial (or volume) initial creep and b called the axial (or volume) creep exponent that is the slope of the fitted curve from the point to the end of test. They can be obtained by the creep test and have relevance with materials and stress state. 0.01
Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.001
Volume creep rate/%/min
Axial creep rate/%/min
0.01
0.0001 0.00001 0.000001
0
5000
10000 TIme/min
15000
20000
Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.001 0.0001 0.00001 0.000001
0
5000
10000
15000
20000
TIme/min
Fig.7. Relationship between creep rate and time of mixture (single logarithm coordinate) (a) Axial creep rate; (b) Volume creep rate
Although the logarithmic function and the exponential function were used to fit the test results, the power function is better. Because there is a great gap in single logarithm coordinates between the curves of the axial or the volume creep and a line, the logarithmic function is not suitable to describe the creep of the rockfill. The curves of the axial and the volume creep rate are not straight lines in single logarithm coordinates, therefore the exponential function is also inappropriate to describe the creep. In the loading condition of the same confining pressure, the relationship in single logarithm coordinates between the axial or the volume creep rate and the time is shown in Fig.7 The axial or the volume creep rate of other rockfill is not linear with the time in single logarithm coordinate in the loading condition of the same confining pressure and the constant stress ratio.
802
LI Haifang YinqiEngineering / Procedia Engineering 28 (2012) 796 – 802 Author and nameZHANG / Procedia 00 (2011) 000–000
6. Conclusion The creep characteristics of the Lianghekou mixture, the Zuoxiagou rockfill and the Xiaolangdi rockfill were analyzed through the same confining loading test and the constant stress ratio loading test. (1) The axial creep, the volume creep and their creep rates of the rockfill are linear with the time in a double logarithmic coordinate. It is suitable to describe the creep characteristics adopting power function. (2) The higher the stress level, the faster the axial creep rate in the condition loading of the same confining pressure. The volume creep rate is not the fastest at the high stress level because it is influenced by the compaction and the shearing dilation. (3) The higher the confining pressure, the faster the axial creep rate in the condition loading of the constant stress ratio. The characteristics of the volume creep rate are complex because they are influenced by the compaction and the shearing dilation. (4) There is a great gap between the curves of the axial or the volume creep and a line in single logarithm coordinate so that the logarithmic function would not be suitable to describe the creep. The curves of the creep rate are not straight lines in single logarithm coordinate, so the exponential function is inappropriate to describe the creep. References [1] YANG Jian. Sedimentation analysis of concrete facing rockfill dam of Tianshengqiao First-cascade Hydropower Station [J]. Yunan Water Power, 2001, 17(2): 59–63. [2] SHEN Zhujiang, ZUO Yuanming. Study on rheology chracterastics of rockfill [A]//Proc. of the 6th China soil mechanics and foundation engineering Conference [C]. Shanghai: Tongji University Press, 1991: 443–446. [3] SHEN Zhujiang, ZHAO Kuizhi. Back analysis of creep deformation of rockfill dams [J]. Journal of Hydraulic Engineering, 1998, (6): 1–6. [4] MI Zhankuan, SHEN Zhujiang, LI Guoying. Creep model for high concrete face rockfill dams [J]. Hydro-Science and Engineering. 2002, (2): 35–41. [5] WANG Yong, YIN Zongze, A rheology model of rockfill used in the rheology analysis of concrete face rockfill [J]. Rock and Soil Mechanics 2000, 21(3): 227–230. [6] WANG Yong. Analysis on rheology mechanism and study method of rockfill [J]. Chinese Journal of Rock Mechanics and Engineering. 2000, 19(4): 526–530. [7] WANG Yong, YIN Zongze. Analysis of effects of rockfill rheology on deformation and stress of force slabs of concrete face rockfill dams [J]. Journal of Hohai University. 2000,28(6): 60–65. [8] CHENG Zhanlin, DING Hongshun. Creep test for rockfill [J]. Chinese Journal of Geotechnical of Engineering, 2004, 26(4): 473–476. [9] Reiko Kuwano and Richard J. Jardine. On measuring creep behaviour in granular materials through triaxial testing [J]. Can. Geotech. J. 2002, 39: 1061–1074. [10] LIANG Jun, LIU Hanlong. Creep test for rockfill of CFRD [J]. Chinese Journal of Geotechnical Engineering. 2002, 24(2): 257–259 [11] LIANG Jun, LIU Hanlong, GAO Yufeng. Creep mechanism and breakage behaviour of rockfill [J]. Rock and Soil Mechanics. 2003, 24(3): 479–483 [12] LI Haifang, XU Zeping, WEN Yanfeng, CHEN Ning. Jiudianxia rockfill creep behavior and model study through triaxial creep test [J]. Journal of Hydroelectric Engineering, 2010, 29(6): 166–171. [13] LI Haifang, ZHANG Yinqi, JIN Wei, WEN Yanfeng, CHEN Ning. Study on the creep model at Lianghekou water power station of rockfill through triaxial creep test [J]. Northwestern Seismological Journal, 2011, 33(supp.1): 285–289. [14] LI Haifang, ZHANG Qincheng, XU Zeping, WEN Yanfeng, CHEN Ning. Xilongchi rockfill creep behavior and model study through triaxial creep test. Chinese Journal of Rock Mechanics and Engineering. 2009, 28(supp.2): 3376–3382.
