Stress and strain of snowpack

Stress and strain of snowpack
Snow Deformation Stress and strain of snowpack Beginning of a slab avalanche. The release was triggered by skis cutting moving near the top of the rounded ridge seen in the upper left corner of the picture. Credit: A. Duclos,

Stress and Strain of Snowpack
Snow Deformation Stress and Strain of Snowpack Sudden fracturing of the snowpack, which is a clear sign of stress & instability. Credit: A. Duclos,

Snow Deformation Stress and strain of snowpack Deformation of the spx occurs in 3 modes: Compression Tension Shear Compression – grains or spx is compressed or forced together Tension – grains or spx is pulled apart Shear – grain slide past one another – initial failure usually due to shear stress In loose snow avalanche shear stress>shear strength For slab avalanches, shear strength is a major factor in resistance of fracture propagation

Snow Deformation Stress and strain of snowpack Creep The alpine snowpack is always creeping, due to metamorphism (90% settlement and 10% deformation of ice grains) and its high porosity. Creep rates in snow are high due to high porosity and snow is always near its melting temperature. Creep rates increase exponentially with 1/T. Settlement from rearrangement of ice grains due to weight of layers above

Snow Deformation Stress and strain of snowpack Creep Long-term effect of compressive stress is increase of density & hardness w/r to depth During densification, snow hardness increases Hardness is more related to strength than density. Term Strength (Pa) Hand test Graphic Very low fist Low 4 fingers Medium 1 finger High pencil Very high > 106 Knife blade Ice

Snow Deformation Stress and strain of snowpack Creep 1. Simple case: horizontal with constant depth All deformation is in the vertical direction: Settlement Rates of settlement vary from 10 cm/day in low-density snow to what? Rate of creep decreases with depth, because density increases w/respect to depth (little room for grain settlement). Less settlement is observed in well-faceted snow (e.g., depth hoar) Settlement of snow is largely by rearrangement of grains caused by the weight above.

Snow Deformation Stress and strain of snowpack Settlement Densification and Strengthening For example one-dimensional equations governing the heat transfer, water transport, vapour diffusion and mechanical deformation of a phase changing snowpack are required to characterize settlement. New snow, wind drift and snow ablation are treated as special mass boundary conditions. Snow is modelled as a three-component (ice, water, air) porous material capable of undergoing large irreversible viscous deformations. Settlement of snow is largely by rearrangement of grains caused by the weight above.

Snow Deformation Stress and strain of snowpack Creep 2. Snowpack on inclined slope Total deformation of snow pack is in the down slope direction Resolve stress into vector components

The stresses that cause deformation in the snowpack
Stress (s) = force/unit area s = F/A

Force Force: changes in the state of rest or motion of a body.
Only a force can cause a stationary object to move or change the motion (direction and velocity) of a moving object. Force = mass x acceleration F = ma Mass = density x volume m = rV r = m/V Weight is the magnitude of the force of gravity (g) acting upon a mass. The newton (N) is the basic (SI) unit of force.

Units of Stress 1 newton = 1 kg meter/sec2 = a unit of force
1 pascal = 1 newton/m2 = a unit of stress 1 kPa = lb/in2 9.81 Pa is the pressure caused by a depth of 1mm of water 1 N = ≈ lb 101,325 Pa = kPa

Two components stress 1. Normal stress, sn and the component that is parallel to the plane, shear stress, ss Normal compressive stresses tend to inhibit sliding along the plane and are considered positive if they are compressive. Normal tensional stresses tend to separate rocks along the plane and values are considered negative. 2. Shear stresses tend to promote sliding along the plane, labeled positive if its right-lateral shear and negative if its left-lateral shear.

Two components stress 1. Normal stress, sn and the component that is parallel to the plane Normal compressive stresses tend to inhibit sliding along the plane and are considered positive if they are compressive. Normal tensional stresses tend to separate rocks along the plane and values are considered negative. 2. Shear stresses, ss , tend to promote sliding along the plane, labeled positive if its right-lateral shear and negative if its left-lateral shear.

