FORMATION, BEHAVIOUR AND CHARACTERISTICS OF ICE RUBBLE PILE-UP AND RIDE-UP ON A CONE

Size: px

Start display at page:

Download "FORMATION, BEHAVIOUR AND CHARACTERISTICS OF ICE RUBBLE PILE-UP AND RIDE-UP ON A CONE"

Elisabeth Wright
5 years ago
Views:

Proceedings oh the th IAHR International Symposium on Ice () FORMATION, BEHAVIOUR AND CHARACTERISTICS OF ICE RUBBLE PILE-UP AND RIDE-UP ON A CONE Mohamed O. ElSeify and Thomas G.

1 Proceedings oh the th IAHR International Symposium on Ice () FORMATION, BEHAVIOUR AND CHARACTERISTICS OF ICE RUBBLE PILE-UP AND RIDE-UP ON A CONE Mohamed O. ElSeify and Thomas G. Brown University of Calgary, Calgary, Canada ABSTRACT Flexure failure of the consolidated layer on conical structures may result in either pile-up of broken ice rubble in front of the structure or ride-up of the consolidated layer on the slope of the cone. These phenomena can increase the load significantly and affect the failure mechanism of the ice. For the last eight years, there has been a full-scale in-situ monitoring Programme to examine the interaction between ice features and the Confederation Bridge piers (Brown, ). Using the data from the Confederation Bridge Monitoring Programme, observations pertaining to rubble pile-up and ride-up will be presented. The study concentrates especially on the effect of ice velocity, consolidated layer thickness, keel depth and slope angles of the pile-up and ride-up on the height of interaction of both phenomena. A detailed statistical analysis has been carried out, resulting in relations between the dependent and independent variables. INTRODUCTION When partially consolidated first-year ridges interact with structures, both the consolidated layer, and the unconsolidated ice of the keel and sail, must fail. As it interacts with the conical piers of Confederation Bridge, the consolidated layer can fail by flexure, crushing, shearing, or splitting. Measurements and observations have shown that highest loads occur when significant rubble pile-up or consolidated layer ride-up are present. Figures (a) is a consolidated layer ride-up while Figure (b) is a rubble pile-up. One of the most important parameters that determines the increase in loads is the height of the interaction. As a result the observations focused on relating the height of interaction the ridge velocity, ice thickness, keel depth and pile-up or ride-up slope angles to. Using the Acoustic Doppler Current Profiler (ADCP) and video records from the Confederation Bridge Monitoring Program, accurate data regarding the geometry and interaction parameters for both phenomena can be obtained. According to Mayne and Brown (a), the initial flexure failure of a level ice sheet interacting with a conical structure will produce rubble pieces that pile over the cone causing rubble pile-up. In case of ridge interactions the ride-up phenomenon is dominant with % of the recorded events being accompanied by ride-up. This dominance of the ride-up phenomenon can be attributed to several reasons. There is a significant upward thrust on the underside of the consolidated layer by the keel rubble trapped between the consolidated layer and the cone. This reduces the force required to cause a flexure failure and subsequently increases the ability of the consolidated layer to ride-up the slope cone. Second, the thickness of the consolidated layer is high enough to be able to ride-up the cone slope without being crushed into small pieces causing rubble pile-up, and this ride-up will often clear an existing rubble pile. --

m above MSL, into a cone that transitions into the main pier shaft (an m, octagon) at a height of m above MSL. The waterline diameter of the cone is m averagely.

2 Proceedings oh the th IAHR International Symposium on Ice () Figure a. Ride-Up Phenomenon Figure b. Pile-Up Phenomenon Each pier of Confederation Bridge consists of a cone at the waterline that transitions, at +. m above MSL, into a cone that transitions into the main pier shaft (an m, octagon) at a height of m above MSL. The waterline diameter of the cone is m averagely. DATA SUMMARY This study is an extension to the study done by Mayne and Brown (b). That study focused on rubble piles resulting from the interactions of level ice with conical structures. Thus, this study specifically focuses on rubble piles and the consolidated layer ride-ups resulting from the interaction of ice ridges with the Confederation Bridge piers. The data for this analysis consists of 9 first year ice ridge events. Data for events accompanied by pileup and ride-up has been separated so as to study each phenomenon separately. The data here was used to derive the relation between the ridge velocity, ice thickness, keel depth and slope angle on one hand and the height of interaction on the other hand. The ridge velocity has been estimated from the ADCP data analysis. The pile-up and the ride-up heights, slope angle, and the consolidated layer thickness were determined from analysis of the video imagery using image processing software. The keel depths were determined from the sonar data analysis. HEIGHT OF INTERACTION ESTIMATION Height of Interaction Vs Ridge Velocity Figures (a) and (b) plot the height of interaction against approaching ice velocity for the events accompanied by pile-up and ride-up respectively. Clearly, many rubble piles and consolidated layer ride-ups do not reach maximum height as predicted by Equation (). However, considering only the maxima, there is a decrease in pile height as the velocity (V) increases for both phenomena. This was also noted by Mayne and Brown (b). In case of pile-up events the trend of maximum heights shown in Figure (a) is a second order polynomial: H= -.V -.V+. () In case of ride-up events the trend of maximum heights shown in Figure (b) is a second order polynomial: H= -.V +.V+. () --

