CRUSHING FAILURE DURING ICE-STRUCTURE INTERACTION
Devinder S. Sodhi
U. S.Army Corps of Engineers
Cold Regions Research and Engineering Laboratory Hanover, NH, USA
Devinder.S.Sodhi@erdc.usace.army.mil or
dsodhi@crrel.usace.army.mil
Estimation of Ice Failure Forces
• Analytical methods
• Small-scale and medium-scale tests
• Full-scale measurements
• We need to follow all three approaches to
understand the ice failure processes and to gain
confidence in our estimation
No movement
Open water
Mixed modes
Crushing Creep Sliding-glancing
Floating loose floes Misc. failure modes
1% 10%
15%
39%
15%
6%
9%
1%
Ice rubble interaction4%
Pressure-Area Curve
Saeki and Ozaki
(1980)
Joensuu & Riska (1989)
Tuhkuri (1995, 1996)
Ice Crushing: Medium-scale Tests
• Field tests near Abashiri (sponsored by JOIA)
• Data from tactile sensors
• No intermittent crushing (Rigid structure)
• Ductile-to-brittle transition speed between 0.3
and 3 mm s
–1Setup for Edge-Indentation Test
Tactile Pressure Sensor
Width = 100 or 146 mm
Crushing Failure Map Edge Indentation
Indentation Speed
Low………..High Transition Speed
Structures:
Rigid Compliant
Transition Speeds
Ductile Brittle
Ductile Intermittent Crushing (Ductile and Brittle)
Brittle
Ductile Deformation: Force and Contact Ratio
Indentation rate = 0.33 mm s
-10 20 40 60 80
Tim e (s)
0 5 10 15 20
Total Force (kN)
0.0 0.2 0.4 0.6 0.8 1.0
Contact Area Ratio
Test 10
Load Cell Data Tactile Sensor Data
Ductile Deformation: indentation speed = 0.33 mm s
-1Ductile Deformation: Pressure Data
Indentation rate = 0.33 mm s
-1MPa
0 1 2 3 4 5 6 7 8 9 10 11 12
Interfacial Pressure (MPa)
0 40 80 120
Minimum: 0.0 MPa Mean: 6.9 MPa Median: 7.7 MPa Maximum:11.5 MPa Std. Dev.: 2.7 MPa
Brittle Failure: Force and Contact Area Indentation rate = 502 mm s-1
3 5 7 9 1 1
T im e (s )
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0
Total Force (kN)
0 .0 0 .2 0 .4 0 .6 0 .8 1 .0
Contact Area Ratio
T e s t 9 3
L o a d C e ll D a ta
T a c tile S e n s o r D a ta
Brittle Crushing: indentation speed 502 mm s
-1Brittle Failure: Pressure Data
MPa
0 1 2 3 4 5 6 7 8 9 10 11 12
Interfacial Pressure (MPa)
0 100 200 300
Minimum: 0.0 MPa Mean: 1.6 MPa Median: 1.1 MPa Maximum: 6.5 MPa Std. Dev.: 1.5 MPa
Dynamic Ice-Structure interaction
0 5 10 15 20 25
Time (s)
0 5 10 15 20 25 30
Total Force (kN)
-5 0 5 10 15
Structural Deflection (mm)
Test 26
0 5 10 15 20 25
Time (s)
0 5 10 15 20 25 30 35
Total Force (kN)
-5 0 5 10 15 20 25 30
Structural Deflection (mm)
Test 27
Structural Stiffness = 2.45 MN m-1 Indentation speed = 37.1 mm s-1
Structural Stiffness = 1.12 MN m-1 Indentation speed = 36.3 mm s-1
Dynamic Ice-Structure Interaction
14.2 14.5 14.8 15.1
Time (s)
740 760 780 800 820
Carriage Position (mm)
740 760 780 800 820
Indentor Position (mm)
Indentor
Test 88
Carriage
14.2 14.5 14.8 15.1
Time (s)
0 5 10 15 20
Total Force (kN)
0.0 0.2 0.4 0.6 0.8 1.0
Contact Area Ratio
Load Cell Data Tactile Sensor Data
Indentation rate
