Cold Regions Science and Technology 71 (2012) 34–43

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Cold Regions Science and Technology

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Design ice load for piles subjected to ice impact

Jiwu Dong ⁎, Zhijun Li, Peng Lu, Qing Jia, Guoyu Wang, Guangwei LiState Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China

⁎ Corresponding author. Tel.: +86 411 84708271; faE-mail addresses: dongjiwu@yahoo.cn (J. Dong), lizh

lupeng@dlut.edu.cn (P. Lu), jiaqing6912@sina.com.cn (Q(G. Wang), lgw1955@163.com.cn (G. Li).

0165-232X/$ – see front matter © 2011 Elsevier B.V. Aldoi:10.1016/j.coldregions.2011.11.002

a b s t r a c t

a r t i c l e i n f o

Article history:Received 25 November 2010Accepted 1 November 2011

Keywords:Sea iceDesign loadCylinder pilesEnvelope methodModel test

Design loads of offshore structures for ice-covered seas are typically based on ice-crushing approach. It al-ways, therefore, makes the design conservative, especially for the loads on vertical offshore structuresexerted by moderate ice mass. Taking the case of sheet-pile-type pier, we conducted a series of tests of iceloads on cylindrical piles subjected to the impacts of drifting ice. The objective is to develop the relationshipbetween ice kinetic energy and the impact force, and finally to establish the design ice load for the piles. Anenvelope of logarithm curve was applied to determine the design load on the piles. The envelopes of ice forcewith known compressive strengths with respect to ice kinetic energy were used to determine the expectedpeak loads. The expected peak loads with different ice uniaxial compression strength were used to form an-other envelope to establish the design load on an individual pile for a special compressive strength. With thesame approach, the total ice force on one pier unit was obtained from an envelope curve. The design load onan individual pile can be applied to real ice as its scaled kinetic energy and compressive strength range from0 to 0.8 J and 30 to 90 kPa. Considering the large force on the corner pile, special tests of force against the pilewere conducted. The results showed that the design load on the corner pile is 0.78 times that of one dockunit, and 1.69 times that of the other six piles. Therefore, the corner pile should be reinforced in engineeringapplications.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

In winter production activities in cold regions are usually infestedwith sea ice. Consequently, ice load is considered a significant factorin designing marine structures in ice-infested waters (Li et al., 2008;Yang, 2000). The jacket platform on a piled foundation is the mostcommon structure for oil exploring platforms (Ou et al., 2007). Ithas been demonstrated that when large ice masses with high kineticenergy collide with vertical-sided structures (i.e. lighthouses, bridgepiers and pile-supported offshore platforms), ice floes fail in crushingat contact surfaces. Intensive researches have been focused on de-signing and managing these structures against ice damage in recentyears (i.e. Eik, 2011). In ice-covered waters, the design load of verticaloffshore structures is typically based on a static ice-crushing force(API RP 2N, 1995; MTPRC, 1998), which is only appropriate whenconsidering the effects of static ice crushing on structures by largeice floes. However, in situ observations of ice crushing are difficult.The field measurements by Cornett and Timco (1998) demonstratedthat ice crushing loading events on the Molikpaq oil platform at theAmauligak I-65 site in the Canadian Beaufort Sea occupied 1.1% ofthe interactions. Impacts occur more easily when ice floes are small

x: +86 411 84708526.ijun@dlut.edu.cn (Z. Li),. Jia), wanggyu@dlut.edu.cn

l rights reserved.

or of low kinetic energy. Consequently, the static crushing approachis possibly overly conservative in ice load design.

Determinations of the impact load from the interaction of ice floeson offshore structures can be very complex (Ibrahim et al., 2007). Theload depends on geographical location, ice type, interaction scenarioand structural configuration, etc. Several methods have been pro-posed for determining impact load on piles by previous studies. Statis-tical techniques (Bekker et al., 2007; Timco and Frederking, 2004) arethought to be effective in predicting or determining ice loads for off-shore structures. Based on the analysis of more than 170 loadingevents, Timco and Johnston (2004) suggested that predicted totalload on caisson structures in the Canadian Beaufort Sea correspondedto a variety of ice failure modes. Enns and Smith (1984) gave an opti-mal design strength for a platform subjected to collision of ice floes oricebergs, using an approach of probability distribution and energyconservation. However, the type of ice-structure impact was nottaken into account. Morland (1996) studied the direct impact ofrigid structures and viscoelastic ice under wind and ocean drag at alow flow velocity. However, central collision from direct impact sel-dom occurs under normal circumstances, and eccentric impact is farmore likely to occur. It has been demonstrated that an eccentric im-pact leads to a notable decrease in themaximum loadwhen comparedwith a head-on collision. Furthermore, the shape of the ice floe hasan influence on the load due to the difference in collision angle(Yamaguchi et al., 1997). Moreover, Matskevitch (1997) pointed outthat horizontal splits in the ice edge were a principal factor in ice

