INVESTIGATING THE MECHANICAL BEHAVIOR OF MUDSTONE SUBJECTED TO CYCLICAL LOADING
Po-Ying Chen1*, Der-Her Lee2, Jian-Hong Wu3, Jun-Jie Chen4
ABSTRACT
Mudstone is classified to be a weak rock and is extensively distributed in southwestern Taiwan. It has high compressive strength under dry situation but slakes easily when it absorbs water because of its short digenesis and poor cementation. Therefore, tunnel construction in mudstone areas will face this special mechanical behavior. On the other hand, the stability of a tunnel not only relates to the mechanical responses of the surrounding rocks when they are subjected to the static/dynamic loadings. Consequently, the dynamic mechanical behavior of mudstone is an essential property for tunnel maintenances, as well as safety of traffic and disaster preventions. In this study, a series of cyclic loading tests have been performed to investigate the mechanical behavior of mudstone under dynamic impact.
Key Words: Tunnel, Cyclic loading, Weak rock
INTRODUCTION
Taiwan is located on the western edge of the Circum-Pacific seismic zone, and was formed with the Philippine Sea and Eurasian plates collision. Hence, faults and steep mountains are not only a major feature of Taiwan’s geological condition, but also are important factors that affect the livelihood of our public construction projects. Because two-thirds of Taiwan’s total area is the mountainous terrain, space available for development and utilization is very limited.
Although the metropolitan area can use tall buildings to attain residential and business spaces,
1 PHD Condicate, Department of Civil Engineering, National Cheng-Kung University, Tainan 701, Taiwan.
(*Corresponding Author, Tel: +886-6-2757575-63156; Email:n6895108@mail.ncku.edu.tw)
the rapid urban and rural networks of roads, storage facilities, railway construction, water transportation facilities, energy generating facilities, nuclear fuel disposal and other major public works related to people's livelihood use underground excavation work quite a lot.
On the other hand, faults or plate activity induced earthquakes is a highly concerned issue to civil engineering in Taiwan. Especially the 921 Chi-Chi earthquake (magnitude 7.3) in 1999 caused multiple houses and numerous livelihood facilities damage, and caused more than 2,000 dead. Subsequently the 331 earthquake (magnitude 6.8) happened off the coast of Hualien in 2002, and the 2006 Hengchun earthquake (magnitude 7.0), also caused many disasters. Therefore, when rocks adjoining to the underground space development subject to the cyclic loading, the mechanical behavior are the key engineering problem and cannot be ignored. Moreover, strata in the foothills of southwestern Taiwan are cosisted of poorly
2 Distinguished Professor, Department of Civil Engineering, National Cheng-Kung University, Tainan 701, Taiwan.
cemented rocks of tertiary sandstone, mudstone and alternating sandstone-mudstone.
Mudstone being the test material in this study, while Gutingken mudstone is the most wide-spreaded rocks in the foothills of
0.01 0.1 1 10 100 1000
Very
soft Soft Film Stiff Very stiff Hard
Extremely
weak Very weak Weak Med
strongStrong Very strong
Extremely strong Clay
Rocks
Uniaxial compressive strength (Mpa)
southwestern Taiwan. Gutingken mudstone is a weak marine sedimentary rock which consists of clay and silt and can easily be decomposed by water because of its poor cementation. Lee (2008) reported that the uniaxial compressive strength of Gutingken mudstone is 20MPa and can be classified as Weak rocks (Fig. 1) under the air-dried condition (water content, w=1-2%). However, under high water content condition (w=9-10%) it is classified as Very weak rocks (Fig. 1) because of its low uniaxial compressive strength 3~4MPa. Therefore, understanding the mechanical behavior of Gutingken mudstone under different water contents has become a primary issue, especially in the cyclic load conditions and high moisture content when performing undergroud excavation works at this mudstone.