Stress on a 2-D plane: Normal stress act perpendicular to the plane Shear stress act along the plane. Normal and shear stresses are perpendicular to one another

Components of stress Three normal stresses Components parallel shear stresses Reference system x, y, z

s1 > s2 > s3 State of Stress s1 = s2 = s3
If the 3 principal stresses are equal in magnitude = isotropic stress If the principal stress are unequal in magnitude = anisotropic stress The greatest stress is called s1 The intermediate stress, s2 and minimum stress is called s3 s1 > s2 > s3 What is it called if all three principal stresses are equal? s1 = s2 = s3

sn = s cos2q ss = s sin2q Stress on an inclined slope 2 components
Normal stress & Shear stress sn = s cos2q ss = s sin2q

STRESS STRENGTH FAILURE OCCURS! VERSUS WHEN STRESS EXCEEDS STRENGTH
An avalanche occurs when the load, or stress, applied to the snow exceeds its strength. WHEN STRESS EXCEEDS STRENGTH FAILURE OCCURS!

Squeeze a block of snow between two planks of wood
AB, trace of fracture plane that makes an angle q with 3. The 2-D case is simple, since 2 = 3 (atmospheric pressure) Snow

Snow Deformation Stress and strain of snowpack Shear Stress & Slope angle Fraction of shear deformation as a percentage of total creep (combined shear and compressive deformation vs slope angle. Two thirds of the total deformation is in shear w/slope angles > 25° and nearly 90% of the total occur on slopes >45°! Slope dependence of the deformation components is one explanation of the slope angle dependence of slab avalanche formation. Calculations for low density snow Shear creep deformation depends on the type of snow and the slope angle.

Snow Deformation Stress and strain of snowpack Glide Entire snowpack slips over the ground or at an interface such as an ice layer. Maritime climate, smooth rock face When snow is dry, glide is small (high internal friction in snowpack) Important in the formation of slab avalanches that involve full depth of snowpack. Also responsible for high forces on lift towers and power lines. Rates vary from 1 to 100mm/d. Fastest rates on smooth grassy slopes or rock slabs From McClung and Clarke 1999 Snow stiffness (viscosity) decreases with increasing water content, making creep easier over ground surface.

Snow Deformation Stress and strain of snowpack Glide Observations show: Smooth interface Temperature at the interface or bottom of spx at 0°C (need free water) Slope angle > 15° (roughness of typical alpine ground cover) Maritime climate, smooth rock face When snow is dry, glide is small (high internal friction in snowpack) Important in the formation of slab avalanches that involve full depth of snowpack. Also responsible for high forces on lift towers and power lines. Rates vary from 1 to 100mm/d. Fastest rates on smooth grassy slopes or rock slabs From McClung and Clarke 1999 Snow stiffness (viscosity) decreases with increasing water content, making creep easier over ground surface.

Snow Deformation Stress and strain of snowpack Glide Models assume that the water within the spx and at the snow/ground interface is the critical parameter that determines glide velocity and glide avalanche release. McClung and Clarke (1987) Clarke and McLung (1999) When snow is dry, glide is small (high internal friction in snowpack) Important in the formation of slab avalanches that involve full depth of snowpack. Also responsible for high forces on lift towers and power lines. Rates vary from 1 to 100mm/d. Fastest rates on smooth grassy slopes or rock slabs Snow stiffness (viscocity) decreases with increasing water content, making creep easier over ground surface.

Snow Deformation Stress and strain of snowpack Glide Clarke and McClung (1999) emphasize the effect of water on the interface geometry, rather than the effects of varying shear viscosity and viscous Poisson Ratio with varying water content. When snow is dry, glide is small (high internal friction in snowpack) Important in the formation of slab avalanches that involve full depth of snowpack. Also responsible for high forces on lift towers and power lines. Rates vary from 1 to 100mm/d. Fastest rates on smooth grassy slopes or rock slabs Snow stiffness (viscocity) decreases with increasing water content, making creep easier over ground surface.

