Guide to Trenching: Angle of Repose

Between 2003 and 2017, 373 people died from trenching-related incidents in the U.S. Of those deaths, 80% of them occurred on professional construction sites. Lack of leadership buy-in, cost-cutting, and lack of safety knowledge among employers and workers are the leading causes in the number of trench accidents every year.

Cave-ins, coming into contact with live power lines, and equipment falling into trenches are a few hazards that come with trenching. To prevent additional deaths, pre-excavation inspections and trench reinforcement are necessary for all job sites. Understanding the angle of repose and shoring, two key considerations for safe trenching, is imperative to having efficient excavations that prioritize safety.

The Angle of Repose Explained

The critical angle of repose is the maximum angle at which materials can be heaped without sliding down the side of a pile. This angle is formed between the slope of the pile and its horizontal base.

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The angle of repose falls between 0 and 90 degrees and varies for different material classes. At angles greater than the angle of repose, the material will slide down the side of the slope and the pile structure will crumble as that material falls at a greater rate.

You can estimate the angle of repose with the following function: Angle of repose = (Tan-1)*(2h/d)

In this formula, h is the height of the pile, while d is its diameter. You multiply the height by two, divide it by the diameter, then take the inverse tangent (tan-1) of this value.

Variables Affecting the Angle of Repose

The critical angle of repose isn't a single value. Several variables affect what that angle is, which accounts for the range of angles found in many material classes. The following variables should be considered when evaluating the angle of repose:

Type of Material: Different materials have different angles of repose since their chemical composition and physical shape affect how easily they slide. Generally, sandy soils have a greater risk of sliding, and in turn, a smaller angle of repose than granular soils do.

Friction: Whenever the particles within materials are squished close together, there is strong friction between those particles. This force densely binds the particles together, resulting in a steeper angle of repose.

Water Content: Increasing the water content within soil causes it to slide faster and reduces friction between particles. It also reduces soil bearing capacity, or the soil's ability to support weight. So, wet materials will always have smaller angles of repose than dry materials.

Measurement Method: The measurement method you choose should align with the material whose critical angle you require. Some methods are better suited to different material classes and applications than others.

Particle Roundness: How round the particles are within a material affects its ability to slide. Generally, materials flow more smoothly when they have round particles. Thus, the angle of repose decreases in materials with round-edged particles.

Measuring the Angle of Repose

It's important to establish how you're going to use the material in question. Testing the angle of repose is important in many applications. For example, the dimensions of a silo are determined by the repose of the grain. Similarly, the soil must be tested before digging a trench to ensure the angle is accurate and safe. Here are a few methods used to measure the angle of repose for different material classes:

Tilting Box Method

The tilting box method, which operates exactly as it sounds, measures the angle of repose for materials with particle widths of up to 10mm. These materials are typically fine-grained, such as silt and clay.

To measure the critical angle, the material is poured into a transparent box and leveled. Then, the operator tilts the box at a rate of 18 degrees per minute until the material starts to significantly slide down the slope. A transparent box provides you with visibility when measuring the sliding angle.

Fixed Funnel Method

With the fixed funnel method, the operator pours the material into a funnel to form a cone-shaped pile. Stop pouring when the pile reaches a pre-established height or width. By taking the inverse tangent of the angle between the pile's height and radius, you'll find the angle of repose value.

Revolving Cylinder Method

Commonly known as the drum method, the operator places material into a spinning cylinder. As the cylinder spins, it forms the dynamic angle of repose or the point where the material rolls down a slope from end to end. It's roughly 3 to 10 degrees less than the static angle of repose.

Hollow Cylinder Method

The hollow cylinder method uses a non-moving cylinder to measure the static angle of repose. It works best for sand, gravel, and other coarse-grain materials with consistent pour flow. The operator places material inside a hollowed-out cylinder, then pulls it up and off at a constant speed. This forms a pile whose angle of repose is measured similarly to the fixed funnel method.

The Angle of Repose Chart

The above-mentioned methods work well but are mainly used for experiments and theoretical applications. Below are the approximate angles of repose for different materials in various conditions:

Relevance to Trenching

To prevent cave-ins and maintain structural integrity, contractors use a technique known as sloping while digging trenches. With sloping, the soil located at the top of the trench walls is cut on an angle facing inwards, which creates a funnel-like shape leading into the trench.

So, how do you determine the magic angle trenches are sloped at? Queue the angle of repose! Any soil sloped at the angle of repose or less won't slide into the trench onto the people working inside of it. When trench walls aren't sloped and remain perpendicular to the ground's surface, the soil will slide into the trench to achieve natural stability.

Soil lying beyond the area of repose is referred to as the zone of influence. Any disturbances to the zone of influence can trigger cave-ins. If your trench walls are set at an angle greater than the angle of repose, additional supports are required to reinforce the trench.

Structural Supports for Trenches

Deep trenches and areas with unstable soil require more structural support than sloping alone can provide. Shoring and trench boxes are the main techniques used to safely reinforce trenches.

Shoring

Shores are structural supports that temporarily bear the load of trench walls or damaged buildings. A shore structure is comprised of beams or walls that push against the sides of the trench while holding the earth in place. Once workers have completed work in the trench, contractors remove shoring from bottom to top. This ensures that workers are protected at every step of the trench construction process.

There are many shoring techniques, including hydraulic shoring, contiguous pile, secant pile, and sheet pile shoring, among others. It's a good idea to reinforce most trenches with shoring. However, shoring is only required for trenches deeper than 4 feet according to Occupational Health and Safety standards and 5 feet according to OSHA standards.

Trench Boxes

Trench boxes mitigate damage in the event of a cave-in. They aren't a shoring technique and are the last line of protection for workers inside the trench. Shoring props up the trench walls to improve structural integrity, while trench boxes step in if shoring efforts fail.

Trench boxes are essentially the airbags of trenches. You're supposed to have a seatbelt on as the priority measure to keep you safe, while the airbag only goes off if needed.

Construction trench boxes are made when two parallel metal panels are connected by struts to form the box, so workers have openings to work from while standing inside. Similar structures called manhole boxes are used to safely complete work in manholes.

Prioritizing Trench Safety

Overall, site managers need to actively prioritize trench safety to prevent further injury and fatalities. Understanding the critical angle at which material starts to slide down a slope and incorporating that angle into trench design is the first step in doing so. Using sloping, shoring, and trench boxes to stabilize deep trenches will reduce the leading cause of death on job sites.

Leaders set the tone for safety prioritization on site. You need to play an active role in creating a culture that promotes safety efforts that go beyond the site inspector's visit day.

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FAQs about the Angle of Repose:

How do you calculate the angle of repose?

The angle of repose formula is as follows:

Angle of repose = Tan-1*(2h/d), where h= the height of the material pile and d= the diameter of the pile

What's the typical angle of repose?

There isn't a typical angle of repose, since it varies for each type of soil or material. However, the angle of repose is always an acute angle, which ranges from 0 to 90 degrees. Refer to the angle of repose table above for the typical angles in each material class.

What does a high angle of repose indicate?

A high angle of repose, a steeper angle, means that the material can be piled higher without sliding down the slope. Soils with higher angles of repose have greater stability and won't slide as easily.