7
ProcediaProcedia Engineering 00 (2011) Engineering 28 000–000 (2012) 796 – 802
Procedia Engineering www.elsevier.com/locate/procedia
2012 International Conference on Modern Hydraulic Engineering
Creep Rate and Creep Model of Rockfill LI Haifanga, ZHANG Yinqi, a* State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, NO.20, West Chegongzhuang Road,Haidian District, Beijing 100048, China
Abstract Due to the test duration restriction, not only the creep strain but also the creep rate should be considered to establish the creep model of the rockfill. The creep rate decides whether the creep model deviates from the actual strain after the test duration. Both the same confining pressure loading and the constant stress ratio loading ways were adopted in this study. In the creep test, the Lianghekou mixture, the Zuoxiagou rockfill and the Xiaolangdi rockfill were used, and their creep characteristics and the creep rate were analyzed. Both the creep strain and the creep rate of the rockfills followed the linear relationship with the time in a double logarithmic coordinate. Therefore a power function model is suitable to describe the creep.
© © 2012 2011 Published Publishedby byElsevier ElsevierLtd. Ltd.Selection and/or peer-review under responsibility of Society for Resources, Environment and Engineering Keywords: rockfill; creep rate; creep model; stress level; stress ratio; confining pressure
1. Introduction As high rockfill dams were constructed, the dam settlement upon completion became a significant issue and its effect on the dam was concerned. The settlement developed in the constant load was often referred as the creep or rheology. The maximum settlement of the concrete facing rockfill dam of Tianshengqiao First-cascade hydropower station reached 3.38m and YANG Jian [1] considered that the creep was one of the main causes for such a large settlement. In 1991 SHEN Zhujiang et al. [2] researched on the rheological characteristics of rockfill, and proposed creep model of rockfill with three parameters. But there was a deficiency that the model was too flat in the latter stage. SHEN Zhujiang et al. [3] did the feedback analysis on the observed data of 4 dams, and put forward three parameters
* Corresponding author. Tel.:13552823801. E-mail address: [email protected] .