35J. Dong et al. / Cold Regions Science and Technology 71 (2012) 34–43

failure mechanism. In fact, the force of floating plates against struc-tures is determined by the ice mass and its drift velocity (Sodhi andHaehnel, 2003). That is to say, the kinetic energy is one of the criticalfactors affecting the impact force.

Laboratory experimentation is one of the most common methodsto determine ice loads on structures. Frederking and Timco (2000)carried out a series of tests in an ice tank to measure the impactforce on an isolated floe against an instrumented structure. In thetests, the ice floe was accelerated to a desired speed by a towing car-riage, and made to drift under its own momentum into the test struc-ture. The aim of this paper is to evaluate the design ice load on cylinderpiles exerted by moderate ice by using of logarithm curve envelopemethod, and then establish the relationship between ice impact forceson an individual pile and pile groups and the kinetic energy of the icefloe through the envelopemethod. As the carrier of drift ice, flowplaysan important role in ice-structure interaction. Therefore, using a pierstructure of sheet-pile type construction as an example and takingadvantage of the return flow system, we conducted tests of moderatesized ice floe impacts against vertical column piles according to themethod of Frederking and Timco (2000).

2. Experimental setup and DUT-1 model ice

Experiments were carried out in awater tank, with a geometry scaleof 1:40. The tankwas 50 m in length, 3 m inwidth and 1 m indepth. Thetotal flux of the bidirectional-return flow system was 0.65 m3/s, andvariations of flow velocity were regulated through a flow control sys-tem. Two video cameras were employed to record each impact.

A dock is always constructed of several similar units. To provide arealistic simulation of the impact on any part of the structure, twounits of the dock model were prepared according to the pile arrange-ment of an existing dock in the north Bohai Sea (Fig. 1). The diameterof the piles was 20 mm. One model dock unit was rigged with loadsensors to measure the impact force, and the other model dock unit,without load sensors, was placed in the upstream direction. The up-stream model dock unit was taken away while measuring the loadon the corner pile of the force-measured element. By this way, thecorner pile could resist the maximum loading. The two dock units,with the seven piles keeping a certain distance from the tank bottom,were fixed to the tank bottom with lead ballast. The center-to-center

50

775

6x112.5=675

Fig. 1. Piles arrangement of one dock element model (in mm). The 15° angle between thevertical planes.

distance of the two closest piles was 5.63 times that of the pile diam-eter. In general, there is no interaction of the ice on the two closestpiles as the distance between the two centers is greater than five tosix times that of the pile diameter (Kato and Sodhi, 1984; Timco,1985). Therefore, we assessed each pile individually. Bidirectionalforce transducers were installed on pile #1, and unidirectional oneson the other six piles, oriented toward the flow. Pile #1 was on theupstream corner of the dock unit and therefore, always the first pileto be impacted.

Non-refrigerated DUT-1 model ice was employed in the experi-ments. Previous studies have showed (Li et al., 2002, 2003a) that thedensity of DUT-1 model ice is between 876 and 926 kg/m3, consistentwith Bohai Sea ice, and is able to simulate the ice-structure interactionwith a scaling factor of 1:10 to 1:50. The ice strength can be restrictedwithin a range by regulating the cement content in themodel ice (Li etal., 2003b). The typical flexural strength and compressive strength ofthe model ice range from 20 to 75 kPa and 20 to 150 kPa, respectively.The ratio of compressive strength to flexural strength is in the range of1:0.8 to 1:2. It's worth noting that this ratio is always higher than thatof natural sea ice, as many other model ice materials (Zufelt andEttema, 1996), because of the differences in material component.However, many studies using model ice material has proved thatsuch differences can be ignored in some conditions (i.e. Leiviskäet al., 2001; Zufelt and Ettema, 1996), for example, in this studywhere no flexural failure is encountered in the tests.