Snow Deformation Stress and strain of snowpack Glide Recent studies suggest that the ground showed only minor variation through the winter, while glide rates fluctuated substantially through the winter. When snow is dry, glide is small (high internal friction in snowpack) Important in the formation of slab avalanches that involve full depth of snowpack. Also responsible for high forces on lift towers and power lines. Rates vary from 1 to 100mm/d. Fastest rates on smooth grassy slopes or rock slabs Snow stiffness (viscocity) decreases with increasing water content, making creep easier over ground surface. Figure 5. Full-depth glide avalanche trigger mechanisms (source data from Lackinger, 1987 and Clarke and McClung, 1999)

Snow Deformation Stress and strain of snowpack Glide This suggests that the effects of water on partial separation of the snowpack from the glide interface and in filling of irregularities in the ground has a greater affect on glide velocity than varying snow properties. When snow is dry, glide is small (high internal friction in snowpack) Important in the formation of slab avalanches that involve full depth of snowpack. Also responsible for high forces on lift towers and power lines. Rates vary from 1 to 100mm/d. Fastest rates on smooth grassy slopes or rock slabs Snow stiffness (viscocity) decreases with increasing water content, making creep easier over ground surface. Figure 5. Full-depth glide avalanche trigger mechanisms (source data from Lackinger, 1987 and Clarke and McClung, 1999)

Snow Deformation Stress and strain of snowpack Glide When snow is dry, glide is small (high internal friction in snowpack) Important in the formation of slab avalanches that involve full depth of snowpack. Also responsible for high forces on lift towers and power lines. Rates vary from 1 to 100mm/d. Fastest rates on smooth grassy slopes or rock slabs Snow stiffness (viscocity) decreases with increasing water content, making creep easier over ground surface.

Snow Deformation Stress and strain of snowpack Shear failure of alpine snow ss Snow on a slope deforms in shear and settlement (compressive forces) almost like a viscous fluid. Elastic portion of deformation occurs – recoverable Unrecoverable or permanent deformation occurs – viscous portion High deformation rates, sudden brittle failure occurs Temperature dependence. Increase T, viscous effects become stronger. With wet snow the it takes a lot of energy to to propagate brittle shear fractures. Mechanism initiating slab avalanche release changes from brittle shear propagation (dry snow) to glide-induced tensile failure (wet snow) when water is found at the failure interface. Elastic, viscoelastic, and permanent deformation

Snow Deformation Stress and strain of snowpack In general, dry snow can not fracture unless a critical rate is exceeded. 100x or greater than the rate of creep deformation When snow is dry, glide is small (high internal friction in snowpack) Important in the formation of slab avalanches that involve full depth of snowpack. Also responsible for high forces on lift towers and power lines. Rates vary from 1 to 100mm/d. Fastest rates on smooth grassy slopes or rock slabs Snow stiffness (viscocity) decreases with increasing water content, making creep easier over ground surface. Ski trigger,snow machine, explosives, etc.

Snow Deformation Stress and strain of snowpack How are high rates produced to cause propagating fractures? Stress concentrations on asperities. Fracture mechanics suggest that flaw or crack will increase local stress by ~102 When snow is dry, glide is small (high internal friction in snowpack) Important in the formation of slab avalanches that involve full depth of snowpack. Also responsible for high forces on lift towers and power lines. Rates vary from 1 to 100mm/d. Fastest rates on smooth grassy slopes or rock slabs Snow stiffness (viscocity) decreases with increasing water content, making creep easier over ground surface.

Snow Deformation Stress and strain of snowpack Strain softening Resistance to deformation decreases after peak strains. Shear bands or slip surfaces form during deformation. Combine the strain softening with natural flaws will concentrate shear deformation Critical stresses and rates produce rapidly propagating shear failure in the weak layer. Shear failure of alpine snow deformed at 0.1mm/min.

