## "If you can't explain it simply, you don't understand it well enough" (Albert Einstein)

## geo

## "If you can't explain it simply, you don't understand it well enough" (Albert Einstein)

## What is the effect of tensile cracks in slope stability analysis?

*In slope stability, an important factor to consider is the presence of tensile cracks, as they typically constitute evidence of a landslide in process. These cracks are quasi-vertical in most cases, and are caused by the separation between grains of soil or rock due to a tensile force resulting from the movement of the land mass. Do you want to learn more about the effect of tensile cracks on slope stability? Continue reading this post...*

#### Table of Contents

### Tensile cracks in soil slopes

Tensile cracks are evidence of a landslide in process, since they are caused by the loss of cohesion or bonding of the soil structure due to a tensile force associated with a movement that has occurred in the land mass.

To understand the effect of these cracks, let us review Figure 1, published by Terzaghi (1956), which illustrates the subject well enough. According to Terzaghi, the effect of the presence of tensile cracks in a slope can be summarized in three fundamental aspects (see Figure 1):

Figure 1 Influence of tensile cracks in slope stability (Soruce: Terzaghi, 1956).

- Tensile cracks eliminate the resistance due to the cohesion provided by the arch e-e'. As a result, cracks reduce the total shear resistance per unit length of the slope.
- Tensile cracks reduce the driving moment produced by the element efe1 of weight ΔW, which is a positive effect on stability

- In case of rainfall, a hydrostatic pressure exerted by the water surface inside the cracks is generated, which favors slope instability.

On the other hand, depending on the characteristics of the materials present in the slope, a softening effect of the soil can be generated due to water entering the slope body through the cracks. This softening effect is basically a reduction in strength due to an increase in moisture content (Barnes, 2010). Figure 2a illustrates this effect for clays of different plasticity, and Figure 2b shows the same effect, but for clays with different sand or gravel contents.

Figure 2 Effect of soil softening due to presence of water (Source: modified from Barnes, 2010)

As can be seen from the figure above, for a moisture content increase of only 1%, the change in shear strength is much greater for low plasticity clays and for clays with high gravel contents. That is, these soils are more sensitive to wetting and more prone to softening due to water that may penetrate into the soil mass through tensile cracks.

### Tensile cracks in rock slopes

In the case of rock slopes, the worst effect associated with tensile cracks occurs when they are filled with water. Under these conditions, a hydrostatic thrust is produced, whose value is of the order of 9.81 kPa (≈ 0.1 kg/cm2) per meter of water height, which can generate a significant negative effect on the slope. To understand this effect, let us consider the example in Figure 3, taken from Sancio (1995).

Figure 3 Effect of hydrostatic thrust of a rock mass (Source: modified from Sancio, 1995).

For illustrative purposes, in this slope it is assumed that the slip surface over which movement can occur is horizontal. Thus, for this potential failure surface, if there are no external forces acting on the mass, the factor of safety FS would be infinite.

Now, if a crack of height h is filled with water, the water exerts a horizontal thrust equal to 1/2γωh2 per meter of crack length (where γω = unit weight of water). Introducing this new force into the equilibrium equations, the FS is now equal to the ratio of the coefficient of friction (tanφ) to the tangent of the slope (tanψ). Thus, if both are 30°, the factor of safety is equal to 1, i.e., the collapse point is reached.

This example demonstrates how drastically the situation on a slope can change when a crack fills with water. It also provides insight into the cause of some landslides when heavy rains occur, although in these cases it must be fulfilled that the crack fills with water faster than the crack can drain. An important detail is that the crack opening does NOT influence the hydrostatic thrust, so a landslide could be generated just by emptying a very small amount of water at the appropriate place on the slope.

### General comments about tensile cracks effects

Based on what has been reviewed in the previous sections, it is essential to consider the presence of tensile cracks in the stability analysis, taking into account the following:

- The depth of the crack;
- That it is full of water;
- The possible softening of the soil if the slope presents more than 20% of clay particles (verification that can be made from a granulometry analysis by sieving and hydrometer, in several samples taken from the slope);
- The drainage characteristics of the slope, to check if the crack fills or drains more quickly.

Finally, it is worth mentioning that the position of the tensile cracks is an important guide to establish the location of the zone where failure surfaces are generated during stability analyses, so that these potential failure surfaces correspond to what is observed on the slope in the field.

### References

- Barnes, G. (2010)
**“Soil Mechanics: Principles and Practice”**. Third Edition. Palgrave – Macmillan. Hampshire, England. - Sancio, R. (1995)
**“Elementos de Hidrología e Hidrogeología”**. I Curso Panamericano de Movimientos de Masas. Barquisimeto, Venezuela. - Terzaghi, K. (1956)
**“Theoretical Soil Mechanics”**. John Wiley & Sons, Inc. New York. USA.