3. Test procedures and measurements

Drifting floes typically attach to or leave vertical marine structureswith a rotation after an impact, and flexural failure of sea ice does notgenerally take place in the process. Consequently, the compressivestrength of the model ice was considered to be the main mechanicalparameter in the tests. The model ice used for the tests was 3.0 m inlength, 1.9 m in width and averaged of 1.1 cm in thickness. The com-pressive strength of the model ice in the tests was in the range of 31to 86 kPa. The drift velocity and equivalent diameter of the ice floewere 10 to 25 cm/s and 5 to 259 cm, respectively. The kinetic energyof the ice floe varied from 0.1 to 1.9 J. A static ice floe was acceleratedto impact the piles by the flow with a certain velocity. The flow veloc-ity varied regularly from the low speed to high speed until this floe

50

62.5

75

487.

5

2x11

2.5=

225

7550

oblique line and the vertical axis represents the angle between the inclined piles and

Tank15o

#7

#6

#5

#4

#3

#2

#1

Pier Unit

Pier Unit Model

Model

Pier UnitModel WithoutLoad Cells

Ice MovementDirection

Plan View

CCD Cameras

Ice MovementDirection

Tank

Side View

Fig. 2. Simplified cross-section of the test set-up. The seven piles of the pier unit model are marked on the plan view, not including the two CCD cameras and other piles. The twoCCD cameras are fixed on a shelf beside the tank. And the pier unit model without load cells is also omitted in the side view.

a3

2

1

0

-1Impa

ct ic

e fo

rce

on a

n in

divi

dual

pile

36 J. Dong et al. / Cold Regions Science and Technology 71 (2012) 34–43

was broken into small pieces. Then the process was repeated by usinganother floe. In this way, the floe could be “reused” for up to 10 to 30times, hence the different impact loads under the same compressivestrength could be measured. However, the size of the ice sheetdecreased with the frequency of use as a result of the repeatedinteractions.

Both the sampling rate for the load cells and CCD cameras were0.01 s. The angle of the flow direction was 15° from the center lineformed by the seven vertical piles. Due to the limitation of the tankwidth (3 m), there was not enough space for the floating ice (1.9 min width). The length of the two pier units was about 1.6 m. Therefore,the two units were placed on the tank bottom at an oblique angle fromflow direction. The angle could not be too wide, so an angle of 15° wasselected for the tests. The direction of the ice floes was monitored byone vertically down-looking CCD camera, and the collision of thepiles was monitored by another camera facing obliquely-downward(Fig. 2).

Fig. 3. Photo of floating ice impacting against the piles. The black triangle is applied tocalibrate the pictures from the vertical-installed CCD camera. Lead blocks on the pierunit model are used as ballast.

b

0 1 2 3 4

Time (s)

Time (s)

Cru

nchi

ng ic

e fo

rce

on a

n in

divi

dual

pile 20

15

10

5

0

-50 1 2 3 4

Fig. 4. The comparison of impact and crushing process on an individual pile for thesame “reused” floe under different kinetic energy. Fig. 4a indicates a typical impact pro-cess. Fig. 4b shows a crushing ice force on an individual pile.

b

a

c

37J. Dong et al. / Cold Regions Science and Technology 71 (2012) 34–43

The kinetic energy and compressive strength of the drifting icewere the key parameters determining the impact force. To get the ki-netic energy of an ice floe, its density, size and velocity should be de-termined. The density of the model ice was obtained by the mass-volume method. The ice drift velocity was analyzed from continuousimages according to Lu et al. (2008). A black triangle of known sizewas attached as a reference on the ice surface to calculate the realsize of the ice floe from the images (Fig. 3). The mass of the triangleitself was negligible. The instantaneous speed of ice floe at the impactagainst piles was acquired by analyzing the sequence of severalimages showing the ice moving to the pier unit. The ice floes were ob-served to rebound, rotate, deviate or scrape the piles after impact, andeven broke into several pieces under high flow velocity. Because ofthe highly random in interaction of the ice floe and the piles, it is dif-ficult to measure the velocity of the ice floe after an impact, so thekinetic energy of the floe after impact is not considered here.

