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# Lateral spring stiffness

## Lateral spring stiffness

(OP)
I appreciate any opinion or suggestion on the following matter:

I have to design a cantilevering retention system for a 7m excavation on a fine to medium clayey sand at founding level.
Unfortunately the geotech report specifies just the soil pressure profile to adopt for the structural design of the piers (bored piers at 2.5m ctrs and shotcrete) as that of Peck (1943) (ref. Bowles 5th ed. Fig 14-5).

I can find the embedment from the equilibrium of the trapezoidal soil pressure and the 200Kpa lateral allowable bearing pressure below excavation, but this doesn't help me to check the deflection.

On Bowles (5th ed) I found that a rough calculation of the spring stiffness can be done using the allowable bearing pressure qa in the following way:

ks=Fw1*Cm*C*SF*qa with Fw1=1.3 (correction factor for circular piles)
Cm=2 (Shape ratio factor to account for front and side shear)
C=40 (SI)
SF=2 safety factor for sand
qa=200 allowable lateral bearing pressure

that makes ks=41600 KN/m^3, in accordance with Table 9-1 of Bowles that specifies stiffness range of 9600-80000 for medium dense sand.
In the report it is specified that the vertical allowable bearing pressure can be taken as 400Kpa at base of excavation, and 1000Kpa at 4D embedment.

1 - does the lateral allowable bearing pressure change with depth? (in my opinion it should)
2 - having a single value of the lateral qa, I can have a single spring stiffness along the embedment length. It doesn't appear to be real, as I would expect to have 0 at the excavation level, increasing with depth.
3 - I do not have any other soil parameter (soil friction angle, soil density), so I cannot calculate the lateral soil pressure. Is it ok adopting the trapezoidal soil pressure given in the soil report for deflection purposes? (I don't think so).
4 - If I had the other soil parameters and being able to calculate Nq, Ng, Nc, and I want to use the general formula A+B*Z^n, what kind of value should I adopt for n? I couldn't find any suggestion in Bowles other than 0.4-0.6 (paragraph 16-15.2), but it is not clarified why and what the "n" factor means.

Thanks

### RE: Lateral spring stiffness

I don't have Bowles' 5th edition but Terzaghi gives an empirical, trapezoidal, pressure diagrams for braced sheeting walls, not cantilevered walls. Make sure you are choosing the correct pressure diagram. Cantilevered sheeting walls are usually designed using a triangular earth pressure distribution.

Your "cantilevered" wall is 7 meters (23 feet) high. This is VERY high for a cantilevered wall. Unless you have a VERY heavy and uneconomical wall design, you will probably have excessive soldier beam deflection, not even considering the soil movement in front of the soldier beam, below subgrade. Walls higher than 3.7 to 5 meters are usually braced or tied back with ground anchors.

Unless there are special circumstances or conditions that you have not indicated, it seems to me that, instead of worrying about spring stiffness, you should first be trying to choose a more appropriate type of wall.

### RE: Lateral spring stiffness

If the geotech specified a trapezoidal earth pressure distribution, I would assume he believes the wall is too high to be cantilevered and needs bracing or tieback anchors.

### RE: Lateral spring stiffness

(OP)
Thanks,
I just called the geotech consultant, and he assumed a ground anchor at the top, and a at rest soil pressure, but he didn't mention in the report.
At the end I calculated the spring stiffness at 2m depth from founding level based on the 200kPa lateral allowable bearing pressure at 1.8m depth as mentioned before.
I applied triangular profile of the spring stiffness from 0 to 2m depth and uniform after 2m. Once modeled, I got the actions in the pier.
I am wondering how reliable are the values I got from the simplified formula I mentioned, and how much they differ from those obtained from the more elaborated formula A+B*Z^n (that I can't use because I don't have the soil parameters).

Thanks

### RE: Lateral spring stiffness

I still am not sure why you are worrying about spring stiffness; Terzaghi & Peck didn't. Simple hand calcs should be sufficient for designing a 7 meter high, tiedback, sheeting wall. Why are you using a triangular pressure? For the situation you described, I would use a trapezoidal distribution. What computer program are you using to design the wall? You may be using a more sophisticated program than you really need. What are you supporting with this wall?

### RE: Lateral spring stiffness

Also, you say you "don't have the soil parameters." If you can't find out or estimate reasonable soil properties (unit weight, cohesion, friction angle), you should not be working with spring constants. GIGO. If you don't have good soil properties, the odds are that your estimated spring constant will not be very accurate either. Maybe you should have a geotech design the wall?

### RE: Lateral spring stiffness

Unless you have an embankment or strip load fairly close to your retaining wall, the E.P. method should work just fine.

### RE: Lateral spring stiffness

(OP)
I guess I haven't been clear enough. I am not trying to work out the soil pressure diagram. I already have the trapezoidal distribution given by the geotech consultant (based on Peck theory).
Given the design soil pressure and diagram, and the allowable lateral bearing pressure for the embedded section of the wall, I want to calculate a reasonable value of the lateral spring stiffness to model the response of the soil in the embedded section of the wall.
I can work out the internal actions in the wall based on forces equilibrium. The problem is that this is not completely correct because this approach assumes uniform reaction of the soil, which is not real, in addition to the fact that soil is not linear.
The soil is softer at the base of the excavation and gets stiffer with the depth. This allows rotation of the wall (decreasing with embedment depth), and this cannot be evaluated just with an approach based on forces equilibrium.
I know geotech engineers don't like springs to model the soil behavior, and I can understand that, but it is the best fast & easy way to consider the soil behaviour.

### RE: Lateral spring stiffness

Remember that you will be using the T&P EMPIRICAL earth pressure diagram (with its built-in adjustment for predicting the maximum anticipated brace load) to run a more exact, sophisticated, embedment analysis. This could be a conflict which will not give you the exactness you are looking for. In order to get what you are looking for, perhaps you need to run a finite element analysis, which probably also is overkill for the design situation you describe.

### RE: Lateral spring stiffness

(OP)
Thanks PEinc,
that is exactly what I am doing, I wanted to work out the soil spring stiffness in the embedded depth (which I assumed based on the force equilibrium of the trapezoidal soil pressure and the lateral allowable bearing pressure in the embedment depth) to put in the FEA model because I want to check the deflection and the internal actions.
The soil pressure that I get from the geotech report is ok to calculate the embeddment depth, but it give over conservative internal actions in the piers because it doesn't account for the nature of the supports (soil springs and the axial stiffness of the tie back).
As I said in my first post, I ended up to adopt the soil spring stiffness as per Bowles formulas (in accordance to the typical range for that kind of soil).
I am not trying to get a fine result, but something that gives me the confidence to have reasonable (non over conservative) numbers for both deflection and internal actions.

I hoped someone could reply to my 4 question I raised.
Thanks

### RE: Lateral spring stiffness

I'm a bit late for this, which I missed previously.
I don't work with FEM models of cantilevered walls usually but conceptually, I'd just refrain from using a spring constant proposed by Bowles for foundation springs. It's like using a screwdriver to drive a nail instead of a hammer.

There is a specific literature on spring stiffness for FEM analysis of cantilevered walls. They usually take up the general pattern, found also in foundations: K= E/B

That's a very general relationship which varies according to the authors.

If you have not a reliable estimate of E, the elastic modulus, then you might as well forget about using FEM methods, this is in line with the other posters' thoughts.

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