THE INFLUENCE OF CUTTING ANGLE ON THE FAILURE PATTERN OF FROZEN SOIL

I. G. Basov, Yu. N. Luzgin

(Presented by the Department of Mining Machines, Mine Transport, and Mining Mechanics)

In most cases, soil is a loose rock. To study the laws of the mechanics of such a rock, many researchers use a structural substitution scheme, which is a set of individual particles of regular shape (most often spherical). From the geometrical point of view, for the plane problem the most probable structure is considered [1] to be one with an arrangement of particles providing four points of contact.

When soil freezes, the water contained in its pores crystallizes. Ice particles commensurate with them appear between the mineral particles. In this case the soil may be represented by a structure with a denser packing of particles, providing six points of contact for the plane problem. The strength of the soil thereby increases sharply.

However, even in this state the soil is capable of compaction under appropriate loads, since even with dense packing of equal-volume spherical particles the pore volume reaches 26% [2].

When frozen soil is destroyed by a tool with cutting angle \(\alpha = 90^\circ\), at the initial moment the soil is compressed by an amount corresponding to the maximum elastic and residual deformations of the soil for the given conditions (temperature, moisture content, etc.). As a result, the solid particles of the soil are rearranged into a denser packing through realization of the pores. Deformation of the soil volume located in front of the cutter occurs under the action of the cutting force and the friction force on the front face of the cutter, which are proportional to the mechanical characteristics of the rock. The friction force prevents the formed chip element from moving upward, while the rock mass prevents its sideways displacement. As a result, a volumetric stressed state of the chip element arises, with concentration of tangential stresses along planes passing along the cutter faces in the direction of its motion.

The stresses in the forming chip element will be greatest near the surface of the front face of the cutter and at a depth amounting to 0.75 of the chip thickness [3].

A further increase in the cutting force will cause, in the forming chip element, a limiting stressed state primarily in the zone of maximum pressures, whence cracks separating the main chip element will begin to develop. Following the propagation of the cracks

from the zone of maximum pressures toward the ground surface along a plane located at an angle \(\varphi\) (equal to the angle of internal friction of the soil), and along the lateral planes of maximum shear stresses, the main chip element will undergo shear.

Because the shearing of the chip element in the cutting plane occurs at an angle to the horizontal, there is always a certain variable volume of soil in front of the cutter, and therefore the cutting forces, while decreasing at the moment when the chip element separates, never reach zero. Further advance of the cutter causes a series of small spalls, increases the area of contact with the soil—which, among other things, depends on the plasticity of the frozen soil—and the cutting process is repeated in the order described above.

The processes occurring during cutting at an angle \(\alpha=90^\circ\) indicate that the profile of the furrow in its transverse section should not have a spoil bank, and experimental studies confirm this.

When frozen soil is destroyed by a wedge-shaped cutter, at the moment it comes into contact with the soil, indentation of the sharp punch occurs near the free surface. The forces required for this are small. The increase in the contact surface of the front face with the soil occurs due to compaction of the volume of soil located in front of the wedge-shaped cutter. As it advances further, an ever larger volume is compacted, and thus a chip element is formed. In this case the indentation forces increase. As the cutter advances in the soil, in addition to the forces of resistance to compaction, it must overcome the adhesion forces between the moving particles of the forming chip element and the soil remaining in the mass.

The indicated processes continue until the deforming volume of soil reaches the limiting stressed state. Only after this will spalling of the main chip element occur, with realization of the surface of least resistance. This surface depends, in addition to the cutting angle, also on the density of the frozen soil.

In the case where the soil density is low and, consequently, the adhesion forces between particles are also small, separation of the chip element occurs similarly to separation during cutting by a cutter with an angle close to \(90^\circ\). In this case no spoil bank of the furrow is observed. In frozen soil, resistances along the cutting planes become greater than the resistances in the direction of action of the tearing force. The wedge-shaped cutter, acting on a bracing medium of particles bonded by ice cement, produces vertical tensile loads in the plane of the transverse section of the cut. When the limiting stressed state is reached, a spall of the chip element is formed in a transverse section having a shape approaching that of a trapezoid.