Components of shear strength in snow
Snow Deformation Components of shear strength in snow Shear failure depends on: Density Hardness Temperature Rate of deformation Quality of bonding to adjacent layers Components of Shear Strength Cohesion Friction Formation of avalanches determined by the mechanical properties of the snow and failure is a result of applied stress. Static stress

Snow Deformation Components of shear strength in snow Components of Shear Strength Cohesion Friction Strength property that determines avalanche type is cohesion. Loose snow avalanche = lack of cohesion Slab avalanches = cohesion that forms blocks Cohesion: Bond strength Shape of snow crystals Density of bonds (bonds/unit volume)

Snow Deformation Components of shear strength in snow Components of Shear Strength Cohesion Friction Loose snow avalanche = lack of cohesion Low Cohesion: Cold temperatures Snow falling w/ windless conditions Low density snow Cold temperatures- slow bond formation Snow falling w/ windless conditions- grains are not fragmented or packed (low number of bonds/unit volume) Low density snow- low number of bonds/unit volume Unrimed, dendritic snow falling during cold, windless conditions Rounded graupel that do not bond to adjacent grains Wet snow – increase water content = decreasing cohesion – wet loose avalanches

Snow Deformation Components of shear strength in snow Components of Shear Strength Cohesion Friction Controlling factor in slab avalanches Friction: Snow texture Water content Weight of snow layers above (increase normal stress) Friction – resistance to motion between layers Friction at top of snowpack = zero and increases with depth. In general, friction and cohesion increase with depth Bond strength and number of bonds/unit volume increase with depth – increase normal stresses With avalanche formation, when cohesion is near zero in near-surface (e.g., loose snow avalanche) or when snow strength (cohesion and friction) is low below the surface of the snow (slab avalanche) compared to adjacent layers

Snow Deformation Components of shear strength in snow Components of Shear Strength Cohesion Friction With avalanche formation, when cohesion is near zero in near-surface (e.g., loose snow avalanche) or when snow strength (cohesion and friction) is low below the surface of the snow (slab avalanche) compared to adjacent layers Shear failure under different normal pressure. Cohesive strength at STP is 3kPa.

Snow Deformation Shear failure in snow Shear Strength Density
Grain size Temperature Overburden Fracture Line Studies Plot shows variation of shear strength w/respect to density. Strength increases with density Shear strength of surface hoar layer = 25 – 400 N/m2

Grain size Temperature Overburden Strength highest in fine-grained snow with rounded grains.

Grain size Temperature Overburden Snow is stiffer and stronger as it gets colder. Snow becomes stiffer and stronger as it gets colder

Snow Deformation Shear failure in snow
Snow becomes stiffer and stronger as it gets colder Stiffness (resistance to deformation) increases by a factor of 3 as snow temperature decreases from -2°C to -15°C

Grain size Temperature Overburden Compressive forces (normal stress) on a weak layer increases to friction component of strength. Snow becomes stiffer and stronger as it gets colder

Snow Deformation Loose snow avalanche Little cohesion
Near surface initiation Low cohesion snow may be either wet or dry Important point w/respect to water content is that wet loose snow avalanches can be more massive than dry ones Slope angle must exceed the angle of repose or static friction angle Free water in snow, subsurface now entrained if wet

Snow Deformation Loose snow avalanche Little cohesion
Near surface initiation Triggered by location loss of cohesion due to metamorphism or effects of sun or rain. Initiation often near rock outcrops (solar radiation causing higher temperatures). Triggering by melt due to warming by sun or rainfall on the snowpack

Snow Deformation Loose snow avalanche Angle of repose for dry snow
Laboratory studies snow Dry snow: stellar crystals have highest angle of repose (up to 80°), decreasing for round forms (to 35°). Wet snow: Water content is the controlling factor. Angle of repose decreases as water content approaches saturation. Two additional important effects from loose snow avalanches: Tend to prevent slab avalanche formation on steep slopes by sluffing Serve as a trigger for slab avalanches below

Snow Deformation Slab avalanche Cohesive layer overlies
thinner, weak layer Dry-snow slab avalanche release is generally believed to proceed in three stages: initiation of a local failure (crack) widespread fast propagation of that fracture beneath the slab detachment of the slab from its margins. Bed surface: the surface over which the slab slides. Crown: breakaway wall of the top of the slab. Formed by tensional stress through the depth of the slab from bottom to top Flanks: Left and right side of the slab. Smooth surfaces formed by shear fractures, tensional fractures or combination Stauchwall: Lowest down slope fracture surface. Forms at the same time as the flanks, before slab moves downhill.