In order to simplify the method and the process of the design load,a certain ice condition was taken as an example in this study. Someice parameters were measured. These were: a uniaxial compressionstrength of 56 kPa, a thickness of 1.1 cm, a diameter of 2.5 m and amaximum velocity of 12.65 cm/s (the kinetic energy was 0.35 J). Acurve envelope of the impact force was drawn in respect of the limitvalue of the kinetic energy at the impact of the ice and the force onthe piles in each test group. The value of the curve corresponding to0.35 J kinetic energywas defined as the expected impact load on a sin-gle pile for the test group.

A design load is always taken to be the limit value in a recurrenceinterval in engineering practice. Therefore, a worst case situation hasbeen considered. The peak values of the forces on different piles atthe same time were used to plot envelopes to ascertain the expectedpeak loads on an individual for a 0.35 J kinetic energy, and with thesame methods, the sum of the force against the several piles of theseven piles at the same time was regarded as the expected peaktotal load on one dock unit. The expected peak loads correspondingto 0.35 J kinetic energy with different compressive strengths were ap-plied to draw another envelope curve with respect to ice compressivestrength. Thus, the design ice load on an individual pile of 56 kPa com-pressive strength was finally determined. The total design ice load onone dock unit could be obtainedwith the samemethod, as well as thaton pile #1.

4. Results

4.1. Comparison of crushing and impact ice force against an individualpile

An ice impact on a single pile is different from that of a quasi-staticcrushing process (Fig. 4). The same “reused” floe of 31 kPa in compres-sive strength was used in the two processes. There are two impactpulses shown in Fig. 4a. It shows that the load on the piles increasesrapidly from about zero up to a peak value in several tenths of one sec-ond as the floe touches the piles. From there on, the force decreases ata very rapid rate. Occasionally, the ice floe impacts again on the pilesdue to flow drag. There are always one or two interactions beforethe floe stays on the ice edge while the flow velocity is low. Thewidth of the pile penetration the floe is typically lower than the pilediameter. For the crushing process (Fig. 4b), the ice force moves upand down during which the mean magnitude remains almost con-stant. This process always occurs with a high indentation speed, andthe width of the contact surface equaled to the pile diameter. It canbe seen by comparing the two curves that the magnitude of averaging

Fig. 5. The impact of the ice floe on the seven piles. (a) Only one pile touches the floe.(b) The floating ice impacts on the several piles simultaneously. (c) There are two im-pacts on a pile in one test run.

Fig. 6. The expected peak ice forces on an individual pile from different compressive-strength floes with 0.35 J in kinetic energy.

38 J. Dong et al. / Cold Regions Science and Technology 71 (2012) 34–43

39J. Dong et al. / Cold Regions Science and Technology 71 (2012) 34–43

crushing ice force is higher than the impact loads. In a word, impactand crushing failure of floes on piles represented incomplete-contactand sufficient-contact crushing failure, respectively. The major differ-ences between the two processes are the action duration, the width ofcontact surface, and the load magnitude.

4.2. Design ice load on an individual pile

The drag force on the piles under several different flow speeds wasgauged before the tests. The results showed that the flowdragwas lowand could be ignored. It can be seen that the impact load on the piles isdifferent for each interaction (Fig. 5). In some interactions, piles with-stood the force concurrently, while sometimes several piles experi-enced loads asynchronously. One of the piles even received actionstwice during a test, because of a rebound, due to the rotation of thefloating ice. However, the force for the second impact was lowerthan the first one, due to the much slower speed.

An impact force with the same ice strength was selected to plot acurve envelope using the peak value data (Fig. 6). The values on thecurves relating to 0.35 J kinetic energy on the horizontal axis werethe expected peak loads on an individual pile. There is a cluster of dis-crete data points in Fig. 6, because the data are the peak loads on theseven piles in any given impact, and there are several different im-pacts under varying flow velocities as shown in Fig. 5. Furthermore,the restriction of the sidewall and a varying shape floe are other rea-sons for the scattered data.

