Li
Zhijun, Qu Yuexia, Wang Yongxue, Li Guangwei and
Shen Zhaowei
State Key Laboratory of Coastal and Offshore Engineering,
Dalian University of Technology, Dalian 116024
Tel: +86.411.4708514 or +86.411.4708520
Fax: +86.411.4708526
E-mail: lizhijun@dlut.edu.cn
Abstract:
Based on the statistical values of Bohai ice physical and mechanical parameters,
such as density, compressive strength, flexural strength, shear strength,
elastic modulus and friction coefficient, an ideal synthetic model ice was
designed following the scale of 1:10-1:30. An almost ideal model ice was found
and called DUT-1 Ice. In order to know DUT-1 Ice flexural strength in detail,
over 500 samples for a series of system tests were done. It is found that
ductile bending happens under less than 350~400 kPa/s in 3-Point bending and
60~65 kPa/s in cantilever bending. Their corresponding failure time are in the
range of 0.03~0.38s and 0.5~0.76s respectively. The failure time is in the range
of simulated natural ice flexural failure time. The comparison of flexural
strength of downward and upward loading cantilever tests gives the certification
of isotropy of the model ice because of its granular structure. After one hour
wetting, the flexural strength of 3-Point tested samples becomes steady and
keeps the state over 4 hours. This period is long enough for performing model
tests of ice behaviors or ice interactions with structures. Similar with natural
ice, DUT-1 Ice flexural strength is increasing with increased wetted density.
The flexural strengths from 3-Point bending and cantilever bending show almost
the same value range. In the normal distribution of their strengths, the scatter
of data from 3-Point bending is little larger. The middle value of the flexural
strength is 45 kPa and the range is 35~65 kPa. These values are suitable with
the requirement of 1:10~1:30 scale based on Bohai natural ice flexural strength
of 450~750kPa.
Keywords: polypropylene, synthetic model ice, flexural strength, experimental study
The
interaction of sea ice and structures is a complex process because of various
ocean environments. By now, no acknowledged math-physical model has been found.
Although the prototype observations are considered to be the most intuitionistic
first hand data, but they are costly and complex due to the overlap of
ice-breaking mechanism. Physical model tests belong to simply technology, and
have been developed greatly in model ices and technologies in recent decades
(Jones et al 1989, Timco 1992, Zufelt & Ettema 1996, Riska et al 1994). In
China, in order to meet the need of water engineering in North of China,
paraffin wax was used as model ice (Chen Chunjun 1983). In addition, two ice
basins were built for the operation of Bohai oil and gas. The urea-doped model
ice was quoted (Shi Qingzeng 1994). After summering the drawbacks of the two
kinds of model ices under Chinese weather conditions from science and economy
view and Beltaos’ SYG-Ice idea (Beltaos et al 1990).
Authors developed a new model ice prescription and making art in 1999, called
DUT-1 Ice. It was made by mixing polypropylene, white cement and water, and then
by molding and curing (Li Zhijun et al 2000a) and was designed based on the
physical and mechanical characteristic parameters of Bohai ice and followed the
scale of 1:10～1:30
(Li Zhijun et al 2000b). For meeting the requirement of environment protection
and resource reusing, the chosen raw materials are non-poisonous, innocuous,
non-corroded and reclaimable. The curing date is 7 days, which is less than that
of SYG-Ice. In order to testify the function and adaptable range of the new
model ice, a lot of physical and mechanical properties are measured and the
experiments on the interaction of the model ice with structures and waves are
conducted. Comparing with other model ices in the world (Timco, 1992, Zufelt
& Ettema, 1996), DUT-1 Ice is a suitable model ice for flexural-break cases
because its compressive is lower. This paper introduces the experimental results
of the model ice flexural strength. Also the effect on the strength from ice
making arts, test methods and wetted densities are discussed.
The samples to measure the flexural strength of DUT-1 Ice are 3-Point beams and cantilever beams. The 3-Point beam was 20mm thick, 30mm wide and 200mm long. A LVDT and a force sensor were put on the middle of a sample to measure relative deflection and load on the sample. 5~6 samples were put into a group and were tested in same speed of indention movement. Considering the instance of sample failure, the frequency of 100Hz was adopted to collect signals. By using the failure load, the flexural strength was calculated.
Cutting the three sides from a model ice sheet makes the samples of cantilever beam and the fourth side was intact with the ice sheet. The dimension range of the cantilever beam is L＝(4.0~7.5)h，B＝(1.75~2.10)h. Force is loaded on the free side of the cantilever beam until it was failed. During the process, a computer collected the force signals at the frequency of 100Hz. In the tests, six to ten beams were put into a group, and were loaded upward and downward in same indention movement.
The model ice is a homogeneous material because of its granular material. The 3-Point flexural strength was conducted over 300 samples so that the relation of flexural strength with stress rate and the stability of flexural strength with wetted time were testified systematically. The cantilever beams were tested over 200 in 4 groups in order to testify the isotropy of DUT-1 Ice and the influence of stress rate and wet density on the strength.