Fig. 1 ISRM classification for geotechnical materials (Brown, 1981)
SPECIMEN & TEST METHOD Specimen preparation
The test rocks were taken from a mudstone slope at Tienliao, Kaohsiung County. Specimens are circular cylinders having a height to diameter ratio of 2.0 and a diameter NX-size 5.4 cm. In order to overcome the collapses of mudstone drilling with water, the air-drilling method was applied to obtain samples. A summary of the basic index properties of Gutingken mudstone is illustrated in Table 1. The dry unit weight is 21.07~22.05kN/m3 and specific gravity is 2.71. Furthermore, water softens mudstone, and its behavior is similar to clay.
Hence, in order to know the Atterberg limits of the Gutingken mudstone, it can used the hydrolysis mudstone specimen to carry out the Atterberg test. The experimental results indicate that the liquid limit, plastic limit, and plastic index are 40.4%, 21.5% and 18.9%, respectively. Fig. 2 is the Grain size distribution curve of Gutingken mudstone, it shows that the mudstone is made up of 4.4 % of sand, 70.6 % of silt and 25.0 % of clay.
Table 1 Basic properties of Gutingken mudstone
Properties Gutingken mudstone
Specific gravity, Gs 2.71
Dry unit weight, γd (kN/m3) 21.07~22.05
Void ratio, e 0.21~0.26
Liquid limit (%) 40.4 Plastic limit (%) 21.5 Plaxtic index (%) 18.9
10 1 0.1 0.01 0.001 0.0001 Diameter of particle in millimeters
0 20 40 60 80 100
Percent passing by weight
GRAIN SIZE DISTRIBUTION TEST REPORT
GRAVEL SAND SILT CLAY
Fig. 2 Grain size distribution of Gutingken mudstone
According to three-phase relationships and Table 1, if the saturation degree is assumed equal to 1.0, then the theory saturated water content of Gutingken mudstone is 7.7%~9.6%. Hence, four water content conditions of 0 %, 1-2%, 4-6% and 9-10 % were conducted to understand the mechanical behavior of the Gutingkeng mudstone under cyclic loading in this study. The water content control methods are shown as follows:
1. 0%：Put the samples in an oven for 24 hr. (105℃).
2. 1-2%：Place the samples at room temperature(25℃) for more than 15 days.
3. 4-6%：Put the samples with water content of 9-10 % into a box with constant temperature and humidity (23℃, Relative humidity 90%
4. 9-10%：Because absorbs water will produce mudstone swell phenomenon, and the swelling pressure is 450 kPa, so place samples in the triaxial cell 4 days with confining pressure of 700 kPa and back pressure of 250 kPa to avoid mudstone swell by absorbing water.
). When the weight of sample equals the estimated weight, it can be removed from the test.
Mechanical parameters of Gutingken mudstone
The mechanical behavior of Gutingken mudstone changes obviously under different water contents. From a series of static uniaxial compressive tests and consolidated-undrained triaxial tests with displacement rate 0.2mm/mim, the stress-strain curves of the mudstones are shown in Fig. 3 and Fig. 4. According to Fig. 3, when the water content increases from 0% to 9-10%, the uniaxial compressive strength of Gutingken mudstone will reduce from 39.6 MPa to 3.5 MPa, and the failure strain increases from 1.42% to 2.5%. Fig. 5 illustrates the peak strength mohr’s circles and the failure envelopes under different water contents of Gutingken mudstone. When the water content increases from 0% to 9-10%, the peak shear strength parameters reduce from cp=15.50MPa, φp=26.1o to cp=2.90MPa, φp=13.1o and the residual strength parameters reduce from cr=4.14MPa,φr=31.0o to cr=2.70MPa, φr=11.0o.