1877-7058 © 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Society for Resources, Environment and Engineering doi:10.1016/j.proeng.2012.01.812
797
LI HaifangAuthor and ZHANG / Procedia Engineering 28 (2012) 796 – 802 name / Yinqi Procedia Engineering 00 (2011) 000–000
2
rheological model which was the exponential decay type. MI Zhankuan et al. [4] improved the creep model proposed by SHEN Zhujiang and calculated the deformation of the dam body and face-plate of Gongboxia concrete facing rockfill Dam. WANG Yong and YIN Zongze [5-7] established a rheology model of the rockfill used in the rheology analysis of the concrete facing rockfill dam. CHENG Zhanlin and DING Hongshun [8] used a large scale stress-controlled triaxial apparatus to study the creep characteristics of the rockfill, proposing nine-parameter mathematical expressions of rockfill creep. The creep model and creep calculation obtained more attention gradually [9-11]. Due to the test duration restriction, not only the creep strain but also the creep rate should be considered to establish the creep model of the rockfill. The creep rate decides whether the creep model deviates from the actual strain after the test duration. The creep characteristics and the creep rate of Lianghekou mixture, Zuoxiagou rockfill and Xiaolangdi rockfill were analyzed through the creep test. Two loading ways, the same confining pressure and constant stress ratio, were adopted in this study. The study provided the basis to establish a reasonable creep model. 2. Test equipment, methods and materials The test used a large scale and high pressure triaxial creep apparatus, and the size of sample was Ф300×700mm. The axial load and the confining pressure were loaded by weight and transmitted to the sample through the hydraulic. The apparatus could meet the requirement of the long-term constant load for the creep test. Lianghekou core dam is 293 meters high and its quarry is a sand alternating slate area. The test materials were the mixture of slate and sandstone of Zuoxiagou. Slate and sandstone accounted for 30 per cent and 70 per cent respectively. Xiaolangdi rockfill came from Shimen borrow area which was megathick layer of siliceous quartz sandstone. Control of dry density of Lianghekou mixture, Zuoxiagou rockfill and Xiaolangdi rockfill were 2.14g/cm3, 2.12g/cm3, 2.13g/cm3 respectively. The gradations of the rockfills were shown in Table1. Table1. Gradations of rockfills (content less than particle size) Particle size / mm Mixture Zuoxiagou Xiaolangdi
natural gradation
600
400
300
200
100
60
40
20
10
5
100
82.5
69.5
56
41
31.5
26
17
10.5
5
100
80.5
51.3
31.2
14.5
100
92.5
88
77
61.5
51.5
44.5
34
25.5
17.5
100
82.3
60.9
41.3
25.5
45.5
38
29.9
22.5
16.3
100
81.8
59.1
41.9
26.5
gradation of sample natural gradation gradation of sample natural gradation gradation of sample
100
87
80
70
57.8
The sample was vacuumed and water was fed from the sample bottom until overflowed from the top. Then the test adopted hydrostatic head saturation in 4 hours. In order to consider the influence of the stress path, the same confining pressure loading and the constant stress ratio loading ways were adopted, detailed in Table2. The confining pressure and the axial pressure were loaded on a sample. When the creep deformation was steady at one stress state, (1) The same confining pressure method would load next axial pressure until the creep was stable. Axial pressure was loaded stage by stage until the test end; (2) The constant stress ratio method would load next axial pressure and the confining pressure but keep the same stress ratio. The axial pressure and the confining pressure were loaded stage by stage until the test end. The test
798
LI Haifang YinqiEngineering / Procedia Engineering 28 (2012) 796 – 802 Author and nameZHANG / Procedia 00 (2011) 000–000
3
duration in every stress state was 7 days. Table2. Test loading programs of rockfill Test methods of loading Same confining pressure
Rockfill
Confining pressure/MPa
Stress level/Stress ratio
Lianghekou mixture
0.5; 1.5; 2.0; 3.0
0.2; 0.4; 0.6; 0.8
Zuoxiagou saturated rockfill
0.5; 1.0; 2.0; 3.0
0.2; 0.4; 0.6; 0.8
Zuoxiagou unsaturated rockfill
0.5; 1.0; 2.0; 3.0
0.2; 0.4; 0.6; 0.8
Lianghekou mixture
0.5; 1.0; 1.5; 2.0; 2.5; 3.0
1.5; 2.0; 3.0; 3.5; 4.0
Xiaolangdi rockfill
1.0; 1.5; 2.0; 2.5; 3.0
1.5; 2.0; 2.5
Constant stress ratio
