calculation of soil weight behind a retaining wall

[NHJ]

Hi..
I want to calculate the resistance forces against sliding in a retaining wall design, the water table is in the surface, so should I use the total unit weight or the the effective unit weight to calculate the soil weight behind the wall? the total unit weight for the soil is 18, so should I use 18 or (18-10) because of the presence of the water?

 

[Okiryu]

The "acting" horizontal force exerted by earth pressure is Ph = 0.5 x (ka or ko)x r' x H^2, where r' is the effective unit weight (~8 kN/m3). Do not forget to consider the force exerting with the water also (0.5 x rw x H^2).

However, I would use the total unit weight (~18 kN/m3) for the "resisting" horizontal force (weight of soil on the heel multiplied by the friction coefficient at the base of the wall).

 

[NHJ]

Thank you for your answer. so, I should calculate the vertical forces (W stem + W base + W soil)using the total unit weight for the soil not the effective in spite of the presence of water, then multiply the summation by the friction coefficient at the base.

 

[oldestguy]

Your concrete section that is submerged also is buoyed up by water.

 

[NHJ]

what do you mean? how does the water affect the concrete section in the calculations???
I have used unit weight 24 Kn/m3 for the concrete to calculate the stem and base weights, and a unit weight 18 Kn/m3 for the soil on the heel to calculate its weight. is this alright?

 

[Ron]

Since the soil is exerting pressure on the wall, trying to slide it, use the total weight of soil (conservative). As OG noted, the concrete is part of the resistance to sliding so you should consider its buoyant weight, not its total weight. Using this approach you maximize the forces on the wall and minimize its sliding resistance force, so your answer has some safety in it.

 

[oldestguy]

For example take any solid material and tie a string to it, attached to a scale. Weight it in air. Then lower it into water. That measurement will be the weight in air minus the weight of water that is displaced. For example a chunk of saturated wood, weighed that way is likely to show zero or close to it when submerged.
Dry wood won't sink, but is buoyed up by the volume of water displaced. So concrete being of heavier unit weight than water will have some weight still under water. of course I am only talking the reduction in effective unit weight for that part of the concrete below the water surface elevation.

 

[BigH]

Let's look at it in a bit of a different light. If you are building this retaining wall, then you will obviously (as anyone in practice would tell you) to ensure that the material behind the wall is drained. This can be done with a drainage layer laying up against the stem (some use a special geomembrane like a big thick PVD). In this case, the hydraulic pressure against the wall will be reduced. How much depends on the capability of the drain to handle the water seepage from the fill/natural soil behind. So in the analysis you would use your bulk density for the soil above the phreatic surface and the bouyant weight below (gammabulk less gammawater) but then also have to include the water pressures in your pressure diagram.

If you don't do provide the drainage, then your retaining wall will be like a dam - check out your text books for flow nets on a dam. Draw a flow net and you will see what OG is saying - the wall will have uplift pressures on the base. These uplift pressures will have to be included in your force/moment diagrams.

 

[Okiryu]

BigH, is anyway to determine/calculate how good your drain may perform, so you can neglect hydraulic pressures in the wall? or is it just based on "engineering judgment"? For example, if you specifiy granular fill plus clean gravel behind the stem, so you have good drain capability there, can hydraulic pressures be neglected?

 

[BigH]

Okiryu - you will need/may need graded filters - but yes, that is why drains are used behind the wall - although many times, now, they are also using geotextile mats (like big pvd mats). You might want to be a little pessimistic and include a couple of meters of hydrostatic (say 1/10th wall height). I would suggest you look into Harry Cedergren's book "Seepage, Drainage, and Flow Nets" 3rd Edition. He quotes Brandl (1987) - 'Drainage measures are absolutely necessary." See Fig 10.1. Always try to have seepage control and seepage should always be vetical (it doesn't destabilize) (Brandl - Chapter 47 as in "Ground Engineer's Reference Book" edited by F.G. Bell).

Cedergren does caution - that with filters - failures have occurred but these were caused by materials used out of spec. (a sand and gravel having too much silt and clay size).

As for you last point - remember that all filter drains must have a positive outlet - in other words water entering must exit - same as dam drains.

 

[AdityaDeshmukh]

Use lateral earth pressure to calculate stress distribution of stresses. Usually for water table conditions, you add the weight of water to lateral earth pressure separately. Due to water, tension zone also might form in the retaining section. I hope this is helpful.

 

[fattdad]

For the long-term design condition you always use effective stress. That requires consideration for pore pressure. If there are engineering controls to limit the pore pressure (i.e., a drain) then that will influence the pore-water pressure. If there are none, then it won't.

You are talking about resistance. You are not talking about the applied horizontal force (i.e., active or at-rest earth pressures). You are also talking only about the sliding mode of failure. So, that's an, "Ntan(delta)" topic. The, "N" is based on the total or buoyant unit weight above the sliding surface. That total weight includes the soil above the failure surface and it includes the concrete above the failure surface. Both the soil and the concrete need to consider the position of the phreatic surface with buoyant below and total unit weights above.

Now the question is how to determine, "Delta," which is the interface friction angle. It may or may not be the same as phi.

Hope I helped!

f-d

ípapß gordo ainÆt no madre flaca!

 

[aeoliantexan]

I like to use a free-body diagram when questions arise regarding total weight and buoyant weight. The top of the footing heel supports the full weight of the overlying soil, water and all. If the water is buoying up the soil, it is also pushing down against the footing.

The bottom of the footing feels the effective stress of the soil and the upward pressure of the water. Frictional sliding resistance is equal to the effective stress normal to the bearing surface times the coefficient of friction between the concrete and the soil (this is smaller than the phi angle) times the area. If you take the total weight of the overlying soil, plus the total weight of the footing and wall, minus the hydrostatic uplift (pressure times area) you have the force that can be multiplied times the coefficient of friction to get the ultimate frictional sliding resistance.

You could definitely use the buoyant weight of the overlying soil and the buoyant weight of the footing as a shortcut and forget the hydrostatic uplift. But the shortcut makes is harder to keep track of the details. If the ground water at the supported side is at the ground surface, the water under the toe of the footing probably does not have the full hydrostatic head, or it would be squirting out from under the footing. So the hydrostatic uplift pressure must not be uniform. If a toe drain is provided to dispose of the seepage while preventing piping, the hydrostatic uplift pressure may be a triangle. It is important to know that when you calculate overturning moments.