Experimental Apparatus

The experimental setup diagram is shown in Figure 1. The apparatus was designed to allow for the following:

• i) use of variously sized sea ice samples

• ii) variable vertical stress

• iii) variable shear velocity

• iv) variable shear stress rate

Testing Procedure

A horizontally movable shear box was used. Shear force was supplied by a hydraulic jack. The sea ice sample was placed in the circular hole in the shear box. Shear failure tests were conducted in this box. Static vertical loading was accomplished by placing weights on the sea ice sample via the steel cap. The shear velocity (thus, shear stress rate) was controlled by varying the hydraulic pressure applied to the jack.

Fig. 1. Diagram of the experimental setup.

Instrumentation

The sea ice sample was held immobile by the fixed lower half of the shear box. Shear velocity was measured using a standard displacement transducer attached to the movable upper half of the shear box. The shearing force was measured using a standard load cell connected to the movable upper half of the shear box. The vertical load was measured by weighing the added weights, steel cap and associated structure.

Diameter to length ratio effects

Figure 3 shows the relation between the shear strength (TS) and the diameter (d) to length (I) ratio (d l l) of the sea ice sample. Although the test results exhibit scatter, it can be seen that the smaller the ratio (d/l) becomes, the larger the value of T_s becomes. Post experiment examinations of the fractured specimens showed two types of failure. In the case of d/l‹2, the failure was induced by shear only; with d/l›2, the failure was not caused by shear alone since the existence of a small gap between the ice sample and shear box introduced a bending moment.

Shear area effects

Figure 4 shows the effects of the shear area on shear strength; ie the larger the ice sample diameter the smaller the value of T_s became. An analogous relation exists in concrete. Future tests with larger sample diameters will have to be conducted to establish the relation between the _s of a test sample and the T_s of the actual ice sheet.

Shear velocity and stress rale effects

Since ice is a visco-elastic solid, its shear strength varies with the strain rate ? and stress rate T_s.; thus, selection of the strain rate or stress rate is important when testing ice. When using cylindrical samples in direct shear tests, the strain rate over the plane of shear failure is not uniform; therefore, the authors determined the relation between T_s and shear velocity δ_δ.The three values, the strain rate i, stress rate TS and shear velocity 6s, are defined by the following equations:

where ∆l = strain, l = shear length, t = time to shear failure

strain rate:

Where τ_s = direct shear strength, t time to shear failure

Shear velocity: δs

Figure 3 shows the relation between the shear strength (τ_S) and the diameter (d) to length (j) ratio (d/j) of the sea ice sample. Although the test results exhibit scatter, it can be seen that the smaller the ratio

where Δ1 = strain, t = time to shear failure

Figure 5 shows the effects of shear velocity 6s on the shear strength. It can be seen that the shear strength T_s is relatively insensitive to changes in shear velocity in the range 0.01 to 1.0 mm/s; T_s broadly peaks about 0.1 mm/s.

Converting the sample’s circular cross section to an equivalent square cross section produces an equivalent shear length B, where B is derived as follows:

where d = diameter of the ice sample.

Fig. 5. Effects of shear velocity ^δ _s on the shear strength ^τ _s.

Fig. 6. Effects of shear stress rate T _s on the shear strength

Using this shear length B in Equation 1 produces a strain rate ofof 0.001 se¹at the maximum shear strength T_s. This value coincides with the rates found in compressive strength tests.

The relation between τ_s and shear stress rate T_s is shown in Figure 6. The shear strength T_s is relatively insensitive to changes in shear stress rate T_s in the range 0.1 x 10⁶ to 10 x 10⁶.N/m’.s.

Sea ice temperature effects

In general, the strength of ice depends on its temperature. The experimental relation between the shear strength and ice temperature is shown in Figure 7. Descriptively, the figure can be divided into two temperature regions: -2 C > T > -6 C and T < - 6 C. The shear strength clearly increases between -2°C and -6°C, but generally remains constant or decreases for T < -6°C. This phenomenon for T < -6°C, the remaining constant or decreasing of T_s, appears to be caused by the dilitancy of sea ice.

Vertical stress effects

The experimental relations between the shear strength T_s and vertical stress σ_v, as a function of ice temperature T, are shown in Figure 8(a) for 1981 and in Figure 8(b) for 1982, As can be seen,T _s increases with decreasing ice temperature T_s increases linearly with increasing vertical stress σ_v for ice temperatures

Fig. 7. Relation of and ^τ _s as a function of σ_v

Fig. 8a. Relation of ^τ _s and σ_v as a function of T (1981).

Fig. 8b. Relation of ^τ _s and σ_v as a function of T (1982).

Fig. 9. Relation between φ* and T.

higher than about -6°C; at lower ice temperatures (-9 C to -14°C in Figure 8(a) and -11 °C to -20°C in Figure 8(b) the relation between τ_s and σ_v is not linear. The results (at temperatures higher than about -6 C) coincide with Coulomb’s equation for direct shear strength; i.e., T_s and <r_ are linearly dependent.

Coulomb’s equation:

where C* friction, =apparent cohesion, Φ* = vertical stress.

angle of internal

Relation between φ* and T

The relation between the angle of internal friction Φ* and ice temperature T is shown in Figure 9. It can be seen that φ* increases with decreasing ice temperature when the shear force is applied perpendicular to the growth direction. With the shear force applied parallel to the growth direction, φ* tends to remain almost constant.

Fig. 10. Relation between C* and T.

Fig. 11. Application envelope of Coulomb’s equation.

Growth direction effects on C*

Figure 10 shows the results of the growth direction effect test on C*; ie, τ_s at σ_v = 0. Although the test results exhibit scatter, it can be seen that C* in shear planes perpendicular to the growth direction is generally greater than C* in planes parallel to the growth direction (at equivalent sample temperatures). With decreasing sample temperatures, the C* in planes perpendicular to the growth direction tends to increase more rapidly than in planes parallel to the growth direction.

The application envelope of Coulomb’s equation

As determined from the results of five years of sea ice experiments summarized in Table I, the application envelope of Coulomb’s equation is shown in Figure 11. In region A, Coulomb’s equation is applicable for the determination of the shear strength of sea ice. The shear strength in region C is independent of vertical stress In C* region B, the relation between τ_s and σ_v is not linear because of the dilitancy of sea ice.

Ice temperature

The shear strength of sea ice increases, approaching a constant, with decreasing ice temperature (see TEST RESULTS - 4).

Shear velocity and stress rate

The shear strength is not greatly dependent on either the shear velocity or stress rate (see TEST RESULTS - 3).

Growth direction of sea ice

The shear strength in planes perpendicular to the growth direction is generally greater than in planes parallel to the growth direction (see TEST RESULTS -7).

Shear Area

The shear area experimental results (see TEST RESULTS - 2) indicate that the shear strength decreases with increasing shear area. Analogous relation exists in concrete.

Diameter to length ratio

The smaller the ratio becomes, the larger the value of τ_S becomes (see TEST RESULTS - 1).