3. Test results of same confining pressure loading way 3.1. Creep characteristics of rockfill Based on the Lianghekou dam height, the maximum confining pressure in the test was 3.0MPa. Before discussing creep laws, we must separate creep from the elasticoplastic deformation of the rockfill, but there was no a division accepted generally. The creep test showed that in a short time after the axial pressure loading, the deformation increased rapidly, and in an hour, the deformation rate became flat gradually. In the Reference [8], an hour was used as the boundary between the elasticoplastic strain and the creep in the Shuibuya rockfill test. In the creep test on the cushion materials of the Xibeikou facing rockfill dam in the Reference [1], the same boundary was used. It is also used in this study. As shown in Fig.1, the axial and the volume creep of the Lianghekou mixture are in a linear relationship with time in a double logarithmic coordinate when confining pressure is 2.0MPa. The laws are similar in the other confining pressure. Creep characteristics of the Zuoxiagou rockfill are also similar. 10
1
Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.1
0.01
1
10
100
1000
10000
100000
Volume creep /%
Axial creep /%
10
1 Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.1
0.01
1
10
Time/min
100
1000
10000
100000
Time/min
Fig.1. Relationship between creep and time of the mixture (same confining pressure) (a) Axial creep; (b) Volume creep
3.2. Creep rate of rockfill Creep rate can be got in the following ways. The test time is divided into several segments, and then strain increment and time increment of each segment can be calculated. According to the following formula, average rate of the segment can be got. ε =
Δε Δt
(1)
With the end time of segments as the abscissa and the creep rate as the ordinate, the relationship
799
LI HaifangAuthor and ZHANG / Procedia Engineering 28 (2012) 796 – 802 name / Yinqi Procedia Engineering 00 (2011) 000–000
4
between the creep rate and the time of the rockfill was obtained. The creep rate is faster at the initial stage of the test, so the segments should be short, and the segments near to the end of the test could be longer. Fig.2 and Fig.3 show that the axial and the volume creep rates of the Lianghekou mixture and the Zuoxiagou rockfill are linear with the time in a double logarithmic coordinate when the confining pressure is 2.0MPa. The characteristics of the axial and the volume creep rates are similar in the other confining pressure. The higher the stress level, the faster the axial creep rate. The volume creep rate is not the fastest at the high stress level, because it is influenced by the compaction and the shearing dilation. This paper also studies the creep characteristics of the Zuoxiagou rockfill at the unsaturated state that are similar to the above. 0.01 Volume creep rate /%/min
Axial creep rate/%/min
0.01 0.001 0.0001
Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.00001
0.000001
0.001 0.0001 0.00001
0.000001 1
10
1000 100 Time/min
10000
Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
100000
1
10
100 1000 Time/min
10000
100000
Fig.2. Relationship between creep rate and time of the mixture (same confining pressure) (a) Axial creep rate; (b) Volume creep rate
0.01 Volume creep rate/%/min
Axial creep rate /%/min
0.01 0.001 0.0001
Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.00001 0.000001
1
10
100 1000 Time/min
10000
100000
0.001 0.0001 Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.00001 0.000001
1
10
100 1000 Time/min
10000
100000
Fig.3. Relationship between creep rate and time of the Zuoxiagou rockfill (same confining pressure) (a) Axial creep rate; (b) Volume creep rate
4. Test results of constant stress ratio loading way 4.1. Creep characteristics of the rockfill In order to consider the influence of the stress path, the loading method of the constant stress ratio was adopted in the creep test of the Lianghekou mixture and the Xiaolangdi rockfill. The maximum confining pressure is 3.0MPa. Fig. 4 shows the relationship between the creep and the time when the loading way is a constant stress ratio. In the figure, 2005 means that the stress ratio is 2.0 and the confining pressure is 0.5MPa, which is similarly for the others. In the loading condition of the constant stress ratio, the axial and the volume
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LI Haifang YinqiEngineering / Procedia Engineering 28 (2012) 796 – 802 Author and nameZHANG / Procedia 00 (2011) 000–000
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creep of the Lianghekou mixture are linear with the time in a double logarithmic coordinate. The characteristics of the axial and the volume creep are similar in the other confining pressure and the stress ratio. Creep characteristics of the Xiaolangdi rockfill are also similar. 10 2005 2010 2015 2020 2025 2030
Axail creep/%
1
0.1
0.01
1
10
100 1000 Time/min
10000
Volume creep/%
10
1
0.1
0.01