Figure
1 shows the load and the deflection curves of a 3-Point beam. These curves are
the same as the flexural loading process of general solid materials. Figure 2
shows the upward and the downward load-curves of two cantilever beams. During
the downward loading, the force on the sample raises from point A to B with
loading indention movement. When the sample is failing, the force lows to point
C. Later the force increases from point C to D with the motion of broken pieces
because of the associated action of buoyancy and gravity. Then it decreases from
point D to E with the ice beam broken off entirely. The process of upward is
like the downward, namely point A’, B’, C’, D’, E’. Jointing point C,
A or point C’, A’, the force value corresponding to B or B’ is the
buoyancy. When compared the flexural strength of the cantilever and the 3-Point
supporting beam, the effect of buoyancy must be removed.
Fig. 1 Test cures of a 3-Point beam
(a) downword process (b) upward process
Fig. 2 Loading curves of cantilever beams
Like the natural ice and the refrigerated model ice, the flexural strength of DUT-1 Ice depends on stress rate, which resembles the experiment relation of sea ice near the Yellow River Entrance (Sui Jixue, et al 1996). The flexural strength increases with the increase of stress rate firstly, and then it has the largest value at certain stress rate. At last the strength decreases with the increase of stress rate. The 3-Point flexural strengths of DUT-1 Ice suggest that the peak flexural strength happens at 350~400kPa/s and the relevant speed of indention is 0.8~1.0mm/s, and the corresponding flexural failure time is 0.03~0.38s. For the cantilever beams, the peak flexural strength occurs at 60~65kPa/s, the relevant speed of indention is 2.46mm/s and the failure time is 0.5~0.76s (seen Figure 3). Unlike the case of 3-Point beams, the load on the cantilever beam can be attributed to the load on the elastic base beam, so the stress rates at peak flexural strength are different in Figure 3a and Figure 3b, but their failure times are approximate.
It is advised that the flexural failure time of natural sea ice is between 1~2s (IAHR Working Group on Ice Problems 1980, Schwartz et al 1981). If the scale of model ice is 1:10~1:30, the corresponding failure time of the model ice is 0.18~0.63s. The measured failure times of DUT-1 Ice are almost in the range mentioned above, which is agree with the fine grain ethanol model ice (Jolonen & Ilves 1990, Li Zhijun & Riska 1999)
.
(a) 3-Point beam (b) cantilever beam
Fig. 3 Limited flexural strength vs. strength rate
The loading process of cantilever beam can evaluate the buoyancy effect on flexural strength (seen Figure 2). The buoyancy exists in the interaction of ice and ships or offshore structures. In practice, the buoyancy can be omitted. From the above, it is better to use the flexural strength with the buoyancy in engineering. If only to compared the test results of cantilever beams with those of 3-Point beams, the effect of the buoyancy must be removed. From the results of cantilever tests, it can be seen that when the downward loads are exerted on cantilever beams, the flexural strengths with the buoyancy are 1.03~1.21 times, the average 1.07 times over the flexural strengths without the buoyancy. And when the reverse loads are exerted, the flexural strengths with the buoyancy are 1.03~1.27 times, the average 1.12 times over the flexural strengths without the buoyancy.
Because of the difference of temperature gradation and crystal structures of natural ice sheets, there are different between the upward and the downward flexural strengths of cantilever beams in-situ. The flexural strength difference results from the tensile strength difference between field ice sheet surface and bottom (Sui Jixue, et al 1988,1996). Even though the crystal structure of an ice sheet is same from its surface to bottom, the tensile strengths at its surface and bottom are still different because of the temperature gradation in the ice sheet. DUT-1 Ice belongs to a homogeneous material and has no the difference of temperature and structure. It should be no difference between the downward and the upward flexural strengths of cantilever beams when the effect of buoyancy is removed (Jolenen & Ilves 1990). Figure 4 shows the relation of the downward and the upward flexural strengths and it can be seen that the DUT-1 Ice is an isotropy.
Fig.
4 Relation of flexural strengths
Fig. 5 Changing of average flexural strength
up-ward and down-ward loading with wetted time
The flexural strength results of 3-Point samples in different wetted time are showed in Figure 5. It can be seen that after one hour wetted in water, the strength of DUT-1 Ice keeps stable and can remain for four hours. The duration is longer enough to conduct model tests with uniform flexural strength.
Like natural ices and refrigerated model ices, the peak flexural strength of DUT-1 Ice is controlled by its physical index. Wet densities of DUT-1 Ice reflect the porosity of the model ice. Figure 6 shows that the peak flexural strength of DUT-1 Ice increases with the increase of wet density in the range of wet densities.
Fig. 6 Relation of flexural strength with wetted density
Like the natural ice, the flexural strengths of DUT-1 Ice change with the flexural stress rate and the corresponding failure time of peak flexural strength happened is the same as the refrigerated fine grain ethanol model ice.
The relation of flexural strengths of downward and upward loading of cantilever beams shows that the DUT-1 Ice is an isotropy material. In the range of the measured wet density, the flexural strengths of the model ice increase with the increase of wet density.
The flexural strengths of DUT-1 Ice are controlled by cement, and the measured flexural strengths are in the range of 35~65kPa. Because the flexural strength of Bohai sea ice is about 700kPa, the model ice can be used in the experiments in which the scale is 1:10～1:30.
After one hour in water, the flexural strengths
of DUT-1 Ice keep stable and can remain four hours, which provides the plenty
time to perform physical model tests with uniform strengths.
Acknowledgements
This study was financially supported by China Excellent Youth Fund (59725919) and China Postdoctoral Science Foundation (98-6).
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