25.0%
95.6% 100.0%
0 1 2 3 4 5 Axial Strain (%)
0 10 20 30 40 50
Uniaxial compressive strength,qu (MPa) Water content 0%
1-2%
4-6%
9-10%
Fig. 3 Results of mudstone uniaxial compressive tests under different water contents
Fig. 4 Stress-Strain curves of mudstone triaxial tests (a) w=0% (b) w=1~2% (c) w=4~6% (d) w=9~10%
Water content 0%
cp:15.5 MPa, φp:26.1o cr:4.7 MPa, φr:30.2o
Peak Mohr's circle Residual Mohr's circle Peak criteria Residual criteria
-30 0 30 60 90 120 150 180 210 240 270
Normal stress,σ (MPa) 0
30 60 90 120 150 180
Shear stress,τ (MPa)
-10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Normal stress,σ (MPa)
0 10 20 30 40 50 60 70 80 90 100
Water content 4-6%
cp:4.7 MPa, φp:20.7o cr:1.9 MPa, φr:22.6o Peak Mohr's circle Residual Mohr's circle Peak criteria Residual criteria
Shear stress,τ (MPa)
Water content 1-2%
cp:9.3 MPa, φp:22.4o cr:4.6 MPa, φr:24.6o Peak Mohr's circle Residual Mohr's circle Peak criteria Residual criteria
-30 0 30 60 90 120 150 180 210 240 270
Normal stress,σ (MPa) 0
30 60 90 120 150 180
Shear stress,τ (MPa)
Water content 9-10%
cp:1.8 MPa, φp:18.5o cr:1.6 MPa, φr:15.7o Peak Mohr's circle Residual Mohr's circle Peak criteria Residual criteria
-10 0 10 20 30 40 50 60 70 80
Normal stress,σ (MPa) 0
10 20 30 40 50
Shear stress,τ (MPa)
Fig. 5 Peak Mohr’s circle of Gutingken mudstone (a) w=0% (b) w=1~2% (c) w=4~6% (d) w=9~10%
Cyclic loading test procedure
In order to understand the Mechanical behavior of Gutingken mudstone under the large amplitude vibrates. This study uses the amplitude of stress ratio (SR) equal to 0.95 of the cyclic loading to test. Besides, the cyclic loading test is similar to the creep test, when the loading imposes on the specimen, it will accumulate the specimen axial strain and make the specimen failures finally. So, if the specimen failures under the cyclic loading or gets into the secondary creep stage that the cyclic loading will stop. Furthermore, if the specimen does not failure under the cyclic loading procedure, the static loading test will carry out to understand the change of mechanical behavior of mudstone. The test procedure of cyclic loading and test sets listed in Table 2, Fig.6 is a schematic for cyclic loading test procedure.
(a) (b) (c) (d)
(a) (b)
(c) (d)
(1)
(2) The deviator stress is increased to stress ratio (SR) of 0.95 under the stress rate of 5MPa/min.
First, the confining pressure is increased to a certain value, and use the servo control system to stabilize confining pressure during the test.
1 3 dc
1 3 sf
( )
SR
( )
σ − σ
= σ − σ (1)
Where (σ1-σ3)sf
(σ is the peak deviator stress of static triaxial tests.
1-σ3)dc
(3) Imposed the 5000 cycles of loadings on the specimen in 0.5 Hz and the amplitude is equal to stress ratio (SR) of 0.95. (5000 cycles can let the specimen gets into the secondary creep stage.)
is the cyclic deviator stress of cyclic loading tests.
(4) If the specimen does not failure in the stage (3), then proceed additional static triaxial test with displacement rate 0.2mm/mim.
Deformation behaviour of mudstones under cyclic loading
Fig. 7 shows the stress-strain curve of mudstones under cyclic loading. The total deformation (εt) of mudstone includes elastic deformation (εe) and the plastic deformation (εp) in a certain cycle. When the external force is removed, the elastic deformations of rocks can recovery but the plastic deformation cannot. Therefore, the plastic deformation will be accumulated continuously under the cyclic loading and finally resulting in specimen failure.
