Breach Mechanics Theorem and Development

The first step in understanding breach mechanics was to evaluate soil mechanics in brief. We then proceeded to discuss the history and cases of breach mechanics in our previous blog. It should thus not seem to be a recent theory since man has been collecting water for ages. This was majorly used to develop agriculture and prevent cases of flooding as seen in ancient Egypt and India etc.

However, some well-intentioned kings ended up experiencing more losses due to poor planning. Recent events have brought about unforeseen events that have radicalized breach mechanics as we know it. It is from recent dam failures that we have developed current models and equations to evaluate breach mechanics.

These Breach Mechanics models have enabled disaster preparedness levels to rise significantly. Predicting the extent of likely damage may not be 100% accurate. The degree of accuracy may not even reach 80%. This is because of the majority of factors that are often ignored in such calculations. It is impossible to incorporate all the factors likely to affect embankments in a single physical-based numerical model.

The table above shows the most recent cases of failures, types, and the extent of the damage.

Types of Embankments and Materials

1. Earthfill Embankments: These are trapezoid-shaped and are made of pervious material. The material is compacted hard enough to retain the water and includes sand, gravel, clay, and silt. These are further categorized into natural (from landslides or large earth movements) and man-made. Man-made, on the other hand, comprises of rockfill dams, coastal dikes, earthfill dams, and river dikes.
2. Non-earthfill Embankments: Non-earthfills are made with material such as masonry (stones sealed with mortar and bricks) and concrete. Unlike the former, these are not affected by failures brought about by soil erosion. Their failure is characterized by abrupt ‘dam-breaks’ with a sudden release of a shock-like wave.

Since we’ll be focusing on earthfill embankments, we’ll also take a look at the types of materials and their characteristics. They include;

• Fine-grained soil – These are characterized by a low shear strength, low permeability, and high compressibility. The pore pressure usually comes when the shear strength is reduced during construction.
• Coarse-grained soil – These are pervious, easy to compact, and not highly affected by changes in moisture. They are at times used in core zones but mostly in shells and drain zones. They have high shear strength, ought to be free draining display homogeneity.
• Broadly graded soil – These fall between fine and coarse. They exhibit low compression, higher shear strength, and lower hydraulic conductivity. They happen to be highly resistant to attacks from earthquakes.

The factors to test and consider when analyzing material properties include;

• Specific gravity
• Unity weight
• Gradation
• Compressibility
• Shear strength
• Permeability.

Modeling the Breach Embankment

The core objective of these models is simply to predict the discharge variation in respect to time. This usually happens downstream and is shown through the evolving breach channel. Embankments brought about by piping and overtopping usually undergoes 3 phases;

• Breach initiation: In these stages, the outflow is rather negligible and the damage extent is felt at the downstream slope. This is the point where crest elevation is at a minimum due to construction problems, design choices, or settlements.
• Breach formation: In overtopping, the breach forming at the downstream vertex is mounting and more noticeable. Overtopping failures are now more prominent as a shallow breach channel develops on the entire slope.
• Breach propagation: By now, there is an increasing hydraulic head in the reservoir region. Erosion levels are much worse due to the continuous breach outflow. Side-slope failures begin to happen as the breach enlarges further. The topsoil collapses the conduits in piping failure. The peak value is attained by the breach outflow. Beyond this phase, the channel created now reaches the valley floor.

Cohesive and non-cohesive embankments typically undergo different breach mechanics erosion processes. These can be illustrated through 2 major approaches to models – mathematically and experimental.

Mathematical Model

• Empirical Modelling

The mission is to find peak outflow done using the power-law below:

The empirical models draw from databases of past experiences. This is simply the statistical data of a considerable sample of previous embankment breach failures. This data of peak flow is not possible to assess during the embankment breach. This presents challenges that lead to measurements being taken during the flood’s stage. Even when this happens, it doesn’t necessarily depict actual flooding peak-flow conditions.