= 54 mm s-1
Dynamic Ice-Structure Interaction
Indentation Speed= 54 mm s
-1Loading Phase: Pressure Data
MPa
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Interfacial Pressure (MPa)
0 20 40 60 80
100 Minimum: 0.0 MPa
Mean: 5.1 MPa Median: 4.5 MPa Maximum:14.1 MPa Std. Dev.: 4.1 MPa
Extrusion Phase:Pressure Data
MPa 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Interfacial Pressure (MPa)
0 50 100 150 200 250
Minimum: 0.0 MPa Mean: 1.9 MPa Median: 1.2 MPa Maximum: 9.9 MPa Std. Dev.: 2.1 MPa
Correlation Length
0 10 20 30 40 50
Distance X (mm)
0.0 0.2 0.4 0.6 0.8 1.0
Correlation Coefficient
exp[-x/(4 mm)]
Test 93 Test 10
Ice Crushing: Edge Indentation
• f(x, t) = ∫ p(x, y, t) dy (force per unit area at a point on the structure)
• Non-simultaneous failure of ice: g(t)=∫ f(x, t) dx
Average local force per unit width µf(t) Standard deviation of local force σf(t) Correlation coefficient: exp(-x /L)
• Average global force: µg(t)=w µf(t)
• Standard deviation: σg(t)2= 2L σf(t)2[w-L{1–exp(–w/L)}]
• Fmax= µg(t) + 3 σg(t)
• pmax= Fmax/(wh)
Aspect Ratio Effect
0 2 4 6 8 10 12 14 16 18 20
Aspect Ratio w/h
0 1 2 3 4 5 6 7
Relative Pressure Ratio
Coefficient of variation = 0.5 Coefficient of variation = 1.0 Coefficient of variation = 2.0
L/h = 1
0 2 4 6 8 10 12 14 16 18 20
Aspect Ratio w/h
0 1 2 3 4 5 6 7
Relative Pressure Ratio
Coefficient of variation = 0.5 Coefficient of variation = 1.0 Coefficient of variation = 2.0
L/h= 0.1
Comparison: small-scale & full-scale
Data from Full-Sale Measurements
Data from Full-Sale Measurements
Data from Small-Scale Tests
0 2 4 6 8 10 12 14 16 18 20
Aspect Ratio (w/h)
0 1 2 3 4 5 6
Maximum Effective Pressure (MPa) Present study
150-mm-wide indentor (Sodhi 1998) 250-mm-wide indentor (Sodhi 1998) 350-mm-wide indentor (Sodhi 1998) Indentation rate > 100 mm s-1
0.01 0.02 0.03 0.04 0.05 0.07 0.10 0.20 0.30 0.40 0.50 0.70 1.00
Ice Thickness (m)
0.1 1.0 10.0
0.2 0.3 0.4 0.5 0.60.7 0.8 2.0 3.0 4.0 5.0 6.07.0 8.0
Maximum Effective Pressure (MPa)
Molikpaq data: ice speed >= 100 mm/s (Wright and Timco 1994) Small-scale data: continuous brittle crushing (Sodhi 2000)
Small-scale data: 3-segment indentor (Sodhi 1998a) Small-scale data: 5-segment indentor (Sodhi 1998a) Small-scale data: 7-segment indentor (Sodhi 1998a)
Medium-scale data: JOIA Indentation Tests ( speed 3-30 mm/s)
Comparison of Small-Scale and Full-Scale Data
Summary
Crushing Processes during Edge Indentation
•Ductile deformation at low indentation rate - high peff
•Brittle failure at high indentation rate - low peff
•Sharp transition between these modes for rigid structures
•Ductile and brittle crushing for compliant structures
•Statistical approach to explain aspect ratio effect
•Derivation of local-pressure-to-global-pressure ratio
Wall indentation is mechanically similar, but geometrically different, to edge indentation
There is speed effect, resulting in ductile and brittle crushing, but there is no size effect