Experimental studies show that at cutting angles in the range \(90^\circ>\alpha>60^\circ\), the separation line of the main chip element passes in the cutting plane at an angle approximately equal to the angle \(\varphi\) of internal friction. However, the cutting forces in this case differ sharply [4]. This occurs because a change in the angle \(\alpha\) causes a change in the values of the normal and tangential components of the cutting forces. When a cutter with \(\alpha=90^\circ\) acts on frozen soil as a bracing medium with angle \(\varphi\approx30^\circ\), the component of the cutting force acting along the line of separation of the chip element will be equal to

\[ P'_{90^\circ}=P_{90^\circ}\operatorname{tg}\varphi=0.577P_{90^\circ}. \]

At $\alpha=60^\circ$, the force expended on separating a chip element is

$$ P'_{60^\circ}=P_{60^\circ}\sin\alpha\cos\varphi=0.75P_{60^\circ}. $$

The forces required to form two identical, newly formed surfaces under equal failure conditions must be equal to one another, i.e. $P'_{60^\circ}=P'_{90^\circ}$.

Then

$$ P_{60^\circ}=0.77P_{90^\circ}. $$

Experiments have shown that the cutting forces at $\alpha=60^\circ$ amount to 75% of the cutting forces at $\alpha=90^\circ$ for clay, 77% for sand, and 73% [5] for loam.

Table

When cutting by the free technology with an angle $\alpha=30^\circ \div 60^\circ$, as experimental data show, the cutting forces vary in proportion to the change in shear areas. Thus, the shear area at $\alpha=45^\circ$ is 70.8% of the shear area at $\alpha=90^\circ$, while the cutting forces, according to experimental investigations, amount to 69.2% for frozen clay, 70.8% for frozen sand, and 65% for loam [5] of the cutting forces at $\alpha=90^\circ$. At a cutting angle $\alpha=30^\circ$, the shear area is 57.8% of the shear area at $\alpha=90^\circ$; and the cutting forces amount to 57.7% for clay, 58% for sand, and 55% for loam [5] of the cutting forces at $\alpha=90^\circ$.

When cutting along a plane surface, lateral surfaces of the cut appear. In those cases where no collapse of the cut occurs, the required area may be found from the expression

$$ F_{\text{b}}=\frac{0.5h^2}{\sin\alpha\cos\alpha}. $$

The lateral shear areas at $\alpha=30^\circ$, $\alpha=60^\circ$, and $\alpha=90^\circ$ are equal to one another and amount to 115.5% of the lateral area at $\alpha=45^\circ$.

The cutting forces going into the formation of equal areas of the cut vary in proportion to the cutting force in cutting by the free technology (Table 1). Thus, for sand it averages 80.8%, and for clay 114%.

A comparison of the relative values of the cutting force going into the formation of the lateral surfaces of a rectangular cut at $\alpha=45^\circ$ with

comparison with analogous values at other cutting angles shows that the forces under consideration vary approximately in proportion to the change in the lateral areas of the cut. Thus, for sand these forces amount to 117%, and for clay to 109.5%, of the analogous cutting forces at \(\alpha = 45^\circ\).

When cutting along a flat surface, the cross-sectional area breaks out, but the breakout begins not from the bottom of the cut, but in its lower part. This is explained by the fact that the separation of a chip element is delayed by the indentation deformation of the sharp punch and occurs only after the cutter edge has penetrated by a certain amount.

Thus, the cutting angle determines the character of soil failure. If at \(\alpha = 90^\circ\) failure occurs mainly as a result of compressive and shear deformations, then at smaller cutting angles failure proceeds as a result of the development of compression and tensile deformations.

LITERATURE

1. I. I. Kandaurov. Mechanics of Granular Media and Its Application in Construction. Publishing House for Construction Literature, Leningrad–Moscow, 1966.

2. M. K. Kaapko. Sandy Rocks. Reference Manual on the Petrography of Sedimentary Rocks, vol. II. Leningrad, 1958.

3. A. N. Zelenin. Cutting of Soils. Publishing House of the Academy of Sciences of the USSR, 1959.

4. I. G. Basov, Yu. N. Luzgin. On the rational cutting angle of the teeth of earth-moving machines. Proceedings of TPI. (The present collection).

5. A. N. Zelenin. Failure of Frozen Soils by Cutting, Impact, and Vibration. TsINTIAM, Series IV. Moscow, 1962.