# Boundary condition for a parallelogram-shaped excavation on an embankment

What we learn in engineering school is often idealistic, with textbook examples showing typical prismatic steel beams with a plastic section classification or excavation in a perfect sand or clay geology. However, in the real world nothing is perfect and engineers will face complex problems not taught in school, where there is little referencing literature and where the design codes do not provide clear guidelines.

One of the tasks I was assigned when I started out as an engineer was to design cofferdams for both abutments of a river bridge with a 30 degree skew across the river due to site constraints. As a result, the abutments at both side of the river are skewed. As a designer for the contractor, often we do not get to dictate the shape of the excavation. Material cost is always a source of great consternation, even more so in temporary works design.

I built a 2D frame for each strut level to do a structural analysis for the odd-shaped cofferdam. However, as the excavation is on a 35 degree slope, the sheet pile wall on the land side has greater lateral earth pressure than the river side. Also, due to the parallelogram shape, I have difficulty balancing the forces.

How should you model the boundary conditions for such an irregularly-shaped cofferdam, where the lateral earth pressure acting at the strut level is not balanced?

Unbalanced Forces

As you noted, the unbalanced soil heights and the skew create unequal forces in the struts. This is likely going to turn the short side into what is effectively a deadman.

The short side will be pushing into the soil. This can mobilize the soil's passive resistance. Since passive resistance is greater than active soil forces, it may be more conservative to assume this lower active force. Also, the short wall may not deflect enough to mobilize the passive pressure.

Modeling

Actually modeling the entire excavation will require using cantilever piles. The excavation can't be just a rigid box since the forces are uneven. The piles will need to mobilize some of the passive reaction of the soil below the excavation.

The forces on the two opposite walls will need to be balanced. These forces can then be used to design the strut frame. The interaction of the opposite walls of the excavation and the soil is not linear, so this will not be easily converted to simple boundary conditions for the frame model. There is a lot of interaction between the deflections of the walls and the soil response.

Construction Staging

The differing soil heights not only create modeling complexities in the final condition, they will also create issues at every depth of excavation. This is a point that is often overlooked in design.

The sheeting or lagging has to be able to support the soil and any additional loads as the excavation progresses. It is good to know where you want a waler to be located in the final condition, but it must be safe to be able to remove enough soil to be able to instal this waler. This means that the wall will be exposed down to a couple of feet below the waler location.

Even somewhat standard excavations can require 6 or more separate construction phases to be analyzed.

• Thanks for answering, but my question is specifically on the boundary condition in structural modelling to obtain forces in the diagonal struts and walers, not geotechnical modelling to obtain the forces in main struts and sheet piles, hence I only show the structural frame of one strut layer. Mar 5, 2015 at 16:04
• @QuestionOverflow Then what do you mean by boundary conditions? Are you looking to put this into a structural analysis program?
– hazzey
Mar 5, 2015 at 16:17
• Yes, boundary conditions refer to the fixity of supports for the 2D model created to be used in structural analysis. It seems you are using another method to to determine the diagonal struts and waler forces instead of doing a structural analysis using a 2D model. But it is not clear from your answer how this is done. Mar 7, 2015 at 1:53
• @QuestionOverflow You are going to have to get your forces from analyzing the walls first. It might be iterative. If all you are analyzing is the frame of the struts, there are not boundary conditions to set. You need your forces from your walls to balance. If you are doing a full 3D model, you could add the soil in as springs.
– hazzey
Mar 7, 2015 at 13:09
• Yes, I did start with a 2D PLAXIS model to analyse the walls first to calculate the forces in the main strut and back-calculate the lateral pressure on waler. Full 3D geotechnical and structural modelling is the new kid on the block. Not every authority is comfortable with accepting analyses directly from 3D modelling. The problem is, as you pointed out, one side of the wall will experience larger lateral earth pressure than the other. Without setting boundary condition, the forces would not balance in a 2D frame model. Are you implying that a 2D analysis is not possible? Mar 8, 2015 at 4:58