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# At rest (ko) wedge?

## At rest (ko) wedge?

(OP)
We can calculate the active (ka) wedge distance and passive (kp)mwedge distance behind/in front of a wall.

is there such thing as an "at-rest" (ko) wedge and if so, how do i calculate it?

### RE: At rest (ko) wedge?

"Wedge distance"? Do you mean a triangular pressure distribution? If so, the calculation is the same as for active and passive, with just a different coefficient of earth pressure.

### RE: At rest (ko) wedge?

it'd be 45 degrees, eh?

f-d

ípapß gordo ainÆt no madre flaca!

### RE: At rest (ko) wedge?

(OP)
Hokie66 - to clarify, i meant the distance back from the wall that the wall supports i.e. for a wall designed for active pressures, the soil in the active wedge is defined by (45 deg + phi/2) e.g. for a clay with a friction angle of 30 deg, the active wedge angle would be 45 + 30/2 = 60 deg from the bottom of the wall. using trigonometry or getting out the protractor, i can then work out the distance back from the wall that the wall supports.

### RE: At rest (ko) wedge?

I have not gone through the trouble, but given a Ko you can back out the wedge angle using something akin to a trial wedge.

### RE: At rest (ko) wedge?

in order for the angle to be less than 45 degrees (greater, depending on your perspective), there'd have to be movement. Ko assumes no movement.

f-d

ípapß gordo ainÆt no madre flaca!

### RE: At rest (ko) wedge?

I have not heard of a failure wedge for the at rest condition. If the wall is not permitted to rotate, hence the at rest condition, there will be no sliding surface therefore a rupture plane will not develop.

If however, you have a case where the wall rotates but the deflection is less than 0.001H (say 1 mm), then you can assume the failure wedge for active condition is an upper bound solution. This gives you a setback of about 0.5H to 0.8H to the failure plane from the back face of the wall.

### RE: At rest (ko) wedge?

I agree with fixedearth. My thoughts are if you are not allowing soil friction to develop (i.e., at rest conditons), that'd be a, "failure wedge" similar to phi=0, so the, "angle" would be 45 degrees.

f-d

ípapß gordo ainÆt no madre flaca!

### RE: At rest (ko) wedge?

I still don't think DougHole is talking about a "failure wedge", and believe he has confused the Rankine triangular pressure distribution with something else.

### RE: At rest (ko) wedge?

(OP)
to clarify further and to give some context around the question....

I have a stepped 2 level basement ret wall that will be propped by the slabs at ground level, -1 level and -2 level.
the upper basement wall is 3m high
the lower basement wall is 3m high
the distance between the upper and lower walls is 5m
the walls will be restrained at the top of the walls by the basement slab so we are assuming ko (at-rest) conditions
unit weight of soil=20kN/m3
ko say 0.5

the question is..

will the upper wall load up the lower wall? or can i assume they are completely independent? i.e. upper wall with a triangular pressure distribution of 0 kPa at the top and 0.5 x 20 x 3 = 30kPa at the bottom and the lower wall with exactly the same pressure distribution (0kPa at the top and 30kPa at the bottom).

### RE: At rest (ko) wedge?

No, that is certainly not correct. The lower wall pressure is going to be much more than the upper wall pressure, just because it is further underground.

The pressure may not be triangular, but rather trapezoidal. And if the offset of the upper wall is to the earth side, the upper levels may also impose a surcharge on the lower level wall.

Suggest you have your geotechnical consultant take a close look at this section through the building and advise accordingly.

### RE: At rest (ko) wedge?

boussinesq has equations for determining the horizontal stress increase from surface loads. We've had some disagreement ont his forum on how to interpret such equations. I was taught to double the calculated results when considering the influence on a retaining wall.

f-d

ípapß gordo ainÆt no madre flaca!

### RE: At rest (ko) wedge?

In my opinion, the upper wall would not directly load the lower wall such that it would make it tip over. However, the upper wall could make the lower wall slide as it loads the soil behind the wall or creates a global stability type of loading.

Not sure this is a solution but I would look at it a couple of ways before I would treat them as being independent.

### RE: At rest (ko) wedge?

Doctormo,
The OP has a 2 level basement wall, braced by the building at 3 levels, not 2 cantilevered walls. Sliding or overturning should not be issues.

### RE: At rest (ko) wedge?

hokie66 - Hmmm, I think a figure by the OP would be helpful.

"I have a stepped 2 level basement ret wall that will be propped by the slabs at ground level, -1 level and -2 level.
the upper basement wall is 3m high
the lower basement wall is 3m high
the distance between the upper and lower walls is 5m
the walls will be restrained at the top of the walls by the basement slab so we are assuming ko (at-rest) conditions"

I am not sure how a basement wall is restrained at the top by the basement slab. I think I need a sketch.

### RE: At rest (ko) wedge?

I can draw two sections from the description, one with the upper wall offset 5m to the earth side, the other offset away from the earth side. So I agree a sketch would help.

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