Creep Rate and Creep Model of Rockfill

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

Full text

Procedia Engineering 28 (2012) 796 – 802
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
Available online at www.sciencedirect.com
Procedia
Engineering
Procedia Engineering 00 (2011) 000–000
www.elsevier.com/locate/procedia
2012 International Conference on Modern Hydraulic Engineering
Creep Rate and Creep Model of Rockfill
LI Haifang
a
, 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.
© 2011 Published by Elsevier Ltd.
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: lihf@iwhr.com .
© 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Society for Resources,
Environment and Engineering
Open access under CC BY-NC-ND license.
Open access under CC BY-NC-ND license.

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2 Author name / Procedia Engineering 00 (2011) 000–000
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 mega-
thick layer of siliceous quartz sandstone. Control of dry density of Lianghekou mixture, Zuoxiagou
rockfill and Xiaolangdi rockfill were 2.14g/cm
3
, 2.12g/cm
3
, 2.13g/cm
3
respectively. The gradations of the
rockfills were shown in Table1.
Table1. Gradations of rockfills (content less than particle size)
Particle size / mm
600
400
300
200
100
60
40
20
10
5
Mixture
natural gradation
100
82.5
69.5
56
41
31.5
26
17
10.5
5
gradation of sample
100
80.5
51.3
31.2
14.5
Zuoxiagou
natural gradation 100 92.5 88 77 61.5 51.5 44.5 34 25.5 17.5
gradation of sample 100 82.3 60.9 41.3 25.5
Xiaolangdi
natural gradation 100 87 80 70 57.8 45.5 38 29.9 22.5 16.3
gradation of sample 100 81.8 59.1 41.9 26.5
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 and ZHANG Yinqi / Procedia Engineering 28 (2012) 796 – 802
Author name / Procedia Engineering 00 (2011) 000–000 3
duration in every stress state was 7 days.
Table2. Test loading programs of rockfill
Test methods of loading Rockfill Confining pressure/MPa Stress level/Stress ratio
Same confining pressure
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
Constant stress ratio
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
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.
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.
t
ε
ε
Δ
Δ
=

(1)
With the end time of segments as the abscissa and the creep rate as the ordinate, the relationship
0.01
0.1
1
10
1
10
100
1000
10000 100000
Time/min
Stress level 0.2
Stress level 0.4
Stress level 0.6
Stress level 0.8
Axial creep /%
0.01
0.1
1
10
1
10
100
1000
10000
100000
Time/min
Volume creep /%
Stress level 0.2
Stress level 0.4
Stress level 0.6
Stress level 0.8

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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.
Fig.2. Relationship between creep rate and time of the mixture (same confining pressure) (a) Axial creep rate; (b) Volume creep rate
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
0.000001
0.00001
0.0001
0.001
0.01
1
10
100
1000
10000
100000
Time/min
Stress level 0.2
Stress level 0.4
Stress level 0.6
Stress level 0.8
Axial creep rate/%/min
0.000001
0.00001
0.0001
0.001
0.01
1
10
100
1000
10000
100000
Time/min
Stress level 0.2
Stress level 0.4
Stress level 0.6
Stress level 0.8
Volume creep rate /%/min
0.000001
0.00001
0.0001
0.001
0.01
1
10
100 1000
10000 100000
Time/min
Axial creep rate /%/min
Stress level 0.2
Stress level 0.4
Stress level 0.6
Stress level 0.8
0.000001
0.00001
0.0001
0.001
0.01
1
10
100
1000
10000
100000
Time/min
Volume creep rate/%/min
Stress level 0.2
Stress level 0.4
Stress level 0.6
Stress level 0.8

800 LI Haifang and ZHANG Yinqi / Procedia Engineering 28 (2012) 796 – 802
Author name / Procedia Engineering 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.
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
Fig.5. Relationship between creep rate and time of the mixture (constant stress ratio) (a) Axial creep rate; (b) Volume creep rate
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
0.01
0.1
1
10
1
10
100
1000
10000
100000
Time/min
Volume creep/%
2005
2010
2015
2020
2025
2030
0.01
0.1
1
10
1
10
100
1000
10000
100000
Time/min
Axail creep/%
2005
2010
2015
2020
2025
2030
0.000001
0.00001
0.0001
0.001
0.01
1
10
100
1000
10000
100000
Time/min
2005
2010
2015
2020
2025
2030
Axial creep rate/%/min
0.000001
0.00001
0.0001
0.001
0.01
1
10
100
1000
10000
100000
Time/min
2005
2010
2015
2020
2025
2030
Volume creep rate/%/min
0.000001
0.00001
0.0001
0.001
0.01
1
10
100
1000
10000
100000
2010
2015
2020
2025
2030
Axial creep rate/%/min
0.000001
0.00001
0.0001
0.001
0.01
1
10
100
1000
10000
100000
Time/min
2010
2015
2020
2025
2030
Volume creep rate/%/min
Time/min

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6 Author name / Procedia Engineering 00 (2011) 000–000
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].
b
0
）
t
t
a
（
ε 
(2)
In which t
0
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.
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.
0.000001
0.00001
0.0001
0.001
0.01
0
5000
10000
15000
20000
TIme/min
Axial creep rate/%/min
Stress level 0.2
Stress level 0.4
Stress level 0.6
Stress level 0.8
0.000001
0.00001
0.0001
0.001
0.01
0
5000
10000
15000
20000
TIme/min
Volume creep rate/%/min
Stress level 0.2
Stress level 0.4
Stress level 0.6
Stress level 0.8

802 LI Haifang and ZHANG Yinqi / Procedia Engineering 28 (2012) 796 – 802
Author name / Procedia Engineering 00 (2011) 000–000 7
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.
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