Snow Deformation Slab avalanche Characteristics Slope angle
Crown thickness Slab density Failure layer density Slab & bed hardness Slab & bed temperature Stratigraphy of slab and failure layer Geometry 200 slabs

Crown thickness Slab density Failure layer density Slab & bed hardness Slab & bed temperature Stratigraphy of slab and failure layer Geometry Data for 200 dry slabs

Crown thickness Slab density Failure layer density Slab & bed hardness Slab & bed temperature Stratigraphy: slab & failure layer Geometry 70 dry slabs Most slabs consist of wind-deposited or well-bonded old snow.

Crown thickness Slab density Failure layer density Slab & bed hardness Slab & bed temperature Stratigraphy: slab & failure layer Geometry 70 dry slabs. Density of failure layer>slab above. Why – density increases w/respect to depth. Density not a reliable indicator of strength in snow stability. Density increases with depth, but strenght may or may not increase.

Crown thickness Slab density Failure layer density Slab & bed hardness Slab & bed temperature Stratigraphy: slab & failure layer Geometry Hardness of weak layer nearly always very low or low. Failure surface of medium hardness or higher is rare – exceptional cases that may be overlooked. Contrast between slab and failure layer hardness is an important factor in instability. Weak layers < 1mm thick are hard to evaluate in a snow profile Hardness of slabs range from very low (fist) to high (pencil). Soft slab = v. low or low hardness Hard slab = medium or harder

Crown thickness Slab density Failure layer density Slab & bed hardness Slab & bed temperature Stratigraphy: slab & failure layer Geometry 100 dry slabs 90% have Temp greater than -10°C. What slabs have a colder bed surface –thin or thick. Freq. of slab avalanches decrease as T approaches 0°C. Also the decrease of slab with colder temperatures. Cold Temperatures occur during cold windless night – thus no wind loading. Creep rates decrease with low Temperatures – snow becomes stiffer

Crown thickness Slab density Failure layer density Slab & bed hardness Slab & bed temperature Stratigraphy: slab & failure layer Geometry 100 dry slabs 90% have Temp greater than -10°C. What slabs have a colder bed surface –thin or thick. Freq. of slab avalanches decrease as T approaches 0°C. Also the decrease of slab with colder temperatures. Cold Temperatures occur during cold windless night – thus no wind loading. Creep rates decrease with low Temperatures – snow becomes stiffer Difficult to classify! Continental climates: greater tendency for slabs fail on weak layers in old snow

Crown thickness Slab density Failure layer density Slab & bed hardness Slab & bed temperature Stratigraphy: slab & failure layer Geometry 26 dry slabs Shear fractures can propagate over 1 km! Flank to flank dimensions are 10 – 1000x slab thickness. Confined regions: length > width – gullies. Creep rates decrease with low Temperatures – snow becomes stiffer Dependent on terrain Unconfined slopes, open slopes: field data suggests slab width>downslope length Confined slopes: length > width

Snow Deformation Dry Slab Avalanche Formation FRACTURE SEQUENCES
Shear stress > shear strength Rate of deformation in weak layer must be fast enough to inititate fracture 26 dry slabs Shear fractures can propagate over 1 km! Flank to flank dimensions are 10 – 1000x slab thickness. Confined regions: length > width – gullies. Creep rates decrease with low Temperatures – snow becomes stiffer

Snow Deformation Dry Slab Avalanche Formation INITIAL FAILURE
26 dry slabs Shear fractures can propagate over 1 km! Flank to flank dimensions are 10 – 1000x slab thickness. Confined regions: length > width – gullies. Creep rates decrease with low Temperatures – snow becomes stiffer INITIAL FAILURE Collapse by a interface layer Shear frx produce tension frx at the crown