Table 2 Cyclic loading tests
NO. Water content (%)
Confine pressure (MPa)
Frequency (Hz)
Amp.
(SR)
DT-A 0 5, 10, 20
0.5 0.95
DT-B 1~2 5, 10, 20
DT-C 4~6 5, 10, 20
DT-D 9~10 5, 10, 20
Fig. 6 Test procedure of cyclic loading
εp εe
εt σ
ε Yield point
Fig. 7 Deformation of rocks under cyclic loading
TEST RESULTS
Fig. 8 show stress-strain of mudstone cyclic loading tests under different water contents, the
loading test results indicate that lower water content of mudstone specimen perform destructive phenomenon. The mudstone specimen with water content=0% have destructive phenomenon under confining pressures of 5MPa, 10MPa and 20MPa. Mudstone specimen with water content=1-2% have destructive phenomenon under confining pressure 10MPa only.
However, if the water content goes up to 4-6% and 9-10%, the destructive phenomenon cannot be observed. Then, the un-failed mudstone specimen after cyclic loading 5000 cycles will proceed to the static triaxial test. Table 3 shows results of cyclic loading tests, in the table, σpeak,s is the peak strength of mudstone under static triaxial tests and σpeak,d
0 2 4 6 8 10
Axial Strain (%) 0
50 100 150
Deviator Stress (MPa) DT-A3Water content 0%
σ3=20MPa f=0.5Hz SR=0.95
0 2 4 6 8 10
Axial Strain (%) 0
50 100 150
Deviator Stress (MPa) DT-A2Water content 0%
σ3=10MPa f=0.5Hz SR=0.95
0 2 4 6 8 10
Axial Strain (%) 0
50 100 150
Deviator Stress (MPa) DT-A1Water content 0%
σ3=5MPa f=0.5Hz SR=0.90
is the peak strength of mudstone after cyclic loading 5000 cycles. Moreover, the peak strength of mudstone proceeded 5000 cycles of cyclic loadings is higher than those of the static triaxial tests. The strengths of the cyclic loaded specimen with water content 1-2%, 4-6%, 9-10%
have 20%, 10-16% and 16-44%, respectively, higher than the static triaxial test results. Cyclic loaded mudstone specimen having higher peak strengths come to the following two reasons, (1) the cyclic loading closes the pores inside the specimen, (2) the amplitude of cyclic loading is below the stress ratio 0.95 for the specimen with water content 4-6% and 9-10%, it means the mudstone specimen may have the higher strength originally.
0 2 4 6 8 10
Axial Strain (%) 0
20 40 60 80 100
Deviator Stress (MPa) DT-B3Water content 1-2%
σ3=20MPa f=0.5Hz SR=0.90
0 2 4 6 8 10
Axial Strain (%) 0
20 40 60 80 100
Deviator Stress (MPa) DT-B2Water content 1-2%
σ3=10MPa f=0.5Hz SR=0.95
0 2 4 6 8 10
Axial Strain (%) 0
20 40 60 80 100
Deviator Stress (MPa) DT-B1Water content 1-2%
σ3=5MPa f=0.5Hz SR=0.95
0 2 4 6 8 10
Axial Strain (%) 0
10 20 30 40 50
Deviator Stress (MPa)
DT-C3 Water content 4-6%
σ3=20MPa f=0.5Hz SR=0.95
0 2 4 6 8 10
Axial Strain (%) 0
10 20 30 40 50
Deviator Stress (MPa) DT-C2Water content 4-6%
σ3=10MPa f=0.5Hz SR=0.95
0 2 4 6 8 10
Axial Strain (%) 0
10 20 30 40 50
Deviator Stress (MPa)
DT-C1 Water content 4-6%
σ3=5MPa f=0.5Hz SR=0.95
0 2 4 6 8 10
Axial Strain (%) 0
10 20 30 40
Deviator Stress (MPa) DT-D3Water content 9-10%
σ3=20MPa f=0.5Hz SR=0.95
0 2 4 6 8 10
Axial Strain (%) 0
10 20 30 40
Deviator Stress (MPa) DT-D2Water content 9-10%
σ3=10MPa f=0.5Hz SR=0.95
0 2 4 6 8 10
Axial Strain (%) 0
10 20 30 40
Deviator Stress (MPa) DT-D1Water content 9-10%
σ3=5MPa f=0.5Hz SR=0.95
Fig. 8 Stress-strain curves of mudstone cyclic loading tests (a) w=0% (b) w=1-2% (c) w=4-6% (d) w=9-10%
Table 3 Results of cyclical loading tests
NO.
