soil lateral surchage pressure 1

[WarrenS]

Hi there

Are the lateral pressures calculated from the Boussinesq equations (for point and line surcharge loads) applied with active and passive pressure coefficients when designing a retaining wall... or are the numbers obtained from the Boussinesq equations absolute values?

Thanks
W

 

[escrowe]

Typically,
for a uniform load adjacent to the top of the wall,
or in the 'active zone' use the approprite EPC, k(0 or A).

Surcharge Pressure =

PQ = QHk(0,A)

Q = vertical surcharge (kPa, psf)
H = height of retaining wall
k = active or at rest earth pressure

Locate resultatnt PQ at wall mid height.

I don't think you should reduce the resultant
based on pressure distribution
unless the surcharge is set well back from the wall.
The solution would tend to be unconservative.

 

[WarrenS]

Thank you escrowe... I was more referring to the relation of the formulas for lateral pressure induced by a uniform surcharge pressure versus a strip load surcharge.

From what I've read, the lateral pressure induced on a retaining wall by a uniform surcharge pressure = kQ (where k = active/passive or at rest earth pressrue, Q = surcharge pressure)

The lateral pressure induced at a specific elevation on a retaining wall by a strip load surcharge pressure = 2Q/pi*(B+sinB*sin2A-sinBcos2A)... (where A and B are the angles from the edges of the strip load to the specific elevation on the wall)

The equation for lateral pressure induced by a strip load does not include a k value. I'm thinking it should although some references I've read do not use it.

 

[escrowe]

In wall design, k generally controls the angle and therefore the volume (and mass)
of the wedge of soil a retaining wall retains.
k is based on:
the internal friction angle (phi) of the retained soil,
and expected movement of the wall.

The zone of influence of a discrete load (point or line)
set back from the wall will intersect the wall
below the top, and Bousinesq or a 2:1 distribution (or whatever)
could be used to calculate the location and degree
of the local pressure increase. k is not applicable.

Consider that a surcharge bearing completely on the active wedge
(or otherwise within the zone of retained material)
is generally assumed to translate to the wall.
You might argue (somewhat unconservatively)
that the effective wall height and location of
the resultant are changed by the location of the surcharge.
(Better have a nice analysis package for the file.)

Specific cases could also be modeled to determine
that a portion of the surcharge will
'not' translate to the wall due to
the location of a part of the surcharge outside
of the active zone (also not conservative).

 

[WarrenS]

That makes sense. I'm just hung up on the mathematical dilema presented by the Boussinesq formula as I have no definition on what it's limitations are:

ie: consider a uniform surcharge on top of the soil. The maximum lateral pressure at the top of the wall is kQ

Alternatively, consider an infinitely long strip load of finite width that is directly adjacent to the wall. The maximum lateral pressure at the top of the wall = Q according to the Boussinesq formula. How can the lateral pressure calculated at the top of a wall for a strip load be greater than for a uniform surcharge load?

If I understand your response correctly, the conservative approach is to assume a uniform surcharge when the strip/line/point load is within the limits of the wedge of soil that is retained?

 

[escrowe]

Almost! I think...

'Uniform' implies one-dimensional (vertical) loading, whereas
the line load is 'plane strain,' with a horizontal component.
Either way, assume the the load is applied to the wall backfill,
and hence the resultant is generally applied to the wall via QHk.

---
Begin pedantry

Just to clear up semantics a bit

Loading of soil is generally characterized as either one,
two, or three dimensional, depending on the shape
of the loaded area. (See NAVFAC DM 7.2 for instance).

One dimensional: caused by loading a relatively large area, such as mass fill.
100% of the load is transferred vertically to depth.

Two dimensional: strip footings (plane strain),
horizontal stress is transferred perpendicularly
from the strip longitudinal axis; vertical stress
is therefor less than the one dimensional case.

Three dimensional: Typical case for axi-symetric
column footings and round tanks;
horizontal stress is transferred along two axis,
so zone of influence of vertical stress
is relatively less than for the one and two dimensional case.

Boussinesq developed point and line equations
for stress distribution using elastic theory.
Because of the characteristics of stress distribution in soil,
the line equation (plane strain) yields a higher value
of vertical stress than the point equation, for the same Q.
And for the reasons discussed above...

End Pedantry
---

So in the case of the infinitely long strip you describe,
such an adjacent continuous footing
would transmit a relatively large percentage of its load
to the 'upper portion' of the wall. You can calculate
how much using 2:1, Boussinesq, etc..
Just keep in mind that the the remaining line load
is transferred to the wall backfill, and hence to the
wall by way of the QHk relationship.