Snow Deformation Dry Slab Avalanche Formation INITIAL SHEAR FRACTURE
26 dry slabs Shear fractures can propagate over 1 km! Flank to flank dimensions are 10 – 1000x slab thickness. Confined regions: length > width – gullies. Creep rates decrease with low Temperatures – snow becomes stiffer INITIAL SHEAR FRACTURE Crown tension fracture near skier

Snow Deformation Wet Slab Avalanche Formation
26 dry slabs Shear fractures can propagate over 1 km! Flank to flank dimensions are 10 – 1000x slab thickness. Confined regions: length > width – gullies. Creep rates decrease with low Temperatures – snow becomes stiffer COMPLEXITY OF WATER FLOW IN WET SNOW

Snow Deformation Snow Deformation
Wet Slab Avalanche Formation Snow Deformation Water reached impermeable boundary – reduced friction – resulting in tensile fracture due to frictional reduction. LUBRICATION MECHANISM FOR GLIDING ON ICE LAYER

Bonding, Failure, and Avalanche Release
If failure reaches a critical point, fracture will result. Fractures propagate by spreading along a layer of snow as bonds between grains break. Fractures also tend to propagate from weak point to weak point in the slab. Weak points: 1) shallow areas in the snowpack, 2) thin spots in the slab, and/or 3) places where the integrity of the slab is disturbed (e.g. rocks or trees protruding into or through the pack).

Stress Strength Strength: the bonds that are holding everything together Stress: F/A applied to the bonds that reduce in bond strength The bonds in the snowpack are always in a state of balance between strength and stress. The process of assessing this balance is called snow stability, although it would probably be more accurate to call it snow instability

Slab avalanche 1) Harder to predict 2) Weak layers hidden below surface 3) Failure propagates Slab failure/fracture: 1) There be cohesion between grains; enough that the snow will act as a unit. 2) A strong layer must overlie a weak layer. 3) A trigger must initiate failure. 4) Stress must overcome strength.

How pronounced the strong over weak layering depends on the characteristics of: Failure layer Terrain Characteristics of the layer(s) that make up the slab. Measuring a difference of two hand hardness grades or more is critical. Slab failure/fracture requirements: Cohesion Strong layer over weak layer. Trigger initiates failure. Stress overcomes strength.

The point where failure is initiated is called the trigger point.
Bonding, Failure, and Avalanche Release The mechanism that initiates failure (the process of failure and fracture) is referred to as a trigger. The point where failure is initiated is called the trigger point. Natural Triggers Artificial Triggers Trigger point

Triggers can be natural or artificial. Natural triggers: related to changes in weather or the snowpack, such as, new snow, wind transported snow, temperature, etc. Artificial triggers: related to human activities,: such as skiing, operating machinery, applying explosives, etc.

Triggers: Natural Artificial. Bonding, Failure, and Avalanche Release
It is important to understand the difference between a start zone and trigger point. Start: where avalanche are likely to start (we see the fracture line here) and Trigger points: where the failure that causes an avalanche to start is initiated. Trigger points may or may not be in start zones. Triggers: Natural Artificial.

For stress to overcome strength, load on the slab has to increase or the strength of the bonds holding the slab in place has to decrease. Natural or artificial loads may be added slowly and gradually or rapidly. The bonds in the snowpack adjust readily to slow loading. Slow Loading: Snowpack adjusts well Rapid Loading: Snowpack adjusts poorly

Slab release: Shear failure Tensile failure Compression failure

Slab release: Shear failure Tensile failure Compression failure What happens first…, followed by…, or is the sequence is always the same, or what is the role of compression in failure, and does it occur sometimes or always.

We observe rapid snow failure even when avalanches do not occur. The “whumpf” or collapse of a slab when we ski onto it is a sign of compressional failure. Cracks that occur in the snow as we ski across it are tensile failures. When we ski across a slope and the slab fails and moves downhill but stops and does not avalanche, shear failure has occurred.

Stress and strain of snowpack

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