SUMMARY
The piers of the Suncor Bridge over the Athabasca River consists of two 2.4 m diameter columns, rock socketted into limestone. This is considered "flexible" as per CSA S6 and a dynamic analysis is required. The paper describes mechanisms producing ice forces and the dynamic analysis, including eigen value and time - history analyses. Since the superstructure serves to distribute the load on piers, the entire structure was modeled using frame elements for pier columns and girders and shell (plate) elements for deck and diaphragms. Spring elements were used to model the soil resistance. Two major failure types of ice floes were considered in developing the input forcing function: (1) crushing failure where the full width of the nose is in contact with the crushing ice; and (2) impact failure, where the ice floe is brought to a halt before full width of the pier is in contact. The results of the dynamic analysis are compared with those obtained using the static analysis. Typical time - history plots of displacement, velocity and acceleration are provided. Some recommendations for revisions to code provisions are given.

1. INTRODUCTION
The design of bridge piers in most parts of Canada is governed by the ice forces acting on them. The Canadian Highway Bridge Design Code, CSA S6-88, provides guidelines for "equivalent" static loads for design of piers which have a height to thickness ratio of 7 or less. Figure 1 shows the Athabasca River Bridge and piers which were designed using equivalent static loads and analyzed for dynamic amplification effects.

2. ICE LOAD MECHANISMS AND CODE PROVISIONS

2.2 Longitudinal Loads
Moving ice floes crushing against the pier nose produce a longitudinal or streamwise load which is a product of the ice thickness, ice strength and pier characteristics. The longitudinal load can increase significantly if the pier is skewed to the floe. For this bridge pier which is aligned with the floe, the web portion is not exposed to the floe until the striking angle is greater than about 4_. However, the ice floe could crush against the rear pile. The force thus induced will be less than that against the front pile and would not act concurrently with the force on the front pile due to the limiting effects of the kinetic energy of the floes. That is, the largest floe to contact a single pier is estimated to penetrate about 7 m past the nose for the design thickness and strength and an initial velocity of 2 m/s. Thus the floe would stop moving before it could contact the rear pile.

The longitudinal load is calculated using clause 5.12.18.2 of CSA S6 as follows:

Fc = Ca p t w

Ca= 5 t/w + 1

Using p = 1200 KPA as the crushing strength of ice, t = 1.3 m as ice thickness and w = 2.5 m for the thickness of the pier, the load Fc is calculated as 7400 kN.

The Code (clause 5.2.18.3) allows for reduction in the load if the kinetic energy of the floes is limited. The maximum diameter of a floe which can strike a single pier is two full spans, that is, 168 m. This size of floe would produce a full design crushing load at velocities as low as 0.5 m/s. Typical breakup velocities are about 2.0 m/s at the site. Velocities greater than 5.0 m/s have been observed in the breakup front, but with smaller floe diameters. In order not to generate the full crushing load of 7400 kN, the floes must be smaller than about 16 m. Therefore, no reduction in design load is applicable .

Ice jam loads: The bridge code recommends an ice jam pressure of up to 10 KPA be used. It has been ascertained that under design ice jam flood conditions, an ice thickness of 6 m would be produced at the bridge. The effect would be a force of about 150 kN on the pier, which is much smaller than that due to ice floes.

2.2 Transverse Loads

2.2.1 Transverse Component of Ice Floe Loads
Transverse loads on the web portion of the pier due to skew of the floe relative to the pier is not anticipated unless the skew angle is greater than 7 degrees. However, the ice floes may strike the nose of the pier at varying angles. Clause 5.2.18.2.4 of CSA S6 specifies that more severe of the following two cases be used.

Case 1: Full longitudinal load and 15% transverse load.

Case 2: 50% longitudinal load plus a transverse load

2.2.2 Thermal Expansion Loads
During winter, it is possible that a pier may have a solid ice cover on one side but no ice on the other. In this case, thermal expansion may produce a transverse load on the pier. However, this occurs under low ice level conditions. For the present pier, the web portion of the pier does not extend below the low ice level. Therefore, the transverse loads due to thermal expansion are only applicable to the piles and the thermal expansion pressures are in the order of 300 KPA. As such, the loads are smaller than those due to ice floes striking at a higher elevation.

2.3 Vertical Loads
A vertical ice load on the pier may be generated due to ice adhesion to the pier combined with rapid water level fluctuations. The rapid rise in water level associated with the breakup ice run may produce this type of vertical load before the ice is broken away from the piers. The vertical ice load is a function of the volume of ice attached to the pier. The ice sheet may crack as it bends, due to the uplift force of the rising water; however, if the ice strength is greater than about 400 KPA, a 0.9 m thick sheet will likely not crack due to bending. In this case, the radius of ice affected by the deflection cone around a pier is estimated to be about 1.5 times the characteristics length of the ice or 33 m.