The expected peak loads from the force-energy envelope on an in-dividual pile in Fig. 6, with respect to a kinetic energy value of 0.35 J,have been used to plot a new envelope curve (Fig. 7). It shows thatthe design load value for an individual pile of 56 kPa compressivestrength is 24 N, which is higher than that calculated from Afanasev'sformula for static crushing failure scenario. It seems that the designload is higher. However, the most serious condition should be consid-ered for the design of structures within an expected service period inengineering practices. A proper safety factor has to be applied beforeapplications. Therefore, envelope method was used for the tests. Ithas a marked effect on the loads. From the measured impact forcesto the design loads, the ice loads have been amplified for twice. Themaximum values of the impact loads on the piles in each impact pro-cess were used to form the envelopes. That is, the data points in Fig. 6were the peak values in each impact process. The peak impact loadsfrom different compressive strengths are used to form the envelopecurves. Then the expected peak loads on the above envelopes wereused to form a new curve to determine the design loads.

Fig. 7. The design ice load on an individual pile with 56 kPa in ice compressive strength.

4.3. Relationship of design ice load on an individual pile, kinetic energy ofdrift ice and its compressive strength

Both the kinetic energy and the compressive strength affect the fail-ure of the floes on the ice-pile interface and thus the force on the piles.Fig. 8 shows the minimum critical kinetic energy of sufficient-contactcrushing failure for a certain strength floe. That is, sufficient-contactcrushing failure occurs as the kinetic energy greater than or equal tothe critical value. The kinetic energy for a sufficient-contact crushingfailure tends to increase with the rising of compressive strength. Thecritical values of the energy for different compressive strengths, howev-er, cannot be accurately defined, due to the large scatter data.

The relationship of the design ice load on an individual pile, ice ki-netic energy and ice compression strength were plotted, based on allthe data points to give the envelope curves in Fig. 6. It shows that iceforce on an individual pile increases with increasing ice compressivestrength (Fig. 9). However, the kinetic energy of the plates greatly in-fluences the ice load on a single pile. This is because the crushing forceis the upper limit of the impact force, and therefore will not increasewith rising kinetic energy after reaching a critical value. The collisionforce acting on an individual pile under a compressive strength of be-tween 30 and 90 kPa and a kinetic energy ranging from 0 to 1 J can bedetermined from the curved surface.

The impact ice force on an individual pile Fm is:

Fm ¼ �121:09� 3:09 lgEmð Þ � 13:17 lgEmð Þ2 � 4:88 lgEmð Þ3 � 0:51 lgEmð Þ4

þ68:28 lgσ cmð Þ � 7:91 lgσ cmð Þ2ð1Þ

where Em is the floe kinetic energy, and σcm is floe compressionstrength. Note Eq. (1) is only for the inner piles rather than the cornerpile.

This equation has the potential to apply for real ice impact load-ings. For a geometry scale factor of λ, the kinetic energy E and thecompressive strength σc of natural ice is λ4 and λ, respectively.

a ¼ E=λ4 ð2Þ

b ¼ σ c=λ ð3Þ

where a and b are parameters of natural ice.If the values of a and b are within the limits of 0 to 0.8 J and 30 to

90 kPa, the force of natural ice on a single pile F can be calculated asfollows:

F ¼ λ3Fm: ð4Þ

Fig. 8. The kinetic energy for sufficient-contact crushing failure increases with the ris-ing of ice compressive strength.

Fig. 11. The compressive strength of DUT-1 model ice with respect to strain rate.From Li et al., 2003b.

Fig. 9. The relationship of design load on an individual pile, kinetic energy and com-pression strength of the ice floe.

40 J. Dong et al. / Cold Regions Science and Technology 71 (2012) 34–43

For example, considering an ice floe of 0.92 Mg/m−3 in density(Timco and Weeks, 2010), 1000 m2 in area, 0.4 m in ice thickness,2.0 MPa in compressive strength, 0.2 ms−1 in velocity, and a cylinderpile of 0.9 m in diameter, the design load on an interior pile is 1.1 MN.