Water content
(%)
Confining Pressure
(MPa)
Peak strength
of triaxial
tests (MPa)
Failure Strain of cyclic
loading tests (%)
Peak strength of cyclic loading tests
Number of cycles σ
(MPa)
peak,s σ (MPa)
peak,d
(%) DT-A1
0
5 57.3 2.84 54.4 -- -- 15
DT-A2 10 71.8 2.60 68.2 -- -- 29
DT-A3 20 88.4 4.83 84.0 -- -- 122
DT-B1
1-2
5 31.4 2.26 31.4 37.9 +21 5000
DT-B2 10 45.0 2.56 42.8 -- -- 31
DT-B3 20 58.0 3.74 58.0 69.3 +19 5000
DT-C1
4-6
5 20.3 2.34 20.3 22.4 +10 5000
DT-C2 10 25.5 4.30 25.5 28.5 +12 5000
DT-C3 20 36.5 6.88 36.5 42.2 +16 5000
DT-D1
9-10
5 10.7 3.90 10.7 12.4 +16 5000
DT-D2 10 16.4 3.72 16.4 21.0 +28 5000
DT-D3 20 22.4 3.66 22.4 32.3 +44 5000
(a) (b) (c) (d)
Using results of mudstone static triaxial tests and cyclic loading tests can calculate the static peak failure envelope and the dynamic peak failure envelope. Fig. 9 illustrates stress paths of cyclic loading tests, the static and the dynamic peak failure envelopes. In the fig., the black dashed line is the static peak failure envelope, the red dashed line is the dynamic peak failure envelope, and according to the Fig. 9 to have the following descriptions:
1. Cyclic loading causes 0% water content of mudstone specimen to be broken, then the major and minor stresses when the specimen broken is used to calculate the dynamic peak envelope. The static and dynamic peak envelopes are almost the same. Furthermore, all stress paths contact the static peak failure envelope while specimen breaks.
2. Mudstone specimen with water content=1-2% fails when the confining pressure is 10MPa, and just one stress path contacts the static peak failure envelope. Therefore, in calculating the dynamic peak failure envelope only when the confining pressure 10 MPa by using the stress state at specimen broken, while the peak strength data of the confining pressure 5MPa and 20MPa are results of cyclic loading tests. The result shows that the gradient of the static peak failure envelope is slightly larger than that of the dynamic peak failure envelope, but the intercept to the vertical axis of the dynamic peak failure envelope is slightly larger than the static one.
3. When the water content are 4-6% and 9-10%, stress paths of the dynamic tests touch the static peak failure envelope, but specimens are not failure. High strength samples or the increasing strength due to cyclic loadings are expected to be the reasons that the Gutingken mudstone samples with high water content condition do not accumulate the axial deformation and do not fail under the designed loading amplitude. Besides, the gradient and the intercept of the dynamic peak failure envelope are clearly larger than those of the static one. The result shows that at the higher water content conditions, the static peak failure envelope is not the same as the dynamic.