The total vertical force on the pier is estimated to be 3000 kN or 1500 kN per pile. This is higher than the force given by the Code.

This force, calculated using clause 5.2.18.5 of the Code is as follows:

FF = 1000 (0.3 + 0.1R) t²
t^3/4

= 1000 (0.3 + 0.1 x 1.25) 0.9²
0.9^3/4

= 352 kN/pile < 1500 kN/pile

2.4 Simultaneous Loads on Two or More Piers
The design load of 7400 kN (longitudinally) can be expected to occur any time on any pier. At the same time during the ice run, a smaller and thinner floe, but with the same velocity and strength will be striking any other, or all other piers at the same elevation. Average floe thickness and size could be used for these concurrent forces and estimated to be about 3000 kN.

Table 1. Summary of Static Ice Load Conditions

Load Case	Pier 1		Pier 2		Pier 3		Pier 4		Elev.
	FL	FT	FL	FT	FL	FT	FL	FT
1	7400	1100	3000	450	3000	450	3000	450	241.5
1a	3700	2100	1500	860	1500	860	1500	860	241.5
1b	4000	2300	—	—	—	—	—	—	241.5

3. DYNAMIC EFFECTS
There are three types of failure of ice floes:

1. Crushing failure where the full width of the pier nose is in contact with the crushing ice.
2. Impact failure, where the ice floe is brought to a halt before full width of the pier is in contact.
3. Bending failure where the ice floe rides up the inclined pier nose and fails by bending. Because the piers here are vertical, this mode of failure is not applicable.

The crushing failure is characterized by rapid force fluctuations of small amplitude about a constant force level. Digitized ice crushing load events from measurements taken at Athabasca River at Hondo were used to develop the input loading function. Event from 1976 and 1977 were selected because the specialist consultant had high speed chart records (at 50 to 100 Hz) for these events.

The measured forces were typically between 500 kN to 2000 kN. The input forcing functions for crushing event were obtained by prorating the observed/measured ice load at Hondo to the design load of 7400 kN at the peak.

The input failure is characterized by impulse type forces, i.e., large amplitude forces of short duration. These impact load sequences were generated by using a log-normal distribution to describe the variation in the floe lengths and widths. The mean length of floe was established as 3 m based on personal observations of ice runs at Fort McMurray. The mean size of the largest floes observed at Hondo was assumed to be equivalent to the 1% exceedance floe length for all the floes at Suncor. This length was established as 10% of the river width, or about 40 m, for the ice moving at a mean velocity of 2 m/s and 5% of the river width, or about 20 m, for ice front velocities of 5 m/s.

Random sequences of 100 floe lengths and widths were generated for both design ice conditions and typical ice conditions. The design ice was 1.3 m thick with a strength of 1200 KPA while the typical ice was 1.0 m with a strength of 600 KPA. For each ice condition, three random floe sequences were generated for a velocity of 2.0 m/s and two random floe sequences were generated for a velocity of 5.0 m/s.

The potential maximum force applied to the pier by each floe was determined by the strength and thickness of the floe. The actual force applied by each floe was limited by the kinetic energy of the floe. The kinetic energy was also used to determine the penetration distance of the pier into the floe. The time-to-peak of the load was then calculated by dividing the penetration distance by one-half of the original velocity.

The load would typically release as the floe split or rotated off the pier. It was assumed that this occurred immediately after the maximum force was reached, since little damping would occur in this case. The load was arbitrarily assumed to release in the same manner as it was applied, producing a symmetrical load.

The time between loads was determined from the length and velocity of the floes. A distance of twice the penetration distance was subtracted from the floe length to account for the floe deceleration and acceleration during the application of the load. It was assumed that the channel was completely covered with ice floes so that the next load event began as soon as the previous floe completely cleared the pier nose.

4. MODELING CONSIDERATION
The dynamic analysis was performed using SAP90 code. The eigen value and time-history analyses were performed. Since the superstructure serves to distribute the load on piers, the entire structure was modeled using frame elements for pier columns and girders and shell (plate) elements for deck and diaphragms. Spring elements were used to model the soil resistance. The soil resistance is deformation dependent in the sand layer and is nearly constant in the rock layer. The resistance of sand layer is dependent upon depth and of the rock layers are dependent on the type of rock. Input files SUNICE* and SUNDYN* are full structure models.

If the movement of the structure parallel to traffic is restrained (say, due to friction) the stiffness of the structure increases. To model this condition, individual piers were analyzed using restraint in the X-direction (i.e. parallel to traffic) and springs to model the effect of the superstructure in the Y-direction. These input files are named PIER*.