3 Proceedings oh the th IAHR International Symposium on Ice ()..... Ridge Velocity (m/s) Figure a. Pile-up Height Vs Ridge Velocity Ridge Velocity (m/s) Figure b. Ride-up Height Vs Ridge Velocity. Height of Interaction Vs Consolidated Layer Thickness Figures (a) and (b) plot the height of interaction against the consolidated layer thickness of the approaching ridge. Clearly, many rubble piles and consolidated layer ride-ups do not reach maximum height, as predicted by Equations and. However, considering only the maxima, there is an increase in pile height as the consolidated ice thickness (h c ) increases for both phenomena. This relationship is consistent over the full range of velocities. The trend lines added here were specified with an intercept of zero. In case of pile-up events the trend shown in Figure (a) is a second order polynomial: H c =. H + 9. h. () c In case of ride-up events the trend shown in Figure (b) is also a second order polynomial: = c H.h c +.h.9 () --

4 Proceedings oh the th IAHR International Symposium on Ice () Consolidated Layer Thickness (m) Figure a. Pile-up Height Vs Consolidated Layer Thickness. From Figures (a), (b), (a) and (b), it can be noted that, for any given velocity or consolidated layer thickness there are many heights below the maximum. Based on this, it can be concluded that there are other conditions for a rubble pileup or ride-up to attain its maximum height, given the ice thickness and velocity Consolidated Layer Thickness (m) Figure b. Ride-up Height Vs Consolidated Layer Thickness. Height of Interaction Vs Keel Depth Figure (a) plots the height of interaction against the approaching ridge keel depth. Considering only the maxima, there is an increase in pile height as the keel depth (h k ) increases till keel depth of m for pile-ups. After this value for the keel depth, there will be a decrease in the pile-up height as the keel depth increases. This decrease in the pile-up height due to the increase in the keel depth is not logic. This unexpected behaviour can be attributed to the small number of ridges in the sample of chosen events,used in the statistical analysis in this research, that have keel depths larger than m for the pile-ups. So, this small number of ridges can not represent the real relation between the height of interaction and the keel depth. Figure (b) plots the ride-up heights against approaching ridge keel depth. Considering only --

5 the maxima, there is no obvious statistical relationship between the ride-up height and the keel depth. In case of pile-up events the trend shown in Figure (a) is second order polynomial: H.h k + h. () = k Proceedings oh the th IAHR International Symposium on Ice () Keel Depth (m) Figure a. Pile-up Height Vs Keel Depth. Keel Depth (m) Figure b. Ride-up Height Vs Keel Depth. Slope Angle Vs Ridge Velocity Figures (a) and (b) plot slope angle against ridge velocity for the events accompanied by pile-up and ride-up phenomena respectively. Since the typical rubble pile profile is bilinear, so the slope angle presented in this research is an average of the two slope angles of the two lines forming the pile profile. As a result, this slope angle can not be used for calculation of the rubble pile volume that is used in load calculation. However, considering only the maxima, there is a decrease in the slope angle (θ) as the ridge velocity increases for both phenomena. In case of pile-up events the trend shown in Figure (a) is second order polynomial: θ = -.9V +.9V+9. () In case of ride-up events the trend shown in Figure (b) is second order polynomial: θ=-. V +.V+. () --

6 Proceedings oh the th IAHR International Symposium on Ice () Slope Angle (Degree) Ridge Velocity (m/s) Figure a. Pile-up Height Vs Slope Angle. It can be concluded from Figures (a) and (b) that the upper bound on slope angle for both phenomena depends on the Confederation Bridge Pier geometry more than any other parameter. This conclusion is based on the fact that the highest rubble pile slope angle is o as shown in Figure (a). This value of the slope angle is compatible with the maximum mathematical value of the slope of a rubble pile having a m height and supported on the bridge cone. Also, the maximum ride-up slope angle is o as shown in Figure (b). This value for the maximum ride-up slope angle is compatible with the fact that the above MSL cone slope angle is o. Slope Angle (Degree) Ridge Velocity (m/s) Figure b. Ride-up Height Vs Slope Angle. COMPARISON TO EXISTING THEORIES Similar relations used for comparison in this paper were developed by Maattanen and Hoikkanen (99), and Mayne and Brown (b). Both relations had been developed for rubble piles resulting from interaction of level ice with conical structures. The approach by Maattanen and Hoikkanen (99) was based on field observations at light piers in the Gulf of Bothnia. The rubble pile is supported by the face of the cone and the advancing ice sheet. The ice sheet can be either in contact or not in contact with the face of the cone, which will significantly affect the ability of the ice sheet to support any rubble pile. Using the --