100000
2005 2010 2015 2020 2025 2030
1
10
100 1000 Time/min
10000
100000
Fig.4. Relationship between creep and time of the mixture (constant stress level) (a) Axial creep; (b) Volume creep
4.2. Creep rate of the rockfill
2005 2010 2015 2020 2025 2030
0.001 0.0001 0.00001
0.000001
1
10
100 1000 Time/min
10000
0.01 Volume creep rate/%/min
Axial creep rate/%/min
0.01
0.001 0.0001 0.00001 0.000001
100000
2005 2010 2015 2020 2025 2030
1
10
100 1000 Time/min
10000
100000
Fig.5. Relationship between creep rate and time of the mixture (constant stress ratio) (a) Axial creep rate; (b) Volume creep rate 0.01 2010 2015 2020 2025 2030
0.001 0.0001 0.00001
0.000001
1
10
100 1000 Time/min
10000
100000
Volume creep rate/%/min
Axial creep rate/%/min
0.01
2010 2015 2020 2025 2030
0.001 0.0001 0.00001 0.000001
1
10
100 1000 Time/min
10000
100000
Fig.6. Relationship between creep rate and time of the Xiaolangdi rockfill (constant stress ratio) (a) Axial creep rate; (b) Volume creep rate
Fig.5 and Fig.6 show that the axial and the volume creep rates of the Lianghekou mixture and the Xiaolangdi rockfill are linear with the time in a double logarithmic coordinate when the stress ratio is 2.0. The higher the confining pressure, the faster the axial creep rate. The characteristics of the volume creep
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LI HaifangAuthor and ZHANG / Procedia Engineering 28 (2012) 796 – 802 name / Yinqi Procedia Engineering 00 (2011) 000–000
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ratio are complex because they are influenced by the compaction and the shearing dilation. At the other confining pressure and the stress ratio, the creep rate characteristics of the Lianghekou mixture and the Xiaolangdi rockfill are similar. 5. The creep model of the rockfill The creep model is a mathematic method to describe the materials creep. There are two methods to establish the creep model of the rockfill. One is a theoretical model combining elements of Hooke elastomer; Newton Viscous body and Saint-Venant plasticity elements. The other one is an empirical model. The deformation variation of the rockfill with the time is obtained through the test and a mathematical function is selected to fit the test curves. Usually, the relationship between the creep and the time should be described with several functions together, but researchers attempt to use the monomial function for simplicity. Some researchers suggested different functions, and the most popular functions are the index fund, the power type, the logarithmic type and so on. As mentioned previously, the axial creep, the volume creep and their rates of the rockfills are linear with the time in a double logarithmic coordinate. A function that both the function and its first derivative are linier in a double logarithmic coordinate is needed. The power function has these features, so it is adopted to fit the relationship between the creep and the time of the rockfills [12-14]. ε a（
t b ） t0
(2)
In which t0 is a point-in-time of the creep test duration, a is the creep in the point that is called the axial (or volume) initial creep and b called the axial (or volume) creep exponent that is the slope of the fitted curve from the point to the end of test. They can be obtained by the creep test and have relevance with materials and stress state. 0.01
Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.001
Volume creep rate/%/min
Axial creep rate/%/min
0.01
0.0001 0.00001 0.000001
0
5000
10000 TIme/min
15000
20000
Stress level 0.2 Stress level 0.4 Stress level 0.6 Stress level 0.8
0.001 0.0001 0.00001 0.000001
0
5000
10000
15000
20000
TIme/min
Fig.7. Relationship between creep rate and time of mixture (single logarithm coordinate) (a) Axial creep rate; (b) Volume creep rate
Although the logarithmic function and the exponential function were used to fit the test results, the power function is better. Because there is a great gap in single logarithm coordinates between the curves of the axial or the volume creep and a line, the logarithmic function is not suitable to describe the creep of the rockfill. The curves of the axial and the volume creep rate are not straight lines in single logarithm coordinates, therefore the exponential function is also inappropriate to describe the creep. In the loading condition of the same confining pressure, the relationship in single logarithm coordinates between the axial or the volume creep rate and the time is shown in Fig.7 The axial or the volume creep rate of other rockfill is not linear with the time in single logarithm coordinate in the loading condition of the same confining pressure and the constant stress ratio.