In the 'uniform loading' case, load is assumed to be
transferred one dimensionally (verticaly) to the
wall backfill, and hence to the wall via QHk.

Do you need to get rid of the surcharge?
Often point loads are founded below the active zone
of wall backfill for that reason.

Wow, that was fun! Any more? : )

 

[WarrenS]

all good. thank you very much

 

[PEinc]

I was taught that the Boussinesq analyses were developed for a rigid wall and therefore gave high lateral earth pressures. That's why the railroads like Boussinesq for track surcharges. Some people, such af CivilTech Software in their Shoring Suite programs, let you use Boussinesq for a rigid structure, a semi-flexible structure, or a flexible structure. For the flexible structure, where movement is allowed, I believe the Boussinesq lateral pressure is multiplied by Ka . For semi-flexible, where less movement is desired, the pressure is between flexible and rigid. I have used all three conditions successfully many times for both strip loads and area loads.

 

[WarrenS]

Thank you for the feedback. I think my biggest hangup was coming from my old California Trenching and Shoring Manual. It used Boussinesq for strip loads and building footprints adjacent to a shoring wall, then used kQ for area loads... but didn't suggest at what width a wide strip load becomes an area load (thus decreasing the lateral pressure by k).

 

[PEinc]

Wide Boussinesq strip load or qKa area load? This is always a question. Use the one you are comfortable with and gives you a design that is reasonable. Then, be prepared to explain (defend?) your choice to the reviewer.

 

[jdonville]

Warrens,

You also need to consider where the load is relative to the assumed failure plane. If the load or a portion thereof is applied to the bearing surface outside the assumed failure plane, then it should not be included in your analysis.

For the design of earth retention systems, for example, the failure plane might be assumed to be planar (Rankine). As the depth of the cut progresses downward, the portion of the original surface that influences the assumed failing wedge becomes wider, and more of the surcharge will need to be accounted for.

The case of the uniformly distributed load, where the lateral stress distribution is taken as k times the UDL stress is a nice conservative simplification, amenable to paper calculations, but can tend to overstate the lateral stress if used without some judgement.

Jeff

 

[jdonville]

Forgot to mention: read up on the "factor of two" argument for rigid vs. flexible walls, per PEInc's comment. This should be Google-able. Also, try and score a copy of Chapter 3 of Poulos and Davis' "Elastic Solutions for Soil and Rock Mechanics". I use this reference whenever I want to sanity check the magnitude of the lateral loads that I am getting from formulae.

Jeff

 

[lovethecold]

Here's a link for Poulos' book in pdf format:

http://www.ce.ncsu.edu/usucger/PandD/PandD.htm

 

[bmike]

Decide if your wall is going to move or not, and in which direction, then remember these three things:

1. Active earth pressure is the lowest state of loading on the wall, when it has moved away from the backfill and all available soil strength has been mobilized.

2. Passive earth pressure is the highest state of loading on the wall, when it has moved towards the backfill and all available soil resistance has been mobilized.

3. At rest earth pressure is the load on the wall when nothing has moved, and no soil strength has been mobilized (same horizontal stress as if it were still somewhere in the ground)

The nice thing about these is they fulfill your predcitions (if you have the parameters right); decide to use active earth pressure for your design and the wall will move until your prediction comes true.

 

[BigH]

lovethecold - good link. I actually had scanned mine so I could take it overseas with me (I have two hard copies).

 

[fattdad]

Warning, I didn't read all replies, so sorry in advance for any redundancy.

Earth pressures acting on retaining walls are typically defined by Rankine or Log Spiral methods. The end result is either a passive or active earth pressure distribution. If it's an at-rest case, you can use several methods to get Ko, but I just use 1.5 Ka and determine the Ka value for my field conditions (i.e., sloping backfill or the like).

Structual loading and its affect on retaining walls is a different subject. For the case of an areal load, you can relate it to Ka. However, for strip loads or point loads you would typically use some elastic theory to get the horizontal component of the load. Please note that these elastic theorum are based on an infinant extent of the elastic media. So, when you calculate the horizontal load 10 ft away from an 10 ft lower than some point load, there is an implication that soil is present 20 ft away from and 10 ft lower than the same point load. For a retaining wall, this is not the case.

When using Boussinesq (or Westergaard) for the horizontal pressure acting on a retaining wall, you must then DOUBLE the calculated stress to determine what the wall must support (i.e., there is no soil to counteract this force).

This is what I learned in graduate school and what I've used for the past 20 years.

Other's may have different ideas, just providing some additional insight.

f-d

¡papá gordo ain’t no madre flaca!