Accuracies rely majorly on the number of documented failures recorded in the database. There are a good number of factors that determine breaching during peak flow. At times, they may vary by a single order of magnitude. Regressions analysis is used to derive empirical relationships. Both single-regression and multiple-regression come in handy to statisticians during making these predictions.

• Parametric and Dimensionless Models

The principles used here are essentially the same. They tend to present the breach channel evolution as a system following a linear growth rate. The final channel is either described as triangular, trapezoidal, or parabolic. Down the slope, the cross-sectional area may evolve from triangular to trapezoidal as the breach channel increases in magnitude.

This model assumes uniformity in erosion plus regular breach shapes which simplifies calculations. Dimensionless models also use the empirical methods used. They express the breach mechanics characteristics and variables in a dimensionless format. This involves an analysis method such as the Buckingham II Theorem. One then progresses to derive the equation through regression analysis.

• Physical-Based Numerical Models

These take the numerical analysis a step further through simulating the predictions made. The processes simulated include soil erosion, sudden collapse mechanisms, hydrodynamics, reservoir routing amongst other geotechnical processes. Coming up with a physical model for these physical processes has been a grand challenge for researchers.

This leads to oversimplification or neglecting certain key features. The result is inaccurate results that are unable to fully depict actual ground conditions. Their ease of computation once these factors are ignored has even led to the development of other simpler models.

Experimental Modeling: Making Use of Labs and Field Tests

It is possible to carry out experiments in the lab and in-situ conditions to portray piping and overtopping. To develop these, laws and legislation had to be developed over the years. These movements started in Europe after realizing the massive impact of dam failures. Later on, the European Union decided to pour money for 2 years on this project. They formed the Concerted Action on Dambreak Modelling (CADAM) which covered 10 European countries.

The goal was to enhance research and foster inter-universities relations. The research was geared towards numerical modeling and dambreak experimentation modeling. During the period, the countries had 4 workshops which reached the following conclusions;

1. Physical-based models bring about the best results in calculations.
2. Breaches do not always necessarily grow in a trapezoidal manner.
3. Developing constant shapes for breaches and erosion is quite unrealistic.
4. Since human observations are unreliable, there’s a general need for improved field and lab tests.
5. Large-scale testing needs to be applied.
6. A numerical and physical breach model need to be identified using better parameters.
7. There was a necessity to model unsteady erosion and sediment transportation.
8. A further need for more collaboration and research.

Since then, it has become imperative to focus research on certain key areas;

• Geophysics data collection
• Uncertainty analysis
• Flood propagation
• Breach formation
• Sediment movement.

Developing and Testing the Breach Mechanics Theorem

There have been multiple methods that have been used in testing breach failures. No matter how computerized the processes are, it is still impossible to incorporate all the factors involved. Tests used in piping are quite different from those used in overtopping.

Scale-series tests have been used to assess overtopping. Some of these tests include the drainage test, compaction test, quasi-exact geometrical test, and the tilted geometric scale tests. Researchers have developed a detailed method for data acquisition as well as data extraction.

Instrumentation has made use of digital and video cameras, piezometers, and wave gauges. As technology progresses, soil mechanics engineers are also trying to establish concrete ways to carry out the data to produce better results.

Conclusion and Winding Remarks

So far, we have established the different models that can be used to predict overtopping and piping breaches. Several tests have had to be established but the research has not stalled yet. Better instruments have had to be used but perfection is still not a reality. Human observations were previously mainly used but this has never since become fully reliable.

The computer age has brought about ease of calculations and simulation models. That notwithstanding, it is impossible to incorporate all the factors into these computer simulations. More research is needed to develop more efficient methods. It is this knowledge that will enable us to step into a bolder future.

There have been far too many deaths over the centuries resulting from breach failures. This calls for the affected parties to pool their minds together in an innovative stance. All hope is not lost yet – we have before us a chance to solve this problem in an innovative, and this innovative age.