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LI Haifang YinqiEngineering / Procedia Engineering 28 (2012) 796 – 802 Author and nameZHANG / Procedia 00 (2011) 000–000
6. Conclusion The creep characteristics of the Lianghekou mixture, the Zuoxiagou rockfill and the Xiaolangdi rockfill were analyzed through the same confining loading test and the constant stress ratio loading test. (1) The axial creep, the volume creep and their creep rates of the rockfill are linear with the time in a double logarithmic coordinate. It is suitable to describe the creep characteristics adopting power function. (2) The higher the stress level, the faster the axial creep rate in the condition loading of the same confining pressure. The volume creep rate is not the fastest at the high stress level because it is influenced by the compaction and the shearing dilation. (3) The higher the confining pressure, the faster the axial creep rate in the condition loading of the constant stress ratio. The characteristics of the volume creep rate are complex because they are influenced by the compaction and the shearing dilation. (4) There is a great gap between the curves of the axial or the volume creep and a line in single logarithm coordinate so that the logarithmic function would not be suitable to describe the creep. The curves of the creep rate are not straight lines in single logarithm coordinate, so the exponential function is inappropriate to describe the creep. References [1] YANG Jian. Sedimentation analysis of concrete facing rockfill dam of Tianshengqiao First-cascade Hydropower Station [J]. Yunan Water Power, 2001, 17(2): 59–63. [2] SHEN Zhujiang, ZUO Yuanming. Study on rheology chracterastics of rockfill [A]//Proc. of the 6th China soil mechanics and foundation engineering Conference [C]. Shanghai: Tongji University Press, 1991: 443–446. [3] SHEN Zhujiang, ZHAO Kuizhi. Back analysis of creep deformation of rockfill dams [J]. Journal of Hydraulic Engineering, 1998, (6): 1–6. [4] MI Zhankuan, SHEN Zhujiang, LI Guoying. Creep model for high concrete face rockfill dams [J]. Hydro-Science and Engineering. 2002, (2): 35–41. [5] WANG Yong, YIN Zongze, A rheology model of rockfill used in the rheology analysis of concrete face rockfill [J]. Rock and Soil Mechanics 2000, 21(3): 227–230. [6] WANG Yong. Analysis on rheology mechanism and study method of rockfill [J]. Chinese Journal of Rock Mechanics and Engineering. 2000, 19(4): 526–530. [7] WANG Yong, YIN Zongze. Analysis of effects of rockfill rheology on deformation and stress of force slabs of concrete face rockfill dams [J]. Journal of Hohai University. 2000,28(6): 60–65. [8] CHENG Zhanlin, DING Hongshun. Creep test for rockfill [J]. Chinese Journal of Geotechnical of Engineering, 2004, 26(4): 473–476. [9] Reiko Kuwano and Richard J. Jardine. On measuring creep behaviour in granular materials through triaxial testing [J]. Can. Geotech. J. 2002, 39: 1061–1074. [10] LIANG Jun, LIU Hanlong. Creep test for rockfill of CFRD [J]. Chinese Journal of Geotechnical Engineering. 2002, 24(2): 257–259 [11] LIANG Jun, LIU Hanlong, GAO Yufeng. Creep mechanism and breakage behaviour of rockfill [J]. Rock and Soil Mechanics. 2003, 24(3): 479–483 [12] LI Haifang, XU Zeping, WEN Yanfeng, CHEN Ning. Jiudianxia rockfill creep behavior and model study through triaxial creep test [J]. Journal of Hydroelectric Engineering, 2010, 29(6): 166–171. [13] LI Haifang, ZHANG Yinqi, JIN Wei, WEN Yanfeng, CHEN Ning. Study on the creep model at Lianghekou water power station of rockfill through triaxial creep test [J]. Northwestern Seismological Journal, 2011, 33(supp.1): 285–289. [14] LI Haifang, ZHANG Qincheng, XU Zeping, WEN Yanfeng, CHEN Ning. Xilongchi rockfill creep behavior and model study through triaxial creep test. Chinese Journal of Rock Mechanics and Engineering. 2009, 28(supp.2): 3376–3382.
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