A paper by Timco (1986) mentions another paper (Ralston, 1979),describing an appropriate strain rate for an individual pile that can beestimated by:

_ε ¼ v=2D ð5Þ

where v is the ice velocity, and D is the structure width.In terms of the strain rate, the relationship between strain rate and

ice compressive strength has to be discussed for natural ice and DUT-1model ice. It has been demonstrated that the strength for natural ice isgenerally related to strain rate when it is less than 10−2 s−1 (Sodhiand Haehnel, 2003) (Fig. 10). There is a brittle-ductile transition forthe crushing strength with strain rate ranging from 10−4 to10−2 s−1, and the peak strength is approximately twice of that in brit-tle stage. The strain rate from 10−2 to 10−1 s−1 or even higher haslittle effect on the ice strength. For DUT-1 model ice, it seems thatthere is no brittle-ductile transition for its compressive strength asthe strain rate is within the range 1.94×10−3 to 7.30×10−3 s−1 (Liet al., 2003b) (Fig. 11). Since only a very limited amount of data areavailable, it is difficult to provide an accurate quantitative correlationbetween compressive strength of the model ice and its strain rate.The strain rate for the model ice in the tests ranged from 10−0.5 to100.9 s−1 (within the ductile stage for real ice). The extrapolation forreal ice can be directly done by Eq. (4). When the estimated strainrate for real ice is higher than 10−2 s−1 the larger of the model icestrength and that of scaled natural ice is employed in Eq. (1).

Fig. 10. Ice compressive strength with respect to strain rate.After Sodhi and Haehnel, 2003.

4.4. Total design ice load on one dock unit

The sum of the forces on the seven outer piles was taken to be thetotal ice load of one pier unit, due to the much lower forces exertedon the other piles. There were only unilateral transducers on the sixmeasured piles, the resultant forces against them were modifiedaccording to that on pile #1. The forces on pile #1 mainly rangedfrom 40 to 60° (accounting for 70% of all the data) counterclockwiseto the flow with an average of 50.8°. The resultant forces on the sixpiles were considered to be the same as that on pile #1. Therefore,the correlation of the measured magnitudes of the load cells on thesix piles FIm and the total loads FI on them can be expressed as:

FI ¼ FIm=cosθ ð6Þ

where I is an integer from 1 to 6, representing one of the six piles, andthe angle of the resultant force on pile #1 counterclockwise to theflow θ=50.8°.

Similar to the expected peak force on an individual pile, the sum-mation of the amended values was taken to be the expected peaktotal loads on one dock unit. Variations of the expected peak forceswith ice kinetic energy under different compressive strengths areshown in Fig. 12. The envelope curve of the total design loads onthe structure is plotted by the curves in Fig. 13.

Scatter of the data points in Fig. 12 is largely due to the differentnumber of piles subjected to the force synchronously. The total designload is 52 N, only 2.16 times of that on an individual pile for a com-pressive strength of 56 kPa. This is because the extreme load casefor the piles is the sum of the design ice load acting on the sevenpiles at the same time, with the maximum load usually found onpile #1. Furthermore, as the other six piles are behind pile #1 theforce exerted on them is obviously lower. The asynchronous actionon the piles is another reason for the low value of the total designload.

The design ice loads on an individual pile and the global loads onone pier unit with respect to a kinetic energy value of 0.35 J havebeen determined from the curves in Figs. 6 and 12 and are listed inTable 1.

4.5. Design load on the corner pile

Generally, pile #1 in the upstream pier unit was the first pile to re-ceive the ice impact. Consequently, the dock unit without sensors wasremoved from the tank so that the ice force on the corner pile could bemeasured. The results show that the design load on pile #1 is 26 N atan ice compression strength σcm=36 kPa. The design load can be de-duced to be 40 N for σcm=56 kPa under a linear relationship. Thisforce is 1.69 times of that on an individual pile, and 0.78 times oftotal design load. Consequently, the corner pile should be reinforced

Fig. 12. The expected peak ice forces on one pier unit with 0.35 J in kinetic energy for different compressive strength.

41J. Dong et al. / Cold Regions Science and Technology 71 (2012) 34–43

in engineering practice. Eccentric collisions were the most commonoccurrences in ice-pile impacts. The ice normally became trappedwith a rotation during an ice floe impact, which caused crushingloads on the piles. There was a visible variation of force direction onpile #1with time. The direction of maximum force was not parallel

to the flow direction, but was at a direction of 25° counterclockwiseto it (Fig. 14). Timco (1985) has reported a similar finding. The anglechanged to 50.8° when the model dock unit without load cells waspresent (Fig. 15). The variation of angle is due to the lateral restrictionof the tank side walls.