Fig. 10 is the strain-N curve, the solid line indicates total strain, the dashed line is plastic strain, and the solid-dashed line is elastic strain. Fig. 10 shows that the total and plastic strains increase with increasing number of cycles. On the other hand, when specimen is subjected to cyclic loadings, specimen have certain elastic strain, when the water content of the specimen is 0% the strain is at 0.75% ~ 1.04%. When the water content is 1-2%, the strain is at 0.47% ~ 0.75%; while the water content is 4-6%, the strain is at 0.28% ~ 0.54%. When the water content is 9-10%, the strain is at 0.16% ~ 0.32%. The elastic strain of mudstone decreases with increasing the water content showing that mudstone specimen behaves larger plastic strain under the high water content. In addition, confining pressure increases the specimen stiffness and increases the elastic strain of mudstone specimen as the increasing confining pressure.
0 30 60 90 120 150
0 30 60 90 120 150
σ1 (MPa)
Mudstone peak criteria Water content 0%
Dynamic Static
q p
) ( 2 2σ =2 σ3MPa 510
Confining pressure 20 104
78.2 59.4
σ1=2.02*sqrt(2)*σ3+47.14 σ1=2.06*sqrt(2)*σ3+46.5
0 20 40 60 80 100
0 20 40 60 80 100
σ1 (MPa)
Mudstone peak criteria Water content 1-2%
Dynamic Static
p q
510
Confining pressure 20 42.9
52.8 89.3
) ( 2 2σ =2 σ3MPa σ1=2.24*sqrt(2)*σ3+24.65
σ1=2.47*sqrt(2)*σ3+19.63
(a) (b)
0 20 40 60 80 0
20 40 60 80
σ1 (MPa)
Mudstone peak criteria Water content 4-6%
Dynamic Static
) ( 2 2σ =2 σ3MPa
p q
5 10
Confining pressure 20 27.4
38.5 62.2 σ1=1.65*sqrt(2)*σ3+15.55
σ1=1.47*sqrt(2)*σ3+13.66
0 10 20 30 40 50 60
0 10 20 30 40 50 60
σ1 (MPa)
Mudstone peak criteria Water content 9-10%
Dynamic Static
) ( 2 2σ =2 σ3MPa
p q
5
Confining pressure 20 17.4
31.0
10 52.3
σ1=1.36*sqrt(2)*σ3+5.17 σ1=1.63*sqrt(2)*σ3+6.75
Fig. 9 Dynamic stress path (a) w=0% (b) w=1-2% (c) w=4-6% (d) w=9-10%
1 10 100 1000
Number of cycles, N 0
2 4 6 8 10
Axial Strain (%)
Water content 0%
σ3=5MPa σ3=10MPa σ3=20MPa
Total Strain Plastic Strain Elastic Strain
1 10 100 1000 10000
Number of cycles, N 0
2 4 6 8 10
Axial Strain (%)
Water content 4-6%
σ3=5MPa σ3=10MPa σ3=20MPa
Total Strain Plastic Strain Elastic Strain
1 10 100 1000 10000
Number of cycles, N 0
2 4 6 8 10
Axial Strain (%)
Water content 1-2%
σ3=5MPa σ3=10MPa σ3=20MPa
Total Strain Plastic Strain Elastic Strain
1 10 100 1000 10000
Number of cycles, N 0
1 2 3 4 5
Axial Strain (%)
Water content 9-10%
σ3=5MPa σ3=10MPa σ3=20MPa
Total Strain Plastic Strain Elastic Strain
Fig. 10 Strain-N curve (a) w=0% (b) w=1-2% (c) w=4-6% (d) w=9-10%
External force deforms the rocks. When a rock specimen is subjected to cyclic loadings, the stress-strain curve performs hysteresis loops. In the energy point of view, when an external energy is given to a specimen, a recoverable elastic energy will be saved, and the other part of non-recoverable plastic energy will be dissipated. The plastic energy generally consumes in viscosity, plasticity, and soak, etc. in the form of heat divergence. The energy dissipation is often discussed by the concept of damping ratio and with the area of the hysteresis loop. Fig.
