I’m obviously doing something wrong here. I’m supposed to find the passive earth pressure on a retaining wall by the “trial wedges” method. Here’s some information about it.
Vertical wall
Height of the wall 15’
depth of the water table 5’
density of the soil 130pcf, assumed to be equal above and below the water table
friction angle 35 degrees
a uniform surcharge of 1000psf
I’m assuming the angle of wall friction is 2/3 the friction angle. I’m aware this is too high for Coulomb to give a good estimate.
In any case My work gets me a failure angle of 78 degrees with respect to vertical, and a passive pressure of 280 kips per foot of wall. Using Rankine theory I get around 100 kips per foot. Clearly something is wrong, and I don’t think I messed up the Rankine.
This is probably not a great summary, but if anybody has any ideas on something I might have messed up, that’d be great. I’m not sure how many civil engineers we have on the board, but you never know.
They are both theories to calculate the horizontal pressure that the earth exerts on a structure, in my case a retaining wall.
Rankine theory says that the horizontal pressure is related to the vertical pressure by a factor, K. You end up with some sort of stress distribution from this. The vertical pressure is related to the depth, density of soil, and water table. Multiply this by K and you get the horizontal force. K is a function of the friction angle (also called the angle of repose) which is a strength property of the soil. The higher the friction angle, the less force is transfered horizontally.
Coulomb theory is based on force equilibrium. You assume that a block of soil will fail along a plane and then sum the forces on it equal to zero. If you do this for several different failure planes you can plot a curve representing the force required to counteract the soil, then you can find the maximum or minimum force depending on which is needed.
Does that help any? A picture would help, I’ll look for one.
Rankine will look something like this, depending on where the water table is, and if there is any load on the backfill. Coulomb looks like this. The wedges marked by 1, 2, and 3 are trials. They are plotted on the right and connected by the curved line. Pa is the greatest force that can be exerted on the wall and so it’s what you look for.