7 Proceedings oh the th IAHR International Symposium on Ice () observations from the Gulf of Bothnia, a relationship had been derived between height of rubble pile (H) and ice thickness (h i ): H= A. (h i ). () where the constant (A) is assumed to be. when the pile is unsupported and when the pile is fully supported (Buckland and Taylor 99). The Mayne and Brown (b) approach was based on field observations made from the Confederation Bridge Monitoring Program. Using the data from the Confederation Bridge a relationship had been derived between height of rubble pile (H) and ice thickness (h i ): H=.9. (h i ). (9) Equations and 9 have been developed for rubble piles resulting from interaction of level ice with conical structures. As may be seen in Figure (), rubble piles resulting from the interaction of both level ice and consolidated layer with conical structures have similar heights. This leads to the conclusion that the rubble in the sail and the keel do not have much influence on the pile-up height. This finding maybe attributed to the absence of sails in about % of the ridges used in this study (ElSeify and Brown, ). In addition, at m above MSL, the Confederation Bridge piers are essentially vertical, and have a narrow effective width of m. Moreover, when the height of the rubble pile increases, its weight increases leading to downward failure of the consolidated layer, which has been commonly observed during the Ice Force Monitoring Program at the Confederation Bridge. So, the results given by the formula in Equation estimated from the consolidated layer rubble pile up height observations can be considered equivalent to the results given by equations and 9. Mayne and Brown s (b) equation represents an upper bound for the maximum rubble pile heights. Maattanen and Hoikkanen s equation for unsupported conditions represents a lower bound for maximum rubble pile height. Height of Rubble Pile (m)..... Consolidated Ice Thickness (m) Observed Mayne Maattanen (Unsup) Maattanen (Sup) Figure. Observed and Theoretical Rubble Pile Heights. --

8 The rubble pile is supported by the face of the cone and the advancing ice sheet. Based on the dynamic conditions of the Northumberland Strait, it can be deduced that the rubble pile is not fully supported by the ice sheet in the case of level ice. Similarly, for the rubble piles resulting from the consolidated layer of first year ice ridges, the keel does not provide much support for the rubble piles. This is caused by two reasons, first, the dynamic conditions in the strait, and secondly, the geometry of the cone that breaks the keel and causes its rubble to clear out around the pier. CONCLUSION The data considered for this paper suggests that, for interactions of first year ice ridges with sloping structures, most of the events will be accompanied by ride-up. The data suggests that the height of interaction of both pile-up and ride-up is related to the ridge velocity, the ice thickness, and the keel depth. A regression of the upper bound heights and the respective ridge velocity, consolidated layer thickness, keel depth and slope angle yielded second order polynomial equations. A comparison had been held between the formula developed for the relation between pile-up height of interaction and consolidated layer thickness and the models developed by Maattanen and Hoikkanen (99) and Mayne and Brown (b). This comparison indicates that rubble pile heights calculated by the formula developed in this paper is equivalent to the rubble pile heights given by Mayne and Brown (b) and Maattanen and Hoikkanen (99). REFERENCES Proceedings oh the th IAHR International Symposium on Ice () Brown T., Ice Monitoring on the Confederation Bridge, What Has Been Learnt Proc. CSCE Annual Conference, Calgary, Alberta, Canada, Paper ST-9. Buckland and Taylor Ltd, 99, Northumberland Strait Crossing Project, Internal Report. ElSeify M.O., Brown T.G., First Year Ice Ridge Geometric Properties in Northumberland Strait: Detailed Video and Sonar Data Analysis Cold Regions Science and Technology Journal, to be submitted. Lemée E., Interaction of Ridges with Offshore Structures, Master thesis, University Of Calgary. Maattanen, M., and Hoikkanen, J., 99, The Effects of Ice Pile Up on the Ice Force of a Conical Structure, Proc. th Intl. Symp on Ice, Vol., Espoo, Finland, p-. Mayne, D.C., and Brown, T.G., a, Comparison of Flexural FailureIce-Force Models, Proc.9 th Intl. Conf. On Offshore Mechanics and Arctic Engineering, New Orleans, USA, paper OMAE--9. Mayne, D.C., and Brown, T.G., b, Rubble Pile Observations, Proceedings of th International Offshore and Polar Engineering Conference, ISOPE,, Seattle, USA, Vol., pp. 9-, Seattle, USA. --

INTRODUCING THE SHEAR-CAP MATERIAL CRITERION TO AN ICE RUBBLE LOAD MODEL

Symosium on Ice (26) INTRODUCING THE SHEAR-CAP MATERIAL CRITERION TO AN ICE RUBBLE LOAD MODEL Mohamed O. ElSeify and Thomas G. Brown University of Calgary, Calgary, Canada ABSTRACT Current ice rubble load