11 illustrates the relationship between damping ratio and number of cycles. In the fig., Gutingken mudstone subjected to cyclic loading but does not yet break under the water content of 0% and 1-2%, its damping ratio will decrease with the cycle increase. It is because that pores inside specimen are mostly filled by the air with low water content. These pores are closed to accumulate less axial strain, hence, the area of the hysteresis loop decreases. So the damping ratio has slightly downward trend and has a smaller plastic energy. However, when the cyclic loading fails the specimen, the axial strain accumulates rapidly increase the area of the hysteresis loop and increases the damping ratio, meaning a large number of internal energy is consumed to the specimen. In addition, with the water content increasing to 4-6%
and 9-10%, pores inside specimen are mostly filled by the water. Pores closure has been insignificant, and the damping ratio maintains at a certain range. Furthermore, the confining pressure affecting the damping ratio becomes significant with the increasing water content.
Damping ratio has insignificant difference with low water content (0% & 1-2%) under
(c) (d)
(a) (b)
(c) (d)
different confining pressures. But, with high water contents (4-6% & 9-10%), damping ratio decreases as the increasing confining pressures because high confining pressure gives a better confining force and reduces the hysteresis loop area.
1 10 100 1000 10000
Number of cycles,N 0
20 40 60 80 100
Damping ratio,D (%)
Water content 0%
σ3 = 5 MPa σ3 = 10 MPa σ3 = 20 MPa
1 10 100 1000 10000
Number of cycles,N 0
20 40 60 80 100
Damping ratio,D (%)
Water content 4-6%
σ3 = 5 MPa σ3 = 10 MPa σ3 = 20 MPa
1 10 100 1000 10000
Number of cycles, N 0
20 40 60 80 100
Damping ratio, D (%)
Water content 1-2%
σ3 = 5 MPa σ3 = 10 MPa σ3 = 20 MPa
1 10 100 1000 10000
Number of cycles,N 0
20 40 60 80 100
Damping ratio,D (%)
Water content 9-10%
σ3 = 5 MPa σ3 = 10 MPa σ3 = 20 MPa
Fig. 11 D-N curve (a) w=0% (b) w=1-2% (c) w=4-6% (d) w=9-10%
CONCLUSION
(1) The cyclic loading test results indicate that the numbers of cyclic loading increases to fail the dried (water content 0%) Gutingken mudstone specimen as the increasing confining pressures. In addition, when the water content of the specimen increases, Gutingken mudstone produces viscosity behavior that is like clay. So that plastic strain of specimen increases but the elastic strain decreases under cyclic loadings.
(2) The peak strength of Gutingken mudstone after cyclic loading 5000 cycles are higher than results of the static triaxial tests, the water content 1-2%, 4-6%, 9-10%, respectively, about 20% higher, 10-16% and 16-44%.
(3) The cyclic loading tests result shows that the static and dynamic peak envelope is almost the same with water content of 0%. With the water content of 1-2%, the gradient of the static peak failure envelope is slightly larger than that of the dynamic one. But the intercept to the vertical axis of the dynamic test results are slightly larger than that of the static one. Moreover, when the water contents are 4-6% and 9-10%, the static peak failure envelope is not the same with the dynamic one.
(4) Gutingken mudstone subjected to cyclic loading but yet to broken under the water content of 0% and 1-2%, its damping ratio will decrease with the cycle increase. So, the damping ratio has slightly downward trend and has a smaller plastic energy. However, when the cyclic loading fails the specimen, the axial strain accumulates rapidly to increasing the area of the hysteresis loop, increasing the damping ratio. In addition, with the water content increases to 4-6% and 9-10%,
(5) The confining pressure affects the damping ratio insignificantly with the low water content (0% & 1-2%) samples under different confining pressures. Oppositely, the
the damping ratio maintains at a certain range.
(a) (b)
(c) (d)
content conditions (4-6% & 9-10%).
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