How can I install an inclinometer with our sheet-pile walls?

One technique is to weld a pipe to the sheet pile. Plug the end of the pipe and drive it in with the pile. Drill out the plug, boring 10 or 20 feet into the soil below the bottom of the wall. Then install your inclinometer casing inside the pipe. Grout it in. With the bottom of the casing in stable ground, you will be able to detect movement at the base of the wall in addition to monitoring the profile of the wall (the pipe is unlikely to add significant strength to the wall).