In order to determine the effect of skew, SUNICE4 was the input file developed. Damping ratio of 5% was used in all analyses. This compares to 19% damping ratio measured at Hondo, therefore, is conservative.

5. RESULTS
The controlling load condition for static analysis is when the full design load of 7400 kN along Y axis and 1100 kN along X axis are acting on Pier 2 and 3000 kN and 446 kN respectively on all other piers; all acting at elevation 241.5.

Eigen analysis of the entire structure indicates the first natural frequency as 0.2 Hz (period = 5.0 sec), predominantly in the longitudinal (X-direction) mode and second mode is along the Y-direction, period = 1.57 sec, 0.6 Hz.

The natural frequency of 20th mode is 3.15 Hz (period = 0.32 sec). These frequencies indicate that the structure is quite flexible. (These are the orders of frequencies for cable-stayed bridges, for example.)

SUNICE4 is an input file where the entire structure is modeled. Dynamic forcing functions due to crushing was applied on Pier 2 for a duration of 10 sec. No load was applied on any other pier. Concurrent lateral loading on Pier 2 (in the X-direction ) was 15% of that in Y-direction. As is seen from the Table 2, the response ratio is very close to 1.0 for the maximum load effect. That is, the bending moment in the pier column about 2-2 axis (i.e. x-x axis) is 18,310 kN.m with dynamic analysis whereas the moment obtained using static analysis is 18,954 kN.m. For impact type forcing function, the bending moment is 17,050 kN.m.

The difference in results of static and dynamic analyses are similar for Pier 1. (12,883 kN.m vs 10,420 kN.m for dynamic analysis.)

When the Pier 1 alone is modeled ("PIER8") the maximum moment increased significantly (17,930 kN.m compared to 10,420 kN.m). However, this maximum moment still does not exceed that due to design static load (SUNICE1).

The maximum acceleration due to the design crushing event (i.e. due to full ice load) is 0.78 m/sec 2 . For an average year, this will be approximately:

0.78 x 3000 = 0.35 m/sec²
7400

This intensity of vibration will be felt but will be acceptable.

Table 2. Results of Analysis

LOAD ON PIER 2
Input File	Type of Analysis	M22	Element	M22	Element	M22	Element
SUNICE 4	Static 1	8954	310	16165	322	7237	322
SUNICE 4	Dynamic, Crushing	18310	310	13010	322	6195	322
SUNDYN 4	Dynamic Impact	17050	310	12260	322	2699	323
DESIGN LOAD COMBINATION (FULL LOAD ON ONE PIER, AVERAGE LOAD ON OTHERS)
SUNICE 1	Static (Full Load on 2)	28010	310	22780	322	7636	522
SUNICE 1	Static (Full Load on 1)	17010	210			7257	215
LOAD ON PIER 1
SUNDYN 3	Static	12883	210	7629	322	4123	215
SUNDYN 3	Dynamic Impact	10420	210	6637	322	2636	215
Pier 8	Dynamic Impact	17930	210			2279	211

6. DISCUSSION

1. It is seen that the natural periods of the structure are such that the dynamic effects do not magnify the static response. This is expected because the natural frequency of the structure is much lower than that of the forcing function.
2. The dynamic analysis is based on the forcing functions being applied to one pier at a time. This is acceptable because the crushing events will not be in phase. When the forcing functions are out of phase, it is conservative to consider one pier at a time.
3. Full scour depth has been used in the analysis. The effect of reducing the scour depth will be to reduce the stresses but increase the dynamic magnification (due to increased stiffness). The net effect will be marginal.
4. The damping ratio used is 5% and is likely conservative. The damping ratio measured on bridge pier near Hondo is 19%. The damping ratio used for some piers at PEI crossing is 5%. Damping will have very little effect on impact type impulse loading.
5. Because of the vibratory nature of ice loading, the reinforcing and other detailing of the piers should provide good ductility. Confinement afforded by the casing is certainly advantageous.

7. ACKNOWLEDGMENTS
The input forcing functions and static loads were developed by Garry Van Der Vinne and David Andres of Trillium Engineering and Hydrographics Inc. The discussions involving the mechanisms of ice failure and development of forcing functions and were extracted from their report.

8. REFERENCES

[1] Montgomery, C.J., Gerard, R. and Lipsett, A.W., Dynamic response of bridge piers to ice forces; Canadian Journal of Civil Engineering, Vol. 7, No. 2, June 1980, pp. 345-356.

[2] Ghali, A., Tadros, G. and Langohr, P.H., "Northumberland Strait Bridge: analysis techniques and results", Canadian Journal of Civil Engineering, Vol. 23, No. 1, February 1996, pp. 86-97.