# R&D Project 5 – The modelling pressure on concrete dam walls project

Concrete dam walls are made up of concrete and steel reinforcements. They face pressure and stresses of different types due to water pressure, weight of dam, waves and ice pressure and many other factors. This creates stability issues in the dam. This report examines all the stress and pressure that concrete dam walls face and devises an algorithm in order to deal with the pressures.

There are various kinds of pressure that a concrete dam wall faces.

## Water stresses and pressure:

The water in the dam acts perpendicularly on the upstream wall’s face. Now there can be two conditions when the upstream face of the wall is vertical and the downstream side of the dam is empty. The water pressure is in a horizontal direction as well as it acts on the upstream wall or the face at a certain height of H/3 from the bottom of dam. The water pressure can be computed by using the equation below: (Joel Anderson)

**Forces acting on dam **

If there is a presence of slope at the upstream side of the dam pressure acts vertically downwards due to presence of a water column that rests on the slope on the upstream side wall. This pressure can be calculated as:

**Stability issue due to water pressure: **

Stability issues arise when there is water pressure at only one side of the concrete wall e.g the upstream side. The concrete wall has to be strong enough to bear the water pressure to ensure stability of wall.

**Weight of dam: **

The weight of dam includes the weight of concrete walls, mass of all the construction material used and all additional shapes or structures given to it. This weight can be calculated using formula as follows: (Joel Anderson)

W= Pc * V * g +Σ Fex

Where ‘Pc’ represents density in Kg/m3

‘V’ represents Volume in m3

‘Σ Fex’ represents the sum of all installations in the dam

**Ice pressure on dam concrete walls: **

As the climatic variations occur snow or ice sheets over the surface of dam can add to the dam weight. If the thickness of the ice sheets is greater than 0.4 m then it cannot be neglected. (Joel Anderson)

**Pressure due to waves: **

There are some loads that are dynamic, such as the variations in the water flow. The waves generated are moving at a faster rate and hit the dam wall with pressure that has the potential to crack the concrete walls. Small magnitudes can be neglected but larger magnitude imparts great pressure. (Joel Anderson)

**Silt and rocks sediments pressure: **

Rock sediments and silt often get deposited over the dam beds. This will create additional pressure on the dam’s walls, depending on the dimensions of the rocks. The pressure due to sediments can be calculated using the formula:

Ps = (Ka * r * Z32)/2

Here r represents the saturated unit weight of the sediments

Z3 represents the depth of sediment

Ka equals to: Ka= 1-sin θ / 1+ sin θ

Where θ is the angle of the shearing resistance of the sediment

**Earthquakes and erosions: **

Whenever any seismic activity occurs, it releases energy and results in the sudden breaking of the dam. This results in tsunamis. In addition, sudden erosions or volcanic eruption can also result in earthquakes.

**Uplift pressure and seepage loads pressure: **

At the base of concrete dams there is pressure due to the creation of cracks and fissures as water penetrates into them. This pressure can be controlled by using relief drains in the lower part of dam.

**Stability issues**

There are three kinds of stability issues or failure modes that can occur in the dam. Those are: (Joel Anderson)

**Rotation and overturning: **

Many types of pressures are exerted on the dam. If the resultant forces at any section of dam pass through the toe of the dam it will rotate and overturn and create instability in dam.

**Translation and sliding: **

This type of instability occurs when the sum of the horizontal forces acting on a dam at its base exceeds the sum of frictional forces, generating a sliding failure.

#### Overstress and material failure:

Sometimes the material used in construction fails, such as cracks in the concrete walls. Water seepage in these cracks can create instability in walls.

**Algorithm to deal with stresses and pressure on dam walls**

## SPECIFIC MILESTONE OBJECTIVES

The project comprises 3 milestones, where:

### Milestone 1 is divided into 4 milestones:

Milestone 1A – Coupling analysis of unsteady seepage and stress fields in discrete fractures network of rock mass in dam foundation

Milestone 1B – Numerical stress-deformation analysis of cut-off wall in clay-core rockfill dam on thick overburden

Milestone 1C – Deformation and cracking of seepage barriers in dams due to changes in the pore pressure regime

Milestone 1D – Develop algorithms to predict capacity to resist forces based on different mixes, extent of reinforcement, dam wall heights, thickness and optimal geometrical structure shapes

### Milestone 2 is divided into 4 milestones:

Milestone 2A – Investigations of blocks in foundations and abutments of concrete dams

Milestone 2B – Analysing the dam-break problem for Herschel–Bulkley viscoplastic fluids down steep flumes

Milestone 2C – Finite element analysis of buttress dams, coffer dams and diversion dams in wide valleys including the effect of crack formation at the concrete-rock interface

Milestone 2D – Finite element analysis of arch dams, gravity dams and embankment dams in wide valleys including the effect of crack formation at the concrete-rock interface

### Milestone 3 is divided into 4 milestones:

Milestone 3A – Predicting near-field dam-break flow and impact force using a 3D model

Milestone 3B – Discrete element simulation of granular flow in 2D and 3D hoppers: dependence of discharge rate and wall stress on particle interactions

Milestone 3C – Develop visualisations and animations for areas investigated

Milestone 3D – Develop decision support matrix for geological shape, concrete mix, required reinforcement and thickness for input volume perimeters