Fig. 13. Global design load on one pier unit with 0.35 J in kinetic energy of floating ice.

Table 1Design impact load on an individual pile with different compression strength.

Model icethickness(mm)

Compressive strengthof model ice (kPa)

Design load on anindividual pile (N)

Total design loadon one pier unit (N)

12 31 13 3011 31 14 3010 33 12 2710 39 13 1310 56 21 2611 62 13 1411 62 26 5412 65 20 4211 86 19 28

42 J. Dong et al. / Cold Regions Science and Technology 71 (2012) 34–43

5. Discussion and conclusions

Ice crushing failure is always used in design ice load. This is appro-priate only when a structure exposes to large ice floes. However, it

b

a

Fig. 14. Time series of ice force on pile #1 and its direction under the floe of 36 kPa in commoved in Fig. 14a.

has shown to be a conservative design method for floating ice of mod-erate size. This is evident when comparing crushing and impactagainst a single pile. The differences come from the action modeand the magnitude of the maximum force. Therefore, an envelopemethod was applied in this paper to determine the design ice loadon an individual pile and that on a dock unit under moderate icefloe impacts.

The kinetic energy of the ice floe before it impacts on the piles isconsidered to be one of the key factors for determining the load onthe structure, and it can easily be acquired by analyzing the imagesfrom the downward CCD camera, providing the ice is of a known den-sity and thickness.

The ice compressive strength was between 31 and 86 kPa with anaverage thickness of 11 mm. The design ice load was gained under thefollowing conditions: the ice compressive strength was 56 kPa, the icemodel was 2.5 m in diameter, and the maximum velocity of the icewas 12.65 cm/s (the kinetic energywas 0.35 J). By plotting the envelopecurve of the peak value of expected peak forcewith the kinetic energy offloating ice, the value of design load corresponding to 0.35 J wasobtained from the curve. The design load on an individual pile for theice conditionswas 24 N. As the kinetic energy and compressive strengthare between 0 and 0.8 J and 30 and 90 kPa, respectively, the design loadfor an interior pile can be calculated by Eq. (1). It can be scaled to real icewhen the scaled kinetic energy and compressive strength arewithin theranges stated above. However, due to the variation of compressivestrength of natural ice with strain rate, the strain rate should be previ-ously estimated with Eq. (5). The corresponding compressive strengthfor real ice can be compared to that of the model ice. If the compressivestrength of model ice is lower than that of natural ice, it should bereplaced by the latter before applying Eq. (1). When there is no com-pressive strength data, due to the ductile-brittle transition in compres-sive strength of real ice, the design load should be increased beforeextrapolating to full scale.

The total design load of one pier element was only 2.16 times thaton an individual pile. The design load on the corner pile was 1.69times that of the other six piles, and 0.78 times that of the total struc-ture. Therefore, it is necessary to increase the load capacity of the cor-ner pile. Due to the lateral restrictions of the tank wall, loading

pressive strength. The meaningless curve in Fig. 14b corresponding to zero loads is re-

Fig. 15. Sketch of the direction of the resultant force on the corner pile. Note piles #2 to#6 and the pier unit without sensors are not shown in the figure. F1 and F2 representthe resultant force on pile #1 for the absence and presence of the non-measured pierunit, respectively.

43J. Dong et al. / Cold Regions Science and Technology 71 (2012) 34–43

direction on the corner pile was not parallel to the direction of flow,but was at an angle of 50.8° counterclockwise of flow direction. Theangle changed to 25° when the model without cells was removed.

Due to different failure modes and the restriction of the tank wall,there is a large scatter for the measured data. The envelope for twiceamplifications was used to determine the design loads. All the abovepossibly lead to the higher design loads. The design load on an indi-vidual pile for envelope method is about 1.7 times of the linear leastsquare method. The loads on the piles in the tests were taken as sta-tistic force. It was found that there were observable vibrations duringthe ice-pile impacts. The dynamic response of the pier units has beenignored in the tests. It is another factor for the loads, which should beconsidered in the future studies.

Acknowledgments

The authors would like to thank the funding supported by theFoundation for Innovative Research Groups of the National NaturalScience Foundation of China (no. 50921001) and the National NaturalScience Foundation of China (no. 50439010 and no. 51079021).

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