I am trying to apply the "Apparent Earth Pressure Diagram" in Figure 8-28-2 of the AREMA Manual for Railway Engineering. The diagram is a trapazoidal shaped pressure diagram for a multi prop temporary wall. The diagram has a formula "F(H+SC)" to define the maximum pressure of the trapazoid. They give some values of F (psf), H is defined as height and SC is surcharge. I think this formula has an error or this diagram is just a schematic representation. Can anyone confirm this please?
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AREMA - Apparent Earth Pressure Diagram 1
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I don't have the AREMA manual with me right now, but I suspect H is the exposed height of the wall in feet, SC is an equivalent earth surcharge in feet, and F may be a multiplier based on the type of soil being retained. For example, for average, competent soils, it is common to use Pa = 25H' where 25 = 0.8 x gamma x Ka and H' = (H + SC). In this example F may equal 25.
You are looking at the braced excavation. The trapezoid shape is typical for braced excavation. Make sure you are applying this right, because the shape will also vary based on the soil type, and type of wall - verify with a geotechnical engineer. I think PEinc is correct, but I see a possible confusion based on the trapezoidal shape shown in the Figure (I did not look at the AREMA Manual). However, it is typical in these shapes that the maximum apparent pressure is achieve prior to the full depth of the cut. So in that case, the formular you are looking at, the maximum pressure will occur at the bottom, but if the pressure is distributed as shown in the figure, the maximum pressure will will occur at a point above the bottom of the cut. Is that your confusion? If that is the case, I just think AREMA is being conservative, and that the formular is not 'WRONG' but does not conform to the depiction on the diagram.
The pressure diagram in AREMA's Figure 8-28-2 is noted as being for a multi-tierd anchored wall. The diagram is very similar to the Schnabel earth pressure diagram where the magnitude of the active earth pressure for average, non-problem soils is 25H or 25H' where H' = H + the height of any earth surcharge and/or an AASHTO traffic surcharge of equivalent earth overburden.
AREMA Figure 8-28-2 basically shows the active earth pressure is 18H (or H') to 36H (or H'). For softer soils Schnabel will use more than 25H or H'. 25H = (0.8 x gamma x Ka) x H. If you use properly matched unit weights and phi angles, the magnitude of the trapezoid should be approximately 25H(psf) and the total earth load per LF of wall should be approximately 20H^2(plf). The problem is that engineers almost always use an extra high unit weight with an extra low phi angle. Therefore, they can easily wind up with an earth pressure magnitude of 35H to 40H.
In nature, granular soils with higher unit weights usually also have higher phi angles. Therefore, as unit weight increases, phi usually increases and Ka usually decreases. The net result is that you still will have about 25H(psf) and 20H^2(plf) unless you have a very soft cohesive soil. See attached comparison.
www.PeirceEngineering.com
AREMA Figure 8-28-2 basically shows the active earth pressure is 18H (or H') to 36H (or H'). For softer soils Schnabel will use more than 25H or H'. 25H = (0.8 x gamma x Ka) x H. If you use properly matched unit weights and phi angles, the magnitude of the trapezoid should be approximately 25H(psf) and the total earth load per LF of wall should be approximately 20H^2(plf). The problem is that engineers almost always use an extra high unit weight with an extra low phi angle. Therefore, they can easily wind up with an earth pressure magnitude of 35H to 40H.
In nature, granular soils with higher unit weights usually also have higher phi angles. Therefore, as unit weight increases, phi usually increases and Ka usually decreases. The net result is that you still will have about 25H(psf) and 20H^2(plf) unless you have a very soft cohesive soil. See attached comparison.
www.PeirceEngineering.com
born2drill
Geotechnical
I lost that diagram years ago and I've been looking for it ever since... Thanks PEInc!
I made that chart myself many years ago. Where did you see one like it? There is one somewhat similar in Geotechnical Engineering Circular No. 4.
born2drill
Geotechnical
The old SWP guys had something just like yours around the office. It covered the exact same 5 pressure envelopes in a similar fashion.
Good summary - the summary didn't address soft to firm clays where the pressure diagram from 0.25H from the top is "straight down" This is shown in Peck Hanson and Thornburn for ("Gamma"xH)/Su > 4. The pressure in the rectangular portion is "gamma"xH less 4xSu. TP&M discusses all this in their article 46 (T&P but with Mesri - 3rd Ed).
The soft clays are covered by T&P's 1967 0.2 to 0.4 x gamma x H (see right side column heading of my table.). Since my table was comparing average (non-soft) soils or better, I used 0.2 x gamma x H for clays. As I said previously, if the soil is soft clay, 25H is not enough and neither is 0.2 x gamma x H.
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